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Biophysical Chemistry
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Biophysics

Principles, Theory and Experimenta

Applications

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Biophysics and Related Fields

Biophysics

Biophysics (also biological physics) is an interdisciplinary science that employs and
develops theories and methods of the physical sciences for the investigation of biological
systems. Studies included under the umbrella of biophysics span all levels of biological
organization, from the molecular scale to whole organisms and ecosystems. Biophysical
research shares significant overlap with biochemistry, nanotechnology, bioengineering,
agrophysics and systems biology.

Molecular biophysics typically addresses biological questions that are similar to those in
biochemistry and molecular biology, but the questions are approached quantitatively.
Scientists in this field conduct research concerned with understanding the interactions
between the various systems of a cell, including the interactions between DNA, RNA and
protein biosynthesis, as well as how these interactions are regulated. A great variety of
techniques are used to answer these questions.

Fluorescent imaging techniques, as well as electron microscopy, x-ray crystallography,
NMR spectroscopy and atomic force microscopy (AFM) are often used to visualize
structures of biological significance. Conformational changes in structure can be measured
using techniques such as dual polarisation interferometry and circular dichroism. Direct
manipulation of molecules using optical tweezers or AFM can also be used to monitor
biological events where forces and distances are at the nanoscale. Molecular biophysicists
often consider complex biological events as systems of interacting units which can be
understood through statistical mechanics, thermodynamics and chemical kinetics. By
drawing knowledge and experimental techniques from a wide variety of disciplines,
biophysicists are often able to directly observe, model or even manipulate the structures
and interactions of individual molecules or complexes of molecules.

In addition to traditional (i.e. molecular and cellular) biophysical topics like structural
biology or enzyme kinetics, modern biophysics encompasses an extraordinarily broad range
of research. It is becoming increasingly common for biophysicists to apply the models and
experimental techniques derived from physics, as well as mathematics and statistics, to
larger systems such as tissues, organs, populations and ecosystems.

Focus as a subfield

Biophysics often does not have university-level departments of its own, but has presence as
groups across departments within the fields of molecular biology, biochemistry, chemistry,
computer science, mathematics, medicine, pharmacology, physiology, physics, and
neuroscience. What follows is a list of examples of how each department applies its efforts
toward the study of biophysics. This list is hardly all inclusive. Nor does each subject of
study belong exclusively to any particular department. Each academic institution makes its
own rules and there is much overlap between departments.

• Biology and molecular biology - Almost all forms of biophysics efforts are included in
some biology department somewhere. To include some: gene regulation, single protein

Biophysics

dynamics, bioenergetics, patch clamping, biomechanics.

• Structural biology - Angstrom-resolution structures of proteins, nucleic acids, lipids,
carbohydrates, and complexes thereof.

• Biochemistry and chemistry - biomolecular structure, siRNA, nucleic acid structure,
structure-activity relationships.

• Computer science - Neural networks, biomolecular and drug databases.

• Computational chemistry - molecular dynamics simulation, molecular docking, quantum
chemistry

• Bioinformatics - sequence alignment, structural alignment, protein structure prediction

• Mathematics - graph/network theory, population modeling, dynamical systems,
phylogenetics.

• Medicine and neuroscience - tackling neural networks experimentally (brain slicing) as
well as theoretically (computer models), membrane permitivity, gene therapy,
understanding tumors.

• Pharmacology and physiology - channel biology, biomolecular interactions, cellular
membranes, polyke tides.

• Physics - biomolecular free energy, stochastic processes, covering dynamics.

• Agronomy Agriculture

Many biophysical techniques are unique to this field. Research efforts in biophysics are
often initiated by scientists who were traditional physicists, chemists, and biologists by
training.

Topics in biophysics and related fields

Theoretical biophysics
Mathematical biophysics
Systems biology
Medical biophysics
Agrophysics
Origin of Life

Molecular biophysics

Biological membranes

Cell membranes

Bioenergetics

Channels, receptors and transporters

Enzyme kinetics

Molecular motors

Phospholipids

Proteins

Biofilms

Supramolecular assemblies

Nucleic acids

Cellular biophysics

Cell division
Cell migration
Cell signalling
Dynamical systems

Biophysics

Electrophysiology

Signaling

Biochemical systems theory

Metabolic control analysis

Techniques used in biophysics

Atomic force microscopy

Biophotonics

Biosensor and Bioelectronics

Calcium imaging

Calorimetry

Circular Dichroism

Cryobiology

Dual polarisation interferometry

Electrophysiology

Fluorescence

Microscopy

Neuroimaging

Neutron spin echo spectroscopy

Patch clamping

Nuclear Magnetic Resonance Spectroscopy

Spectroscopy, imaging, etc.

x-ray crystallography

Other

Animal locomotion
Bioacoustics
Biomechanics
Biomineralisation
Bionics
Evolution

Evolutionary algorithms
Evolutionary computing
Evolutionary theory
Gravitational biology
Mathematical biology
Morphogenesis
Muscle and contractility
Negentropy
Neural encoding
Radiobiology
Sensory systems
Systems neuroscience
Tensegrity
Theoretical biology

Biophysics

Famous biophysicists

Luigi Galvani, discoverer of bioelectricity

Hermann von Helmholtz, first to measure the velocity of nerve impulses; studied hearing

and vision

Alan Hodgkin & Andrew Huxley, mathematical theory of how ion fluxes produce nerve

impulses

Georg von Bekesy, research on the human ear

Bernard Katz, discovered how synapses work

Hermann J. Muller, discovered that X-rays cause mutations

George Palade Nobel Laureate in physiology or medicine for protein secretion and cell

ultra-structure from electron microscopy studies

Linus Pauling & Robert Corey, co-discoverers of the alpha helix and beta sheet structures

in proteins

J. D. Bernal, X-ray crystallography of plant viruses and proteins

Rosalind Franklin, Maurice Wilkins, James D. Watson and Francis Crick, pioneers of DNA

crystallography and co-discoverers of the structure of DNA. Francis Crick later

participated in the Crick, Brenner et al. experiment which established the basis for

understanding the genetic code

Max Perutz & John Kendrew, pioneers of protein crystallography

Sir John Randall, X-ray and neutron diffraction of proteins and DNA

Ronald Burge, X-ray diffraction of nerve myelin, bacterial cell walls and membranes

Allan Cormack & Godfrey Hounsfield, development of computer assisted tomography

Kurt Wiithrich Nobel Laureate in physiology or medicine for 2D-FT NMR of protein

n 1

structure in solution 1 J

Paul Lauterbur & Peter Mansfield, development of magnetic resonance imaging
Stephen D. Levene, DNA-protein Interactions, DNA looping, and DNA topology.
Seiji Ogawa, development of functional magnetic resonance imaging

Other notable biophysicists

• Adolf Eugen Fick, responsible for Fick's law of diffusion and a method to determine
cardiac output.

• Howard Berg, characterized properties of bacterial chemotaxis

• Steven Block, observed the motions of enzymes such as kinesin and RNA polymerase
with optical tweezers

• Carlos Bustamante, known for single-molecule biophysics of molecular motors and
biological polymer physics

• Steven Chu, Nobel laureate who helped develop optical trapping techniques used by
many biophysicists

• Christoph Cremer, overcoming the conventional limit of resolution that applies to light
based investigations (the Abbe limit) by a range of different methods

• Friedrich Dessauer, research on radiation, especially X-rays

• Julio Fernandez

• Govindjee, professor emeritus at the University of Illinois, research in photosynthesis and
photosynthetic mechanisms by fluorescence and NMR methods

• Enrico Gratton research on frequency domain spectroscopy and correlation spectroscopy
on biological and biomedical systems

Biophysics

Stefan Hell, developed the principle of STED microscopy

Richard Henderson, scientist at the MRC Laboratory of Molecular Biology, developed the

use of cryo-EM to study membrane protein structures.

John J. Hopfield, worked on error correction in transcription and translation (kinetic

proof-reading), and associative memory models (Hopfield net)

Martin Karplus, research on molecular dynamical simulations of biological

macromolecules.

Franklin Offner, professor emeritus at Northwestern University of professor of

biophysics, biomedical engineering and electronics who developed a modern prototype of

the electroencephalograph and electrocardiograph called the dynograph.

Nicolas Rashevsky, ] , former Editor of the first journal of mathematical and theoretical

biophysics entitled " The Bulletin of Mathematical Biophysics " (1940--1973) and author

of the two-factor model of neuronal excitation, biotopology and organismic set theory.

Robert Rosen, theoretical biophysicist and mathematical biologist, author of:

metabolic-replication systems, categories of metabolic and genetic networks, quantum

genetics in terms of von Neumann's approach, non-reductionist complexity theories,

dynamical and anticipatory systems in biology. ^

Benoit Roux

Mikhail Volkenshtein, Revaz Dogonadze & Zurab Urushadze, authors of the first

quantum-mechanical model of enzyme catalysis, supported a theory that enzyme catalysis

use quantum-mechanical effects such as tunneling.

John P. Wikswo, research on biomagnetism

Douglas Warrick, specializing in bird flight (hummingbirds and pigeons)

Ernest C. Pollard — founder of the Biophysical Society

Marvin Makinen, pioneer of the structural basis of enzyme action

Gopalasamudram Narayana Iyer Ramachandran, developer of the Ramachandran plot

and pioneer of the collagen triple-helix structure prediction

Doug Barrick, repeat protein folding

Naomi Courtemanche, kinetics of leucine rich repeat protein folding

Ellen Kloss, salt-dependence of leucine rich repeat protein folding

Bertrand Garcia Moreno E., Dielectric Constant of Globular Protein 'hydrophobic' core

Ludwig Brand, Time resolved fluorescence anisotropy decay in Biological systems

See also

• Important publications in biophysics

Notes

[1] http://nobelprize.org/nobel_prizes/chemistry/laureates/2002/wuthrich-autobio.html

[2] http://planetmath.org/encyclopedia/NicolasRashevsky.html

[3] Robert Rosen's Research and Biography http://planetmath.org/encyclopedia/RobertRosen.html

References

• Perutz MF (1962). Proteins and Nucleic Acids: Structure and Function. Amsterdam
Elsevier. ASIN B000TS8P4G (http://www.amazon.com/dp/B000TS8P4G).

Biophysics

Perutz MF (1969). "The haemoglobin molecule". Proceedings of the Royal Society of

London. Series B 173 (31): 113-40. PMID 4389425

Dogonadze RR, Urushadze ZD (1971). "Semi-Classical Method of Calculation of Rates of

Chemical Reactions Proceeding in Polar Liquids". J Electroanal Chem 32: 235-245.

Volkenshtein M.V., Dogonadze R.R., Madumarov A.K., Urushadze Z.D. and Kharkats Yu.I.

Theory of Enzyme Catalysis.- Molekuliarnaya Biologia (Moscow), 6, 1972, pp. 431-439 (In

Russian, English summary)

Rodney M.J. Cotterill (2002). Biophysics : An Introduction. Wiley. ISBN 978-0471485384.

Sneppen K, Zocchi G (2005-10-17). Physics in Molecular Biology (1 ed.). Cambridge

University Press. ISBN 0-521-84419-3.

Glaser, Roland (2004-11-23). Biophysics: An Introduction (Corrected ed.). Springer. ISBN

3-540-67088-2.

Hobbie RK, Roth BJ (2006).

http://personalwebs.oak.land. edu/~roth/hobbie.htm\Intermediate Physics for Medicine

and Biology (4th ed.). Springer. ISBN 978-0387309422. http://personalwebs. Oakland.

edu/~roth/hobbie.htm.

External links

• Biophysical Society (http://www.biophysics.org/)

• Educational Resources from Biophysical Society (http://www.biophysics.org/
education/resources. htm|)

• The European Biophysical Societies Association (http://www.ebsa.org/)

• The Wellcome Trust Physiome Project (http://www.physiome.ox.ac.uk/) - Links

• Nasif Nahle, Biophysics (http://biocab.org/Biophysics.html)

Biochemistry

Biochemistry is the study of the chemical processes in living organisms. It deals with the
structure and function of cellular components such as proteins, carbohydrates, lipids,
nucleic acids and other biomolecules.

Although there are a vast number of different biomolecules many are complex and large
molecules (called polymers) that are composed of similar repeating subunits (called

monomers). Each class of polymeric biomolecule has a different set of subunit types. For
example, a protein is a polymer whose subunits are selected from a set of 20 or more amino
acids. Biochemistry studies the chemical properties of important biological molecules, like
proteins, in particular the chemistry of enzyme-catalyzed reactions.

The biochemistry of cell metabolism and the endocrine system has been extensively
described. Other areas of biochemistry include the genetic code (DNA, RNA), protein
synthesis, cell membrane transport, and signal transduction.

Since all known life forms that are still alive today are descended from the same common
ancestor, they have generally similar biochemistries. It is unknown whether alternative

biochemistries are possible or practical.

History

Originally, it was generally believed that life was not subject to the laws of science the way
non-life was. It was thought that only living beings could produce the molecules of life (from
other, previously existing biomolecules). Then, in 1828, Friedrich Wohler published a paper
on the synthesis of urea, proving that organic compounds can be created artificially.

The dawn of biochemistry may have been the discovery of the first enzyme, diastase (today
called amylase), in 1833 by Anselme Payen. Eduard Buchner contributed the first
demonstration of a complex biochemical process outside of a cell in 1896: alcoholic
fermentation in cell extracts of yeast. Although the term "biochemistry" seems to have been
first used in 1882, it is generally accepted that the formal coinage of biochemistry occurred
in 1903 by Carl Neuberg, a German chemist. Previously, this area would have been referred
to as physiological chemistry. Since then, biochemistry has advanced, especially since the
mid-2 0th century, with the development of new techniques such as chromatography, X-ray
diffraction, dual polarisation interferometry, NMR spectroscopy, radioisotopic labeling,
electron microscopy and molecular dynamics simulations. These techniques allowed for the
discovery and detailed analysis of many molecules and metabolic pathways of the cell, such
as glycolysis and the Krebs cycle (citric acid cycle).

Another significant historic event in biochemistry is the discovery of the gene and its role in
the transfer of information in the cell. This part of biochemistry is often called molecular
biology. In the 1950s, James D. Watson, Francis Crick, Rosalind Franklin, and Maurice
Wilkins were instrumental in solving DNA structure and suggesting its relationship with
genetic transfer of information. In 1958, George Beadle and Edward Tatum received the
Nobel Prize for work in fungi showing that one gene produces one enzyme. In 1988, Colin
Pitchfork was the first person convicted of murder with DNA evidence, which led to growth
of forensic science. More recently, Andrew Z. Fire and Craig C. Mello received the 2006
Nobel Prize for discovering the role of RNA interference (RNAi), in the silencing of gene
expression

Biochemistry

Today, there are three main types of biochemistry. Plant biochemistry involves the study of
the biochemistry of autotrophic organisms such as photosynthesis and other plant specific
biochemical processes. General biochemistry encompasses both plant and animal
biochemistry. Human/medical/medicinal biochemistry focuses on the biochemistry of
humans and medical illnesses.

Monomers and Polymers

Monomers and polymers are a structural basis in which the four main macromolecules
(Carbohydrates, lipids, proteins, and nucleic acids), or biopolymers, of biochemistry are
based on. Monomers are smaller micromolecules that are put together to make
macromolecules. Polymers are those macromolecules that are created when monomers are
synthesized together. When they are synthesized, the two molecules undergo a process
called dehydration synthesis.

Carbohydrates

Carbohydrates have monomers called monosaccharides. Some of

these monosaccharides

(C 6 H 12 6 ),

and

include glucose (C H O ),

fructose

deoxyribose

< C 5 H 10°4>-

When

two

monosaccharides undergo dehydration synthesis, water is
produced, as two hydrogen atoms and one oxygen atom are lost
from the two monosaccharides' carboxyl group.

ch 2 oh

r\ u CH2OH n

°\" /O. H

OH H

oHi — r °' n — v ch 2 oh

H OH OH H

A molecule of sucrose

(glucose + fructose), a

disaccharide.

Lipids

H 2 C — O

HC —

h 2 c-ct x

A triglyceride with a glycerol

molecule on the left and three

fatty acids coming off it.

Lipids are usually made up of a molecule of glycerol and
other molecules. In triglycerides, or the main lipid, there is
one molecule of glycerol, and three fatty acids. Fatty acids
are considered the monomer in that case, and could be
saturated or unsaturated. Lipids, especially phospholipids,
are also used in different pharmaceutical products, either as
co-solubilisers e.g. in Parenteral infusions or else as drug
carrier components (e.g. in a Liposome or Transfersome).

Biochemistry

Proteins

Proteins are large molecules, and have monomers of amino acids.
There are 20 standard amino acids, and they contain a carboxyl
group, an amino group, and an "R" group. The "R" group is what
makes each amino acid different. When Amino acids combine, they
form a special bond called a peptide bond, and become a
polypeptide, or a protein.

The general structure
of an ot-amino acid,

with the amino group

on the left and the

carboxyl group on

the right.

Nucleic Acids

Adenine

Thymine

5' end

Phosphate- \
d e ox y r i b o s e ^^

backbone

\ »IH--N

O— H2N

• \

o. jyi-— \ J I

NH2

4 v-

OH ^ . >W»

3' end Cytosme o /^°

Guanine vend

The structure of deoxyribonucleic acid
(DNA), the picture shows the monomers

being put together.

Nucleic acids are very important in biochemistry, as
they are what make up DNA, something all cellular
organism use to store their genetic information. The
most common nucleic acids are deoxyribonucleic
acid and ribonucleic acid. Their monomers are
called nucleotides. The most common nucleotides
are called adenine, cytosine, guanine, thymine, and
uracil. Adenine binds with thymine and uracil,
thymine only binds with adenine, and cytosine and
guanine can only bind with each other.

Carbohydrates

The function of carbohydrates includes energy
storage and providing structure. Sugars are
carbohydrates, but not all carbohydrates are sugars.
There are more carbohydrates on Earth than any
other known type of biomolecule; they are used to

store energy and genetic information, as well as play important roles in cell to cell

interactions and communications.

Monosaccharides

The simplest type of carbohydrate is a monosaccharide,
which among other properties contains carbon,
hydrogen, and oxygen, mostly in a ratio of 1:2:1
(generalized formula C H n O , where n is at least 3).

^ n 2n n

Glucose, one of the most important carbohydrates, is an
example of a monosaccharide. So is fructose, the sugar
that gives fruits their sweet taste. Some carbohydrates

Biochemistry

(especially after condensation to oligo- and polysaccharides) contain less carbon relative to
H and O, which still are present in 2:1 (H:0) ratio. Monosaccharides can be grouped into
aldoses (having an aldehyde group at the end of the chain, e. g. glucose) and ketoses
(having a keto group in their chain; e. g. fructose). Both aldoses and ketoses occur in an
equilibrium between the open-chain forms and (starting with chain lengths of C4) cyclic
forms. These are generated by bond formation between one of the hydroxyl groups of the
sugar chain with the carbon of the aldehyde or keto group to form a hemiacetal bond. This
leads to saturated five-membered (in furanoses) or six-membered (in pyranoses)
heterocyclic rings containing one O as heteroatom.

CH 2 OH

Disaccharides

Two monosaccharides can be joined together using

dehydration synthesis, in which a hydrogen atom is

removed from the end of one molecule and a hydroxyl

group (—OH) is removed from the other; the remaining

residues are then attached at the sites from which the

atoms were removed. The H— OH or H 2 is then

released as a molecule of water, hence the term

dehydration. The new molecule, consisting of two

monosaccharides, is called a disacchahde and is

conjoined together by a glycosidic or ether bond. The

reverse reaction can also occur, using a molecule of water to split up a disaccharide and

break the glycosidic bond; this is termed hydrolysis. The most well-known disaccharide is

sucrose, ordinary sugar (in scientific contexts, called table sugar or cane sugar to

differentiate it from other sugars). Sucrose consists of a glucose molecule and a fructose

molecule joined together. Another important disaccharide is lactose, consisting of a glucose

molecule and a galactose molecule. As most humans age, the production of lactase, the

enzyme that hydrolyzes lactose back into glucose and galactose, typically decreases. This

results in lactase deficiency, also called lactose intolerance.

Sucrose: ordinary table sugar and

probably the most familiar

carbohydrate.

Sugar polymers are characterised by having reducing or non-reducing ends. A reducing end
of a carbohydrate is a carbon atom which can be in equilibrium with the open-chain
aldehyde or keto form. If the joining of monomers takes place at such a carbon atom, the
free hydroxy group of the pyranose or furanose form is exchanged with an OH-side chain of
another sugar, yielding a full acetal. This prevents opening of the chain to the aldehyde or
keto form and renders the modified residue non-reducing. Lactose contains a reducing end
at its glucose moiety, whereas the galactose moiety form a full acetal with the C4-OH group
of glucose. Saccharose does not have a reducing end because of full acetal formation
between the aldehyde carbon of glucose (CI) and the keto carbon of fructose (C2).

Biochemistry

Oligosaccharides and polysaccharides

When a few (around three to six) monosaccharides are
joined together, it is called an oligosaccharide (oligo-
meaning "few"). These molecules tend to be used as
markers and signals, as well as having some other uses.
Many monosaccharides joined together make a
polysaccharide. They can be joined together in one long
linear chain, or they may be branched. Two of the most
common polysaccharides are cellulose and glycogen,
both consisting of repeating glucose monomers.

• Cellulose is made by plants and is an important structural component of their cell walls.
Humans can neither manufacture nor digest it.

• Glycogen, on the other hand, is an animal carbohydrate; humans and other animals use it
as a form of energy storage.

Use of carbohydrates as an energy source

See also

Lists

List of basic biochemistry topics

List of biochemistry topics

List of biochemists

List of biomolecules

List of geneticists & biochemists

List of nucleic acid simulation software

Important publications in biochemistry (biology)

Important publications in biochemistry (chemistry)

Further reading

• Hunter, Graeme K. (2000). Vital Forces: The Discovery of the Molecular Basis of Life. San
Diego: Academic Press. ISBN 0-12-361810-X. OCLC 162129355 191848148 44187710
(http://worldcat.org/oclc/162129355 + 191848148+44187710).

• Proceedings of National academy of Science of the United States of America (http://
www.pnas.org/), ISSN: 1091-6490 (electronic)

External links

• The Virtual Library of Biochemistry and Cell Biology (http://www.biochemweb.org/)

• Biochemistry, 5th ed. (http://www.ncbi.nlm.nih. gov/books/bv.fcgi?call=bv. View..
ShowTOC&rid=stryer.TOC&depth=2) Full text of Berg, Tymoczko, and Stryer,
courtesy of NCBI.

• Biochemistry, 2nd ed. (http://www.web.virginia.edu/Heidi/home.htm) Full text of
Garrett and Grisham.

• Biochemistry Animation (http://www.llec.com/Biochemistry/) (Narrated Flash
animations.)

• SystemsX.ch - The Swiss Initiative in Systems Biology (http://www.systemsX.ch/)

Major families of biochemicals

Saccharides/Carbohydrates/Glycosides • Amino acids/Peptides/Proteins/Glycoproteins
Lipids/Terpenes/Steroids/Carotenoids • Alkaloids/Nucleobases/Nucleic acids

Cofactors/Flavonoids/Polyketides/Tetrapyrroles

Quantum biocehmistry

Quantum chemistry is a branch of theoretical chemistry, which applies quantum
mechanics and quantum field theory to address issues and problems in chemistry. The
description of the electronic behavior of atoms and molecules as pertaining to their
reactivity is one of the applications of quantum chemistry. Quantum chemistry lies on the
border between chemistry and physics, and significant contributions have been made by
scientists from both fields. It has a strong and active overlap with the field of atomic
physics and molecular physics, as well as physical chemistry.

Quantum chemistry mathematically describes the fundamental behavior of matter at the

n 1
molecular scale. J It is, in principle, possible to describe all chemical systems using this

theory. In practice, only the simplest chemical systems may realistically be investigated in

purely quantum mechanical terms, and approximations must be made for most practical

purposes (e.g., Hartree-Fock, post Hartree-Fock or Density functional theory, see

computational chemistry for more details). Hence a detailed understanding of quantum

mechanics is not necessary for most chemistry, as the important implications of the theory

(principally the orbital approximation) can be understood and applied in simpler terms.

In quantum mechanics the Hamiltonian, or the physical state, of a particle can be expressed
as the sum of two operators, one corresponding to kinetic energy and the other to potential
energy. The Hamiltonian in the Schrodinger wave equation used in quantum chemistry does
not contain terms for the spin of the electron.

Solutions of the Schrodinger equation for the hydrogen atom gives the form of the wave
function for atomic orbitals, and the relative energy of the various orbitals. The orbital
approximation can be used to understand the other atoms e.g. helium, lithium and carbon.

History

The history of quantum chemistry essentially began with the 1838 discovery of cathode
rays by Michael Faraday, the 1859 statement of the black body radiation problem by Gustav
Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical
system could be discrete, and the 1900 quantum hypothesis by Max Planck that any energy
radiating atomic system can theoretically be divided into a number of discrete energy
elements s such that each of these energy elements is proportional to the frequency v with
which they each individually radiate energy, as defined by the following formula:

e = kv

where h is a numerical value called Planck's Constant. Then, in 1905, to explain the
photoelectric effect (1839), i.e., that shining light on certain materials can function to eject
electrons from the material, Albert Einstein postulated, based on Planck's quantum
hypothesis, that light itself consists of individual quantum particles, which later came to be
called photons (1926). In the years to follow, this theoretical basis slowly began to be
applied to chemical structure, reactivity, and bonding.

Quantum biocehmistry

Electronic structure

The first step in solving a quantum chemical problem is usually solving the Schrodinger
equation (or Dirac equation in relativistic quantum chemistry) with the electronic molecular
Hamiltonian. This is called determining the electronic structure of the molecule. It can be
said that the electronic structure of a molecule or crystal implies essentially its chemical
properties. An exact solution for the Schrodinger equation can only be obtained for the
hydrogen atom. Since all other atomic, or molecular systems, involve the motions of three
or more "particles", their Schrodinger equations cannot be solved exactly and so
approximate solutions must be sought.

Wave model

The foundation of quantum mechanics and quantum chemistry is the wave model, in which
the atom is a small, dense, positively charged nucleus surrounded by electrons. Unlike the
earlier Bohr model of the atom, however, the wave model describes electrons as "clouds"
moving in orbitals, and their positions are represented by probability distributions rather
than discrete points. The strength of this model lies in its predictive power. Specifically, it
predicts the pattern of chemically similar elements found in the periodic table. The wave
model is so named because electrons exhibit properties (such as interference) traditionally
associated with waves. See wave-particle duality.

Valence bond

Although the mathematical basis of quantum chemistry had been laid by Schrodinger in

1926, it is generally accepted that the first true calculation in quantum chemistry was that
of the German physicists Walter Heitler and Fritz London on the hydrogen (H ) molecule in

1927. Heitler and London's method was extended by the American theoretical physicist
John C. Slater and the American theoretical chemist Linus Pauling to become the
Valence-Bond (VB) [or Heitler-London-Slater-Pauling (HLSP)] method. In this
method, attention is primarily devoted to the pairwise interactions between atoms, and this
method therefore correlates closely with classical chemists' drawings of bonds.

Molecular orbital

An alternative approach was developed in 1929 by Friedrich Hund and Robert S. Mulliken,
in which electrons are described by mathematical functions delocalized over an entire
molecule. The Hund-Mulliken approach or molecular orbital (MO) method is less
intuitive to chemists, but has turned out capable of predicting spectroscopic properties
better than the VB method. This approach is the conceptional basis of the Hartree-Fock
method and further post Hartree-Fock methods.

Density functional theory

The Thomas-Fermi model was developed independently by Thomas and Fermi in 1927.
This was the first attempt to describe many-electron systems on the basis of electronic
density instead of wave functions, although it was not very successful in the treatment of
entire molecules. The method did provide the basis for what is now known as density
functional theory. Though this method is less developed than post Hartree-Fock methods,
its lower computational requirements allow it to tackle larger polyatomic molecules and
even macromolecules, which has made it the most used method in computational chemistry

Quantum biocehmistry

at present.

Chemical dynamics

A further step can consist of solving the Schrodinger equation with the total molecular
Hamiltonian in order to study the motion of molecules. Direct solution of the Schrodinger
equation is called quantum molecular dynamics, within the semiclassical approximation
semiclassical molecular dynamics, and within the classical mechanics framework molecular
dynamics (MD). Statistical approaches, using for example Monte Carlo methods, are also
possible.

Adiabatic chemical dynamics

In adiabatic dynamics, interatomic interactions are represented by single scalar
potentials called potential energy surfaces. This is the Born-Oppenheimer approximation
introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry
were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into
the RRKM theory in 1952 by Marcus who took the transition state theory developed by
Eyring in 1935 into account. These methods enable simple estimates of unimolecular
reaction rates from a few characteristics of the potential surface.

Non-adiabatic chemical dynamics

Non-adiabatic dynamics consists of taking the interaction between several coupled
potential energy surface (corresponding to different electronic quantum states of the
molecule). The coupling terms are called vibronic couplings. The pioneering work in this
field was done by Stueckelberg, Landau, and Zener in the 1930s, in their work on what is
now known as the Landau-Zener transition. Their formula allows the transition probability
between two diabatic potential curves in the neighborhood of an avoided crossing to be
calculated.

Quantum chemistry and quantum field theory

The application of quantum field theory (QFT) to chemical systems and theories has become
increasingly common in the modern physical sciences. One of the first and most
fundamentally explicit appearances of this is seen in the theory of the photomagneton. In
this system, plasmas, which are ubiquitous in both physics and chemistry, are studied in
order to determine the basic quantization of the underlying bosonic field. However,
quantum field theory is of interest in many fields of chemistry, including: nuclear chemistry,
astrochemistry, sonochemistry, and quantum hydrodynamics. Field theoretic methods have
also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical
pi-electron methods.

Quantum biocehmistry

See also

Atomic physics

Computational chemistry

Condensed matter physics

International Academy of Quantum Molecular Science

Physical chemistry

Quantum chemistry computer programs

Quantum electrochemistry

QMC@Home

Theoretical physics

Further reading

• Pauling, L. (1954). General Chemistry. Dover Publications. ISBN 0-486-65622-5.

• Pauling, L., and Wilson, E. B. Introduction to Quantum Mechanics with Applications to
Chemistry (Dover Publications) ISBN 0-486-64871-0

• Atkins, P.W. Physical Chemistry (Oxford University Press) ISBN 0-19-879285-9

• McWeeny, R. Coulson's Valence (Oxford Science Publications) ISBN 0-19-855144-4

• Landau, L.D. and Lifshitz, E.M. Quantum Mechanics:Non-relativistic Theory (Course of
Theoretical Physics vol.3) (Pergamon Press)

• Bernard Pullman and Alberte Pullman. 1963. Quantum Biochemistry., New York and
London: Academic Press.

• Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press,
2006. Considers the extent to which chemistry and especially the periodic system has
been reduced to quantum mechanics. ISBN 0-19-530573-6.

• Simon, Z. 1976. Quantum Biochemistry and Specific Interactions., Taylor & Francis;
ISBN 978-0856260872 and ISBN 0-85-6260878 .

References

[1] http://cmmxit.nih.gov/modeling/guide_documents/quantum_mechanics_document.htm Chemistry"

The NIH Guide to Molecular Modeling. National Institutes of Health, http://cmm.cit.nih.gov/modeling/
guidedocuments/quantummechanicsdocument.html. Retrieved on 2007-09-08.

External links

• The Sherrill Group - Notes (http://vergil.chemistry.gatech.edu/notes/index.html)

• ChemViz Curriculum Support Resources (http://www.shodor.org/chemviz/)

• Early ideas in the history of quantum chemistry (http://www.
quantum-chemistry-history, com/)

Quantum biocehmistry

Nobel lectures by quantum chemists

• Walter Kohn's Nobel lecture (http://nobelprize.org/chemistry/laureates/1998/
kohn-lecture.html)

• Rudolph Marcus' Nobel lecture (http://nobelprize.org/chemistry/laureates/1992/
marcus-lecture.html)

• Robert Mulliken's Nobel lecture (http://nobelprize.org/chemistry/laureates/1966/
mulliken-lecture.html)

• Linus Pauling's Nobel lecture (http://nobelprize.org/chemistry/laureates/1954/
pauling-lecture.html)

• John Pople's Nobel lecture (http://nobelprize.org/chemistry/laureates/1998/
pople-lecture.html)

Biophysical Chemistry

The Max Planck Institute for Biophysical Chemistry (Karl Friedrich Bonhoeffer
Institute) in Gottingen is a research institute of the Max Planck Society. Currently, 730
people work at the Institute, 370 of them are scientists.

As one of the institutes within the Max Planck Society it combines the three classical
scientific disciplines - biology, physics and chemistry. Founded in 1971, research in the
institute initially focussed on physical and chemical problems. It has since undergone a
continuous evolution manifested by an expanding range of core subjects and work areas
such as neurobiology, biochemistry and molecular biology.

History

The history of the Institute goes back to the
year 1949. At that time, the Max Planck
Society established the Max Planck
Institute for Physical Chemistry in
Gottingen as follow-up of the former
Kaiser-Wilhelm Institute for Physical
Chemistry in Berlin. Karl Friedrich
Bonhoeffer, who already worked at the
Kaiser Wilhelm Institute became the
founding director of the new institute. He
was one of the first researchers who
applied physical-chemical methods in
biological research and thus combined
different disciplines of natural sciences in
research.

The Max Planck Institute for Biophysical Chemistry was created in 1971 through the
merger of Max Planck Institute for Physical Chemistry and for Spectroscopy in Gottingen.
This was largely initiated by Nobel Prize winner Manfred Eigen, who was at that time
director of the Max Planck Institute for Physical Chemistry. His vision of an

interdisciplinary approach to biological research was decisive and the creative impulse for
the development of the Institute. To honour Karl Friedrich Bonhoeffer, the new institute

Aerial picture of the Max Planck Institute for
biophysical Chemistry, Gottingen (Picture: Jorg

Winkler, 2007)

Biophysical Chemistry

was named after him.

Although the Institute is dedicated to basic research - by virtue of the charter of the Max
Planck Society - its policy has been to encourage the transfer of numerous technological
innovations to the marketplace. As a consequence, many licensing agreements and start-up
firms have arisen from research conducted at the Institute, e. g. Lambda Physik, DeveloGen
and Evotec.

The history of the Institute also lists numerous prizes to honor outstanding scientific
achievements. In 1967, Manfred Eigen received the Nobel Prize for Chemistry for his
unique contributions to the field of rapid reaction kinetics. Two scientists of the Institute,
Erwin Neher and Bert Sakmann, shared the Nobel Prize for Physiology or Medicine in
1991, awarded for pioneering single channel recording techniques and applications.
Numerous science prizes have been awarded to other directors such as the Gottfried
Wilhelm Leibniz Prize (Herbert Jackie 1986, Fritz Peter Schafer 1986, Erwin Neher and
Bert Sakmann 1986, Peter Gruss 1994, Reinhard Luhrmann 1996, Christian Griesinger
1998, Reinhard Jahn 2000, Stefan W. Hell 2008) and the "Deutsche Zukunftspreis" by the
Federal President (Peter Gruss and Herbert Jackie 1999, Stefan Hell 2006). Other prizes
awarded to scientists of the Institute are the Louis Jeantet Prize (Peter Gruss 1995, Herbert
Jackie 1999) and the Ernst Jung Prize for Medicine (Klaus Weber 1984, Reinhard Luhrmann
2003, Reinhard Jahn 2006).

Furthermore, several junior scientists have been awarded different prizes, among them the
renowned BioFuture-Prize (Petra Schwille 1998, Tom Tuschl 1999, Holger Stark 2005).

Departments and Independent Research Groups

The research conducted at the Max Planck Institute for Biophysical Chemistry covers a
broad spectrum. Its aim is to understand biophysical and biochemical processes at a
fundamental level.

Departments

The Max Planck Institute for Biophysical Chemistry currently encompasses 11 departments

Prof. Gregor Eichele - Genes and Behavior

Prof. Dirk Gorlich - Cellular Logistics

Prof. Christian Griesinger - NMR based Structural Biology

Prof. Helmut Grubmuller - Theoretical and Computational Biophysics

Prof. Peter Gruss - Molecular Cell Biology

Prof. Stefan W. Hell - NanoBiophotonics

Prof. Herbert Jackie - Molecular Developmental Biology

Prof. Reinhard Jahn - Neurobiology

Prof. Reinhard Luhrmann - Cellular Biochemistry

Prof. Erwin Neher - Membrane Biophysics

Prof. Jiirgen Troe - Spectroscopy and Photochemical Kinetics

Biophysical Chemistry

Research Groups

The Institute is particularly engaged in the support of junior scientists, which is also
indicated by the numerous Junior Research Groups hosted here.

Dr Donna Arndt-Jovin - Structure and Regulation of Chromatin

Dr Adam Lange - Solid-state NMR

Dr Marina Bennati - Electron Paramagnetic Resonance

Prof. Christof Biebricher - RNA Replication

Dr Berend de Groot - Computational Biomolecular Dynamics

Dr Dirk Fasshauer - Structural Biochemistry

Dr Wolfgang Fischle - Chromatin Biochemistry

Dr Stefan Jakobs - Mitochondrial Structure and Dynamics

Prof. Michael Kessel - Developmental Biology

Prof. Jiirgen Klingauf - Microscopy of Synaptic Transmission

Dr Martin Kollmar - Structural investigations

Dr Manfred Konrad - Enzyme Biochemistry

Prof. Ahmed Mansouri - Molecular Cell Differentiation

Prof. Dietmar Porschke - Biomolecular Dynamics

Dr. Takeshi Sakaba - Biophysics of Synaptic Transmission

Dr. Reinhard Schuh - Molecular Organogenesis

Prof. Dirk Schwarzer - Reaction Dynamics

Dr Jaokob Sorensen - Molecular Mechanismens ofExocytosis

Dr Holger Stark - 3D Electron Cryo-microscopy

Dr Anastassia Stoykova / Dr. Kamal Chowdhury - Molecular Developmental

Neurobiology

Prof. Michael Stuke - Laser Chemical Processing

Dr Simone Techert - Structural Dynamics of (Bio)chemical Systems

Dr Henning Urlaub - Bioanalytical Mass Spectrometry

Dr Markus Wahl - X-Ray Crystallography

Prof. Peter Jomo Walla - Labelfree Biomolecular Analysis and Single-Molecule

Detection

Dr Markus Zweckstetter - Protein Structure Determination using NMR

Emeritus Groups

After being retired, directors of the Institute can actively continue their research for a
couple of years.

• Prof. Dieter Gallwitz - Molecular Genetics

• Prof. Thomas Jovin - Laboratory for Cellular Dynamics

• Prof. Klaus Weber - Biochemistry and Cell Biology

Biophysical Chemistry

Former Departments

The Institute has undergone a permanent change in research by closing of departments
after their heads being retired and by continuous establishing new departments. Some of
the former directors pursue their research even after their Emeritus Group has been
expired and can still be contacted at the Institute (*).

Prof. Otto D. Creutzfeldt -Neurobiology (1971-1992)

Prof. Manfred Eigen (*) - Biochemical Kinetics (1971-1995)

Prof. Manfred Kahlweit (*) - Kinetics of Phase Transformations (1971-1996)

Prof. Hans Kuhn - Molecular Systems (1971-1984)

Prof. Leo de Maeyer (*) - Experimental Methods (1971-1996)

Prof. Bert Sakman - Cell Physiology (1985-1988)

Prof. Fritz-Peter Schafer - Laser Physics (1971-1994)

Prof. Hans Strehlow - Electrochemistry and Reaction Kinetics (1971-1984)

Prof. Albert Weller - Spectroscopy (1971-1990)

Prof. Victor P. Whittaker - Neurochemistry (1973-1987)

Biomedizinische NMR Forschungs GmbH

The Institute also accommodates the independent Biomedizinische NMR Forschungs GmbH
[ ^ headed by Jens Frahm, which was founded in 1993. The focus of his team is the
development and application of spatially resolved NMR techniques for non-invasive studies
of the central nervous system in animals and humans. These innovative approaches allow
for unique insights into the structure, metabolism and function of the intact living brain.
Jens Frahm and his coworkers invented a rapid acquisition technique for magnetic
resonance imaging termed FLASH MRI (fast low angle shot) technique, that allowed for a
100-fold reduction of the measuring times of cross-sectional and three-dimensional images.
The FLASH technique led the ground for many modern MRI applications in diagnostic
imaging.

Service Groups

Scientific service groups such as Electron Microscopy (Dr Dietmar Riedel), Mass
Spectrometry (Dr Henning Urlaub) and Innovative Light Microscopy (Dr Alexander Egner)
develop specific and complex methods. The service facilities are available to all scientists of
the Institute and provide help and training in terms of sample preparation and data
analysis.

An expert Information Technology group maintains the very complex and sophisticated
network of computational facilities. The EU Liaison Office provides support for all phases of
the EU grant application procedure. The Otto Hahn Library offers more than 80000 journal
volumes, in addition to nearly 40000 monographs. Current journal subscriptions include
more than 380 titles. Employees in the workshops of the Institute collaborate with the
researchers in order to construct special-purpose equipment. Moreover, they continuously
seek improved methods for the graphical and photographic reproduction of scientific
results. Two child care facilities operated by the Kinderhaus Gottingen e.V. take care of
children aged 1 to 4 years.

Biophysical Chemistry

Activities of the Institute

The Institute offers many activities for the public. Besides guided tours for visitors and
students from different schools, the Institute arranges public lectures introducing research
of different departments and junior research groups. A one-week Science and Youth
Program operated every year by the City of Gottingen provides students with insights into
the laboratories of the Institute. „Open doors" offer the possibility to visit departments and
research groups.

Moreover, the Institute offers a special programme, the Hands-on Laboratory of the
European Initiative for Communicators of Science (EICOS), which invites journalists from
all over Europe and Israel to gain a close-up view of research in the laboratories.

Cooperation with the University of Gottingen and other
Research Facilities

The European Neuroscience Institute (ENI) in Gottingen has existed since 2000 and is
dedicated to the support of independent work of Young Investigators in the field of
neurosciences. It presently houses three Young Investigator groups working in the fields of
neuroendocrinology, neuroplasticity, and cell biophysics. It is jointly funded by the Medical
School of Gottingen University and the Max Planck Institutes for Experimental Medicine
and for Biophysical Chemistry.

The DFG Research Center for Molecular Physiology of the Brain (CMPB) is a

research center funded by the German Research Community (DFG) and unites research
groups of the Georg August University Gottingen, the Max Planck Society and the German
Primate Center in Gottingen. Their research activities focus on molecular processes
underlying brain function and the application of new knowledge from these studies in the
development of therapies for psychiatric and neurological disorders.

The Bernstein Center for Computational Neuroscience (BCCN) Gottingen was

established in 2007. In cooperation with research groups from the Max Planck Institute for
Dynamics and Self-Organization, the University of Gottingen, the German Primate Center,
and the research lab of Otto Bock HealthCare GmbH, research is conducted in joint
projects on the adaptivity of the nervous system ranging from the level of single synapses to
the level of cognitive processes.

In 2000, two International Max Planck Research Schools (IMPRS) were established
together with the Georg August University Gottingen, the German Primate Center and the
Max Planck Institute for Experimental Medicine: the IMPRS for Molecular Biology and the
IMPRS for Neurosciences (in cooperation with the Max Planck Institute for Dynamics and
Self-Organization and the ENI Gottingen). Entering with a Bachelor's degree, the students
receive a broad theoretical and practical training in the first year that is both intensive and
interdisciplinary. Upon successful completion of a qualifying exam by the end of the first
year (Master of Science, M.Sc), the students join one of the participating research groups
to begin their doctoral thesis, which is to be submitted within three years (PhD).

Biophysical Chemistry

External links

Max Planck Institute for Biophysical Chemistry L J

Max Planck Society [3]

Biomedical NMR Research GmbH L J

Eicos [5]

ENI [6]

CMPB [7]

BCCN [8]

IMPRS for Molecular Biology [9]

IMPRS for Neurosciences °

References

[1] http://www.biomednmr.mpg.de

[2] http ://www. mpibpc.gwdg.de/english/

[3] http://www.mpg.de/english/portal/index.html/

[4] http://www.biomednmr.mpg.de/

[5] http://www.eicos.mpg.de/

[6] http://www.eni.gwdg.de/

[ 7 ] http :// www. cmpb . uni-go ettingen . de/

[8] http://www.bccn-goettingen.de/

[ 9 ] http :// www. gpmolbio . uni-goettingen . de/

[ 1 0] http ://www. gpneuro. uni-goettingen. de/

Theoretical/Mathematical
Biophysics and Related Fields of

Theoretical Science]]

Mathematical biology

n 1
Mathematical biology is also called theoretical biology/ J and sometimes

biomathematics. It includes at least four major subfields: biological mathematical

modeling, relational biology/complex systems biology (CSB), bioinformatics and

computational biomodeling/biocomputing. It is an interdisciplinary academic research field

with a wide range of applications in biology, medicine 1 ^ and biotechnology. - 1

Mathematical biology aims at the mathematical representation, treatment and modeling of
biological processes, using a variety of applied mathematical techniques and tools. It has
both theoretical and practical applications in biological, biomedical and biotechnology
research. For example, in cell biology, protein interactions are often represented as
"cartoon" models, which, although easy to visualize, do not accurately describe the systems
studied. In order to do this, precise mathematical models are required. By describing the
systems in a quantitative manner, their behavior can be better simulated, and hence
properties can be predicted that might not be evident to the experimenter.

Importance

Applying mathematics to biology has a long history, but only recently has there been an
explosion of interest in the field. Some reasons for this include:

• the explosion of data-rich information sets, due to the genomics revolution, which are
difficult to understand without the use of analytical tools,

• recent development of mathematical tools such as chaos theory to help understand
complex, nonlinear mechanisms in biology,

• an increase in computing power which enables calculations and simulations to be
performed that were not previously possible, and

• an increasing interest in in silico experimentation due to ethical considerations, risk,
unreliability and other complications involved in human and animal research.

For use of basic arithmetics in biology, see relevant topic, such as Serial dilution.

Areas of research

Several areas of specialized research in mathematical and theoretical biology J

L J as well as external links to related projects in various universities are concisely
presented in the following subsections, including also a large number of appropriate
validating references from a list of several thousands of published authors contributing to
this field. Many of the included examples are characterised by highly complex, nonlinear,
and supercomplex mechanisms, as it is being increasingly recognised that the result of such

Mathematical biology

interactions may only be understood through a combination of mathematical, logical,
physical/chemical, molecular and computational models. Due to the wide diversity of
specific knowledge involved, biomathematical research is often done in collaboration
between mathematicians, biomathematicians, theoretical biologists, physicists,
biophysicists, biochemists, bioengineers, engineers, biologists, physiologists, research
physicians, biomedical researchers, oncologists, molecular biologists, geneticists,
embryologists, zoologists, chemists, etc.

Computer models and automata theory

A monograph on this topic summarizes an extensive amount of published research in this
area up to 1987, J including subsections in the following areas: computer modeling in
biology and medicine, arterial system models, neuron models, biochemical and oscillation

networks, quantum automata , quantum computers in molecular biology and genetics,
cancer modelling, neural nets, genetic networks, abstract relational biology,

ri2i ri3i

metabolic-replication systems, category theory applications in biology and medicine,
automata theory, cellular automata, tessallation models and complete

self-reproduction L , chaotic systems in organisms, relational biology and organismic

n 71 n Ri
theories. This published report also includes 390 references to peer-reviewed

rim r?01 T211

articles by a large number of authors.
Modeling cell and molecular biology

This area has received a boost due to the growing importance of molecular biology. J

• Mechanics of biological tissues

• Theoretical enzymology and enzyme kinetics

• Cancer modelling and simulation L J L J

• Modelling the movement of interacting cell populations

[271

• Mathematical modelling of scar tissue formation 1 J

• Mathematical modelling of intracellular dynamics

• Mathematical modelling of the cell cycle

Modelling physiological systems

• Modelling of arterial disease

[Q1 ]

• Multi-scale modelling of the heart

Molecular set theory

Molecular set theory was introduced by Anthony Bartholomay, and its applications were
developed in mathematical biology and especially in Mathematical Medicine. Molecular
set theory (MST) is a mathematical formulation of the wide-sense chemical kinetics of
biomolecular reactions in terms of sets of molecules and their chemical transformations
represented by set-theoretical mappings between molecular sets. In a more general sense,
MST is the theory of molecular categories defined as categories of molecular sets and their
chemical transformations represented as set-theoretical mappings of molecular sets. The
theory has also contributed to biostatistics and the formulation of clinical biochemistry
problems in mathematical formulations of pathological, biochemical changes of interest to
Physiology, Clinical Biochemistry and Medicine. L

Mathematical biology

Population dynamics

Population dynamics has traditionally been the dominant field of mathematical biology.
Work in this area dates back to the 19th century. The Lotka-Volterra predator-prey
equations are a famous example. In the past 30 years, population dynamics has been
complemented by evolutionary game theory, developed first by John Maynard Smith. Under
these dynamics, evolutionary biology concepts may take a deterministic mathematical form.
Population dynamics overlap with another active area of research in mathematical biology:
mathematical epidemiology, the study of infectious disease affecting populations. Various
models of viral spread have been proposed and analyzed, and provide important results that
may be applied to health policy decisions.

Mathematical methods

A model of a biological system is converted into a system of equations, although the word
'model' is often used synonymously with the system of corresponding equations. The
solution of the equations, by either analytical or numerical means, describes how the
biological system behaves either over time or at equilibrium. There are many different
types of equations and the type of behavior that can occur is dependent on both the model
and the equations used. The model often makes assumptions about the system. The
equations may also make assumptions about the nature of what may occur.

Mathematical biophysics

The earlier stages of mathematical biology were dominated by mathematical biophysics,
described as the application of mathematics in biophysics, often involving specific
physical/mathematical models of biosystems and their components or compartments.

The following is a list of mathematical descriptions and their assumptions.

Deterministic processes (dynamical systems)

A fixed mapping between an initial state and a final state. Starting from an initial condition
and moving forward in time, a deterministic process will always generate the same
trajectory and no two trajectories cross in state space.

• Difference equations - discrete time, continuous state space.

• Ordinary differential equations - continuous time, continuous state space, no spatial
derivatives. See also: Numerical ordinary differential equations.

• Partial differential equations - continuous time, continuous state space, spatial
derivatives. See also: Numerical partial differential equations.

• Maps - discrete time, continuous state space.

Stochastic processes (random dynamical systems)

A random mapping between an initial state and a final state, making the state of the system
a random variable with a corresponding probability distribution.

• Non-Markovian processes - generalized master equation - continuous time with memory
of past events, discrete state space, waiting times of events (or transitions between
states) discretely occur and have a generalized probability distribution.

• Jump Markov process - master equation - continuous time with no memory of past
events, discrete state space, waiting times between events discretely occur and are
exponentially distributed. See also: Monte Carlo method for numerical simulation
methods, specifically continuous-time Monte Carlo which is also called kinetic Monte

Mathematical biology

Carlo or the stochastic simulation algorithm.

• Continuous Markov process - stochastic differential equations or a Fokker-Planck
equation - continuous time, continuous state space, events occur continuously according
to a random Wiener process.

Spatial modelling

One classic work in this area is Alan Turing's paper on morphogenesis entitled The
Chemical Basis of Morphogenesis, published in 1952 in the Philosophical Transactions of
the Royal Society.

• Travelling waves in a wound-healing assay

• Swarming behaviour ]

T371

• A mechanochemical theory of morphogenesis

• Biological pattern formation^ ^

• Spatial distribution modeling using plot samples 1 ]

Phylogenetics

Phylogenetics is an area of mathematical biology that deals with the reconstruction and
analysis of phylogenetic (evolutionary) trees and networks based on inherited
characteristics. The main mathematical concepts are trees, X-trees and maximum
parsimony trees.

Model example: the cell cycle

The eukaryotic cell cycle is very complex and is one of the most studied topics, since its
misregulation leads to cancers. It is possibly a good example of a mathematical model as it
deals with simple calculus but gives valid results. Two research groups c ^ c ] have
produced several models of the cell cycle simulating several organisms. They have recently
produced a generic eukaryotic cell cycle model which can represent a particular eukaryote
depending on the values of the parameters, demonstrating that the idiosyncrasies of the
individual cell cycles are due to different protein concentrations and affinities, while the
underlying mechanisms are conserved (Csikasz-Nagy et al., 2006).

By means of a system of ordinary differential equations these models show the change in
time (dynamical system) of the protein inside a single typical cell; this type of model is
called a deterministic process (whereas a model describing a statistical distribution of
protein concentrations in a population of cells is called a stochastic process).
To obtain these equations an iterative series of steps must be done: first the several models
and observations are combined to form a consensus diagram and the appropriate kinetic
laws are chosen to write the differential equations, such as rate kinetics for stoichiometric
reactions, Michaelis-Menten kinetics for enzyme substrate reactions and
Goldbeter-Koshland kinetics for ultrasensitive transcription factors, afterwards the
parameters of the equations (rate constants, enzyme efficiency coefficients and Michealis
constants) must be fitted to match observations; when they cannot be fitted the kinetic
equation is revised and when that is not possible the wiring diagram is modified. The
parameters are fitted and validated using observations of both wild type and mutants, such
as protein half-life and cell size.

In order to fit the parameters the differential equations need to be studied. This can be
done either by simulation or by analysis.
In a simulation, given a starting vector (list of the values of the variables), the progression

Mathematical biology

of the system is calculated by solving the equations at each time-frame in small increments.

In analysis, the proprieties of
the equations are used to
investigate the behavior of the
system depending of the
values of the parameters and

variables.

system

BIFURCATION DfAGRAM

i .

S io

■ 1 -

■•f

M 10

-?. ■

^Q^

F/xed PoMs

Sjjore
siarUng -area

CKI

inhibition

Cell cycle trajectory

Stable steady state:

Mass dictates the active cyclinS levels because stable steady-
states attract (negative eigenvalues) keeping [MPF] constant

Saddle steady-state:

System is in an oxitatory pnase indipondent of mass because
^stable steady-state's repell (one or more positive eigenvalues)

* o Stable/Unstable limit cycle max/min:

The system is in a loop, so at that mass tho |.MPF] will oscillate

with a certain period (complex eigenvalues}

Singularities

Saddle Node:

5" ' A stable and an unstable steady-states annihilate, beyond
SN2 \vhich there are no equilibrium points: those bifurcation
events will trigger the exit from G1 and G2 respectively

SN1 i 2

cell mass (au,l

SN2 3
(SNIPER)

dMass/dt = kg rQw in-Mas-5 {exponential growth)

d[Cin2]/dt = {hu+ ^ [SBF]) mass - k<j- [Cin2]

The parameter mass, directly controls cyclin levels, expressing

implicitly its yet MnKnawn mass dependant control mechanism

HQ Hopf Bifurcation

A stable and an unslable steady-stages annihilate resulling in
an unstable- limit cycle {eigenvalues have no Real part)

SNIPER SNIPER Bifurcation

A limit cycle with infinite period emerges from a stable and
en unstable stcady-stato annihilation

differential equations can be
represented as a vector field,
where each vector described
the change (in concentration
of two or more protein)
determining where and how

fast the trajectory (simulation) is heading. Vector fields can have several special points: a
stable point, called a sink, that attracts in all directions (forcing the concentrations to be at
a certain value), an unstable point, either a source or a saddle point which repels (forcing
the concentrations to change away from a certain value), and a limit cycle, a closed
trajectory towards which several trajectories spiral towards (making the concentrations
oscillate).

A better representation which can handle the large number of variables and parameters is
called a bifurcation diagram(Bifurcation theory): the presence of these special steady-state
points at certain values of a parameter (e.g. mass) is represented by a point and once the
parameter passes a certain value, a qualitative change occurs, called a bifurcation, in which
the nature of the space changes, with profound consequences for the protein
concentrations: the cell cycle has phases (partially corresponding to Gl and G2) in which
mass, via a stable point, controls cyclin levels, and phases (S and M phases) in which the
concentrations change independently, but once the phase has changed at a bifurcation
event (Cell cycle checkpoint), the system cannot go back to the previous levels since at the
current mass the vector field is profoundly different and the mass cannot be reversed back
through the bifurcation event, making a checkpoint irreversible. In particular the S and M
checkpoints are regulated by means of special bifurcations called a Hopf bifurcation and an
infinite period bifurcation.

Mathematical/theoretical biologists

Pere Alberch
Anthony F. Bartholomay
J. T. Bonner
Jack Cowan

Gerd B. Miiller
Walter M. Elsasser
Claus Emmeche
Andree Ehresmann
Marc Feldman
Ronald A. Fisher
Brian Goodwin
Bryan Grenfell

Mathematical biology

J. B. S. Haldane

William D. Hamilton

Lionel G. Harrison

Michael Hassell

Sven Erik j0rgensen

George Karreman

Stuart Kauffman

Kalevi Kull

Herbert D. Landahl

Richard Lewontin

Humberto Maturana

Robert May

John Maynard Smith

Howard Pattee

George R. Price

Erik Rauch

Nicolas Rashevsky

Ronald Brown (mathematician)

Johannes Reinke

Robert Rosen

Rene Thorn

Jakob von Uexkull

Robert Ulanowicz

Francisco Varela

C. H. Waddington

Arthur Winfree

Lewis Wolpert

Sewall Wright

Christopher Zeeman

Mathematical, theoretical and computational biophysicists

Nicolas Rashevsky
Ludwig von Bertalanffy
Francis Crick
Manfred Eigen
Walter Elsasser
Herbert Frohlich, FRS
Francois Jacob
Martin Karplus
George Karreman
Herbert D. Landahl
Ilya, Viscount Prigogine
Sirjohn Randall
James D. Murray
Bernard Pullman
Alberte Pullman
Erwin Schrodinger

Mathematical biology

Klaus Schulten
Peter Schuster
Zeno Simon
D'Arcy Thompson
Murray Gell-Mann

See also

Abstract relational biology [42][43] [44]

Biocybernetics

Bioinformatics

Biologically inspired computing

Biostatistics

Cellular automata [45]

Coalescent theory

Complex systems biology [46] [47] [48]

Computational biology

Dynamical systems in biology [49] [50] [51] [52] [53] [54]

Epidemiology

Evolution theories and Population Genetics

• Population genetics models

• Molecular evolution theories
Ewens's sampling formula
Excitable medium
Mathematical models

• Molecular modelling

• Software for molecular modeling

• Metabolic-replication systems [55][56]

• Models of Growth and Form

• Neighbour-sensing model
Morphometries

Organismic systems (OS) [57][58]
Organismic supercategories J

Population dynamics of fisheries
Protein folding, also blue Gene and folding@home
Quantum computers
Quantum genetics
Relational biology

Self-reproduction L J (also called self-replication in a more general context).
Computational gene models
Systems biology [63]
Theoretical biology
Topological models of morphogenesis

• DNA topology

• DNA sequencing theory

For use of basic arithmetics in biology, see relevant topic, such as Serial dilution
Biographies

Mathematical biology

Charles Darwin
D'Arcy Thompson
Joseph Fourier
Charles S. Peskin
Nicolas Rashevsky [65]
Robert Rosen
Rosalind Franklin
Francis Crick
Rene Thorn
Vito Volterra

References

• Nicolas Rashevsky. (1938)., Mathematical Biophysics. Chicago: University of Chicago
Press.

• Robert Rosen, Dynamical system theory in biology. New York, Wiley-Interscience (1970)
ISBN 0471735507 [66]

• Israel, G., 2005, "Book on mathematical biology" in Grattan-Guinness, I., ed., Landmark
Writings in Western Mathematics. Elsevier: 936-44.

• Israel, G (1988), "http://www.ncbi.nlm.nih.gov/pubmed/3045853IOn the contribution of
Volterra and Lotka to the development of modern biomathematics.", History and
philosophy of the life sciences 10 (1): 37-49, PMID:3045853, http://www.ncbi.nlm.nih.
gov/pubmed/3045853

• Scudo, F M (1971), "http://www.ncbi.nlm.nih.gov/pubmed/4950157IVito Volterra and
theoretical ecology.", Theoretical population biology 2 (1): 1-23, 1971 Mar,
PMID:4950157, http://www.ncbi.nlm.nih.gov/pubmed/4950157

• S.H. Strogatz, Nonlinear dynamics and Chaos: Applications to Physics, Biology,
Chemistry, and Engineering. Perseus, 2001, ISBN 0-7382-0453-6

• N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North Holland., 3rd
ed. 2001, ISBN 0-444-89349-0

• I. C. Baianu., Computer Models and Automata Theory in Biology and Medicine.,

Monograph, Ch.ll in M. Witten (Editor), Mathematical Models in Medicine, vol. 7., Vol.

7: 1513-1577 (1987),Pergamon Press:New York, (updated by Hsiao Chen Lin in 2004 [67]
[68] [69] ISBN 0080363776 [70] .

• P.G. Drazin, Nonlinear systems. C.U.P., 1992. ISBN 0-521-40668-4

• L. Edelstein-Keshet, Mathematical Models in Biology. SIAM, 2004. ISBN 0-07-554950-6

• G. Forgacs and S. A. Newman, Biological Physics of the Developing Embryo. C.U.P.,
2005. ISBN 0-521-78337-2

• A. Goldbeter, Biochemical oscillations and cellular rhythms. C.U.P., 1996. ISBN
0-521-59946-6

• L.G. Harrison, Kinetic theory of living pattern. C.U.P., 1993. ISBN 0-521-30691-4

• F. Hoppensteadt, Mathematical theories of populations: demographics, genetics and
epidemics. SIAM, Philadelphia, 1975 (reprinted 1993). ISBN 0-89871-017-0

• D.W. Jordan and P. Smith, Nonlinear ordinary differential equations, 2nd ed. O.U.P.,
1987. ISBN 0-19-856562-3

• J.D. Murray, Mathematical Biology. Springer-Verlag, 3rd ed. in 2 vols.: Mathematical
Biology: I. An Introduction, 2002 ISBN 0-387-95223-3; Mathematical Biology: II. Spatial
Models and Biomedical Applications, 2003 ISBN 0-387-95228-4.

Mathematical biology

E. Renshaw, Modelling biological populations in space and time. C.U.P., 1991. ISBN

0-521-44855-7

S.I. Rubinow, Introduction to mathematical biology. John Wiley, 1975. ISBN

0-471-74446-8

L.A. Segel, Modeling dynamic phenomena in molecular and cellular biology. C.U.P., 1984.

ISBN 0-521-27477-X

L. Preziosi, Cancer Modelling and Simulation. Chapman Hall/CRC Press, 2003. ISBN

1-58488-361-8.

Lists of references

A general list of Theoretical biology/Mathematical biology references, including an

T711

updated list of actively contributing authors .

A list of references for applications of category theory in relational biology J .

An updated list of publications of theoretical biologist Robert Rosen 1 J

External

F. Hoppensteadt, Getting Started in Mathematical Biology . Notices of American
Mathematical Society, Sept. 1995.

rye:]

M. C. Reed, Why Is Mathematical Biology So Hard? Notices of American

Mathematical Society, March, 2004.

R. M. May, Uses and Abuses of Mathematics in Biology . Science, February 6, 2004.

T771

J. D. Murray, How the leopard gets its spots? Scientific American, 258(3): 80-87,

1988.

S. Schnell, R. Grima, P. K. Maini, Multiscale Modeling in Biology , American Scientist,

Vol 95, pages 134-142, March-April 2007.

Chen KC et al. Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell.

2004Aug;15(8):3841-62.

Csikasz-Nagy A et al. Analysis of a generic model of eukaryotic cell-cycle regulation.

BiophysJ. 2006 Jun 15;90(12):4361-79.

Fuss H, et al. Mathematical models of cell cycle regulation. Brief Bioinform. 2005

Jun;6(2):163-77.

Lovrics A et al. Time scale and dimension analysis of a budding yeast cell cycle model.

[79] BMC Bioinform. 2006 Nov 9;7:494.

Notes: Inline and online

[I] Mathematical Biology and Theoretical Biophysics-An Outline: What is Life? http://planetmath.org/
?op=getobj&from=objects&id= 10921

[2] http://www.kli.ac.at/theorylab/EditedVol/W/WittenM1987a.html

[3] http://en.scientificcommons.org/1857372

[4] http ://www.kli. ac. at/theorylab/index. html

[5] http://www.springerlink.com/content/w2733h7280521632/

[6] http://en.scientificcommons.org/1857371

[7] http://cogprints.org/3687/

[8] http://www.maths.gla.ac.uk/research/groups/biology/kal.html "Research in Mathematical Biology".

Maths.gla.ac.uk. http://www.maths.gla.ac.uk/research/groups/biology/kal.htm. Retrieved on 2008-09-10.
[9] http://acube.org/volume_23/v23-lpll-36.pdfJ. R. Junck. Ten Equations that Changed Biology: Mathematics

in Problem-Solving Biology Curricula, Bioscene, (1997), 1-36
[10] http://en. scientificcommons. org/1 85 737 1

[II] http://planetphysics.org/encyclopedia/QuantumAutomaton.html

Mathematical biology

[12] http ://planetphysics. org/encyclopedia/

BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html
[13] http ://planetphysics. org/encyclopedia/BibliographyForMathematicalBiophysicsAndMathematicalMedicine.

html
[14] Modern Cellular Automata by Kendall Preston and M.J. B. Duff http://books.google.co.uk/

books?id=10_0q_e-u_UC&dq=cellular+automata+and+tessalation&pg=PPl&ots=ciXYCF3AYm&

source=citation&sig=CtaUDhisM7MalS7rZfXvp689y-8&hl=en&sa=X&oi=book_result&resnum=12&

ct=result
[15] http://mathworld.wolfram.com/DualTessellation.html
[16] http://planetphysics.org/encyclopedia/ETACAxioms.html
[17] Baianu, I. C. 1987, Computer Models and Automata Theory in Biology and Medicine., in M. Witten

ed.), Mathematical Models in Medicine, vol. 7 ., Ch.ll Pergamon Press, New York, 1513-1577. http://cogprints

org/3687/

[18
[19
[20

01/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefnew.pdf
[21] http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysics.html
[22] http://www.maths.gla.ac.uk/research/groups/biology/kal.html "Research in Mathematical Biology".

Maths.gla.ac.uk. http://www.maths.gla.ac.uk/research/groups/biology/kal.htm. Retrieved on 2008-09-10.

[23
[24
[25
[26
[27
[28
[29
[30
[31
[32
[33

Transformations http://planetmath.org/?op=getobj&from=objects&id= 10770

[34
[35
[36
[37
[38
[39

[40

[46

[47

[48
[49

[50

[51

http://www.kli.ac.at/theorylab/EditedVol/VV/WittenM1987a.html

http://www.springerlink.com/content/w2733h7280521632/

Currently available for download as an updated PDF: http://cogprints.ecs.soton.ac.uk/archive/00003718/

http://www.maths.gla.ac.uk/~rwo/research_areas.htm

http://www.springerlink.com/content/71958358k273622q/

http://calvino.polito.it/~mcrtn/

http ://www. ma. hw. ac. uk/~jas/researchinterests/index. html

http://www.ma.hw.ac.uk/~jas/researchinterests/scartissueformation.html

http ://www. sbi. uni-rostock. de/dokumente/p_gilles_paper . pdf

http://mpf.biol.vt.edu/Research.html

http://www.maths.gla.ac.uk/~nah/research interests.html

http://www.integrativebiology.ox.ac.uk/heartmodel.html

http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html

Representation of Uni-molecular and Multimolecular Biochemical Reactions in terms of Molecular Set

http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html

http://www.maths.ox.ac.uk/~maini/public/gallery/twwha.htm

http://www.math.ubc.ca/people/faculty/keshet/research.html

http://www.maths.ox.ac.uk/~maini/public/gallery/mctom.htm

http://www.maths.ox.ac.uk/~maini/public/gallery/bpf.htm

http://links.jstor.org/sici?sici=0030-1299%28199008%2958%3A3%3C257%3ASDOTMU%3E2.0.

CO%3B2-S&size=LARGE&origin=JSTOR-enlargePage

http://mpf.biol.vt.edu/Tyson Lab.html|"The JJ Tyson Lab". Virginia Tech. http://mpf.biol.vt.edu/

Tyson%20Lab.html. Retrieved on 2008-09-10.
[41] http://cellcycle.mkt.bme.hu/! "The Molecular Network Dynamics Research Group". Budapest University of

Technology and Economics, http://cellcycle.mkt.bme.hu/.
[42 ] http ://www. kli. ac . at/theorylab/ALists/Authors_R. html
[43] http://planetphysics.org/encyclopedia/AbstractRelationalBiologyARB.html
[44] http://www. kli. ac.at/theorylab/EditedVol/M/MatsunoKDose_84. html
[45] Baianu, I. C. 1987, Computer Models and Automata Theory in Biology and Medicine., in M. Witten

ed.), Mathematical Models in Medicine, vol. 7., Ch.ll Pergamon Press, New York, 1513-1577. http://www.

springerlink.com/content/w2733h7280521632/

http://www.springerlink.com/content/vlrt05876h74v607/?p=2bd3993c33644512ba7069ed7fad0046&

pi=l

http://www.springerlink.com/content/j7t56r530140r88p/?p=2bd3993c33644512ba7069ed7fad0046&

pi=3

http://www.springerlink.com/content/98303486x3107jx3/

Robert Rosen, Dynamical system theory in biology. New York, Wiley-Interscience (1970) ISBN 0471735507

http://www.worldcat.org/oclc/101642

http://www.springerlink.com/content/j7t56r530140r88p/?p=2bd3993c33644512ba7069ed7fad0046&

pi=3

http://cogprints.org/3674/

Mathematical biology

[52
[53
[54
[55
[56
[57
[58
[59
[60
[61
[62

name=NaturalTransformationsOfOrganismicStructures&op=getobj

[63
[64
[65
[66
[67
[68
[69
[70
[71
[72
[73
[74
[75
[76
[77
[78
[79

http ://cogprints. org/3829/

http://www.ncbi.nlm.nih.gov/pubmed/4327361

http://www.springerlink.com/content/98303486x3107jx3/

http://planetphysics.org/encyclopedia/RSystemsCategoryOfM.html

http://www.kli.ac.at/theorylab/ALists/Authors_R.html

http://planetphysics.org/encyclopedia/OrganismicSetTheory.html

Organisms as Super-complex Systems http://planetmath.org/?op=getobj&from=objects&id= 10890

http://www.springerlink.com/content/98303486x3107jx3/

http://planetmath.org/encyclopedia/SupercategoriesOfComplexSystems.html

http ://planetmath.org/?op=getobj&from=objects&id= 10921

http://planetmath.org/?method=12h&from=objects&

http://www.kli.ac.at/theorylab/ALists/Authors_R.html

http://www.kli.ac.at/theorylab/index.html

http://planetphysics.org/encyclopedia/NicolasRashevsky.html

http://www.worldcat.org/oclc/101642

http://cogprints.Org/3718/l/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefnew.pdf

http://www.springerlink.com/content/w2733h7280521632/

http://www.springerlink.com/content/n8gw445012267381/

http://www.bookfinder.eom/dir/i/Mathematical_Models_in_Medicine/0080363776/

http://www.kli.ac.at/theorylab/index.html

http://planetmath.org/?method=12h&from=objects&id=10746&op=getobj

Publications list for Robert Rosen http://www.people.vcu.edu/~mikuleck/rosen.htm

http://www.ams.org/notices/199509/hoppensteadt.pdf

http://www.resnet.wm.edu/~jxshix/math490/reed.pdf

http://www.resnet.wm.edu/~jxshix/math490/may.pdf

http://www.resnet.wm.edu/~jxshix/math490/murray.doc

http://eprints.maths.ox.ac.uk/567/01/224.pdf

http://www.biomedcentral.com/content/pdf/1471-2105-7-494.pdf

External links

• Theoretical and mathematical biology website (http://www.kli.ac.at/theorylab/index.
html)

• Complexity Discussion Group (http://www.complex.vcu.edu/)

• Integrative cancer biology modeling and Complex systems biology (http://fs512.fshn.
uiuc.edu/ComplexSystemsBiology.htm)

• UCLA Biocybernetics Laboratory (http://biocyb.cs.ucla.edu/research.html)

• TUCS Computational Biomodelling Laboratory (http://www.tucs.fi/research/labs/
combio.php)

• Nagoya University Division of Biomodeling (http://www.agr.nagoya-u.ac.jp/english/
e3senko-l.html)

• Technische Universiteit Biomodeling and Informatics (http://www.bmi2.bmt.tue.nl/
Biomedinf/)

• BioCybernetics Wiki, a vertical wiki on biomedical cybernetics and systems biology (http:/
/wiki. biological-cybernetics.de)

• Society for Mathematical Biology (http://www.smb.org/)

• Bulletin of Mathematical Biology (http://www.springerlink.eom/content/l 19979/)

• European Society for Mathematical and Theoretical Biology (http://www.esmtb.org/)

• Journal of Mathematical Biology (http://www.springerlink.com/content/100436/)

• Biomathematics Research Centre at University of Canterbury (http://www.math.
canterbury, ac.nz/bio/)

• Centre for Mathematical Biology at Oxford University (http://www.maths.ox.ac.uk/
cmb/)

Mathematical biology

Mathematical Biology at the National Institute for Medical Research (http://mathbio.

nimr . mrc . ac . uk/)

Institute for Medical BioMathematics (http://www.imbm.org/)

Mathematical Biology Systems of Differential Equations (http://eqworld.ipmnet.ru/en/

solutions/syspde/spde-toc2.pdf) from EqWorld: The World of Mathematical Equations

Systems Biology Workbench - a set of tools for modelling biochemical networks (http://

sbw.kgi.edu)

The Collection of Biostatistics Research Archive (http://www.biostatsresearch.com/

repository/)

Statistical Applications in Genetics and Molecular Biology (http://www.bepress.com/

sagmb/)

The International Journal of Biostatistics (http://www.bepress.com/ijb/)

Theoretical Modeling of Cellular Physiology at Ecole Normale Superieure, Paris (http://

www.biologie.ens.fr/bcsmcbs/)

Theoretical biology

Theoretical biology is a field of academic study and research that involves the use of
models and theories in biology.

Many separate areas of biology fall under the concept of theoretical biology, according to
the way they are studied. Some of these areas include: animal behaviour (ethology),
biomechanics, biorhythms, cell biology, complexity of biological systems, ecology, enzyme
kinetics, evolutionary biology, genetics, immunology, membrane transport, microbiology,
molecular structures, morphogenesis, physiological mechanisms, systems biology and the
origin of life. Neurobiology is an example of a subdiscipline of biology which already has a
theoretical version of its own, theoretical or computational neuroscience.

The ultimate goal of the theoretical biologist is to explain the biological world using mainly
mathematical and computational tools. Though it is ultimately based on observations and
experimental results, the theoretical biologist's product is a model or theory, and it is this
that chiefly distinguishes the theoretical biologist from other biologists.

Theoretical biologists

Pere Alberch

Anthony F. Bartholomay

Ervin Bauer

Ludwig von Bertalanffy

Jan Charles Biro

J. T. Bonner

Jack Cowan

Francis Crick

Gerd B. Miiller

Walter M. Elsasser

Claus Emmeche

Andree Ehresmann

Marc Feldman

Theoretical biology

Ronald A. Fisher

Brian Goodwin

Bryan Grenfell

J. B. S. Haldane

William D. Hamilton

Lionel G. Harrison

Michael Hassell

Sven Erik j0rgensen

George Karreman

Stuart Kauffman

Kalevi Kull

Herbert D. Landahl

Richard Lewontin

Humberto Maturana

Robert May

John Maynard Smith

James D. Murray

Howard Pattee

George R. Price

Erik Rauch

Nicolas Rashevsky

Ronald Brown (mathematician)

Johannes Reinke

Robert Rosen

Peter Schuster

Rene Thorn
D'Arcy Thompson
Jakob von Uexkiill
Robert Ulanowicz
Francisco Varela
C. H. Waddington
Arthur Winfree
Lewis Wolpert
Sewall Wright
Christopher Zeeman

See also

• Journal of Theoretical Biology

• Bioinformatics

• Biosemiotics

• Mathematical biology

• Theoretical ecology

• Artificial life

Theoretical biology

Bibliographical references

• Bonner, J. T. 1988. The Evolution of Complexity by Means of Natural Selection.
Princeton: Princeton University Press.

Hertel, H. 1963. Structure, Form, Movement. New York: Reinhold Publishing Corp.
Mangel, M. 1990. Special Issue, Classics of Theoretical Biology (part 1). Bull. Math. Biol.

52(1/2): 1-318.

Mangel, M. 2006. The Theoretical Biologist's Toolbox. Quantitative Methods for Ecology

and Evolutionary Biology. Cambridge University Press.

Prusinkiewicz, P. & Lindenmeyer, A. 1990. The Algorithmic Beauty of Plants. Berlin:

Springer- Verlag.

Reinke, J. 1901. Einleitung in die theoretische Biologie. Berlin: Verlag von Gebriider

Paetel.

Thompson, D.W. 1942. On Growth and Form. 2nd ed. Cambridge: Cambridge University

Press: 2. vols.

Uexkiill, J.v. 1920. Theoretische Biologie. Berlin: Gebr. Paetel.

Vogel, S. 1988. Life's Devices: The Physical World of Animals and Plants. Princeton:

Princeton University Press.

Waddington, C.H. 1968-1972. Towards a Theoretical Biology. 4 vols. Edinburg: Edinburg

University Press.

External links

• Theory of Biological Anthropology (Documents No. 9 and 10 in English) ^ - 1

• Drawing the Line Between Theoretical and Basic Biology (a forum article by Isidro T.
Savillo) [2]

Related Journals

Acta Biotheoretica
Bioinformatics
Biological Theory L J
BioSystems [6]

T71

Bulletin of Mathematical Biology
Ecological Modelling L J
Journal of Mathematical Biology
Journal of Theoretical Biology J
Journal of the Royal Society Interface

ri2i

Mathematical Biosciences

Medical Hypotheses

Rivista di Biologia-Biology Forum L J

ri 5]

Theoretical and Applied Genetics J
Theoretical Biology and Medical Modelling L J

n 71

Theoretical Population Biology

Theory in Biosciences (formerly: Biologisches Zentralblatt)

Theoretical biology

Related societies

• American Mathematical Society J

• British Society of Developmental Biology

• European Mathematical Society

T221

• ESMTB: European Society for Mathematical and Theoretical Biology

• The International Biometric Society

• International Society for Ecological Modelling

• The Israeli Society for Theoretical and Mathematical Biology L

• London Mathematical Society

• Societe Francophone de Biologie Theorique

• Society for Industrial and Applied Mathematics J

• Society for Mathematical Biology J

• International Society for Biosemiotic Studies

[24]

References

[ 1 ] http ://homepage . uibk. ac . at/ ~ c7 2 1 2 6/humanethologie/ws/medicus/blockl /inhalt. html

[2] http://www.scientistsolutionsxom/t5844-Drawing+the+line+between+Theoretical+and+Basic+

Biology.html
[3] http://www.springerlink. com/link. asp?id= 102835
[4] http://bioinformatics.oupjournals.org/
[ 5 ] http ://www. mitpressj ournals . org/loi/biot/
[6] http ://www. elsevier. com/locate/biosystems
[7] http://www.springerlink.eom/content/l 19979/
[8] http://www.elsevier.com/locate/issn/03043800
[9] http://www.springerlink.com/content/100436/

[10
[11
[12
[13
[14
[15
[16
[17
[18
[19
[20
[21
[22
[23
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[27
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[29
[30

http ://www. elsevier. com/locate/issn/0022-5 1 93

http ://publishing . royalsociety . org/index. cfm?page = 1 5 8 #

http :// www. elsevier. com/locate/mbs

http://www.harcourt-international.com/journals/mehy/

http ://www. tilgher . it/biologiae . html

http://www.springerlink.com/content/100386/

http ://www. tbiomed. com/

http :// www. elsevier. com/locate/issn/00405 809

http ://www. elsevier. com/ wps/product/ews home/70 1 802

http : //www. am s. org/

http://www.dundee.ac.uk/lifesciences/BSDB/

http ://www. maths, soton. ac.uk/EMIS

http ://www. esmtb . org/

http ://www. tibs. org/

http ://www. isemna. org/

http ://bioinf ormatics . weizmann . ac. il/istmb/

http://www.lms.ac.uk/

http://www.necker.fr/sfbt/

http ://www. siam . org/

http ://www. smb . org/

http ://www. biosemiotics. org/

Complex Systems Biology

Systems

biology

biology-based inter-disciplinary
study field that focuses on the
systematic study of complex

in biological

interactions

systems, thus using a new
perspective (holism instead of
reduction) to study them.
Particularly from year 2000
onwards, the term is used
widely in the biosciences, and
in a variety of contexts.
Because the scientific method
has been used primarily toward
reductionism, one of the goals

PfOlCc! worUrS

and the public

Apply knowledge of
microbial functional

eop-abililies

ICA

ROY

NOVATIVEI KOAC

coNVEurioiKi^L

lf.5. DEPARTMENT OP ENERGY

DMA SEQUENCE DATA
**. FROM GENOME PROJECTS

Clean up the
Sequester

attest**

Produce ond
use energy

<§mL>v.

FUNCTIO

IN MICROS

COMMUNITIES,

OMMUNITY

or CELLS

Genes ond clher
DNA sequences -
'*' contain instnciions
on how and when
ro build proteins

IFV
PROTEIN

MACHINE?'

COMPUTATIONAL
CAPABILITIES

TO UNDERSTAND
COM PLtX
BIOLOGICAL

SYSTEMS

PROTEINS

Proteins perior m many o\ life's* most essential func'ions. To carry ou3 iheir
specific rolfii, ihey often work together in the coll as protein machines.

■ ^*4M>U««««J«^| 1 ' ^ - »

ACT ERIie GENE
ULATORY NETWORKS

WO RK INC
CELL

Many prolein
machines interact

through complex,,

interconnected
poihwoys. Analyzing

iheie dynamic processei

will lead :o models of lifo

prcxxs&ics,

url OOlOcf>cmsTolrfc.crQ

Example of systems biology research

of systems biology is to discover new emergent properties that may arise from the systemic
view used by this discipline in order to understand better the entirety of processes that
happen in a biological system.

Overview

Systems biology can be considered from a number of different aspects:

• Some sources discuss systems biology as a field of study, particularly, the study of the
interactions between the components of biological systems, and how these interactions
give rise to the function and behavior of that system (for example, the enzymes and
metabolites in a metabolic pathway). * c ^

• Other sources consider systems biology as a paradigm, usually defined in antithesis to
the so-called reductionist paradigm, although fully consistent with the scientific method.
The distinction between the two paradigms is referred to in these quotations:

"The reductionist approach has successfully identified most of the components and
many of the interactions but, unfortunately, offers no convincing concepts or methods
to understand how system properties emerge. ..the pluralism of causes and effects in
biological networks is better addressed by observing, through quantitative measures,
multiple components simultaneously and by rigorous data integration with
mathematical models" Science

"Systems biology. ..is about putting together rather than taking apart, integration
rather than reduction. It requires that we develop ways of thinking about integration
that are as rigorous as our reductionist programmes, but different.... It means changing
our philosophy, in the full sense of the term" Denis Noble 1 - *

• Still other sources view systems biology in terms of the operational protocols used for
performing research, namely a cycle composed of theory, analytic or computational
modelling to propose specific testable hypotheses about a biological system,
experimental validation, and then using the newly acquired quantitative description of

Complex Systems Biology

cells or cell processes to refine the computational model or theory. ] c ] Since the
objective is a model of the interactions in a system, the experimental techniques that
most suit systems biology are those that are system-wide and attempt to be as complete
as possible. Therefore, transcriptomics, metabolomics, proteomics and high-throughput
techniques are used to collect quantitative data for the construction and validation of
models.

• Engineers consider systems biology as the application of dynamical systems theory to
molecular biology.

• Finally, some sources see it as a socioscientific phenomenon defined by the strategy of
pursuing integration of complex data about the interactions in biological systems from
diverse experimental sources using interdisciplinary tools and personnel.

This variety of viewpoints is illustrative of the fact that systems biology refers to a cluster of
peripherally overlapping concepts rather than a single well-delineated field. However the
term has widespread currency and popularity as of 2007, with chairs and institutes of
systems biology proliferating worldwide (Such as the Institute for Systems Biology).

History

Systems biology finds its roots in:

• the quantitative modelling of enzyme kinetics, a discipline that flourished between 1900
and 1970,

• the simulations developed to study neurophysiology, and

• control theory and cybernetics.

One of the theorists who can be seen as a precursor of systems biology is Ludwig von
Bertalanffy with his general systems theory, and his book titled "General Systems Theory in
Physics and Biology" was published in 1950. One of the first numerical simulations in
biology was published in 1952 by the British neurophysiologists and Nobel prize winners
Alan Lloyd Hodgkin and Andrew Fielding Huxley, who constructed a mathematical model

T71

that explained the action potential propagating along the axon of a neuronal cell. Their
model described a cellular function emerging from the interaction between two different
molecular components, a potassium and a sodium channels, and can therefore be seen as
the beginning of computational systems biology. In 1960, Denis Noble developed the first
computer model of the heart pacemaker. J

The formal study of systems biology, as a distinct discipline, was launched by systems
theorist Mihajlo Mesarovic in 1966 with an international symposium at the Case Institute of

noi rm

Technology in Cleveland, Ohio entitled "Systems Theory and Biology."

The 1960s and 1970s saw the development of several approaches to study complex
molecular systems, such as the Metabolic Control Analysis and the biochemical systems
theory. The successes of molecular biology throughout the 1980s, coupled with a skepticism
toward theoretical biology, that then promised more than it achieved, caused the
quantitative modelling of biological processes to become a somewhat minor field.

Since the established of the systems theory, the terms of systems ecology (Van Dyne
GM.1966), systems physiology (Sagawa K.1973), system psychology (Edward B. Titchener
1992), system biomedicine (Kamada T.1992), systems biology (Zieglgansberger W, Tolle
TR.1993) can be searched from the PubMed of NIH, USA. The concept and model of system
medicine (Zeng BJ.) was published at the first national conference on Chinese Traditional

Complex Systems Biology

Medicince and west medicine in Guangzhou, China 1992. During 1990s years, Zeng B.J.
(Institute of Microbiology, CAS, Beijing) established the concepts of "systems genetics" and
"system biological engineering" for the third wave of genetics and engineering of artificial
biosystems, and created the genbrain biosystem network of the (world) associates for
biosystem science and engineering in Jan. 1999.

However the birth of functional genomics in the 1990s meant that large quantities of high
quality data became available, while the computing power exploded, making more realistic
models possible. In 1997, the group of Masaru Tomita published the first quantitative
model of the metabolism of a whole (hypothetical) cell.

Around the year 2000, when Institutes of Systems Biology were established in Seattle and
Tokyo, systems biology emerged as a movement in its own right, spurred on by the
completion of various genome projects, the large increase in data from the omics (e.g.
genomics and proteomics) and the accompanying advances in high-throughput experiments
and bioinformatics. Since then, various research institutes dedicated to systems biology
have been developed. As of summer 2006, due to a shortage of people in systems biology^ ]
several doctoral training centres in systems biology have been established in many parts of
the world.

Survival Factors
(eg-JGFi;

Cheirtokirtes.

Hormona*.

Transmitters

|eg. intertfrukms.

s&rotonrrv. etc.)

-GPCR

Growth Factor*
e.g.TGFu. EGF)

Cytokines
<e g.. EPC>"

Death factors,
(eg Fasl.Tnf)

Overview of signal transduction pathways

Writ

Hed-gehog

Techniques associated with systems biology

According to the interpretation of
System Biology as the ability to
obtain, integrate and analyze complex
data from multiple experimental
sources using interdisciplinary tools,
some typical technology platforms
are:

• Transcriptomics: whole cell or
tissue gene expression
measurements by DNA microarrays
or serial analysis of gene expression

• Proteomics: complete identification
of proteins and protein expression
patterns of a cell or tissue through
two-dimensional gel electrophoresis

and mass spectrometry or multi-dimensional protein identification techniques (advanced
HPLC systems coupled with mass spectrometry). Sub disciplines include
phosphoproteomics, glycoproteomics and other methods to detect chemically modified
proteins.

• Metabolomics: identification and measurement of all small-molecules metabolites within
a cell or tissue

• Glycomics: identification of the entirety of all carbohydrates in a cell or tissue.

• Lipidomics: identification of the entirety of all lipids in a cell or tissue.

In addition to the identification and quantification of the above given molecules further
techniques analyze the dynamics and interactions within a cell. This includes:

Complex Systems Biology

• Interactomics which is used mostly in the context of protein-protein interaction but in
theory encompasses interactions between all molecules within a cell,

• Fluxomics, which deals with the dynamic changes of molecules within a cell over time,

• Biomics: systems analysis of the biome.

The investigations are frequently combined with large scale perturbation methods,
including gene-based (RNAi, mis-expression of wild type and mutant genes) and chemical
approaches using small molecule libraries. Robots and automated sensors enable such
large-scale experimentation and data acquisition. These technologies are still emerging and
many face problems that the larger the quantity of data produced, the lower the quality. A
wide variety of quantitative scientists (computational biologists, statisticians,
mathematicians, computer scientists, engineers, and physicists) are working to improve the
quality of these approaches and to create, refine, and retest the models to accurately
reflect observations.

The investigations of a single level of biological organization (such as those listed above)
are usually referred to as Systematic Systems Biology. Other areas of Systems Biology
includes Integrative Systems Biology, which seeks to integrate different types of
information to advance the understanding the biological whole, and Dynamic Systems
Biology, which aims to uncover how the biological whole changes over time (during
evolution, for example, the onset of disease or in response to a perturbation). Functional
Genomics may also be considered a sub-field of Systems Biology.

The systems biology approach often involves the development of mechanistic models, such
as the reconstruction of dynamic systems from the quantitative properties of their
elementary building blocks. For instance, a cellular network can be modelled

mathematically using methods coming from chemical kinetics and control theory. Due to
the large number of parameters, variables and constraints in cellular networks, numerical
and computational techniques are often used. Other aspects of computer science and
informatics are also used in systems biology. These include new forms of computational
model, such as the use of process calculi to model biological processes, the integration of
information from the literature, using techniques of information extraction and text mining,
the development of online databases and repositories for sharing data and models (such as
BioModels Database), approaches to database integration and software interoperability via
loose coupling of software, websites and databases^ 5] and the development of syntactically
and semantically sound ways of representing biological models, such as the Systems
Biology Markup Language (SBML).

Complex Systems Biology

See also

Related fields

• Complex systems
biology

Complex systems
Complex systems
biology
Bioinformatics
Biological network
inference
Biological systems
engineering
Biomedical cybernetics
Biostatistics
Theoretical Biophysics
Relational Biology
Translational Research
Computational biology
Computational systems
biology

Scotobiology
Synthetic biology
Systems biology
modeling
Systems ecology
Systems immunology

Related terms

Life

Artificial life

Gene regulatory network

Metabolic network modelling

Living systems theory

Network Theory of Aging

Regulome

Systems Biology Markup Language

(SBML)

SBO

Viable System Model

Antireductionism

Systems biologists

• Category: Systems biologists
Lists

• Category: Systems biologists

• List of systems biology conferences

• List of omics topics in biology

• List of publications in systems biology

• List of systems biology research groups

References

[I] Snoep J.L. and Westerhoff H.V.; Alberghina L. and Westerhoff H.V. (Eds.) (2005.). "From isolation to
integration, a systems biology approach for building the Silicon Cell". Systems Biology: Definitions and
Perspectives: p7, Springer-Verlag.

[2] http://www.systemsbiology.org/Intro_to_ISB_and_Systems_Biology/Systems_Biology_--_the_21st_Century_Sciencel "Systems

Biology - the 21st Century Science". http://www.systemsbiology.org/Intro_to_ISB andSystemsBiology/

SystemsBiology— _the_21st_Century_Science.
[3] Sauer, U. et al. (27 April 2007). "Getting Closer to the Whole Picture". Science 316: 550. doi:

10. 1126/science. 1142502 (http://dx.doi.org/10.1126/science.1142502). PMID 17463274.
[4] Denis Noble (2006). The Music of Life: Biology beyond the genome. Oxford University Press. ISBN

978-0199295739. p21
[5] http://www.bbsrc.ac.uk/science/areas/ebs/themes/main_sysbio.htmll "Systems Biology: Modelling, Simulation

and Experimental Validation" . http ://www. bbsrc . ac . uk/science/areas/ebs/themes/main_sysbio . html.
[6] Kholodenko B.N., Bruggeman F.J., Sauro H.M.; Alberghina L. and Westerhoff H.V.(Eds.) (2005.). "Mechanistic

and modular approaches to modeling and inference of cellular regulatory networks". Systems Biology:

Definitions and Perspectives: pl43, Springer-Verlag.
[7] Hodgkin AL, Huxley AF (1952). "A quantitative description of membrane current and its application to

conduction and excitation in nerve". J Physiol 117: 500-544. PMID 12991237.
[8] Le Novere (2007). "The long journey to a Systems Biology of neuronal function". BMC Systems Biology 1: 28.

doi: 10.1186/1752-0509-1-28 (http://dx.doi.org/10.1186/1752-0509-l-28).
[9] Noble D (1960). "Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations". Nature

188: 495-497. doi: 10.1038/188495b0 (http://dx.doi.org/10.1038/188495b0). PMID 13729365.
[10] Mesarovic, M. D. (1968). Systems Theory and Biology. Springer-Verlag.

[II] "http://www.jstor.org/view/00368075/ap004022/00a00220/0IA Means Toward a New Holism". Science 161
(3836): 34-35. doi: 10. 1126/science. 161. 3836. 34 (http://dx.doi.org/10.1126/science.161.3836.34). http://
www.jstor.org/view/00368075/ap004022/00a00220/0.

[12] http://sciencecareers.sciencemag.org/career_development/previous_issues/articles/2006_03_03/working_the_systems/(parent^
the Systems", http://sciencecareers.sciencemag.org/career_development/previous_issues/articles/

Complex Systems Biology

2006_03_03/working_the_systems/(parent)/158.
[13] Gardner, TS; di Bernardo D, Lorenz D and Collins JJ (4 July 2003). "Inferring genetic networks and identifying

compound of action via expression profiling". Science 301: 102-1005. doi: 10. 1126/science. 1081900 (http://dx.

doi.org/10.1126/science.1081900). PMID 12843395.
[14] di Bernardo, D; Thompson MJ, Gardner TS, Chobot SE, Eastwood EL, Wojtovich AP, Elliot SJ, Schaus SE and

Collins JJ (March 2005). "Chemogenomic profiling on a genome-wide scale using reverse-engineered gene

networks". Nature Biotechnology 23: 377-383. doi: 10.1038/nbtl075 (http://dx.doi.org/10.1038/nbtl075).

PMID 15765094.
[15] such as Gaggle (http://gaggle.systemsbiology.net), SBW (http://sys-bio.org)), or commercial suits, e.g.,

MetaCore (http://www.genego.com/metacore.php) and MetaDrug (http://www.genego.com/metadrug.

php)

Further reading

Books

Zeng BJ. Structurity - Pan-evolution theory of biosystems, Hunan Changsha Xinghai, May,

1994.

Hiroaki Kitano (editor). Foundations of Systems Biology. MIT Press: 2001. ISBN

0-262-11266-3

CP Fall, E Marland, J Wagner and JJ Tyson (Editors). "Computational Cell Biology."

Springer Verlag: 2002 ISBN 0-387-95369-8

G Bock and JA Goode (eds)Jn Silico" Simulation of Biological Processes, Novartis

Foundation Symposium 247. John Wiley & Sons: 2002. ISBN 0-470-84480-9

E Klipp, R Herwig, A Kowald, C Wierling, and H Lehrach. Systems Biology in Practice.

Wiley-VCH: 2005. ISBN 3-527-31078-9

L. Alberghina and H. Westerhoff (Editors) - Systems Biology: Definitions and

Perspectives, Topics in Current Genetics 13, Springer Verlag (2005), ISBN

978-3540229681

A Kriete, R Eils. Computational Systems Biology., Elsevier - Academic Press: 2005. ISBN

0-12-088786-X

K. Sneppen and G. Zocchi, (2005) Physics in Molecular Biology, Cambridge University

Press, ISBN 0-521-84419-3

D. Noble, The Music of life. Biology beyond the genome Oxford University Press (http://

www.musicoflife.co.uk/) 2006. ISBN 0199295735, ISBN 978-0199295739

Z. Szallasi, J. Stelling, and V.Periwal (eds.) System Modeling in Cellular Biology: From

Concepts to Nuts and Bolts (Hardcover), MIT Press: 2006, ISBN 0-262-19548-8

B Palsson, Systems Biology - Properties of Reconstructed Networks. Cambridge

University Press: 2006. (http://gcrg.ucsd.edu/book/index.html) ISBN

978-0-521-85903-5

K Kaneko. Life: An Introduction to Complex Systems Biology. Springer: 2006. ISBN

3540326669

U Alon. An Introduction to Systems Biology: Design Principles of Biological Circuits. CRC

Press: 2006. ISBN 1-58488-642-0 - emphasis on Network Biology (For a comparative

review of Alon, Kaneko and Palsson see Werner, E. (March 29, 2007).

"http://www.nature.com/nature/journal/v446/n7135/pdf/446493a.pdflAll systems go"

(PDF). Nature 446: 493-494. doi: 10.1038/446493a (http://dx.doi.org/10.1038/

446493a). http://www.nature.com/nature/journal/v446/n7135/pdf/446493a.pdf.)

Andriani Daskalaki (editor) "Handbook of Research on Systems Biology Applications in

Medicine" Medical Information Science Reference, October 2008 ISBN

Complex Systems Biology

978-1-60566-076-9

Journals

• BMC Systems Biology (http://www.biomedcentral.com/bmcsystbiol) - open access
journal on systems biology

• Molecular Systems Biology (http://www.nature.com/msb) - open access journal on
systems biology

• IET Systems Biology (http://www.ietdl.org/IET-SYB) - not open access journal on
systems biology

Articles

• Zeng BJ., On the concept of system biological engineering, Communication on Transgenic
Animals, CAS, June, 1994.

• Zeng BJ., Transgenic expression system - goldegg plan (termed system genetics as the
third wave of genetics), Communication on Transgenic Animals, CAS, Nov. 1994.

• Zeng BJ., From positive to synthetic medical science, Communication on Transgenic
Animals, CAS, Nov. 1995.

• Binnewies, Tim Terence, Miller, WG, Wang, G. The complete genome sequence and
analysis of the human pathogen Campylobacter lari (http://www.bio.dtu.dk/English/
Publications/l/all.aspx?lg=showcommon&id=231324). Published in journal:
Foodborne Pathog Disease (ISSN 1535-3141) , vol: 5, issue: 4, pages: 371-386, 2008,
Mary Ann Liebert, Inc. Publishers.

• M. Tomita, Hashimoto K, Takahashi K, Shimizu T, Matsuzaki Y, Miyoshi F, Saito K,
Tanida S, Yugi K, Venter JC, Hutchison CA. E-CELL: Software Environment for Whole
Cell Simulation. Genome Inform Ser Workshop Genome Inform. 1997;8:147-155. (http://
web.sfc.keio.ac.jp/-mt/mt-lab/publications/Paper/ecell/bioinfo99/btc007_gml.

html)

• ScienceMag.org (http://www.sciencemag.org/content/vol295/issue5560/) - Special
Issue: Systems Biology, Science, Vol 295, No 5560, March 1, 2002

• Marc Vidal and Eileen E. M. Furlong. Nature Reviews Genetics 2004 From OMICS to
systems biology (http://www.nature.com/nrg/journal/v5/nl0/poster/omics/index.
html)

• Marc Facciotti, Richard Bonneau, Leroy Hood and Nitin Baliga. Current Genomics 2004
Systems Biology Experimental Design - Considerations for Building Predictive Gene
Regulatory Network Models for Prokaryotic Systems (http://www.ingentaconnect.com/
content/ben/cg/2004/00000005/00000007/art00002)

• Katia Basso, Adam A Margolin, Gustavo Stolovitzky, Ulf Klein, Riccardo Dalla-Favera,
Andrea Califano, (2005) "Reverse engineering of regulatory networks in human B cells"
(http://www.ncbi.nlm.nih.gov/entrez/ query. fcgi?cmd=Retrieve&db=pubmed&
dopt=Abstract&list_uids = 15778709&query_hl=7). Nat Genet;37(4):382-90

• Mario Jardon Systems Biology: An Overview (http://www.scq. ubc.ca/?p=253) - a
review from the Science Creative Quarterly, 2005

• Johnjoe McFadden, Guardian.co.uk (http://www.guardian.co.uk/life/science/story/
0,12996, 1477776, 00. html) - 'The unselfish gene: The new biology is reasserting the
primacy of the whole organism - the individual - over the behaviour of isolated genes',
The Guardian (May 6, 2005)

Complex Systems Biology

Pharoah, M.C. (online). Looking to systems theory for a reductive explanation of

phenomenal experience and evolutionary foundations for higher order thought (http://

homepage.ntlworld.com/rn.pharoah/) Retrieved Jan, 15 2008.

WTEC Panel Report on International Research and Development in Systems Biology

(http://www.wtec.org/sysbio/welcome.htm) (2005)

E. Werner, "The Future and Limits of Systems Biology", Science STKE (http://stke.

sciencemag.org/content/vol2005/issue278/) 2005, pel6 (2005).

Francis J. Doyle and Jorg Stelling, "Systems interface biology" (http://www .journals.

royalsoc.ac.uk/openurl.asp?genre=article&doi=10.1098/rsif.2006.0143) J. R. Soc.

Interface Vol 3, No 10 2006

Kahlem, P. and Birney E. (2006). "Dry work in a wet world: computation in systems

biology." Mol Syst Biol 2: 40. (http://www.nature.com/doifinder/10.1038/

msb4100080)

E. Werner, "All systems go" (http://www.nature.com/nature/journal/v446/n7135/pdf/

446493a.pdf), "Nature" (http://www.nature.com/nature/journal/v446/n7135/index.

html) vol 446, pp 493-494, March 29, 2007. (Review of three books (Alon, Kaneko, and

Palsson) on systems biology.)

Santiago Schnell, Ramon Grima, Philip K. Maini, "Multiscale Modeling in Biology" (http:/

/www. americanscientist.org/template/AssetDetail/assetid/54784), American

Scientist, Vol 95, pages 134-142, March-April 2007.

TS Gardner, D di Bernardo, D Lorenz and JJ Collins. "Inferring genetic networks and

identifying compound of action via expression profiling." (http://www.bu.edu/abl/

publications.html) Science 301: 102-105 (2003).

Jeffery C. Way and Pamela A. Silver, Why We Need Systems Biology (http://cs.

calstatela.edu/wiki/images/9/9b/Silver.pdf)

H.S. Wiley, "Systems Biology - Beyond the Buzz." The Scientist (http://www.

the-scientist.eom/2006/6/l/52/l/). June 2006.]

Nina Flanagan, "Systems Biology Alters Drug Development." (http://www.genengnews.

com/articles/chitem.aspx?aid=2337) Genetic Engineering & Biotechnology News,

January 2008

External links

• Systems Biology - BioChemWeb.org (http://www.biochemweb.org/systems.shtml)

• Systems Biology Portal (http://www.systems-biology.org/) - administered by the
Systems Biology Institute

• Semantic Systems Biology (http://www.semantic-systems-biology.org)

• SystemsX.ch (http://www.systemsx.ch/) - The Swiss Initiative in Systems Biology

• Systems Biology at the Pacific Northwest National Laboratory (http://www.sysbio.org/

)

Complexity

In general usage, complexity tends to be used to characterize something with many parts
in intricate arrangement. In science there are at this time a number of approaches to

characterizing complexity, many of which are reflected in this article. Seth Lloyd of M.I.T.

n 1
writes that he once gave a presentation which set out 32 definitions of complexity. 1 J

Definitions are often tied to the concept of a 'system' - a set of parts or elements which
have relationships among them differentiated from relationships with other elements
outside the relational regime. Many definitions tend to postulate or assume that complexity
expresses a condition of numerous elements in a system and numerous forms of
relationships among the elements. At the same time, what is complex and what is simple is
relative and changes with time.

Some definitions key on the question of the probability of encountering a given condition of
a system once characteristics of the system are specified. Warren Weaver has posited that
the complexity of a particular system is the degree of difficulty in predicting the properties
of the system if the properties of the system's parts are given. In Weaver's view, complexity
comes in two forms: disorganized complexity, and organized complexity. Weaver's paper
has influenced contemporary thinking about complexity. c ]

The approaches which embody concepts of systems, multiple elements, multiple relational
regimes, and state spaces might be summarized as implying that complexity arises from the
number of distinguishable relational regimes (and their associated state spaces) in a
defined system.

Some definitions relate to the algorithmic basis for the expression of a complex
phenomenon or model or mathematical expression, as is later set out herein.

Disorganized
complexity vs.
organized
complexity

One of the problems in
addressing complexity issues

has

been

distinguishing

conceptually between

the

large number of variances in
relationships extant in random
collections, and the sometimes
large, but smaller, number of
relationships between

elements in systems where

constraints

(related

'Map of Complexity Science. *HERE FOR WEB VERSION OF MAP
The web version of this map provides internet links to all the
leading scholars and areas of research in complexity science.

correlation of otherwise independent elements) simultaneously reduce the

Complexity

variations from element independence

and

create

distinguishable regimes of more-uniform, or correlated,
relationships, or interactions.

Weaver perceived and addressed this problem, in at least a
preliminary way, in drawing a distinction between
'disorganized complexity 1 and 'organized complexity'.

In Weaver's view, disorganized complexity results from the
particular system having a very large number of parts, say
millions of parts, or many more. Though the interactions of the
parts in a 'disorganized complexity' situation can be seen as
largely random, the properties of the system as a whole can be
understood by using probability and statistical methods.

A prime example of disorganized complexity is a gas in a
container, with the gas molecules as the parts. Some would
suggest that a system of disorganized complexity may be
compared, for example, with the (relative) simplicity of the
planetary orbits - the latter can be known by applying
Newton's laws of motion, though this example involved highly
correlated events.

HOW TO READ MAP:

The above map is a conceptual and historical overview of

complex ity science.

The Map is to be read as follows:

First, the Map is roughly historicaLworkingasa timeline that is
divided i nto five major periods that one ca n read from left to
right; 1 ) old-school, 2) perco lation, 3) the new science of
complexity^) a work in progressed 5) recent developments,

Each fields of si udy is represented as dou ble-lined ellipse, with

a double-lined arrow moving from left to the right, The
relative size of these ellipses Is meaning less.and is strictly a
function of the space needed to write the name of each field
Double lined arrows represent the trajectory of each field of

study. Space constraints required that the length of these

arrows be lim ited; readers should therefore assume that a II of
them extend outward to 2006.

Tile decision where to place the various fields of research
respective to one another is somewhat arbitrary- However, we

did try to position relative to some degree of intellectual
similarity. For example, those sciences oriented toward the
study of systems are located at the top of the map; the
sciences that tend to extend outward from or around cyber-
netics and a rtificial intelligence and a re oriented toward the

development of computational method are located at the
bottom.

Areas of research identified for each field of study are repre-
sented as single-lined circles. As with the fields of study, the
size of these circles is strictly a function of the space needed to
write the different names.

The intel lectual links amongst the fields of study and amongst

theareas of research are represented with a bold single-lined

arrow, The head of the arrow indicates the direction of the
relationship. In some cases, the relationship Is mutual To keep
the map simple, rather than drawthis link to the trajectory for
a field of study or area of research (as in the case of the recip-
rocal relationship between complexity science and agent-
based modeling), we draw it to the ellipse representing the
field of study or area of research.

For each area of research, we also include a short list of the

leading scholars. This IFsl is not exhaustive; bul it is representa-

tive.basedon number of citations, genera I recognition.and
importance In the historical development of the area of
research. For each scholar we provide the following Informa-
tion: name, most widely known contribution. and links to key

areas of research. The links amongst the scholars and their

respective areas of research are represented by a dashed lin e.
One will also note that the names of the scholars differ in font
size. Thfs was done to demonstrate their relative importance
within complexity science and the sociology of complexity.

Because of the diversity of research in complexity science, we
focused on the key topics In the field.

MAP LEGEND.

Organized complexity, in Weaver's view, resides in nothing else than the non-random, or
correlated, interaction between the parts. These non-random, or correlated, relationships
create a differentiated structure which can, as a system, interact with other systems. The
coordinated system manifests properties not carried by, or dictated by, individual parts.
The organized aspect of this form of complexity vis a vis other systems than the subject
system can be said to "emerge," without any "guiding hand."

The number of parts does not have to be very large for a particular system to have
emergent properties. A system of organized complexity may be understood in its properties
(behavior among the properties) through modeling and simulation, particularly modeling
and simulation with computers. An example of organized complexity is a city neighborhood
as a living mechanism, with the neighborhood people among the system's parts. L J

Sources and factors of complexity

The source of disorganized complexity is the large number of parts in the system of
interest, and the lack of correlation between elements in the system.

There is no consensus at present on general rules regarding the sources of organized
complexity, though the lack of randomness implies correlations between elements. See e.g.
Robert Ulanowicz's treatment of ecosystems. Consistent with prior statements here, the
number of parts (and types of parts) in the system and the number of relations between the
parts would have to be non-trivial - however, there is no general rule to separate "trivial"
from "non-trivial.

Complexity

Complexity of an object or system is a relative property. For instance, for many functions
(problems), such a computational complexity as time of computation is smaller when
multitape Turing machines are used than when Turing machines with one tape are used.
Random Access Machines allow one to even more decrease time complexity (Greenlaw and
Hoover 1998: 226), while inductive Turing machines can decrease even the complexity
class of a function, language or set (Burgin 2005). This shows that tools of activity can be
an important factor of complexity.

Specific meanings of complexity

In several scientific fields, "complexity" has a specific meaning :

• In computational complexity theory, the amounts of resources required for the execution
of algorithms is studied. The most popular types of computational complexity are the
time complexity of a problem equal to the number of steps that it takes to solve an
instance of the problem as a function of the size of the input (usually measured in bits),
using the most efficient algorithm, and the space complexity of a problem equal to the
volume of the memory used by the algorithm (e.g., cells of the tape) that it takes to solve
an instance of the problem as a function of the size of the input (usually measured in
bits), using the most efficient algorithm. This allows to classify computational problems
by complexity class (such as P, NP ... ). An axiomatic approach to computational
complexity was developed by Manuel Blum. It allows one to deduce many properties of
concrete computational complexity measures, such as time complexity or space
complexity, from properties of axiomatically defined measures.

• In algorithmic information theory, the Kolmogorov complexity (also called descriptive
complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the
shortest binary program which outputs that string. Different kinds of Kolmogorov
complexity are studied: the uniform complexity, prefix complexity, monotone complexity,
time-bounded Kolmogorov complexity, and space-bounded Kolmogorov complexity. An
axiomatic approach to Kolmogorov complexity based on Blum axioms (Blum 1967) was
introduced by Mark Burgin in the paper presented for publication by Andrey Kolmogorov
(Burgin 1982). The axiomatic approach encompasses other approaches to Kolmogorov
complexity. It is possible to treat different kinds of Kolmogorov complexity as particular
cases of axiomatically defined generalized Kolmogorov complexity. Instead, of proving
similar theorems, such as the basic invariance theorem, for each particular measure, it is
possible to easily deduce all such results from one corresponding theorem proved in the
axiomatic setting. This is a general advantage of the axiomatic approach in mathematics.
The axiomatic approach to Kolmogorov complexity was further developed in the book
(Burgin 2005) and applied to software metrics (Burgin and Debnath, 2003; Debnath and
Burgin, 2003).

• In information processing, complexity is a measure of the total number of properties
transmitted by an object and detected by an observer. Such a collection of properties is
often referred to as a state.

• In physical systems, complexity is a measure of the probability of the state vector of the
system. This should not be confused with entropy; it is a distinct mathematical measure,
one in which two distinct states are never conflated and considered equal, as is done for
the notion of entropy statistical mechanics.

Complexity

• In mathematics, Krohn-Rhodes complexity is an important topic in the study of finite
semigroups and automata.

There are different specific forms of complexity:

• In the sense of how complicated a problem is from the perspective of the person trying to
solve it, limits of complexity are measured using a term from cognitive psychology,
namely the hrair limit.

• Unruly complexity denotes situations that do not have clearly defined boundaries,
coherent internal dynamics, or simply mediated relations with their external context, as
coined by Peter Taylor.

• Complex adaptive system denotes systems which have some or all of the following
attributes [7]

• The number of parts (and types of parts) in the system and the number of relations
between the parts is non-trivial - however, there is no general rule to separate "trivial"

from "non-trivial;"

The system has memory or includes feedback;

The system can adapt itself according to its history or feedback;

The relations between the system and its environment are non-trivial or non-linear;

The system can be influenced by, or can adapt itself to, its environment; and

The system is highly sensitive to initial conditions.

Study of complexity

Complexity has always been a part of our environment, and therefore many scientific fields
have dealt with complex systems and phenomena. Indeed, some would say that only what is
somehow complex - what displays variation without being random - is worthy of interest.

The use of the term complex is often confused with the term complicated. In today's
systems, this is the difference between myriad connecting "stovepipes" and effective
"integrated" solutions. L J This means that complex is the opposite of independent, while
complicated is the opposite of simple.

While this has led some fields to come up with specific definitions of complexity, there is a
more recent movement to regroup observations from different fields to study complexity in
itself, whether it appears in anthills, human brains, or stock markets. One such
interndisciplinary group of fields is relational order theories.

Complexity topics

Complex behaviour

The behaviour of a complex system is often said to be due to emergence and
self-organization. Chaos theory has investigated the sensitivity of systems to variations in
initial conditions as one cause of complex behaviour.

Complex mechanisms

Recent developments around artificial life, evolutionary computation and genetic
algorithms have led to an increasing emphasis on complexity and complex adaptive
systems.

Complexity

Complex simulations

In social science, the study on the emergence of macro-properties from the
micro-properties, also known as macro-micro view in sociology. The topic is commonly
recognized as social complexity that is often related to the use of computer simulation in
social science, i.e.: computational sociology.

Complex systems

Systems theory has long been concerned with the study of complex systems (In recent
times, complexity theory and complex systems have also been used as names of the field).
These systems can be biological, economic, technological, etc. Recently, complexity is a
natural domain of interest of the real world socio-cognitive systems and emerging systemics
research. Complex systems tend to be high-dimensional, non-linear and hard to model. In
specific circumstances they may exhibit low dimensional behaviour.

Complexity in data

In information theory, algorithmic information theory is concerned with the complexity of
strings of data.

Complex strings are harder to compress. While intuition tells us that this may depend on
the codec used to compress a string (a codec could be theoretically created in any arbitrary
language, including one in which the very small command "X" could cause the computer to
output a very complicated string like '18995316'"), any two Turing-complete languages can
be implemented in each other, meaning that the length of two encodings in different
languages will vary by at most the length of the "translation" language - which will end up
being negligible for sufficiently large data strings.

These algorithmic measures of complexity tend to assign high values to random noise.
However, those studying complex systems would not consider randomness as complexity.

Information entropy is also sometimes used in information theory as indicative of
complexity.

Applications of complexity

Computational complexity theory is the study of the complexity of problems - that is, the
difficulty of solving them. Problems can be classified by complexity class according to the
time it takes for an algorithm - usually a computer program - to solve them as a function of
the problem size. Some problems are difficult to solve, while others are easy. For example,
some difficult problems need algorithms that take an exponential amount of time in terms
of the size of the problem to solve. Take the travelling salesman problem, for example. It
can be solved in time 0(n 2*) (where n is the size of the network to visit - let's say the

number of cities the travelling salesman must visit exactly once). As the size of the network
of cities grows, the time needed to find the route grows (more than) exponentially.

Even though a problem may be computationally solvable in principle, in actual practice it
may not be that simple. These problems might require large amounts of time or an
inordinate amount of space. Computational complexity may be approached from many
different aspects. Computational complexity can be investigated on the basis of time,
memory or other resources used to solve the problem. Time and space are two of the most
important and popular considerations when problems of complexity are analyzed.

Complexity

There exist a certain class of problems that although they are solvable in principle they
require so much time or space that it is not practical to attempt to solve them. These
problems are called intractable.

There is another form of complexity called hierarchical complexity. It is orthogonal to the
forms of complexity discussed so far, which are called horizontal complexity

See also

Chaos theory

Command and Control Research Program

Complexity theory (disambiguation page)

Cyclomatic complexity

Evolution of complexity

Game complexity

Holism in science

Interconnectedness

Model of hierarchical complexity

Occam's razor

Process architecture

Programming Complexity

Sociology and complexity science

Systems theory

Variety (cybernetics)

References

[1] Lloyd, Seth (2006). Programming the Universe. Knopf. ISBN 978-1400033867..

[2] Weaver, Warren (1948), "http://www.ceptualinstitute.com/genre/weaver/weaver-l 947b. htm| Science and

Complexity", American Scientist 36: 536 (Retrieved on 2007-11-21.), http://www.ceptualinstitute.com/

genre/weaver/weaver- 1 947b . htm
[3] Johnson, Steven (2001). Emergence: the connected lives of ants, brains, cities, and software. New York:

Scribner. pp. p.46. ISBN 0-684-86875-X..
[4] http://www.art-sciencefactory.com/complexity-map_feb09.html" 'CLICK

[5] Jacobs, Jane (1961). The Death and Life of Great American Cities. New York: Random House.
[6] Ulanowicz, Robert, "Ecology, the Ascendant Perspective", Columbia, 1997
[7] Johnson, Neil F. (2007). Two's Company, Three is Complexity: A simple guide to the science of all sciences

Oxford: Oneworld. ISBN 978-1-85168-488-5.
[8] (Lissack and Roos, 2000)

Further reading

• Lewin, Roger (1992). Complexity: Life at the Edge of Chaos. New York: Macmillan
Publishing Co. ISBN 9780025704855.

• Waldrop, M. Mitchell (1992). Complexity: The Emerging Science at the Edge of Order
and Chaos. New York: Simon & Schuster. ISBN 9780671767891.

• Czerwinski, Tom; David Alberts (1997). Complexity, Global Politics, and National Security
(http://www.dodccrp.org/files/Alberts_Complexity_Global.pdf). National Defense
University. ISBN 9781579060466.

• Czerwinski, Tom (1998). Coping with the Bounds: Speculations on Nonlinearity in
Military Affairs (http://www.dodccrp.org/files/Czerwinski_Coping.pdf). CCRP. ISBN
9781414503158 (from Pavilion Press, 2004).

Complexity

Lissack, Michael R.; Johan Roos (2000). The Next Common Sense, The e-Manager's Guide

to Mastering Complexity. Intercultural Press. ISBN 9781857882353.

Sole, R. V.; B. C. Goodwin (2002). Signs of Life: How Complexity Pervades Biology. Basic

Books. ISBN 9780465019281.

Moffat, James (2003). Complexity Theory and Network Centric Warfare (http://www.

dodccrp.org/files/Moffat_Complexity.pdf). CCRP. ISBN 9781893723115.

Smith, Edward (2006). Complexity, Networking, and Effects Based Approaches to

Operations (http://www.dodccrp.org/files/Smith_Complexity.pdf). CCRP. ISBN

9781893723184.

Heylighen, Francis (2008), " Complexity and Self-Organization (http://pespmcl.vub.ac.

be/Papers/ELIS-Complexity.pdf)", in Bates, Marcia J.; Maack, Mary Niles, Encyclopedia

of Library and Information Sciences, CRC, ISBN 9780849397127

Greenlaw, N. and Hoover, H.J. Fundamentals of the Theory of Computation, Morgan

Kauffman Publishers, San Francisco, 1998

Blum, M. (1967) On the Size of Machines, Information and Control, v. 11, pp. 257-265

Burgin, M. (1982) Generalized Kolmogorov complexity and duality in theory of

computations, Notices of the Russian Academy of Sciences, v.25, No. 3, pp. 19-23

Mark Burgin (2005), Super-recursive algorithms, Monographs in computer science,

Springer.

Burgin, M. and Debnath, N. Hardship of Program Utilization and User-Friendly Software,

in Proceedings of the International Conference "Computer Applications in Industry and

Engineering", Las Vegas, Nevada, 2003, pp. 314-317

Debnath, N.C. and Burgin, M., (2003) Software Metrics from the Algorithmic Perspective,

in Proceedings of the ISCA 18th International Conference "Computers and their

Applications" , Honolulu, Hawaii, pp. 279-282

Meyers, R.A., (2009) "Encyclopedia of Complexity and Systems Science", ISBN

978-0-387-75888-6

External links

• Quantifying Complexity Theory (http://www.calresco.org/lucas/quantify.htm) -
classification of complex systems

• Complexity Measures (http://cscs.umich.edu/~crshalizi/notebooks/
complexity-measures.html) - an article about the abundance of not-that-useful complexity
measures.

• UC Four Campus Complexity Videoconferences (http://eclectic.ss.uci.edu/~drwhite/
center/cac.html) - Human Sciences and Complexity

• Complexity Digest (http://www.comdig.com) - networking the complexity community

• The Santa Fe Institute (http://www.santafe.edu/) - engages in research in complexity
related topics

Complex adaptive system

Complex adaptive systems are special cases of complex systems. They are complex in
that they are diverse and made up of multiple interconnected elements and adaptive in that
they have the capacity to change and learn from experience. The term complex adaptive
systems (CAS) was coined at the interdisciplinary Santa Fe Institute (SFI), by John H.
Holland, Murray Gell-Mann and others.

Overview

The term complex adaptive systems, or complexity science, is often used to describe the
loosely organized academic field that has grown up around the study of such systems.
Complexity science is not a single theory— it encompasses more than one theoretical
framework and is highly interdisciplinary, seeking the answers to some fundamental
questions about living, adaptable, changeable systems.

Examples of complex adaptive systems include the stock market, social insect and ant
colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and
the developing embryo, manufacturing businesses and any human social group-based
endeavour in a cultural and social system such as political parties or communities. There
are close relationships between the field of CAS and artificial life. In both areas the
principles emergence and self-organization are very important.

CAS ideas and models are essentially evolutionary, grounded in modern biological views on
adaptation and evolution. The theory of complex adaptive systems bridges developments of
systems theory with the ideas of generalized Darwinism, which suggests that Darwinian
principles of evolution can explain a range of complex material phenomena, from cosmic to
social objects.

Definitions

A CAS is a complex, self-similar collection of interacting adaptive agents. The study of CAS
focuses on complex, emergent and macroscopic properties of the system. Various
definitions have been offered by different researchers:

• John H. Holland

A Complex Adaptive System (CAS) is a dynamic network of many agents (which may
represent cells, species, individuals, firms, nations) acting in parallel, constantly acting
and reacting to what the other agents are doing. The control of a CAS tends to be
highly dispersed and decentralized. If there is to be any coherent behavior in the
system, it has to arise from competition and cooperation among the agents themselves.

The overall behavior of the system is the result of a huge number of decisions made

n 1
every moment by many individual agents. J

• Kevin Dooley

A CAS behaves/evolves according to three key principles: order is emergent as
opposed to predetermined (c.f. Neural Networks), the system's history is irreversible,
and the system's future is often unpredictable. The basic building blocks of the CAS
are agents. Agents scan their environment and develop schema representing
interpretive and action rules. These schema are subject to change and evolution. ^

Complex adaptive system

Other definitions

Macroscopic collections of simple (and typically nonlinearly) interacting units that are
endowed with the ability to evolve and adapt to a changing environment.

General properties

What distinguishes a CAS
from a pure multi-agent
system (MAS) is the focus on
top-level

properties

and

features like self-similarity,
complexity, emergence and
self-organization. A MAS is
simply defined as a system

composed

multiple,

interacting agents. In CASs,
the agents as well as the
system are adaptive: the
system is self-similar. A CAS is

complex,

collectivity

self-similar
interacting

adaptive agents. Complex

Adaptive

Systems

are

Changing

External

Environment

Changing
External
Environment

Adoptive Behavior

C7^

^^9e/7 C|

Changing

External

Environment

Simple Self -Organized
Local Relationships

Changing

External

Environment

Complex Adaptive System

characterised by a high degree of adaptive capacity, giving them resilience in the face of
perturbation.

Other important properties are adaptation (or homeostasis), communication, cooperation,
specialization, spatial and temporal organization, and of course reproduction. They can be
found on all levels: cells specialize, adapt and reproduce themselves just like larger
organisms do. Communication and cooperation take place on all levels, from the agent to
the system level. The forces driving co-operation between agents in such a system can be
analysed with game theory, many of the issues of compelixty science and new tools for the
anlysis of complexity are being developed within Network Science.

Complex adaptive system

Evolution of complexity

Living organisms are complex

adaptive

systems.

Although

complexity is hard to quantify in
biology, evolution has produced

complex

some

remarkably
[4]

organisms. This observation has
led to the common idea of
evolution being progressive and
leading towards what are viewed
as "higher organisms".

If this were generally true,
evolution would possess an active
trend towards complexity. As
shown below, in this type of
process the value of the most
common amount of complexity
would increase over time.
Indeed,

some

artificial

life

Passive trend

Itti

Minimal
complexity

■

Complexity

Active trend

£.1

Complexity

Passive versus active trends in the evolution of complexity. CAS

at the beginning of the processes are colored red. Changes in the

number of systems are shown by the height of the bars, with

each set of graphs moving up in a time series.

simulations have suggested that
the generation of CAS is an
inescapable feature of evolution.

However, the idea of a general trend towards complexity in evolution can also be explained
through a passive process. ^ This involves an increase in variance but the most common
value, the mode, does not change. Thus, the maximum level of complexity increases over
time, but only as an indirect product of there being more organisms in total. This type of
random process is also called a bounded random walk.

In this hypothesis, the apparent trend towards more complex organisms is an illusion
resulting from concentrating on the small number of large, very complex organisms that
inhabit the right-hand tail of the complexity distribution and ignoring simpler and much
more common organisms. This passive model emphasizes that the overwhelming majority of
species are microscopic prokaryotes, which comprise about half the world's biomass,
constitute the vast majority of Earth's biodiversity. Therefore, simple life remains
dominant on Earth, and complex life appears more diverse only because of sampling bias.

This lack of an overall trend towards complexity in biology does not preclude the existence
of forces driving systems towards complexity in a subset of cases. These minor trends are
balanced by other evolutionary pressures that drive systems towards less complex states.

See also

Artificial life

Center for Complex Systems and Brain Sciences

Center for Social Dynamics & Complexity (CSDC) at Arizona State
University

Enterprise systems
engineering

Generative sciences

Santa Fe Institute

Complex adaptive system

Cognitive Science

Command and Control Research Program

Simulated reality
Sociology and complexity

science

Computational Sociology

Swarm Development Group

References

[I] Complexity: the emerging science at the edge of order and chaos. Harmondsworth [Eng.]: Penguin. 1994.
ISBN 0-14-017968-2.

[2] K. Dooley, AZ State University (http://www.eas.asu.edu/~kdooley/casopdef.html)

[3] Complexity in Social Science glossary (http://www. irit.fr/COSI/glossary/fulllist. php?letter=C) a research

training project of the European Commission
[4] Adami C (2002). "What is complexity?". Bioessays 24 (12): 1085-94. doi: 10. 1002/bies. 10192 (http://dx.doi.

org/10. 1002/bies. 10192). PMID 12447974.
[5] McShea D (1991). "Complexity and evolution: What everybody knows". Biology and Philosophy 6 (3): 303-24.

doi: 10.1007/BF00132234 (http://dx.doi.org/10.1007/BF00132234).
[6] Carroll SB (2001). "Chance and necessity: the evolution of morphological complexity and diversity". Nature

409 (6823): 1102-9. doi: 10.1038/35059227 (http://dx.doi.org/10.1038/35059227). PMID 11234024.
[7] Furusawa C, Kaneko K (2000). "Origin of complexity in multicellular organisms". Phys. Rev. Lett. 84 (26 Pt 1):

6130-3. doi: 10.1103/PhysRevLett.84.6130 (http://dx.doi.org/10.1103/PhysRevLett.84.6130). PMID

10991141.
[8] Adami C, Ofria C, Collier TC (2000). "http://www.pnas. org/cgi/content/full/9 7/9/446 3 1 Evolution of biological

complexity". Proc. Natl. Acad. Sci. U.S.A. 97 (9): 4463-8. doi: 10. 1073/pnas. 97. 9.4463 (http://dx.doi.org/10.

1073/pnas.97.9.4463). PMID 10781045. http://www.pnas.Org/cgi/content/full/97/9/4463.
[9] OrenA(2004).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=l 693353 |Prokaryote diversity

and taxonomy: current status and future challenges". Philos. Trans. R. Soc. Lond., B, Biol. Sci. 359 (1444):

623-38. doi: 10. 1098/rstb. 2003. 1458 (http://dx.doi.org/10.1098/rstb.2003.1458). PMID 15253349.
[10] Whitman W, Coleman D, Wiebe W (1998). "http://www.pnas.org/cgi/content/full/95/12/6578IProkaryotes: the

unseen majority". Proc Natl Acad Sci USA 95 (12): 6578-83. doi: 10. 1073/pnas. 95. 12.6578 (http://dx.doi.org/

10. 1073/pnas. 95. 12. 6578). PMID 9618454. http://www.pnas.org/cgi/content/full/95/12/6578.

[II] Schloss P, Handelsman J (2004). "http://mmbr.asm.org/cgi/pmidlookup?view=long&pmid=l 5590780 1 Status
of the microbial census". Microbiol Mol Biol Rev 68 (4): 686-91. doi: 10.1128/MMBR.68.4. 686-691.2004 (http:/
/dx.doi.org/10.1128/MMBR.68. 4. 686-691. 2004). PMID 15590780. PMC: 539005 (http://www.
pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid= 539005). http://mmbr.asm.org/cgi/
pmidlookup?view=long&pmid= 1 5590780.

[12] http://csdc.asu.edu/

Literature

• Ahmed E, Elgazzar AS, Hegazi AS (28 June 2005). "http://arxiv.org/abs/nlin/0506059IAn
overview of complex adaptive systems". MansouraJ. Math 32. arXiv:nlin/0506059vl
[nlin.AO]. http://arxiv.org/abs/nlin/0506059.

• Bullock S, Cliff D (2004).
http://www.hpl.hp.com/techreports/2004/HPL-2004-l 87. html\Complexity and Emergent
Behaviour in ICT Systems. Hewlett-Packard Labs. HP-2004-187. http://www.hpl.hp.
com/techreports/2004/HPL-2004-187.html.; commissioned as a report (http://www.
foresight.gov.uk/OurWork/CompletedProjects/IIS/Docs/

ComplexityandEmergentBehaviour.asp) by the UK government's Foresight Programme
(http://www.foresight.gov.uk/).

• Dooley, K., Complexity in Social Science glossary a research training project of the
European Commission.

Complex adaptive system

Gell-Mann, Murray (1994). The quark and the jaguar: adventures in the simple and the

complex. San Francisco: W.H. Freeman. ISBN 0-7167-2581-9.

Holland, John H. (1992). Adaptation in natural and artificial systems: an introductory

analysis with applications to biology, control, and artificial intelligence. Cambridge,

Mass: MIT Press. ISBN 0-262-58111-6.

Holland, John H. (1999). Emergence: from chaos to order. Reading, Mass: Perseus Books.

ISBN 0-7382-0142-1.

Kelly, Kevin (1994) (Full text available online).

http://www.kk.org/outofcontrol/contents.phplOut of control: the new biology of machines,

social systems and the economic world. Boston: Addison-Wesley. ISBN 0-201-48340-8.

http://www.kk.org/outofcontrol/contents.php.

Pharoah, M.C. (online). Looking to systems theory for a reductive explanation of

phenomenal experience and evolutionary foundations for higher order thought (http://

homepage. ntlworld.com/m. pharoah/) Retrieved Jan, 15 2008.

External links

• Complexity Digest (http://www.comdig.org/) comprehensive digest of latest CAS
related news and research.

• DNA Wales Research Group (http://www.dnawales.co.uk/) Current Research in
Organisational change CAS/CES related news and free research data. Also linked to the
Business Doctor & BBC documentary series

• A description (http://pespmcl.vub.ac.be/CAS.html) of complex adaptive systems on
the Principia Cybernetica Web.

• Quick reference (http://bactra.org/notebooks/complexity.html) single-page description
of the 'world' of complexity and related ideas hosted by the Center for the Study of
Complex Systems at the University of Michigan.

• Complex systems research network (http://www.complexsystems.net.au/)

• The Open Agent-Based Modeling Consortium (http://www.openabm.org/site/)

Biostatistics

Biostatistics (a combination of the words biology and statistics; sometimes referred to as
biometry or biometrics) is the application of statistics to a wide range of topics in biology.
The science of biostatistics encompasses the design of biological experiments, especially in
medicine and agriculture; the collection, summarization, and analysis of data from those
experiments; and the interpretation of, and inference from, the results.

Biostatistics and the history of biological thought

Biostatistical reasoning and modeling were of critical importance to the foundation theories
of modern biology. In the early 1900s, after the rediscovery of Mendel's work, the
conceptual gaps in understanding between genetics and evolutionary Darwinism led to
vigorous debate between biometricians such as Walter Weldon and Karl Pearson and
Mendelians such as Charles Davenport, William Bateson and Wilhelm Johannsen. By the
1930s statisticians and models built on statistical reasoning had helped to resolve these
differences and to produce the neo-Darwinian modern evolutionary synthesis.

The leading figures in the establishment of this synthesis all relied on statistics and
developed its use in biology.

• Sir Ronald A. Fisher developed several basic statistical methods in support of his work
The Genetical Theory of Natural Selection

• Sewall G. Wright used statistics in the development of modern population genetics

• J. B. S Haldane's book, The Causes of Evolution, reestablished natural selection as the
premier mechanism of evolution by explaining it in terms of the mathematical
consequences of Mendelian genetics.

These individuals and the work of other biostatisticians, mathematical biologists, and
statistically inclined geneticists helped bring together evolutionary biology and genetics
into a consistent, coherent whole that could begin to be quantitatively modeled.

In parallel to this overall development, the pioneering work of D'Arcy Thompson in On
Growth and Form also helped to add quantitative discipline to biological study.

Despite the fundamental importance and frequent necessity of statistical reasoning, there
may nonetheless have been a tendency among biologists to distrust or deprecate results
which are not qualitatively apparent. One anecdote describes Thomas Hunt Morgan
banning the Frieden calculator from his department at Caltech, saying "Well, I am like a
guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a
little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do
that, I'm not going to let any people in my department waste scarce resources in placer

mining." 1 J Educators are now adjusting their curricula to focus on more quantitative
concepts and tools.

Biostatistics

Education and training programs

Almost all educational programmes in biostatistics are at postgraduate level. They are most
often found in schools of public health, affiliated with schools of medicine, forestry, or
agriculture or as a focus of application in departments of statistics.

In the United States, while several universities have dedicated biostatistics departments,
many other top-tier universities integrate biostatistics faculty into statistics or other
departments, such as epidemiology. Thus departments carrying the name "biostatistics"
may exist under quite different structures. For instance, relatively new biostatistics
departments have been founded with a focus on bioinformatics and computational biology,
whereas older departments, typically affiliated with schools of public health, will have more
traditional lines of research involving epidemiological studies and clinical trials as well as
bioinformatics. In larger universities where both a statistics and a biostatistics department
exist, the degree of integration between the two departments may range from the bare
minimum to very close collaboration. In general, the difference between a statistics
program and a biostatistics one is twofold: (i) statistics departments will often host
theoretical/methodological research which are less common in biostatistics programs and
(ii) statistics departments have lines of research that may include biomedical applications
but also other areas such as industry (quality control), business and economics and
biological areas other than medicine.

Applications of biostatistics

• Public health, including epidemiology, health services research, nutrition, and
environmental health

• Design and analysis of clinical trials in medicine

• Genomics, population genetics, and statistical genetics in populations in order to link
variation in genotype with a variation in phenotype. This has been used in agriculture to
improve crops and farm animals (animal breeding). In biomedical research, this work can
assist in finding candidates for gene alleles that can cause or influence predisposition to
disease in human genetics

• Ecology, ecological forecasting

• Biological sequence analysis

Statistical methods are beginning to be integrated into medical informatics, public health
informatics, and bioinformatics

Biostatistics journals

Biometrics
Biometrika

Biostatistics

International Journal of Biostatistics, The

Journal of Agricultural, Biological, and Environmental Statistics

Journal of Biopharmaceutical Statistics

Pharmaceutical Statistics

Statistical Applications in Genetics and Molecular Biology

Statistics in Biopharmaceutical Research

Statistics in Medicine

Biostatistics

Turkiye Klinikleri Journal of Biostatistics

Related fields

Biostatistics shares several methods with quantitative fields such as

• statistics,

• operations research,

• computer science,

• psychometrics,

• econometrics, and

• mathematical demography

See also

• Quantitative parasitology

• Ecological forecasting

References

[1] Charles T. Munger (2003-10-03). http://www.tilsonfunds.com/MungerUCSBspeech. pdf| "Academic Economics

Strengths and Faults After Considering Interdisciplinary Needs", http://www.tilsonfunds.com/

MungerUCSBspeech.pdf.
[2] http://www.reinventioncenter.miami.edu/Spotlights/BioMath.html "Spotlight: application of quantitative

concepts and techniques in undergraduate biology". http://www.reinventioncenter.miami.edu/Spotlights/

BioMath.htm.

External links

• The International Biometric Society (http://www.tibs.org)

• The Collection of Biostatistics Research Archive (http://www.biostatsresearch.com/
repository/)

• Guide to Biostatistics (MedPageToday.com) (http://www.medpagetoday.com/
Medpage-Guide-to-Biostatistics.pdf)

• Biostatistician (http://biostatistician.eu)

Journals

• Statistical Applications in Genetics and Molecular Biology (http://www.bepress.com/
sagmb/)

• Statistics in Medicine (http://www3.interscience.wiley.com/cgi-bin/jhome/2988)

• The International Journal of Biostatistics (http://www.bepress.com/ijb/)

• Journal of Agricultural, Biological, and Environmental Statistics (http://www.amstat.
org/publications/jabes/)

• Journal of Biopharmaceutical Statistics (http://www.tandf.co.uk/journals/titles/
10543406. asp)

• Biostatistics (http://www.biostatistics.oxfordjournals.org/)

• Biometrics (http://www.tibs.org/biometrics/)

• Biometrika (http://biomet.oxfordjournals.org/)

• Biometrical Journal (http://www.biometrical-journal.de/)

• Genetics Selection Evolution (http://www.gse-journal.org/)

Bioinformatics

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Bioinformatics is the application of information

technology to the field of molecular biology. The

term bioinformatics was coined by Paulien

Hogeweg in 1978 for the study of informatic

processes in biotic systems. Bioinformatics now

entails the creation and advancement of

databases, algorithms, computational and

statistical techniques, and theory to solve formal

and practical problems arising from the

management and analysis of biological data.

Over the past few decades rapid developments

in genomic and other molecular research

technologies and developments in information

technologies have combined to produce a

tremendous amount of information related to

molecular biology. It is the name given to these

mathematical and computing approaches used to

glean understanding of biological processes.

Common activities in bioinformatics include

mapping and analyzing DNA and protein

sequences, aligning different DNA and protein sequences to compare them and creating

and viewing 3-D models of protein structures.

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Map of the human X chromosome (from the

NCBI website). Assembly of the human genome

is one of the greatest achievements of

bioinformatics.

The primary goal of bioinformatics is to increase our understanding of biological processes.
What sets it apart from other approaches, however, is its focus on developing and applying
computationally intensive techniques (e.g., data mining, machine learning algorithms, and
visualization) to achieve this goal. Major research efforts in the field include sequence
alignment, gene finding, genome assembly, protein structure alignment, protein structure
prediction, prediction of gene expression and protein-protein interactions, genome-wide
association studies and the modeling of evolution.

Introduction

Bioinformatics was applied in the creation and maintenance of a database to store
biological information at the beginning of the "genomic revolution", such as nucleotide and
amino acid sequences. Development of this type of database involved not only design issues
but the development of complex interfaces whereby researchers could both access existing
data as well as submit new or revised data.

In order to study how normal cellular activities are altered in different disease states, the
biological data must be combined to form a comprehensive picture of these activities.
Therefore, the field of bioinformatics has evolved such that the most pressing task now

invo

Ives the analysis and interpretation of various types of data, including nucleotide and
amino acid sequences, protein domains, and protein structures. The actual process of
analyzing and interpreting data is referred to as computational biology. Important
sub-disciplines within bioinformatics and computational biology include:

Bioinformatics

a) the development and implementation of tools that enable efficient access to, and use and
management of, various types of information, b) the development of new algorithms
(mathematical formulas) and statistics with which to assess relationships among members
of large data sets, such as methods to locate a gene within a sequence, predict protein
structure and/or function, and cluster protein sequences into families of related sequences.

Major research areas

Sequence analysis

Since the Phage 0-X174 was sequenced in 1977, the DNA sequences of hundreds of
organisms have been decoded and stored in databases. The information is analyzed to
determine genes that encode polypeptides, as well as regulatory sequences. A comparison
of genes within a species or between different species can show similarities between
protein functions, or relations between species (the use of molecular systematics to
construct phylogenetic trees). With the growing amount of data, it long ago became
impractical to analyze DNA sequences manually. Today, computer programs are used to
search the genome of thousands of organisms, containing billions of nucleotides. These
programs would compensate for mutations (exchanged, deleted or inserted bases) in the
DNA sequence, in order to identify sequences that are related, but not identical. A variant
of this sequence alignment is used in the sequencing process itself. The so-called shotgun
sequencing technique (which was used, for example, by The Institute for Genomic Research
to sequence the first bacterial genome, Haemophilus influenzae) does not give a sequential
list of nucleotides, but instead the sequences of thousands of small DNA fragments (each
about 600-800 nucleotides long). The ends of these fragments overlap and, when aligned in
the right way, make up the complete genome. Shotgun sequencing yields sequence data
quickly, but the task of assembling the fragments can be quite complicated for larger
genomes. In the case of the Human Genome Project, it took several days of CPU time (on
one hundred Pentium III desktop machines clustered specifically for the purpose) to
assemble the fragments. Shotgun sequencing is the method of choice for virtually all
genomes sequenced today, and genome assembly algorithms are a critical area of
bioinformatics research.

Another aspect of bioinformatics in sequence analysis is the automatic search for genes and
regulatory sequences within a genome. Not all of the nucleotides within a genome are
genes. Within the genome of higher organisms, large parts of the DNA do not serve any
obvious purpose. This so-called junk DNA may, however, contain unrecognized functional
elements. Bioinformatics helps to bridge the gap between genome and proteome
projects-for example, in the use of DNA sequences for protein identification.

See also: sequence analysis, sequence profiling tool, sequence motif.

Genome annotation

In the context of genomics, annotation is the process of marking the genes and other
biological features in a DNA sequence. The first genome annotation software system was
designed in 1995 by Dr. Owen White, who was part of the team that sequenced and
analyzed the first genome of a free-living organism to be decoded, the bacterium
Haemophilus influenzae. Dr. White built a software system to find the genes (places in the
DNA sequence that encode a protein), the transfer RNA, and other features, and to make

Bioinformatics

initial assignments of function to those genes. Most current genome annotation systems
work similarly, but the programs available for analysis of genomic DNA are constantly
changing and improving.

Computational evolutionary biology

Evolutionary biology is the study of the origin and descent of species, as well as their
change over time. Informatics has assisted evolutionary biologists in several key ways; it
has enabled researchers to:

• trace the evolution of a large number of organisms by measuring changes in their DNA,
rather than through physical taxonomy or physiological observations alone,

• more recently, compare entire genomes, which permits the study of more complex
evolutionary events, such as gene duplication, horizontal gene transfer, and the
prediction of factors important in bacterial speciation,

• build complex computational models of populations to predict the outcome of the system
over time

• track and share information on an increasingly large number of species and organisms

Future work endeavours to reconstruct the now more complex tree of life.

The area of research within computer science that uses genetic algorithms is sometimes
confused with computational evolutionary biology, but the two areas are unrelated.

Measuring biodiversity

Biodiversity of an ecosystem might be defined as the total genomic complement of a
particular environment, from all of the species present, whether it is a biofilm in an
abandoned mine, a drop of sea water, a scoop of soil, or the entire biosphere of the planet
Earth. Databases are used to collect the species names, descriptions, distributions, genetic
information, status and size of populations, habitat needs, and how each organism interacts
with other species. Specialized software programs are used to find, visualize, and analyze
the information, and most importantly, communicate it to other people. Computer
simulations model such things as population dynamics, or calculate the cumulative genetic
health of a breeding pool (in agriculture) or endangered population (in conservation). One
very exciting potential of this field is that entire DNA sequences, or genomes of endangered
species can be preserved, allowing the results of Nature's genetic experiment to be
remembered in silico, and possibly reused in the future, even if that species is eventually
lost. [1]

Analysis of gene expression

The expression of many genes can be determined by measuring mRNA levels with multiple
techniques including microarrays, expressed cDNA sequence tag (EST) sequencing, serial
analysis of gene expression (SAGE) tag sequencing, massively parallel signature
sequencing (MPSS), or various applications of multiplexed in-situ hybridization. All of these
techniques are extremely noise-prone and/or subject to bias in the biological measurement,
and a major research area in computational biology involves developing statistical tools to
separate signal from noise in high-throughput gene expression studies. Such studies are
often used to determine the genes implicated in a disorder: one might compare microarray
data from cancerous epithelial cells to data from non-cancerous cells to determine the
transcripts that are up-regulated and down-regulated in a particular population of cancer

Bioinformatics

cells.

Analysis of regulation

Regulation is the complex orchestration of events starting with an extracellular signal such
as a hormone and leading to an increase or decrease in the activity of one or more proteins.
Bioinformatics techniques have been applied to explore various steps in this process. For
example, promoter analysis involves the identification and study of sequence motifs in the
DNA surrounding the coding region of a gene. These motifs influence the extent to which
that region is transcribed into mRNA. Expression data can be used to infer gene regulation:
one might compare microarray data from a wide variety of states of an organism to form
hypotheses about the genes involved in each state. In a single-cell organism, one might
compare stages of the cell cycle, along with various stress conditions (heat shock,
starvation, etc.). One can then apply clustering algorithms to that expression data to
determine which genes are co-expressed. For example, the upstream regions (promoters) of
co-expressed genes can be searched for over-represented regulatory elements.

Analysis of protein expression

Protein microarrays and high throughput (HT) mass spectrometry (MS) can provide a
snapshot of the proteins present in a biological sample. Bioinformatics is very much
involved in making sense of protein microarray and HT MS data; the former approach faces
similar problems as with microarrays targeted at mRNA, the latter involves the problem of
matching large amounts of mass data against predicted masses from protein sequence
databases, and the complicated statistical analysis of samples where multiple, but
incomplete peptides from each protein are detected.

Analysis of mutations in cancer

In cancer, the genomes of affected cells are rearranged in complex or even unpredictable
ways. Massive sequencing efforts are used to identify previously unknown point mutations
in a variety of genes in cancer. Bioinformaticians continue to produce specialized
automated systems to manage the sheer volume of sequence data produced, and they
create new algorithms and software to compare the sequencing results to the growing
collection of human genome sequences and germline polymorphisms. New physical
detection technology are employed, such as oligonucleotide microarrays to identify
chromosomal gains and losses (called comparative genomic hybridization), and single
nucleotide polymorphism arrays to detect known point mutations. These detection methods
simultaneously measure several hundred thousand sites throughout the genome, and when
used in high-throughput to measure thousands of samples, generate terabytes of data per
experiment. Again the massive amounts and new types of data generate new opportunities
for bioinformaticians. The data is often found to contain considerable variability, or noise,
and thus Hidden Markov model and change-point analysis methods are being developed to
infer real copy number changes.

Another type of data that requires novel informatics development is the analysis of lesions
found to be recurrent among many tumors .

Bioinformatics

Prediction of protein structure

Protein structure prediction is another important application of bioinformatics. The amino
acid sequence of a protein, the so-called primary structure, can be easily determined from
the sequence on the gene that codes for it. In the vast majority of cases, this primary
structure uniquely determines a structure in its native environment. (Of course, there are
exceptions, such as the bovine spongiform encephalopathy - aka Mad Cow Disease - prion.)
Knowledge of this structure is vital in understanding the function of the protein. For lack of
better terms, structural information is usually classified as one of secondary, tertiary and
quaternary structure. A viable general solution to such predictions remains an open
problem. As of now, most efforts have been directed towards heuristics that work most of
the time.

One of the key ideas in bioinformatics is the notion of homology. In the genomic branch of
bioinformatics, homology is used to predict the function of a gene: if the sequence of gene
A, whose function is known, is homologous to the sequence of gene B, whose function is
unknown, one could infer that B may share A's function. In the structural branch of
bioinformatics, homology is used to determine which parts of a protein are important in
structure formation and interaction with other proteins. In a technique called homology
modeling, this information is used to predict the structure of a protein once the structure of
a homologous protein is known. This currently remains the only way to predict protein
structures reliably.

One example of this is the similar protein homology between hemoglobin in humans and the
hemoglobin in legumes (leghemoglobin). Both serve the same purpose of transporting
oxygen in the organism. Though both of these proteins have completely different amino
acid sequences, their protein structures are virtually identical, which reflects their near
identical purposes.

Other techniques for predicting protein structure include protein threading and de novo
(from scratch) physics-based modeling.

See also: structural motif and structural domain.

Comparative genomics

The core of comparative genome analysis is the establishment of the correspondence
between genes (orthology analysis) or other genomic features in different organisms. It is
these intergenomic maps that make it possible to trace the evolutionary processes
responsible for the divergence of two genomes. A multitude of evolutionary events acting at
various organizational levels shape genome evolution. At the lowest level, point mutations
affect individual nucleotides. At a higher level, large chromosomal segments undergo
duplication, lateral transfer, inversion, transposition, deletion and insertion. Ultimately,
whole genomes are involved in processes of hybridization, polyploidization and
endosymbiosis, often leading to rapid speciation. The complexity of genome evolution poses
many exciting challenges to developers of mathematical models and algorithms, who have
recourse to a spectra of algorithmic, statistical and mathematical techniques, ranging from
exact, heuristics, fixed parameter and approximation algorithms for problems based on
parsimony models to Markov Chain Monte Carlo algorithms for Bayesian analysis of
problems based on probabilistic models.

Many of these studies are based on the homology detection and protein families
computation.

Bioinformatics

Modeling biological systems

Systems biology involves the use of computer simulations of cellular subsystems (such as
the networks of metabolites and enzymes which comprise metabolism, signal transduction
pathways and gene regulatory networks) to both analyze and visualize the complex
connections of these cellular processes. Artificial life or virtual evolution attempts to
understand evolutionary processes via the computer simulation of simple (artificial) life
forms.

High-throughput image analysis

Computational technologies are used to accelerate or fully automate the processing,
quantification and analysis of large amounts of high-information-content biomedical
imagery. Modern image analysis systems augment an observer's ability to make
measurements from a large or complex set of images, by improving accuracy, objectivity, or
speed. A fully developed analysis system may completely replace the observer. Although
these systems are not unique to biomedical imagery, biomedical imaging is becoming more
important for both diagnostics and research. Some examples are:

• high-throughput and high-fidelity quantification and sub-cellular localization
(high-content screening, cytohistopathology)

• morphometries

• clinical image analysis and visualization

• determining the real-time air-flow patterns in breathing lungs of living animals

• quantifying occlusion size in real-time imagery from the development of and recovery
during arterial injury

• making behavioral observations from extended video recordings of laboratory animals

• infrared measurements for metabolic activity determination

• inferring clone overlaps in DNA mapping, e.g. the Sulston score

Protein-protein docking

In the last two decades, tens of thousands of protein three-dimensional structures have
been determined by X-ray crystallography and Protein nuclear magnetic resonance
spectroscopy (protein NMR). One central question for the biological scientist is whether it
is practical to predict possible protein-protein interactions only based on these 3D shapes,
without doing protein-protein interaction experiments. A variety of methods have been
developed to tackle the Protein-protein docking problem, though it seems that there is still
much work to be done in this field.

Software and tools

Software tools for bioinformatics range from simple command-line tools, to more complex
graphical programs and standalone web-services available from various bioinformatics
companies or public institutions. The computational biology tool best-known among
biologists is probably BLAST, an algorithm for determining the similarity of arbitrary
sequences against other sequences, possibly from curated databases of protein or DNA
sequences. BLAST is one of a number of generally available programs for doing sequence
alignment. The NCBI provides a popular web-based implementation that searches their
databases.

Bioinformatics

Web services in bioinformatics

SOAP and REST-based interfaces have been developed for a wide variety of bioinformatics
applications allowing an application running on one computer in one part of the world to
use algorithms, data and computing resources on servers in other parts of the world. The
main advantages lay in the end user not having to deal with software and database
maintenance overheads. Basic bioinformatics services are classified by the EBI into three
categories: SSS (Sequence Search Services), MSA (Multiple Sequence Alignment) and BSA
(Biological Sequence Analysis). The availability of these service-oriented bioinformatics
resources demonstrate the applicability of web based bioinformatics solutions, and range
from a collection of standalone tools with a common data format under a single, standalone
or web-based interface, to integrative, distributed and extensible bioinformatics workflow
management systems.

See also

• International Society of Intelligent Biological Medicine (ISIBM)

Biocybernetics

Biocybernetics is the application of cybernetics to biological science, composed of
biological disciplines that benefit from the application of cybernetics: neurology,
multicellular systems and others. Biocybernetics plays a major role in systems biology,
seeking to integrate different levels of information to understand how biological systems
function.

Biocybernetics as an abstract science is a part of theoretical biology, and based upon the
principles of systemics.

Terminology

Biocybernetics is a cojoined word from bio (Greek: (3io / life) and cybernetics (Greek:
KuftepvrixiKri / controlling-governing). It is sometimes written together or with a blank or
written fully as biological cybernetics, whilst the same rules apply. Most write it together
though, as Google statistics show. The same applies to neuro cybernetics which should also
be looked up as neurological, when doing extensive research.

Same or familiar fields

As those disciplines are dealing on theoretical/abstract foundations and are in accordance
with the popularity of computers. Thus papers and research is in greater numbers going on
under different names: e.g. molecular cybernetics -> molecular computational systems OR
molecular systems theory OR molecular systemics OR molecular information/informational
systems

Please heed this when you engage in an extensive search for information to assure access
to a broad range of papers.

Biocybernetics

See also

• Bioinformatics

• Biosemiotics

• Computational biology

• Computational biomodeling

• Medical cybernetics

References

External links

• Journal "Biological Cybernetics"

• Scientific portal on biological cybernetics

roi

• UCLA Biocybernetics Laboratory

References

[1] http://www.springerlink. com/link. asp?id= 100465
[2 ] http :// www. biological-cybernetics . de
[3] http://biocyb.cs.ucla.edu/research.html

Molecular dynamics

Molecular dynamics (MD) is a form of computer simulation in which atoms and molecules
are allowed to interact for a period of time by approximations of known physics, giving a
view of the motion of the atoms. Because molecular systems generally consist of a vast
number of particles, it is impossible to find the properties of such complex systems
analytically. When the number of bodies are more than two no analytical solutions can be
found and result in chaotic motion (see n-body problem). MD simulation circumvents this
problem by using numerical methods. It represents an interface between laboratory
experiments and theory, and can be understood as a "virtual experiment". MD probes the
relationship between molecular structure, movement and function. Molecular dynamics is a
multidisciplinary method. Its laws and theories stem from mathematics, physics, and
chemistry, and it employs algorithms from computer science and information theory. It was
originally conceived within theoretical physics in the late 1950s [ ^ and early 1960s c ^ , but
is applied today mostly in materials science and modeling of biomolecules.

Before it became possible to simulate molecular dynamics with computers, some undertook
the hard work of trying it with physical models such as macroscopic spheres. The idea was
to arrange them to replicate the properties of a liquid. J.D. Bernal said, in 1962: "... I took a
number of rubber balls and stuck them together with rods of a selection of different lengths
ranging from 2.75 to 4 inches. I tried to do this in the first place as casually as possible,
working in my own office, being interrupted every five minutes or so and not remembering
what I had done before the interruption. " L J Fortunately, now computers keep track of
bonds during a simulation.

Molecular dynamics is a specialized discipline of molecular modeling and computer
simulation based on statistical mechanics; the main justification of the MD method is that
statistical ensemble averages are equal to time averages of the system, known as the
ergodic hypothesis. MD has also been termed "statistical mechanics by numbers" and
"Laplace's vision of Newtonian mechanics" of predicting the future by animating nature's
forces J and allowing insight into molecular motion on an atomic scale. However, long
MD simulations are mathematically ill-conditioned, generating cumulative errors in
numerical integration that can be minimized with proper selection of algorithms and
parameters, but not eliminated entirely. Furthermore, current potential functions are, in
many cases, not sufficiently accurate to reproduce the dynamics of molecular systems, so
the much more computationally demanding Ab Initio Molecular Dynamics method must be
used. Nevertheless, molecular dynamics techniques allow detailed time and space
resolution into representative behavior in phase space.

Molecular dynamics

Areas of Application

There is a significant difference
between the focus and methods

used

chemists

and

physicists, and this is reflected
in differences in the jargon
used by the different fields. In
chemistry and biophysics, the

interaction

between

the

particles is either described by
a "force field" (classical MD),

a quantum chemical model, or
a mix between the two. These
terms are not used in physics,
where the interactions are
usually described by the name
of the theory or approximation
being used and called the
potential energy, or just "potential"

Give atoms initial positions r^, choose short At

Get forces F = - V V(r®) and a = F/m

Move atoms: r< M > = r® +v^ At + 1 / 2 a At 2 + . .

Move time forward: t = t + At

Repeat as long as you need

Highly simplified description of the molecular dynamics simulation

algorithm. The simulation proceeds iteratively by alternatively

calculating forces and solving the equations of motion based on the

accelerations obtained from the new forces. In practise, almost all

MD codes use much more complicated versions of the algorithm,

including two steps (predictor and corrector) in solving the equations

of motion and many additional steps for e.g. temperature and

pressure control, analysis and output.

Beginning in theoretical physics, the method of MD gained popularity in materials science
and since the 1970s also in biochemistry and biophysics. In chemistry, MD serves as an
important tool in protein structure determination and refinement using experimental tools
such as X-ray crystallography and NMR. It has also been applied with limited success as a
method of refining protein structure predictions. In physics, MD is used to examine the
dynamics of atomic-level phenomena that cannot be observed directly, such as thin film
growth and ion-subplantation. It is also used to examine the physical properties of
nanotechnological devices that have not or cannot yet be created.

In applied mathematics and theoretical physics, molecular dynamics is a part of the
research realm of dynamical systems, ergodic theory and statistical mechanics in general.
The concepts of energy conservation and molecular entropy come from thermodynamics.
Some techniques to calculate conformational entropy such as principal components analysis
come from information theory. Mathematical techniques such as the transfer operator
become applicable when MD is seen as a Markov chain. Also, there is a large community of
mathematicians working on volume preserving, symplectic integrators for more
computationally efficient MD simulations.

MD can also be seen as a special case of the discrete element method (DEM) in which the
particles have spherical shape (e.g. with the size of their van der Waals radii.) Some
authors in the DEM community employ the term MD rather loosely, even when their
simulations do not model actual molecules.

Molecular dynamics

Design Constraints

Design of a molecular dynamics simulation should account for the available computational
power. Simulation size (n=number of particles), timestep and total time duration must be
selected so that the calculation can finish within a reasonable time period. However, the
simulations should be long enough to be relevant to the time scales of the natural processes
being studied. To make statistically valid conclusions from the simulations, the time span
simulated should match the kinetics of the natural process. Otherwise, it is analogous to
making conclusions about how a human walks from less than one footstep. Most scientific
publications about the dynamics of proteins and DNA use data from simulations spanning
nanoseconds (1E-9 s) to microseconds (1E-6 s). To obtain these simulations, several
CPU-days to CPU-years are needed. Parallel algorithms allow the load to be distributed
among CPUs; an example is the spatial decomposition in LAMMPS.

During a classical MD simulation, the most CPU intensive task is the evaluation of the
potential (force field) as a function of the particles' internal coordinates. Within that energy
evaluation, the most expensive one is the non-bonded or non-covalent part. In Big O
notation, common molecular dynamics simulations scale by 0(n )if all pair-wise
electrostatic and van der Waals interactions must be accounted for explicitly. This
computational cost can be reduced by employing electrostatics methods such as Particle
Mesh Ewald ( 0(nlog{n))) or good spherical cutoff techniques ( 0(n)).

Another factor that impacts total CPU time required by a simulation is the size of the
integration timestep. This is the time length between evaluations of the potential. The
timestep must be chosen small enough to avoid discretization errors (i.e. smaller than the
fastest vibrational frequency in the system). Typical timesteps for classical MD are in the
order of 1 femtosecond (1E-15 s). This value may be extended by using algorithms such as
SHAKE, which fix the vibrations of the fastest atoms (e.g. hydrogens) into place. Multiple
time scale methods have also been developed, which allow for extended times between
updates of slower long-range forces.

For simulating molecules in a solvent, a choice should be made between explicit solvent and
implicit solvent. Explicit solvent particles (such as the TIP3P and SPC/E water models) must
be calculated expensively by the force field, while implicit solvents use a mean-field
approach. Using an explicit solvent is computationally expensive, requiring inclusion of
about ten times more particles in the simulation. But the granularity and viscosity of
explicit solvent is essential to reproduce certain properties of the solute molecules. This is
especially important to reproduce kinetics.

In all kinds of molecular dynamics simulations, the simulation box size must be large
enough to avoid boundary condition artifacts. Boundary conditions are often treated by
choosing fixed values at the edges, or by employing periodic boundary conditions in which
one side of the simulation loops back to the opposite side, mimicking a bulk phase.

Microcanonical ensemble (NVE)

In the microcanonical, or NVE ensemble, the system is isolated from changes in moles
(N), volume (V) and energy (E). It corresponds to an adiabatic process with no heat
exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of
potential and kinetic energy, with total energy being conserved. For a system of N particles
with coordinates X and velocities V, the following pair of first order differential equations
may be written in Newton's notation as

Molecular dynamics

F(X) = -VU(X) =
V(t) = X(t).

The potential energy function U(X) of the system is a function of the particle coordinates
X . It is referred to simply as the "potential" in Physics, or the "force field" in Chemistry.
The first equation comes from Newton's laws; the force Facting on each particle in the
system can be calculated as the negative gradient of U(X) .

For every timestep, each particle's position A and velocity V r may be integrated with a
symplectic method such as Verlet. The time evolution of A^and lis called a trajectory.
Given the initial positions (e.g. from theoretical knowledge) and velocities (e.g. randomized
Gaussian), we can calculate all future (or past) positions and velocities.

One frequent source of confusion is the meaning of temperature in MD. Commonly we have
experience with macroscopic temperatures, which involve a huge number of particles. But
temperature is a statistical quantity. If there is a large enough number of atoms, statistical
temperature can be estimated from the instantaneous temperature, which is found by
equating the kinetic energy of the system to nk T/2 where n is the number of degrees of
freedom of the system.

A temperature-related phenomenon arises due to the small number of atoms that are used
in MD simulations. For example, consider simulating the growth of a copper film starting
with a substrate containing 500 atoms and a deposition energy of 100 eV. In the real world,
the 100 eV from the deposited atom would rapidly be transported through and shared
among a large number of atoms ( 10 10 or more) with no big change in temperature. When
there are only 500 atoms, however, the substrate is almost immediately vaporized by the
deposition. Something similar happens in biophysical simulations. The temperature of the
system in NVE is naturally raised when macromolecules such as proteins undergo
exothermic conformational changes and binding.

Canonical ensemble (NVT)

In the canonical ensemble, moles (N), volume (V) and temperature (T) are conserved. It is
also sometimes called constant temperature molecular dynamics (CTMD). In NVT, the
energy of endothermic and exothermic processes is exchanged with a thermostat.

A variety of thermostat methods are available to add and remove energy from the
boundaries of an MD system in a realistic way, approximating the canonical ensemble.
Popular techniques to control temperature include the Nose-Hoover thermostat, the
Berendsen thermostat, and Langevin dynamics. Note that the Berendsen thermostat might
introduce the flying ice cube effect, which leads to unphysical translations and rotations of
the simulated system.

Molecular dynamics

Isothermal-Isobaric (NPT) ensemble

In the isothermal-isobaric ensemble, moles (N), pressure (P) and temperature (T) are
conserved. In addition to a thermostat, a barostat is needed. It corresponds most closely to
laboratory conditions with a flask open to ambient temperature and pressure.

In the simulation of biological membranes, isotropic pressure control is not appropriate.
For lipid bilayers, pressure control occurs under constant membrane area (NPAT) or
constant surface tension "gamma" (NPyT).

Generalized ensembles

The replica exchange method is a generalized ensemble. It was originally created to deal
with the slow dynamics of disordered spin systems. It is also called parallel tempering. The
replica exchange MD (REMD) formulation L J tries to overcome the multiple-minima
problem by exchanging the temperature of non-interacting replicas of the system running
at several temperatures.

Potentials in MD simulations

A molecular dynamics simulation requires the definition of a potential function, or a
description of the terms by which the particles in the simulation will interact. In chemistry
and biology this is usually referred to as a force field. Potentials may be defined at many
levels of physical accuracy; those most commonly used in chemistry are based on molecular
mechanics and embody a classical treatment of particle-particle interactions that can
reproduce structural and conformational changes but usually cannot reproduce chemical
reactions.

The reduction from a fully quantum description to a classical potential entails two main
approximations. The first one is the Born-Oppenheimer approximation, which states that
the dynamics of electrons is so fast that they can be considered to react instantaneously to
the motion of their nuclei. As a consequence, they may be treated separately. The second
one treats the nuclei, which are much heavier than electrons, as point particles that follow
classical Newtonian dynamics. In classical molecular dynamics the effect of the electrons is
approximated as a single potential energy surface, usually representing the ground state.

When finer levels of detail are required, potentials based on quantum mechanics are used;
some techniques attempt to create hybrid classical/quantum potentials where the bulk of
the system is treated classically but a small region is treated as a quantum system, usually
undergoing a chemical transformation.

Empirical potentials

Empirical potentials used in chemistry are frequently called force fields, while those used in
materials physics are called just empirical or analytical potentials.

Most force fields in chemistry are empirical and consist of a summation of bonded forces
associated with chemical bonds, bond angles, and bond dihedrals, and non-bonded forces
associated with van der Waals forces and electrostatic charge. Empirical potentials
represent quantum-mechanical effects in a limited way through ad-hoc functional
approximations. These potentials contain free parameters such as atomic charge, van der
Waals parameters reflecting estimates of atomic radius, and equilibrium bond length,
angle, and dihedral; these are obtained by fitting against detailed electronic calculations

Molecular dynamics

(quantum chemical simulations) or experimental physical properties such as elastic
constants, lattice parameters and spectroscopic measurements.

Because of the non-local nature of non-bonded interactions, they involve at least weak
interactions between all particles in the system. Its calculation is normally the bottleneck in
the speed of MD simulations. To lower the computational cost, force fields employ
numerical approximations such as shifted cutoff radii, reaction field algorithms, particle
mesh Ewald summation, or the newer Particle-Particle Particle Mesh (P3M).

Chemistry force fields commonly employ preset bonding arrangements (an exception being
ab-initio dynamics), and thus are unable to model the process of chemical bond breaking
and reactions explicitly. On the other hand, many of the potentials used in physics, such as
those based on the bond order formalism can describe several different coordinations of a
system and bond breaking. Examples of such potentials include the Brenner potential J for
hydrocarbons and its further developments for the C-Si-H and C-O-H systems. The ReaxFF
potential can be considered a fully reactive hybrid between bond order potentials and
chemistry force fields.

Pair potentials vs. many-body potentials

The potential functions representing the non-bonded energy are formulated as a sum over
interactions between the particles of the system. The simplest choice, employed in many
popular force fields, is the "pair potential", in which the total potential energy can be
calculated from the sum of energy contributions between pairs of atoms. An example of
such a pair potential is the non-bonded Lennard -Jones potential (also known as the 6-12
potential), used for calculating van der Waals forces.

U(r) = 4e

a\ 12 f^ 6

Another example is the Born (ionic) model of the ionic lattice. The first term in the next
equation is Coulomb's law for a pair of ions, the second term is the short-range repulsion
explained by Pauli's exclusion principle and the final term is the dispersion interaction
term. Usually, a simulation only includes the dipolar term, although sometimes the
quadrupolar term is included as well.

^;) = £ j£tj- + £ * exp ^ + £ <W* + ■ ■ ■

In many-body potentials, the potential energy includes the effects of three or more particles
interacting with each other. In simulations with pairwise potentials, global interactions in
the system also exist, but they occur only through pairwise terms. In many-body potentials,
the potential energy cannot be found by a sum over pairs of atoms, as these interactions are
calculated explicitly as a combination of higher-order terms. In the statistical view, the
dependency between the variables cannot in general be expressed using only pairwise

ri2i

products of the degrees of freedom. For example, the Tersoff potential , which was
originally used to simulate carbon, silicon and germanium and has since been used for a
wide range of other materials, involves a sum over groups of three atoms, with the angles
between the atoms being an important factor in the potential. Other examples are the
embedded-atom method (EAM) L J and the Tight-Binding Second Moment Approximation
(TBSMA) potentials , where the electron density of states in the region of an atom is
calculated from a sum of contributions from surrounding atoms, and the potential energy
contribution is then a function of this sum.

Molecular dynamics

Semi-empirical potentials

Semi-empirical potentials make use of the matrix representation from quantum mechanics.
However, the values of the matrix elements are found through empirical formulae that
estimate the degree of overlap of specific atomic orbitals. The matrix is then diagonalized to
determine the occupancy of the different atomic orbitals, and empirical formulae are used
once again to determine the energy contributions of the orbitals.

There are a wide variety of semi-empirical potentials, known as tight-binding potentials,
which vary according to the atoms being modeled.

Polarizable potentials

Most classical force fields implicitly include the effect of polarizability, e.g. by scaling up
the partial charges obtained from quantum chemical calculations. These partial charges are
stationary with respect to the mass of the atom. But molecular dynamics simulations can
explicitly model polarizability with the introduction of induced dipoles through different
methods, such as Drude particles or fluctuating charges. This allows for a dynamic
redistribution of charge between atoms which responds to the local chemical environment.

For many years, polarizable MD simulations have been touted as the next generation. For
homogenous liquids such as water, increased accuracy has been achieved through the
inclusion of polarizability. Some promising results have also been achieved for

proteins. ] However, it is still uncertain how to best approximate polarizability in a
simulation.

Ab-initio methods

In classical molecular dynamics, a single potential energy surface (usually the ground state)
is represented in the force field. This is a consequence of the Born-Oppenheimer
approximation. If excited states, chemical reactions or a more accurate representation is
needed, electronic behavior can be obtained from first principles by using a quantum
mechanical method, such as Density Functional Theory. This is known as Ab Initio
Molecular Dynamics (AIMD). Due to the cost of treating the electronic degrees of freedom,
the computational cost of this simulations is much higher than classical molecular
dynamics. This implies that AIMD is limited to smaller systems and shorter periods of time.

Ab-initio quantum-mechanical methods may be used to calculate the potential energy of a
system on the fly, as needed for conformations in a trajectory. This calculation is usually
made in the close neighborhood of the reaction coordinate. Although various
approximations may be used, these are based on theoretical considerations, not on
empirical fitting. Ab-initio calculations produce a vast amount of information that is not
available from empirical methods, such as density of electronic states or other electronic
properties. A significant advantage of using ab-initio methods is the ability to study
reactions that involve breaking or formation of covalent bonds, which correspond to
multiple electronic states.

A popular software for ab-initio molecular dynamics is the Car-Parrinello Molecular
Dynamics (CPMD) package based on the density functional theory.

Molecular dynamics

Hybrid QM/MM

QM (quantum-mechanical) methods are very powerful. However, they are computationally
expensive, while the MM (classical or molecular mechanics) methods are fast but suffer
from several limitations (require extensive parameterization; energy estimates obtained are
not very accurate; cannot be used to simulate reactions where covalent bonds are
broken/formed; and are limited in their abilities for providing accurate details regarding the
chemical environment). A new class of method has emerged that combines the good points
of QM (accuracy) and MM (speed) calculations. These methods are known as mixed or
hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM). The
methodology for such techniques was introduced by Warshel and coworkers. In the recent
years have been pioneered by several groups including: Arieh Warshel (University of
Southern California), Weitao Yang (Duke University), Sharon Hammes-Schiffer (The
Pennsylvania State University), Donald Truhlar and Jiali Gao (University of Minnesota) and
Kenneth Merz (University of Florida).

The most important advantage of hybrid QM/MM methods is the speed. The cost of doing
classical molecular dynamics (MM) in the most straightforward case scales 0(n ), where N
is the number of atoms in the system. This is mainly due to electrostatic interactions term
(every particle interacts with every other particle). However, use of cutoff radius, periodic
pair-list updates and more recently the variations of the particle-mesh Ewald's (PME)

method has reduced this between O(N) to 0(n ). In other words, if a system with twice
many atoms is simulated then it would take between twice to four times as much computing
power. On the other hand the simplest ab-initio calculations typically scale 0(n ) or worse

2 7

(Restricted Hartree-Fock calculations have been suggested to scale ~0(n " )). To overcome
the limitation, a small part of the system is treated quantum-mechanically (typically
active-site of an enzyme) and the remaining system is treated classically.

In more sophisticated implementations, QM/MM methods exist to treat both light nuclei
susceptible to quantum effects (such as hydrogens) and electronic states. This allows
generation of hydrogen wave-functions (similar to electronic wave-functions). This
methodology has been useful in investigating phenomenon such as hydrogen tunneling. One
example where QM/MM methods have provided new discoveries is the calculation of
hydride transfer in the enzyme liver alcohol dehydrogenase. In this case, tunneling is

ri7i

important for the hydrogen, as it determines the reaction rate.

Coarse-graining and reduced representations

At the other end of the detail scale are coarse-grained and lattice models. Instead of
explicitly representing every atom of the system, one uses "pseudo-atoms" to represent
groups of atoms. MD simulations on very large systems may require such large computer
resources that they cannot easily be studied by traditional all-atom methods. Similarly,
simulations of processes on long timescales (beyond about 1 microsecond) are prohibitively
expensive, because they require so many timesteps. In these cases, one can sometimes
tackle the problem by using reduced representations, which are also called coarse-grained
models.

Examples for coarse graining (CG) methods are discontinuous molecular dynamics

n Ri n qi r9ni

(CG-DMD) L J L J and Go-models . Coarse-graining is done sometimes taking larger

pseudo-atoms. Such united atom approximations have been used in MD simulations of

biological membranes. The aliphatic tails of lipids are represented by a few pseudo-atoms

Molecular dynamics

by gathering 2-4 methylene groups into each pseudo-atom.

The parameterization of these very coarse-grained models must be done empirically, by
matching the behavior of the model to appropriate experimental data or all-atom
simulations. Ideally, these parameters should account for both enthalpic and entropic
contributions to free energy in an implicit way. When coarse-graining is done at higher
levels, the accuracy of the dynamic description may be less reliable. But very
coarse-grained models have been used successfully to examine a wide range of questions in
structural biology.

Examples of applications of coarse-graining in biophysics:

• protein folding studies are often carried out using a single (or a few) pseudo-atoms per
amino acid;

• DNA supercoiling has been investigated using 1-3 pseudo-atoms per basepair, and at
even lower resolution;

• Packaging of double-helical DNA into bacteriophage has been investigated with models
where one pseudo-atom represents one turn (about 10 basepairs) of the double helix;

• RNA structure in the ribosome and other large systems has been modeled with one
pseudo-atom per nucleotide.

The simplest form of coarse-graining is the "united atom" (sometimes called "extended
atom") and was used in most early MD simulations of proteins, lipids and nucleic acids. For
example, instead of treating all four atoms of a CH methyl group explicitly (or all three
atoms of CH methylene group), one represents the whole group with a single pseudo-atom.
This pseudo-atom must, of course, be properly parameterized so that its van der Waals
interactions with other groups have the proper distance-dependence. Similar
considerations apply to the bonds, angles, and torsions in which the pseudo-atom
participates. In this kind of united atom representation, one typically eliminates all explicit
hydrogen atoms except those that have the capability to participate in hydrogen bonds
("polar hydrogens"). An example of this is the Charmm 19 force-field.

The polar hydrogens are usually retained in the model, because proper treatment of
hydrogen bonds requires a reasonably accurate description of the directionality and the
electrostatic interactions between the donor and acceptor groups. A hydroxyl group, for
example, can be both a hydrogen bond donor and a hydrogen bond acceptor, and it would
be impossible to treat this with a single OH pseudo-atom. Note that about half the atoms in
a protein or nucleic acid are nonpolar hydrogens, so the use of united atoms can provide a
substantial savings in computer time.

Examples of applications

Molecular dynamics is used in many fields of science.

• First macromolecular MD simulation published (1977, Size: 500 atoms, Simulation Time:
9.2 ps=0.0092 ns, Program: CHARMM precursor) Protein: Bovine Pancreatic Trypsine
Inhibitor. This is one of the best studied proteins in terms of folding and kinetics. Its
simulation published in Nature magazine paved the way for understanding protein

["91 ]

motion as essential in function and not just accessory.

• MD is the standard method to treat collision cascades in the heat spike regime, i.e. the
effects that energetic neutron and ion irradiation have on solids an solid surfaces. J L

Molecular dynamics

The following two biophysical examples are not run-of-the-mill MD simulations. They
illustrate almost heroic efforts to produce simulations of a system of very large size (a
complete virus) and very long simulation times (500 microseconds):

• MD simulation of the complete satellite tobacco mosaic virus (STMV) (2006, Size: 1
million atoms, Simulation time: 50 ns, program: NAMD) This virus is a small, icosahedral
plant virus which worsens the symptoms of infection by Tobacco Mosaic Virus (TMV).
Molecular dynamics simulations were used to probe the mechanisms of viral assembly.
The entire STMV particle consists of 60 identical copies of a single protein that make up
the viral capsid (coating), and a 1063 nucleotide single stranded RNA genome. One key
finding is that the capsid is very unstable when there is no RNA inside. The simulation
would take a single 2006 desktop computer around 35 years to complete. It was thus
done in many processors in parallel with continuous communication between them. ^

• Folding Simulations of the Villin Headpiece in All-Atom Detail (2006, Size: 20,000 atoms;
Simulation time: 500 jis = 500,000 ns, Program: folding@home) This simulation was run
in 200,000 CPU's of participating personal computers around the world. These
computers had the folding@home program installed, a large-scale distributed computing
effort coordinated by Vijay Pande at Stanford University. The kinetic properties of the
Villin Headpiece protein were probed by using many independent, short trajectories run
by CPU's without continuous real-time communication. One technique employed was the
Pfold value analysis, which measures the probability of folding before unfolding of a
specific starting conformation. Pfold gives information about transition state structures
and an ordering of conformations along the folding pathway. Each trajectory in a Pfold
calculation can be relatively short, but many independent trajectories are needed. 5]

Molecular dynamics algorithms

Integrators

• Verlet-Stoermer integration

• Runge-Kutta integration

• Beeman's algorithm

• Gear predictor - corrector

• Constraint algorithms (for constrained systems)

• Symplectic integrator

Short-range interaction algorithms

• Cell lists

• Verlet list

• Bonded interactions

Long-range interaction algorithms

• Ewald summation

• Particle Mesh Ewald (PME)

• Particle-Particle Particle Mesh P3M

• Reaction Field Method

Molecular dynamics

Parallelization strategies

• Domain decomposition method (Distribution of system data for parallel computing)

• Molecular Dynamics - Parallel Algorithms L J

Major software for MD simulations

Abalone (classical, implicit water)

ABINIT (DFT)

ACEMD [27] (running on NVIDIA GPUs: heavily optimized with CUDA)

ADUN [28] (classical, P2P database for simulations)

AMBER (classical)

Ascalaph (classical, GPU accelerated)

CASTEP (DFT)

CPMD (DFT)

CP2K [30] (DFT)

CHARMM (classical, the pioneer in MD simulation, extensive analysis tools)

roi I

COSMOS (classical and hybrid QM/MM, quantum-mechanical atomic charges with
BPT)

T321

Desmond (classical, parallelization with up to thousands of CPU's)

DLPOLY [33] (classical)

ESPResSo (classical, coarse-grained, parallel, extensible)

Fireball [34] (tight-binding DFT)

GROMACS (classical)

GROMOS (classical)

GULP (classical)

Hippo [35] (classical)

LAMMPS (classical, large-scale with spatial-decomposition of simulation domain for

parallelism)

MDynaMix (classical, parallel)

MOLDY [36] (classical, parallel) latest release [37]

Materials Studio [38] (Forcite MD using COMPASS, Dreiding, Universal, cvff and pcff

forcefields in serial or parallel, QMERA (QM + MD), ONESTEP (DFT), etc.)

MOSCITO (classical)

NAMD (classical, parallelization with up to thousands of CPU's)

NEWTON-X L J (ab initio, surface-hopping dynamics)

ProtoMol (classical, extensible, includes multigrid electrostatics)

PWscf (DFT)

S/PHI/nX [41] (DFT)

SIESTA (DFT)

VASP (DFT)

TINKER (classical)

YASARA [42] (classical)

ORAC [43] (classical)

XMD (classical)

Molecular dynamics

Related software

• VMD - MD simulation trajectories can be visualized and analyzed.

• PyMol - Molecular Visualization software written in python

• Packmol L Package for building starting configurations for MD in an automated fashion

• Sirius - Molecular modeling, analysis and visualization of MD trajectories

• esra - Lightweight molecular modeling and analysis library
(Java/Jython/Mathematica) .

• Molecular Workbench L J - Interactive molecular dynamics simulations on your desktop

• BOSS - MC in OPLS

Specialized hardware for MD simulations

• Anton - A specialized, massively parallel supercomputer designed to execute MD
simulations.

• MDGRAPE - A special purpose system built for molecular dynamics simulations,
especially protein structure prediction.

See also

Molecular graphics

Molecular modeling

Computational chemistry

Energy drift

Force field in Chemistry

Force field implementation

Monte Carlo method

Molecular Design software

Molecular mechanics

Molecular modeling on GPU

Protein dynamics

Implicit solvation

Car-Parrinello method

Symplectic numerical integration

Software for molecular mechanics modeling

Dynamical systems

Theoretical chemistry

Statistical mechanics

Quantum chemistry

Discrete element method

List of nucleic acid simulation software

Molecular dynamics

References

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10.1098/rspa.l964.0147 (http://dx.doi.org/10.1098/rspa.1964.0147).
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Sumners. Mathematical Applications to Biomolecular Structure and Dynamics, IMA Volumes in Mathematics

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10.1016/j.cplett.2005.10.135 (http://dx.doi.Org/10.1016/j.cplett.2005.10.135).
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prot. 10468).
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10.1038/267585a0 (http://dx.doi.org/10.1038/267585a0).
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in H. Ehrenfest and F. Spaepen. Solid State Physics. 51. New York: Academic Press, p. 281-402.
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Cambridge, UK: Cambridge University Press.
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http://www.ks.uiuc.edu/Research/STMV/! "Molecular dynamics simulation of the Satellite Tobacco Mosaic Virus

Molecular dynamics

(STMV)". Theoretical and Computational Biophysics Group. University of Illinois at Urbana Champaign, http://

www.ks.uiuc.edu/Research/STMV/.
[25] The Folding@Home Project (http://folding.stanford.edu/) and recent papers (http://folding.stanford.edu/

papers.html) published using trajectories from it. Vijay Pande Group. Stanford University
[26] http://www.cs.sandia.gov/~sjplimp/md.html
[27] http://www.acellera. com/index. php?arg=acemd
[28] http://cbbl.imim.es/Adun
[29] http://www.agilemolecule.com/Products.html
[30] http://cp2k.berlios.de/

[31] http://www.cosmos-software.de/ce_intro.html
[32] http://www.DEShawResearch.com/resources.html
[33] http://www.ccp5.ac.uk/DL_POLY/
[34] http://fireball-dft.org
[35] http://www.biowerkzeug.com/
[36] http://www.ccp5.ac.uk/moldy/moldy.html
[37] http://ccpforge.cse.rl.ac.uk/frs/?group_id=34
[38] http://accelrys.com/products/materials-studio/
[39] http://www.univie.ac.at/newtonx/
[40] http://protomol.sourceforge.net/
[41] http://www.sphinxlib.de
[42] http://www.yasara.org
[43] http://www.chim.unifi.it/orac/
[44] http://www.ime.unicamp.br/~martinez/packmol
[45] http://esra.sourceforge.net/cgi-bin/index.cgi
[46] http ://mw. concord. org/modeler/

General references

• M. P. Allen, D. J. Tildesley (1989) Computer simulation of liquids. Oxford University
Press. ISBN 0-19-855645-4.

• J. A. McCammon, S. C. Harvey (1987) Dynamics of Proteins and Nucleic Acids.
Cambridge University Press. ISBN 0521307503 (hardback).

• D. C. Rapaport (1996) The Art of Molecular Dynamics Simulation. ISBN 0-521-44561-2.

• Frenkel, Daan; Smit, Berend (2002) [2001]. Understanding Molecular Simulation : from
algorithms to applications. San Diego, California: Academic Press. ISBN 0-12-267351-4.

• J. M. Haile (2001) Molecular Dynamics Simulation: Elementary Methods. ISBN
0-471-18439-X

• R. J. Sadus, Molecular Simulation of Fluids: Theory, Algorithms and Object-Orientation,
2002, ISBN 0-444-51082-6

• Oren M. Becker, Alexander D. Mackerell Jr, Benoit Roux, Masakatsu Watanabe (2001)
Computational Biochemistry and Biophysics. Marcel Dekker. ISBN 0-8247-0455-X.

• Andrew Leach (2001) Molecular Modelling: Principles and Applications. (2nd Edition)
Prentice Hall. ISBN 978-0582382107.

• Tamar Schlick (2002) Molecular Modeling and Simulation. Springer. ISBN
0-387-95404-X.

• William Graham Hoover (1991) Computational Statistical Mechanics, Elsevier, ISBN
0-444-88192-1.

Molecular dynamics

External links

• The Blue Gene Project (http://researchweb.watson.ibm.com/bluegene/) (IBM)

• D. E. Shaw Research (http://deshawresearch.com/) (D. E. Shaw Research)

• Molecular Physics (http://www.tandf.co.uk/journals/titles/00268976.asp)

• Statistical mechanics of Nonequilibrium Liquids (http://www.phys.unsw.edu.au/
~gary/book.html) Lecture Notes on non-equilibrium MD

• Introductory Lecture on Classical Molecular Dynamics (http://www.fz-juelich.de/
nic-series/volumelO/sutmann.pdf) by Dr. Godehard Sutmann, NIC, Forschungszentrum
Jiilich, Germany

• Introductory Lecture on Ab Initio Molecular Dynamics and Ab Initio Path Integrals (http:/
/www. fz-juelich.de/nic-series/volumel0/tuckerman2.pdf) by Mark E. Tuckerman,

New York University, USA

• Introductory Lecture on Ab initio molecular dynamics: Theory and Implementation (http:/
/www.fz-juelich.de/nic-series/Volumel/marx.pdf) by Dominik Marx, Ruhr-Universitat
Bochum and Jiirg Hutter, Universitat Zurich

Computer model

1. REDIRECT Computer simulation

Quantum Monte Carlo

Electronic structure methods

Tight binding

Nearly-free electron model

Hartree-Fock

Modern valence bond

Generalized valence bond

M0ller-Plesset perturbation theory

Configuration interaction

Coupled cluster

Multi-configurational self-consistent field

Density functional theory

Quantum chemistry composite methods

Quantum Monte Carlo

k-p perturbation theory

Muffin-tin approximation

LCAO method

Quantum Monte Carlo is a large class of computer algorithms that simulate quantum
systems with the idea of solving the many-body problem. They use, in one way or another,
the Monte Carlo method to handle the many-dimensional integrals that arise. Quantum

Quantum Monte Carlo

Monte Carlo allows a direct representation of many-body effects in the wavefunction, at the
cost of statistical uncertainty that can be reduced with more simulation time. For bosons,
there exist numerically exact and polynomial-scaling algorithms. For fermions, there exist
very good approximations and numerically exact exponentially scaling quantum Monte
Carlo algorithms, but none that are both.

Background

In principle, any physical system can be described by the many-body Schrodinger equation
as long as the constituent particles are not moving "too" fast; that is, they are not moving
near the speed of light. This includes the electrons in almost every material in the world, so
if we could solve the Schrodinger equation, we could predict the behavior of any electronic
system, which has important applications in fields from computers to biology. This also
includes the nuclei in Bose-Einstein condensate and superfluids such as liquid helium. The
difficulty is that the Schrodinger equation involves a function of three times the number of
particles and is difficult to solve even using parallel computing technology in a reasonable
amount of time (less than 2 years). Traditionally, theorists have approximated the
many-body wave function as an antisymmetric function of one-body orbitals, as shown

concisely at this link. 1 J This kind of formulation either limits the possible wave functions, as
in the case of the Hartree-Fock (HF) approximation, or converges very slowly, as in
configuration interaction. One of the reasons for the difficulty with an HF initial estimate
(ground state seed, also known as Slater determinant) is that it is very difficult to model the
electronic and nuclear cusps in the wavefunction. However, one does not generally model
at this point of the approximation. As two particles approach each other, the wavefunction
has exactly known derivatives.

Quantum Monte Carlo is a way around these problems because it allows us to model a
many-body wavefunction of our choice directly. Specifically, we can use a Hartree-Fock
approximation as our starting point but then multiplying it by any symmetric function, of
which Jastrow functions are typical, designed to enforce the cusp conditions. Most methods
aim at computing the ground-state wavefunction of the system, with the exception of path
integral Monte Carlo and finite-temperature auxiliary field Monte Carlo, which calculate the
density matrix.

There are several quantum Monte Carlo methods, each of which uses Monte Carlo in
different ways to solve the many-body problem:

Quantum Monte Carlo methods

• Stochastic Green function (SGF) algorithm : An algorithm designed for bosons that can
simulate any complicated lattice Hamiltonian that does not have a sign problem. Used in
combination with a directed update scheme, this is a powerful tool.

• Variational Monte Carlo : A good place to start; it is commonly used in many sorts of
quantum problems.

• Diffusion Monte Carlo : The most common high-accuracy method for electrons (that is,
chemical problems), since it comes quite close to the exact ground-state energy fairly
efficiently. Also used for simulating the quantum behavior of atoms, etc.

• Path integral Monte Carlo : Finite-temperature technique mostly applied to bosons where
temperature is very important, especially superfluid helium.

Quantum Monte Carlo

Auxiliary field Monte Carlo : Usually applied to lattice problems, although there has been

recent work on applying it to electrons in chemical systems.

Reptation Monte Carlo : Recent zero-temperature method related to path integral Monte

Carlo, with applications similar to diffusion Monte Carlo but with some different

tradeoffs.

Gaussian quantum Monte Carlo

See also

Stochastic Green Function (SGF) algorithm

Monte Carlo method

QMC@Home

Quantum chemistry

Density matrix renormalization group

Time-evolving block decimation

Metropolis algorithm

Wavefunction optimization

Implementations

ALPS [2]
CASINO [3]
CHAMP [4]
Monte Python [5]
PIMC + + [6]

[7]

pi-qmc J
QMcBeaver [8]
QmcMol [9]
QMCPACK [10]
Qumax [11]
Qwalk [12]
TurboRVB [13]
Zori [14]

References

[ 1 ] http ://www. attaccalite . altervista.org/PhDThesis/html/node9. html

[2] http://alps.comp-phys.org/mediawiki/

[3] http://www.tcm.phy.cam.ac.uk/~mdt26/casino2.html

[4] http://pages.physics.cornell.edu/~cyrus/champ.html

[ 5 ] http ://code . google . com/p/montepython/

[6] http://cms.mcc.uiuc.edu/pimcpp/

[7] http ://code . google . com/p/pi-qmc/

[8] http://qmcbeaver.sourceforge.net/

[9] http://www.lct.jussieu.fr/pagesequipe/qmcmol/qmcmol/

[10] http ://www. mcc .uiuc . edu/qmc/qmcpack/index. html

[11] http ://attaccalite. altervista. org/qumax/index.php

[12] http://www.qwalk.org/

[13] http://turborvb.qe-forge.org

[14] http://www.zori-code.com/

Quantum Monte Carlo

V. G. Rousseau (May 2008).

"http://link.aps.org/doi/10.1103/PhysRevE.77.056705IStochastic Green Function (SGF)

algorithm" (in English) (abstract). Phys. Rev. E 77: 056705. doi:

10.1 103/PhysRevE. 77. 056705 (http://dx.doi.org/10.1103/PhysRevE.77.056705).

http://link.aps.org/doi/10.1103/PhysRevE.77.056705. Retrieved on 05/2008.

Hammond, B.J.; W.A. Lester & P.J. Reynolds (1994) (in English).

http://www.worldscibooks.com/chemistry/ll 70.html\Monte Carlo Methods in Ab Initio

Quantum Chemistry. Singapore: World Scientific. ISBN 981-02-0321-7. OCLC 29594695

(http://worldcat.org/oclc/29594695). http://www.worldscibooks.com/chemistry/

1170.html. Retrieved on 2007-01-18.

Nightingale, M.P.; Umrigar, Cyrus J., ed (1999) (in English).

http://www. springer. com/west/0-7923-5552-0\Quantum Monte Carlo Methods in Physics

and Chemistry. Springer. ISBN 978-0-7923-5552-6. http://www.springer.com/west/

0-7923-5552-0. Retrieved on 2007-01-18.

W. M. C. Foulkes; L. Mitas, R. J. Needs and G. Rajagopal (5 January 2001).

"http://link.aps.org/abstract/RMP/v73/p33IQuantum Monte Carlo simulations of solids" (in

English) (abstract). Rev. Mod. Phys. 73: 33-83. doi: 10.1103/RevModPhys.73.33 (http://

dx.doi.org/10.1103/RevModPhys.73.33). http://link.aps.org/abstract/RMP/v73/

p33. Retrieved on 2007-01-18.

Raimundo R. dos Santos (2003). "http://arxiv.org/abs/cond-mat/0303551vlllntroduction

to Quantum Monte Carlo simulations for fermionic systems" (in English) (full text). Braz.

J. Phys. 33: 36. http://arxiv.org/abs/cond-mat/0303551vl. Retrieved on 2007-01-18.

External links

• QMCWIKI (http://www.qmcwiki.org/)

• Joint DEMOCRITOS-ICTP School on Continuum Quantum Monte Carlo Methods (http://
cdsagenda5.ictp.trieste.it/full_display.php?ida=a0332&fid=)

• FreeScience Library -> Quantum Monte Carlo (http://freescience.info/books.
php?id=35)

• UIUC 2007 Summer School on Computational Materials Science: Quantum Monte Carlo
from Minerals and Materials to Molecules (http://www.mcc.uiuc.edu/summerschool/
2007/qmc/)

• Quantum Monte Carlo in the Apuan Alps V (http://www.vallico.net/tti/tti.html) -
international workshop, Vallico Sotto, Tuscany, 25 July-1 August 2009 (Click PUBLIC
EVENTS) - Announcement (http://www.vallico.net/tti/qmcitaa_09/announcement.
html), Poster (http://www.tcm.phy.cam.ac.uk/-mdt26/tti2/poster/
tti_c_poster_2009.png)

• Quantum Monte Carlo and the CASINO program IV (http://www.vallico.net/tti/tti.

html) - summer school, Vallico Sotto, Tuscany, 2-9 August 2009 (Click PUBLIC EVENTS) -
Announcement (http://www.vallico.net/tti/qmcatcp_09/announcement.html), Poster
(http://www.tcm.phy.cam.ac.uk/-mdt26/tti2/poster/tti_ss_poster_2009.png)

Molecular graphics

Molecular graphics (MG) is the discipline and philosophy of studying molecules and their

n 1
properties through graphical representation. J IUPAC limits the definition to

representations on a "graphical display device". Ever since Dalton's atoms and Kekule's

benzene, there has been a rich history of hand-drawn atoms and molecules, and these

representations have had an important influence on modern molecular graphics. This

article concentrates on the use of computers to create molecular graphics. Note, however,

that many molecular graphics programs and systems have close coupling between the

graphics and editing commands or calculations such as in molecular modelling.

Relation to molecular models

There has been a long tradition of creating
molecular models from physical materials.
Perhaps the best known is Crick and
Watson's model of DNA built from rods and
planar sheets, but the most widely used
approach is to represent all atoms and
bonds explicitly using the "ball and stick"
approach. This can demonstrate a wide
range of properties, such as shape, relative
size, and flexibility. Many chemistry
courses expect that students will have
access to ball and stick models. One goal of
mainstream molecular graphics has been to
represent the "ball and stick" model as
realistically as possible and to couple this
with calculations of molecular properties.

I^^l ^^H ^^^^^H

hk Jmol

Fig. 1. Key: Hydrogen = white, carbon = grey,
nitrogen = blue, oxygen = red, and phosphorus =

orange.

Figure 1 shows a small molecule (NH 3 CH 2 CH 2 C(OH)(P0 3 H)(P0 3 H)-), as drawn by the Jmol
program. It is important to realise that the colours are purely a convention. Molecules can
never be visible under any light microscope and atoms are not coloured, do not have hard
surfaces and do not reflect light. Bonds are not rod-shaped. If physical molecular models
had not existed, it is unlikely that molecular graphics would currently use this metaphor.

Comparison of physical models with molecular graphics

Physical models and computer models have partially complementary strengths and
weaknesses. Physical models can be used by those without access to a computer and now
can be made cheaply out of plastic materials. Their tactile and visual aspects cannot be
easily reproduced by computers (although haptic devices have occasionally been built). On
a computer screen, the flexibility of molecules is also difficult to appreciate; illustrating the
pseudorotation of cyclohexane is a good example of the value of mechanical models.

However, it is difficult to build large physical molecules, and all-atom physical models of
even simple proteins could take weeks or months to build. Moreover, physical models are
not robust and they decay over time. Molecular graphics is particularly valuable for
representing global and local properties of molecules, such as electrostatic potential.

Molecular graphics

Graphics can also be animated to represent molecular processes and chemical reactions, a
feat that is not easy to reproduce physically.

History

Initially the rendering was on early CRT screens or through plotters drawing on paper.
Molecular structures have always been an attractive choice for developing new computer
graphics tools, since the input data are easy to create and the results are usually highly
appealing. The first example of MG was a display of a protein molecule (Project MAC, 1966)
by Cyrus Levin thai and Robert Langridge. Among the milestones in high-performance MG
was the work of Nelson Max in "realistic" rendering of macromolecules using reflecting
spheres.

By about 1980 many laboratories both in academia and industry had recognized the power
of the computer to analyse and predict the properties of molecules, especially in materials
science and the pharmaceutical industry. The discipline was often called "molecular
graphics" and in 1982 a group of academics and industrialists in the UK set up the
Molecular Graphics Society (MGS). Initially much of the technology concentrated either on
high-performance 3D graphics, including interactive rotation or 3D rendering of atoms as
spheres (sometimes with radiosity). During the 1980s a number of programs for calculating
molecular properties (such as molecular dynamics and quantum mechanics) became
available and the term "molecular graphics" often included these. As a result the MGS has
now changed its name to the Molecular Graphics and Modelling Society (MGMS).

The requirements of macromolecular crystallography also drove MG because the traditional
techniques of physical model-building could not scale. Alwyn Jones' FRODO program (and
later "O") were developed to overlay the molecular electron density determined from X-ray
crystallography and the hypothetical molecular structure.

Molecular graphics

Art, science and technology in molecular graphics

Both computer technology and graphic arts have

contributed to molecular graphics. The development
of structural biology in the 1950s led to a
requirement to display molecules with thousands of
atoms. The existing computer technology was
limited in power, and in any case a naive depiction
of all atoms left viewers overwhelmed. Most systems
therefore used conventions where information was
implicit or stylistic. Two vectors meeting at a point
implied an atom or (in macromolecules) a complete
residue (10-20 atoms).

The macromolecular approach was popularized by
Dickerson and Gels' presentation of proteins and the
graphic work of Jane Richardson through
high-quality hand-drawn diagrams such as the
"ribbon" representation. In this they strove to
capture the intrinsic 'meaning' of the molecule. This
search for the "messages in the molecule" has
always accompanied the increasing power of
computer graphics processing. Typically the
depiction would concentrate on specific areas of the
molecule (such as the active site) and this might
have different colours or more detail in the number
of explicit atoms or the type of depiction (e.g.,
spheres for atoms).

In some cases the limitations of technology have led
to serendipitous methods for rendering. Most early graphics devices used vector graphics,
which meant that rendering spheres and surfaces was impossible. Michael Connolly's
program "MS" calculated points on the surface-accessible surface of a molecule, and the
points were rendered as dots with good visibility using the new vector graphics technology,
such as the Evans and Sutherland PS300 series. Thin sections ("slabs") through the
structural display showed very clearly the complementarity of the surfaces for molecules
binding to active sites, and the "Connolly surface" became a universal metaphor.

The relationship between the art and science of molecular graphics is shown in the
exhibitions sponsored by the Molecular Graphics Society. Some exhibits are created with
molecular graphics programs alone, while others are collages, or involve physical materials.
An example from Mike Hann (1994), inspired by Magritte's painting Ceci riest pas une
pipe, uses an image of a salmeterol molecule.

"Ceci riest pas une molecule," writes Mike Hann, "serves to remind us that all of the
graphics images presented here are not molecules, not even pictures of molecules, but
pictures of icons which we believe represent some aspects of the molecule's properties."

Fig. 2. Image of hemagglutinin with alpha

helices depicted as cylinders and the rest

of the chain as silver coils. The individual

protein atoms (several thousand) have

been hidden. All of the non-hydrogen atoms

in the two ligands (presumably sialic acid)

have been shown near the top of the

diagram. Key: Carbon = grey, oxygen =

red, nitrogen = blue.

Molecular graphics

100

Space-filling models

Fig. 4 is a "space-filling" representation of formic acid,

where atoms are drawn to suggest the amount of space

they occupy. This is necessarily an icon: in the quantum

mechanical representation of molecules, there are only

(positively charged) nuclei and a "cloud" of negative

electrons. The electron cloud defines an approximate

size for the molecule, though there can be no single

precise definition of size. For many years the size of

atoms has been approximated by mechanical models

(CPK), where the atoms have been represented by

plastic spheres whose radius (van der Waals radius)

describes a sphere within which "most" of the electron

density can be found. These spheres could be clicked

together to show the steric aspects of the molecule

rather than the positions of the nuclei. Fig. 4 shows the

intricacy required to make sure that all spheres intersect correctly, and also demonstrates

a reflective model.

Fig. 4. Space-filling model of formic
acid. Key: Hydrogen = white, carbon =

black, oxygen = red.

Fig. 5. A molecule (zirconocene) where

part (left) is rendered as ball-and-stick

and part (right) as an isosurface.

Since the atomic radii (e.g. in Fig. 4) are only slightly
less than the distance between bonded atoms, the
iconic spheres intersect, and in the CPK models, this
was achieved by planar truncations along the bonding
directions, the section being circular. When raster
graphics became affordable, one of the common
approaches was to replicate CPK models in silico. It is
relatively straightforward to calculate the circles of
intersection, but more complex to represent a model
with hidden surface removal. A useful side product is
that a conventional value for the molecular volume can
be calculated.

The use of spheres is often for convenience, being
limited both by graphics libraries and the additional effort required to compute complete
electronic density or other space-filling quantities. It is now relatively common to see
images of isosurfaces that have been coloured to show quantities such as electrostatic
potential. The commonest isosurfaces are the Connolly surface, or the volume within which
a given proportion of the electron density lies. The isosurface in Fig. 5 appears to show the
electrostatic potential, with blue colours being negative and red/yellow (near the metal)
positive. (There is no absolute convention of colouring, and red/positive, blue/negative are
often confusingly reversed!) Opaque isosurfaces do not allow the atoms to be seen and
identified and it is not easy to deduce them. Because of this, isosurfaces are often drawn
with a degree of transparency.

Molecular graphics

101

Technology

Molecular graphics has always pushed the limits of display technology, and has seen a
number of cycles of integration and separation of compute-host and display. Early systems
like Project MAC were bespoke and unique, but in the 1970s the MMS-X and similar
systems used (relatively) low-cost terminals, such as the Tektronix 4014 series, often over
dial-up lines to multi-user hosts. The devices could only display static pictures but, were
able to evangelize MG. In the late 1970s, it was possible for departments (such as
crystallography) to afford their own hosts (e.g., PDP-11) and to attach a display (such as
Evans & Sutherland's MPS) directly to the bus. The display list was kept on the host, and
interactivity was good since updates were rapidly reflected in the display— at the cost of
reducing most machines to a single-user system.

In the early 1980s, Evans & Sutherland (E&S) decoupled their PS300 display, which
contained its own display information transformable through a dataflow architecture.
Complex graphical objects could be downloaded over a serial line (e.g. 9600 baud) and then
manipulated without impact on the host. The architecture was excellent for high
performance display but very inconvenient for domain-specific calculations, such as
electron-density fitting and energy calculations. Many crystallographers and modellers
spent arduous months trying to fit such activities into this architecture.

The benefits for MG were considerable, but by the later 1980s, UNIX workstations such as
Sun-3 with raster graphics (initially at a resolution of 256 by 256) had started to appear.
Computer-assisted drug design in particular required raster graphics for the display of
computed properties such as atomic charge and electrostatic potential. Although E&S had a
high-end range of raster graphics (primarily aimed at the aerospace industry) they failed to
respond to the low-end market challenge where single users, rather than engineering
departments, bought workstations. As a result the market for MG displays passed to Silicon
Graphics, coupled with the development of minisupercomputers (e.g., CONVEX and Alliant)
which were affordable for well-supported MG laboratories. Silicon Graphics provided a
graphics language, IrisGL, which was easier to use and more productive than the PS300
architecture. Commercial companies (e.g., Biosym, Polygen/MSI) ported their code to
Silicon Graphics, and by the early 1990s, this was the "industry standard".

Stereoscopic displays were developed based on liquid crystal polarized spectacles, and
while this had been very expensive on the PS300, it now became a commodity item. A
common alternative was to add a polarizable screen to the front of the display and to
provide viewers with extremely cheap spectacles with orthogonal polarization for separate
eyes. With projectors such as Barco, it was possible to project stereoscopic display onto
special silvered screens and supply an audience of hundreds with spectacles. In this way
molecular graphics became universally known within large sectors of chemical and
biochemical science, especially in the pharmaceutical industry. Because the backgrounds of
many displays were black by default, it was common for modelling sessions and lectures to
be held with almost all lighting turned off.

In the last decade almost all of this technology has become commoditized. IrisGL evolved to
OpenGL so that molecular graphics can be run on any machine. In 1992, Roger Sayle
released his RasMol program into the public domain. RasMol contained a very
high-performance molecular renderer that ran on Unix/X Window, and Sayle later ported
this to the Windows and Macintosh platforms. The Richardsons developed kinemages and
the Mage software, which was also multi-platform. By specifying the chemical MIME type,

Molecular graphics

102

molecular models could be served over the Internet, so that for the first time MG could be
distributed at zero cost regardless of platform. In 1995, Birkbeck College's crystallography
department used this to run "Principles of Protein Structure", the first multimedia course
on the Internet, which reached 100 to 200 scientists.

Fig. 6. A molecule of Porin (protein) shown without ambient occlusion (left) and with (right). Advanced rendering
effects can improve the comprehension of the 3D shape of a molecule.

MG continues to see innovation that balances technology and art, and currently zero-cost or
open source programs such as PyMOL and Jmol have very wide use and acceptance.

Recently the wide spread diffusion of advanced graphics hardware, has improved the
rendering capabilities of the visualization tools. The capabilities of current shading
languages allow the inclusion of advanced graphic effects (like ambient occlusion, cast
shadows and non-photorealistic rendering techniques) in the interactive visualization of
molecules. These graphic effects, beside being eye candy, can improve the comprehension
of the three dimensional shapes of the molecules. An example of the effects that can be
achieved exploiting recent graphics hardware can be seen in the simple open source
visualization system QuteMol.

Algorithms

Reference frames

Drawing molecules requires a transformation between molecular coordinates (usually, but
not always, in Angstrom units) and the screen. Because many molecules are chiral it is
essential that the handedness of the system (almost always right-handed) is preserved. In
molecular graphics the origin (0, 0) is usually at the lower left, while in many computer
systems the origin is at top left. If the z-coordinate is out of the screen (towards the viewer)
the molecule will be referred to right-handed axes, while the screen display will be
left-handed.

Molecular transformations normally require:

• scaling of the display (but not the molecule).

• translations of the molecule and objects on the screen.

• rotations about points and lines.

Conformational changes (e.g. rotations about bonds) require rotation of one part of the
molecule relative to another. The programmer must decide whether a transformation on the

Molecular graphics

103

screen reflects a change of view or a change in the molecule or its reference frame.

Simple

In early displays only vectors could be drawn e.g. (Fig.
7) which are easy to draw because no rendering or
hidden surface removal is required.

On vector machines the lines would be smooth but on
raster devices Bresenham's algorithm is used (note the
"jaggies" on some of the bonds, which can be largely
removed with antialiasing software.)

Atoms can be drawn as circles, but these should be
sorted so that those with the largest z-coordinates
(nearest the screen) are drawn last. Although
imperfect, this often gives a reasonably attractive
display. Other simple tricks which do not include
hidden surface algorithms are:

• colouring each end of a bond with the same colour as the atom to which it is attached
(Fig. 7).

• drawing less than the whole length of the bond (e.g. 10%-90%) to simulate the bond
sticking out of a circle.

• adding a small offset white circle within the circle for an atom to simulate reflection.

Typical pseudocode for creating Fig. 7 (to fit the molecule exactly to the screen):

// assume:

// atoms with x, y, z coordinates (Angstrom) and elementSymbol
// bonds with pointers/references to atoms at ends
// table of colours for elementTypes

// find limits of molecule in molecule coordinates as xMin, yMin, xMax,
yMax
scale = min(xScreenMax/(xMax-xMin) , yScreenMax/(yMax-yMin) )
xOffset = -xMin * scale; yOffset = -yMin * scale
for (bond in $bonds) {

atom© = bond .getAtom(O)

atoml = bond .getAtom(l)

xO = xOffset+atom0.getX()*scale; y0 = yOff set+atom0.getY( )*scale //

(1)
xl = xOffset+atoml.getX()*scale; yl = yOff set+atoml.getY( )*scale //

(2)

xl = atoml. getX() ; yl = atoml. getY()

xMid = (x0 + xl) /2; yMid = (yO + yl) /2;

colourO = ColourTable.getColour(atom0.getSymbol( ) )

drawLine (colourO, xO, yQ, xMid, yMid)

colourl = ColourTable.getColour(atoml.getSymbol( ) )

drawLine (colourl, xl, yl, xMid, yMid)

}

Molecular graphics

104

Note that this assumes the origin is in the bottom left corner of the screen, with Y up the
screen. Many graphics systems have the origin at the top left, with Y down the screen. In
this case the lines (1) and (2) should have the y coordinate generation as:

y0 = yScreenMax - (yOff set+atomQ. getY( )*scale) // (1)
yl = yScreenMax - (yOff set+atoml.getY( )*scale) // (2)

Changes of this sort change the handedness of the axes so it is easy to reverse the chirality
of the displayed molecule unless care is taken.

Advanced

For greater realism and better comprehension of the 3D structure of a molecule many
computer graphics algorithms can be used. For many years molecular graphics has
stressed the capabilities of graphics hardware and has required hardware-specific
approaches. With the increasing power of machines on the desktop, portability is more
important and programs such as Jmol have advanced algorithms that do not rely on
hardware. On the other hand recent graphics hardware is able to interactively render very
complex molecule shapes with a quality that would not be possible with standard software
techniques.

Chronology

This table provides an incomplete chronology of molecular graphics advances.

Developer(s)

Approximate
date

Technology

Comments

Crystallographers

< 1960

Hand-drawn

Crystal structures, with hidden atom
and bond removal. Often clinographic
projections.

Cyrus Levinthal, Bob
Langridge

1960s

CRT

First protein display on screen (Project
MAC).

Johnson, Motherwell

ca 1970

Pen plotter

ORTEP, PLUTO. Very widely deployed
for publishing crystal structures.

Langridge, White,
Marshall

Late 1970s

Departmental systems
(PDP-11, Tektronix
displays or DEC-VT11, e.g.

MMS-X)

Mixture of commodity computing with
early displays.

T. Alwyn Jones

1978

FRODO

Crystallographic structure solution.

Davies, Hubbard

Mid-1980s

CHEM-X, HYDRA

Laboratory systems with multicolor,
raster and vector devices (Sigmex,
PS300).

Biosym, Tripos, Polygen

Mid-1980s

PS300 and lower cost
dumb terminals (VT200,
SIGMEX)

Commercial integrated modelling and
display packages.

Silicon Graphics, Sun

Late 1980s

IRIS GL (UNIX)
workstations

Commodity-priced single-user
workstations with stereoscopic
display.

EMBL - WHAT IF [4]

1989, 2000

Machine independent

Nearly free, multifunctional, still fully
supported, many free servers
based on it

Molecular graphics

105

Sayle, Richardson

1992, 1993

RasMol, Kinemage

Platform-independent MG.

MDL (van Vliet, Maffett,
Adler, Holt)

1995-1998

Chime

proprietary C++ ; free browser plugin
for Mac (OS9) and PCs

ChemAxon

1998-

MarvinSketch [6] &

[7]
MarvinView

MarvinSpace [8] (2005)

proprietary Java applet or stand-alone
application.

Community efforts

2000-

Jmol, PyMol, Protein
Workshop (www.pdb.org)

Open-source Java applet or
stand-alone application.

NOCH

2002-

NOC [9]

Powerful and open source code
molecular structure explorer

LION Bioscience / EMBL

2004-

SRS 3D [10]

Free, open-source system based on
Java3D. Integrates 3D structures with
sequence and feature data (domains,
SNPs, etc.).

San Diego Supercomputer
Center

2006-

Sirius

Free for academic/non-profit
institutions

Weizmann Institute of
Science - Community
efforts

2008-

Proteopedia

Collaborative, 3D wiki encyclopedia of
proteins & other molecules

References

[1] Dickerson, R.E.; Geis, I. (1969). The structure and action of proteins. Menlo Park, CA: W.A. Benjamin.

[2] International Union of Pure and Applied Chemistry (1997). " molecular graphics (http://goldbook.iupac.org/

MT06970.html)". Compendium of Chemical Terminology Internet edition.
[ 3 ] http ://www. scripps . edu/mb/goodsell/mgs_art/
[4] http :// swift. cmbi.ru.nl/whatif/
[5] http://swift.cmbi.ru.nl/

[6] http ://www. chemaxon. com/product/msketch. html
[7] http ://www. chemaxon. com/product/mview. html
[8] http ://www. chemaxon. com/product/mspace. html
[9] http://noch.sourceforge.net
[10] http://srs3d.org

See also

• List of Molecular Graphics Systems

• Molecular Design software

• Molecular model

• Molecular modelling

• Molecular geometry

• Software for molecular mechanics modeling

Molecular graphics

106

External links

The PyMOL Molecular Graphics System (http://pymol.sf.net) -- open source

• PyMOLWiki (http://pymolwiki.org) -- community supported wiki for PyMOL

History of Visualization of Biological Macromolecules (http://www.umass.edu/

microbio/rasmol/history.htm) by Eric Martz and Eric Francoeur.

Brief History of Molecular Mechanics/Graphics (http://stanley.chem.lsu.edu/webpub/

7770-Lecture-l-intro.pdf) in LSU CHEM7770 lecture notes.

Historical slides (http://luminary.stanford.edu/langridge/slides.htm) from Robert

(Bob) Langridge. These show the influence of Crick and Watson on molecular graphics

(including Levinthal's) and the development of early display technology, finishing with

displays which were common in the mid-1980s on machines such as Evans and

Sutherland's PS300 series.

Interview with Langridge. (http://luminary.stanford.edu/langridge/langridge.html)

The display looking down the axis of B-DNA has been likened to a rose window.

Nelson Max's home page (http://accad.osu.edu/~waynec/history/tree/max.html)

with links to 1982 classics.

Jmol home page (http://jmol.sourceforge.net/) contains an applet with an automatic

display of many features of molecular graphics including metaphors, scripting,

annotation and animation.

Richardson Lab (http://kinemage.biochem.duke.edu/) includes Kinemage and

molecular graphics images.

History of RasMol. (http://www.openrasmol.org/history.html)

Molecule of the Month (http://www.rcsb. org/pdb/static.do?p=education_discussion/

moleculeofthemonth/index.html) at RCSB/PDB.

xeo (http://sourceforge.net/projects/xeo) xeo is a free (GPL) open project management

for nanostructures using Java

Exhibitions of Molecular Graphics Art (http://www.scripps.edu/mb/goodsell/mgs_art/

), 1994, 1998.

NOCH home page (http://noch.sourceforge.net) A powerful, efficient and open source

molecular graphics tool.

eMovie (http://www.weizmann.ac.il/ISPC/eMovie.html): a tool for creation of

molecular animations with PyMOL.

Proteopedia (http://www.proteopedia.org): The collaborative, 3D encyclopedia of

proteins and other molecules.

Ascalaph Graphics (http://www.agilemolecule.com/Ascalaph/Ascalaph_Graphics.

html): a molecular viewer with some geometry editing capabilities.

Molecular Graphics and Modelling Society, (http://www.mgms.org/)

Journal of Molecular Graphics and Modelling (http://www.sciencedirect.com/

science?_ob=JournalURL&_cdi=5260&_auth=y&_acct=C000053194&_version=l&

_urlVersion=0&_userid=1495569&md5 = le86bcce088e98890cea52f6eda84b64)

(formally Journal of Molecular Graphics). This journal is not open access.

107

Mathematical, Logical and
Theoretical Physics Foundations

Theoretical physics

Theoretical physics employs mathematical models and abstractions of physics in an
attempt to explain natural phenomena in a mathematical form. Its central core is
mathematical physics , though other conceptual techniques are also used. The goal is to
rationalize, explain and predict physical phenomena. The advancement of science depends
in general on the interplay between experimental studies and theory. In some cases,
theoretical physics adheres to standards of mathematical rigor while giving little weight to
experiments and observations. For example, while developing special relativity, Albert
Einstein was concerned with the Lorentz transformation which left Maxwell's equations
invariant, but was apparently uninterested in the Michelson-Morley experiment on Earth's
drift through a luminiferous ether. On the other hand, Einstein was awarded the Nobel
Prize for explaining the photoelectric effect, previously an experimental result lacking a
theoretical formulation.

Overview

A physical theory is a model of physical events. It is judged by the extent to which its
predictions agree with empirical observations. The quality of a physical theory is also
judged on its ability to make new predictions which can be verified by new observations. A
physical theory differs from a mathematical theorem in that while both are based on some
form of axioms, judgment of mathematical applicability is not based on agreement with any
experimental results.

Ricci = kg

The equations for an Einstein manifold, used in general relativity to describe the curvature of
space time

A physical theory involves one or more relationships between various measurable
quantities. Archimedes realized that a ship floats by displacing its mass of water,
Pythagoras understood the relation between the length of a vibrating string and the musical
tone it produces, and how to calculate the length of a rectangle's diagonal. Other examples
include entropy as a measure of the uncertainty regarding the positions and motions of
unseen particles and the quantum mechanical idea that (action and) energy are not
continuously variable.

Sometimes the vision provided by pure mathematical systems can provide clues to how a
physical system might be modeled; e.g., the notion, due to Riemann and others, that space
itself might be curved.

Theoretical advances may consist in setting aside old, incorrect paradigms (e.g., Burning
consists of evolving phlogiston, or Astronomical bodies revolve around the Earth) or may be
an alternative model that provides answers that are more accurate or that can be more

Theoretical physics

108

widely applied.

Physical theories become accepted if they are able to make correct predictions and (few)
incorrect ones. The theory should have, at least as a secondary objective, a certain economy
and elegance (compare to mathematical beauty), a notion sometimes called "Occam's razor"
after the 13th-century English philosopher William of Occam (or Ockham), in which the
simpler of two theories that describe the same matter just as adequately is preferred. (But
conceptual simplicity may mean mathematical complexity.) They are also more likely to be
accepted if they connect a wide range of phenomena. Testing the consequences of a theory
is part of the scientific method.

Physical theories can be grouped into three categories: mainstream theories, proposed
theories and fringe theories.

History

Theoretical physics began at least 2,300 years ago, under the pre-Socratic Greek
philosophers, and continued by Plato; and Aristotle, whose views held sway for a
millennium. In medieval times, during the rise of the universities, the only acknowledged
intellectual disciplines were theology, mathematics, medicine, and law. As the concepts of
matter, energy, space, time and causality slowly began to acquire the form we know today,
other sciences spun off from the rubric of natural philosophy. During the Middle Ages and
Renaissance, the concept of experimental science, the counterpoint to theory, began with
scholars such as Ibn al-Haytham and Francis Bacon. The modern era of theory began
perhaps with the Copernican paradigm shift in astronomy, soon followed by Johannes
Kepler's expressions for planetary orbits, which summarized the meticulous observations of
Tycho Brahe.

The great push toward the modern concept of explanation started with Galileo, one of the
few physicists who was both a consummate theoretician and a great experimentalist. The
analytic geometry and mechanics of Descartes were incorporated into the calculus and
mechanics of Isaac Newton, another theoretician/experimentalist of the highest order.
Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton would extend the
theory of classical mechanics considerably. Each of these individuals picked up the
interactive intertwining of mathematics and physics begun two millennia earlier by
Pythagoras.

Among the great conceptual achievements of the 19th and 20th centuries were the
consolidation of the idea of energy by the inclusion of heat, then electricity and magnetism
and light, and finally mass. The laws of thermodynamics, and especially the introduction of
the singular concept of entropy began to provide a macroscopic explanation for the
properties of matter.

The pillars of modern physics, and perhaps the most revolutionary theories in the history of
physics, have been relativity theory and quantum mechanics. Newtonian mechanics was
subsumed under special relativity and Newton's gravity was given a kinematic explanation
by general relativity. Quantum mechanics led to an understanding of blackbody radiation
and of anomalies in the specific heats of solids — and finally to an understanding of the
internal structures of atoms and molecules.

All of these achievements depended on the theoretical physics as a moving force both to
suggest experiments and to consolidate results — often by ingenious application of existing
mathematics, or, as in the case of Descartes and Newton (with Leibniz), by inventing new

Theoretical physics

109

mathematics. Fourier's studies of heat conduction led to a new branch of mathematics:
infinite, orthogonal series.

Modern theoretical physics attempts to unify theories and explain phenomena in further
attempts to understand the Universe, from the cosmological to the elementary particle
scale. Where experimentation cannot be done, theoretical physics still tries to advance
through the use of mathematical models. Some of their most prominent and well thought
out advancements in this field include:

Prominent theoretical physicists

Famous theoretical physicists include

Christiaan Huyghens (1629-1695)

Isaac Newton (1643-1727)

Leonhard Euler (1707-1783)

Joseph Louis Lagrange (1736-1813)

Pierre-Simon Laplace (1749-1827)

Joseph Fourier (1768-1830)

Nicolas Leonard Sadi Carnot (1796-1842)

William Rowan Hamilton (1805-1865)

Rudolf Clausius (1822-1888)

James Clerk Maxwell (1831-1879)

J. Willard Gibbs (1839-1903)

Ludwig Boltzmann (1844-1906)

Hendrik A. Lorentz (1853-1928)

Henri Poincare (1854-1912)

Nikola Tesla (1856-1943)

Max Planck (1858-1947)

Albert Einstein (1879-1955)

Amalie Emmy Noether (1882-1935)

Niels Bohr (1885-1962)

Max Born (1882-1970)

Erwin Schrodinger (1887-1961)

Louis de Broglie (1892-1987)

Satyendra Nath Bose (1894-1974)

Wolfgang Pauli (1900-1958)

Enrico Fermi (1901-1954)

Werner Heisenberg (1901-1976)

PaulDirac (1902-1984)

Eugene Wigner (1902-1995)

Robert Oppenheimer (1904-1967)

Sin-Itiro Tomonaga (1906-1979)

Hideki Yukawa (1907-1981)

Lev Landau (1908-1967)

John Bardeen (1908-1991)

Anatoly Vlasov (1908-1975)

Nikolay Bogolyubov (1909-1992)

Subrahmanyan Chandrasekhar (1910-1995)

Julian Schwinger (1918-1994)

Theoretical physics

110

Richard Feynman (1918-1988)
Feza Gursey (1921-1992)
Chen Ning Yang (1922- )
Freeman Dyson (1923- )
Gunnar Kallen (1926-1968)
Abdus Salam (1926-1996)
Murray Gell-Mann (1929- )
Riazuddin(1930-)
George Sudarshan (1931- )
Roger Penrose (1931- )
Sheldon Glashow (1932- )
Steven Weinberg (1933- )
C. R. Hagen (1936 -)
Michael Berry (1941- )
Stephen Hawking (1942- )
Alexander Polyakov (1945-)
Gerardus 't Hooft (1946- )
Jacob Bekenstein (1947-)
Bertrand Halperin
Robert Laughlin (1950-)
Edward Witt en (1951- )

Mainstream theories

Mainstream theories (sometimes referred to as central theories) are the body of
knowledge of both factual and scientific views and possess a usual scientific quality of the
tests of repeatability, consistency with existing well-established science and
experimentation. There do exist mainstream theories that are generally accepted theories
based solely upon their effects explaining a wide variety of data, although the detection,
explanation and possible composition are subjects of debate.

Examples

Black hole thermodynamics
Classical mechanics
Condensed matter physics
Dynamics
Dark matter
Electromagnetism
Field theory
Fluid dynamics
Solid mechanics
General relativity
Molecular modeling
Particle physics
Physical cosmology
Quantum computers
Quantum mechanics

Theoretical physics

111

Quantum field theory

Quantum information theory

Quantum electrodynamics

Quantum electrochemistry

Quantum chromodynamics

Solid state physics or Condensed Matter Physics and the electronic structure of materials

Special relativity

Standard Model

Statistical mechanics

Conservation of energy

Thermodynamics

Proposed theories

The proposed theories of physics are usually relatively new theories which deal with the
study of physics which include scientific approaches, means for determining the validity of
models and new types of reasoning used to arrive at the theory. However, some proposed
theories include theories that have been around for decades and have eluded methods of
discovery and testing. Proposed theories can include fringe theories in the process of
becoming established (and, sometimes, gaining wider acceptance). Proposed theories
usually have not been tested.

Examples

Causal Sets

Dark energy or Einstein's Cosmological Constant

Einstein-Rosen Bridge

Emergence

Grand unification theory

Loop quantum gravity

M-theory

String theory

Supersymmetry

Theory of everything

Fringe theories

Fringe theories include any new area of scientific endeavor in the process of becoming
established and some proposed theories. It can include speculative sciences. This includes
physics fields and physical theories presented in accordance with known evidence, and a
body of associated predictions have been made according to that theory.

Some fringe theories go on to become a widely accepted part of physics. Other fringe
theories end up being disproven. Some fringe theories are a form of protoscience and
others are a form of pseudoscience. The falsification of the original theory sometimes leads
to reformulation of the theory.

Theoretical physics

112

Examples

Dynamic theory of gravity
Grand unification theory
Luminiferous aether
Steady state theory
Theory of everything
Metatheory

"Thought Experiments" versus real experiments

Important is also the subtle difference between "Thought Experiments" and real
experiments. The "Thought Experiment" is theoretical, whereas real experiments belong to
"Experimental Physics". A good example for this difference is the paper by Albert Einstein
and coworkers on the EPR effect (1935), which (by the discovery of the consequences of the
possibility of entanglement of quantum-mechanical states) confirms again Einstein's
incredible logical sharpness and creativity, which led him to important conclusions
(important till now, see e.g. quantum cryptography), although the paper contains
philosophical assumptions on a certain reality and locality of physical properties which

were basically wrong 1 J , and could be falsified later-on by real experiments. In any case,
the wrong basic assumptions led Einstein to the erroneous conclusion of a necessity to
complement quantum theory, e.g. by "hidden variables". The falsification of the
above-mentioned assumptions was by definite experiments, e.g. those of Alain Aspect,
based on rigorous theoretical work of the Bell inequalities. Einstein's (t 1955) work was
also rigorous, apart from the underlying basic postulate that quantum mechanics should be
of essentially "classical" nature, as e.g. Newton's mechanics or Maxwell's electrodynamics.
Only after Bell's inequalities (1964) this assumption could be falsified by real experiments.

See also

• Experimental physics

• List of theoretical physicists

References

[1] See e.g. U. Krey, A. Owen, Basic Theoretical Physics -A Concise Overview, Berlin, Springer 2007

Notes

• Note 1: Sometimes mathematical physics and theoretical physics are used synonymously
to refer to the latter.

External links

• Timeline of Theoretical Physics (http://superstringtheory.com/history/history3.html)

• MIT Center for Theoretical Physics (http://ctp.lns.mit.edu/index.html)

• Electronic Journal of Theoretical Physics (EJTP) (http://www.ejtp.com)

• How to Become a Theoretical Physicist by a Nobel Laureate (http://www.phys.uu.nl/
-thooft/theorist.html)

• Theory of longitudinal and transversal angular momentums (http://www.odomann.com)

Dynamical system

113

Dynamical system

The dynamical system concept is a mathematical
formalization for any fixed "rule" which describes
the time dependence of a point's position in its
ambient space. Examples include the mathematical
models that describe the swinging of a clock
pendulum, the flow of water in a pipe, and the
number of fish each spring in a lake.

At any given time a dynamical system has a state
given by a set of real numbers (a vector) which can
be represented by a point in an appropriate state
space (a geometrical manifold). Small changes in
the state of the system correspond to small changes
in the numbers. The evolution rule of the dynamical
system is a fixed rule that describes what future
states follow from the current state. The rule is
deterministic: for a given time interval only one
future state follows from the current state.

The Lorenz attractor is an example of a

non-linear dynamical system. Studying this

system helped give rise to Chaos theory.

Overview

The concept of a dynamical system has its origins in Newtonian mechanics. There, as in
other natural sciences and engineering disciplines, the evolution rule of dynamical systems
is given implicitly by a relation that gives the state of the system only a short time into the
future. (The relation is either a differential equation, difference equation or other time
scale.) To determine the state for all future times requires iterating the relation many
times— each advancing time a small step. The iteration procedure is referred to as solving
the system or integrating the system. Once the system can be solved, given an initial point
it is possible to determine all its future points, a collection known as a trajectory or orbit.

Before the advent of fast computing machines, solving a dynamical system required
sophisticated mathematical techniques and could only be accomplished for a small class of
dynamical systems. Numerical methods executed on computers have simplified the task of
determining the orbits of a dynamical system.

For simple dynamical systems, knowing the trajectory is often sufficient, but most
dynamical systems are too complicated to be understood in terms of individual trajectories.
The difficulties arise because:

The

systems studied may only be known approximately— the parameters of the system

may not be known precisely or terms may be missing from the equations. The
approximations used bring into question the validity or relevance of numerical solutions.
To address these questions several notions of stability have been introduced in the study
of dynamical systems, such as Lyapunov stability or structural stability. The stability of
the dynamical system implies that there is a class of models or initial conditions for which
the trajectories would be equivalent. The operation for comparing orbits to establish
their equivalence changes with the different notions of stability.

Dynamical system

114

• The type of trajectory may be more important than one particular trajectory. Some
trajectories may be periodic, whereas others may wander through many different states
of the system. Applications often require enumerating these classes or maintaining the
system within one class. Classifying all possible trajectories has led to the qualitative
study of dynamical systems, that is, properties that do not change under coordinate
changes. Linear dynamical systems and systems that have two numbers describing a
state are examples of dynamical systems where the possible classes of orbits are
understood.

• The behavior of trajectories as a function of a parameter may be what is needed for an
application. As a parameter is varied, the dynamical systems may have bifurcation points
where the qualitative behavior of the dynamical system changes. For example, it may go
from having only periodic motions to apparently erratic behavior, as in the transition to
turbulence of a fluid.

• The trajectories of the system may appear erratic, as if random. In these cases it may be
necessary to compute averages using one very long trajectory or many different
trajectories. The averages are well defined for ergodic systems and a more detailed
understanding has been worked out for hyperbolic systems. Understanding the
probabilistic aspects of dynamical systems has helped establish the foundations of
statistical mechanics and of chaos.

It was in the work of Poincare that these dynamical systems themes developed.

Basic definitions

A dynamical system is a manifold M called the phase (or state) space and a smooth
evolution function <P t that for any element of t D T, the time, maps a point of the phase
space back into the phase space. The notion of smoothness changes with applications and
the type of manifold. There are several choices for the set T. When T is taken to be the
reals, the dynamical system is called a flow; and if T is restricted to the non-negative reals,
then the dynamical system is a semi-flow. When T is taken to be the integers, it is a cascade
or a map; and the restriction to the non-negative integers is a semi-cascade.

Examples

The evolution function <P t is often the solution of a differential equation of motion

x = v(x) .
The equation gives the time derivative, represented by the dot, of a trajectory x(t) on the
phase space starting at some point x . The vector field v(x) is a smooth function that at
every point of the phase space M provides the velocity vector of the dynamical system at
that point. (These vectors are not vectors in the phase space M, but in the tangent space
TM of the point x.) Given a smooth <2> , an autonomous vector field can be derived from it.

There is no need for higher order derivatives in the equation, nor for time dependence in
v(x) because these can be eliminated by considering systems of higher dimensions. Other
types of differential equations can be used to define the evolution rule:

G(x, ±)=0

is an example of an equation that arises from the modeling of mechanical systems with
complicated constraints.

Dynamical system

115

The differential equations determining the evolution function & t are often ordinary
differential equations: in this case the phase space M is a finite dimensional manifold. Many
of the concepts in dynamical systems can be extended to infinite-dimensional
manifolds— those that are locally Banach spaces— in which case the differential equations
are partial differential equations. In the late 20th century the dynamical system perspective
to partial differential equations started gaining popularity.

Further examples

Logistic map

Double pendulum

Arnold's cat map

Horseshoe map

Baker's map is an example of a chaotic piecewise linear map

Billiards and outer billiards

Henon map

Lorenz system

Circle map

Rossler map

List of chaotic maps

Swinging Atwood's machine

Quadratic map simulation system

Bouncing ball simulation system

Linear dynamical systems

Linear dynamical systems can be solved in terms of simple functions and the behavior of all
orbits classified. In a linear system the phase space is the N-dimensional Euclidean space,
so any point in phase space can be represented by a vector with N numbers. The analysis of
linear systems is possible because they satisfy a superposition principle: if u(t) and w(t)
satisfy the differential equation for the vector field (but not necessarily the initial
condition), then so will u(t) + w(t).

Flows

For a flow, the vector field &(x) is a linear function of the position in the phase space, that

is,

(p(x) = Ax + b 7

with A a matrix, b a vector of numbers and x the position vector. The solution to this system
can be found by using the superposition principle (linearity). The case b ^ with A = is
just a straight line in the direction of b:

<&*(:ri) = Xi + ht.
When b is zero and A ^ the origin is an equilibrium (or singular) point of the flow, that is,

if x = 0, then the orbit remains there. For other initial conditions, the equation of motion is

given by the exponential of a matrix: for an initial point x n ,

$\x Q ) = e tA x .

When b = 0, the eigenvalues of A determine the structure of the phase space. From the
eigenvalues and the eigenvectors of A it is possible to determine if an initial point will

Dynamical system

116

converge or diverge to the equilibrium point at the origin.

The distance between two different initial conditions in the case A *■ will change
exponentially in most cases, either converging exponentially fast towards a point, or
diverging exponentially fast. Linear systems display sensitive dependence on initial
conditions in the case of divergence. For nonlinear systems this is one of the (necessary but
not sufficient) conditions for chaotic behavior.

o o

Linear vector fields and a few trajectories

Maps

A discrete-time, affine dynamical system has the form

Zn+i

Ax n + b

•

with A a matrix and b a vector. As in the continuous case, the change of coordinates x -> x +
(1 - A) b removes the term b from the equation. In the new coordinate system, the origin
is a fixed point of the map and the solutions are of the linear system A n x . The solutions for
the map are no longer curves, but points that hop in the phase space. The orbits are
organized in curves, or fibers, which are collections of points that map into themselves
under the action of the map.

As in the continuous case, the eigenvalues and eigenvectors of A determine the structure of
phase space. For example, if u. is an eigenvector of A, with a real eigenvalue smaller than
one, then the straight lines given by the points along a u., with a □ R, is an invariant curve
of the map. Points in this straight line run into the fixed point.

There are also many other discrete dynamical systems.

Local dynamics

The qualitative properties of dynamical systems do not change under a smooth change of
coordinates (this is sometimes taken as a definition of qualitative): a singular point of the

vector field (a point where v(x)

0) will remain a singular point under smooth

transformations; a periodic orbit is a loop in phase space and smooth deformations of the
phase space cannot alter it being a loop. It is in the neighborhood of singular points and
periodic orbits that the structure of a phase space of a dynamical system can be well
understood. In the qualitative study of dynamical systems, the approach is to show that
there is a change of coordinates (usually unspecified, but computable) that makes the
dynamical system as simple as possible.

Dynamical system

117

Rectification

A flow in most small patches of the phase space can be made very simple. If y is a point
where the vector field v(y) * 0, then there is a change of coordinates for a region around y
where the vector field becomes a series of parallel vectors of the same magnitude. This is
known as the rectification theorem.

The rectification theorem says that away from singular points the dynamics of a point in a
small patch is a straight line. The patch can sometimes be enlarged by stitching several
patches together, and when this works out in the whole phase space M the dynamical
system is integrable. In most cases the patch cannot be extended to the entire phase space.
There may be singular points in the vector field (where v(x) = 0); or the patches may
become smaller and smaller as some point is approached. The more subtle reason is a
global constraint, where the trajectory starts out in a patch, and after visiting a series of
other patches comes back to the original one. If the next time the orbit loops around phase
space in a different way, then it is impossible to rectify the vector field in the whole series
of patches.

Near periodic orbits

In general, in the neighborhood of a periodic orbit the rectification theorem cannot be used.
Poincare developed an approach that transforms the analysis near a periodic orbit to the
analysis of a map. Pick a point x in the orbit y and consider the points in phase space in
that neighborhood that are perpendicular to v(x J. These points are a Poincare section S(y,

x J, of the orbit. The flow now defines a map, the Poincare map F : S -> S, for points starting
in S and returning to S. Not all these points will take the same amount of time to come
back, but the times will be close to the time it takes x .

The intersection of the periodic orbit with the Poincare section is a fixed point of the
Poincare map F. By a translation, the point can be assumed to be at x = 0. The Taylor series
of the map is F(x) = J • x + 0(x 2 ), so a change of coordinates h can only be expected to
simplify F to its linear part

h~ o F o h{x) = J • x .
This is known as the conjugation equation. Finding conditions for this equation to hold has

been one of the major tasks of research in dynamical systems. Poincare first approached it

assuming all functions to be analytic and in the process discovered the non-resonant

condition. If A ,...,A are the eigenvalues of J they will be resonant if one eigenvalue is an

integer linear combination of two or more of the others. As terms of the form A. - ^

(multiples of other eigenvalues) occurs in the denominator of the terms for the function h,

the non-resonant condition is also known as the small divisor problem.

Conjugation results

The results on the existence of a solution to the conjugation equation depend on the
eigenvalues of J and the degree of smoothness required from h. As J does not need to have
any special symmetries, its eigenvalues will typically be complex numbers. When the
eigenvalues of J are not in the unit circle, the dynamics near the fixed point x of F is called
hyperbolic and when the eigenvalues are on the unit circle and complex, the dynamics is
called elliptic.

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118

In the hyperbolic case the Hartman-Grobman theorem gives the conditions for the existence
of a continuous function that maps the neighborhood of the fixed point of the map to the
linear map J • x. The hyperbolic case is also structurally stable. Small changes in the vector
field will only produce small changes in the Poincare map and these small changes will
reflect in small changes in the position of the eigenvalues of J in the complex plane,
implying that the map is still hyperbolic.

The Kolmogorov-Arnold-Moser (KAM) theorem gives the behavior near an elliptic point.

Bifurcation theory

When the evolution map O f (or the vector field it is derived from) depends on a parameter
li, the structure of the phase space will also depend on this parameter. Small changes may
produce no qualitative changes in the phase space until a special value ]i is reached. At
this point the phase space changes qualitatively and the dynamical system is said to have
gone through a bifurcation.

Bifurcation theory considers a structure in phase space (typically a fixed point, a periodic
orbit, or an invariant torus) and studies its behavior as a function of the parameter ]i. At the
bifurcation point the structure may change its stability, split into new structures, or merge
with other structures. By using Taylor series approximations of the maps and an
understanding of the differences that may be eliminated by a change of coordinates, it is
possible to catalog the bifurcations of dynamical systems.

The bifurcations of a hyperbolic fixed point x of a system family F can be characterized by
the eigenvalues of the first derivative of the system DF (x ) computed at the bifurcation
point. For a map, the bifurcation will occur when there are eigenvalues of DF on the unit
circle. For a flow, it will occur when there are eigenvalues on the imaginary axis. For more
information, see the main article on Bifurcation theory.

Some bifurcations can lead to very complicated structures in phase space. For example, the
Ruelle-Takens scenario describes how a periodic orbit bifurcates into a torus and the torus
into a strange attractor. In another example, Feigenbaum period-doubling describes how a
stable periodic orbit goes through a series of period-doubling bifurcations.

Ergodic systems

In many dynamical systems it is possible to choose the coordinates of the system so that the
volume (really a v-dimensional volume) in phase space is invariant. This happens for
mechanical systems derived from Newton's laws as long as the coordinates are the position
and the momentum and the volume is measured in units of (position) x (momentum). The
flow takes points of a subset A into the points O l (A) and invariance of the phase space
means that

vol(/l) = vol(*%4)) .
In the Hamiltonian formalism, given a coordinate it is possible to derive the appropriate

(generalized) momentum such that the associated volume is preserved by the flow. The

volume is said to be computed by the Liouville measure.

In a Hamiltonian system not all possible configurations of position and momentum can be
reached from an initial condition. Because of energy conservation, only the states with the
same energy as the initial condition are accessible. The states with the same energy form
an energy shell Q, a sub-manifold of the phase space. The volume of the energy shell,

Dynamical system

119

computed using the Liouville measure, is preserved under evolution.

For systems where the volume is preserved by the flow, Poincare discovered the recurrence
theorem: Assume the phase space has a finite Liouville volume and let F be a phase space
volume-preserving map and A a subset of the phase space. Then almost every point of A
returns to A infinitely often. The Poincare recurrence theorem was used by Zermelo to
object to Boltzmann's derivation of the increase in entropy in a dynamical system of
colliding atoms.

One of the questions raised by Boltzmann's work was the possible equality between time
averages and space averages, what he called the ergodic hypothesis. The hypothesis states
that the length of time a typical trajectory spends in a region A is vol(A)/vol(Q).

The ergodic hypothesis turned out not to be the essential property needed for the
development of statistical mechanics and a series of other ergodic-like properties were
introduced to capture the relevant aspects of physical systems. Koopman approached the
study of ergodic systems by the use of functional analysis. An observable a is a function that
to each point of the phase space associates a number (say instantaneous pressure,
average height). The value of an observable can be computed at another time by using the
evolution function cp t . This introduces an operator U , the transfer operator,

(U t a)(x)=a{^- t (x)).
By studying the spectral properties of the linear operator U it becomes possible to classify

the ergodic properties of O t . In using the Koopman approach of considering the action of

the flow on an observable function, the finite-dimensional nonlinear problem involving O l

gets mapped into an infinite-dimensional linear problem involving U.

The Liouville measure restricted to the energy surface Q is the basis for the averages
computed in equilibrium statistical mechanics. An average in time along a trajectory is
equivalent to an average in space computed with the Boltzmann factor exp(-(3H). This idea
has been generalized by Sinai, Bowen, and Ruelle (SRB) to a larger class of dynamical
systems that includes dissipative systems. SRB measures replace the Boltzmann factor and
they are defined on attractors of chaotic systems.

Chaos theory

Simple nonlinear dynamical systems and even piecewise linear systems can exhibit a
completely unpredictable behavior, which might seem to be random. (Remember that we
are speaking of completely deterministic systems!). This seemingly unpredictable behavior
has been called chaos. Hyperbolic systems are precisely defined dynamical systems that
exhibit the properties ascribed to chaotic systems. In hyperbolic systems the tangent space
perpendicular to a trajectory can be well separated into two parts: one with the points that
converge towards the orbit (the stable manifold) and another of the points that diverge
from the orbit (the unstable manifold).

This branch of mathematics deals with the long-term qualitative behavior of dynamical
systems. Here, the focus is not on finding precise solutions to the equations defining the
dynamical system (which is often hopeless), but rather to answer questions like "Will the
system settle down to a steady state in the long term, and if so, what are the possible
attractors?" or "Does the long-term behavior of the system depend on its initial condition?"

Note that the chaotic behavior of complicated systems is not the issue. Meteorology has
been known for years to involve complicated— even chaotic— behavior. Chaos theory has

Dynamical system

120

been so surprising because chaos can be found within almost trivial systems. The logistic
map is only a second-degree polynomial; the horseshoe map is piecewise linear.

Geometrical definition

A dynamical system is the tuple (jMj/,T} , with A4 a manifold (locally a Banach space or
Euclidean space), Tthe domain for time (non-negative reals, the integers, ...) and /an
evolution rule t-^f 1 (with t £ T) such that f l is a diffeomorphism of the manifold to itself.
So, f is a mapping of the time-domain Tinto the space of diffeomorphisms of the manifold
to itself. In other terms, f(t) is a diffeomorphism, for every time t in the domain T.

Measure theoretical definition

See main article measure-preserving dynamical system.

A dynamical system may be defined formally, as a measure-preserving transformation of a
sigma-algebra, the quadruplet (A r ; I!,/z,r). Here, X is a set, and 2 is a sigma-algebra onX,
so that the pair (X y E)is a measurable space. ]x is a finite measure on the sigma-algebra, so
that the triplet (-X", E,/z)is a probability space. A map r : X — > Xis said to be
2-measurable if and only if, for every u €= E, one has r~~ l a £ E. A map x is said to
preserve the measure if and only if, for every u C E, one has m( t_ cr ) = / i -( CJ )-
Combining the above, a map x is said to be a measure-preserving transformation of X ,
if it is a map from X to itself, it is Z-measurable, and is measure-preserving. The quadruple
(X^ E, //, t), for such a x, is then defined to be a dynamical system.

The map x embodies the time evolution of the dynamical system. Thus, for discrete
dynamical systems the iterates r n = r o r o . . . o rfor integer n are studied. For continuous
dynamical systems, the map x is understood to be finite time evolution map and the
construction is more complicated.

Examples of dynamical systems

Wikipedia links

Arnold's cat map

Baker's map is an example of a chaotic piecewise linear map

Circle map

Double pendulum

Billiards and Outer Billiards

Henon map

Horseshoe map

Irrational rotation

List of chaotic maps

Logistic map

Lorenz system

Rossler map

Dynamical system

121

External links

• Bouncing Ball

• Mechanical Strings

• Journal of Advanced Research in Dynamical and Control Systems

• Swinging Atwood's Machine (SAM) [ ]

• Interactive applet for the Standard and Henon Maps by A. Luhn

See also

Behavioral modeling
Dynamical systems theory
List of dynamical system topics
Oscillation

People in systems and control
Sarkovskii's theorem
System dynamics
Systems theory

References

[ 1 ] http :// www. drchaos . net/drchaos/bb . html

[2] http://www.drchaos.net/drchaos/string webpage/index. html

[ 3 ] http :// www. i-asr . org/ dynamic . html

[4] http://www.drchaos.net/drchaos/Sam/sam.html

[ 5 ] http ://complexity . xozzox. de/nonlinmappings . html

Further reading

Works providing a broad coverage:

• Ralph Abraham and Jerrold E. Marsden (1978). Foundations of mechanics.
Benjamin-Cummings. ISBN 0-8053-0102-X. (available as a reprint: ISBN 0-201-40840-6)

• Encyclopaedia of Mathematical Sciences (ISSN 0938-0396) has a sub-series on dynamical
systems (http://en.wikipedia.Org/wiki/User:XaosBits/EMP) with reviews of current
research.

• Anatole Katok and Boris Hasselblatt (1996). Introduction to the modern theory of
dynamical systems. Cambridge. ISBN 0-521-57557-5.

• Christian Bonatti, Lorenzo J. Diaz, Marcelo Viana (2005). Dynamics Beyond Uniform
Hyperbolicity: A Global Geometric and Probabilistic Perspective. Springer. ISBN
3-540-22066-6.

• Diederich Hinrichsen and Anthony J. Pritchard (2005). Mathematical Systems Theory I -
Modelling, State Space Analysis, Stability and Robustness. Springer Verlag. ISBN
978-3-540-44125-0.

Introductory texts with a unique perspective:

• V. I. Arnold (1982). Mathematical methods of classical mechanics. Springer-Verlag. ISBN
0-387-96890-3.

• Jacob Palis and Wellington de Melo (1982). Geometric theory of dynamical systems: an
introduction. Springer-Verlag. ISBN 0-387-90668-1.

Dynamical system

122

• David Ruelle (1989). Elements of Differentiable Dynamics and Bifurcation Theory.
Academic Press. ISBN 0-12-601710-7.

• Tim Bedford, Michael Keane and Caroline Series, eds. (1991). Ergodic theory, symbolic
dynamics and hyperbolic spaces. Oxford University Press. ISBN 0-19-853390-X.

• Ralph H. Abraham and Christopher D. Shaw (1992). Dynamics— the geometry of
behavior, 2nd edition. Addison-Wesley. ISBN 0-201-56716-4.

Textbooks

• Steven H. Strogatz (1994). Nonlinear dynamics and chaos: with applications to physics,
biology chemistry and engineering. Addison Wesley. ISBN 0-201-54344-3.

• Kathleen T. Alligood, Tim D. Sauer and James A. Yorke (2000). Chaos. An introduction to
dynamical systems. Springer Verlag. ISBN 0-387-94677-2.

• Morris W. Hirsch, Stephen Smale and Robert Devaney (2003). Differential Equations,
dynamical systems, and an introduction to chaos. Academic Press. ISBN 0-12-349703-5.

Popularizations :

• Florin Diacu and Philip Holmes (1996). Celestial Encounters. Princeton. ISBN
0-691-02743-9.

• James Gleick (1988). Chaos: Making a New Science. Penguin. ISBN 0-14-009250-1.

• Ivar Ekeland (1990). Mathematics and the Unexpected (Paperback). University Of
Chicago Press. ISBN 0-226-19990-8.

• Ian Stewart (1997). Does God Play Dice? The New Mathematics of Chaos. Penguin. ISBN
0140256024.

External links

• A collection of dynamic and non-linear system models and demo applets (http://vlab.
infotech.monash.edu.au/simulations/non-linear/) (in Monash University's Virtual Lab)

• Arxiv preprint server (http://www.arxiv.org/list/math.DS/recent) has daily
submissions of (non-refereed) manuscripts in dynamical systems.

• DSWeb (http://www.dynamicalsystems.org/) provides up-to-date information on
dynamical systems and its applications.

• Encyclopedia of dynamical systems (http://www.scholarpedia.org/article/
EncyclopediaofDynamicalSystems) A part of Scholarpedia — peer reviewed and
written by invited experts.

• Nonlinear Dynamics (http://www.egwald.ca/nonlineardynamics/index.php). Models of
bifurcation and chaos by Elmer G. Wiens

• Oliver Knill (http://www.dynamical-systems.org) has a series of examples of dynamical
systems with explanations and interactive controls.

• Sci. Nonlinear FAQ 2.0 (Sept 2003) (http://amath.colorado.edu/faculty/jdm/
faq-Contents.html) provides definitions, explanations and resources related to nonlinear
science

Online books or lecture notes:

• Geometrical theory of dynamical systems (http://arxiv.org/pdf/math.HO/0111177).
Nils Berglund's lecture notes for a course at ETH at the advanced undergraduate level.

• Dynamical systems (http://www.ams.org/online_bks/coll9/). George D. Birkhoff s
1927 book already takes a modern approach to dynamical systems.

• Chaos: classical and quantum (http://chaosbook.org). An introduction to dynamical
systems from the periodic orbit point of view.

Dynamical system

123

Modeling Dynamic Systems (http://www.embedded.com/2000/0008/0008feat2.htm).
An introduction to the development of mathematical models of dynamic systems.
Learning Dynamical Systems (http://www.cs.brown.edu/research/ai/dynamics/
tutorial/home. html). Tutorial on learning dynamical systems.

Ordinary Differential Equations and Dynamical Systems (http://www.mat.univie.ac.at/
~gerald/ftp/book-ode/). Lecture notes by Gerald Teschl

Research groups:

Dynamical Systems Group Groningen (http://www.math.rug.nl/-broer/), IWI,

University of Groningen.

Chaos @ UMD (http://www-chaos.umd.edu/). Concentrates on the applications of

dynamical systems.

Dynamical Systems (http://www.math.sunysb.edu/dynamics/), SUNY Stony Brook.

Lists of conferences, researchers, and some open problems.

Center for Dynamics and Geometry (http://www.math.psu.edu/dynsys/), Penn State.

Control and Dynamical Systems (http://www.cds.caltech.edu/), Caltech.

Laboratory of Nonlinear Systems (http://lanoswww.epfl.ch/), Ecole Polytechnique

Federale de Lausanne (EPFL).

Center for Dynamical Systems (http://www.math.uni-bremen.de/ids.html/),

University of Bremen

Systems Analysis, Modelling and Prediction Group (http://www.eng.ox.ac.uk/samp/),

University of Oxford

Non-Linear Dynamics Group (http://sd.ist.utl.pt/), Instituto Superior Tecnico,

Technical University of Lisbon

Dynamical Systems (http://www.impa.br/), IMPA, Instituto Nacional de Matematica

Pura e Aplicada.

Nonlinear Dynamics Workgroup (http://ndw.cs.cas.cz/), Institute of Computer

Science, Czech Academy of Sciences.

Simulation software based on Dynamical Systems approach:

FyDiK (http://fydik.kitnarf.cz/)

Bifurcation diagram

124

Bifurcation diagram

In mathematics, particularly in dynamical systems, a bifurcation diagram shows the
possible long-term values (equilibria/fixed points or periodic orbits) of a system as a
function of a bifurcation parameter in the system. It is usual to represent stable solutions
with a solid line and unstable solutions with a dotted line.

Bifurcations in the ID discrete dynamical systems ( maps )

Logistic map

An example is the bifurcation
diagram of the logistic map:

■^ n-\- 1 * ■** n \ J- ^ n ) •

The bifurcation parameter r is shown on the horizontal axis of the plot and the vertical axis
shows the possible long-term population values of the logistic function. Only the stable
solutions are shown here, there are many other unstable solutions which are not shown in
this diagram.

The bifurcation diagram nicely shows the forking of the possible periods of stable orbits
from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation.
The ratio of the lengths of successive intervals between values of r for which bifurcation
occurs converges to the first Feigenbaum constant.

Real quadratic map

For :r n +i =

close all;
clear all;
c=0;
y=0.0;

2
n

C; the code in MATLAB can be written as

hold on
while c < 4

Bifurcation diagram

125

for i=l:100;

y = y.^2 -c; ^converge the iteration

end

for 1=1:29

y = y.^2 - c;

plot(c,y, ' . ' ) ; % plot the converged points

end

c=c+0.01;

end

Symmetry breaking in bifurcation sets

In a dynamical system such as

[j-

Symmetry breaking in pitchfork bifurcation as the parameter
epsilon is varied, epsilon = is the case of symmetric pitchfork

bifurcation.

x + f(x] fi) + eg(x)

which is structurally stable when /i- ^ 0, if a bifurcation diagram is plotted, treating £*as
the bifurcation parameter, but for different values of e, the case e = Ois the symmetric
pitchfork bifurcation. When e ^ 0, we say we have a pitchfork with broken symmetry. This
is illustrated in the animation on the right.

Bifurcation diagram

126

See also

• Bifurcation theory

• Phase portrait

References

• Paul Glendinning, "Stability, Instability and Chaos", Cambridge University Press, 1994.

• Steven Strogatz, "Non-linear Dynamics and Chaos: With applications to Physics, Biology,
Chemistry and Engineering", Perseus Books, 2000.

External links

• Logistic Map Simulation L J . A Java applet simulating the Logistic Map by Yuval Baror.

T21

• The Logistic Map and Chaos

• A small application for drawing the Logistic Map L J

References

[1] http
[2] http
[3] http

//yuval. bar-or.org/index.php?item=4

//www. egwald.com/nonlineardynamics/logisticsmapchaos.php

//home . scarlet, be/kpm/vb/winattract. html

Phase space

In mathematics and physics, a
phase space, introduced by
Willard Gibbs in 1901, is a space
in which all possible states of a
system are represented, with each
possible state of the system
corresponding to one unique point

the

phase

space.

For

i r

7 r

0,10

0,05

0.00

-0,05 --

-0,10

•:

H h

t r

* 1 1 h

■I h

H h

mechanical systems, the phase

space usually consists of all

possible values of position and

momentum variables. A plot of

position and momentum variables

as a function of time is sometimes

called a phase plot or a phase

diagram. Phase diagram, however,

is more usually reserved in the

physical sciences for a diagram showing the various regions of stability of the

thermodynamic phases of a chemical system, which consists of pressure, temperature, and

composition.

0,5

0,6

0.7

0,8

0,9

Phase space of a dynamical system with focal stability.

In a phase space, every degree of freedom or parameter of the system is represented as an
axis of a multidimensional space. For every possible state of the system, or allowed
combination of values of the system's parameters, a point is plotted in the multidimensional

Phase space

127

space. Often this succession of plotted points is analogous to the system's state evolving
over time. In the end, the phase diagram represents all that the system can be, and its
shape can easily elucidate qualities of the system that might not be obvious otherwise. A
phase space may contain very many dimensions. For instance, a gas containing many
molecules may require a separate dimension for each particle's x, y and z positions and
velocities as well as any number of other properties.

In classical mechanics the phase space co-ordinates are the generalized coordinates q. and
their conjugate generalized momenta p.. The motion of an ensemble of systems in this
space is studied by classical statistical mechanics. The local density of points in such
systems obeys Liouville's Theorem, and so can be taken as constant. Within the context of a
model system in classical mechanics, the phase space coordinates of the system at any
given time are composed of all of the system's dynamical variables. Because of this, it is
possible to calculate the state of the system at any given time in the future or the past,
through integration of Hamilton's or Lagrange's equations of motion. Furthermore, because
each point in phase space lies on exactly one phase trajectory, no two phase trajectories
can intersect.

For simple systems, such as a single particle moving in one dimension for example, there
may be as few as two degrees of freedom, (typically, position and velocity), and a sketch of
the phase portrait may give qualitative information about the dynamics of the system, such
as the limit-cycle of the Van der Pol oscillator shown in the diagram.

Here, the horizontal axis gives the
position and vertical axis the
velocity. As the system evolves, its
state follows one of the lines

(trajectories)
diagram.

the

phase

Classic

examples

phase

diagrams from chaos theory are

the

Lorenz

attractor

and

Mandelbrot set.

Quantum mechanics

quantum mechanics,

the

coordinates p and q of phase space
become hermitian operators in a
Hilbert space, but may alternatively retain their classical interpretation, provided functions
of them compose in novel algebraic ways (through Groenewold's 1946 star product). Every
quantum mechanical observable corresponds to a unique function or distribution on phase
space, and vice versa, as specified by Hermann Weyl (1927) and supplemented by John von
Neumann (1931); Eugene Wigner (1932); and, in a grand synthesis, by H J Groenewold
(1946). With Jose Enrique Moyal (1949), these completed the foundations of phase-space
quantization, a logically autonomous reformulation of quantum mechanics. Its modern
abstractions include deformation quantization and geometric quantization.

Phase space

128

Thermodynamics and statistical mechanics

In thermodynamics and statistical mechanics contexts, the term phase space has two
meanings: It is used in the same sense as in classical mechanics. If a thermodynamical
system consists of N particles, then a point in the 6N-dimensional phase space describes
the dynamical state of every particle in that system, as each particle is associated with
three position variables and three momentum variables. In this sense, a point in phase
space is said to be a microstate of the system. N is typically on the order of Avogadro's
number, thus describing the system at a microscopic level is often impractical. This leads us
to the use of phase space in a different sense.

The phase space can refer to the space that is parametrized by the macroscopic states of
the system, such as pressure, temperature, etc. For instance, one can view the
pressure-volume diagram or entropy-temperature diagrams as describing part of this phase
space. A point in this phase space is correspondingly called a macrostate. There may easily
be more than one microstate with the same macrostate. For example, for a fixed
temperature, the system could have many dynamic configurations at the microscopic level.
When used in this sense, a phase is a region of phase space where the system in question is
in, for example, the liquid phase, or solid phase, etc.

Since there are many more microstates than macrostates, the phase space in the first sense
is usually a manifold of much larger dimensions than the second sense. Clearly, many more
parameters are required to register every detail of the system up to the molecular or atomic
scale than to simply specify, say, the temperature or the pressure of the system.

See also

Classical mechanics

Dynamical system

Molecular dynamics

Hamiltonian mechanics

Lagrangian mechanics

Cotangent bundle

Symplectic manifold

Phase plane

Phase space method

Parameter space

Optical Phase Space

State space (controls) for information about state space (similar to phase state) in control

engineering.

State space (physics) for information about state space in physics

State space for information about state space with discrete states in computer science.

Phase portrait

129

Phase portrait

A phase portrait is a geometric
representation of the trajectories
of a dynamical system in the phase
plane. Each set of initial conditions
is representated by a different
curve, or point.

Phase portraits are an invaluable
tool in studying dynamical
systems. They consist of a plot of
typical trajectories in the state
space. This reveals information
such as whether an attractor, a
repellor or limit cycle is present
for the chosen parameter value.

The

concept

topological

equivalence

important

classifying the behaviour of
systems by specifying when two
different phase portraits represent
the same qualitative dynamic
behavior.

A phase portrait graph of a
dynamical system depicts the
system's trajectories (with arrows)
and stable steady states (with
dots) and unstable steady states
(with circles) in a state space. The
axes are of state variables.

0.5

-0.5-

-1

4 6 8 10 12

Potential energy and phase portrait of a simple pendulum. Note
that the x-axis, being angular, wraps onto itself after every 2n

radians.

Plmt Portrait, van (tor PcJE.*qu30orv &p&ib*i = 1

■ 4 ■ I ■ J ■

. . \ \ X \

- . N \ \ \

Phase portrait of van der Pol's equation,

dt 2

Examples

• Simple pendulum see picture
(right) .

• Simple Harmonic Oscillator
where the phase portrait is made up of ellipses centred at the origin, which is a fixed
point.

• Van der Pol oscillator see picture (right).

• Bifurcation diagram

• Mandelbrot set

Phase portrait

130

See also

• Phase space

• Phase plane

• Phase plane method

References

• Steven Strogatz, "Non-linear Dynamics and Chaos: With applications to Physics, Biology,
Chemistry and Engineering", Perseus Books, 2000.

• http://economics.about.eom/od/economicsglossary/g/phase.htm

• http ://www. enm. bris . ac . uk/staff/berndk/chaos web/state . html

Bifurcation theory

Bifurcation theory is the mathematical study of changes in the qualitative or topological
structure of a given family. Examples of such families are the integral curves of a family of
vector fields or, the solutions of a family of differential equations. Most commonly applied
to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth
change made to the parameter values (the bifurcation parameters) of a system causes a
sudden 'qualitative' or topological change in its behaviour. Bifurcations occur in both
continuous systems (described by ODEs, DDEs or PDEs), and discrete systems (described
by maps).

Bifurcation Types

It is useful to divide bifurcations into two principal classes:

• Local bifurcations, which can be analysed entirely through changes in the local stability
properties of equilibria, periodic orbits or other invariant sets as parameters cross
through critical thresholds; and

• Global bifurcations, which often occur when larger invariant sets of the system 'collide'
with each other, or with equilibria of the system. They cannot be detected purely by a
stability analysis of the equilibria (fixed points).

Bifurcation theory

131

Local bifurcations

A local bifurcation occurs when a
parameter change causes the
stability of an equilibrium (or fixed
point) to change. In continuous
systems, this corresponds to the
real part of an eigenvalue of an
equilibrium passing through zero.

discrete

systems

(those

described by maps rather than
ODEs), this corresponds to a fixed
point having a Floquet multiplier
with modulus equal to one. In both

cases,

the

equilibrium

non-hyperbolic at the bifurcation
point. The topological changes in
the phase portrait of the system
can be confined to arbitrarily small
neighbourhoods of the bifurcating
fixed points by moving the
bifurcation parameter close to the
bifurcation point (hence 'local').

More technically, consider the
continuous dynamical system
described by the ODE

0.8 -

0.6 :

0.4

0.2 -

-0.2 -

-0.4

-0.6 =

-0.8 -

-1

-2

a =-0.5

-1.5

-1

0.5
x

0.5

Phase portrait showing Saddle-node bifurcation.

Period-halving bifurcations (L) leading to order, followed by
period doubling bifurcations (R) leading to chaos.

x = f{x 1 X) /:I"xM

ffi

,','

A local bifurcation occurs at (:Tq, Ao)if the Jacobian matrix dj^Aohas an eigenvalue with

zero real part. If the eigenvalue is equal to zero, the bifurcation is a steady state

bifurcation, but if the eigenvalue is non-zero but purely imaginary, this is a Hopf

bifurcation.

For discrete dynamical systems, consider the system

x n-\-l

/(a™ A).

Then a local bifurcation occurs at (^OjAo)if the matrix dj^^ohas an eigenvalue with
modulus equal to one. If the eigenvalue is equal to one, the bifurcation is either a
saddle-node (often called fold bifurcation in maps), transcritical or pitchfork bifurcation. If
the eigenvalue is equal to -1, it is a period-doubling (or flip) bifurcation, and otherwise, it is
a Hopf bifurcation.
Examples of local bifurcations include:

• Saddle-node (fold) bifurcation

• Transcritical bifurcation

• Pitchfork bifurcation

• Period-doubling (flip) bifurcation

• Hopf bifurcation

Bifurcation theory

132

Neimark (secondary Hopf) bifurcation

Global bifurcations

Global bifurcations occur when 'larger' invariant sets, such as periodic orbits, collide with
equilibria. This causes changes in the topology of the trajectories in the phase space which
cannot be confined to a small neighbourhood, as is the case with local bifurcations. In fact,
the changes in topology extend out to an arbitrarily large distance (hence 'global').

Examples of global bifurcations include:

• Homoclinic bifurcation in which a limit cycle collides with a saddle point.

• Heteroclinic bifurcation in which a limit cycle collides with two or more saddle points.

• Infinite-period bifurcation in which a stable node and saddle point simultaneously occur
on a limit cycle.

• Blue sky catastrophe in which a limit cycle collides with a nonhyperbolic cycle.

Global bifurcations can also involve more complicated sets such as chaotic attractors.

Codimension of a bifurcation

The codimension of a bifurcation is the number of parameters which must be varied for the
bifurcation to occur. This corresponds to the codimension of the parameter set for which
the bifurcation occurs within the full space of parameters. Saddle-node bifurcations are the
only generic local bifurcations which are really codimension-one (the others all having
higher codimension). However, often transcritical and pitchfork bifurcations are also often
thought of as codimension-one, because the normal forms can be written with only one
parameter.

An example of a well-studied codimension-two bifurcation is the Bogdanov-Takens
bifurcation.

See also

• Bifurcation diagram

• Catastrophe theory

• Feigenbaum constant

• Phase portrait

References

• Nonlinear dynamics

• Bifurcations and Two Dimensional Flows by Elmer G. Wiens

• Introduction to Bifurcation theory L J by John David Crawford

Bifurcation theory

133

References

[1] http://monet.physik.unibas.ch/~elmer/pendulum/nldyn.htm
[2] http://www.egwald.ca/nonlineardynamics/bifurcations.php
[3] http://prola.aps.org/abstract/RMP/v63/i4/p991_l

Relation algebra

In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra

equipped with an involution called "converse". The motivating example of a relation algebra

x 2
is the algebra 2 of all binary relations on a set X, with R m S interpreted as the usual

composition of binary relations and the converse of R as the inverse relation. Relation

algebra emerged in the 19th century work of Augustus De Morgan and Charles Peirce,

which culminated in the algebraic logic of Ernst Schroder. The present-day purely

equational form or relation algebra was developed by Alfred Tarski and his students,

starting in the 1940s.

Definition

A relation algebra (L, A, v, -«, 0, 1, •, I,\>, <\, ) is an algebraic structure such that
(i) (L, A, v, •, I, >, <) is a residuated Boolean algebra, and

hj , • /"■• V *. W -W V

(ii) the unary operation x satisfies x >I = x = I<x

Since x\>y can be defined in terms of composition and converse as x v •y, and dually x<\y as
x # y '"' , it is not necessary to include > or <\ in the signature, which can therefore be
simplified to (L, A, v, -«, 0, 1, •, I, v ), the more usual form of the signature for relation
algebras. On the other hand x 'is definable as either x>I or I<x, in which case a relation
algebra can have the same signature as a residuated Boolean algebra. With that definition
the axioms become (x>I)>I = x = I<(I<x). But this simply asserts that >I and I< are
involutions. Jonsson and Tsinakis have shown that if either one is an involution then so is
the other and they are then the same operation, namely converse. This leads to a
particularly straightforward definition:

A relation algebra is a residuated Boolean algebra (L, A, v, -«, 0, 1, •, I, >, <) such that
l<\ is an involution.

When x<\y is viewed as a form of quotient of x by y, with I as the corresponding
multiplicative unit, x ' = I<x can be understood as the reciprocal of x by syntactic analogy
with 1/x, a term some authors use synonymously with converse.

Since residuated Boolean algebras are axiomatized with finitely many equations, so are
relation algebras, which therefore form a finitely axiomatized variety called RA, the variety
of relation algebras.

Relation algebra

134

Axioms

The axioms B1-B10 below are adapted from Givant (2006: 283), and were first set out by
Tarski in 1948. This axiomatization is predicated on a relation algebra being an algebraic

structure over some Cartesian square L, having signature QL,v,«, / , I[] of type
02,2,14,00.

L is a Boolean algebra under binary disjunction, v, and unary complementation ()~:

Bl: A V B = B V A

B2A v (B v C) = (A v B) v C

B3: (A~ V B)~ V (A~ V B~)~ = A

This axiomatization of Boolean algebra is due to Huntington (1933).
L is a monoid under binary composition (•) and miliary identity I:

B4: A'(B^C) = (A<B)*C
B5:A«I =A

Unary converse () "is an involution with respect to composition:

B6:A =A

^ T-* V A

B7: (A*B) = B •A

Converse and composition distribute over disjunction

^ a ■--■ T-*

B8: (A\/B) =A MB

B9: (A\/B)»C = (A»C)M(B»C)

BIO is Tarski's equational form of the fact, discovered by Augustus De Morgan, that A*B

S-* -r-fc— ■. S~> T-» '-'

C~ <-> A •C < B~ *-> C-B < A".

BIO: (A •(A«B)")VB" = B"

These axioms are ZFC theorems; for the purely Boolean B1-B3, this fact is trivial. After
each of the following axioms is shown the number of the corresponding theorem in chpt. 3
of Suppes (1960), an exposition of ZFC: B4 27, B5 45, B6 14, B7 26, B8 16, B9 23.

Expressing properties of binary relations in RA

The following table shows how many of the usual properties of binary relations can be
expressed as succinct inequalities or equalities using RA operations. Below, an inequality of
the form A<B is shorthand for a Boolean equation of the form AmB = B.

The most complete set of results of this nature is chpt. C of Carnap (1958), where the
notation is rather distant from those of this entry. Chpt. 3.2 of Suppes (1960) contains
fewer results, but they are presented as ZFC theorems, using a notation that more
resembles that of this entry. Neither Carnap nor Suppes formulate their results using the
RA of this entrv. or in an eauational manner.

jR is

If and only if:

Surjective

R "*R < I

Injective

(R surjective)

R*R < I

1-to-l

R is surjective and injective.

Total or Connected

I < RvR "

Relation algebra

135

Functional

Function

R is functional and total.

1-1 Function

R *R = I and R*R "= I. R is total, functional, and injective.

Reflexive

I < R

Irreflexive

R A I = 0. (0 = I")

Transitive

R*R <R

Preorder

R is reflexive and transitive.

Antisymmetric

R h R"<I

Partial order

R is an antisymmetric preorder.

Total order

R is a total partial order.

Strict partial order

R is transitive and irreflexive.

Strict total order

R is a total strict partial order.

Symmetric

R = R "

Equivalence

R*R "= R. R is a symmetric preorder.

Asymmetric

R * R "

Dense

KaO < (RaO)-(RaO).

Expressive power

The metamathematics of RA are discussed at length in Tarski and Givant (1987), and more
briefly in Givant (2006).

RA consists entirely of equations manipulated using nothing more than uniform
replacement and the substitution of equals for equals. Both rules are wholly familiar from
school mathematics and from abstract algebra generally. Hence RA proofs are carried out
in a manner familiar to all mathematicians, unlike the case in mathematical logic generally.

RA can express any (and up to logical equivalence, exactly the) first-order logic (FOL)
formulas containing no more than three variables. (A given variable can be quantified
multiple times as long as the quantifiers do not nest more than 3 deep.) Surprisingly, this
fragment of FOL suffices to express Peano arithmetic and almost all axiomatic set theories
ever proposed. Hence RA is, in effect, a way of algebraizing nearly all mathematics, while
dispensing with FOL and its connectives, quantifiers, turnstiles, and modus ponens.
Because RA can express Peano arithmetic and set theory, Godel's incompleteness theorems
apply to it; RA is incomplete, incompletable, and undecidable. (N.B. The Boolean algebra
fragment of RA is complete and decidable.)

The representable relation algebras, forming the class RRA, are those relation algebras
isomorphic to some relation algebra comprised of binary relations on some set, and closed
under the standard interpretations of the RA operations. It is easily shown, e.g. using the
method of pseudoelementary classes, that RRA is a quasivariety, that is, axiomatizable by a
universal Horn theory. In 1950, Roger Lyndon proved the existence of equations holding in
RRA that did not hold in RA, that is, the variety generated by RRA is a proper subvariety of
the variety RA. In 1955, Alfred Tarski showed that RRA is itself a variety, which however,
as shown by Donald Monk in 1964, has no finite axiomatization, unlike RA which is finitely

Relation algebra

136

axiomatized by definition. That not every relation algebra is representable is a fundamental
way relation algebras differ from Boolean algebras, which are always representable as sets
of subsets of some set closed under union, intersection, and complement.

Examples

1. Any Boolean algebra can be turned into a relation algebra by interpreting conjunction as
composition (the monoid multiplication •), i.e. x*y is defined as xAy. This interpretation
requires that converse interpret identity (y = y), and that both residuals y\x and x/y
interpret the conditional j/->x (i.e., -\yvx).

2. The motivating example of a relation algebra depends on the definition of a binary

x 2
relation R on a set X as any subset R U X 2 . The power set 2 consisting of all binary

x 2
relations on X is a Boolean algebra. While 2 can be made a relation algebra by taking R 9 S

= KaS as for the preceding example, the standard interpretation of • is instead given by

x(R 9 S)z = Uy-xRySz. That is, the pair (x,z) belongs to the relation R*S just when there exists

y D X such that (x,y) Q R and {y,z) D S. This interpretation uniquely determines R\S to consist

of all pairs (y,z) such that for all x Q X, if xRy then xSz. Dually SIR consists of all pairs {x,y)

such that for all z R X, if yRz then xSz. The translation y = ->(y\-«I) then establishes the

converse R 'ofR as consisting of all pairs (y,x) such that (x,y) U R.

3. An important generalization of the previous example is the power set 2 where E U X 2 is
any equivalence relation on the set X. This is a generalization because X 2 is itself an

equivalence relation, namely the complete relation consisting of all pairs. While 2 is not a

x 2
subalgebra of 2 when E ^ X 2 (since in that case it does not contain the relation X 2 , the top

element 1 being E instead of X 2 ), it is nevertheless made a relation algebra using the same

definitions of the operations. Its importance resides in the definition of a representable

relation algebra as any relation algebra isomorphic to a subalgebra of the relation algebra

2 for some equivalence relation E on some set. Refer to the previous section for more on

the relevant metamathematics.

4. If group sum or product interprets composition, group inverse interprets converse, group
identity interprets I, and if R is a one to one correspondence, so that R " m R = R m R "= I, J
then L is a group as well as a monoid. B4-B7 become well-known theorems of group theory,
so that relation algebra becomes a proper extension of group theory as well as of Boolean
algebra, a fact indicative of its great expressive power.

Historical remarks

DeMorgan founded RA in 1860, but C. S. Peirce took it much further and became
fascinated with its philosophical power. The work of DeMorgan and Peirce came to be
known mainly in the extended and definitive form Ernst Schroder gave it in Vol. 3 of his
Vorlesungen (1890-1905). Principia Mathematica drew strongly on Schroder's RA, but
acknowledged him only as the inventor of the notation. In 1912, Alwin Korselt proved that a

roi

particular formula in which the quantifiers were nested 4 deep had no RA equivalent.
This fact led to a loss of interest in RA until Tarski (1941) began writing about it. His
students have continued to develop RA down to the present day. Tarski returned to RA in
the 1970s with the help of Steven Givant; this collaboration resulted in the monograph
Tarski and Givant (1987), the definitive reference for this subject. For more on the history
of RA, see Maddux (1991, 2006).

Relation algebra

137

Software

• RelMICS / Relational Methods in Computer Science L J maintained by Wolfram Kahl L J

• Carsten Sinz: ARA / An Automatic Theorem Prover for Relation Algebras

[6]

See also

Algebraic logic
Allegory (category theory)
Binary relation
Cartesian product
Cartesian square
Composition of relations

Converse of a relation

Relational calculus

Relational algebra
Relative product of relations
Residuated Boolean algebra
Spatial-temporal reasoning
Theory of relations

Triadic relation

Cylindric algebras
Extension in logic

Involution

Logic of relatives

Relation

Relation construction

Relation reduction

Footnotes

[1] Alfred Tarski (1948) "Abstract: Representation Problems for Relation Algebras," Bulletin oftheAMS 54: 80.

[2] Tarski, A. (1941), p. 87.

[3] Korselt did not publish his finding. It was first published in Leopold Loewenheim (1915) "Uber Moglichkeiten
im Relativkalkul, " Mathematische Annalen 76: 447-470. Translated as "On possibilities in the calculus of
relatives" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press
228-251.

[4] http ://relmics. mcmaster. ca/html/ index. html

[ 5 ] http :// www. cas . mcmaster. ca/ ~ kahl/

[6] http ://www-sr . informatik. uni-tuebingen. de/ ~ sinz/ARA/

References

• Rudolf Carnap (1958) Introdution to Symbolic Logic and its Applications. Dover
Publications.

• Givant, Steven, 2006, "The calculus of relations as a foundation for mathematics/' Journal
of Automated Reasoning 37: 277-322.

• Halmos, P. R., 1960. Naive Set Theory. Van Nostrand.

• Leon Henkin, Alfred Tarski, and Monk, J. D., 1971. Cylindric Algebras, Part 1, and 1985,
Part 2. North Holland.

• Hirsch R., and Hodkinson, I., 2002, Relation Algebra by Games, vol. 147 in Studies in
Logic and the Foundations of Mathematics. Elsevier Science.

• Bjarni Jonsson and Constantine Tsinakis, 1993, "Relation algebras as residuated Boolean
algebras," Algebra Universalis 30: 469-78.

Relation algebra

138

Roger Maddux, 1991, " The Origin of Relation Algebras in the Development and
Axiomatization of the Calculus of Relations, (http://orion.math.iastate.edu/maddux/
papers/Madduxl 991.pdf)" Studia Logica 50(3/4): 421-55.

, 2006. Relation Algebras, vol. 150 in Studies in Logic and the Foundations of

Mathematics. Elsevier Science.

Patrick Suppes, 1960. Axiomatic Set Theory. Van Nostrand. Dover reprint, 1972. Chpt. 3.
Alfred Tarski, 1941, "On the calculus of relations," Journal of Symbolic Logic 6: 73-89.
, and Givant, Steven, 1987. A Formalization of Set Theory without Variables.

Providence RI: American Mathematical Society.

External links

• Yohji AKAMA, Yasuo Kawahara, and Hitoshi Furusawa, " Constructing Allegory from
Relation Algebra and Representation Theorems. (http://nicosia. is. s. u-tokyo.ac.jp/
pub/staff/akama/repr . ps ) "

• Richard Bird, Oege de Moor, Paul Hoogendijk, " Generic Programming with Relations
and Functors, (http://citeseer.ist.psu.edu/bird99generic.html)"

• R.P. de Freitas and Viana, " A Completeness Result for Relation Algebra with Binders.
(http://www.cos.ufrj.br/-naborges/fv02.ps)"

• Peter Jipsen (http://wwwl.chapman.edu/-jipsen/):

• Relation algebras (http://math.chapman.edu/structuresold/files/Relation_algebras.
pdf). In Mathematical structures, (http://math.chapman.edu/cgi-bin/structures) If
there are problems with LaTeX, see an old HTML version here. (http://math.
chapman. edu/cgi-bin/structures.pl?Relation_algebras)

• " Foundations of Relations and Kleene Algebra, (http://math.chapman.edu/-jipsen/
talks/RelMiCS2006/JipsenRAKAtutorial.pdf)"

• " Computer Aided Investigations of Relation Algebras, (http://wwwl.chapman.edu/
-jipsen/ dissertation/)"

• " A Gentzen System And Decidability For Residuated Lattices." (http://citeseer.ist.
psu.edu/337149.html)

• Vaughan Pratt:

• " Origins of the Calculus of Binary Relations, (http://boole.stanford.edu/pub/ocbr.
pdf)" A historical treatment.

• " The Second Calculus of Binary Relations, (http://boole.stanford.edu/pub/scbr.
pdf)"

• Priss, Uta, " An FCA interpretation of Relation Algebra, (http://citeseer.ist.psu.edu/
739624.html)"

• Kahl, Wolfram, (http://www.cas.mcmaster.ca/-kahl/) and Schmidt, Gunther, (http://
ist.unibw-muenchen.de/People/schmidt/) " Exploring (Finite) Relation Algebras Using
Tools Written in Haskell. (http://relmics.mcmaster.ca/-kahl/Publications/TR/
2000-02/)" See homepage (http://relmics.mcmaster.ca/tools/RATH/index.html) of
the whole project.

Category theory

139

Category theory

A category with objects X, Y, Z and

morphisms f, g

In mathematics, category theory deals in an
abstract way with mathematical structures and
relationships between them: it abstracts from sets
and functions to objects linked in diagrams by
morphisms or arrows.

One of the simplest examples of a category (which is

a very important concept in topology) is that of

groupoid, defined as a category whose arrows or

morphisms are all invertible. Categories now appear

in most branches of mathematics and also in some

areas of theoretical computer science where they

correspond to types and mathematical physics

where they can be used to describe vector spaces.

Category theory provides both with a unifying

notion and terminology. Categories were first

introduced by Samuel Eilenberg and Saunders Mac Lane in 1942-45, in connection with

algebraic topology.

Category theory has several faces known not just to specialists, but to other
mathematicians. A term dating from the 1940s, "general abstract nonsense", refers to its
high level of abstraction, compared to more classical branches of mathematics.
Homological algebra is category theory in its aspect of organising and suggesting
manipulations in abstract algebra. Diagram chasing is a visual method of arguing with
abstract "arrows" joined in diagrams. Note that arrows between categories are called
functors, subject to specific defining commutativity conditions; moreover, categorical
diagrams and sequences can be defined as functors (viz. Mitchell, 1965). An arrow between
two functors is a natural transformation when it is subject to certain naturality or
commutativity conditions. Both functors and natural transformations are key concepts in
category theory, or the " real engines" of category theory. To paraphrase a famous sentence
of the mathematicians who founded category theory: 'Categories were introduced to define
functors, and functors were introduced to define natural transformations'. Topos theory is a
form of abstract sheaf theory, with geometric origins, and leads to ideas such as pointless
topology. A topos can also be considered as a specific type of category with two additional
topos axioms.

Background

The study of categories is an attempt to axiomatically capture what is commonly found in
various classes of related mathematical structures by relating them to the
structure-preserving functions between them. A systematic study of category theory then
allows us to prove general results about any of these types of mathematical structures from
the axioms of a category.

Consider the following example. The class Grp of groups consists of all objects having a
"group structure". More precisely, Grp consists of all sets G endowed with a binary
operation satisfying a certain set of axioms. One can proceed to prove theorems about

Category theory

140

groups by making logical deductions from the set of axioms. For example, it is immediately
proved from the axioms that the identity element of a group is unique.

Instead of focusing merely on the individual objects (e.g., groups) possessing a given
structure, category theory emphasizes the morphisms - the structure-preserving mappings
- between these objects; it turns out that by studying these morphisms, we are able to learn
more about the structure of the objects. In the case of groups, the morphisms are the group
homomorphisms. A group homomorphism between two groups "preserves the group
structure" in a precise sense - it is a "process" taking one group to another, in a way that
carries along information about the structure of the first group into the second group. The
study of group homomorphisms then provides a tool for studying general properties of
groups and consequences of the group axioms.

A similar type of investigation occurs in many mathematical theories, such as the study of
continuous maps (morphisms) between topological spaces in topology (the associated
category is called Top), and the study of smooth functions (morphisms) in manifold theory.

If one axiomatizes relations instead of functions, one obtains the theory of allegories.

Functors

Abstracting again, a category is itself a type of mathematical structure, so we can look for
"processes" which preserve this structure in some sense; such a process is called a functor.
A functor associates to every object of one category an object of another category, and to
every morphism in the first category a morphism in the second.

In fact, what we have done is define a category of categories and functors - the objects are
categories, and the morphisms (between categories) are functors.

By studying categories and functors, we are not just studying a class of mathematical
structures and the morphisms between them; we are studying the relationships between
various classes of mathematical structures. This is a fundamental idea, which first surfaced
in algebraic topology. Difficult topological questions can be translated into algebraic
questions which are often easier to solve. Basic constructions, such as the fundamental

group or fundamental groupoid of a topological space, can be expressed as fundamental

functors to the category of groupoids in this way, and the concept is pervasive in algebra
and its applications.

Natural transformation

Abstracting yet again, constructions are often "naturally related" - a vague notion, at first
sight. This leads to the clarifying concept of natural transformation, a way to "map" one
functor to another. Many important constructions in mathematics can be studied in this
context. "Naturality" is a principle, like general covariance in physics, that cuts deeper than
is initially apparent.

Historical notes

In 1942-45, Samuel Eilenberg and Saunders Mac Lane were the first to introduce
categories, functors, and natural transformations as part of their work in topology,
especially algebraic topology. Their work was an important part of the transition from
intuitive and geometric homology to axiomatic homology theory. Eilenberg and Mac Lane
later wrote that their goal was to understand natural transformations; in order to do that,

Category theory

141

functors had to be defined, which required categories.

Stanislaw Ulam, and some writing on his behalf, have claimed that related ideas were
current in the late 1930s in Poland. Eilenberg was Polish, and studied mathematics in
Poland in the 1930s. Category theory is also, in some sense, a continuation of the work of
Emmy Noether (one of Mac Lane's teachers) in formalizing abstract processes; Noether
realized that in order to understand a type of mathematical structure, one needs to
understand the processes preserving that structure. In order to achieve this understanding,
Eilenberg and Mac Lane proposed an axiomatic formalization of the relation between
structures and the processes preserving them.

The subsequent development of category theory was powered first by the computational
needs of homological algebra, and later by the axiomatic needs of algebraic geometry, the
field most resistant to being grounded in either axiomatic set theory or the
Russell-Whitehead view of united foundations. General category theory, an extension of
universal algebra having many new features allowing for semantic flexibility and
higher-order logic, came later; it is now applied throughout mathematics.

Certain categories called topoi (singular topos) can even serve as an alternative to
axiomatic set theory as a foundation of mathematics. These foundational applications of
category theory have been worked out in fair detail as a basis for, and justification of,
constructive mathematics. More recent efforts to introduce undergraduates to categories as
a foundation for mathematics include Lawvere and Rosebrugh (2003) and Lawvere and
Schanuel(1997).

Categorical logic is now a well-defined field based on type theory for intuitionistic logics,
with applications in functional programming and domain theory, where a cartesian closed
category is taken as a non-syntactic description of a lambda calculus. At the very least,
category theoretic language clarifies what exactly these related areas have in common (in
some abstract sense).

Categories, objects and morphisms

A category C consists of the following three mathematical entities:

• A class ob(C), whose elements are called objects;

• A class hom(C), whose elements are called morphisms or maps or arrows. Each
morphism /has a unique source object a and target object b. We write f: a -> b, and we
say "/is a morphism from a to b". We write hom(a, b) (or Hom(a, b), or horn (a, b), or
Mor(a, b), or C(a, b)) to denote the hom-class of all morphisms from a to b.

• A binary operation o t called composition of morphisms, such that for any three objects
a, b, and c, we have hom(a, b) x hom(b, c) -> hom(a, c). The composition of f: a -> b and g
b -> c is written as 9 ° f or gf (some authors write fg), governed by two axioms:

• Associativity: If / : a -> b, g : b -> c and h : c -> d then h o (g o f ) = (h o g) o f t and

• Identity: For every object x, there exists a morphism 1 : x -> x called the identity

morphism for x, such that for every morphism / ' : a -> b, we have l&°/ = / = /°l

From these axioms, it can be proved that there is exactly one identity morphism for every
object. Some authors deviate from the definition just given by identifying each object with
its identity morphism.

Relations among morphisms (such as fg = h) are often depicted using commutative
diagrams, with "points" (corners) representing objects and "arrows" representing

Category theory

142

morphisms.

Properties of morphisms

Some morphisms have important properties. A morphism f : a -» b is:

• a monomorphism (or monic) if fog 1 = fog 2 implies g 1 = g 2 for all morphisms g y g 2 \ x -> a.

• an epimorphism (or epic) if g«of= g of implies 5 = 5 for all morphisms g , g :b -> x.

• an isomorphism if there exists a morphism g : b ^ a with /bg = 1, and gof = 1 .

• an endomorphism if a = b. end(a) denotes the class of endomorphisms of a.

• an automorphism if /is both an endomorphism and an isomorphism, aut(a) denotes the
class of automorphisms of a.

Functors

Functors are structure-preserving maps between categories. They can be thought of as
morphisms in the category of all (small) categories.

A (covariant) functor F from a category C to a category D, written F:C -> D, consists of:

• for each object x in C, an object F(x) in D; and

• for each morphism f : x -* y in C, a morphism F(j) : F(x) -> F(y),

such that the following two properties hold:

• For every object x in C, F(l x ) = l p(x) ;

• For all morphisms f : x -> y and 3 : j; ^ z, f (ff ° /) = -^(ff) F(f).

A contravariant functor F: C ^ D, is like a covariant functor, except that it "turns
morphisms around" ("reverses all the arrows"). More specifically, every morphism f : x -> y
in C must be assigned to a morphism F(f) : F(y) -^ F(x) in D. In other words, a contravariant
functor is a covariant functor from the opposite category C op to D.

Natural transformations and isomorphisms

A natural transformation is a relation between two functors. Functors often describe
"natural constructions" and natural transformations then describe "natural
homomorphisms" between two such constructions. Sometimes two quite different
constructions yield "the same" result; this is expressed by a natural isomorphism between
the two functors.

If F and G are (covariant) functors between the categories C and D, then a natural
transformation from F to G associates to every object x in C a morphism r\ : F(x) -» G(x) in

D such that for every morphism f : x -> y in C, we have r| o F(/) = G(f) o r) ; this means that
the following diagram is commutative:

Category theory

143

The two functors F and G are called naturally isomorphic if there exists a natural
transformation from F to G such that r| is an isomorphism for every object x in C.

Universal constructions, limits, and colimits

Using the language of category theory, many areas of mathematical study can be cast into
appropriate categories, such as the categories of all sets, groups, topologies, and so on.
These categories surely have some objects that are "special" in a certain way, such as the
empty set or the product of two topologies, yet in the definition of a category, objects are
considered to be atomic, i.e., we do not know whether an object A is a set, a topology, or
any other abstract concept - hence, the challenge is to define special objects without
referring to the internal structure of those objects. But how can we define the empty set
without referring to elements, or the product topology without referring to open sets?

The solution is to characterize these objects in terms of their relations to other objects, as
given by the morphisms of the respective categories. Thus, the task is to find universal
properties that uniquely determine the objects of interest. Indeed, it turns out that
numerous important constructions can be described in a purely categorical way. The
central concept which is needed for this purpose is called categorical limit, and can be
dualized to yield the notion of a colimit.

Equivalent categories

It is a natural question to ask: under which conditions can two categories be considered to
be "essentially the same", in the sense that theorems about one category can readily be
transformed into theorems about the other category? The major tool one employs to
describe such a situation is called equivalence of categories, which is given by appropriate
functors between two categories. Categorical equivalence has found numerous applications
in mathematics.

Category theory

144

Further concepts and results

The definitions of categories and functors provide only the very basics of categorical
algebra; additional important topics are listed below. Although there are strong
interrelations between all of these topics, the given order can be considered as a guideline
for further reading.

• The functor category D has as objects the functors from C to D and as morphisms the
natural transformations of such functors. The Yoneda lemma is one of the most famous
basic results of category theory; it describes representable functors in functor categories.

• Duality: Every statement, theorem, or definition in category theory has a dual which is
essentially obtained by "reversing all the arrows". If one statement is true in a category C
then its dual will be true in the dual category C op . This duality, which is transparent at
the level of category theory, is often obscured in applications and can lead to surprising
relationships.

• Adjoint functors: A functor can be left (or right) adjoint to another functor that maps in
the opposite direction. Such a pair of adjoint functors typically arises from a construction
defined by a universal property; this can be seen as a more abstract and powerful view
on universal properties.

Higher-dimensional categories

Many of the above concepts, especially equivalence of categories, adjoint functor pairs, and
functor categories, can be situated into the context of higher-dimensional categories.
Briefly, if we consider a morphism between two objects as a "process taking us from one
object to another", then higher-dimensional categories allow us to profitably generalize this
by considering "higher-dimensional processes".

For example, a (strict) 2-category is a category together with "morphisms between
morphisms", i.e., processes which allow us to transform one morphism into another. We can
then "compose" these "bimorphisms" both horizontally and vertically, and we require a
2-dimensional "exchange law" to hold, relating the two composition laws. In this context,
the standard example is Cat, the 2-category of all (small) categories, and in this example,
bimorphisms of morphisms are simply natural transformations of morphisms in the usual
sense. Another basic example is to consider a 2-category with a single object; these are
essentially monoidal categories. Bicategories are a weaker notion of 2-dimensional
categories in which the composition of morphisms is not strictly associative, but only
associative "up to" an isomorphism.

This process can be extended for all natural numbers n, and these are called n-categories.
There is even a notion of co-category corresponding to the ordinal number go.

Higher-dimensional categories are part of the broader mathematical field of
higher-dimensional algebra,a concept introduced by Ronald Brown. For a conversational

ron

introduction to these ideas, see John Baez, 'A Tale of n-categories' (1996).

Category theory

145

See also

List of category theory topics

Important publications in category theory

Glossary of category theory

Domain theory

Enriched category theory

Higher category theory

Timeline of category theory and related mathematics

Higher-dimensional algebra

Notes

[1] http://planetphysics.org/encyclopedia/FundamentalGroupoidFunctor.html

[2] Note that a morphism that is both epic and monic is not necessarily an isomorphism! For example, in the

category consisting of two objects A and B, the identity morphisms, and a single morphism /from A to B, /is

both epic and monic but is not an isomorphism.
[3] http://math.ucr.edu/home/baez/week73.html

References

Freely available online:

• Adamek, Jifi, Herrlich, Horst, & Strecker, George E. (1990) Abstract and concrete
categories (http://katmat.math.uni-bremen.de/acc/acc.htm). John Wiley & Sons.
ISBN 0-471-60922-6.

• Freyd, Peter J. (1964) Abelian Categories, (http://www.tac.mta.ca/tac/reprints/
articles/3/tr3abs.html) New York: Harper and Row.

• Michael Barr and Charles Wells (1999) Category Theory Lecture Notes. (http://folli.
loria.fr/cds/1999/library/pdf/barrwells.pdf) Based on their book Category Theory for
Computing Science.

• (2002) Toposes, triples and theories, (http://www.cwru.edu/artsci/math/wells/

pub/ttt.html) Revised and corrected translation of Grundlehren der mathematischen
Wissenschaften (Springer-Verlag, 1983).

• Leinster, Tom (2004) Higher operads, higher categories (http://www.maths.gla.ac.uk/
~tl/book.html) (London Math. Society Lecture Note Series 298). Cambridge Univ. Press.

• Schalk, A. and Simmons, H. (2005) An introduction to Category Theory in four easy
movements. (http://www.cs.man.ac.uk/-hsimmons/BOOKS/CatTheory.pdf) Notes

for a course offered as part of the MSc. in Mathematical Logic, Manchester University.

• Turi, Daniele (1996-2001) Category Theory Lecture Notes, (http://www.dcs.ed.ac.uk/
home/dt/CT/categories.pdf) Based on Mac Lane (1998).

• Goldblatt, R (1984) Topoi: the Categorial Analyis of Logic (http://dlxs2. library. Cornell.
edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=Gold010) A
clear introduction to categories, with particular emphasis on the recent applications to
logic.

• A. Martini, H. Ehrig, and D. Nunes (1996) Elements of Basic Category Theory (http://
citeseer.ist.psu.edu/martini96element.html) (Technical Report 96-5, Technical
University Berlin)

Other:

Category theory

146

Awodey, Steven (2006). Category Theory (Oxford Logic Guides 49). Oxford University

Press.

Borceux, Francis (1994). Handbook of categorical algebra (Encyclopedia of Mathematics

and its Applications 50-52). Cambridge Univ. Press.

Freyd, Peter J. & Scedrov, Andre (http://www.cis.upenn.edu/-scedrov/), (1990).

Categories, allegories (North Holland Mathematical Library 39). North Holland.

Hatcher, William S. (1982). The Logical Foundations of Mathematics, 2nd ed. Pergamon.

Chpt. 8 is an idiosyncratic introduction to category theory, presented as a first order

theory.

Lawvere, William, & Rosebrugh, Robert (2003). Sets for mathematics. Cambridge

University Press.

Lawvere, William, & Schanuel, Steve (1997). Conceptual mathematics: a first

introduction to categories. Cambridge University Press.

Mac Lane, Saunders (1998). Categories for the Working Mathematician. 2nd ed.

(Graduate Texts in Mathematics 5). Springer- Verlag.

and Garrett Birkhoff (1967). Algebra. 1999 reprint of the 2nd ed., Chelsea. ISBN

0-8218-1646-2. An introduction to the subject making judicious use of category theoretic

concepts, especially commutative diagrams.

May, Peter (1999). A Concise Course in Algebraic Topology. University of Chicago Press,

ISBN 0-226-51183-9.

Pedicchio, Maria Cristina & Tholen, Walter (2004). Categorical foundations

(Encyclopedia of Mathematics and its Applications 97). Cambridge University Press.

Taylor, Paul (1999). Practical Foundations of Mathematics. Cambridge University Press.

An introduction to the connection between category theory and constructive

mathematics.

Pierce, Benjamin (1991). Basic Category Theory for Computer Scientists. MIT Press.

External links

Chris Hillman, Categorical primer (http://citeseer.ist.psu.edu/cache/papers/cs/

23543/http:zSzzSzwww-aix.gsi.dezSz~appelzSzskriptezSzotherzSzcategories.pdf/

hillman01categorical.pdf), formal introduction to Category Theory.

J. Adamek, H. Herrlich, G. Stecker, Abstract and Concrete Categories-The Joy of Cats

(http://katmat.math.uni-bremen.de/acc/acc.pdf)

Stanford Encyclopedia of Philosophy: " Category Theory (http://plato.stanford.edu/

entries/category- theory/)" ~ by Jean-Pierre Marquis. Extensive bibliography.

Homepage of the Categories mailing list, (http://www.mta.ca/~cat-dist/categories.

html) with extensive resource list.

Baez, John, 1996," The Tale of n-categories. (http://math.ucr.edu/home/baez/week73.

html)" An informal introduction to higher order categories.

The catsters (http://www.youtube.com/user/TheCatsters)" a Youtube channel about

category theory.

Category Theory (http://planetmath.org/?op=getobj&from=objects&

amp;id=5622) on PlanetMath

Categories, Logic and the Foundations of Physics (http://categorieslogicphysics.wikidot.

com/), Webpage dedicated to the use of Categories and Logic in the Foundations of

Physics.

Category theory

147

Interactive Web page (http://www.j-paine.org/cgi-bin/webcats/webcats.php) which
generates examples of categorical constructions in the category of finite sets. Written by
Jocelyn Paine (http://www.j-paine.org/)

Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to
study topological spaces. The basic goal is to find algebraic invariants that classify
topological spaces up to homeomorphism. In many situations this is too much to hope for
and it is more prudent to aim for a more modest goal, classification up to homotopy
equivalence.

Although algebraic topology primarily uses algebra to study topological problems, the
converse, using topology to solve algebraic problems, is sometimes also possible. Algebraic
topology, for example, allows for a convenient proof that any subgroup of a free group is
again a free group.

The method of algebraic invariants

An older name for the subject was combinatorial topology, implying an emphasis on how a
space X was constructed from simpler ones (the modern standard tool for such construction
is the CW-complex). The basic method now applied in algebraic topology is to investigate
spaces via algebraic invariants by mapping them, for example, to groups which have a great
deal of manageable structure in a way that respects the relation of homeomorphism (or
more general homotopy) of spaces. This allows one to recast statements about topological
spaces into statements about groups, which are often easier to prove.

Two major ways in which this can be done are through fundamental groups, or more
generally homotopy theory, and through homology and cohomology groups. The
fundamental groups give us basic information about the structure of a topological space,
but they are often nonabelian and can be difficult to work with. The fundamental group of a
(finite) simplicial complex does have a finite presentation.

Homology and cohomology groups, on the other hand, are abelian and in many important
cases finitely generated. Finitely generated abelian groups are completely classified and
are particularly easy to work with.

Setting in category theory

In general, all constructions of algebraic topology are functorial; the notions of category,
functor and natural transformation originated here. Fundamental groups and homology and
cohomology groups are not only invariants of the underlying topological space, in the sense
that two topological spaces which are homeomorphic have the same associated groups, but
their associated morphisms also correspond — a continuous mapping of spaces induces a
group homomorphism on the associated groups, and these homomorphisms can be used to
show non-existence (or, much more deeply, existence) of mappings.

Algebraic topology

148

Results on homology

Several useful results follow immediately from working with finitely generated abelian
groups. The free rank of the n-th homology group of a simplicial complex is equal to the
n-th Betti number, so one can use the homology groups of a simplicial complex to calculate
its Euler-Poincare characteristic. As another example, the top-dimensional integral
homology group of a closed manifold detects orientability: this group is isomorphic to either
the integers or 0, according as the manifold is orientable or not. Thus, a great deal of
topological information is encoded in the homology of a given topological space.

Beyond simplicial homology, which is defined only for simplicial complexes, one can use the
differential structure of smooth manifolds via de Rham cohomology, or Cech or sheaf
cohomology to investigate the solvability of differential equations defined on the manifold in
question. De Rham showed that all of these approaches were interrelated and that, for a
closed, oriented manifold, the Betti numbers derived through simplicial homology were the
same Betti numbers as those derived through de Rham cohomology. This was extended in
the 1950s, when Eilenberg and Steenrod generalized this approach. They defined homology
and cohomology as functors equipped with natural transformations subject to certain
axioms (e.g., a weak equivalence of spaces passes to an isomorphism of homology groups),
verified that all existing (co)homology theories satisfied these axioms, and then proved that
such an axiomatization uniquely characterized the theory.

Applications of algebraic topology

Classic applications of algebraic topology include:

• The Brouwer fixed point theorem: every continuous map from the unit n-disk to itself has
a fixed point.

• The n-sphere admits a nowhere-vanishing continuous unit vector field if and only if n is
odd. (For n = 2, this is sometimes called the "hairy ball theorem".)

• The Borsuk-Ulam theorem: any continuous map from the n-sphere to Euclidean n-space
identifies at least one pair of antipodal points.

• Any subgroup of a free group is free. This result is quite interesting, because the
statement is purely algebraic yet the simplest proof is topological. Namely, any free
group G may be realized as the fundamental group of a graph X. The main theorem on
covering spaces tells us that every subgroup H of G is the fundamental group of some
covering space Y of X; but every such Y is again a graph. Therefore its fundamental group
H is free.

• Topological combinatorics

Algebraic topology

149

Notable algebraic topologists

Karol Borsuk

Luitzen Egbertus Jan Brouwer

Ronald Brown (mathematician)

Nicolas Bourbaki

Jean Dieudonne

Otto Hermann Kiinneth

Charles Ehresmann

Samuel Eilenberg

Peter Freyd

Alexander Grothendieck

Heinz Hopf

Saunders Mac Lane

J. H. C. Whitehead

Witold Hurewicz

Egbert van Kampen

William Lawvere

J.P. May

Barry Mitchell (mathematician)

Grigori Perelman

Nicolae Popescu

Daniel Quillen

Robert Rosen

Jean-Pierre Serre

Dennis Sullivan

J.A. Zilber

Important theorems in algebraic topology

Borsuk-Ulam theorem
Brouwer fixed point theorem
Cellular approximation theorem
Eilenberg-Zilber theorem
Hurewicz theorem
Kunneth theorem
Poincare duality theorem
Universal coefficient theorem

Van Kampen 1 s theorem

n 1
Generalized van Kampen' s theorems L J

Higher homotopy, generalized van Kampen's theorenr J

Whitehead's theorem

Algebraic topology

150

Further reading

roi

• Allen Hatcher, Algebraic topology. (2002) Cambridge University Press, Cambridge,
xii+544 pp. ISBN 052179160X and ISBN 0521795400

• May, J. P. (1999), http://www.mathMchicago.edu/~may/CONCISE/ConciseRevised. pdf]A
Concise Course in Algebraic Topology, U. Chicago Press, Chicago, http://www.math.
uchicago.edu/~may/CONCISE/ConciseRevised.pdf, retrieved on 2008-09-27. (Section

2.7 provides a category-theoretic presentation of the theorem as a colimit in the category
of groupoids).

• Higher dimensional algebra

• Ronald Brown, Philip J. Higgins and Rafael Sivera. 2008. Higher dimensional, higher
homotopy, generalized van Kampen Theorem., in Nonabelian Algebraic Topology: Higher
homotopy groupoids of filtered spaces. Part III. 512 pp, (Preprint).

• Ronald Brown, Topology and groupoids [6] (2006) Booksurge LLC ISBN 1-4196-2722-8 .

See also

Important publications in algebraic topology

GNUL Textbook on Algebraic Topology vol.1 [7][8]

Higher dimensional algebra

Higher category theory

Van Kampen 1 s theorem

Groupoid

Lie groupoid

Lie algebroid

Grothendieck topology

Serre spectral sequence

Sheaf

Homotopy

Homotopy theory

Fundamental group

Homology theory

Homological algebra

Cohomology theory

K-theory

Algebraic K-theory

TQFT

Homotopy quantum field theory(HQFT)

CW complex

Simplicial complex

Homology complex

Algebroid

Exact sequence

Algebraic topology

151

References

[i] http://pianetphysics.org/encyciopedia/GeneraiizedvanKampenTheoremsHDGVKT.htmi#BHKP

[2] R. Brown, K.A. Hardie, K.H. Kamps and T. Porter, A homotopy double groupoid of a Hausdorff space, Theory

and Applications of Categories. 10 (2002) 71-93. http://www.emis.de/journals/TAC/volumes/! 4/9/ 14-09.

pdf
[3] http://www.math.cornell.edu/~hatcher/AT/ATpage.html
[4] http://www.bangor.ac.uk/~mas010/pdffiles/rbrsbookb-e040609.pdf
[5] Ronald Brown, Philip J. Higgins and Rafael Sivera. Nonabelian Algebraic Topology: Higher homotopy

groupoids of filtered spaces. 512 pp, (Preprint 2009). http://planetphysics.org/?op=getobj&from=books&

id=249
[6] http://www.bangor.ac.Uk/r.brown/topgpds.html
[7] http://en.wikipedia.Org/wiki/User:Bci2/Books/Algebraic_Topology
[8] I.C. Baianu et al. Algebraic Topology, Category Theory and Higher Dimensional Algebra (v.2 and 3.), 485

pages, June 17, 2009 Preprint. http://planetphysics.org/?op=getobj&from=books&id=266

• Bredon, Glen E. (1993),

http://books. google. com/books?id=G74V6UzL_PUC&printsec=frontcover&dq=bredon-\-topology-\-and-
and Geometry, Graduate Texts in Mathematics 139, Springer, ISBN 0-387-97926-3, http:/
/books. google. com/books?id=G74V6UzL_PUC&printsec=frontcover&dq=bredon+
topology+and+geometry&client=firefox-a&sig=4IMV0fFDS / retrieved on 2008-04-01.

• Hatcher, Allen (2002), http://www.math.cornell.edu/~hatcher/AT/ATpage.html\Algebraic
Topology, Cambridge: Cambridge University Press, ISBN 0-521-79540-0, http://www.
math.cornell.edu/~hatcher/AT/ATpage.html. A modern, geometrically flavored
introduction to algebraic topology.

Maunder, C.R.F. (1970), Algebraic Topology, London: Van Nostrand Reinhold, ISBN
0-486-69131-4.

R. Brown and A. Razak, vv Avan Kampen theorem for unions of non-connected spaces,
Archiv. Math. 42 (1984) 85-88.

P.J. Higgins, Categories and groupoids (1971) Van Nostrand-Reinhold. (http://138.73.
27.39/tac/reprints/articles/7/tr7abs.html)

Ronald Brown, Higher dimensional group theory (http://www.bangor.ac. uk/r.brown/
hdaweb2.html) (2007) (Gives a broad view of higher dimensional van Kampen theorems
involving multiple groupoids).

E. R. van Kampen. On the connection between the fundamental groups of some related
spaces. American Journal of Mathematics, vol. 55 (1933), pp. 261-267.
Ronald Brown, Higgins, P.J. and R. Sivera. 2007, vol. 1 N on- Abelian Algebraic Topology
(http://www.bangor.ac.uk/-mas010/nonab-a-t.html), (vol. 2 in preparation);
downloadable PDF: (http://www.bangor.ac.uk/-mas010/nonab-t/partI010604.pdf)
Van Kampen's theorem (http://planetmath.org/?op=getobj&from=objects&
amp;id=3947) on PlanetMath

Van Kampen's theorem result (http://planetmath.org/?op=getobj&from=objects&
amp;id=5576) on PlanetMath

Ronald Brown R, K. Hardie, H. Kamps, T. Porter T.: The homotopy double groupoid of a
Hausdorff space., Theory Appl. Categories, 10:71—93 (2002).

Dylan G.L. Allegretti, Simplicial Sets and van Kampen's Theorem (http://www.math.
uchicago.edu/-may/VIGRE/VIGREREU2008.html) (Discusses generalized versions of
van Kampen's theorem applied to topological spaces and simplicial sets).

Algebraic logic

152

Algebraic logic

In mathematical logic, algebraic logic is the study of logic presented in an algebraic style.

Algebras as models of logics

Algebraic logic treats algebraic structures, often bounded lattices, as models
(interpretations) of certain logics, making logic a branch of order theory.

In algebraic logic:

• Variables are tacitly universally quantified over some universe of discourse. There are no
existentially quantified variables or open formulas;

• Terms are built up from variables using primitive and defined operations. There are no
connectives;

• Formulas, built from terms in the usual way, can be equated if they are logically
equivalent. To express a tautology, equate a formula with a truth value;

• The rules of proof are the substitution of equals for equals, and uniform replacement.
Modus ponens remains valid, but is seldom employed.

In the table below, the left column contains one or more logical or mathematical systems,
and the algebraic structure which are its models are shown on the right in the same row.
Some of these structures are either Boolean algebras or proper extensions thereof. Modal
and other nonclassical logics are typically modeled by what are called "Boolean algebras
with operators."

Algebraic formalisms going beyond first-order logic in at least some respects include:

• Combinatory logic, having the expressive power of set theory;

• Relation algebra, arguably the paradigmatic algebraic logic, can express Peano
arithmetic and most axiomatic set theories, including the canonical ZFC.

logical system

its models

Classical sentential logic

Lindenbaum-Tarski algebra Two-element Boolean algebra

Intuitionistic propositional logic

Heyting algebra

Lukasiewicz logic

MV-algebra

Modal logic K

Modal algebra

Lewis's S4

Interior algebra

Lewis's S5; Monadic predicate logic

Monadic Boolean algebra

First-order logic

Cylindric algebra Polyadic algebra
Predicate functor logic

Set theory

Combinatory logic Relation algebra

Algebraic logic

153

History

On the history of algebraic logic before World War II, see Brady (2000) and
Grattan-Guinness (2000) and their ample references. On the postwar history, see Maddux
(1991) andQuine (1976).

Algebraic logic has at least two meanings:

• The study of Boolean algebra, begun by George Boole, and of relation algebra, begun by
Augustus DeMorgan, extended by Charles Sanders Peirce, and taking definitive form in
the work of Ernst Schroder;

• Abstract algebraic logic, a branch of contemporary mathematical logic.

Perhaps surprisingly, algebraic logic is the oldest approach to formal logic, arguably
beginning with a number of memoranda Leibniz wrote in the 1680s, some of which were
published in the 19th century and translated into English by Clarence Lewis in 1918. But
nearly all of Leibniz's known work on algebraic logic was published only in 1903, after
Louis Couturat discovered it in Leibniz's Nachlass. Parkinson (1966) and Loemker (1969)
translated selections from Couturat's volume into English.

Brady (2000) discusses the rich historical connections between algebraic logic and model
theory. The founders of model theory, Ernst Schroder and Leopold Loewenheim, were
logicians in the algebraic tradition. Alfred Tarski, the founder of set theoretic model theory
as a major branch of contemporary mathematical logic, also:

• Co-discovered Lindenbaum-Tarski algebra;

• Invented cylindric algebra;

• Wrote the 1940 paper that revived relation algebra, and that can be seen as the starting
point of abstract algebraic logic.

Modern mathematical logic began in 1847, with two pamphlets whose respective authors
were Augustus DeMorgan and George Boole. They, and later C.S. Peirce, Hugh Mac Coll,
Frege, Peano, Bertrand Russell, and A. N. Whitehead all shared Leibniz's dream of
combining symbolic logic, mathematics, and philosophy. Relation algebra is arguably the
culmination of Leibniz's approach to logic. With the exception of some writings by Leopold
Loewenheim and Thoralf Skolem, algebraic logic went into eclipse soon after the 1910-13
publication of Principia Mathematica, not to revive until Tarski's 1940 reexposition of
relation algebra.

Leibniz had no influence on the rise of algebraic logic because his logical writings were
little studied before the Parkinson and Loemker translations. Our present understanding of
Leibniz the logician stems mainly from the work of Wolfgang Lenzen, summarized in

Lenzen (2004). L J To see how present-day work in logic and metaphysics can draw
inspiration from, and shed light on, Leibniz's thought, see Zalta (2000).

Algebraic logic

154

See also

Abstract algebraic logic
Algebraic structure
Boolean algebra (logic)
Boolean algebra (structure)
Cylindric algebra
Lindenbaum-Tarski algebra
Mathematical logic
Model theory
Monadic Boolean algebra
Predicate functor logic
Relation algebra
Universal algebra

References

• Brady, Geraldine, 2000. From Peirce to Skolem: A neglected chapter in the history of

roi

logic. North-Holland/Elsevier Science BV: catalog page , Amsterdam, Netherlands, 625
pages.

• Burris, Stanley, 2009. The Algebra of Logic Tradition L . Stanford Encyclopedia of
Philosophy.

• Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots. Princeton Univ. Press.

n l

• Lenzen, Wolfgang, 2004, "Leibniz's Logic L J " in Gabbay, D., and Woods, J., eds.,

Handbook of the History of Logic, Vol. 3: The Rise of Modern Logic from Leibniz to
Frege. North-Holland: 1-84.

• Loemker, Leroy (1969 (1956)), Leibniz: Philosophical Papers and Letters, Reidel.

• Roger Maddux, 1991, "The Origin of Relation Algebras in the Development and
Axiomatization of the Calculus of Relations," Studia Logica 50: 421-55.

• Parkinson, G.H.R., 1966. Leibniz: Logical Papers. Oxford Uni. Press.

• Willard Quine, 1976, "Algebraic Logic and Predicate Functors" in The Ways of Paradox.
Harvard Univ. Press: 283-307.

• Zalta, E. N., 2000, "A (Leibnizian) Theory of Concepts ," Philosophiegeschichte und
logische Analyse / Logical Analysis and History of Philosophy 3: 137-183.

External links

• Stanford Encyclopedia of Philosophy: "Propositional Consequence Relations and
Algebraic Logic - by Ramon Jansana.

References

[ 1 ] http :// www. philosophie . uni-osnabrueck. de/Publikationen%2 Lenzen/Lenzen%2 0Leibniz%2 OLogic . pdf

[2] http://mally.stanford.edu/Papers/leibniz.pdf

[3] http://www.elsevier.com/wps/find/bookdescription.cws_home/621535/description

[4] http://plato.stanford.edu/entries/algebra-logic-tradition/

[5] http://mally.stanford.edu/leibniz.pdf

[6] http ://plato. Stanford. edu/entries/consequence-algebraic/

Quantum logic

155

Quantum logic

In quantum mechanics, quantum logic is a set of rules for reasoning about propositions
which takes the principles of quantum theory into account. This research area and its name
originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who were
attempting to reconcile the apparent inconsistency of classical boolean logic with the facts
concerning the measurement of complementary variables in quantum mechanics, such as
position and momentum.

Quantum logic can be formulated either as a modified version of propositional logic or as a
non-commutative and non-associative many-valued (MV) logic . It has some

properties which clearly distinguish it from classical logic, most notably, the failure of the
distributive law of propositional logic:

p and (q or r) = (p and q) or (p and r),

where the symbols p, q and r are propositional variables. To illustrate why the distributive
law fails, consider a particle moving on a line and let

p = "the particle is moving to the right"

q = "the particle is in the interval [-1,1]"

= "the particle is not in the interval [-1,1]"

then the proposition "q or r" is true, so

p and (q or r) = p

On the other hand, the propositions "p and q" and "p and r" are both false, since they assert
tighter restrictions on simultaneous values of position and momentum than is allowed by
the uncertainty principle. So,

(p and q) or (p and r) = false

Thus the distributive law fails.

Quantum logic has been proposed as the correct logic for propositional inference generally,
most notably by the philosopher Hilary Putnam, at least at one point in his career. This
thesis was an important ingredient in Putnam's paper Is Logic Empirical? in which he
analysed the epistemological status of the rules of propositional logic. Putnam attributes
the idea that anomalies associated to quantum measurements originate with anomalies in
the logic of physics itself to the physicist David Finkelstein. It should be noted, however,
that this idea had been around for some time and had been revived several years earlier by
George Mackey's work on group representations and symmetry.

The more common view regarding quantum logic, however, is that it provides a formalism
for relating observables, system preparation filters and states. In this view, the quantum
logic approach resembles more closely the C*-algebraic approach to quantum mechanics; in
fact with some minor technical assumptions it can be subsumed by it. The similarities of the
quantum logic formalism to a system of deductive logic may then be regarded more as a
curiosity than as a fact of fundamental philosophical importance.

Quantum logic

156

Introduction

In his classic treatise Mathematical Foundations of Quantum Mechanics, John von
Neumann noted that projections on a Hilbert space can be viewed as propositions about
physical observables. The set of principles for manipulating these quantum propositions
was called quantum logic by von Neumann and Birkhoff. In his book (also called
Mathematical Foundations of Quantum Mechanics) G. Mackey attempted to provide a set of
axioms for this propositional system as an orthocomplemented lattice. Mackey viewed
elements of this set as potential yes or no questions an observer might ask about the state
of a physical system, questions that would be settled by some measurement. Moreover
Mackey defined a physical observable in terms of these basic questions. Mackey 1 s axiom
system is somewhat unsatisfactory though, since it assumes that the partially ordered set is
actually given as the orthocomplemented closed subspace lattice of a separable Hilbert
space. Piron, Ludwig and others have attempted to give axiomatizations which do not
require such explicit relations to the lattice of subspaces.

The remainder of this article assumes the reader is familiar with the spectral theory of
self-adjoint operators on a Hilbert space. However, the main ideas can be understood using
the finite-dimensional spectral theorem.

Projections as propositions

The so-called Hamiltonian formulations of classical mechanics have three ingredients:
states, observables and dynamics. In the simplest case of a single particle moving in R , the
state space is the position-momentum space R . We will merely note here that an
observable is some real-valued function f on the state space. Examples of observables are
position, momentum or energy of a particle. For classical systems, the value f{x), that is the
value of /for some particular system state x, is obtained by a process of measurement off.
The propositions concerning a classical system are generated from basic statements of the
form

• Measurement of /yields a value in the interval [a, b] for some real numbers a, b.

It follows easily from this characterization of propositions in classical systems that the
corresponding logic is identical to that of some Boolean algebra of subsets of the state
space. By logic in this context we mean the rules that relate set operations and ordering
relations, such as de Morgan's laws. These are analogous to the rules relating boolean
conjunctives and material implication in classical propositional logic. For technical reasons,
we will also assume that the algebra of subsets of the state space is that of all Borel sets.
The set of propositions is ordered by the natural ordering of sets and has a
complementation operation. In terms of observables, the complement of the proposition {/
> a} is {/< a}.

We summarize these remarks as follows:

• The proposition system of a classical system is a lattice with a distinguished
orthocomplementation operation: The lattice operations of meet and join are respectively
set intersection and set union. The orthocomplementation operation is set complement.
Moreover this lattice is sequentially complete, in the sense that any sequence {£.}. of
elements of the lattice has a least upper bound, specifically the set-theoretic union:

LUB({Ei}) = |J Et.

1=1

Quantum logic

157

In the Hilbert space formulation of quantum mechanics as presented by von Neumann, a
physical observable is represented by some (possibly unbounded) densely-defined
self-adjoint operator A on a Hilbert space H. A has a spectral decomposition, which is a
projection-valued measure E defined on the Borel subsets of R. In particular, for any
bounded Borel function/, the following equation holds:

f(A)= /"/(A)dE(A).

In case f is the indicator function of an interval [a, b], the operator f(A) is a self-adjoint
projection, and can be interpreted as the quantum analogue of the classical proposition

• Measurement of A yields a value in the interval [a, fa].

The propositional lattice of a quantum mechanical system

This suggests the following quantum mechanical replacement for the orthocomplemented
lattice of propositions in classical mechanics. This is essentially Mackey's Axiom VII:

• The orthocomplemented lattice Q of propositions of a quantum mechanical system is the
lattice of closed subspaces of a complex Hilbert space H where orthocomplementation of
Vis the orthogonal complement V°.

Q is also sequentially complete: any pairwise disjoint sequence! V.}. of elements of Q has a

1 l n

least upper bound. Here disjointness of W and W means W is a subspace of W u . The

least upper bound of {V.}. is the closed internal direct sum.

Henceforth we identify elements of Q with self-adjoint projections on the Hilbert space H.

The structure of Q immediately points to a difference with the partial order structure of a
classical proposition system. In the classical case, given a proposition p, the equations

I =pWq

= p A q

have exactly one solution, namely the set-theoretic complement of p. In these equations /
refers to the atomic proposition which is identically true and the atomic proposition which
is identically false. In the case of the lattice of projections there are infinitely many
solutions to the above equations.

Having made these preliminary remarks, we turn everything around and attempt to define
observables within the projection lattice framework and using this definition establish the
correspondence between self-adjoint operators and observables : A Mackey observable is a
countably additive homomorphism from the orthocomplemented lattice of the Borel subsets
of R to Q. To say the mapping cp is a countably additive homomorphism means that for any
sequence {S.}. of pairwise disjoint Borel subsets of R, {cp(S.)}. are pairwise orthogonal
projections and

DO \ oc

v U 5 * =!>(*>■

i=l / z=l

Theorem. There is a bijective correspondence between Mackey observables and
densely-defined self-adjoint operators on H.

This is the content of the spectral theorem as stated in terms of spectral measures.

Quantum logic

158

Statistical structure

Imagine a forensics lab which has some apparatus to measure the speed of a bullet fired
from a gun. Under carefully controlled conditions of temperature, humidity, pressure and
so on the same gun is fired repeatedly and speed measurements taken. This produces some
distribution of speeds. Though we will not get exactly the same value for each individual
measurement for each cluster of measurements, we would expect the experiment to lead to
the same distribution of speeds. In particular, we can expect to assign probability
distributions to propositions such as {a < speed < b}. This leads naturally to propose that
under controlled conditions of preparation, the measurement of a classical system can be
described by a probability measure on the state space. This same statistical structure is
also present in quantum mechanics.

A quantum probability measure is a function P defined on Q with values in [0,1] such that
P(0) = 0, P(I) = 1 and if {£".}. is a sequence of pairwise orthogonal elements of Q then

p X> =E p w-

The following highly non-trivial theorem is due to Andrew Gleason:

Theorem. Suppose H is a separable Hilbert space of complex dimension at least 3. Then for
any quantum probability measure on Q there exists a unique trace class operator S such
that

P(E) = Tt(SE)

for any self-adjoint projection E.

The operator S is necessarily non-negative (that is all eigenvalues are non-negative) and of
trace 1. Such an operator is often called a density operator.

Physicists commonly regard a density operator as being represented by a (possibly infinite)
density matrix relative to some orthonormal basis.

For more information on statistics of quantum systems, see quantum statistical mechanics.

Automorphisms

An automorphism of Q is a bijective mapping cc:Q -> Q which preserves the
orthocomplemented structure of Q, that is

>D \ OC

for any sequence {£.}. of pairwise orthogonal self-adjoint projections. Note that this
property implies monotonicity of a. If P is a quantum probability measure on Q, then E ->
a(E) is also a quantum probability measure on Q. By the Gleason theorem characterizing
quantum probability measures quoted above, any automorphism a induces a mapping a* on
the density operators by the following formula:

Ti(a*{S)E) = Tr{Sa(E)).

The mapping a* is bijective and preserves convex combinations of density operators. This
means

^(nS-L + r 2 S 2 ) = na'(5i) + r 2 a*(S 2 )

whenever 1 = r + r and r , r are non-negative real numbers. Now we use a theorem of
Richard Kadison:

Quantum logic

159

Theorem. Suppose P is a bijective map from density operators to density operators which
is convexity preserving. Then there is an operator U on the Hilbert space which is either
linear or conjugate-linear, preserves the inner product and is such that

j3(S) = USU*

for every density operator S. In the first case we say U is unitary, in the second case U is
anti-unitary.

Remark. This note is included for technical accuracy only, and should not
concern most readers. The result quoted above is not directly stated in Kadison's
paper, but can be reduced to it by noting first that P extends to a positive trace
preserving map on the trace class operators, then applying duality and finally
applying a result of Kadison's paper.

The operator U is not quite unique; if r is a complex scalar of modulus 1, then r U will be
unitary or anti-unitary if U is and will implement the same automorphism. In fact, this is the
only ambiguity possible.

It follows that automorphisms of Q are in bijective correspondence to unitary or anti-unitary
operators modulo multiplication by scalars of modulus 1. Moreover, we can regard
automorphisms in two equivalent ways: as operating on states (represented as density
operators) or as operating on Q.

Non-relativistic dynamics

In non-relativistic physical systems, there is no ambiguity in referring to time evolution
since there is a global time parameter. Moreover an isolated quantum system evolves in a
deterministic way: if the system is in a state S at time t then at time s > t, the system is in a
state F XS). Moreover, we assume

• The dependence is reversible: The operators F are bijective.

• The dependence is homogeneous: F = F .

• The dependence is convexity preserving: That is, each F XS) is convexity preserving.

• The dependence is weakly continuous: The mapping R^ R given by t -> Tr(F XS) E) is

O m L

continuous for every E in Q.

By Kadison's theorem, there is a 1 -parameter family of unitary or anti-unitary operators
{IT} such that

F s>t (S) = u s . t su;

s-t

In fact,

Theorem. Under the above assumptions, there is a strongly continuous 1 -parameter group
of unitary operators {U } such that the above equation holds.

Note that it easily from uniqueness from Kadison's theorem that

U t + s =a(t,s)U t U s
where a(t,s) has modulus 1. Now the square of an anti-unitary is a unitary, so that all the U
are unitary. The remainder of the argument shows that o(t,s) can be chosen to be 1 (by
modifying each U by a scalar of modulus 1.)

Quantum logic

160

Pure states

A convex combinations of statistical states S. and S is a state of the form S = p. S, +p S
where p y p 2 are non-negative and p 1 + p 2 =1. Considering the statistical state of system as
specified by lab conditions used for its preparation, the convex combination S can be
regarded as the state formed in the following way: toss a biased coin with outcome
probabilities p., p 2 and depending on outcome choose system prepared to S. or S

Density operators form a convex set. The convex set of density operators has extreme
points; these are the density operators given by a projection onto a one-dimensional space.
To see that any extreme point is such a projection, note that by the spectral theorem S can
be represented by a diagonal matrix; since S is non-negative all the entries are
non-negative and since S has trace 1, the diagonal entries must add up to 1. Now if it
happens that the diagonal matrix has more than one non-zero entry it is clear that we can
express it as a convex combination of other density operators.

The extreme points of the set of density operators are called pure states. If S is the
projection on the 1 -dimensional space generated by a vector \\f of norm 1 then

Tr(S£) = (£i/#>
for any E in Q. In physics jargon, if

where vj/ has norm 1, then

Tr(SE) = <V>|E|V>>-

Thus pure states can be identified with rays in the Hilbert space H.

The measurement process

Consider a quantum mechanical system with lattice Q which is in some statistical state
given by a density operator S. This essentially means an ensemble of systems specified by a
repeatable lab preparation process. The result of a cluster of measurements intended to
determine the truth value of proposition E, is just as in the classical case, a probability
distribution of truth values T and F. Say the probabilities are p for T and q = 1 - p for F. By

the previous section p = Tr(S E) and q = Tr(S (I-E)).

Perhaps the most fundamental difference between classical and quantum systems is the
following: regardless of what process is used to determine E immediately after the
measurement the system will be in one of two statistical states:

• If the result of the measurement is T

1 ESE.

Tr(ES)

• If the result of the measurement is F

1 (/ - E)S(I - E).

Tr ((I-E) S)

(We leave to the reader the handling of the degenerate cases in which the denominators
may be 0.) We now form the convex combination of these two ensembles using the relative
frequencies p and q. We thus obtain the result that the measurement process applied to a
statistical ensemble in state S yields another ensemble in statistical state:

M E (S) = ESE + (I - E)S(I - E).

Quantum logic

161

We see that a pure ensemble becomes a mixed ensemble after measurement. Measurement,
as described above, is a special case of quantum operations.

Limitations

Quantum logic derived from propositional logic provides a satisfactory foundation for a
theory of reversible quantum processes. Examples of such processes are the covariance
transformations relating two frames of reference, such as change of time parameter or the
transformations of special relativity. Quantum logic also provides a satisfactory
understanding of density matrices. Quantum logic can be stretched to account for some
kinds of measurement processes corresponding to answering yes-no questions about the
state of a quantum system. However, for more general kinds of measurement operations
(that is quantum operations), a more complete theory of filtering processes is necessary.
Such an approach is provided by the consistent histories formalism. On the other hand,
quantum logics derived from MV-logic extend its range of applicability to irreversible
quantum processes and/or 'open' quantum systems.

In any case, these quantum logic formalisms must be generalized in order to deal with
super-geometry (which is needed to handle Fermi-fields) and non-commutative geometry
(which is needed in string theory and quantum gravity theory). Both of these theories use a
partial algebra with an "integral" or "trace". The elements of the partial algebra are not
observables; instead the "trace" yields "greens functions" which generate scattering
amplitudes. One thus obtains a local S-matrix theory (see D. Edwards).

Since around 1978 the Flato school ( see F. Bayen ) has been developing an alternative to
the quantum logics approach called deformation quantization (see Weyl quantization ).

In 2004, Prakash Panangaden described how to capture the kinematics of quantum causal
evolution using System BV, a deep inference logic originally developed for use in structural
proof theory. [6] Alessio Guglielmi, Lutz StraEburger, and Richard Blute have also done
work in this area. [7]

Cited references

[1] http://arxiv.org/PS_cache/quant-ph/pdf/0101/0101028v2.pdf Maria Luisa Dalla Chiara and Roberto

Giuntini. 2008. Quantum Logic, 102 pages PDF
[2] Dalla Chiara, M. L. and Giuntini, R.: 1994, Unsharp quantum logics, Foundations of Physics,, 24, 1161-1177.
[3] http://planetphysics.org/encyclopedia/QuantumLMAlgebraicLogic.html I. C. Baianu. 2009. Quantum LMn

Algebraic Logic.
[4] Georgescu, G. and C. Vraciu. 1970, On the characterization of centered Lukasiewicz algebras., J. Algebra, 16

486-495.
[5] Georgescu, G. 2006, N-valued Logics and Lukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123-
[6] http://cs.bath.ac.Uk/ag/p/BVQuantCausEvol.pdf
[7] http :// alessio. guglielmi. name/res/cos/crt.html#CQE

Quantum logic

162

See also

• Mathematical formulation of quantum mechanics

• Multi-valued logic

• Quasi-set theory

• HPO formalism (An approach to temporal quantum logic)

• Quantum field theory

Literature

• S. Auyang, How is Quantum Field Theory Possible?, Oxford University Press, 1995.

• F.Bayen,M.Flato,C.Fronsdal,A.Lichnerowicz and D.Sternheimer, Deformation theory and

quantization I, JJ, Ann. Phys. (N.Y.),111 (1978) pp. 61-110411-151.

• G. Birkhoff and J. von Neumann, The Logic of Quantum Mechanics, Annals of
Mathematics, vol 37 pp 823-843, 1936.

• D. Cohen, An Introduction to Hilbert Space and Quantum Logic, Springer- Verlag, 1989.
This is a thorough but elementary and well-illustrated introduction, suitable for advanced
undergraduates.

• D. Edwards, The Mathematical Foundations of Quantum Field Theory: Fermions, Gauge
Fields, and Super-symmetry, Part I: Lattice Field Theories, International J. of Theor.
Phys., Vol. 20, No. 7 (1981).

• D. Finkelstein, Matter, Space and Logic, Boston Studies in the Philosophy of Science vol
V, 1969

• A. Gleason, Measures on the Closed Subspaces of a Hilbert Space, Journal of
Mathematics and Mechanics, 1957.

• R. Kadison, Isometries of Operator Algebras, Annals of Mathematics, vol 54 pp 325-338,
1951

• G. Ludwig, Foundations of Quantum Mechanics, Springer-Verlag, 1983.

• G. Mackey, Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, 1963
(paperback reprint by Dover 2004).

• J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University
Press, 1955. Reprinted in paperback form.

• R. Omnes, Understanding Quantum Mechanics, Princeton University Press, 1999. An
extraordinarily lucid discussion of some logical and philosophical issues of quantum
mechanics, with careful attention to the history of the subject. Also discusses consistent
histories.

• N. Papanikolaou, Reasoning Formally About Quantum Systems: An Overview, ACM
SIGACT News, 36(3), pp. 51-66, 2005.

• C. Piron, Foundations of Quantum Physics, W. A. Benjamin, 1976.

• H. Putnam, Is Logic Empirical?, Boston Studies in the Philosophy of Science vol. V, 1969

• H. Weyl, The Theory of Groups and Quantum Mechanics, Dover Publications, 1950.

External links

• Stanford Encyclopedia of Philosophy entry on Quantum Logic and Probability Theory
(http://plato.stanford.edu/entries/qt-quantlog/)

Lukasiewicz logic

163

Lukasiewicz logic

1. REDIRECT Lukasiewicz logic

MV- algebra

In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic
structure with a binary operation © , a unary operation ~ 1 , and the constant 0, satisfying
certain axioms. MV-algebras are models of Lukasiewicz logic; the letters MV refer to
multi-valued logic of Lukasiewicz.

Definitions

An MV-algebra is an algebraic structure {A,©, _, ,0} ? consisting of

• a non-empty set A

• a binary operation © on ^4,

• a unary operation n on A and

• a constant denoting a fixed element of A
which satisfies the following identities:

• {x®y)®z = x®(y®z),

• x(B0 =x,

. x(Dy = y© x y

. s©-t0 = -.(), and

By virtue of the first three axioms, {A, ©., 0} is a commutative monoid. Being defined by
identities, MV-algebras form a variety of algebras. The variety of MV-algebras is a
subvariety of the variety of BL-algebras and contains all Boolean algebras.
An MV-algebra can equivalently be defined (Hajek 1998) as a prelinear commutative

bounded integral residuated lattice {£, A, V, <g> 5 — >, 0, 1} satisfying the additional identity

x V y = (x -> y) -> y.

Examples of MV-algebras

A simple numerical example is A = [0, l],with operations x © y = niin{x + y y l)and
—it = 1 — x. In mathematical fuzzy logic, this MV-algebra is called the standard

MV-algebra, as it forms the standard real-valued semantics of Lukasiewicz logic.

The trivial MV-algebra has the only element and the operations defined in the only

possible way, 0$0 = Oand -i0 = 0.

The two-element MV-algebra is actually the two-element Boolean algebra {0 ? l},with ©

coinciding with Boolean disjunction and ""with Boolean negation.

Other finite linearly ordered MV-algebras are obtained by restricting the universe and

operations of the standard MV-algebra to the set of n + 1 equidistant real numbers

M,2/?i, ...,1}

the operations © and ^ of the standard MV-algebra.

MV- algebra

164

Another important example is Chang's MV-algebra, consisting just of infinitesimals (with
the order type cj) and their co-infinitesimals.

Relation to Lukasiewicz logic

Chang devised MV-algebras to study multi-valued logics, introduced by Jan Lukasiewicz in
1920. In particular, MV-algebras form the algebraic semantics of Lukasiewicz logic, as
described below.

Given an MV-algebra A, an A-valuation is a homomorphism from the algebra of
propositional formulas (in the language consisting of ©>" sand 0) into A. Formulas mapped
to 1 (or ■~ I 0) for all A-valuations are called A-tautologies. If the standard MV-algebra over
[0,1] is employed, the set of all [0,l]-tautologies determines so-called infinite-valued
Lukasiewicz logic.

Chang's (1958, 1959) completeness theorem states that any MV-algebra equation holding in
the standard MV-algebra over the interval [0,1] will hold in every MV-algebra.
Algebraically, this means that the standard MV-algebra generates the variety of all
MV-algebras. Equivalently, Chang's completeness theorem says that MV-algebras
characterize infinite-valued Lukasiewicz logic, defined as the set of [0,l]-tautologies.

The way the [0,1] MV-algebra characterizes all possible MV-algebras parallels the
well-known fact that identities holding in the two-element Boolean algebra hold in all
possible Boolean algebras. Moreover, MV-algebras characterize infinite-valued Lukasiewicz
logic in a manner analogous to the way that Boolean algebras characterize classical
bivalent logic (see Lindenbaum-Tarski algebra).

References

• Chang, C. C. (1958) "Algebraic analysis of many-valued logics," Transactions of the
American Mathematical Society 88: 476-490.

• (1959) "A new proof of the completeness of the Lukasiewicz axioms," Transactions of

the American Mathematical Society 88: 74-80.

Cignoli, R. L. O., D'Ottaviano, I. M. L., Mundici, D. (2000) Algebraic Foundations of

Many-valued Reasoning. Kluwer.

Di Nola A., Lettieri A. (1993) "Equational characterization of all varieties of

MV-algebras," Journal of Algebra 221: 123-131.

Hajek, Petr (1998) Metamathematics of Fuzzy Logic. Kluwer.

External links

n l
• Stanford Encyclopedia of Philosophy: "Many-valued logic L J " ~ by Siegfried Gottwald.

References

[ 1 ] http ://plato. Stanford. edu/entries/logic-manyvalued/

165

Biophysical Chemistry Applications

Molecular evolution

Molecular evolution is the process of evolution at the scale of DNA, RNA, and proteins.
Molecular evolution emerged as a scientific field in the 1960s as researchers from
molecular biology, evolutionary biology and population genetics sought to understand
recent discoveries on the structure and function of nucleic acids and protein. Some of the
key topics that spurred development of the field have been the evolution of enzyme
function, the use of nucleic acid divergence as a "molecular clock" to study species
divergence, and the origin of non-functional or junk DNA. Recent advances in genomics,
including whole-genome sequencing, high-throughput protein characterization, and
bioinformatics have led to a dramatic increase in studies on the topic. In the 2000s, some of
the active topics have been the role of gene duplication in the emergence of novel gene
function, the extent of adaptive molecular evolution versus neutral drift, and the
identification of molecular changes responsible for various human characteristics especially
those pertaining to infection, disease, and cognition.

Principles of molecular evolution

Mutations

Mutations are permanent, transmissible changes to the genetic material (usually DNA or
RNA) of a cell. Mutations can be caused by copying errors in the genetic material during
cell division and by exposure to radiation, chemicals, or viruses, or can occur deliberately
under cellular control during the processes such as meiosis or hypermutation. Mutations
are considered the driving force of evolution, where less favorable (or deleterious)
mutations are removed from the gene pool by natural selection, while more favorable (or
beneficial) ones tend to accumulate. Neutral mutations do not affect the organism's
chances of survival in its natural environment and can accumulate over time, which might
result in what is known as punctuated equilibrium; the modern interpretation of classic
evolutionary theory.

Causes of change in allele frequency

There are three known processes that affect the survival of a characteristic; or, more
specifically, the frequency of an allele (variant of a gene):

• Genetic drift describes changes in gene frequency that cannot be ascribed to selective
pressures, but are due instead to events that are unrelated to inherited traits. This is
especially important in small mating populations, which simply cannot have enough
offspring to maintain the same gene distribution as the parental generation.

• Gene flow or Migration: or gene admixture is the only one of the agents that makes
populations closer genetically while building larger gene pools.

• Selection, in particular natural selection produced by differential mortality and fertility.
Differential mortality is the survival rate of individuals before their reproductive age. If

Molecular evolution

166

they survive, they are then selected further by differential fertility - that is, their total
genetic contribution to the next generation. In this way, the alleles that these surviving
individuals contribute to the gene pool will increase the frequency of those alleles. Sexual
selection, the attraction between mates that results from two genes, one for a feature
and the other determining a preference for that feature, is also very important.

Molecular study of phylogeny

Molecular systematics is a product of the traditional field of systematics and molecular
genetics. It is the process of using data on the molecular constitution of biological
organisms' DNA, RNA, or both, in order to resolve questions in systematics, i.e. about their
correct scientific classification or taxonomy from the point of view of evolutionary biology.

Molecular systematics has been made possible by the availability of techniques for DNA
sequencing, which allow the determination of the exact sequence of nucleotides or bases in
either DNA or RNA. At present it is still a long and expensive process to sequence the
entire genome of an organism, and this has been done for only a few species. However, it is
quite feasible to determine the sequence of a defined area of a particular chromosome.
Typical molecular systematic analyses require the sequencing of around 1000 base pairs.

The driving forces of evolution

Depending on the relative importance assigned to the various forces of evolution, three

perspectives provide evolutionary explanations for molecular evolution. 1 J

While recognizing the importance of random drift for silent mutations, selectionists
hypotheses argue that balancing and positive selection are the driving forces of molecular
evolution. Those hypotheses are often based on the broader view called panselectionism,
the idea that selection is the only force strong enough to explain evolution, relaying random

drift and mutations to minor roles. J

Neutralists hypotheses emphasize the importance of mutation, purifying selection and
random genetic drift. ] The introduction of the neutral theory by Kimura, ^ quickly
followed by King and Jukes' own findings, lead to a fierce debate about the relevance of
neodarwinism at the molecular level. The Neutral theory of molecular evolution states that
most mutations are deleterious and quickly removed by natural selection, but of the
remaining ones, the vast majority are neutral with respect to fitness while the amount of
advantageous mutations is vanishingly small. The fate of neutral mutations are governed by
genetic drift, and contribute to both nucleotide polymorphism and fixed differences
between species.

Mutationists hypotheses emphasize random drift and biases in mutation patterns.
Sueoka was the first to propose a modern mutationist view. He proposed that the variation
in GC content was not the result of positive selection, but a consequence of the GC
mutational pressure. - 1

Molecular evolution

167

Related fields

An important area within the study of molecular evolution is the use of molecular data to
determine the correct biological classification of organisms. This is called molecular
systematics or molecular phylogenetics.

Tools and concepts developed in the study of molecular evolution are now commonly used
for comparative genomics and molecular genetics, while the influx of new data from these
fields has been spurring advancement in molecular evolution.

Key researchers in molecular evolution

Some researchers who have made key contributions to the development of the field

• Motoo Kimura — Neutral theory

• Masatoshi Nei — Adaptive evolution

• Walter M. Fitch — Phylogenetic reconstruction

• Walter Gilbert — RNA world

• Joe Felsenstein — Phylogenetic methods

• Susumu Ohno — Gene duplication

• John H. Gillespie — Mathematics of adaptation

Journals and societies

Journals dedicated to molecular evolution include Molecular Biology and Evolution, Journal
of Molecular Evolution, and Molecular Phylogenetics and Evolution. Research in molecular
evolution is also published in journals of genetics, molecular biology, genomics,

systematics, or evolutionary biology. The Society for Molecular Biology and Evolution L J
publishes the journal "Molecular Biology and Evolution" and holds an annual international
meeting.

See also

History of molecular evolution

Chemical evolution

Evolution

Genetic drift

E. coli long-term evolution experiment

Evolutionary physiology

Neutral theory of molecular evolution

Nucleotide diversity

Parsimony

Population genetics

Selection

Genomic organization
Horizontal gene transfer

Human evolution

Molecular clock

Comparative phylogenetics

Molecular evolution

168

Further reading

• Li, W.-H. (2006). Molecular Evolution. Sinauer. ISBN 0878934804.

• Lynch, M. (2007). The Origins of Genome Architecture. Sinauer. ISBN 0878934847.

References

[I] Graur, D. and Li, W.-H. (2000). Fundamentals of molecular evolution. Sinauer.

[2] Gillespie, J. H (1991). The Causes of Molecular Evolution. Oxford University Press, New York. ISBN

0-19-506883-1.
[3] Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge. ISBN

0-521-23109-4.
[4] Kimura, Motoo (1968).

"http://www2.hawaii.edu/~khayes/Journal Club/fall2006/Kimura_l 968_Nature.pdf (Evolutionary rate at the

molecular level". Nature 217: 624-626. doi: 10.1038/217624a0 (http://dx.doi.org/10.1038/217624a0). http:/

/www2. hawaii.edu/~khayes/Journal_Club/fall2006/Kimura_l 968_Nature.pdf.
[5] King, J.L. and Jukes, T.H. (1969).

"http://www.blackwellpublishing.com/ridley/classictexts/king.pdflNon-Darwinian Evolution". Science 164:

788-798. doi: 10.1126/science.l64.3881.788 (http://dx.doi.org/10.1126/science.164.3881.788). PMID

5767777. http ://w ww . blackwellpublishing . com/ridley/class ic texts/king . p df .
[6] Nachman M. (2006). "Detecting selection at the molecular level" in: Evolutionary Genetics: concepts and case

studies, pp. 103-118.
[7] The nearly neutral theory expanded the neutralist perspective, suggesting that several mutations are nearly

neutral, which means both random drift and natural selection is relevant to their dynamics.
[8] Ohta, T (1992). "The nearly neutral theory of molecular evolution". Annual Review of Ecology and Systematics

23: 263-286. doi: 10. 1146/annurev.es. 23. 110192. 001403 (http://dx.doi.org/10.1146/annurev.es.23.

110192.001403).
[9] Nei, M. (2005). "Selectionism and Neutralism in Molecular Evolution". Molecular Biology and Evolution

22(12): 2318-2342. doi: 10.1093/molbev/msi242 (http://dx.doi.org/10.1093/molbev/msi242). PMID

16120807.
[10] Sueoka, N. (1964). "On the evolution of informational macromolecules". in In: Bryson, V. and Vogel, H.J..

Evolving genes and proteins. Academic Press, New-York. pp. 479-496.

[II] http://www.smbe.org

Radiobiology

169

Radiobiology

Radiobiology (or radiation biology) is the interdisciplinary field of science that studies the
biological effects of ionizing and non-ionizing radiation of the whole electromagnetic
spectrum, including radioactivity (alpha, beta and gamma), x-rays, ultraviolet radiation,
visible light, microwaves, radio wave, low-frequency radiation (such as used in alternate
electric transmission, ultrasound thermal radiation (heat), and related modalities. It is a
subset of biophysics.

Areas of interest

The interactions between electromagnetic fields (EMF) and organisms can be studied at
several levels:

radiation physics

radiation chemistry

molecular and cell biology

molecular genetics

cell death and apoptosis

dose modifying agents

protection and repair mechanisms

tissue responses to radiation

high and low-level electromagnetic radiation and health

specific absorption rates of organisms

radiation poisoning

radiation oncology (radiation therapy in cancer)

Radiobiology of non-ionizing radiation includes:

Bioelectromagnetics
Magnetobiology

Radiation sources for radiobiology

Radiobiology experiments typically make use of a radiation source which could be:

• An isotopic source, typically Cs or Co.

• A particle accelerator generating high energy protons, electrons or charged ions.
Biological samples can be irradiated using either a broad, uniform beam or using a
microbeam, focused down to cellular or subcellular sizes.

• A UV lamp.

Radiobiology

170

See also

Radiosensitivity

Radiology

Nuclear medicine

Radioactivity in biology

Radiophobia

Cell survival curve

Relative biological effectiveness

Notes

• WikiMindMap [1]

[1] http://www.wikimindmap.org/viewmap.php?wiki=en.wikipedia.org&topic=radiobiology

References and further reading

• Eric Hall, Radiobiology for the Radiobiologist. 2006. Lippincott

• G.Gordon Steel, "Basci Clinical Radiobiology". 2002. Hodder Arnold.

• The Institute for Radiation Biology at the Helmholtz-Center for Environmental Health
(http://www.helmholtz-muenchen.de/en/isb/isb-home/index.html)

Weblinks

• The Institute for Radiation Biology at the Helmholtz-Center for Environmental Health
(http://www.helmholtz-muenchen.de/en/isb/isb-home/index.html)

Photosynthesis

171

Photosynthesis

Photosynthesis LocJ is

process that converts carbon

dioxide

into

organic

compounds, especially sugars,

using

the

energy

from

Photosynthesis

sunlight. 1 J
occurs in plants, algae, and
many species of Bacteria, but
not in Archaea. Photosynthetic

called

since

Composite image showing the global distribution of photosynthesis,
including both oceanic phytoplankton and land vegetation.

organisms are

photo autotrophs,

allows them to create their

own food. In plants, algae and

cyanobacteria photosynthesis

uses carbon dioxide and

water, releasing oxygen as a

waste product. Photosynthesis is vital for life on Earth. As well as maintaining the normal

level of oxygen in the atmosphere, nearly all life either depends on it directly as a source of

energy, or indirectly as the ultimate source of the energy in their food. ^ * The amount of

energy trapped by photosynthesis is immense, approximately 100 terawatts: J which is

about six times larger than the power consumption of human civilization. ] As well as

energy, photosynthesis is also the source of the carbon in all the organic compounds within

organisms' bodies. In all, photosynthetic organisms convert around 100,000,000,000 tonnes

rci

of carbon into biomass per year. 1 J

Although photosynthesis can occur in different ways in different species, some features are
always the same. For example, the process always begins when energy from light is
absorbed by proteins called photosynthetic reaction centers that contain chlorophylls. In
plants, these proteins are held inside organelles called chloroplasts, while in bacteria they
are embedded in the plasma membrane. Some of the light energy gathered by chlorophylls
is stored in the form of adenosine triphosphate (ATP). The rest of the energy is used to
remove electrons from a substance such as water. These electrons are then used in the
reactions that turn carbon dioxide into organic compounds. In plants, algae and
cyanobacteria this is done by a sequence of reactions called the Calvin cycle, but different
sets of reactions are found in some bacteria, such as the reverse Krebs cycle in Chlorobium.
Many photosynthetic organisms have adaptations that concentrate or store carbon dioxide.
This helps reduce a wasteful process called photorespiration that can consume part of the
sugar produced during photosynthesis.

Photosynthesis

172

Photosynthesis evolved early in the
evolutionary history of life, when
all forms of life on Earth were

microorganisms .

The

first

photosynthetic organisms probably

[6]

evolved about 3500

million

years ago, and used hydrogen or
hydrogen sulfide as sources of
electrons, rather than water. J
Cyanobacteria appeared later,
around 3000 million years ago,
and changed the Earth forever
when they began to oxygenate the
atmosphere, beginning about 2400
L J million years ago. This new
atmosphere allowed the evolution

of complex life such as protists.

n 1 1
Eventually, about 550 L J million

years ago, one of these protists

formed a symbiotic relationship

with a cyanobacterium, producing

the ancestor of the plants and

algae. The chloroplasts in

modern plants are the descendants

symbiotic

these

ancient

cyanobacteria.

Plants, algae, many bacteria
(Autotrophs)

anic

Carbon dioxide

compounds

Oxygen

Animals, fungi,
many bacteria

(Heterotrophs)

Overview of cycle between autotrophs and heterotrophs.
Photosynthesis is the main means by which plants, algae and
many bacteria produce organic compounds and oxygen from

carbon dioxide and water (green arrow).

Overview

Photosynthetic organisms are photoautotrophs, which
means that they are able to synthesize food directly
from carbon dioxide using energy from light. However,
not all organisms that use light as a source of energy
carry out photosynthesis, since photoheterotrophs use
organic compounds, rather than carbon dioxide, as a
source of carbon [ ] . In plants, algae and
cyanobacteria, photosynthesis releases oxygen. This is
called oxygenic photosynthesis. Although there are
some differences between oxygenic photosynthesis in
plants, algae and cyanobacteria, the overall process is
quite similar in these organisms. However, there are
some types of bacteria that carry out anoxygenic
photosynthesis, which consumes carbon dioxide but
does not release oxygen.

H,0

■■■•■

Light reactions

sugar

Photosynthesis splits water to liberate
O and fixes CO into sugar

Photosynthesis

173

Carbon dioxide is converted into sugars in a process called carbon fixation. Carbon fixation
is a redox reaction, so photosynthesis needs to supply both a source of energy to drive this
process, and also the electrons needed to convert carbon dioxide into carbohydrate, which
is a reduction reaction. In general outline, photosynthesis is the opposite of cellular
respiration, where glucose and other compounds are oxidized to produce carbon dioxide,
water, and release chemical energy. However, the two processes take place through a
different sequence of chemical reactions and in different cellular compartments.

The general equation for photosynthesis is therefore:

C0 2 + 2 H 2 A + photons

(CH 2 0) n + 2 + 2A

carbon dioxide + electron donor + light energy -» carbohydrate + oxygen + oxidized
electron donor

Since water is most often used as the electron donor in oxygenic photosynthesis, the
equation for this process is:

C0 2 + 2 H 2 + photons

carbon dioxide + water + light energy -» carbohydrate + oxygen + water

Other processes (e.g. as used by microbial species in Mono Lake, California) substitute
other compounds (such as arsenite) for water in the electron-supply role; the microbes use
sunlight to oxidize arsenite to arsenates ] The equation for this reaction is:

(CH 2 0) n + H 2 + 2

(AsO 3 ~) + C0 2 + photons

CO + (As0 4 3 ") [14]

carbon dioxide + arsenite + light energy -> arsenate + carbon monoxide (used to build
other compounds in subsequent reactions)

Photosynthesis occurs in two stages. In the first stage, light-dependent reactions or light
reactions capture the energy of light and use it to make the energy-storage molecules ATP
and NADPH. During the second stage, the light-independent reactions use these products
to capture and reduce carbon dioxide.

Photosynthetic membranes and organelles

The proteins that gather light for
photosynthesis are embedded within
cell membranes. The simplest way
these are arranged is in photosynthetic

bacteria, where these proteins are held
within the plasma membrane.
However, this membrane may be
tightly-folded into cylindrical sheets

called thylakoids,

[16]

or bunched up

into

round

vesicles

called

ri7i

intracytoplasmic membranes. These
structures can fill most of the interior
of a cell, giving the membrane a very
large surface area and therefore
increasing the amount of light that the
bacteria can absorb. J

®
®

Chloroplast ultrastructure: 1. outer membrane 2.

intermembrane space 3. inner membrane (1+2+3:
envelope) 4. stroma (aqueous fluid) 5. thylakoid lumen
(inside of thylakoid) 6. thylakoid membrane 7. granum
(stack of thylakoids) 8. thylakoid (lamella) 9. starch 10.
ribosome 11. plastidial DNA 12. plastoglobule (drop of

lipids)

Photosynthesis

174

In plants and algae, photosynthesis takes place in organelles called chloroplasts. A
chloroplast has both an inner and an outer phospholipid membrane. Between these two
layers is the intermembrane space. A typical plant cell contains about 10 to 100
chloroplasts. Within the stroma are stacks of thylakoids, the sub-organelles which are the
site of photosynthesis. The thylakoids are arranged in stacks called grana (singular:
granum). A thylakoid has a flattened disk shape. Inside it is an empty area called the
thylakoid space or lumen. The thylakoid membrane contains many integral and peripheral
membrane proteins. The proteins complexes which contain special pigments absorbing light
energy are called photosystems.

Plants absorb light primarily using the pigment chlorophyll, which is the reason that most
plants have a green color. Besides chlorophyll, plants also use pigments such as carotenes
and xanthophylls. ] Algae also use chlorophyll, but various other pigments are present as
phycocyanin, carotenes, and xanthophylls in green algae, phycoerythrin in red algae
(rhodophytes) and fucoxanthol in brown algae and diatoms resulting in a wide variety of
colors.

These pigments are embedded in plants and algae in special antenna-proteins. In such
proteins all the pigments are ordered to work well together. Such a protein is also called a
light-harvesting complex.

Although all cells in the green parts of a plant have chloroplasts, most of the energy is
captured in the leaves. The cells in the interior tissues of a leaf, called the mesophyll, can
contain between 450,000 and 800,000 chloroplasts for every square millimeter of leaf. The
surface of the leaf is uniformly coated with a water-resistant waxy cuticle that protects the
leaf from excessive evaporation of water and decreases the absorption of ultraviolet or blue
light to reduce heating. The transparent epidermis layer allows light to pass through to the
palisade mesophyll cells where most of the photosynthesis takes place.

chloroplast stroma

ferredoxin-NADP reductase

Light reactions

In the light reactions, one molecule of the

pigment chlorophyll absorbs one photon

and loses one electron. This electron is

passed to a modified form of chlorophyll

called pheophytin, which passes the

electron to a quinone molecule, allowing

the start of a flow of electrons down an

electron transport chain that leads to the

ultimate reduction of NADP to NADPH. In

addition, this creates a proton gradient

across the chloroplast membrane; its

dissipation is used by ATP synthase for the

concomitant synthesis of ATP. The chlorophyll molecule regains the lost electron from a

water molecule through a process called photolysis, which releases a dioxygen (O )

molecule. The overall equation for the light-dependent reactions under the conditions of

non-cyclic electron flow in green plants is:

oxygen-evolving complex

thylakoid lumen

Light-dependent reactions of photosynthesis at the

thylakoid membrane

2 H 2 + 2 NADP + + 2 ADP + 2P. + light

2 NADPH + 2H T +2 ATP + O

Photosynthesis

175

Not all wavelengths of light can support photosynthesis. The photosynthetic action
spectrum depends on the type of accessory pigments present. For example, in green plants,
the action spectrum resembles the absorption spectrum for chlorophylls and carotenoids
with peaks for violet-blue and red light. In red algae, the action spectrum overlaps with the
absorption spectrum of phycobilins for blue-green light, which allows these algae to grow in
deeper waters that filter out the longer wavelengths used by green plants. The
non-absorbed part of the light spectrum is what gives photosynthetic organisms their color
(e.g., green plants, red algae, purple bacteria) and is the least effective for photosynthesis
in the respective organisms.

Z scheme

In plants, light-dependent reactions occur
in the thylakoid membranes of the
chloroplasts and use light energy to
synthesize

ATP

and

NAD PH.

The

light-dependent reaction has two forms:
cyclic and non-cyclic. In the non-cyclic
reaction, the photons are captured in the
light-harvesting antenna complexes of
photosystem II by chlorophyll and other
accessory pigments (see diagram at right).
When a chlorophyll molecule at the core of
the photosystem II reaction center obtains
sufficient excitation energy from the
adjacent antenna pigments, an electron is

stroma

thylaKoid
membrane

accessory pigments

photosystem

primary pigment reaction
centre P700 or P680

thylakoid

A Photosystem: A light-harvesting cluster of
photosynthetic pigments present in the thylakoid

membrane of chloroplasts.

transferred

the

primary

HjO

OxypcncvoKinj! i-omplH

l/K>i-2H

HHiCimytiL-ni II

"Cytochrome Ivf complex
vj \\ir ^^ PLivUievanin

Membrane bourul iron Mil fur ptuicins

m m ^ 2NAW-2IT

■»», ■

2c NADP L rvJuwki^c

reric^uAin

1*1 ■ I. ^vurtu I

The "Z scheme"

electron-acceptor molecule, Pheophytin,
through a process called photoinduced
charge separation. These electrons are
shuttled through an electron transport
chain, the so called Z-scheme shown in the
diagram, that initially functions to generate
a chemiosmotic potential across the
membrane. An ATP synthase enzyme uses the chemiosmotic potential to make ATP during
photophosphorylation, whereas NADPH is a product of the terminal redox reaction in the
Z-scheme. The electron enters the Photosystem I molecule. The electron is excited due to
the light absorbed by the photosystem. A second electron carrier accepts the electron,
which again is passed down lowering energies of electron acceptors. The energy created by
the electron acceptors is used to move hydrogen ions across the thylakoid membrane into
the lumen. The electron is used to reduce the co-enzyme NADP, which has functions in the
light-independent reaction. The cyclic reaction is similar to that of the non-cyclic, but
differs in the form that it generates only ATP, and no reduced NADP (NADPH) is created.
The cyclic reaction takes place only at photosystem I. Once the electron is displaced from
the photosystem, the electron is passed down the electron acceptor molecules and returns
back to photosystem I, from where it was emitted, hence the name cyclic reaction.

Photosynthesis

176

Water photolysis

The NADPH is the main reducing agent in chloroplasts, providing a source of energetic
electrons to other reactions. Its production leaves chlorophyll with a deficit of electrons
(oxidized), which must be obtained from some other reducing agent. The excited electrons
lost from chlorophyll in photosystem I are replaced from the electron transport chain by
plastocyanin. However, since photosystem II includes the first steps of the Z-scheme, an
external source of electrons is required to reduce its oxidized chlorophyll a molecules. The
source of electrons in green-plant and cyanobacterial photosynthesis is water. Two water
molecules are oxidized by four successive charge-separation reactions by photosystem II to
yield a molecule of diatomic oxygen and four hydrogen ions; the electron yielded in each
step is transferred to a redox-active tyrosine residue that then reduces the photoxidized
paired-chlorophyll a species called P680 that serves as the primary (light-driven) electron
donor in the photosystem II reaction center. The oxidation of water is catalyzed in
photosystem II by a redox-active structure that contains four manganese ions and a calcium
ion; this oxygen-evolving complex binds two water molecules and stores the four oxidizing
equivalents that are required to drive the water-oxidizing reaction. Photosystem II is the
only known biological enzyme that carries out this oxidation of water. The hydrogen ions
contribute to the transmembrane chemiosmotic potential that leads to ATP synthesis.
Oxygen is a waste product of light-dependent reactions, but the majority of organisms on
Earth use oxygen for cellular respiration, including photosynthetic organisms. ] [ ^

Oxygen and photosynthesis

Light-independent reactions

The Calvin Cycle

In the Light-independent or dark reactions the enzyme RuBisCO captures CO from the
atmosphere and in a process that requires the newly formed NADPH, called the
Calvin-Benson Cycle, releases three-carbon sugars, which are later combined to form
sucrose and starch. The overall equation for the light-independent reactions in green plants

is: [19]

3 C0 2 + 9 ATP + 6 NADPH + 6 H + -» C 3 H 6 3 -phosphate + 9 ADP + 8P.+ 6 NADP + +
3H 2

Photosynthesis

177

To be more specific, carbon fixation
produces an intermediate product, which is
then converted to the final carbohydrate
products. The carbon skeletons produced
by photosynthesis are then variously used
to form other organic compounds, such as
the building material cellulose, as
precursors for lipid and amino acid
biosynthesis, or as a fuel in cellular
respiration. The latter occurs not only in
plants but also in animals when the energy
from plants gets passed through a food
chain.

Cental MeHlwfic Pathway*

-j- ^ fiibulnwlrS-bbphoiphdTe

ATP

X*Xx.

Ribulose 5-phospKaie

Cuban d I a rid*

RuBisCO

Phase 1:

Carbon Fixation

^ (-mulMflabolk Pathway*

3-phoipHoglycef.sie

Phase 3:

Regeneration of
Ribulose

Phase 2:

Reduction

tjlyceraldehyde 3- phosphate
(G3P)

ATP

1 3-bKphoiplicMjlyce-raie
+

Onlral Metabolic Pathway*

Central Metabolic Pathways

Overview of the Calvin cycle and carbon fixation

The fixation or reduction of carbon dioxide
is a process in which carbon dioxide
combines with a five-carbon sugar, ribulose 1,5-bisphosphate (RuBP), to yield two
molecules of a three-carbon compound, glycerate 3-phosphate (GP), also known as
3-phosphoglycerate (PGA). GP, in the presence of ATP and NADPH from the
light-dependent stages, is reduced to glyceraldehyde 3-phosphate (G3P). This product is
also referred to as 3-phosphoglyceraldehyde (PGAL) or even as triose phosphate. Triose is a
3-carbon sugar (see carbohydrates). Most (5 out of 6 molecules) of the G3P produced is
used to regenerate RuBP so the process can continue (see Calvin-Benson cycle). The 1 out
of 6 molecules of the triose phosphates not "recycled" often condense to form hexose
phosphates, which ultimately yield sucrose, starch and cellulose. The sugars produced
during carbon metabolism yield carbon skeletons that can be used for other metabolic
reactions like the production of amino acids and lipids.

C. and CL photosynthesis and CAM

In hot and dry conditions, plants will close
their stomata to prevent loss of water.
Under these conditions, CO will decrease,
and dioxygen gas, produced by the light
reactions of photosynthesis, will increase in
the leaves, causing an increase of
photorespiration by the oxygenase activity
of ribulose-l,5-bisphosphate

carboxylase/oxygenase and decrease in
carbon fixation. Some plants have evolved

mechanisms

increase

the

concentration in the leaves under these
conditions.

C. plants chemically fix carbon dioxide in
the cells of the mesophyll by adding it to

Carbon dioxide

Phosphoenol pyruvate
{PEP}

phyll Cell j

Bundle Sheath Cell

Pyrophosphate

Calvin Cycle

Carbon dioxide

Inorganic Phosphate

Overview of C4 carbon fixation

Photosynthesis

178

the three-carbon molecule phosphoenolpyruvate (PEP), a reaction catalyzed by an enzyme
called PEP carboxylase and which creates the four-carbon organic acid, oxaloacetic acid.
Oxaloacetic acid or malate synthesized by this process is then translocated to specialized
bundle sheath cells where the enzyme, rubisco, and other Calvin cyle enzymes are located,
and where CO released by decarboxylation of the four-carbon acids is then fixed by rubisco
activity to the three-carbon sugar 3-Phosphoglyceric acids. The physical separation of
rubisco from the oxygen-generating light reactions reduces photorespiration and increases

["221

C0 2 fixation and thus photosynthetic capacity of the leaf. C 4 plants can produce more

sugar than C plants in conditions of high light and temperature. Many important crop
plants are C. plants including maize, sorghum, sugarcane, and millet. Plants lacking
PEP-carboxylase are called C plants because the primary carboxylation reaction, catalyzed
by rubisco, produces the three-carbon sugar 3-phosphoglyceric acids directly in the
Calvin-Benson Cycle.

Xerophytes such as cacti and most succulents also use PEP carboxylase to capture carbon
dioxide in a process called Crassulacean acid metabolism (CAM). In contrast to C4
metabolism, which physically separates the CO fixation to PEP from the Calvin cycle, CAM
only temporally separates these two processes. CAM plants have a different leaf anatomy
than C. plants, and fix the CO at night, when their stomata are open. CAM plants store the
CO mostly in the form of malic acid via carboxylation of phosphoenolpyruvate to
oxaloacetate, which is then reduced to malate. Decarboxylation of malate during the day
releases C0 2 inside the leaves thus allowing carbon fixation to 3-phosphoglycerate by
rubisco.

Order and kinetics

The overall process of photosynthesis takes place in four stages. The first, energy transfer

— 15

in antenna chlorophyll takes place in the femtosecond [1 femtosecond (fs) = 10, s] to

— 12

picosecond [1 picosecond (ps) = 10 s] time scale. The next phase, the transfer of
electrons in photochemical reactions, takes place in the picosecond to nanosecond time
scale [1 nanosecond (ns) = 10~ s]. The third phase, the electron transport chain and ATP
synthesis, takes place on the microsecond [1 microsecond (jis) = 10~ s] to millisecond [1
millisecond (ms) = 10~ s) time scale. The final phase is carbon fixation and export of stable
products and takes place in the millisecond to second time scale. The first three stages
occur in the thylakoid membranes.

Efficiency

Plants usually convert light into chemical energy with a photosynthetic efficiency of
3-6%. J Actual plants' photosynthetic efficiency varies with the frequency of the light
being converted, light intensity, temperature and proportion of CO in the atmosphere, and
can vary from 0.1% to 8%. By comparison, solar panels convert light into electric energy
at a photosynthetic efficiency of approximately 6-20% for mass-produced panels, and up to
41% in a research laboratory. 1 J

Photosynthesis

179

Evolution

Early photosynthetic systems, such as those from green
and purple sulfur and green and purple non-sulfur
bacteria, are thought to have been anoxygenic, using
various molecules as electron donors. Green and purple
sulfur bacteria are thought to have used hydrogen and
sulfur as an electron donor. Green nonsulfur bacteria
used various amino and other organic acids. Purple
nonsulfur bacteria used a variety of non-specific
organic molecules. The use of these molecules is
consistent with the geological evidence that the
atmosphere was highly reduced at that time.

Fossils of what are thought to be filamentous photosynthetic organisms have been dated at
3.4 billion years old. [26]

The main source of oxygen in the atmosphere is oxygenic photosynthesis, and its first
appearance is sometimes referred to as the oxygen catastrophe. Geological evidence
suggests that oxygenic photosynthesis, such as that in cyanobacteria, became important
during the Paleoproterozoic era around 2 billion years ago. Modern photosynthesis in
plants and most photosynthetic prokaryotes is oxygenic. Oxygenic photosynthesis uses
water as an electron donor which is oxidized to molecular dioxygen (O ) in the
photosynthetic reaction center.

Symbiosis and the origin of chloroplasts

Several groups of animals have formed symbiotic relationships with photosynthetic algae.
These are most common in corals, sponges and sea anemones, possibly due to these
animals having particularly simple body plans and large surface areas compared to their
volumes. In addition, a few marine molluscs Elysia viridis and Elysia chlorotica also
maintain a symbiotic relationship with chloroplasts that they capture from the algae in their
diet and then store in their bodies. This allows the molluscs to survive solely by
photosynthesis for several months at a time. ] c ] Some of the genes from the plant cell
nucleus have even been transferred to the slugs, so that the chloroplasts can be supplied
with proteins that they need to survive. ]

An even closer form of symbiosis may explain the origin of chloroplasts. Chloroplasts have
many similarities with photosynthetic bacteria including a circular chromosome,
prokaryotic-type ribosomes, and similar proteins in the photosynthetic reaction center. ]
] The endosymbiotic theory suggests that photosynthetic bacteria were acquired (by
endocytosis) by early eukaryotic cells to form the first plant cells. Therefore, chloroplasts
may be photosynthetic bacteria that adapted to life inside plant cells. Like mitochondria,
chloroplasts still possess their own DNA, separate from the nuclear DNA of their plant host
cells and the genes in this chloroplast DNA resemble those in cyanobacteria. DNA in
chloroplasts codes for redox proteins such as photosynthetic reaction centers. The CoRR
Hypothesis proposes that this Co-location is required for Redox Regulation.

Photosynthesis

180

Cyanobacteria and the evolution of photosynthesis

The biochemical capacity to use water as the source for electrons in photosynthesis evolved
once, in a common ancestor of extant cyanobacteria. The geological record indicates that
this transforming event took place early in Earth's history, at least 2450-2320 million years
ago (Ma), and possibly much earlier. J Available evidence from geobiological studies of
Archean (>2500 Ma) sedimentary rocks indicates that life existed 3500 Ma, but the
question of when oxygenic photosynthesis evolved is still unanswered. A clear
paleontological window on cyanobacterial evolution opened about 2000 Ma, revealing an
already-diverse biota of blue-greens. Cyanobacteria remained principal primary producers
throughout the Proterozoic Eon (2500-543 Ma), in part because the redox structure of the
oceans favored photoautotrophs capable of nitrogen fixation. Green algae joined
blue-greens as major primary producers on continental shelves near the end of the
Proterozoic, but only with the Mesozoic (251-65 Ma) radiations of dinoflagellates,
coccolithophorids, and diatoms did primary production in marine shelf waters take modern
form. Cyanobacteria remain critical to marine ecosystems as primary producers in oceanic
gyres, as agents of biological nitrogen fixation, and, in modified form, as the plastids of
marine algae.

Discovery

Although some of the steps in photosynthesis are still not completely understood, the
overall photosynthetic equation has been known since the 1800s.

Jan van Helmont began the research of the process in the mid-1 600s when he carefully
measured the mass of the soil used by a plant and the mass of the plant as it grew. After
noticing that the soil mass changed very little, he hypothesized that the mass of the
growing plant must come from the water, the only substance he added to the potted plant.
His hypothesis was partially accurate— much of the gained mass also comes from carbon
dioxide as well as water. However, this was a signaling point to the idea that the bulk of a
plant's biomass comes from the inputs of photosynthesis, not the soil itself.

Joseph Priestley, a chemist and minister, discovered that when he isolated a volume of air
under an inverted jar, and burned a candle in it, the candle would burn out very quickly,
much before it ran out of wax. He further discovered that a mouse could similarly "injure"
air. He then showed that the air that had been "injured" by the candle and the mouse could
be restored by a plant.

In 1778, Jan Ingenhousz, court physician to the Austrian Empress, repeated Priestley's
experiments. He discovered that it was the influence of sunlight on the plant that could
cause it to rescue a mouse in a matter of hours.

In 1796, Jean Senebier, a Swiss pastor, botanist, and naturalist, demonstrated that green
plants consume carbon dioxide and release oxygen under the influence of light. Soon
afterwards, Nicolas-Theodore de Saussure showed that the increase in mass of the plant as
it grows could not be due only to uptake of CO , but also to the incorporation of water. Thus
the basic reaction by which photosynthesis is used to produce food (such as glucose) was
outlined.

Cornells Van Niel made key discoveries explaining the chemistry of photosynthesis. By
studying purple sulfur bacteria and green bacteria he was the first scientist to demonstrate
that photosynthesis is a light-dependent redox reaction, in which hydrogen reduces carbon

Photosynthesis

181

dioxide.

Robert Emerson discovered two light reactions by testing plant productivity using different
wavelengths of light. With the red alone, the light reactions were suppressed. When blue
and red were combined, the output was much more substantial. Thus, there were two
photosystems, one aborbing up to 600 nm wavelengths, the other up to 700. The former is
known as PSII, the latter is PSI. PSI contains only chlorophyll a, PSII contains primarily
chlorophyll a with most of the available chlorophyll b, among other pigments.

Further experiments to prove that the oxygen developed during the photosynthesis of green
plants came from water, were performed by Robert Hill in 1937 and 1939. He showed that
isolated chloroplasts give off oxygen in the presence of unnatural reducing agents like iron
oxalate, ferricyanide or benzoquinone after exposure to light. The Hill reaction is as follows:

2 H 2 + 2 A + (light, chloroplasts) -> 2 AH 2 + 2

where A is the electron acceptor. Therefore, in light the electron acceptor is reduced and
oxygen is evolved. Cyt b fi , now known as a plastoquinone, is one electron acceptor.

Samuel Ruben and Martin Kamen used radioactive isotopes to determine that the oxygen
liberated in photosynthesis came from the water.

Melvin Calvin and Andrew Benson, along with James Bassham, elucidated the path of
carbon assimilation (the photosynthetic carbon reduction cycle) in plants. The carbon
reduction cycle is known as the Calvin cycle, which inappropriately ignores the contribution
of Bassham and Benson. Many scientists refer to the cycle as the Calvin-Benson Cycle,
Benson-Calvin, and some even call it the Calvin-Benson-Bassham (or CBB) Cycle.

A Nobel Prize winning scientist, Rudolph A. Marcus, was able to discover the function and
significance of the electron transport chain.

Factors

There are three main factors affecting photosynthesis and several corollary factors. The
three main are:

• Light irradiance and wavelength

• Carbon dioxide concentration

• Temperature.

Light intensity (irradiance), wavelength and temperature

In the early 1900s Frederick Frost Blackman along with Gabrielle Matthaei investigated the
effects of light intensity (irradiance) and temperature on the rate of carbon assimilation.

• At constant temperature, the rate of carbon assimilation varies with irradiance, initially
increasing as the irradiance increases. However at higher irradiance this relationship no
longer holds and the rate of carbon assimilation reaches a plateau.

• At constant irradiance, the rate of carbon assimilation increases as the temperature is
increased over a limited range. This effect is only seen at high irradiance levels. At low
irradiance, increasing the temperature has little influence on the rate of carbon
assimilation.

These two experiments illustrate vital points: firstly, from research it is known that
photochemical reactions are not generally affected by temperature. However, these
experiments clearly show that temperature affects the rate of carbon assimilation, so there

Photosynthesis

182

must be two sets of reactions in the full process of carbon assimilation. These are of course
the light-dependent 'photochemical' stage and the light-independent,
temperature-dependent stage. Second, Blackman's experiments illustrate the concept of
limiting factors. Another limiting factor is the wavelength of light. Cyanobacteria, which
reside several meters underwater, cannot receive the correct wavelengths required to
cause photoinduced charge separation in conventional photosynthetic pigments. To combat
this problem, a series of proteins with different pigments surround the reaction center.This
unit is called a phycobilisome.

Carbon dioxide levels and photorespiration

As carbon dioxide concentrations rise, the rate at which sugars are made by the
light-independent reactions increases until limited by other factors. RuBisCO, the enzyme
that captures carbon dioxide in the light-independent reactions, has a binding affinity for
both carbon dioxide and oxygen. When the concentration of carbon dioxide is high,
RuBisCO will fix carbon dioxide. However, if the carbon dioxide concentration is low,
RuBisCO will bind oxygen instead of carbon dioxide. This process, called photorespiration,
uses energy, but does not produce sugars.

RuBisCO oxygenase activity is disadvantageous to plants for several reasons:

1. One product of oxygenase activity is phosphoglycolate (2 carbon) instead of
3-phosphoglycerate (3 carbon). Phosphoglycolate cannot be metabolized by the
Calvin-Benson cycle and represents carbon lost from the cycle. A high oxygenase activity,
therefore, drains the sugars that are required to recycle ribulose 5-bisphosphate and for
the continuation of the Calvin-Benson cycle.

2. Phosphoglycolate is quickly metabolized to glycolate that is toxic to a plant at a high
concentration; it inhibits photosynthesis.

3. Salvaging glycolate is an energetically expensive process that uses the glycolate
pathway and only 75% of the carbon is returned to the Calvin-Benson cycle as
3-phosphoglycerate. The reactions also produce ammonia (NHL) which is able to diffuse
out of the plant leading to a loss of nitrogen.

A highly-simplified summary is:

2 glycolate + ATP -> 3-phosphoglycerate + carbon dioxide + ADP +NH

The salvaging pathway for the products of RuBisCO oxygenase activity is more commonly
known as photorespiration, since it is characterized by light-dependent oxygen consumption
and the release of carbon dioxide.

See also

Artificial photosynthesis
Calvin-Benson cycle
Carbon fixation
Cellular respiration
Chemosynthesis
Light-dependent reaction
Photobiology
Photoinhibition
Photosynthetic reaction center

Photosynthesis

183

Photosynthetically active radiation

Quantum biology

Red edge

Jan Anderson (scientist)

Footnotes

a. The word photosynthesis comes from the Greek cpojTO- (photo-), "light/ 1 and avvOsaiQ
(synthesis), "placing with."

p. The exceptions are chemoautotrophs that live in rocks or around deep sea

hydro thermal vents.

References

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Photosynthesis

185

Further reading

Asimov, Isaac (1968). Photosynthesis. New York, London: Basic Books, Inc.. ISBN

0-465-05703-9.

Bidlack JE; Stern KR, Jansky S (2003). Introductory plant biology. New York:

McGraw-Hill. ISBN 0-07-290941-2.

Blankenship RE (2008). Molecular Mechanisms of Photosynthesis (2nd ed.). John Wiley &

Sons Inc. ISBN 0-470-71451-4.

Govindjee (1975). Bioenergetics of photosynthesis. Boston: Academic Press. ISBN

0-12-294350-3.

Govindjee BeattyJT,Gest H, Allen JF (2006). Discoveries in Photosynthesis. Advances in

Photosynthesis and Respiration. 20. Berlin: Springer. ISBN 1-4020-3323-0.

Gregory RL (1971). Biochemistry of photosynthesis. New York: Wiley-Interscience. ISBN

0-471-32675-5.

Rabinowitch E, Govindjee (1969). Photosynthesis. London: J. Wiley. ISBN 0-471-70424-5.

Reece, J, Campbell, N (2005). Biology. San Francisco: Pearson, Benjamin Cummings.

ISBN 0-8053-7146-X.

External links

A collection of photosynthesis pages for all levels from a renowned expert (Govindjee)

(http://www.life.uiuc.edu/govindjee/linksPSed.htm)

UC Berkeley video lecture (http://academicearth.org/lectures/

photosynthesis-from-light-to-atp) on Photosynthesis

In depth, advanced treatment of photosynthesis, also from Govindjee (http://www.life.

uiuc.edu/govindjee/paper/gov.html)

Science Aid: Photosynthesis (http://scienceaid.co.uk/biology/biochemistry/

photosynthesis.html) Article appropriate for high school science

Liverpool John Moores University, Dr. David Wilkinson (http://www.ljmu.ac.uk/

NewsCentre/6301 2.htm)

Metabolism, Cellular Respiration and Photosynthesis - The Virtual Library of

Biochemistry and Cell Biology (http://www.biochemweb.org/metabolism.shtml)

Overall examination of Photosynthesis at an intermediate level (http://www.chemsoc.

org/networks/learnnet/cfb/Photosynthesis.htm)

Overall Energetics of Photosynthesis (http://www.life.uiuc.edu/govindjee/

photosynBook.html)

Photosynthesis Discovery Milestones (http://www.juliantrubin.com/bigten/

photosynthesisexperiments.html) - experiments and background

Computational biology

186

Computational biology

Computational biology is an interdisciplinary field that applies the techniques of
computer science, applied mathematics and statistics to address biological problems. The
main focus lays on developing mathematical modeling and computational simulation
techniques. By these means it addresses scientific reaserch topics with their theoretical and
experimental questions without a laboratory. It encompasses the fields of:

• Bioinformatics, which applies algorithms and statistical techniques to the interpretation,
classification and understanding of biological datasets. These typically consist of large
numbers of DNA, RNA, or protein sequences. Sequence alignment is used to assemble
the datasets for analysis. Comparisons of homologous sequences, gene finding, and
prediction of gene expression are the most common techniques used on assembled
datasets; however, analysis of such datasets have many applications throughout all fields
of biology.

• Computational biomodeling, a field within biocybernetics concerned with building
computational models of biological systems.

• Computational genomics, a field within genomics which studies the genomes of cells and
organisms. High-throughput genome sequencing produces lots of data, which requires
extensive post-processing (genome assembly) and uses DNA microarray technologies to
perform statistical analyses on the genes expressed in individual cell types. This can help
find genes of interests for certain diseases or conditions. This field also studies the
mathematical foundations of sequencing.

• Molecular modeling, which consists of modelling the behaviour of molecules of biological
importance.

• Protein structure prediction and structural genomics, which attempt to systematically
produce accurate structural models for three-dimensional protein structures that have
not been determined experimentally.

• Computational biochemistry and biophysics, which make extensive use of structural
modeling and simulation methods such as molecular dynamics and Monte Carlo
method-inspired Boltzmann sampling methods in an attempt to elucidate the kinetics and
thermodynamics of protein functions.

Goldbeter-Koshland kinetics

187

Goldbeter-Koshland kinetics

The

Goldbeter-Koshland

kinetics

describe a steady-state solution for a
2-state biological system. In this system,
the interconversion between these two
states is performed by two enzymes with
opposing effect. One example would be a
protein Z that exists in a phosphorylated
form Z and in an unphosphorylated form
Z; the corresponding kinase Y and
phosphatase X interconvert the two forms.
In this case we would be interested in the
equilibrium concentration of the protein Z
(Goldbeter-Koshland kinetics only describe
equilibrium properties, thus no dynamics
can be modeled). It has many applications
in the description of biological systems.

The

Goldbeter-Koshland

kinetics

described by the Goldbeter-Koshland
function:

k 2 a

A kinase Y and a phosphotase X that act on a protein
Z; one possible application for the Goldbeter-Koshland

kinetics

.:.

G(l'!,l'2, Ji, J 2 )

with the constants

v 2 =k 1 [X]; i/ 2 =fc 2 [F]; J :

2v x J,

B + ^/B

4(U 2 - Ui)t'i J;

Ail

.1/2

[2]o'

B = V 2 - Vi + Jil? 2 + JgU!

Graphically the function takes values between and 1 and has a sigmoid behavior. The
smaller the parameters J 1 and L the steeper the function gets and the more of a switch-like
behavior is observed.

Derivation

Since we are looking at equilibrium properties we can write

d\Z]

From Michaelis-Menten kinetics we know that the rate at which Z is dephosphorylated is

*i[A r ][Z P ] h[Y\[Z\

Tl = 1? TTt — an d the rate at which Z is phosphorylated is ^ = — r „ 1# Here the

K stand for the Michaelis Menten constant which describes how well the enzymes X and Y
bind and catalyze the conversion whereas the kinetic parameters k and k denote the rate
constants for the catalyzed reactions. Assuming that the total concentration of Z is constant

we can additionally write that [Z]

[Z ] + [Z] and we thus get:

Goldbeter-Koshland kinetics

188

d\Z]

1*1 - r 2

^[X]([Z] -[Z])

K An +([Z] -[Z}) K M2 +[Z]

^[A1([Z] -[Z])

k 2 [Y][Z]

Ami + ([2]o - [£]) #M2 + [Z]

fci[X](l

)

h[Y\

[2]o

Kyi

+ (!■
«i(l

)

Jl + (1 - 2)

■ft"A72

[2)o

J<2 +

J3_

[Z)o

(1)

with the constants

[Z| ; Vl = fc,[X]; v 2 = h[Y]] Ji = &-= ■*

I^lo

j. ; 2

[2]o'

(2)

If we thus solve the quadratic equation (1) for z we get:

«i(l

)

t'2*

Jl + (1 - z)

J* + z

J%V\ + ZVi — JjV\Z — Z 2 V\ = ZVjJl + V2Z

z 2 (v 2 - v x ) - z (v 2 - vx + J\V2 + J^i) +V1J2 =

z 2 v 2

B - V fi2 _ 4(l , 2 _ Vl ) Vl j 2

v /S 2 -4(ls ! -l'i)t'lJ , 2 S + V'^ 2 - 4 ( 1 '2

«l)

2(t'

Vi )

2(« 2 - t'i)

B + v'B 2 - 4 (^

«0

4(u 2 - ui)wi J 2

I ■ I

2(u 2 - vi) B + Y/^-^-t'iJuiJj

2^7.

B + V'B 2 - 4(i' 2 - i'i ) v 1 J 2

(3)

Thus (3) is a solution to the initial equilibrium problem and describes the equilibrium
concentration of [Z] and [Z ] as a function of the kinetic parameters of the phoshorylation
and dephoshorylation reaction and the concentrations of the kinase and phosphotase. The
solution is the Goldbeter-Koshland function with the constants from (2):

\z\

G(v 1 ,v 2 ,J u J 2 )

2i'i J.

B + y/'B 2 -i(y 2 -wi)i'iJ 2

Literature

• Goldbeter A, Koshland DE (November 1981).

M http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=349147|An

amplified sensitivity arising from covalent modification in biological systems". Proc. Natl.

Acad. Sci. U.S.A. 78 (11): 6840-4. PMID 6947258.

Zoltan Szallasi, Jorg Stelling, Vipul Periwal: System Modeling in Cellular Biology. The

MIT Press, p 108. ISBN 978-0262195485

Metabolic network

189

Metabolic network

A metabolic network is the complete set of metabolic and physical processes that
determine the physiological and biochemical properties of a cell. As such, these networks
comprise the chemical reactions of metabolism as well as the regulatory interactions that
guide these reactions.

With the sequencing of complete genomes, it is now possible to reconstruct the network of
biochemical reactions in many organisms, from bacteria to human. Several of these
networks are available online: Kyoto Encyclopedia of Genes and Genomes (KEGG)[1],
EcoCyc [2] and BioCyc [3]. Metabolic networks are powerful tools, for studying and
modelling metabolism. From the study of metabolic networks' topology with graph theory to
predictive toxicology and ADME.

See also

• Metabolic network modelling

• Metabolic pathway

References

[1] http://www.genome.ad.jp
[2] http://www.ecocyc.org
[3] http://biocyc.org

Signalling pathway

1. REDIRECT signal transduction

Cell cycle

190

Cell cycle

The cell cycle, or cell-division cycle, is the series of events that take place in a cell
leading to its division and duplication (replication). In cells without a nucleus (prokaryotes),
the cell cycle occurs via a process termed binary fission. In cells with a nucleus
(eukaryotes), the cell cycle can be divided in two brief periods: interphase— during which
the cell grows, accumulating nutrients needed for mitosis and duplicating its DNA— and the
mitosis (M) phase, during which the cell splits itself into two distinct cells, often called
"daughter cells". The cell-division cycle is a vital process by which a single-celled fertilized
egg develops into a mature organism, as well as the process by which hair, skin, blood cells,
and some internal organs are renewed.

Phases

The cell cycle consists of five distinct phases: G 1 phase, S phase (synthesis), G phase
(collectively known as interphase) and M phase (mitosis). M phase is itself composed of two
tightly coupled processes: mitosis, in which the cell's chromosomes are divided between the
two daughter cells, and cytokinesis, in which the cell's cytoplasm divides forming distinct
cells. Activation of each phase is dependent on the proper progression and completion of
the previous one. Cells that have temporarily or reversibly stopped dividing are said to have
entered a state of quiescence called G phase.

•

Schematic of the cell cycle, outer ring: I=Interphase, M=Mitosis;
inner ring: M=Mitosis, G =Gap 1, G =Gap 2, S=Synthesis; not in
ring: G =Gap 0/Resting. The duration of mitosis in relation to the

other phases has been exaggerated in this diagram.

State

Phase

Abbreviation

Description

quiescent/
senescent

Gap

G o

A resting phase where the cell has left the cycle and has stopped
dividing.

Cell cycle

191

Interphase

Gap 1

G i

Cells increase in size in Gap 1. The G checkpoint control
mechanism ensures that everything is ready for DNA synthesis.

Synthesis

DNA replication occurs during this phase.

Gap 2

G 2

During the gap between DNA synthesis and mitosis, the cell will
continue to grow. The G checkpoint control mechanism ensures
that everything is ready to enter the M (mitosis) phase and
divide.

Cell division

Mitosis

Cell growth stops at this stage and cellular energy is focused on
the orderly division into two daughter cells. A checkpoint in the
middle of mitosis (Metaphase Checkpoint) ensures that the cell
is ready to complete cell division.

After cell division, each of the daughter cells begin the interphase of a new cycle. Although
the various stages of interphase are not usually morphologically distinguishable, each
phase of the cell cycle has a distinct set of specialized biochemical processes that prepare
the cell for initiation of cell division.

Resting (G Q phase)

The term "post-mitotic" is sometimes used to refer to both quiescent and senescent cells.
Nonproliferative cells in multicellular eukaryotes generally enter the quiescent G Q state
from G 1 and may remain quiescent for long periods of time, possibly indefinitely (as is often
the case for neurons). This is very common for cells that are fully differentiated. Cellular
senescence is a state that occurs in response to DNA damage or degradation that would
make a cell's progeny nonviable; it is often a biochemical alternative to the self-destruction
of such a damaged cell by apoptosis.

Interphase

G phase

The first phase within interphase, from the end of the previous M phase until the beginning
of DNA synthesis is called G 1 (G indicating gap). During this phase the biosynthetic
activities of the cell, which had been considerably slowed down during M phase, resume at
a high rate. This phase is marked by synthesis of various enzymes that are required in S
phase, mainly those needed for DNA replication. Duration of G 1 is highly variable, even

among different cells of the same species.

S phase

The ensuing S phase starts when DNA synthesis commences; when it is complete, all of the
chromosomes have been replicated, i.e., each chromosome has two (sister) chromatids.
Thus, during this phase, the amount of DNA in the cell has effectively doubled, though the
ploidy of the cell remains the same. Rates of RNA transcription and protein synthesis are
very low during this phase. An exception to this is histone production, most of which occurs
during the S phase. [2] [3] [4]

Cell cycle

192

G phase

The cell then enters the G 2 phase, which lasts until the cell enters mitosis. Again,
significant protein synthesis occurs during this phase, mainly involving the production of
microtubules, which are required during the process of mitosis. Inhibition of protein
synthesis during G phase prevents the cell from undergoing mitosis.

Mitosis (M Phase)

The relatively brief M phase consists of nuclear division (karyokinesis) and cytoplasmic
division (cytokinesis). In plants and algae, cytokinesis is accompanied by the formation of a
new cell wall. The M phase has been broken down into several distinct phases, sequentially
known as prophase, Prometaphase, metaphase, anaphase and telophase leading to
cytokinesis.

Regulation of eukaryotic cell cycle

Regulation of the cell cycle involves
processes crucial to the survival of a cell,
including the detection and repair of
genetic damage as well as the prevention
of uncontrolled cell division. The

molecular events that control the cell
cycle are ordered and directional; that is,
each process occurs in a sequential
fashion and it is impossible to "reverse"
the cycle.

Role of cyclins and CDKs

Two key classes of regulatory molecules,
cyclins and cyclin-dependent kinases
(CDKs), determine a cell's progress

through the cell cycle.

[5]

Leland H.

Regulation of cell cycle - Schematic

Extracellular growth signal

DNA damage by irradiation

Cyclin D

CDK4

Cyclin D-CDK4 complex

p16INK4a

f P21

Activation of E2F responsive
genes via phosphorylation and

deactivation of RB

Cyclin E

Cyclin A J

Other proteins necessary for

DNA synthesis (S phase

specific)

Cyclin E-CDK2 complex

| Cyclin A-CDK2 complex

vjiimmiiMir "'■■■Mm

Cell cycle

G1/SChk

G2/MChk

iinniiiiiiiiwmuw

ffllMW**"*

CDK - Cyclin Dependent Kinase
G1/S Chk-G1/S checkpoint
G2M1 Chk - G2/WI checkpoint

Hartwell, R. Timothy Hunt, and Paul M.
Nurse won the 2001 Nobel Prize in
Physiology or Medicine for their discovery
of these central molecules. Many of the
genes encoding cyclins and CDKs are
conserved among all eukaryotes, but in
general more complex organisms have
more elaborate cell cycle control systems
that incorporate more individual components. Many of the relevant genes were first

T71

identified by studying yeast, especially Saccharomyces cerevisiae; genetic nomenclature
in yeast dubs many these genes cdc (for "cell division cycle") followed by an identifying
number, e.g., cdc25.

Regulation of cell cycle: Schematic

Cyclins form the regulatory subunits and CDKs the catalytic subunits of an activated
heterodimer; cyclins have no catalytic activity and CDKs are inactive in the absence of a
partner cyclin. When activated by a bound cyclin, CDKs perform a common biochemical

Cell cycle

193

reaction called phosphorylation that activates or inactivates target proteins to orchestrate
coordinated entry into the next phase of the cell cycle. Different cyclin-CDK combinations
determine the downstream proteins targeted. CDKs are constitutively expressed in cells
whereas cyclins are synthesised at specific stages of the cell cycle, in response to various
molecular signals. ^

General mechanism of cyclin-CDK interaction

Upon receiving a pro-mitotic extracellular signal, G 1 cyclin-CDK complexes become active
to prepare the cell for S phase, promoting the expression of transcription factors that in
turn promote the expression of S cyclins and of enzymes required for DNA replication. The
G 1 cyclin-CDK complexes also promote the degradation of molecules that function as S
phase inhibitors by targeting them for ubiquitination. Once a protein has been
ubiquitinated, it is targeted for proteolytic degradation by the proteasome. Active S
cyclin-CDK complexes phosphorylate proteins that make up the pre-replication complexes
assembled during G 1 phase on DNA replication origins. The phosphorylation serves two
purposes: to activate each already-assembled pre-replication complex, and to prevent new
complexes from forming. This ensures that every portion of the cell's genome will be
replicated once and only once. The reason for prevention of gaps in replication is fairly
clear, because daughter cells that are missing all or part of crucial genes will die. However,
for reasons related to gene copy number effects, possession of extra copies of certain genes
would also prove deleterious to the daughter cells.

Mitotic cyclin-CDK complexes, which are synthesized but inactivated during S and G 2
phases, promote the initiation of mitosis by stimulating downstream proteins involved in
chromosome condensation and mitotic spindle assembly. A critical complex activated
during this process is a ubiquitin ligase known as the anaphase-promoting complex (APC),
which promotes degradation of structural proteins associated with the chromosomal
kinetochore. APC also targets the mitotic cyclins for degradation, ensuring that telophase
and cytokinesis can proceed. Interphase: Interphase generally lasts at least 12 to 24 hours
in mammalian tissue. During this period, the cell is constantly synthesizing RNA, producing
protein and growing in size. By studying molecular events in cells, scientists have
determined that interphase can be divided into 4 steps: Gap (GO), Gap 1 (Gl), S
(synthesis) phase, Gap 2 (G2).

Specific action of cyclin-CDK complexes

Cyclin D is the first cyclin produced in the cell cycle, in response to extracellular signals
(eg. growth factors). Cyclin D binds to existing CDK4, forming the active cyclin D-CDK4
complex. Cyclin D-CDK4 complex in turn phosphorylates the retinoblastoma susceptibility
protein (Rb). The hyperphosphorylated Rb dissociates from the E2F/DPl/Rb complex (which
was bound to the E2F responsive genes, effectively "blocking" them from transcription),
activating E2F. Activation of E2F results in transcription of various genes like cyclin E,
cyclin A, DNA polymerase, thymidine kinase, etc. Cyclin E thus produced binds to CDK2,
forming the cyclin E-CDK2 complex, which pushes the cell from G 1 to S phase (G../S
transition). Cyclin B along with cdc2 (cdc2 - fission yeasts (CDK1 - mammalia)) forms the
cyclin B-cdc2 complex, which initiates the G /M transition. ^ Cyclin B-cdc2 complex
activation causes breakdown of nuclear envelope and initiation of prophase, and
subsequently, its deactivation causes the cell to exit mitosis. ^

Cell cycle

194

Inhibitors

Two families of genes, the cip/kip family and the INK4a/ARF (inhibitor of Kinase
4/Alternative .Reading Frame) prevent the progression of the cell cycle. Because these
genes are instrumental in prevention of tumor formation, they are known as tumor
suppressors.

The cip/kip family includes the genes p21, p27 and p57. They halt cell cycle in G 1 phase,
by binding to, and inactivating, cyclin-CDK complexes. p21 is activated by p53 (which, in
turn, is triggered by DNA damage eg. due to radiation). p27 is activated by Transforming
Growth Factor (3 (TGF (3), a growth inhibitor.

The INK4a/ARF family includes pl6INK4a, which binds to CDK4 and arrests the cell cycle
in G 1 phase, and pl4arf which prevents p53 degradation. And the amount of chromosomes
are able to double at the same rate as in phase 2.

Checkpoints

Cell cycle checkpoints are used by the cell to monitor and regulate the progress of the cell
cycle. Checkpoints prevent cell cycle progression at specific points, allowing verification
of necessary phase processes and repair of DNA damage. The cell cannot proceed to the
next phase until checkpoint requirements have been met.

Several checkpoints are designed to ensure that damaged or incomplete DNA is not passed
on to daughter cells. Two main checkpoints exist: the Gl/S checkpoint and the G2/M
checkpoint. Gl/S transition is a rate-limiting step in the cell cycle and is also known as
restriction point. An alternative model of the cell cycle response to DNA damage has also
been proposed, known as the postreplication checkpoint.

p53 plays an important role in triggering the control mechanisms at both Gl/S and G2/M
checkpoints.

Role in tumor formation

A disregulation of the cell cycle components may lead to tumor formation. As mentioned
above, some genes like the cell cycle inhibitors, RB, p53 etc., when they mutate, may cause
the cell to multiply uncontrollably, forming a tumor. Although the duration of cell cycle in
tumor cells is equal to or longer than that of normal cell cycle, the proportion of cells that
are in active cell division (versus quiescent cells in GO phase) in tumors is much higher than
that in normal tissue. Thus there is a net increase in cell number as the number of cells that
die by apoptosis or senescence remains the same.

The cells which are actively undergoing cell cycle are targeted in cancer therapy as the
DNA is relatively exposed during cell division and hence susceptible to damage by drugs or
radiation. This fact is made use of in cancer treatment; by a process known as debulking, a
significant mass of the tumor is removed which pushes a significant number of the
remaining tumor cells from GO to Gl phase (due to increased availability of nutrients,
oxygen, growth factors etc.). Radiation or chemotherapy following the debulking procedure
kills these cells which have newly entered the cell cycle. c *

Cell cycle

195

Synchronization of cell cultures

Several methods can be used to synchronise cell cultures by halting the cell cycle at a
particular phase. For example, Serum starvation 1 J and treatment with Thymidine or
Aphidicolin 1 J halt the cell in the Gl phase, Mitotic shake-off, treatment with colchicine
and treatment with Nocodazole J halt the cell in M phase and treatment with
5-fluorodeoxyuridine halts the cell in S phase.

See also

• cell cycle mathematical model

• Mitosis

• Meiosis

• Interphase

References

[I] Smith JA, Martin L (April 1973).
,, http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=433472|Do cells cycle?". Proc.
Natl. Acad. Sci. U.S.A. 70 (4): 1263-7. PMID 4515625.

[2] Wu RS, Bonner WM (December 1981). "Separation of basal histone synthesis from S-phase histone synthesis in

dividing cells". Cell 27 (2 Pt 1): 321-30. doi: 10.1016/0092-8674(81)90415-3 (http://dx.doi.org/10.1016/

0092-8674(81)90415-3). PMID 7199388.
[3] Nelson DM, Ye X, Hall C, Santos H, Ma T, Kao GD, Yen TJ, Harper JW, Adams PD (November 2002).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid= 13 5676 1 Coupling of DNA

synthesis and histone synthesis in S phase independent of cyclin/cdk2 activity". Mol. Cell. Biol. 22 (21):

7459-72. PMID 12370293.
[4] Cameron IL, Greulich RC (July 1963).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=21 06275 |Evidence for an

essentially constant duration of DNA synthesis in renewing epithelia of the adult mouse". J. Cell Biol. 18: 31-40.

PMID 14018040.
[5] Nigg EA (June 1995). "Cyclin-dependent protein kinases: key regulators of the eukaryotic cell cycle". Bioessays

17 (6): 471-80. doi: 10. 1002/bies. 950170603 (http://dx.doi.org/10.1002/bies.950170603). PMID 7575488.
[6] http://nobelprize.org/nobel_prizes/medicine/laureates/2001/press.htmll "Press release". Nobelprize.org. http://

nobelprize.org/nobel_prizes/medicine/laureates/2001/press.html.
[7] Spellman PT, Sherlock G, Zhang MQ, Iyer VR, Anders K, Eisen MB, Brown PO, Botstein D, Futcher B

(December 1998).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=25624|Comprehensive

identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization".

Mol. Biol. Cell 9 (12): 3273-97. PMID 9843569.
[8] Robbins and Cotran; Kumar, Abbas, Fausto (2004). Pathological Basis of Disease. Elsevier. ISBN

81-8147-528-3.
[9] Norbury C (1995). "Cdc2 protein kinase (vertebrates)", in Hardie, D. Grahame; Hanks, Steven. Protein kinase

factsBook. Boston: Academic Press, pp. 184. ISBN 0-12-324719-5.
[10] Stephen J. Elledge (6 December 1996). "http://www.sciencemag.org/cgi/content/abstract/274/5293/1664ICell

Cycle Checkpoints: Preventing an Identity Crisis". Science 274 (5293): 1664-1672. doi:

10. 1126/science.274. 5293. 1664 (http://dx.doi.org/10.1126/science.274.5293.1664). PMID 8939848. http:/

/www. sciencemag.org/cgi/content/abstract/274/5293/1664.

[II] Kues WA, Anger M, Carnwath JW, Paul D, MotlikJ, Niemann H (February 2000). "Cell cycle synchronization
of porcine fetal fibroblasts: effects of serum deprivation and reversible cell cycle inhibitors". Biol. Reprod. 62
(2): 412-9. doi: 10.1095/biolreprod62.2.412 (http://dx.doi.Org/10.1095/biolreprod62.2.412). PMID
10642581.

[12] Pedrali-Noy G, Spadari S, Miller-Faures A, Miller AO, Kruppa J, Koch G (January 1980).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=32 7273 1 Synchronization of HeLa
cell cultures by inhibition of DNA polymerase alpha with aphidicolin". Nucleic Acids Res. 8 (2): 377-87. doi:
10.1093/nar/8.2.377 (http://dx.doi.Org/10.1093/nar/8.2.377). PMID 6775308.

Cell cycle

196

[13] Prather RS, Boquest AC, Day BN (1999). "Cell cycle analysis of cultured porcine mammary cells". Cloning 1

(1): 17-24. doi: 10.1089/15204559950020067 (http://dx.doi.org/10.1089/15204559950020067). PMID

16218827.
[14] Samake S, Smith LC (October 1997). "Synchronization of cell division in eight-cell bovine embryos produced

in vitro: effects of aphidicolin". Theriogenology 48 (6): 969-76. doi: 10.1016/S0093-691X(97)00323-3 (http://

dx.doi.org/10.1016/S0093-691X(97)00323-3). PMID 16728186.

Further reading

• Morgan DL (2007). The Cell Cycle: Principles of Control. London: Published by New
Science Press in association with Oxford University Press. ISBN 0-87893-508-8.

• Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2002). "Chapter 17".
Molecular Biology of the Cell (4th ed.). New York: Garland Science. ISBN 0-8153-3218-1.

• Krieger M, Scott MP; Matsudaira PT, Lodish HF, Darnell JE, Zipursky L, Kaiser C; Berk A
(2004). Molecular cell biology. New York: W.H. Freeman and CO. ISBN 0-7167-4366-3.

• Watson JD, Baker TA, Bell SP, Gann A, Levine M, Losick R (2004). "Chapter 7". Molecular
biology of the gene (5th ed.). San Francisco: Pearson/Benjamin Cummings. ISBN
0-8053-4642-2.

External links

• This article contains material from the Science Primer (http://www.ncbi.nlm.nih.gov/
About/primer/index. html) published by the NCBI, which, as a U.S. government
publication, is in the public domain.

• Transcriptional program of the cell cycle: high-resolution timing (http://www.cell cycle,
info)

• Cell cycle and metabolic cycle regulated transcription in yeast (http://www.sceptrans.
org)

• Cell Cycle Animation (http://www.llec.com/Genetics/Cell Cycle/index. html)
lLec.com

• Cell Cycle and Cytokinesis - The Virtual Library of Biochemistry and Cell Biology (http://
www.biochemweb.org/cell_cycle.shtml)

• Cell Cycle (http://www.landesbioscience.com/journals/cc/index.php)

• Cell Cycle Portal (http://www.cellcycles.org)

• Fucci:Using GFP to visualize the cell-cycle (http://www.conncoll.edu/ccacad/zimmer/
GFP-ww/cooluses 1 9 .html)

• Science Creative Quarterly's overview of the cell cycle (http://www.scq.ubc.ca/
?p=248)

• Cells alive (http://www.cellsalive.com)

• CCO (http://www.cellcycleontology.org) The Cell-Cycle Ontology

• KEGG - Human Cell Cycle (http://www.genome.ad.jp/kegg/pathway/hsa/hsa04110.
html)

• Cell cycle modeling (http://mpf.biol.vt.edu/Research.html)

DNA

197

DNA

Deoxyribonucleic acid (DNA) is a nucleic acid that
contains the genetic instructions used in the
development and functioning of all known living
organisms and some viruses. The main role of DNA
molecules is the long-term storage of information.
DNA is often compared to a set of blueprints or a
recipe, or a code, since it contains the instructions
needed to construct other components of cells, such
as proteins and RNA molecules. The DNA segments
that carry this genetic information are called genes,
but other DNA sequences have structural purposes,
or are involved in regulating the use of this genetic
information.

Chemically, DNA consists of two long polymers of

simple units called nucleotides, with backbones made

of sugars and phosphate groups joined by ester

bonds. These two strands run in opposite directions

to each other and are therefore anti-parallel.

Attached to each sugar is one of four types of

molecules called bases. It is the sequence of these

four bases along the backbone that encodes

information. This information is read using the

genetic code, which specifies the sequence of the

amino acids within proteins. The code is read by copying stretches of DNA into the related

nucleic acid RNA, in a process called transcription.

Within cells, DNA is organized into X-shaped structures called chromosomes. These
chromosomes are duplicated before cells divide, in a process called DNA replication.
Eukaryotic organisms (animals, plants, fungi, and protists) store most of their DNA inside

the cell nucleus and some of their DNA in the mitochondria (animals and plants) and

n 1
chloroplasts (plants only) 1 J . Prokaryotes (bacteria and archaea) however, store their DNA

in the cell's cytoplasm. Within the chromosomes, chromatin proteins such as histones

compact and organize DNA. These compact structures guide the interactions between DNA

and other proteins, helping control which parts of the DNA are transcribed.

DNA

198

Properties

Strands of purified DNA
precipitated from solutions of
cell components are visible as

viscous white substance.

DNA is a long polymer made from repeating units called
nucleotides. J These nucleotides are adenine (A),

guanine (G), cytosine (C) and thymine (T). In the related
nucleic acid RNA, thymine is replaced by uracil (U). These
nucleotides can be classified into two groups: purines
(adenine and guanine) and pyrimidines (thymine and
cytosine).

The DNA chain is 22 to 26 Angstroms wide (2.2 to
2.6 nanometres), and one nucleotide unit is 3.3 A (0.33 nm)
long. ] Although each individual repeating unit is very small,
DNA polymers can be very large molecules containing
millions of nucleotides. For instance, the largest human
chromosome, chromosome number 1, is approximately 220
million base pairs long. ^

In living organisms, DNA does
not usually exist as a single
molecule, but instead as a pair
of molecules that are held
tightly together. J L J These two
long strands entwine like vines,
in the shape of a double helix.
The nucleotide repeats contain
both the segment of the
backbone of the molecule,
which holds the chain together,
and a base, which interacts with
the other DNA strand in the
helix. In general, a base linked
to a sugar is called a nucleoside
and a base linked to a sugar and
one or more phosphate groups
is called a nucleotide. If
multiple nucleotides are linked
together, as in DNA, this
polymer is

polynucleotide. J

called

The backbone of the DNA
strand is made from alternating
phosphate

and

sugar

Adenine

Thymine

5' end

3' end

Phosphate-

deoxyribose

backbone

Guanine

V-

Cytosine /-°

5' end

The chemical structure of DNA. Hydrogen bonds are shown as

dotted lines.

residues. The sugar in DNA is 2-deoxyribose, which is a pentose (five-carbon) sugar. The
sugars are joined together by phosphate groups that form phosphodiester bonds between

DNA

199

the third and fifth carbon atoms of adjacent sugar rings. These asymmetric bonds mean a
strand of DNA has a direction. In a double helix the direction of the nucleotides in one
strand is opposite to their direction in the other strand. This arrangement of DNA strands is
called antiparallel. The asymmetric ends of DNA strands are referred to as the 5Q (five
prime) and 3D (three prime) ends, with the 5' end being that with a terminal phosphate
group and the 3' end that with a terminal hydroxyl group. One of the major differences
between DNA and RNA is the sugar, with 2-deoxyribose being replaced by the alternative
pentose sugar ribose in RNA. J

The DNA double helix is stabilized by hydrogen bonds between the bases attached to the
two strands. The four bases found in DNA are adenine (abbreviated A), cytosine (C),
guanine (G) and thymine (T). These four bases are attached to the sugar/phosphate to form
the complete nucleotide, as shown for adenosine monophosphate.

These bases are classified into two types; adenine and guanine are fused five- and
six-membered heterocyclic compounds called purines, while cytosine and thymine are
six-membered rings called pyrimidines. ] A fifth pyrimidine base, called uracil (U), usually
takes the place of thymine in RNA and differs from thymine by lacking a methyl group on its
ring. Uracil is not usually found in DNA, occurring only as a breakdown product of cytosine.

Grooves

Twin helical strands form the DNA backbone. Another
double helix may be found by tracing the spaces, or
grooves, between the strands. These voids are adjacent
to the base pairs and may provide a binding site. As the
strands are not directly opposite each other, the
grooves are unequally sized. One groove, the major
groove, is 22 A wide and the other, the minor groove, is
12 A wide. J The narrowness of the minor groove
means that the edges of the bases are more accessible
in the major groove. As a result, proteins like
transcription factors that can bind to specific sequences
in double-stranded DNA usually make contacts to the
sides of the bases exposed in the major groove.

[13]

This

situation varies in unusual conformations of DNA within
the cell (see below), but the major and minor grooves
are always named to reflect the differences in size that
would be seen if the DNA is twisted back into the
ordinary B form.

Structure of a section of DNA. The

bases lie horizontally between the two

[11]

spiraling strands. Animated

version at File: DNA orbit animated.gif

- over 3 megabytes.

Base pairing

Each type of base on one strand forms a bond with just
one type of base on the other strand. This is called
complementary base pairing. Here, purines form
hydrogen bonds to pyrimidines, with A bonding only to T, and C bonding only to G. This

arrangement of two nucleotides binding together across the double helix is called a base
pair. As hydrogen bonds are not covalent, they can be broken and rejoined relatively easily.

DNA

200

The two strands of DNA in a double helix can therefore be pulled apart like a zipper, either
by a mechanical force or high temperature. As a result of this complementarity, all the
information in the double-stranded sequence of a DNA helix is duplicated on each strand,
which is vital in DNA replication. Indeed, this reversible and specific interaction between
complementary base pairs is critical for all the functions of DNA in living organisms. ]

Guanine H Cytosine

Adenine Thymine

Top, a GC base pair with three hydrogen bonds. Bottom, an AT base pair with two
hydrogen bonds. Non-covalent hydrogen bonds between the pairs are shown as dashed
lines.

The two types of base pairs form different numbers of hydrogen bonds, AT forming two
hydrogen bonds, and GC forming three hydrogen bonds (see figures, left). DNA with high
GC-content is more stable than DNA with low GC-content, but contrary to popular belief,
this is not due to the extra hydrogen bond of a GC basepair but rather the contribution of
stacking interactions (hydrogen bonding merely provides specificity of the pairing, not
stability). As a result, it is both the percentage of GC base pairs and the overall length of
a DNA double helix that determine the strength of the association between the two strands
of DNA. Long DNA helices with a high GC content have stronger-interacting strands, while
short helices with high AT content have weaker-interacting strands. In biology, parts of
the DNA double helix that need to separate easily, such as the TATAAT Pribnow box in

ri7i

some promoters, tend to have a high AT content, making the strands easier to pull apart. J
In the laboratory, the strength of this interaction can be measured by finding the
temperature required to break the hydrogen bonds, their melting temperature (also called
T value). When all the base pairs in a DNA double helix melt, the strands separate and
exist in solution as two entirely independent molecules. These single-stranded DNA
molecules have no single common shape, but some conformations are more stable than
others. [18]

DNA

201

Sense and antisense

A DNA sequence is called "sense"

if its sequence is the same as that of a messenger RNA
copy that is translated into protein. J The sequence on the opposite strand is called the
"antisense" sequence. Both sense and antisense sequences can exist on different parts of
the same strand of DNA (i.e. both strands contain both sense and antisense sequences). In
both prokaryotes and eukaryotes, antisense RNA sequences are produced, but the functions
of these RNAs are not entirely clear. J One proposal is that antisense RNAs are involved in

T211

regulating gene expression through RNA-RNA base pairing. 1 J

A few DNA sequences in prokaryotes and eukaryotes, and more in plasmids and viruses,

T221

blur the distinction between sense and antisense strands by having overlapping genes.
In these cases, some DNA sequences do double duty, encoding one protein when read along
one strand, and a second protein when read in the opposite direction along the other
strand. In bacteria, this overlap may be involved in the regulation of gene transcription/ J
while in viruses, overlapping genes increase the amount of information that can be encoded
within the small viral genome.

Supercoiling

DNA can be twisted like a rope in a process called DNA supercoiling. With DNA in its
"relaxed" state, a strand usually circles the axis of the double helix once every 10.4 base
pairs, but if the DNA is twisted the strands become more tightly or more loosely wound. 1 J
If the DNA is twisted in the direction of the helix, this is positive supercoiling, and the bases
are held more tightly together. If they are twisted in the opposite direction, this is negative
supercoiling, and the bases come apart more easily. In nature, most DNA has slight
negative supercoiling that is introduced by enzymes called topoisomerases. These
enzymes are also needed to relieve the twisting stresses introduced into DNA strands
during processes such as transcription and DNA replication. J

Alternate DNA structures

DNA exists in many possible
conformations that include A-DNA,
B-DNA, and Z-DNA forms, although,
only B-DNA and Z-DNA have been
directly observed in functional
organisms. J The conformation
that DNA adopts depends on the
hydration level, DNA sequence, the

amount

and

direction

supercoiling, chemical modifications
of the bases, the type and
concentration of metal ions, as well
as the presence of polyamines in solution. J

The first published reports of A-DNA X-ray diffraction patterns— and also B-DNA used
analyses based on Patterson transforms that provided only a limited amount of structural
information for oriented fibers of DNA. J L J An alternate analysis was then proposed by
Wilkins et ah, in 1953, for the in vivo B-DNA X-ray diffraction/scattering patterns of highly

DNA

202

hydrated DNA fibers in terms of squares of Bessel functions. ] In the same journal,
Watson and Crick presented their molecular modeling analysis of the DNA X-ray diffraction
patterns to suggest that the structure was a double-helix. ]

Although the X B-DNA form' is most common under the conditions found in cells, ] it is not
a well-defined conformation but a family of related DNA conformations 1 J that occur at the
high hydration levels present in living cells. Their corresponding X-ray diffraction and
scattering patterns are characteristic of molecular paracrystals with a significant degree of
disorder. [34] [35]

Compared to B-DNA, the A-DNA form is a wider right-handed spiral, with a shallow, wide
minor groove and a narrower, deeper major groove. The A form occurs under
non-physiological conditions in partially dehydrated samples of DNA, while in the cell it
may be produced in hybrid pairings of DNA and RNA strands, as well as in enzyme-DNA
complexes. * c ] Segments of DNA where the bases have been chemically modified by
methylation may undergo a larger change in conformation and adopt the Z form. Here, the
strands turn about the helical axis in a left-handed spiral, the opposite of the more common
B form. J These unusual structures can be recognized by specific Z-DNA binding proteins
and may be involved in the regulation of transcription. *

Quadruplex structures

Structure of a DNA quadruplex formed by telomere repeats. The
looped conformation of the DNA backbone is very different from

the typical helical structure.

At the ends of the linear

chromosomes

are

specialized

regions of DNA called telomeres.
The main function of these regions
is to allow the cell to replicate
chromosome ends using the

enzyme

telomerase,

the

enzymes that normally replicate
DNA cannot copy the extreme 3D
ends of chromosomes. These
specialized chromosome caps also
help protect the DNA ends, and
stop the DNA repair systems in the
cell from treating them as damage
to be corrected. J In human cells,
telomeres are usually lengths of
single-stranded DNA containing
several thousand repeats of a
simple TTAGGG sequence. [43]

These guanine-rich sequences may
stabilize chromosome ends by forming structures of stacked sets of four-base units, rather
than the usual base pairs found in other DNA molecules. Here, four guanine bases form a
flat plate and these flat four-base units then stack on top of each other, to form a stable
G-quadruplex structure. These structures are stabilized by hydrogen bonding between
the edges of the bases and chelation of a metal ion in the centre of each four-base unit.

DNA

203

Other structures can also be formed, with the central set of four bases coming from either a
single strand folded around the bases, or several different parallel strands, each
contributing one base to the central structure.

In addition to these stacked structures, telomeres also form large loop structures called
telomere loops, or T-loops. Here, the single-stranded DNA curls around in a long circle
stabilized by telomere-binding proteins. ^ At the very end of the T-loop, the
single-stranded telomere DNA is held onto a region of double-stranded DNA by the
telomere strand disrupting the double-helical DNA and base pairing to one of the two
strands. This triple-stranded structure is called a displacement loop or D-loop. J

Branched DNA

In DNA fraying occurs when non-complementary regions exist at the end of an otherwise
complementary double-strand of DNA. However, branched DNA can occur if a third strand
of DNA is introduced and contains adjoining regions able to hybridize with the frayed
regions of the pre-existing double-strand. Although the simplest example of branched DNA
involves only three strands of DNA, complexes involving additional strands and multiple
branches are also possible. J

Chemical modifications

cytosine

5-methylcytosine

thymine

DNA

204

Structure of cytosine with and without the 5-methyl group. After deamination the 5-methylcytosine
has the same structure as thymine

Base modifications

The expression of genes is influenced by how the DNA is packaged in chromosomes, in a
structure called chromatin. Base modifications can be involved in packaging, with regions
that have low or no gene expression usually containing high levels of methylation of
cytosine bases. For example, cytosine methylation, produces 5-methylcytosine, which is

important for X-chromosome inactivation.

[48]

The average level of methylation varies

between organisms - the worm Caenorhabditis elegans lacks cytosine methylation, while
vertebrates have higher levels, with up to 1% of their DNA containing 5-methylcytosine. J
Despite the importance of 5-methylcytosine, it can deaminate to leave a thymine base,
methylated cytosines are therefore particularly prone to mutations. J Other base
modifications include adenine methylation in

bacteria,

the

presence

rcii

5-hydroxymethylcytosine in the brain, 1 J and the glycosylation of uracil to produce the
"J-base" in kinetoplastids. [52] [53]

Damage

DNA can be damaged by many different
sorts of mutagens, which change the DNA
sequence. Mutagens include oxidizing
agents, alkylating agents and also
high-energy electromagnetic radiation such
as ultraviolet light and X-rays. The type of
DNA damage produced depends on the
type of mutagen. For example, UV light can
damage DNA by producing thymine dimers,
which are cross-links between pyrimidine
bases. On the other hand, oxidants such
as free radicals or hydrogen peroxide
produce multiple forms of damage,
including base modifications, particularly of
guanosine, and double-strand breaks. A
typical human cell contains about 150,000
bases that have suffered oxidative
damage. 1 J Of these oxidative lesions, the
most dangerous are double-strand breaks,
as these are difficult to repair and can
produce point mutations, insertions and
deletions from the DNA sequence, as well
as chromosomal translocations.

A covalent adduct between benzo[a]pyrene, the major

mutagen in tobacco smoke, and DNA

Many mutagens fit into the space between two adjacent base pairs, this is called
intercalating. Most intercalators are aromatic and planar molecules, and include Ethidium
bromide, daunomycin, and doxorubicin. In order for an intercalator to fit between base

DNA

205

pairs, the bases must separate, distorting the DNA strands by unwinding of the double
helix. This inhibits both transcription and DNA replication, causing toxicity and mutations.
As a result, DNA intercalators are often carcinogens, and Benzo[cz]pyrene diol epoxide,
acridines, aflatoxin and ethidium bromide are well-known examples. L J L

Nevertheless, due to their ability to inhibit DNA transcription and replication, other similar
toxins are also used in chemotherapy to inhibit rapidly growing cancer cells.

Biological functions

DNA usually occurs as linear chromosomes in eukaryotes, and circular chromosomes in
prokaryotes. The set of chromosomes in a cell makes up its genome; the human genome has
approximately 3 billion base pairs of DNA arranged into 46 chromosomes. J The
information carried by DNA is held in the sequence of pieces of DNA called genes.
Transmission of genetic information in genes is achieved via complementary base pairing.
For example, in transcription, when a cell uses the information in a gene, the DNA
sequence is copied into a complementary RNA sequence through the attraction between
the DNA and the correct RNA nucleotides. Usually, this RNA copy is then used to make a
matching protein sequence in a process called translation which depends on the same
interaction between RNA nucleotides. Alternatively, a cell may simply copy its genetic
information in a process called DNA replication. The details of these functions are covered
in other articles; here we focus on the interactions between DNA and other molecules that
mediate the function of the genome.

Genes and genomes

Genomic DNA is located in the cell nucleus of eukaryotes, as well as small amounts in
mitochondria and chloroplasts. In prokaryotes, the DNA is held within an irregularly shaped
body in the cytoplasm called the nucleoid. The genetic information in a genome is held
within genes, and the complete set of this information in an organism is called its genotype.
A gene is a unit of heredity and is a region of DNA that influences a particular
characteristic in an organism. Genes contain an open reading frame that can be
transcribed, as well as regulatory sequences such as promoters and enhancers, which
control the transcription of the open reading frame.

In many species, only a small fraction of the total sequence of the genome encodes protein.
For example, only about 1.5% of the human genome consists of protein-coding exons, with
over 50% of human DNA consisting of non-coding repetitive sequences. ^ The reasons for
the presence of so much non-coding DNA in eukaryotic genomes and the extraordinary
differences in genome size, or C-value, among species represent a long-standing puzzle
known as the "C-value enigma.' However, DNA sequences that do not code protein may
still encode functional non-coding RNA molecules, which are involved in the regulation of
gene expression. J

DNA

206

T7 RNA polymerase (blue) producing a mRNA (green) from a

DNA template (orange).

T711

and divergence.

Some non-coding DNA sequences

play

structural

roles

chromosomes.

Telomeres

in
and

centromeres typically contain few
genes, but are important for the

function

and

stability

chromosomes. An abundant

form of non-coding DNA in humans
are pseudogenes, which are copies
of genes that have been disabled
by mutation. J These sequences
are usually just molecular fossils,
although they can occasionally
serve as raw genetic material for
the creation of new genes through
the process of gene duplication

Transcription and translation

A gene is a sequence of DNA that contains genetic information and can influence the
phenotype of an organism. Within a gene, the sequence of bases along a DNA strand
defines a messenger RNA sequence, which then defines one or more protein sequences.
The relationship between the nucleotide sequences of genes and the amino-acid sequences
of proteins is determined by the rules of translation, known collectively as the genetic code.
The genetic code consists of three-letter 'words' called codons formed from a sequence of
three nucleotides (e.g. ACT, CAG, TTT).

In transcription, the codons of a gene are copied into messenger RNA by RNA polymerase.
This RNA copy is then decoded by a ribosome that reads the RNA sequence by base-pairing
the messenger RNA to transfer RNA, which carries amino acids. Since there are 4 bases in
3-letter combinations, there are 64 possible codons ( 4 3 combinations). These encode the
twenty standard amino acids, giving most amino acids more than one possible codon. There
are also three 'stop' or 'nonsense' codons signifying the end of the coding region; these are
the TAA, TGA and TAG codons.

DNA

207

Replication

Cell division is essential for an
organism to grow, but when a
cell divides it must replicate
the DNA in its genome so that
the two daughter cells have
the same genetic information

their

parent.

The

double-stranded structure of

DNA provides
mechanism

for

simple
DNA

replication. Here, the two
strands are separated and

then

each

strand's

DNA ligase
DNA Polymerase (Pola)

DNA primase
RNA primer

Leading

strand

Topoisomerase

DNA Polymerase (P0I6)

Helicase'

Single strand,
Binding proteins

DNA replication. The double helix is unwound by a helicase and

topoisomerase. Next, one DNA polymerase produces the leading

strand copy. Another DNA polymerase binds to the lagging strand.

This enzyme makes discontinuous segments (called Okazaki

fragments) before DNA ligase joins them together.

complementary DNA sequence

is recreated by an enzyme called DNA polymerase. This enzyme makes the complementary
strand by finding the correct base through complementary base pairing, and bonding it
onto the original strand. As DNA polymerases can only extend a DNA strand in a 5Q to 3[]
direction, different mechanisms are used to copy the antiparallel strands of the double

T721

helix. 1 J In this way, the base on the old strand dictates which base appears on the new
strand, and the cell ends up with a perfect copy of its DNA.

Interactions with proteins

All the functions of DNA depend on interactions with proteins. These protein interactions
can be non-specific, or the protein can bind specifically to a single DNA sequence. Enzymes
can also bind to DNA and of these, the polymerases that copy the DNA base sequence in
transcription and DNA replication are particularly important.

DNA-binding proteins

DNA

208

Interaction of DNA with histones (shown in white, top). These proteins' basic amino acids
(below left, blue) bind to the acidic phosphate groups on DNA (below right, red).

Structural proteins that bind DNA are well-understood examples of non-specific
DNA-protein interactions. Within chromosomes, DNA is held in complexes with structural
proteins. These proteins organize the DNA into a compact structure called chromatin. In
eukaryotes this structure involves DNA binding to a complex of small basic proteins called
histones, while in prokaryotes multiple types of proteins are involved. The histones

form a disk-shaped complex called a nucleosome, which contains two complete turns of
double-stranded DNA wrapped around its surface. These non-specific interactions are
formed through basic residues in the histones making ionic bonds to the acidic
sugar-phosphate backbone of the DNA, and are therefore largely independent of the base
sequence. ] Chemical modifications of these basic amino acid residues include
methylation, phosphorylation and acetylation. J These chemical changes alter the strength
of the interaction between the DNA and the histones, making the DNA more or less
accessible to transcription factors and changing the rate of transcription. J Other
non-specific DNA-binding proteins in chromatin include the high-mobility group proteins,
which bind to bent or distorted DNA. J These proteins are important in bending arrays of
nucleosomes and arranging them into the larger structures that make up chromosomes. ^

A distinct group of DNA-binding proteins are the DNA-binding proteins that specifically
bind single-stranded DNA. In humans, replication protein A is the best-understood member
of this family and is used in processes where the double helix is separated, including DNA

replication, recombination and DNA repair.

[80]

These binding proteins seem to stabilize

single-stranded DNA and protect it from forming stem-loops or being degraded by
nucleases.

In contrast, other proteins have evolved to bind to
particular DNA sequences. The most intensively
studied of these are the various transcription factors,
which are proteins that regulate transcription. Each
transcription factor binds to one particular set of DNA
sequences and activates or inhibits the transcription of
genes that have these sequences close to their
promoters. The transcription factors do this in two
ways. Firstly, they can bind the RNA polymerase
responsible for transcription, either directly or through
other mediator proteins; this locates the polymerase at
the promoter and allows it to begin transcription. ]
Alternatively, transcription factors can bind enzymes
that modify the histones at the promoter; this will
change the accessibility of the DNA template to the
polymerase. ]

The lambda repressor helix-turn-helix
transcription factor bound to its DNA

target

As these DNA targets can occur throughout an
organism's genome, changes in the activity of one type
of transcription factor can affect thousands of
genes. Consequently, these proteins are often the

targets of the signal transduction processes that control responses to environmental
changes or cellular differentiation and development. The specificity of these transcription

DNA

209

factors' interactions with DNA come from the proteins making multiple contacts to the
edges of the DNA bases, allowing them to "read" the DNA sequence. Most of these
base-interactions are made in the major groove, where the bases are most accessible. ]

Nucleases and ligases

Nucleases are enzymes that cut DNA
strands by catalyzing the hydrolysis of the
phosphodiester bonds. Nucleases that
hydrolyse nucleotides from the ends of
DNA strands are called exonucleases,
while endonucleases cut within strands.
The most frequently used nucleases in
molecular biology are the restriction
endonucleases, which cut DNA at specific
sequences. For instance, the EcoRV
enzyme shown to the left recognizes the
6-base sequence 5[]-GAT|ATC-3[] and makes a cut at the vertical line. In nature, these
enzymes protect bacteria against phage infection by digesting the phage DNA when it

The restriction enzyme EcoRV (green) in a complex

with its substrate DNA

DNA-modifying enzymes

[87]

enters the bacterial cell, acting as part of the restriction modification system,
technology, these sequence-specific nucleases are used in molecular cloning and DNA
fingerprinting.

Enzymes called DNA ligases can rejoin cut or broken DNA strands. Ligases are
particularly important in lagging strand DNA replication, as they join together the short
segments of DNA produced at the replication fork into a complete copy of the DNA
template. They are also used in DNA repair and genetic recombination. J

Topoisomerases and helicases

Topoisomerases are enzymes with both nuclease and ligase activity. These proteins change
the amount of supercoiling in DNA. Some of these enzyme work by cutting the DNA helix
and allowing one section to rotate, thereby reducing its level of supercoiling; the enzyme
then seals the DNA break. J Other types of these enzymes are capable of cutting one DNA
helix and then passing a second strand of DNA through this break, before rejoining the
helix. J Topoisomerases are required for many processes involving DNA, such as DNA
replication and transcription. J

Helicases are proteins that are a type of molecular motor. They use the chemical energy in
nucleoside triphosphates, predominantly ATP, to break hydrogen bonds between bases and
unwind the DNA double helix into single strands. These enzymes are essential for most
processes where enzymes need to access the DNA bases.

DNA

210

Polymerases

Polymerases are enzymes that synthesize polynucleotide chains from nucleoside
triphosphates. The sequence of their products are copies of existing polynucleotide chains -
which are called templates. These enzymes function by adding nucleotides onto the 3D
hydroxyl group of the previous nucleotide in a DNA strand. Consequently, all polymerases
work in a 5Q to 3D direction. ] In the active site of these enzymes, the incoming nucleoside
triphosphate base-pairs to the template: this allows polymerases to accurately synthesize
the complementary strand of their template. Polymerases are classified according to the
type of template that they use.

In DNA replication, a DNA-dependent DNA polymerase makes a copy of a DNA sequence.
Accuracy is vital in this process, so many of these polymerases have a proofreading activity.
Here, the polymerase recognizes the occasional mistakes in the synthesis reaction by the
lack of base pairing between the mismatched nucleotides. If a mismatch is detected, a 3Q to
5Q exonuclease activity is activated and the incorrect base removed. J In most organisms
DNA polymerases function in a large complex called the replisome that contains multiple
accessory subunits, such as the DNA clamp or helicases. J

RNA-dependent DNA polymerases are a specialized class of polymerases that copy the
sequence of an RNA strand into DNA. They include reverse transcriptase, which is a viral
enzyme involved in the infection of cells by retroviruses, and telomerase, which is required
for the replication of telomeres. ] c ^ Telomerase is an unusual polymerase because it
contains its own RNA template as part of its structure. J

Transcription is carried out by a DNA-dependent RNA polymerase that copies the sequence
of a DNA strand into RNA. To begin transcribing a gene, the RNA polymerase binds to a
sequence of DNA called a promoter and separates the DNA strands. It then copies the gene
sequence into a messenger RNA transcript until it reaches a region of DNA called the
terminator, where it halts and detaches from the DNA. As with human DNA-dependent DNA
polymerases, RNA polymerase II, the enzyme that transcribes most of the genes in the
human genome, operates as part of a large protein complex with multiple regulatory and
accessory subunits. ]

Genetic recombination

DNA

211

■

Structure of the Holliday junction intermediate in genetic recombination. The four separate
DNA strands are coloured red, blue, green and yellow. ]

A DNA helix usually does not interact with
other segments of DNA, and in human cells
the different chromosomes even occupy
separate areas in the nucleus called
"chromosome territories". * This physical
separation of different chromosomes is
important for the ability of DNA to function
as a stable repository for information, as
one of the few times chromosomes interact
is during chromosomal crossover when
they recombine. Chromosomal crossover is
when two DNA helices break, swap a
section and then rejoin.

H-s-i

■

Recombination involves the breakage and rejoining of

two chromosomes (M and F) to produce two

re-arranged chromosomes (CI and C2).

Recombination allows chromosomes to exchange genetic information and produces new
combinations of genes, which increases the efficiency of natural selection and can be
important in the rapid evolution of new proteins. J Genetic recombination can also be
involved in DNA repair, particularly in the cell's response to double-strand breaks.

[99]

The most common form of chromosomal crossover is homologous recombination, where the
two chromosomes involved share very similar sequences. Non-homologous recombination
can be damaging to cells, as it can produce chromosomal translocations and genetic
abnormalities. The recombination reaction is catalyzed by enzymes known as recombinases,

The first step in recombination is a double-stranded break either

such as RAD51.

[100]

n on

caused by an endonuclease or damage to the DNA. L J A series of steps catalyzed in part
by the recombinase then leads to joining of the two helices by at least one Holliday
junction, in which a segment of a single strand in each helix is annealed to the
complementary strand in the other helix. The Holliday junction is a tetrahedral junction
structure that can be moved along the pair of chromosomes, swapping one strand for
another. The recombination reaction is then halted by cleavage of the junction and
re-ligation of the released DNA. 02]

DNA

212

Evolution

DNA contains the genetic information that allows all modern living things to function, grow
and reproduce. However, it is unclear how long in the 4-billion-year history of life DNA has
performed this function, as it has been proposed that the earliest forms of life may have
used RNA as their genetic material. RNA may have acted as the central part of early

cell metabolism as it can both transmit genetic information and carry out catalysis as part
of ribozymes. J This ancient RNA world where nucleic acid would have been used for
both catalysis and genetics may have influenced the evolution of the current genetic code
based on four nucleotide bases. This would occur since the number of unique bases in such
an organism is a trade-off between a small number of bases increasing replication accuracy
and a large number of bases increasing the catalytic efficiency of ribozymes.

Unfortunately, there is no direct evidence of ancient genetic systems, as recovery of DNA
from most fossils is impossible. This is because DNA will survive in the environment for less
than one million years and slowly degrades into short fragments in solution. J Claims for
older DNA have been made, most notably a report of the isolation of a viable bacterium
from a salt crystal 250-million years old, but these claims are controversial.

Uses in technology

Genetic engineering

Methods have been developed to purify DNA from organisms, such as phenol-chloroform
extraction and manipulate it in the laboratory, such as restriction digests and the
polymerase chain reaction. Modern biology and biochemistry make intensive use of these
techniques in recombinant DNA technology. Recombinant DNA is a man-made DNA
sequence that has been assembled from other DNA sequences. They can be transformed
into organisms in the form of plasmids or in the appropriate format, by using a viral

n 1 01

vector. 1 J The genetically modified organisms produced can be used to produce products

rim ni2i

such as recombinant proteins, used in medical research/ J or be grown in agriculture.

[113]

Forensics

Forensic scientists can use DNA in blood, semen, skin, saliva or hair found at a crime scene
to identify a matching DNA of an individual, such as a perpetrator. This process is called
genetic fingerprinting, or more accurately, DNA profiling. In DNA profiling, the lengths of
variable sections of repetitive DNA, such as short tandem repeats and minisatellites, are
compared between people. This method is usually an extremely reliable technique for
identifying a matching DNA. J However, identification can be complicated if the scene is

n 1 ^i

contaminated with DNA from several people. DNA profiling was developed in 1984 by

British geneticist Sir Alec Jeffreys, and first used in forensic science to convict Colin

n 171

Pitchfork in the 1988 Enderby murders case.

People convicted of certain types of crimes may be required to provide a sample of DNA for
a database. This has helped investigators solve old cases where only a DNA sample was

obtained from the scene. DNA profiling can also be used to identify victims of mass casualty

n 1 8i
incidents. On the other hand, many convicted people have been released from prison on

the basis of DNA techniques, which were not available when a crime had originally been
committed.

DNA

213

Bioinformatics

Bioinformatics involves the manipulation, searching, and data mining of DNA sequence
data. The development of techniques to store and search DNA sequences have led to widely
applied advances in computer science, especially string searching algorithms, machine

n 191

learning and database theory. 1 J String searching or matching algorithms, which find an
occurrence of a sequence of letters inside a larger sequence of letters, were developed to
search for specific sequences of nucleotides. J In other applications such as text editors,
even simple algorithms for this problem usually suffice, but DNA sequences cause these
algorithms to exhibit near-worst-case behaviour due to their small number of distinct
characters. The related problem of sequence alignment aims to identify homologous
sequences and locate the specific mutations that make them distinct. These techniques,
especially multiple sequence alignment, are used in studying phylogenetic relationships and

ri2ii

protein function. 1 J Data sets representing entire genomes' worth of DNA sequences, such
as those produced by the Human Genome Project, are difficult to use without annotations,
which label the locations of genes and regulatory elements on each chromosome. Regions
of DNA sequence that have the characteristic patterns associated with protein- or
RNA-coding genes can be identified by gene finding algorithms, which allow researchers to
predict the presence of particular gene products in an organism even before they have been
isolated experimentally. J

DNA nanotechnology

DNA nanotechnology uses the
unique molecular recognition
properties of DNA and other

nucleic

acids

create

self-assembling branched DNA

complexes

with

useful

properties. [124] DNA is thus
used as a structural material
rather than as a carrier of
biological information. This
has led to the creation of

periodic

two-dimensional

lattices (both tile-based as well
as using the "DNA origami"
method) as

well

three-dimensional structures

the

shapes

100 nm

The DNA structure at left (schematic shown) will self-assemble into

the structure visualized by atomic force microscopy at right. DNA

nanotechnology is the field which seeks to design nanoscale structures

using the molecular recognition properties of DNA molecules. Image

from Strong, 2004. [123]

polyhedra. ^ Nanomechanical devices and algorithmic self-assembly have also been
demonstrated/ and these DNA structures have been used to template the arrangement
of other molecules such as gold nanoparticles and streptavidin proteins. *

DNA

214

History and anthropology

Because DNA collects mutations over time, which are then inherited, it contains historical
information and by comparing DNA sequences, geneticists can infer the evolutionary

history of organisms, their phylogeny.

[128]

This field of phylogenetics is a powerful tool in

evolutionary biology. If DNA sequences within a species are compared, population
geneticists can learn the history of particular populations. This can be used in studies
ranging from ecological genetics to anthropology; for example, DNA evidence is being used
to try to identify the Ten Lost Tribes of Israel. 11291 [130]

DNA has also been used to look at modern family relationships, such as establishing family
relationships between the descendants of Sally Hemings and Thomas Jefferson. This usage
is closely related to the use of DNA in criminal investigations detailed above. Indeed, some
criminal investigations have been solved when DNA from crime scenes has matched
relatives of the guilty individual.

History of DNA research

DNA was first isolated by the Swiss physician Friedrich Miescher who, in 1869, discovered
a microscopic substance in the pus of discarded surgical bandages. As it resided in the
nuclei of cells, he called it "nuclein 1 . J In 1919, Phoebus Levene identified the base,
sugar and phosphate nucleotide unit. Levene suggested that DNA consisted of a string

of nucleotide units linked together through the phosphate groups. However, Levene
thought the chain was short and the bases repeated in a fixed order. In 1937 William
Astbury produced the first X-ray diffraction patterns that showed that DNA had a regular
structure. 11 34]

In 1928, Frederick Griffith discovered that traits of the "smooth" form of the Pneumococcus
could be transferred to the "rough" form of the same bacteria by mixing killed "smooth"
bacteria with the live "rough" form. J This system provided the first clear suggestion that
DNA carried genetic information— the Avery-MacLeod-McCarty experiment— when Oswald
Avery, along with coworkers Colin MacLeod and Maclyn McCarty, identified DNA as the
transforming principle in 1943. DNA's role in heredity was confirmed in 1952, when

Alfred Hershey and Martha Chase in the Hershey-Chase experiment showed that DNA is

r i 371

the genetic material of the T2 phage.

Francis Crick

DNA

215

Erwin Chargaff

tr a km <W*t Hate ifcir vr H*«

n A/j/iyHS the o»w, •«> *w»t "W S*» >W*

of A.MJL Mn.li ({tfttXUMie)

barn iHim4 A. Atfffcam£ «**«SfM».c«

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DNA Helix controversy

In 1953 James D. Watson and Francis Crick suggested what is now accepted as the first

T71

correct double-helix model of DNA structure in the journal Nature. Their double-helix,
molecular model of DNA was then based on a single X-ray diffraction image (labeled as
"Photo 51") taken by Rosalind Franklin and Raymond Gosling in May 1952, as well as

the information that the DNA bases were paired— also obtained through private
communications from Erwin Chargaff in the previous years. Chargaff s rules played a very
important role in establishing double-helix configurations for B-DNA as well as A-DNA.

Experimental evidence supporting the Watson and Crick model were published in a series
of five articles in the same issue of Nature. Of these, Franklin and Gosling's paper was
the first publication of their own X-ray diffraction data and original analysis method that
partially supported the Watson and Crick model L J L ,• this issue also contained an article
on DNA structure by Maurice Wilkins and two of his colleagues, whose analysis and in vivo
B-DNA X-ray patterns also supported the presence in vivo of the double-helical DNA
configurations as proposed by Crick and Watson for their double-helix molecular model of

roil

DNA in the previous two pages of Nature. In 1962, after Franklin's death, Watson, Crick,
and Wilkins jointly received the Nobel Prize in Physiology or Medicine. Unfortunately,

Nobel rules of the time allowed only living recipients, but a vigorous debate continues on
who should receive credit for the discovery. J

In an influential presentation in 1957, Crick laid out the "Central Dogma" of molecular
biology, which foretold the relationship between DNA, RNA, and proteins, and articulated
the "adaptor hypothesis". J Final confirmation of the replication mechanism that was
implied by the double-helical structure followed in 1958 through the Meselson-Stahl
experiment. Further work by Crick and coworkers showed that the genetic code was

based on non-overlapping triplets of bases, called codons, allowing Har Gobind Khorana,
Robert W. Holley and Marshall Warren Nirenberg to decipher the genetic code. These

findings represent the birth of molecular biology.

DNA

216

See also

Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid

Molecular models of DNA

DNA microarray

DNA sequencing

Paracrystal model and theory

X-ray scattering

Crystallography

X-ray crystallography

Genetic disorder

Junk DNA

Nucleic acid analogues

Nucleic acid methods

Nucleic acid modeling

Nucleic Acid Notations

Phosphoramidite

Plasmid

Polymerase chain reaction

Proteopedia DNA [146]

Southern blot

Triple-stranded DNA

Notes

[I] Russell, Peter (2001). iGenetics. New York: Benjamin Cummings. ISBN 0-805-34553-1.

[2] Saenger, Wolfram (1984). Principles of Nucleic Acid Structure. New York: Springer-Verlag. ISBN 0387907629.
[3] Alberts, Bruce; Alexander Johnson, Julian Lewis, Martin Raff, Keith Roberts, and Peter Walters (2002).

http://www.ncbi.nlm.nih.goWbooks/bv.fcgi?call=bv.View..ShowTOC&rid=mboc4.TOC&o^

Biology of the Cell; Fourth Edition. New York and London: Garland Science. ISBN 0-8153-3218-1. OCLC

145080076 48122761 57023651 69932405 (http://worldcat.org/oclc/145080076+48122761 + 57023651 +

69932405). http://www.ncbi.nlm. nih.gov/books/bv.fcgi?call=bv. View.. ShowTOC&rid=mboc4.TOC&

depth=2.
[4] Butler, John M. (2001). Forensic DNA Typing. Elsevier. ISBN 978-0-12-147951-0. OCLC 223032110 45406517

(http://worldcat.org/oclc/223032110+45406517). pp. 14-15.
[5] Mandelkern M, Elias J, Eden D, Crothers D (1981). "The dimensions of DNA in solution". J Mol Biol 152 (1):

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Further reading

• Calladine, Chris R.; Drew, Horace R.; Luisi, Ben F. and Travers, Andrew A. (2003).
Understanding DNA: the molecule & how it works. Amsterdam: Elsevier Academic Press.
ISBN 0-12-155089-3.

• Dennis, Carina; Julie Clayton (2003). 50 years of DNA. Basingstoke: Palgrave Macmillan.
ISBN 1-4039-1479-6.

• Judson, Horace Freeland (1996). The eighth day of creation: makers of the revolution in
biology. Plainview, N.Y: CSHL Press. ISBN 0-87969-478-5.

• Olby, Robert C. (1994). The path to the double helix: the discovery of DNA. New York:
Dover Publications. ISBN 0-486-68117-3., first published in October 1974 by MacMillan,
with foreword by Francis Crick; the definitive DNA textbook,revised in 1994 with a 9 page
postscript.

• Olby, Robert C. (2009). Francis Crick: A Biography. Plainview, N.Y: Cold Spring Harbor
Laboratory Press. ISBN 0-87969-798-9.

• Ridley, Matt (2006). Francis Crick: discoverer of the genetic code. [Ashland, OH: Eminent
Lives, Atlas Books. ISBN 0-06-082333-X.

• Berry, Andrew; Watson, James D. (2003). DNA: the secret of life. New York: Alfred A.
Knopf. ISBN 0-375-41546-7.

DNA

224

Stent, Gunther Siegmund; Watson, James D. (1980). The double helix: a personal account
of the discovery of the structure of DNA. New York: Norton. ISBN 0-393-95075-1.
Wilkins, Maurice (2003). The third man of the double helix the autobiography of Maurice
Wilkins. Cambridge, Eng: University Press. ISBN 0-19-860665-6.

External links

• DNA (http://www.dmoz.org/Science/Biology/Biochemistry_and_Molecular_Biology/
Biomolecules/Nucleic_Acids/DNA//) at the Open Directory Project
DNA binding site prediction on protein (http://pipe.scs.fsu.edu/displar.html)
DNA coiling to form chromosomes (http://biostudio.com/c_ education mac. htm)
DNA from the Beginning (http://www.dnaftb.org/dnaftb/) Another DNA Learning
Center site on DNA, genes, and heredity from Mendel to the human genome project.
DNA Lab, demonstrates how to extract DNA from wheat using readily available
equipment and supplies. (http://ca.youtube.com/watch?v=iyb7fwduuGM)
DNA the Double Helix Game (http://nobelprize.org/educational_games/medicine/
dnadoublehelix/) From the official Nobel Prize web site

DNA under electron microscope (http://www.fidelitysystems.com/Unlinked_DNA.
html)

Dolan DNA Learning Center (http://www.dnalc.org/)

Double Helix: 50 years of DNA (http://www.nature.com/nature/dna50/archive.html),
Nature

Double Helix 1953-2003 (http://www.ncbe.reading.ac.uk/DNA50/) National Centre
for Biotechnology Education

Francis Crick and James Watson talking on the BBC in 1962, 1972, and 1974 (http://
www.bbc.co.uk/bbcfour/audiointerviews/profilepages/crickwatsonl.shtml)
Genetic Education Modules for Teachers (http://www.genome.gov/10506718) — DNA
from the Beginning Study Guide

Guide to DNA cloning (http://www.blackwellpublishing.com/trun/artwork/
Animations/cloningexp/cloningexp.html)

Olby R (January 2003). "http://chem-faculty.ucsd.edu/joseph/CHEM13/DNAl.pdflQuiet
debut for the double helix". Nature 421 (6921): 402-5. doi: 10.1038/nature01397 (http://
dx.doi.org/10.1038/nature01397). PMID 12540907. http://chem-faculty.ucsd.edu/
joseph/CHEM13/DNAl.pdf.

PDB Molecule of the Month pdb23_l (http://www.rcsb.org/pdb/static.
do?p=education_discussion/molecule_of_the_month/pdb23_l.html)
Rosalind Franklin's contributions to the study of DNA (http://mason.gmu.edu/
- emoody/rfranklin. html)

The Register of Francis Crick Personal Papers 1938 - 2007 (http://orpheus.ucsd.edu/
speccoll/testing/html/mss0660a.html#abstract) at Mandeville Special Collections
Library, Geisel Library, University of California, San Diego

U.S. National DNA Day (http://www.genome.gov/10506367) — watch videos and
participate in real-time chat with top scientists

"http://www.nytimes.com/packages/pdf/science/dna-article.pdflClue to chemistry of
heredity found". The New York Times. Saturday, June 13, 1953. http://www.ny times,
com/packages/pdf/science/dna-article.pdf. The first American newspaper coverage of
the discovery of the DNA structure.
(http://www.elmhurst.edu/~chm/vchembook/581nucleotides.html)

DNA

225

Molecular models of DNA

Molecular models of DNA structures are representations of the molecular geometry and
topology of Deoxyribonucleic acid (DNA) molecules using one of several means, such as:
closely packed spheres (CPK models) made of plastic, metal wires for 'skeletal models',
graphic computations and animations by computers, artistic rendering, and so on, with the
aim of simplifying and presenting the essential, physical and chemical, properties of DNA
molecular structures either in vivo or in vitro. Computer molecular models also allow
animations and molecular dynamics simulations that are very important for understanding
how DNA functions in vivo. Thus, an old standing dynamic problem is how DNA
"self-replication" takes place in living cells that should involve transient uncoiling of
supercoiled DNA fibers. Although DNA consists of relatively rigid, very large elongated
biopolymer molecules called "fibers" or chains (that are made of repeating nucleotide units
of four basic types, attached to deoxyribose and phosphate groups), its molecular structure
in vivo undergoes dynamic configuration changes that involve dynamically attached water
molecules and ions. Supercoiling, packing with histones in chromosome structures, and
other such supramolecular aspects also involve in vivo DNA topology which is even more
complex than DNA molecular geometry, thus turning molecular modeling of DNA into an
especially challenging problem for both molecular biologists and biotechnologists. Like
other large molecules and biopolymers, DNA often exists in multiple stable geometries (that
is, it exhibits conformational isomerism) and configurational, quantum states which are
close to each other in energy on the potential energy surface of the DNA molecule. Such
geometries can also be computed, at least in principle, by employing ab initio quantum
chemistry methods that have high accuracy for small molecules. Such quantum geometries
define an important class of ab initio molecular models of DNA whose exploration has
barely started.

In an interesting twist of roles, the DNA molecule itself was proposed to
be utilized for quantum computing. Both DNA nanostructures as well as
DNA 'computing' biochips have been built (see biochip image at right).

The more advanced, computer-based molecular models of DNA involve
molecular dynamics simulations as well as quantum mechanical
computations of vibro-rotations, delocalized molecular orbitals (MOs),
electric dipole moments, hydrogen-bonding, and so on.

DNA computing
biochip :3D

Molecular models of DNA

226

Spinning DNA
generic model.

Importance

From the very early stages of structural studies of DNA by X-ray

diffraction and biochemical means, molecular models such as the

Watson-Crick double-helix model were successfully employed to solve the

'puzzle' of DNA structure, and also find how the latter relates to its key

functions in living cells. The first high quality X-ray diffraction patterns

of A-DNA were reported by Rosalind Franklin and Raymond Gosling in

1953 . The first calculations of the Fourier transform of an atomic helix

were reported one year earlier by Cochran, Crick and Vand [ ] , and were

followed in 1953 by the computation of the Fourier transform of a

coiled-coil by Crick c * . The first reports of a double-helix molecular

model of B-DNA structure were made by Watson and Crick in 1953 L J L .

Last-but-not-least, Maurice F. Wilkins, A. Stokes and H.R. Wilson,

reported the first X-ray patterns of in vivo B-DNA in partially oriented

[6]

salmon sperm heads

The development of the first correct

double-helix molecular model of DNA by Crick and Watson may not have
been possible without the biochemical evidence for the nucleotide base-pairing ([A — T];
[C-G]), or Chargaff's rules [7] [8] [9] [10] [11] [12] .

Examples of DNA molecular models

Animated molecular models allow one to visually explore the three-dimensional (3D)
structure of DNA. The first DNA model is a space-filling, or CPK, model of the DNA
double-helix whereas the third is an animated wire, or skeletal type, molecular model of
DNA. The last two DNA molecular models in this series depict quadruplex DNA L J that
may be involved in certain cancers . The last figure on this panel is a molecular

model of hydrogen bonds between water molecules in ice that are similar to those found in
DNA.

Molecular models of DNA

227

Adenine

Thymine

3' end

Phosphate-

deoxyribose "^'^

backbone

3' end Cytosine f"

Guanine 5- en d

DNA ligaw
CWA Polymerase (PoUr.i*

DMA pi (mate
RfM p»i*ncJ

Lagging
strand

LMdJnij
strand

DfW Polymeme (MA) I

Hclicow*

Single K/and,
Ginciflg prolans

Tope t;o™ erase

A-DNA B-DNA

Molecular models of DNA

228

Spacefilling model or CPK model - a molecule is represented by overlapping spheres
representing the atoms.

Images for DNA Structure Determination from X-Ray
Patterns

The following images illustrate both the principles and the main steps involved in
generating structural information from X-ray diffraction studies of oriented DNA fibers with
the help of molecular models of DNA that are combined with crystallographic and
mathematical analysis of the X-ray patterns. From left to right the gallery of images shows:

• First row:

• 1. Constructive X-ray interference, or diffraction, following Bragg's Law of X-ray
"reflection by the crystal planes";

• 2. A comparison of A-DNA (crystalline) and highly hydrated B-DNA (paracrystalline) X-ray
diffraction, and respectively, X-ray scattering patterns (courtesy of Dr. Herbert R. Wilson,
FRS- see refs. list);

• 3. Purified DNA precipitated in a water jug;

• 4. The major steps involved in DNA structure determination by X-ray crystallography
showing the important role played by molecular models of DNA structure in this iterative,
structure-determination process;

• Second row:

Molecular models of DNA

229

5. Photo of a modern X-ray diffractometer employed for recording X-ray patterns of DNA
with major components: X-ray source, goniometer, sample holder, X-ray detector and/or
plate holder;

6. Illustrated animation of an X-ray goniometer;

7. X-ray detector at the SLAC synchrotron facility;

8. Neutron scattering facility at ISIS in UK;

• Third and fourth rows: Molecular models of DNA structure at various scales; figure
#11 is an actual electron micrograph of a DNA fiber bundle, presumably of a single
bacterial chromosome loop.

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diffraction
pattern

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atomic
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230

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Paracrystalline lattice models of B-DNA structures

A paracrystalline lattice, or paracrystal, is a molecular or atomic lattice with significant
amounts (e.g., larger than a few percent) of partial disordering of molecular
arranegements. Limiting cases of the paracrystal model are nanostructures, such as
glasses, liquids, etc., that may possess only local ordering and no global order. Liquid
crystals also have paracrystalline rather than crystalline structures.

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Molecular models of DNA

231

Highly hydrated B-DNA occurs naturally in living cells in such a paracrystalline state, which
is a dynamic one in spite of the relatively rigid DNA double-helix stabilized by parallel
hydrogen bonds between the nucleotide base-pairs in the two complementary, helical DNA
chains (see figures). For simplicity most DNA molecular models ommit both water and ions
dynamically bound to B-DNA, and are thus less useful for understanding the dynamic
behaviors of B-DNA in vivo. The physical and mathematical analysis of X-ray L J L J and
spectroscopic data for paracrystalline B-DNA is therefore much more complicated than that
of crystalline, A-DNA X-ray diffraction patterns. The paracrystal model is also important for
DNA technological applications such as DNA nanotechnology. Novel techniques that
combine X-ray diffraction of DNA with X-ray microscopy in hydrated living cells are now
also being developed (see, for example, "Application of X-ray microscopy in the analysis of
living hydrated cells" [18] ).

Genomic and Biotechnology Applications of DNA molecular
modeling

The following gallery of images illustrates various uses of DNA molecular modeling in
Genomics and Biotechnology research applications from DNA repair to PCR and DNA
nanostructures; each slide contains its own explanation and/or details. The first slide
presents an overview of DNA applications, including DNA molecular models, with emphasis
on Genomics and Biotechnology.

Gallery: DNA Molecular modeling applications

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Molecular models of DNA

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Molecular models of DNA

233

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Databases for DNA molecular models and sequences

X-ray diffraction

• NDB ID: UD0017 Database [13]

• X-ray Atlas -database *■ ]

• PDB files of coordinates for nucleic acid structures from X-ray diffraction by NA (incl
DNA) crystals [20]

• Structure factors dowloadable files in CIF format [ ^

Molecular models of DNA

234

Neutron scattering

• ISIS neutron source

• ISIS pulsed neutron source:A world centre for science with neutrons & muons at
Harwell, near Oxford, UK. [22]

X-ray microscopy

• Application of X-ray microscopy in the analysis of living hydrated cells L J

Electron microscopy

T231

• DNA under electron microscope

Atomic Force Microscopy (AFM)

Two-dimensional DNA junction arrays have been visualized by Atomic Force Microscopy
(AFM) L J . Other imaging resources for AFM/Scanning probe microscopy(SPM) can be
freely accessed at:

• How SPM Works [25]

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [26]

Gallery of AFM Images

K ■

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Molecular models of DNA

235

Mass spectrometry— Maldi informatics

Data acquisition

Mass spectrum

Background
subtraction

Mass spectrum
w/o background

Peak detection

List of peak
masses

Nucleic acid
identification

Peak integration

Genotype,
mutations, etc

List of peak
intensities

Nudeic acid
quantitation

Spectroscopy

• Vibrational circular dichroism (VCD)

• FT-NMR [27] [28]

• NMR Atlas-database [29]

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data

[30]

• NMR constraints files for NAs in PDB format [3 ]
NMR microscopy [ 2 ^
Microwave spectroscopy
FT-IR

p T _ NIR [33] [34] [35]

Spectral Hyperspectral, and Chemical imaging) [36] [37] [38] [39] [40] [41] [42] .

Raman spectroscopy/microscopy and CARS .

Fluorescence correlation spectroscopy [45] [46] [47] [48] [49] [50] [51] [52] , Fluorescence

rcQi [541 rRRl

cross-correlation spectroscopy and FRET L J L J L J .
Confocal microscopy J

Molecular models of DNA

236

Gallery: CARS (Raman spectroscopy), Fluorescence confocal
microscopy, and Hyperspectral imaging

IS)

c
c

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absorption

emission

wavelength

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Multispectral/
erspectral Comparison

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detector

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light source

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Molecular models of DNA

237

Enzymes and shell proteins

Genomic and structural databases

CBS Genome Atlas Database L J — contains examples of base skews.

[58]

The Z curve database of genomes

r591[601

genomes

a 3-dimensional visualization and analysis tool of

DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids
molecular structure models in PDB and CIF formats L J

Notes

[I] Franklin, R.E. and Gosling, R.G. reed. 6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium
Thymonucleate Fibres I. The Influence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium
Thymonucleate Fibres II. The Cylindrically Symmetrical Patterson Function.

[2] Cochran, W., Crick, F.H.C. and Vand V. 1952. The Structure of Synthetic Polypeptides. 1. The Transform of

Atoms on a Helix. Acta Cryst. 5(5):581-586.
[3] Crick, F.H.C. 1953a. The Fourier Transform of a Coiled-Coil., Acta Crystallographica 6(8-9):685-689.
[4] Watson, J.D; Crick F.H.C. 1953a. Molecular Structure of Nucleic Acids- A Structure for Deoxyribose Nucleic

Acid., Nature 171(4356):737-738.
[5] Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Qunatitative Biology

18:123-131.
[6] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953).

"http://www.nature.com/nature/dna50/wilkins.pdflMolecular Structure of Deoxypentose Nucleic Acids" (PDF).

Nature 111. 738-740. doi: 10.1038/171738a0 (http://dx.doi.org/10.1038/171738a0). PMID 13054693. http:/

/www . nature . com/nature/dna5 0/ wilkins . pdf .
[7] Elson D, Chargaff E (1952). "On the deoxyribonucleic acid content of sea urchin gametes". Expehentia 8 (4):

143-145.
[8] Chargaff E, Lipshitz R, Green C (1952). "Composition of the deoxypentose nucleic acids of four genera of

sea-urchin". J Biol Chem 195 (1): 155-160. PMID 14938364.
[9] Chargaff E, Lipshitz R, Green C, Hodes ME (1951). "The composition of the deoxyribonucleic acid of salmon

sperm". J Biol Chem 192 (1): 223-230. PMID 14917668.
[10] Chargaff E (1951). "Some recent studies on the composition and structure of nucleic acids". J Cell Physiol

Suppl 38 (Suppl).

[II] Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E (1950). "The separation and estimation of
ribonucleotides in minute quantities". J Biol Chem 186 (1): 37-50. PMID 14778802.

[12] Chargaff E (1950). "Chemical specificity of nucleic acids and mechanism of their enzymatic degradation".
Expehentia 6 (6): 201-209.

[13] http
[14] http
[15] http

//ndbserver.rutgers.edu/atlas/xray/structures/U/ud0017/ud0017.html
//www. phy . cam. ac . uk/research/bss/molbiophysics . php
//planetphysics.org/encyclopedia/TheoreticalBiophysics.html

[16] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam - New

York, 1962.
[17] Baianu, I.C. (1978). "X-ray scattering by partially disordered membrane systems.". Acta Cryst., A34 (5):

751-753. doi: 10.1107/S0567739478001540 (http://dx.doi.org/10.1107/S0567739478001540).
[18] http://www.ncbi. nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&

list_uids=12379938
[19] http ://ndbserver. rutgers . edu/atlas/xray/ index. html
[20] http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-biol/

Molecular models of DNA

238

[21] http ://ndb server. rutgers. edu/ftp/NDB/structure-f actors/

[22] http://www.isis.rl.ac.uk/

[23] http://www.fidelitysystems.com/Unlinked_DNA.html

[24] Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA

Holliday Junction Arrays Visualized by Atomic Force Microscopy". Journal of the American Chemical Society

121 (23): 5437-5443. doi: 10.1021/ja9900398 (http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863

(http://worldcat.org/issn/0002-7863).
[25] http://www.parkafm.com/New html/resources/01 general. php
[26] http://www.rhk-tech.com/results/showcase.php

[27] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants
[28] (http://www.spectroscopynow.com/FCKeditor/UserFiles/File/specNOW/HTML files/

General_Karplus_Calculator.htm) Another Javascript-like NMR coupling constant to dihedral
[29] http ://ndbserver. rutgers . edu/atlas/nmr/index. html
[30] http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-nmr-mmcif/
[31] http ://ndbserver. rutgers. edu/ftp/NDB/nmr-restraints/

[32] Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.
[33] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[34] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[35] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.
[36] http://www.imaging.net/chemical-imaging/Chemical imaging
[37] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee

and L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical

Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.
[38] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy.,

Microchimica Acta, 104, (1-6) January 1991, doi: 10.1007/BF01245536
[39] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[40] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[41] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical

Industry, G.I.T. Laboratory Journal Europe, No. 1-2, 2007.
[42] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology. (June 2004)., I. C.

Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047)
[43] Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/ImagingMicroscopy04.pdf)
[44] C.L. Evans and X.S. Xie.2008. Coherent An ti-Stokes Raman Scattering Microscopy: Chemical Imaging for

Biology and Medicine., doi:10.1146/annurev.anchem.l. 031207. 112754 Annual Review of Analytical Chemistry,

1: 883-909.
[45] Eigen, M., Rigler, M. Sorting single molecules: application to diagnostics and evolutionary

biotechnology, (1994) Proc. Natl. Acad. Sci. USA, 91,5740-5747.
[46] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in

biotechnology,(1995) J. Biotechnol., 41,177-186.
[47] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation

spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.
[48] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al.,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[49] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based

amplification combined with fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.
[50] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in

giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.

Molecular models of DNA

239

[51] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by
fluorescence correlation spectroscopy with one- and two-photon excitation. Biophysical Journal,

77(10):2251-2265.

[52] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[53] FRET description (http://dwb.unl.edu/Teacher/NSF/C08/C08Links/pps99.cryst.bbk.ac.uk/projects/

gmocz/fret.htm)
[54] doi:10.1016/S0959-440X(00)00190-l (http://dx.doi.org/10. 1016/S0959-440X(00)00190-l)Recent

advances in FRET: distance determination in protein-DNA complexes. Current Opinion in Structural Biology

2001, 11(2), 201-207
[55] http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction
[56] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary

biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.
[57] http://www.cbs.dtu.dk/services/GenomeAtlas/
[58] Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic results

and DNA sequence data". Bioinformatics 20: 3682-3686.
[59] http://tubic.tju.edu.cn/zcurve/
[60] Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences".

Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041
[61] http://ndbserver.rutgers.edu/ftp/NDB/models/

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Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by

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Two-Dimensional DNA Holliday Junction Arrays Visualized by Atomic Force Microscopy".

Journal of the American Chemical Society 121 (23): 5437-5443. doi: 10.1021/ja9900398

(http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863 (http://worldcat.org/issn/

0002-7863).

Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping;

Ding, Baoquan; Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie &

Seeman, Nadrian C. (2006). "Double cohesion in structural DNA nanotechnology".

Organic and Biomolecular Chemistry 4: 3414-3419. doi: 10.1039/b605212f (http://dx.

doi.org/10.1039/b605212f).

Molecular models of DNA

241

See also

DNA

Molecular graphics

DNA structure

DNA Dynamics

X-ray scattering

Neutron scattering

Crystallography

Crystal lattices

Paracrystalline lattices/Paracrystals

2D-FT NMRI and Spectroscopy

NMR Spectroscopy

Microwave spectroscopy

Two-dimensional IR spectroscopy

Spectral imaging

Hyperspectral imaging

Chemical imaging

NMR microscopy

VCD or Vibrational circular dichroism

FRET and FCS- Fluorescence correlation spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS)

Molecular structure

Molecular geometry

Molecular topology

DNA topology

Sirius visualization software

Nanostructure

DNA nanotechnology

Imaging

Atomic force microscopy

X-ray microscopy

Liquid crystal

Glasses

QMC@Home

Sir Lawrence Bragg, FRS

Sir John Randall

James Watson

Francis Crick

Maurice Wilkins

Herbert Wilson, FRS

Alex Stokes

Molecular models of DNA

242

External links

DNA the Double Helix Game (http://nobelprize.org/educational_games/medicine/

dnadoublehelix/) From the official Nobel Prize web site

MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. wesleyan.edu:8080/

MDDNA/)

Double Helix 1953-2003 (http://www.ncbe.reading.ac.uk/DNA50/) National Centre

for Biotechnology Education

DNA under electron microscope (http://www.fidelitysystems.com/Unlinked_DNA.

html)

Ascalaph DNA (http://www.agilemolecule.com/Ascalaph/Ascalaph_DNA.html) —

Commercial software for DNA modeling

DNAlive: a web interface to compute DNA physical properties (http://mmb.pcb.ub.es/

DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and

DNA dynamics.

DiProDB: Dinucleotide Property Database (http://diprodb.fli-leibniz.de). The database

is designed to collect and analyse thermodynamic, structural and other dinucleotide

properties.

Further details of mathematical and molecular analysis of DNA structure based on X-ray

data (http://planetphysics.org/encyclopedia/

BesselFunctionsApplicationsToDiffractionByHelicalStructures.html)

Bessel functions corresponding to Fourier transforms of atomic or molecular helices.

(http ://planetphy sics . org/?op = getobj &from = obj ec ts &

name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures)

Application of X-ray microscopy in analysis of living hydrated cells (http://www.ncbi.

nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&

list_uids = 12379938)

Characterization in nanotechnology some pdfs (http://nanocharacterization.sitesled.

com/)

overview of STM/AFM/SNOM principles with educative videos (http://www.ntmdt.ru/

SPM-Techniques/Principles/)

SPM Image Gallery - AFM STM SEM MFM NSOM and More (http://www.rhk-tech.com/

results/showcase. php)

How SPM Works (http://www.parkafm.com/New_html/resources/01general.php)

U.S. National DNA Day (http://www.genome.gov/10506367) — watch videos and

participate in real-time discussions with scientists.

The Secret Life of DNA - DNA Music compositions (http://www.tjmitchell.com/stuart/

dna.html)

DNA structure

243

DNA structure

DNA structure shows a variety of forms, both double-stranded and single-stranded. The
mechanical properties of DNA, which are directly related to its structure, are a significant
problem for cells. Every process which binds or reads DNA is able to use or modify the
mechanical properties of DNA for purposes of recognition, packaging and modification. The
extreme length (a chromosome may contain a 10 cm long DNA strand), relative rigidity and
helical structure of DNA has led to the evolution of histones and of enzymes such as
topoisomerases and helicases to manage a cell's DNA. The properties of DNA are closely
related to its molecular structure and sequence, particularly the weakness of the hydrogen
bonds and electronic interactions that hold strands of DNA together compared to the
strength of the bonds within each strand.

Experimental techniques which can directly measure the mechanical properties of DNA are
relatively new, and high-resolution visualization in solution is often difficult. Nevertheless,
scientists have uncovered large amount of data on the mechanical properties of this
polymer, and the implications of DNA's mechanical properties on cellular processes is a
topic of active current research.

It is important to note the DNA found in many cells can be macroscopic in length - a few
centimetres long for each human chromosome. Consequently, cells must compact or
"package" DNA to carry it within them. In eukaryotes this is carried by spool-like proteins
known as histones, around which DNA winds. It is the further compaction of this
DNA-protein complex which produces the well known mitotic eukaryotic chromosomes.

Structure determination

DNA structures can be determined using either nuclear magnetic resonance spectroscopy
or X-ray crystallography. The first published reports of A-DNA X-ray diffraction patterns-
and also B-DNA— employed analyses based on Patterson transforms that provided only a
limited amount of structural information for oriented fibers of DNA isolated from calf
thymus. An alternate analysis was then proposed by Wilkins et al. in 1953 for B-DNA

X-ray diffraction/scattering patterns of hydrated, bacterial oriented DNA fibers and trout
sperm heads in terms of squares of Bessel functions. J Although the B-DNA form' is most
common under the conditions found in cells, it is not a well-defined conformation but a
family or fuzzy set of DNA-conformations that occur at the high hydration levels present in
a wide variety of living cells. Their corresponding X-ray diffraction & scattering patterns
are characteristic of molecular paracrystals with a significant degree of disorder (>20%)
L J , and concomitantly the structure is not tractable using only the standard analysis.

On the other hand, the standard analysis, involving only Fourier transforms of Bessel
functions and DNA molecular models, is still routinely employed for the analysis of
A-DNA and Z-DNA X-ray diffraction patterns. [9]

[6]

DNA structure

244

Base pair geometry

The geometry of a base, or base pair step can be characterized by 6 coordinates: Shift,
Slide, Rise, Tilt, Roll, and Twist. These values precisely define the location and orientation
in space of every base or base pair in a DNA molecule relative to its predecessor along the
axis of the helix. Together, they characterize the helical structure of the molecule. In
regions of DNA where the "normal" structure is disrupted the change in these values can be
used to describe such disruption.

noi rm r 1 21

For each base pair, considered relative to its predecessor 1 J L J L J :

Shear

Stretch

Stagger

Buckle

Propeller twist

Rotation of one base with respect to the other in the same base pair.
Opening

Shift

displacement along an axis in the base-pair plane perpendicular to the first, directed
from the minor to the major groove.

Slide

displacement along an axis in the plane of the base pair directed from one strand to
the other.

Rise

displacement along the helix axis.

Tilt

rotation around this axis

Roll

rotation around this axis

Twist

rotation around the helix axis.
x-displacement
y-displacement
inclination
tip
pitch

the number of base pairs per complete turn of the helix

Rise and twist determine the handedness and pitch of the helix. The other coordinates, by
contrast, can be zero. Slide and shift are typically small in B-DNA, but are substantial in A-
and Z-DNA. Roll and tilt make successive base pairs less parallel, and are typically small. A
diagram L J of these coordinates can be found in 3DNA L J website.

Note that "tilt" has often been used differently in the scientific literature, referring to the
deviation of the first, inter-strand base-pair axis from perpendicularity to the helix axis. This

DNA structure

245

corresponds to slide between a succession of base pairs, and in helix-based coordinates is
properly termed "inclination".

DNA helix geometries

Three DNA conformations are believed to be found in nature, A-DNA, B-DNA, and Z-DNA.
The "B" form described by James D. Watson and Francis Crick is believed to predominate in
cells L . It is 23.7 A wide and extends 34 A per 10 bp of sequence. The double helix makes
one complete turn about its axis every 10.4-10.5 base pairs in solution. This frequency of
twist (known as the helical pitch) depends largely on stacking forces that each base exerts
on its neighbours in the chain.

Other conformations are possible; A-DNA, B-DNA, C-DNA, D-DNA [16] , E-DNA [17] ,
L-DNA(enantiomeric form of D-DNA) [16] , P-DNA [18] , S-DNA, Z-DNA, etc. have been
described so far. J In fact, only the letters F, Q, U, V, and Y are now available to describe

[201 T211

any new DNA structure that may appear in the future. However, most of these forms

have been created synthetically and have not been observed in naturally occurring
biological systems. Also note the triple-stranded DNA possibility.

A- and Z-DNA

A-DNA and Z-DNA differ significantly in their geometry and dimensions to B-DNA, although
still form helical structures. The A form appears likely to occur only in dehydrated samples
of DNA, such as those used in crystallographic experiments, and possibly in hybrid pairings
of DNA and RNA strands. Segments of DNA that cells have methylated for regulatory
purposes may adopt the Z geometry, in which the strands turn about the helical axis the
opposite way to A-DNA and B-DNA. There is also evidence of protein-DNA complexes
forming Z-DNA structures.

Guanine

Cytosine

anti

N-H'

C5'

axis of helix
of Z-DNA

The helix axis of A-, B-, and Z-DNA.

Geometry attribute

A-DNA

B-DNA

Z-DNA

Helix sense

right-handed

left-handed

Repeating unit

1 bp

lbp

2bp

Rotation/bp

33.6°

35.9°

60°/2bp

Mean bp/turn

10.7

10.0

Inclination of bp to axis

+ 19°

-1.2°

-9°

Rise/bp along axis

2.3 A

3.32 A

3.8 A

DNA structure

246

Pitch/turn of helix

24.6 A

33.2 A

45.6 A

Mean propeller twist

+ 18°

+ 16°

0°

Glycosyl angle

anti

C: anti,
G: syn

Sugar pucker

C3'-endo

C2'-endo

C: C2'-endo,
G: C2'-exo

Diameter

25.5 A

23.7 A

18.4 A

Supercoiled DNA

The B form of the DNA helix twists 360° per 10.4-10.5 bp in the absence of torsional strain.
But many molecular biological processes can induce torsional strain. A DNA segment with
excess or insufficient helical twisting is referred to, respectively, as positively or negatively
"supercoiled". DNA in vivo is typically negatively supercoiled, which facilitates the
unwinding (melting) of the double-helix required for RNA transcription.

Non-helical forms

Other non-double helical forms of DNA have been described, for example side-by-side (SBS)
and triple helical configurations. Single stranded DNA may exist in statu nascendi or as
thermally induced despiralized DNA.

DNA bending

DNA is a relatively rigid polymer, typically modelled as a worm-like chain. It has three
significant degrees of freedom; bending, twisting and compression, each of which cause
particular limitations on what is possible with DNA within a cell. Twisting/torsional stiffness
is important for the circularisation of DNA and the orientation of DNA bound proteins
relative to each other and bending/axial stiffness is important for DNA wrapping and
circularisation and protein interactions. Compression/extension is relatively unimportant in
the absence of high tension.

Persistence length/ Axial stiffness

Example sequences and their persistence lengths (B DNA)

Sequence

Persistence Length
/base pairs

Random

154±10

(CA)

repeat

133±10

( CAG Wat

124±10

(TATA)

repeat

137±10

DNA in solution does not take a rigid structure but is continually changing conformation
due to thermal vibration and collisions with water molecules, which makes classical
measures of rigidity impossible. Hence, the bending stiffness of DNA is measured by the
persistence length, defined as:

DNA structure

247

"The length of DNA over which the time-averaged orientation of the polymer becomes
uncorrelated by a factor of e."

This value may be directly measured using an atomic force microscope to directly image
DNA molecules of various lengths. In aqueous solution the average persistence length is
46-50 nm or 140-150 base pairs (the diameter of DNA is 2 nm), although can vary
significantly. This makes DNA a moderately stiff molecule.

The persistence length of a section of DNA is somewhat dependent on its sequence, and
this can cause significant variation. The variation is largely due to base stacking energies
and the residues which extend into the minor and major grooves.

Models for DNA bending

Stacking stability of base steps (B DNA)

Step

Stacking AG
/kcal mol"

T A

-0.19

T G or C A

-0.55

-0.91

A G or C T

-1.06

A A or T T

-1.11

-1.34

G A or T C

-1.43

CCorGG

-1.44

A C or G T

-1.81

G C

-2.17

The entropic flexibility of DNA is remarkably consistent with standard polymer physics
models such as the Kratky-Porod worm-like chain model. Consistent with the worm-like
chain model is the observation that bending DNA is also described by Hooke's law at very
small (sub-piconewton) forces. However for DNA segments less than the persistence length,
the bending force is approximately constant and behaviour deviates from the worm-like
chain predictions.

This effect results in unusual ease in circularising small DNA molecules and a higher
probability of finding highly bent sections of DNA.

Bending preference

DNA molecules often have a preferred direction to bend, ie. anisotropic bending. This is,
again, due to the properties of the bases which make up the DNA sequence - a random
sequence will have no preferred bend direction, i.e. isotropic bending.

Preferred DNA bend direction is determined by the stability of stacking each base on top of
the next. If unstable base stacking steps are always found on one side of the DNA helix then
the DNA will preferentially bend away from that direction. As bend angle increases then
steric hindrances and ability to roll the residues relative to each other also play a role,
especially in the minor groove. A and T residues will be preferentially be found in the minor

DNA structure

248

grooves on the inside of bends. This effect is particularly seen in DNA-protein binding
where tight DNA bending is induced, such as in nucleosome particles. See base step
distortions above.

DNA molecules with exceptional bending preference can become intrinsically bent. This
was first observed in trypanosomatid kinetoplast DNA. Typical sequences which cause this
contain stretches of 4-6 T and A residues separated by G and C rich sections which keep
the A and T residues in phase with the minor groove on one side of the molecule. For
example:

GATTCCCAAAAATGTCAAAAAATAGGCAAAAAATGC
CAAAAAATCCCAAAC

The intrinsically bent structure is induced by the 'propeller twist' of base pairs relative to
each other allowing unusual bifurcated Hydrogen-bonds between base steps. At higher
temperatures this structure, and so the intrinsic bend, is lost.

All DNA which bends anisotropically has, on average, a longer persistence length and
greater axial stiffness. This increased rigidity is required to prevent random bending which
would make the molecule act isotropically.

DNA circularisation

DNA circularisation depends on both the axial (bending) stiffness and torsional (rotational)
stiffness of the molecule. For a DNA molecule to successfully circularise it must be long
enough to easily bend into the full circle and must have the correct number of bases so the
ends are in the correct rotation to allow bonding to occur. The optimum length for
circularisation of DNA is around 400 base pairs (136 nm), with an integral number of turns
of the DNA helix, i.e. multiples of 10.4 base pairs. Having a non integral number of turns
presents a significant energy barrier for circularisation, for example a 10.4 x 30 = 312 base
pair molecule will circularise hundreds of times faster than 10.4 x 30.5 « 317 base pair
molecule.

DNA stretching

Longer stretches of DNA are entropically elastic under tension. When DNA is in solution, it
undergoes continuous structural variations due to the energy available in the solvent. This
is due to the thermal vibration of the molecule combined with continual collisions with
water molecules. For entropic reasons, more compact relaxed states are thermally
accessible than stretched out states, and so DNA molecules are almost universally found in
a tangled relaxed layouts. For this reason, a single molecule of DNA will stretch under a
force, straightening it out. Using optical tweezers, the entropic stretching behavior of DNA
has been studied and analyzed from a polymer physics perspective, and it has been found
that DNA behaves largely like the Kratky-Porod worm-like chain model under
physiologically accessible energy scales.

Under sufficient tension and positive torque, DNA is thought to undergo a phase transition
with the bases splaying outwards and the phosphates moving to the middle. This proposed
structure for overstretched DNA has been called "P-form DNA," in honor of Linus Pauling
who originally presented it as a possible structure of DNA C *

DNA structure

249

The mechanical properties DNA under compression have not been characterized due to
experimental difficulties in preventing the polymer from bending under the compressive
force.

DNA melting

Melting stability of base steps (B DNA)

Step

Melting AG
/Kcal mol" 1

T A

-0.12

T G or C A

-0.78

C G

-1.44

A G or C T

-1.29

A A or T T

-1.04

-1.27

G A or T C

-1.66

CCorGG

-1.97

A C or G T

-2.04

G C

-2.70

DNA melting is the process by which the interactions between the strands of the double
helix are broken, separating the two strands of DNA. These bonds are weak, easily
separated by gentle heating, enzymes, or physical force. DNA melting preferentially occurs

T221

at certain points in the DNA. L J T and A rich sequences are more easily melted than C and
G rich regions. Particular base steps are also susceptible to DNA melting, particularly T A
and T G base steps. These mechanical features are reflected by the use of sequences
such as TATAA at the start of many genes to assist RNA polymerase in melting the DNA for
transcription.

Strand separation by gentle heating, as used in PCR, is simple providing the molecules have
fewer than about 10,000 base pairs (10 kilobase pairs, or 10 kbp). The intertwining of the
DNA strands makes long segments difficult to separate. The cell avoids this problem by
allowing its DNA-melting enzymes (helicases) to work concurrently with topoisomerases,
which can chemically cleave the phosphate backbone of one of the strands so that it can
swivel around the other. Helicases unwind the strands to facilitate the advance of
sequence-reading enzymes such as DNA polymerase.

DNA structure

250

DNA topology

Within the cell most DNA is topologically restricted.
DNA is typically found in closed loops (such as plasmids
in prokaryotes) which are topologically closed, or as
very long molecules whose diffusion coefficients
produce effectively topologically closed domains. Linear
sections of DNA are also commonly bound to proteins
or physical structures (such as membranes) to form
closed topological loops.

Francis Crick was one of the first to propose the
importance of linking numbers when considering DNA
supercoils. In a paper published in 1976, Crick outlined
the problem as follows:

In considering supercoils formed by closed
double-stranded molecules of DNA certain
mathematical concepts, such as the linking
number and the twist, are needed. The
meaning of these for a closed ribbon is
explained and also that of the writhing
number of a closed curve. Some simple
examples are given, some of which may be
relevant to the structure of chromatin. J

0^*360

Twist = -1, Writhe = 0.

Twist = 0, Writhe = -1

Vto360'

Twist = +1, Writhe = 0.

Twist = 0. Writhe = +1

720

V^720'

Twist = -2, Writhe = 0.

Twist = +2, Writhe = 0.

Twist = 0, Writhe = -2.

Twist = 0, Writhe = +2.

(p\ 5§) Twist = 0, Writhe = -4.
O

Plectonemic

Toroidal

Supercoiled structure of circular DNA

molecules with low writhe. Note that

the helical nature of the DNA duplex is

omitted for clarity.

Analysis of DNA topology uses three values:

L = linking number - the number of times one DNA strand wraps around the other. It
is an integer for a closed loop and constant for a closed topological domain.

T = twist - total number of turns in the double stranded DNA helix. This will normally
try to be equal to the number turns a DNA molecule will make while free in solution,
ie. number of bases/10.4.

writhe

number of turns of the double stranded DNA helix around the

superhelical axis

L = T + W and AL = AT + AW

Any change of T in a closed topological domain must be balanced by a change in W, and
vice versa. This results in higher order structure of DNA. A circular DNA molecule with a
writhe of will be circular. If the twist of this molecule is subsequently increased or
decreased by supercoiling then the writhe will be appropriately altered, making the
molecule undergo plectonemic or toroidal superhelical coiling.

When the ends of a piece of double stranded helical DNA are joined so that it forms a circle
the strands are topologically knotted. This means the single strands cannot be separated
any process that does not involve breaking a strand (such as heating). The task of
un-knotting topologically linked strands of DNA falls to enzymes known as topoisomerases.
These enzymes are dedicated to un-knotting circular DNA by cleaving one or both strands
so that another double or single stranded segment can pass through. This un-knotting is
required for the replication of circular DNA and various types of recombination in linear
DNA which have similar topological constraints.

DNA structure

251

The linking number paradox

For many years, the origin of residual supercoiling in eukaryotic genomes remained
unclear. This topological puzzle was referred to by some as the "linking number

[251

paradox". 1 J However, when experimentally determined structures of the nucleosome
displayed an overtwisted left-handed wrap of DNA around the histone octamer J L , this
"paradox" was solved.

See also

• DNA nanotechnology

• Molecular models of DNA

References

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1038/38444). PMID 9305837.
[27] Davey CA, Sargent DF, Luger K, Maeder AW, Richmond TJ (2002). "Solvent mediated interactions in the

structure of the nucleosome core particle at 1.9 A resolution". Journal of Molecular Biology 319 (5): 1097-1113.

doi: 10.1016/S0022-2836(02)00386-8 (http://dx.doi.org/10.1016/S0022-2836(02)00386-8). PMID 12079350.

External links

• MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. wesleyan.edu:8080/
MDDNA/)

• Ascalaph DNA (http://www.agilemolecule.com/Ascalaph/Ascalaph_DNA.html) —
Commercial software for DNA modeling

• DNAlive: a web interface to compute DNA physical properties (http://mmb.pcb.ub.es/
DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and
DNA dynamics.

• DiProDB: Dinucleotide Property Database (http://diprodb.fli-leibniz.de). The database
is designed to collect and analyse thermodynamic, structural and other dinucleotide
properties.

Paracrystalline

253

Paracrystalline

Paracrystalline materials are defined as having short and medium range ordering in their
lattice (similar to the liquid crystal phases) but lacking long-range ordering at least in one
direction. J

Ordering is the regularity in which atoms appear in a predictable lattice, as measured from
one point. In a highly ordered, perfectly crystalline material, or single crystal, the location
of every atom in the structure can be described exactly measuring out from a single origin.
Conversely, in a disordered structure such as a liquid or amorphous solid, the location of
the first and perhaps second nearest neighbors can be described from an origin (with some
degree of uncertainty) and the ability to predict locations decreases rapidly from there out.
The distance at which atom locations can be predicted is referred to as the correlation
length f . A paracrystalline material exhibits correlation somewhere between the fully
amorphous and fully crystalline.

The primary, most accessible source of crystallinity information is X-ray diffraction,
although other techniques may be needed to observe the complex structure of

T21

paracrystalline materials, such as fluctuation electron microscopy in combination with
Density of states modeling^ ] of electronic and vibrational states.

Paracrystalline Model

The paracrystalline model is a revision of the Continuous Random Network model first
proposed by W. H. Zachariasen in 1932 L J . The paracrystal model is defined as highly
strained, microcrystalline grains surrounded by fully amorphous material . This is a
higher energy state then the continuous random network model. The important distinction
between this model and the microcrystalline phases is the lack of defined grain boundaries
and highly strained lattice parameters, which makes calculations of molecular and lattice
dynamics difficult. A general theory of paracrystals has been formulated in a basic
textbook^ J , and then further developed/refined by various authors.

Applications

The paracrystal model has been useful, for example, in describing the state of partially
amorphous semiconductor materials after deposition. It has also been successfully applied
to: synthetic polymers, liquid crystals, biopoloymers , and biomembranes .

See also

X-ray scattering
Amorphous solid
Single Crystal
Polycrystalline
Crystallography
DNA

X-ray pattern of a B-DNA Paracrystal [10]

Paracrystalline

254

Notes

[1] Voyles, et al. Structure and physical properties of paracrystalline atomistic models of amorphous silicon. J. Ap.

Phys., 90(2001) 4437, doi: 10.1063/1.1407319
[2] Biswas, P, et al. J. Phys.-.Condens. Matter, 19 (2007) 455202, doi:10. 1088/0953-8984/19/45/455202
[3] Nakhmanson, Voyles, Mousseau, Barkema, and Drabold. Phys. Rev. B 63(2001) 235207. doi:

10. 1103/PhysRevB. 63. 235207
[4] Zachariasen, W.H., J. Am. Chem. Soc, 54(1932) 3841.
[5] J.M. Cowley, Diffraction Studies on Non-Cryst. Substan. 13 (1981)
[6] Hosemann R., Bagchi R.N., Direct analysis of diffraction by matter, North-Holland Pubis., Amsterdam - New

York, 1962
[7] Bessel functions and diffraction by helical structures http://planetphysics.org/encyclopedia/

BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures.html
[8] X-Ray Diffraction Patterns of Double-Helical Deoxyribonucleic Acid (DNA) Crystals and Paracrystalline Fibers

http://planetphysics.org/encyclopedia/BesselFunctionsApplicationsToDiffractionByHelicalStructures.html
[9] Baianu I.C., X-ray scattering by partially disordered membrane systems, Acta Cryst. A, 34 (1978), 751-753.
[10] http://commons.wikimedia.Org/wiki/File:ABDNAxrgpj.jpg

DNA Dynamics

DNA Molecular dynamics modeling involves simulations of DNA molecular geometry
and topology changes with time as a result of both intra- and inter- molecular interactions
of DNA. Whereas molecular models of Deoxyribonucleic acid (DNA) molecules such as
closely packed spheres (CPK models) made of plastic or metal wires for 'skeletal models'
are useful representations of static DNA structures, their usefulness is very limited for
representing complex DNA dynamics. Computer molecular modeling allows both
animations and molecular dynamics simulations that are very important for understanding
how DNA functions in vivo.

An old standing dynamic problem is how DNA "self-replication" takes place in living cells
that should involve transient uncoiling of supercoiled DNA fibers. Although DNA consists of
relatively rigid, very large elongated biopolymer molecules called "fibers" or chains its
molecular structure in vivo undergoes dynamic configuration changes that involve
dynamically attached water molecules, ions or proteins/enzymes. Supercoiling, packing
with histones in chromosome structures, and other such supramolecular aspects also
involve in vivo DNA topology which is even more complex than DNA molecular geometry,
thus turning molecular modeling of DNA dynamics into a series of challenging problems for
biophysical chemists, molecular biologists and biotechnologists. Thus, DNA exists in
multiple stable geometries (called conformational isomerism) and has a rather large
number of configurational, quantum states which are close to each other in energy on the
potential energy surface of the DNA molecule.

Such varying molecular geometries can also be computed, at least in principle, by
employing ab initio quantum chemistry methods that can attain high accuracy for small
molecules, although claims that acceptable accuracy can be also achieved for
polynucleotides, as well as DNA conformations, were recently made on the basis of VCD
spectral data. Such quantum geometries define an important class of ab initio molecular
models of DNA whose exploration has barely started especially in connection with results
obtained by VCD in solutions. More detailed comparisons with such ab initio quantum
computations are in principle obtainable through 2D-FT NMR spectroscopy and relaxation
studies of polynucleotide solutions or specifically labeled DNA, as for example with

DNA Dynamics

255

deuterium labels

Importance of DNA molecular structure and dynamics
modeling for Genomics and beyond

From the very early stages of structural studies of DNA by X-ray diffraction and
biochemical means, molecular models such as the Watson-Crick double-helix model were
successfully employed to solve the 'puzzle' of DNA structure, and also find how the latter
relates to its key functions in living cells. The first high quality X-ray diffraction patterns of

A-DNA were reported by Rosalind Franklin and Raymond Gosling in 1953 . The first
reports of a double-helix molecular model of B-DNA structure were made by Watson and
Crick in 1953 [2] [3] . Then Maurice F. Wilkins, A. Stokes and H.R. Wilson, reported the first
X-ray patterns of in vivo B-DNA in partially oriented salmon sperm heads [ ^ . The
development of the first correct double-helix molecular model of DNA by Crick and Watson
may not have been possible without the biochemical evidence for the nucleotide
base-pairing ([A— T] ; [C— G]), or Chargaff's rules [5] [6] [7] [8] [9] [10] . Although such initial
studies of DNA structures with the help of molecular models were essentially static, their
consequences for explaining the in vivo functions of DNA were significant in the areas of
protein biosynthesis and the quasi-universality of the genetic code. Epigenetic
transformation studies of DNA in vivo were however much slower to develop in spite of
their importance for embryology, morphogenesis and cancer research. Such chemical
dynamics and biochemical reactions of DNA are much more complex than the molecular
dynamics of DNA physical interactions with water, ions and proteins/enzymes in living cells.

Animated DNA molecular models and hydrogen-bonding

rm n 21

may be involved in certain cancers . The first CPK model in the second row is a

molecular model of hydrogen bonds between water molecules in ice that are broadly similar
to those found in DNA; the hydrogen bonding dynamics and proton exchange is however
very different by many orders of magnitude between the two systems of fully hydrated DNA
and water molecules in ice. Thus, the DNA dynamics is complex, involving nanosecond and
several tens of picosecond time scales, whereas that of liquid ice is on the picosecond time
scale, and that of proton exchange in ice is on the millisecond time scale; the proton
exchange rates in DNA and attached proteins may vary from picosecond to nanosecond,
minutes or years, depending on the exact locations of the exchanged protons in the large
biopolymers. The simple harmonic oscillator 'vibration' in the third, animated image of the
next gallery is only an oversimplified dynamic representation of the longitudinal vibrations
of the DNA intertwined helices which were found to be anharmonic rather than harmonic as
often assumed in quantum dynamic simulations of DNA.

DNA Dynamics

256

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DNA Dynamics

257

Human Genomics and Biotechnology Applications of DNA
Molecular Modeling

The following two galleries of images illustrate various uses of DNA molecular modeling in
Genomics and Biotechnology research applications from DNA repair to PCR and DNA
nanostructures; each slide contains its own explanation and/or details. The first slide
presents an overview of DNA applications, including DNA molecular models, with emphasis
on Genomics and Biotechnology.

Applications of DNA molecular dynamics computations

• First row images present a DNA biochip and DNA nanostructures designed for DNA
computing and other dynamic applications of DNA nanotechnology; last image in this row
is of DNA arrays that display a representation of the Sierpinski gasket on their surfaces.

• Second row: the first two images show computer molecular models of RNA polymerase,
followed by that of an E. coli, bacterial DNA primase template suggesting very complex
dynamics at the interfaces between the enzymes and the DNA template; the fourth image
illustrates in a computed molecular model the mutagenic, chemical interaction of a
potent carcinogen molecule with DNA, and the last image shows the different
interactions of specific fluorescence labels with DNA in human and orangoutan
chromosomes.

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DNA Dynamics

258

Image Gallery: DNA Applications and Technologies at various scales
in Biotechnology and Genomics research

The first figure is an actual electron micrograph of a DNA fiber bundle, presumably of a
single plasmid, bacterial DNA loop.

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DNA Dynamics

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Databases for Genomics, DNA Dynamics and Sequencing

Genomic and structural databases

CBS Genome Atlas Database L J — contains examples of base skews. J

The Z curve database of genomes
genomes [59][14] .

a 3-dimensional visualization and analysis tool of

DNA and other nucleic acids' molecular models: Coordinate files of nucleic acids
molecular structure models in PDB and CIF formats

DNA Dynamics

260

Mass spectrometry— Maldi informatics

Data acquisition

Mass spectrum

Background
subtraction

Mass spectrum
w/o background

Peak detection

List of peak
masses

Peak integration

List of peak
intensities

Nucleic acid
identification

Genotype,
mutations, etc

Nudeic acid
quantitation

DNA Dynamics Data from Spectroscopy

• FT-NMR [15] [16]

• NMR Atlas-database [29]

• mmcif downloadable coordinate files of nucleic acids in solution from 2D-FT NMR data

[30]

• NMR constraints files for NAs in PDB format [ ]

ri7i

NMR microscopy

Vibrational circular dichroism (VCD)

Microwave spectroscopy

FT-IR

FT . NIR [18] [19] [20]

Spectral Hyperspectral, and Chemical imaging) [21] [22] [23] [24] [25] [26] [27] .

Raman spectroscopy/microscopy and CARS .

Fluorescence correlation spectroscopy [30] [31] [32] [33] [34] [35] [36] [37] , Fluorescence

cross-correlation spectroscopy and FRET J L J L .

Confocal microscopy

DNA Dynamics

261

Gallery: CARS (Raman spectroscopy), Fluorescence confocal
microscopy, and Hyperspectral imaging

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DNA Dynamics

262

X-ray microscopy

• Application of X-ray microscopy in the analysis of living hydrated cells

[18]

Atomic Force Microscopy (AFM)

Two-dimensional DNA junction arrays have been visualized by Atomic Force Microscopy
(AFM) C * . Other imaging resources for AFM/Scanning probe microscopy(SPM) can be
freely accessed at:

• How SPM Works [25]

• SPM Image Gallery - AFM STM SEM MFM NSOM and more. [26]

Gallery of AFM Images of DNA Nanostructures

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Notes

[1] Franklin, R.E. and Gosling, R.G. reed. 6 March 1953. Acta Cryst. (1953). 6, 673 The Structure of Sodium

Thymonucleate Fibres I. The Influence of Water Content Acta Cryst. (1953). and 6, 678 The Structure of Sodium

Thymonucleate Fibres II. The Cylindrically Symmetrical Patterson Function.
[2] Watson, J.D; Crick F.H.C. 1953a. Molecular Structure of Nucleic Acids- A Structure for Deoxyribose Nucleic

Acid., Nature 171(4356):737-738.
[3] Watson, J.D; Crick F.H.C. 1953b. The Structure of DNA., Cold Spring Harbor Symposia on Quantitative Biology

18:123-131.
[4] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953).

"http://www.nature.com/nature/dna50/wilkins.pdflMolecular Structure of Deoxypentose Nucleic Acids" (PDF).

Nature 111. 738-740. doi: 10.1038/171738a0 (http://dx.doi.org/10.1038/171738a0). PMID 13054693. http:/

/www . nature . com/nature/dna5 0/ wilkins . pdf .
[5] Elson D, Chargaff E (1952). "On the deoxyribonucleic acid content of sea urchin gametes". Expehentia 8 (4):

143-145.
[6] Chargaff E, Lipshitz R, Green C (1952). "Composition of the deoxypentose nucleic acids of four genera of

sea-urchin". J Biol Chem 195 (1): 155-160. PMID 14938364.
[7] Chargaff E, Lipshitz R, Green C, Hodes ME (1951). "The composition of the deoxyribonucleic acid of salmon

sperm". J Biol Chem 192 (1): 223-230. PMID 14917668.

DNA Dynamics

263

[8] Chargaff E (1951). "Some recent studies on the composition and structure of nucleic acids". J Cell Physiol

Suppl 38 (Suppl).
[9] Magasanik B, Vischer E, Doniger R, Elson D, Chargaff E (1950). "The separation and estimation of

ribonucleotides in minute quantities". J Biol Chem 186 (1): 37-50. PMID 14778802.
[10] Chargaff E (1950). "Chemical specificity of nucleic acids and mechanism of their enzymatic degradation".

Experientia 6 (6): 201-209.
[11] http://www.phy.cam.ac.uk/research/bss/molbiophysics.php
[12] http ://planetphysics . org/encyclopedia/TheoreticalBiophysics. html
[13] Hallin PF, David Ussery D (2004). "CBS Genome Atlas Database: A dynamic storage for bioinformatic results

and DNA sequence data". Bioinformatics 20: 3682-3686.
[14] Zhang CT, Zhang R, Ou HY (2003). "The Z curve database: a graphic representation of genome sequences".

Bioinformatics 19 (5): 593-599. doi:10.1093/bioinformatics/btg041
[15] (http://www.jonathanpmiller.com/Karplus.html)- obtaining dihedral angles from J coupling constants
[ 1 6] (http ://www. spectroscopynow. com/FCKeditor/UserFiles/File/specNOW/HTML files/

General_Karplus_Calculator.htm) Another Javascript-like NMR coupling constant to dihedral
[17] Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.
[18] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[19] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[20] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.
[21] http://www.imaging.net/chemical-imaging/Chemical imaging
[22] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee

and L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical

Imaging. Microscopy Today, Volume 12, No. 6, 11/2004.
[23] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy.,

Microchimica Acta, 104, (1-6) January 1991, doi: 10.1007/BF01245536
[24] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[25] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[26] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical

Industry, G.I.T. Laboratory Journal Europe, No. 1-2, 2007.
[27] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology. (June 2004)., I. C.

Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047)
[28] Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/ImagingMicroscopy04.pdf)
[29] C.L. Evans and X.S. Xie.2008. Coherent An ti-Stokes Raman Scattering Microscopy: Chemical Imaging for

Biology and Medicine., doi:10.1146/annurev.anchem. 1.031207. 112754 Annual Review of Analytical Chemistry,

1. 883-909.
[30] Eigen, M., Rigler, M. Sorting single molecules: application to diagnostics and evolutionary

biotechnology, (1994) Proc. Natl. Acad. Sci. USA, 91,5740-5747.
[31] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in

biotechnology, (199 5) J. Biotechnol., 41,177-186.
[32] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation

spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.
[33] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al.,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[34] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based

amplification combined with fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.
[35] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in

giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.

DNA Dynamics

264

[36] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by
fluorescence correlation spectroscopy with one- and two-photon excitation. Biophysical Journal,

77(10):2251-2265.

[37] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[38] FRET description (http://dwb.unl.edu/Teacher/NSF/C08/C08Links/pps99.cryst.bbk.ac.uk/projects/

gmocz/fret.htm)
[39] doi:10.1016/S0959-440X(00)00190-l (http://dx.doi.org/10. 1016/S0959-440X(00)00190-l)Recent

advances in FRET: distance determination in protein-DNA complexes. Current Opinion in Structural Biology

2001, 11(2), 201-207
[40] http://www.fretimaging.org/mcnamaraintro.html FRET imaging introduction
[41] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary

biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.
[42] Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed Two-Dimensional DNA

Holliday Junction Arrays Visualized by Atomic Force Microscopy". Journal of the American Chemical Society

121 (23): 5437-5443. doi: 10.1021/ja9900398 (http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863

(http://worldcat.org/issn/0002-7863).

References

Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and

Sons, Ltd., vols. 1 and 2., 1966., 2024 pages.

F. Bessel, Untersuchung des Theils der planetarischen Storungen, Berlin Abhandlungen

(1824), article 14.

Cantor, C. R. and Schimmel, P.R. Biophysical Chemistry, Parts I and II. , San Franscisco:

W.H. Freeman and Co. 1980. 1,800 pages.

Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics

and evolutionary biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.

Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology,

Marcel-Dekker, New York, NY.

Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by

fluorescence correlation spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.

Applications of Novel Techniques to Health Foods, Medical and Agricultural

Biotechnology. (June 2004) I. C. Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin.,

q-bio/0406047.

Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical

Imaging and Fluorescence Microspectroscopy.2004. I. C. Baianu, D. Costescu, N. E.

Hofmann, S. S. Korban and et al., q-bio/0407006 (July 2004).

Voet, D. and J.G. Voet. Biochemistry, 2nd Edn., New York, Toronto, Singapore: John Wiley

& Sons, Inc., 1995, ISBN 0-471-58651-X., 1361 pages.

Watson, G. N. A Treatise on the Theory of Bessel Functions., (1995) Cambridge

University Press. ISBN 0-521-48391-3.

Watson, James D. and Francis H.C. Crick. A structure for Deoxyribose Nucleic Acid

(http://www.nature.com/nature/dna50/watsoncrick.pdf) (PDF). Nature 111, 737-738,

25 April 1953.

Watson, James D. Molecular Biology of the Gene. New York and Amsterdam: W.A.

Benjamin, Inc. 1965., 494 pages.

Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science,

Inc. 2000.

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Herbert R. Wilson, FRS. Diffraction of X-rays by proteins, Nucleic Acids and Viruses.,

London: Edward Arnold (Publishers) Ltd. 1966.

Kurt Wuthrich. NMR of Proteins and Nucleic Acids., New York, Brisbane, Chicester,

Toronto, Singapore: J. Wiley & Sons. 1986., 292 pages.

Robinson, Bruche H.; Seeman, Nadrian C. (August 1987). "The Design of a Biochip: A

Self-Assembling Molecular-Scale Memory Device". Protein Engineering 1 (4): 295-300.

ISSN 0269-2139 (http://worldcat.org/issn/0269-2139). Link (http://peds.

oxf ordj ournals . org/cgi/content/abstract/ 1 /4/2 9 5 )

Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson,

Deborah Kuchnir & Winfree, Erik (22 December 2004). "Design and Characterization of

Programmable DNA Nanotubes". Journal of the American Chemical Society 126 (50):

16344-16352. doi: 10. 1021/ja0443191 (http://dx.doi.org/10.1021/ja0443191). ISSN

0002-7863 (http://worldcat.org/issn/0002-7863).

Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun

(November 2003).

"http://www.sciencemag.org/cgi/content/abstract/sci; 302/5649/1 380 1 DNA-Templated

Carbon Nanotube Field-Effect Transistor". Science 302 (6549): 1380-1382. doi:

10.1 126/science. 1091 022 (http://dx.doi.org/10.1126/science.1091022). ISSN

1095-9203 (http://worldcat.org/issn/1095-9203). http://www.sciencemag.org/cgi/

content/abstract/sci;302/5649/1380.

Zheng, Jiwen; Constantinou, Pamela E.; Micheel, Christine; Alivisatos, A. Paul; Kiehl,

Richard A. & Seeman Nadrian C. (2006). "2D Nanoparticle Arrays Show the

Organizational Power of Robust DNA Motifs". Nano Letters 6: 1502-1504. doi:

10.1021/nl060994c (http://dx.doi.org/10.1021/nl060994c). ISSN 1530-6984 (http://

worldcat.org/issn/1530-6984).

Cohen, Justin D.; Sadowski, John P.; Dervan, Peter B. (2007). "Addressing Single

Molecules on DNA Nanostructures ". Angewandte Chemie 46 (42): 7956-7959. doi:

10. 1002/anie. 200702767 (http://dx.doi.org/10.1002/anie.200702767). ISSN

0570-0833 (http://worldcat.org/issn/0570-0833).

Mao, Chengde; Sun, Weiqiong & Seeman, Nadrian C. (16 June 1999). "Designed

Two-Dimensional DNA Holliday Junction Arrays Visualized by Atomic Force Microscopy".

Journal of the American Chemical Society 121 (23): 5437-5443. doi: 10.1021/ja9900398

(http://dx.doi.org/10.1021/ja9900398). ISSN 0002-7863 (http://worldcat.org/issn/

0002-7863).

Constantinou, Pamela E.; Wang, Tong; Kopatsch, Jens; Israel, Lisa B.; Zhang, Xiaoping;

Ding, Baoquan; Sherman, William B.; Wang, Xing; Zheng, Jianping; Sha, Ruojie &

Seeman, Nadrian C. (2006). "Double cohesion in structural DNA nanotechnology".

Organic and Biomolecular Chemistry 4: 3414-3419. doi: 10.1039/b605212f (http://dx.

doi.org/10.1039/b605212f).

DNA Dynamics

266

See also

DNA

Molecular modeling of DNA

Genomics

Signal transduction

Transcriptomics

Interactomics

Biotechnology

Molecular graphics

Quantum computing

MAYA-II

DNA computing

DNA structure

Molecular structure

Molecular dynamics

Molecular topology

DNA topology

DNA, the Genome and Interactome

Molecular structure

Molecular geometry fluctuations

Molecular interactions

Molecular topology

Hydrogen bonding

Hydrophobic interactions

DNA dynamics and conformations

DNA Conformational isomerism

2D-FT NMRI and Spectroscopy

Paracrystalline lattices/Paracrystals

NMR Spectroscopy

VCD or Vibrational circular dichroism

Microwave spectroscopy

Two-dimensional IR spectroscopy

FRET and FCS- Fluorescence correlation spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS)

Spectral imaging

Hyperspectral imaging

Chemical imaging

NMR microscopy

X-ray scattering

Neutron scattering

Crystallography

Crystal lattices

Molecular geometry

Nanostructure

DNA nanotechnology

Imaging

Sirius visualization software

DNA Dynamics

267

Atomic force microscopy

X-ray microscopy

Liquid crystals

Glasses

QMC@Home

Sir Lawrence Bragg, FRS

Sir John Randall

Francis Crick

Manfred Eigen

Felix Bloch

Paul Lauterbur

Maurice Wilkins

Herbert Wilson, FRS

Alex Stokes

External links

DNAlive: a web interface to compute DNA physical properties (http://mmb.pcb.ub.es/

DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and

DNA dynamics.

Application of X-ray microscopy in analysis of living hydrated cells (http://www.ncbi.

nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&

list_uids = 12379938)

DiProDB: Dinucleotide Property Database (http://diprodb.fli-leibniz.de). The database

is designed to collect and analyse thermodynamic, structural and other dinucleotide

properties.

DNA the Double Helix Game (http://nobelprize.org/educational_games/medicine/

dnadoublehelix/) From the official Nobel Prize web site

MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. wesleyan.edu:8080/

MDDNA/)

Double Helix 1953-2003 (http://www.ncbe.reading.ac.uk/DNA50/) National Centre

for Biotechnology Education

DNA under electron microscope (http://www.fidelitysystems.com/Unlinked_DNA.

html)

Further details of mathematical and molecular analysis of DNA structure based on X-ray

data (http://planetphysics.org/encyclopedia/

BesselFunctionsApplicationsToDiffractionByHelicalStructures.html)

Bessel functions corresponding to Fourier transforms of atomic or molecular helices.

(http ://planetphy sics . org/?op = getobj &from = obj ec ts &

name=BesselFunctionsAndTheirApplicationsToDiffractionByHelicalStructures)

Characterization in nanotechnology some pdfs (http://nanocharacterization.sitesled.

com/)

An overview of STM/AFM/SNOM principles with educative videos (http://www.ntmdt.

ru/SPM-Techniques/Principles/)

SPM Image Gallery - AFM STM SEM MFM NSOM and More (http://www.rhk-tech.com/

results/showcase. php)

How SPM Works (http://www.parkafm.com/New_html/resources/01general.php)

DNA Dynamics

268

U.S. National DNA Day (http://www.genome.gov/10506367) — watch videos and

participate in real-time discussions with scientists.

The Secret Life of DNA - DNA Music compositions (http://www.tjmitchell.com/stuart/

dna.html)

Ascalaph DNA (http://www.agilemolecule.com/Ascalaph/Ascalaph_DNA.html) —

Commercial software for DNA modeling

Genomics

Genomics is the study of the genomes of organisms. The field includes intensive efforts to
determine the entire DNA sequence of organisms and fine-scale genetic mapping efforts.
The field also includes studies of intragenomic phenomena such as heterosis, epistasis,
pleiotropy and other interactions between loci and alleles within the genome. In contrast,
the investigation of the roles and functions of single genes is a primary focus of molecular
biology and is a common topic of modern medical and biological research. Research of
single genes does not fall into the definition of genomics unless the aim of this genetic,
pathway, and functional information analysis is to elucidate its effect on, place in, and

^__ _ ^ j — _ _ __ — _ —

response to the entire genome's networks.

For the United States Environmental Protection Agency, "the term "genomics"
encompasses a broader scope of scientific inquiry associated technologies than when
genomics was initially considered. A genome is the sum total of all an individual organism's
genes. Thus, genomics is the study of all the genes of a cell, or tissue, at the DNA

(genotype), mRNA (transcriptome), or protein (proteome) levels." 1

History

Genomics was established by Fred Sanger when he first sequenced the complete genomes
of a virus and a mitochondrion. His group established techniques of sequencing, genome
mapping, data storage, and bioinformatic analyses in the 1970-1 980s. A major branch of
genomics is still concerned with sequencing the genomes of various organisms, but the
knowledge of full genomes has created the possibility for the field of functional genomics,
mainly concerned with patterns of gene expression during various conditions. The most
important tools here are microarrays and bioinformatics. Study of the full set of proteins in
a cell type or tissue, and the changes during various conditions, is called proteomics. A
related concept is materiomics, which is defined as the study of the material properties of
biological materials (e.g. hierarchical protein structures and materials, mineralized
biological tissues, etc.) and their effect on the macroscopic function and failure in their
biological context, linking processes, structure and properties at multiple scales through a
materials science approach. The actual term 'genomics' is thought to have been coined by
Dr. Tom Roderick, a geneticist at the Jackson Laboratory (Bar Harbor, ME) over beer at a
meeting held in Maryland on the mapping of the human genome in 1986.

In 1972, Walter Fiers and his team at the Laboratory of Molecular Biology of the University
of Ghent (Ghent, Belgium) were the first to determine the sequence of a gene: the gene for
Bacteriophage MS2 coat protein. 1 J In 1976, the team determined the complete
nucleotide-sequence of bacteriophage MS2-RNA. 1 J The first DNA-based genome to be
sequenced in its entirety was that of bacteriophage 0-X174; (5,368 bp), sequenced by

Genomics

269

Frederick Sanger in 1977.

[4]

The first free-living organism to be sequenced was that of Haemophilus influenzae (1.8 Mb)
in 1995, and since then genomes are being sequenced at a rapid pace. A rough draft of the
human genome was completed by the Human Genome Project in early 2001, creating much
fanfare .

As of September 2007, the complete sequence was known of about 1879 viruses , 577
bacterial species and roughly 23 eukaryote organisms, of which about half are fungi. c ]
Most of the bacteria whose genomes have been completely sequenced are problematic
disease-causing agents, such as Haemophilus influenzae. Of the other sequenced species,
most were chosen because they were well-studied model organisms or promised to become
good models. Yeast (Saccharomyces cerevisiae) has long been an important model
organism for the eukaryotic cell, while the fruit fly Drosophila melanogaster has been a
very important tool (notably in early pre-molecular genetics). The worm Caenorhabditis
elegans is an often used simple model for multicellular organisms. The zebrafish
Brachydanio rerio is used for many developmental studies on the molecular level and the
flower Arabidopsis thaliana is a model organism for flowering plants. The Japanese
pufferfish (Takifugu rubripes) and the spotted green pufferfish (Tetraodon nigroviridis) are
interesting because of their small and compact genomes, containing very little non-coding
DNA compared to most species. c ^ [ ] The mammals dog (Canis familiaris), c ] brown rat
(Rattus norvegicus), mouse (Mus musculus), and chimpanzee (Pan troglodytes) are all
important model animals in medical research.

Bacteriophage genomics

Bacteriophages have played and continue to play a key role in bacterial genetics and
molecular biology. Historically, they were used to define gene structure and gene
regulation. Also the first genome to be sequenced was a bacteriophage. However,
bacteriophage research did not lead the genomics revolution, which is clearly dominated by
bacterial genomics. Only very recently has the study of bacteriophage genomes become
prominent, thereby enabling researchers to understand the mechanisms underlying phage
evolution. Bacteriophage genome sequences can be obtained through direct sequencing of
isolated bacteriophages, but can also be derived as part of microbial genomes. Analysis of
bacterial genomes has shown that a substantial amount of microbial DNA consists of
prophage sequences and prophage-like elements. A detailed database mining of these
sequences offers insights into the role of prophages in shaping the bacterial genome.

Cyanobacteria genomics

At present there are 24 cyanobacteria for which a total genome sequence is available. 15 of
these cyanobacteria come from the marine environment. These are six Prochlorococcus
strains, seven marine Synechococcus strains, Trichodesmium erythraeum IMS101 and
Crocosphaera watsonii WH8501. Several studies have demonstrated how these sequences
could be used very successfully to infer important ecological and physiological
characteristics of marine cyanobacteria. However, there are many more genome projects
currently in progress, amongst those there are further Prochlorococcus and marine
Synechococcus isolates, Acaryochloris and Prochloron, the INL-fixing filamentous
cyanobacteria Nodularia spumigena, Lyngbya aestuarii and Lyngbya majuscula, as well as
bacteriophages infecting marine cyanobaceria. Thus, the growing body of genome

Genomics

270

information can also be tapped in a more general way to address global problems by
applying a comparative approach. Some new and exciting examples of progress in this field
are the identification of genes for regulatory RNAs, insights into the evolutionary origin of
photosynthesis, or estimation of the contribution of horizontal gene transfer to the genomes

M 1 "I

that have been analyzed. 1 J

See also

• Full Genome Sequencing

• Computational genomics

• Nitrogenomics

• Metagenomics

• Predictive Medicine

• Personal genomics

References

[I] EPA Interim Genomics Policy (http://epa.gov/osa/spc/pdfs/genomics.pdf)

[2] Min Jou W, Haegeman G, Ysebaert M, Fiers W (1972). "Nucleotide sequence of the gene coding for the

bacteriophage MS2 coat protein". Nature 237 (5350): 82-88. doi: 10.1038/237082a0 (http://dx.doi.org/10.

1038/237082a0). PMID 4555447.
[3] Fiers W, Contreras R, Duerinck F, Haegeman G, Iserentant D, Merregaert J, Min Jou W, Molemans F,

Raeymaekers A, Van den Berghe A, Volckaert G, Ysebaert M (1976). "Complete nucleotide sequence of

bacteriophage MS2 RNA: primary and secondary structure of the replicase gene". Nature 260 (5551): 500-507.

doi: 10.1038/260500a0 (http://dx.doi.org/10.1038/260500a0). PMID 1264203.
[4] Sanger F, Air GM, Barrell BG, Brown NL, Coulson AR, Fiddes CA, Hutchison CA, Slocombe PM, Smith M

(1977). "Nucleotide sequence of bacteriophage phi X174 DNA". Nature 265 (5596): 687-695. doi:

10.1038/265687a0 (http://dx.doi.org/10.1038/265687a0). PMID 870828.
[5] The Viral Genomes Resource, NCBI Friday, 14 September 2007 (http://www.ncbi.nlm.nih.gov/genomes/

VIRUSES/virostat.html)
[6] Genome Project Statistic, NCBI Friday, 14 September 2007 (http://www.ncbi.nlm.nih.gov/genomes/static/

gpstat.html)
[7] BBC article Human gene number slashed from Wednesday, 20 October 2004 (http://news.bbc. co.uk/1/hi/

sci/tech/3760766.stm)
[8] CBSE News, Thursday, 16 October 2003 (http://www.cbse.ucsc.edu/news/2003/10/16/pufferfish_fruitfly/

index, shtml)
[9] NHGRI, pressrelease of the publishing of the dog genome (http://www.genome.gov/12511476)
[10] McGrath S and van Sinderen D, ed (2007). http://www .horizonpress .com/phage\Bacteriophage: Genetics and

Molecular Biology (1st ed.). Caister Academic Press. ISBN 978-1-904455-14-1. http://www.horizonpress.com/

phage.

[II] Herrero A and Flores E, ed (2008). http://www. horizonpress. com/cyan\The Cyanobacteria: Molecular Biology,
Genomics and Evolution (1st ed.). Caister Academic Press. ISBN 978-1-904455-15-8. http:// www. horizonpress.
com/cyan.

Genomics

271

External links

• Genomics Directory (http://www.genomicsdirectory.com): A one-stop biotechnology
resource center for bioentrepreneurs, scientists, and students

• Annual Review of Genomics and Human Genetics (http://arjournals.annualreviews.org/
loi/genom/)

• BMC Genomics (http://www.biomedcentral.com/bmcgenomics/): A BMC journal on
Genomics

• Genomics (http://www.genomics.co.uk/companylist.php): UK companies and
laboratories* Genomics journal (http://www.elsevier.com/wps/find/journaldescription.
cws_home/622838/description#description)

• Genomics.org (http://genomics.org): An openfree wiki based Genomics portal

• NHGRI (http://www.genome.gov/): US government's genome institute

• Pharmacogenomics in Drug Discovery and Development (http://www.springer.com/
humana-h press/pharmacology -I- and+toxicology/book/978-1-58829-887-4), a book on
pharmacogenomics, diseases, personalized medicine, and therapeutics

• Tishchenko P. D. Genomics: New Science in the New Cultural Situation (http://www.
zpu-journal. ru/en/ articles/detail. php?ID= 342)

• Undergraduate program on Genomic Sciences (Spanish) (http://www.lcg.unam.mx/):
One of the first undergraduate programs in the world

• JCVI Comprehensive Microbial Resource (http://cmr.jcvi.org/)

• Pathema: A Clade Specific Bioinformatics Resource Center (http://pathema.jcvi.org/)

• KoreaGenome.org (http://koreagenome.org): The first Korean Genome published and
the sequence is available freely.

• GenomicsNetwork (http://genomicsnetwork.ac.uk): Looks at the development and use
of the science and technologies of genomics.

Gene regulatory network

272

Gene regulatory network

A gene regulatory network

genetic

regulatory

network (GRN) is a collection
of DNA segments in a cell
which interact with each other
(indirectly through their RNA

and

protein

expression

products) and with other
substances in the cell, thereby
governing the rates at which
genes in the network are
transcribed into mRNA. In
general, each mRNA molecule
goes on to make a specific
protein (or set of proteins). In
some cases this protein will be

structural,

and

will

accumulate at the cell-wall or
within the cell to give it
particular structural

LIFE

A GENE REGULATORY NETWORK

INPUT

ixgfial A

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interacting

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INPUT

wgrol

<■

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transcription

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mRNA

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I
I
I

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Structure of a Gene Regulatory Network.

I
■

Input
signals

►

Gene

regulatory

network

component

►

Primary
outputs =

Changed RNA
and protein
complements

►

Terminal

outputs =

Changed cell
behaviors and
structures

feedback circuitry

properties. In other cases the

protein will be an enzyme; a

micro-machine that catalyses a

certain reaction, such as the

breakdown of a food source or

toxin. Some proteins though

serve only to activate other

genes, and these are the

transcription factors that are

the main players in regulatory

networks or cascades. By

binding to the promoter region at the start of other genes they turn them on, initiating the

production of another protein, and so on. Some transcription factors are inhibitory.

YGG 01 -GOBS

Control process of a Gene Regulatory Network

In single-celled organisms regulatory networks respond to the external environment,
optimising the cell at a given time for survival in this environment. Thus a yeast cell, finding
itself in a sugar solution, will turn on genes to make enzymes that process the sugar to
alcohol. * This process, which we associate with wine-making, is how the yeast cell makes
its living, gaining energy to multiply, which under normal circumstances would enhance its
survival prospects.

In multicellular animals the same principle has been put in the service of gene cascades

T21

that control body-shape. 1 J Each time a cell divides, two cells result which, although they
contain the same genome in full, can differ in which genes are turned on and making
proteins. Sometimes a 'self-sustaining feedback loop' ensures that a cell maintains its

Gene regulatory network

273

identity and passes it on. Less understood is the mechanism of epigenetics by which
chromatin modification may provide cellular memory by blocking or allowing transcription.
A major feature of multicellular animals is the use of morphogen gradients, which in effect
provide a positioning system that tells a cell where in the body it is, and hence what sort of
cell to become. A gene that is turned on in one cell may make a product that leaves the cell
and diffuses through adjacent cells, entering them and turning on genes only when it is
present above a certain threshold level. These cells are thus induced into a new fate, and
may even generate other morphogens that signal back to the original cell. Over longer
distances morphogens may use the active process of signal transduction. Such signalling
controls embryogenesis, the building of a body plan from scratch through a series of
sequential steps. They also control maintain adult bodies through feedback processes, and
the loss of such feedback because of a mutation can be responsible for the cell proliferation
that is seen in cancer. In parallel with this process of building structure, the gene cascade
turns on genes that make structural proteins that give each cell the physical properties it
needs.

Overview

At one level, biological cells can be thought of as "partially-mixed bags" of biological
chemicals - in the discussion of gene regulatory networks, these chemicals are mostly the
mRNAs and proteins that arise from gene expression. These mRNA and proteins interact
with each other with various degrees of specificity. Some diffuse around the cell. Others are
bound to cell membranes, interacting with molecules in the environment. Still others pass
through cell membranes and mediate long range signals to other cells in a multi-cellular
organism. These molecules and their interactions comprise a gene regulatory network. A
typical gene regulatory network looks something like this:

The nodes of this network are proteins, their corresponding mRNAs, and protein/protein
complexes. Nodes that are depicted as lying along vertical lines are associated with the
cell/environment interfaces, while the others are free-floating and diffusible. Implied are
genes, the DNA sequences which are transcribed into the mRNAs that translate into
proteins. Edges between nodes represent individual molecular reactions, the
protein/protein and protein/mRNA interactions through which the products of one gene
affect those of another, though the lack of experimentally obtained information often
implies that some reactions are not modeled at such a fine level of detail. These interactions
can be inductive (the arrowheads), with an increase in the concentration of one leading to
an increase in the other, or inhibitory (the filled circles), with an increase in one leading to
a decrease in the other. A series of edges indicates a chain of such dependences, with
cycles corresponding to feedback loops. The network structure is an abstraction of the
system's chemical dynamics, describing the manifold ways in which one substance affects
all the others to which it is connected. In practice, such GRNs are inferred from the
biological literature on a given system and represent a distillation of the collective
knowledge about a set of related biochemical reactions.

Genes can be viewed as nodes in the network, with input being proteins such as
transcription factors, and outputs being the level of gene expression. The node itself can
also be viewed as a function which can be obtained by combining basic functions upon the
inputs (in the Boolean network described below these are Boolean functions, typically AND,
OR, and NOT). These functions have been interpreted as performing a kind of information

Gene regulatory network

274

processing within the cell, which determines cellular behavior. The basic drivers within
cells are concentrations of some proteins, which determine both spatial (location within the
cell or tissue) and temporal (cell cycle or developmental stage) coordinates of the cell, as a
kind of "cellular memory". The gene networks are only beginning to be understood, and it is
a next step for biology to attempt to deduce the functions for each gene "node", to help
understand the behavior of the system in increasing levels of complexity, from gene to
signaling pathway, cell or tissue level (see systems biology).

Mathematical models of GRNs have been developed to capture the behavior of the system
being modeled, and in some cases generate predictions corresponding with experimental
observations. In some other cases, models have proven to make accurate novel predictions,
which can be tested experimentally, thus suggesting new approaches to explore in an
experiment that sometimes wouldn't be considered in the design of the protocol of an
experimental laboratory. The most common modeling technique involves the use of coupled
ordinary differential equations (ODEs). Several other promising modeling techniques have
been used, including Boolean networks, Petri nets, Bayesian networks, graphical Gaussian
models, Stochastic, and Process Calculi. Conversely, techniques have been proposed for
generating models of GRNs that best explain a set of time series observations.

Modelling

Coupled ODEs

It is common to model such a network with a set of coupled ordinary differential equations
(ODEs) or stochastic ODEs, describing the reaction kinetics of the constituent parts.
Suppose that our regulatory network has A r nodes, and let Si(t), S^i), . . . , 5jv(t) represent
the concentrations of the N corresponding substances at time t. Then the temporal
evolution of the system can be described approximately by

~JT = fj {$1 ? ^2i ■ ■ ■ 5 -Sjv)

where the functions fj express the dependence of ^jon the concentrations of other

substances present in the cell. The functions fj are ultimately derived from basic principles

of chemical kinetics or simple expressions derived from these e.g. Michaelis-Menten

enzymatic kinetics. Hence, the functional forms of the fj are usually chosen as low-order

polynomials or Hill functions that serve as an ansatz for the real molecular dynamics. Such

models are then studied using the mathematics of nonlinear dynamics. System-specific

information, like reaction rate constants and sensitivities, are encoded as constant

parameters.

By solving for the fixed point of the system:

for all j , one obtains (possibly several) concentration profiles of proteins and mRNAs that
are theoretically sustainable (though not necessarily stable). Steady states of kinetic
equations thus correspond to potential cell types, and oscillatory solutions to the above
equation to naturally cyclic cell types. Mathematical stability of these attractors can usually
be characterized by the sign of higher derivatives at critical points, and then correspond to
biochemical stability of the concentration profile. Critical points and bifurcations in the
equations correspond to critical cell states in which small state or parameter perturbations

Gene regulatory network

275

could switch the system between one of several stable differentiation fates. Trajectories
correspond to the unfolding of biological pathways and transients of the equations to
short-term biological events. For a more mathematical discussion, see the articles on
nonlinearity, dynamical systems, bifurcation theory, and chaos theory.

Boolean network

The following example illustrates how a Boolean network can model a GRN together with
its gene products (the outputs) and the substances from the environment that affect it (the
inputs). Stuart Kauffman was amongst the first biologists to use the metaphor of Boolean
networks to model genetic regulatory networks.

1. Each gene, each input, and each output is represented by a node in a directed graph in
which there is an arrow from one node to another if and only if there is a causal link
between the two nodes.

2. Each node in the graph can be in one of two states: on or off.

3. For a gene, "on" corresponds to the gene being expressed; for inputs and outputs, "on"
corresponds to the substance being present.

4. Time is viewed as proceeding in discrete steps. At each step, the new state of a node is a
Boolean function of the prior states of the nodes with arrows pointing towards it.

The validity of the model can be tested by comparing simulation results with time series
observations.

Continuous networks

Continuous network models of GRNs are an extension of the boolean networks described
above. Nodes still represent genes and connections between them regulatory influences on
gene expression. Genes in biological systems display a continuous range of activity levels
and it has been argued that using a continuous representation captures several properties
of gene regulatory networks not present in the Boolean model. Formally most of these
approaches are similar to an artificial neural network, as inputs to a node are summed up
and the result serves as input to a sigmoid function, e.g., but proteins do often control
gene expression in a synergistic, i.e. non-linear, way. However there is now a continuous

T71

network model that allows grouping of inputs to a node thus realizing another level of
regulation. This model is formally closer to a higher order recurrent neural network. The
same model has also been used to mimic the evolution of cellular differentiation^ J and even
multicellular morphogenesis.

Stochastic gene networks

n ni n 1 1
Recent experimental results 1 J L J have demonstrated that gene expression is a stochastic

process. Thus, many authors are now using the stochastic formalism, after the first work

by. ] Works on single gene expression 1 ^ * and small synthetic genetic networks, * c *

such as the genetic toggle switch of Tim Gardner and Jim Collins, provided additional

experimental data on the phenotypic variability and the stochastic nature of gene

expression. The first versions of stochastic models of gene expression involved only

instantaneous reactions and were driven by the Gillespie algorithm. ^

Since some processes, such as gene transcription, involve many reactions and could not be
correctly modeled as an instantaneous reaction in a single step, it was proposed to model
these reactions as single step multiple delayed reactions in order to account for the time it

Gene regulatory network

276

takes for the entire process to be complete. ^

From here, a set of reactions were proposed^ ] that allow generating GRNs. These are then
simulated using a modified version of the Gillespie algorithm, that can simulate multiple
time delayed reactions (chemical reactions where each of the products is provided a time
delay that determines when will it be released in the system as a "finished product").

For example, basic transcription of a gene can be represented by the following single-step
reaction (RNAP is the RNA polymerase, RBS is the RNA ribosome binding site, and Pro . is
the promoter region of gene z):

RNAP + Pro^PrOifa 1 ) + RBS* fa 1 ) + RNAPfa 2 )

A recent work proposed a simulator (SGNSim, Stochastic Gene Networks Simulator)} ]
that can model GRNs where transcription and translation are modeled as multiple time
delayed events and its dynamics is driven by a stochastic simulation algorithm (SSA) able to
deal with multiple time delayed events. The time delays can be drawn from several
distributions and the reaction rates from complex functions or from physical parameters.
SGNSim can generate ensembles of GRNs within a set of user-defined parameters, such as
topology. It can also be used to model specific GRNs and systems of chemical reactions.
Genetic perturbations such as gene deletions, gene over-expression, insertions, frame shift
mutations can also be modeled as well.

The GRN is created from a graph with the desired topology, imposing in-degree and
out-degree distributions. Gene promoter activities are affected by other genes expression
products that act as inputs, in the form of monomers or combined into multimers and set as
direct or indirect. Next, each direct input is assigned to an operator site and different
transcription factors can be allowed, or not, to compete for the same operator site, while
indirect inputs are given a target. Finally, a function is assigned to each gene, defining the
gene's response to a combination of transcription factors (promoter state). The transfer
functions (that is, how genes respond to a combination of inputs) can be assigned to each
combination of promoter states as desired.

In other recent work, multiscale models of gene regulatory networks have been developed
that focus on synthetic biology applications. Simulations have been used that model all
biomolecular interactions in transcription, translation, regulation, and induction of gene
regulatory networks, guiding the design of synthetic systems.

Network connectivity

Empirical data indicate that biological gene networks are sparsely connected, and that the

T211

average number of upstream-regulators per gene is less than two. Theoretical results
show that selection for robust gene networks will favor minimally complex, more sparsely

roil

connected, networks. These results suggest that a sparse, minimally connected, genetic
architecture may be a fundamental design constraint shaping the evolution of gene network
complexity.

Gene regulatory network

277

See also

• Operon

• Systems biology

• Synexpression

• Cis-regulatory module

• Body plan

• Morphogen

References

[I] http://web.wi.mit.edu/young/regulator_network/
[2] http://www.pnas.org/cgi/content/full/102/14/4935
[3] Kauffman, Stuart (1993). The Origins of Order.

[4] Vohradsky, J. (2001). Neural model of the genetic network. The Journal of Biological Chemistry, 276,

36168-36173.
[5] Geard, N. and Wiles, J. A Gene Network Model for Developing Cell Lineages. In Artificial Life, 11 (3): 249-268,

2005.
[6] Schilstra, M.J. and Bolouri, H. The Logic of Gene Regulation., http://strc.herts.ac.uk/bio/maria/

NetBuilder/Theory/NetBuilderModelling.htm
[7] Knabe, J. F., Nehaniv, C. L., Schilstra, M. J. and Quick, T. Evolving Biological Clocks using Genetic Regulatory

Networks. In Artificial Life X: Proceedings of the Tenth International Conference on the Simulation and

Synthesis of Living Systems, pages 15-21, MIT Press, 2006.
[8] Knabe, J. F., Nehaniv, C. L. and Schilstra, M. J. Evolutionary Robustness of Differentiation in Genetic

Regulatory Networks. In Proceedings of the 7th German Workshop on Artificial Life 2006 (GWAL-7), pages

75-84, Akademische Verlagsgesellschaft Aka, Berlin, 2006.
[9] Knabe, J. F., Schilstra, M. J. and Nehaniv, C. L. Evolution and Morphogenesis of Differentiated Multicellular

Organisms: Autonomously Generated Diffusion Gradients for Positional Information. In Artificial Life XI:

Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, MIT

Press, 2008.
[10] Elowitz, M.B., Levine, A.J., Siggia, E.D., and Swain, P.S. 2002. Stochastic gene expression in a single cell.

Science 297: 1183-1186

[II] Blake, W.J., Kaern, M., Cantor, C.R., and Collins, J.J. 2003. Noise in eukaryotic gene expression, (http://
www.bu.edu/abl/publications.html) Nature 422: 633-637

[12] Arkin, A. and McAdams, H.H. 1998. Stochastic kinetic analysis of developmental pathway bifurcation in

phage lambda-infected Escherichia coli cells. Genetics 149: 1633-1648.
[13] Raser, J.M., and O'Shea, E.K., (2005) Noise in gene expression: origins, consequences, and control, Science,

309, 2010-2013
[14] Elowitz, M. B., and Leibler, S., (2000) A synthetic oscillatory network of transcriptional regulators., Nature,

403, 335-338
[15] Gardner, T. S., Cantor, C. R., and Collins., J. J., (2000) Construction of a genetic toggle switch in Escherichia

coli., Nature, 403, 339-342
[16] Gillespie, D.T., A general method for numerically simulating the stochastic time evolution of coupled chemical

reactions, 1976, J. Comput. Phys., 22, 403-434.
[17] Roussel, M.R., and Zhu, R., Validation of an algorithm for delay stochastic simulation of transcription and

translation in prokaryotic gene expression, 2006, Phys. Biol. 3, 274-284
[18] Ribeiro, Andre S., Zhu, R., Kauffman, S.A. (2006). "A General Modeling Strategy for Gene Regulatory

Networks with Stochastic Dynamics", Journal of Computational Biology, 13(9), 1630-1639.
[19] Andre S. Ribeiro and Jason Lloyd-Price, (2007) "SGN Sim, a Stochastic Genetic Networks Simulator",

Bioinformatics, 23(6):777-779. doi:10.1093/bioinformatics/btm004., doi:10.1093/bioinformatics/btm004.
[20] Y. N. Kaznessis, (2007) "Models for Synthetic Biology", BMC Systems Biology, 2007, 1:47

doi:10. 1186/1752-0509-1-47 (http://www.biomedcentral.eom/1752-0509/l/47).
[21] Leclerc R. (August 2008). " Survival of the sparsest: robust gene networks are parsimonious (http://www.

nature.com/msb/journal/v4/nl/full/msb200852.html)". Mol Syst Biol. 4 (213).

• James M. Bower, Hamid Bolouri (editors), (2001) Computational Modeling of Genetic and
Biochemical Networks Computational Molecular Biology Series, MIT Press, ISBN
0-262-02481-0

Gene regulatory network

278

L. Franke, H. van Bakel, L. Fokkens, E. de Jong, M. Egmont-Petersen, C. Wijmenga,
(2006) Reconstruction of a probabilistic human gene network, with an application for
prioritizing positional candidate genes, Amer. J. of Human Genetics, 78(6), 1011-25.
Human gene network (http://www.genenetwork.nl), Prioritizer software application
(http://www.prioritizer.nl).

S. A. Kauffman, "Metabolic stability and epigenesis in randomly constructed genetic
nets", J. Theoret. Biol (1969) 22, 434-467

External links

• Gene Regulatory Networks (http://www.doegenomestolife.org/science/
generegulatorynetwork.shtml) — Short introduction

• BIB: Yeast Biological Interaction Browser (http://sergi5.com/bio)

• Graphical Gaussian models for genome data (http://strimmerlab.org/notes/ggm.html)
— Inference of gene association networks with GGMs

• A bibliography on learning causal networks of gene interactions (http://www.molgen.
mpg.de/-markowet/docs/network-bib.pdf) - regularly updated, contains hundreds of
links to papers from bioinformatics, statistics, machine learning.

• http://mips.gsf.de/proj/biorel/BIOREL is a web-based resource for quantitative
estimation of the gene network bias in relation to available database information about
gene activity/function/properties/associations/interactio.

• Evolving Biological Clocks using Genetic Regulatory Networks (http://panmental.de/
GRNclocks) - Information page with model source code and Java applet.

• Engineered Gene Networks (http://www.bu.edu/abl)

• Tutorial: Genetic Algorithms and their Application to the Artificial Evolution of Genetic
Regulatory Networks (http://panmental.de/ICSBtut/)

Computational genomics

279

Computational genomics

Computational genomics is the study of deciphering biology from genome sequences

n 1
using computational analysis. J , including both DNA and RNA. Computational genomics

focuses on understanding the human genome, and more generally the principles of how

DNA controls the biology of any species at the molecular level. With the current abundance

of massive biological datasets, computational studies have become one of the most

important means to biological discovery. [ ]

History

Computational genomics began in spirit, if not in name, during the 1960s with the research
of Margaret Dayhoff and others at the National Biomedical Research Foundation, who first
assembled a database of protein sequences. Their research developed a phylogenetic tree
that determined the evolutionary changes that were required for a particular protein to
change into another protein based on the underlying amino acid sequences. This led them
to create a scoring matrix that assessed the likelihood of one protein being related to
another.

Beginning in the 1980s, databases of genome sequences began to be recorded, but this
presented new challenges in the form of searching and comparing the databases of gene
information. Unlike text-searching algorithms that are used on websites such as google or
Wikipedia, searching for sections of genetic similarity requires one to find strings that are
not simply identical, but similar. This led to the development of the Needleman-Wunsch
algorithm, which is a dynamic programming algorithm for comparing sets of amino acid
sequences with each other by using scoring matrices derived from the earlier research by
Dayhoff. Later, the BLAST algorithm was developed for performing fast, optimized searches
of gene sequence databases. BLAST and its derivatives are probably the most widely-used
algorithms for this purpose.

The first meeting of the Annual Conference on Computational Genomics was in 1998,
providing a forum for this speciality and effectively distinguishing this area of science from
the more general fields of Genomics or Computational Biology. The first use of this term
in scientific literature, according to MEDLINE abstracts, was just one year earlier in
Nucleic Acids Research. L J .

The development of computer-assisted mathematics (using products such as Mathematica
or Matlab) has helped engineers, mathematicians and computer scientists to start operating
in this domain, and a public collection of case studies and demonstrations is growing,

T71

ranging from whole genome comparisons to gene expression analysis. . This has

increased the introduction of different ideas, including concepts from systems and control,
information theory, strings analysis and data mining. It is anticipated that computational
approaches will become and remain a standard topic for research and teaching, while
students fluent in both topics start being formed in the multiple courses created in the past
few years.

Computational genomics

280

Contributions of computational genomics research to
biology

T21

Contributions of computational genomics research to biology include :

• discovering subtle patterns in genomic sequences

• proposing cellular signalling networks

• proposing mechanisms of genome evolution

• predict precise locations of all human genes using [comparative genomics] techniques
with several mammalian and vertebrate species

• predict conserved genomic regions that are related to early embryonic development

• discover potential links between repeated sequence motifs and tissue-specific gene
expression

• measure regions of genomes that have undergone unusually rapid evolution

See also

Bioinformatics

Biowiki

Computational biology

Genomics

Microarray

BLAST

Computational epigenetics

References

[1] Koonin EV (2001) Computational Genomics, National Center for Biotechnology Information, National Library

of Medicine, NIH (PubMed ID: 11267880)
[2] Computational Genomics and Proteomics at MIT (http://www.eecs.mit.edu/bioeecs/CompGenProt.html)
[3] David Mount (2000), Bioinformatics, Sequence and Genome Analysis, pp. 2-3, Cold Spring Harbor Laboratory

Press, ISBN 0-87969-597-8
[4] T.A. Brown (1999), Genomes, John Wiley & Sons, ISBN 0-471-31618-0

[5] The 9th Annual Conference on Computational Genomics (2006) (http://www.cpe.vt.edu/genomics/)
[6] A. Wagner (1997), A computational genomics approach to the identification of gene networks, Nucleic Acids

Res., Sep 15;25(18):3594-604, ISSN 0305-1048
[7] Cristianini, N. and Hahn, M. Introduction to Computational Genomics (http://www.computational-genomics.

net/), Cambridge University Press, 2006. (ISBN 9780521671910 [ ISBN 0521671914)

External links

• Harvard Extension School Biophysics 101, Genomics and Computational Biology, http://
www.courses.fas.harvard.edu/~bphysl01/info/syllabus.html

• University of Bristol course in Computational Genomics, http://www.
computational-genomics.net/

DNA nanotechnology

281

DNA nanotechnology

Part of a series of articles on

Molecular self-assembly

Self-assembled monolayer

Supramolecular assembly

DNA nanotechnology

See also

• Mechanical properties of DNA

External links

Chengde Mao page at Purdue University [19]

John Reif lab at Duke University [20]

Nadrian Seeman lab at NYU [21]

William M. Shih lab at Harvard Medical School [22]

Andrew Turberfield lab at Oxford University [23]

Erik Winfree lab at Caltech [24]

Hao Yan lab at Arizona State University [25]

Bernard Yurke formerly at Bell Labs [26] now at Boise State University [27]

Thorn LaBean at Duke University [28]

Software for 3D DNA design, modeling and/or simulation:

• Ascalaph Designer L J

• caDNAno [30]

• GIDEON [31]

• NanoEngineer-1 [ *
International Society for Nanoscale Science, Computation and Engineering [33]

References

Note: Click on the doi to access the text of the referenced article.

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• Seeman, Nadrian C. (January 2001). "DNA Nicks and Nodes and Nanotechnology". Nano Letters 1 (1):
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• Kumara, Mudalige T. (July 2008). "Assembly pathway analysis of DNA nanostructures and the construction of
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• Liu, Furong; Sha, Ruojie & Seeman, Nadrian C. (10 February 1999). "Modifying the Surface Features of
Two-Dimensional DNA Crystals". Journal of the American Chemical Society 121 (5): 917-922. doi:
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• Shih, William M. ; Quispe, Joel D. ; Joyce, Gerald F. (12 February 2004). "A 1.7-kilobase single-stranded DNA
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• Mao, Chengde; Sun, Weiqiong; Shen, Zhiyong & Seeman, Nadrian C. (14 January 1999). "A DNA
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[11] DNA Logic Gates (https://digamma.cs.unm.edu/wiki/bin/view/McogPublicWeb/MolecularLogicGates)
[12] (http://www.duke.edu/~jmel7/Joshua_E._Mendoza-Elias/Research_Ideas.html)
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[17] Park, Sung Ha; Sung Ha Park, Constantin Pistol, Sang Jung Ahn, John H. Reif, Alvin R. Lebeck, Chris Dwyer,
Thomas H. LaBean (October 2006).

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org/issn/1 52 1-3757). http://www3.interscience.wiley.com/journal/113390879/abstract.

[18] Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003).
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[19] http://www.chem.purdue.edu/people/faculty/faculty.asp?itemID=46

[20] http://www.cs.duke.edu/~reif/BMC/Reif.BMCproject.html

[21] http://seemanlab4.chem.nyu.edu/

[22] http://research2.dfci.harvard.edu/shih/SHIH_LAB/Home.html

[23] http://www.physics.ox.ac.uk/cm/people/turberfield.htm

[24] http://dna.caltech.edu/

[25] http ://chemistry . asu . edu/faculty/haoyan . asp

[26] http://www.bell-labs.com/org/physicalsciences/profiles/yurke.html

[27] http://coen.boisestate.edu/departments/faculty.asp?ID=134

[28] http ://www. cs. duke. edu/~thl/

[29] http://www.agilemolecule.com/Ascalaph/Ascalaph_Designer.html

[30] http://cadnano.org

[31] http://www.subirac.com

[32] http://www.nanoengineer-l.net

[33] http://www.isnsce.org/

DNA computing

288

DNA computing

DNA computing is a form of computing which uses DNA, biochemistry and molecular
biology, instead of the traditional silicon-based computer technologies. DNA computing, or,
more generally, molecular computing, is a fast developing interdisciplinary area. Research
and development in this area concerns theory, experiments and applications of DNA
computing.

History

This field was initially developed by Leonard Adleman of the University of Southern

California, in 1994. L J Adleman demonstrated a proof-of-concept use of DNA as a form of
computation which solved the seven-point Hamiltonian path problem. Since the initial
Adleman experiments, advances have been made and various Turing machines have been
proven to be constructive. 1 J L J

In 2002, researchers from the Weizmann Institute of Science in Rehovot, Israel, unveiled a
programmable molecular computing machine composed of enzymes and DNA molecules
instead of silicon microchips. On April 28 2004, Ehud Shapiro, Yaakov Benenson,
Binyamin Gil, Uri Ben-Dor, and Rivka Adar at the Weizmann Institute announced in the
journal Nature that they had constructed a DNA computer. J This was coupled with an
input and output module and is capable of diagnosing cancerous activity within a cell, and
then releasing an anti-cancer drug upon diagnosis.

Capabilities

DNA computing is fundamentally similar to parallel computing in that it takes advantage of
the many different molecules of DNA to try many different possibilities at once.

For certain specialized problems, DNA computers are faster and smaller than any other
computer built so far. But DNA computing does not provide any new capabilities from the
standpoint of computability theory, the study of which problems are computationally
solvable using different models of computation. For example, if the space required for the
solution of a problem grows exponentially with the size of the problem (EXPSPACE
problems) on von Neumann machines it still grows exponentially with the size of the
problem on DNA machines. For very large EXPSPACE problems, the amount of DNA
required is too large to be practical. (Quantum computing, on the other hand, does provide
some interesting new capabilities).

DNA computing overlaps with, but is distinct from, DNA nanotechnology. The latter uses
the specificity of Watson-Crick basepairing and other DNA properties to make novel
structures out of DNA. These structures can be used for DNA computing, but they do not
have to be. Additionally, DNA computing can be done without using the types of molecules
made possible by DNA nanotechnology (as the above examples show).

DNA computing

289

Examples

• MAYA II

• Computational Genes

See also

• Peptide computing

• Parallel computing

• Quantum computing

References

[1] Leonard M. Adleman (1994-11-11). "http://www.usc.edu/dept/molecular-science/papers/fp-sci94.pdflMolecular
Computation Of Solutions To Combinatorial Problems". Science (journal) 266 (11): 1021-1024. http://www.
usc.edu/dept/molecular-science/papers/fp-sci94.pdf. — The first DNA computing paper. Describes a solution
for the directed Hamiltonian path problem.

[2] Dan Boneh, Christopher Dunworth, Richard J. Lipton, and Jiri Sgall (1996).

"http://citeseer.ist.psu.edu/boneh95computational.htmllOn the Computational Power of DNA". DAMATH:
Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science 71. http://
citeseer.ist.psu.edu/boneh95computational.html. — Describes a solution for the boolean satisfiability
problem.

[3] Lila Kari, Greg Gloor, Sheng Yu (January 2000). "http://citeseer.ist.psu.edu/kariOOusing.htmllUsing DNA to
solve the Bounded Post Correspondence Problem". Theoretical Computer Science 231 (2): 192-203. http://
citeseer.ist.psu.edu/kariOOusing.html. — Describes a solution for the bounded Post correspondence problem,
a hard-on-average NP-complete problem.

[4] Computer Made from DNA and Enzymes (http://news.nationalgeographic.com/news/2003/02/
0224_030224_DNAcomputer.html)

[5] Yaakov Benensonl, Binyamin Gil Uri Ben-Dor, Rivka Adar, Ehud Shapiro (2004-04-28).

"http://www.wisdom.weizmann.ac.il/~lbn/other_links/ShapiroNature2004.pdflAn autonomous molecular
computer for logical control of gene expression". Nature (journal) 429: 423-429. http ://www. wisdom.
weizmann.ac.il/~lbn/other_links/ShapiroNature2004.pdf.

Additional Literatures

• Martyn Amos (June 2005).
http://www.sphngeronline.eom/sgw/cda/frontpage/0 ,1 1855 ,3-0-22-1 995351 -0,00. html\Theoretical
and Experimental DNA Computation. Springer. ISBN 3-540-65773-8. http://www.
springeronline.com/sgw/cda/frontpage/04 1855, 3-0-22-1995351-0, 00. html. — The

first general text to cover the whole field.

• Gheorge Paun, Grzegorz Rozenberg, Arto Salomaa (October 1998). DNA Computing -
New Computing Paradigms. Springer- Verlag. ISBN 3-540-64196-3. — The book starts
with an introduction to DNA-related matters, the basics of biochemistry and language
and computation theory, and progresses to the advanced mathematical theory of DNA
computing.

• JB. Waldner (January 2007). Nanocomputers and Swarm Intelligence. ISTE. pp. 189.
ISBN 2746215160.

DNA computing

290

External links

• How Stuff Works explanation (http://computer.howstuffworks.com/dna-computer.
htm)

• Physics Web (http://physicsweb.Org/article/news/6/3/ll)

• Ars Technica (http://www.arstechnica.com/reviews/2q00/dna/dna-l.html)

• A Bibliography of Molecular Computation and Splicing Systems (http://www.dcs.ex.ac.
uk/~pf201/dna.html)

• NY Times DNA Computer for detecting Cancer (http://www.nytimes.com/2004/04/29/
science/29DNA.html)

• Bringing DNA computers to life, in Scientific American (http://www.sciam.com/article.
cfm?articleID=0005BC6A-97DF-1446-951483414B7F0101)

• Japanese Researchers store information in bacteria DNA (http://www.tfot.info/index.
php?option=com_rsgallery2&page=inline&id= 1 97&catid= 1 &limitstart= 1 77)

• International Meeting on DNA Computing (http://hagi.is. s. u-tokyo.ac.jp/dna/)

Synexpression

Synexpression is a type of non-random eukaryotic gene organization. Genes in a
synexpression group may not be physically linked, but they are involved in the same
process and they are coordinately expressed. It is expected that genes that function in the
same process be regulated coordinately. Synexpression groups in particular represent
genes that are simultaneously up- or down-regulated, often because their gene products are

required in stoichiometric amounts or are protein-complex subunits. It is likely that these
gene groups share common cis- and trans-acting control elements to achieve coordinate
expression.

Synexpression groups are determined mainly by analysis of expression profiles compiled by
the use of DNA microarrays. c ] The use of this technology helps researchers monitor
changes in expression patterns for large numbers of genes in a given experiment. Analysis
of DNA microarray expression profiles has led to the discovery of a number of genes that

are tightly co-regulated. J

One simplified example of a synexpression group is the genes cdc6, cdc3, cdc46, and swi4
in yeast, which are all co-expressed early in the G-l stage of the cell cycle. ^ , ] These
genes share one common czs-regulatory element, called ECB, which serves as a binding site
for the MCM1 trans-acting protein. Although these genes are not spatially clustered,
co-regulation seems to be achieved via this common cis and trans control mechanism. Most
synexpression groups are more complicated than the ECB group in yeast, involving a
myriad of cis and trans control elements. ,

The identification of synexpression groups has had an impact on the way some scientists

n l
view evolutionary change in higher eukaryotes. L J Since groups of genes involved in the

same biological process often share one or more common control elements, it has been

suggested that the differential expression of these synexpression groups in different tissues

of organisms can contribute to co-evolution tissues, organs, and appendages. Today it is
commonly believed that it is not primarily the gene products themselves that evolve, but
that it is the control networks for groups of genes that contribute most to the evolution of
higher eukaryotes. ^

Synexpression

291

Developmental processes provide an example of how changes in synexpression control
networks could have a significant impact on an organism's capacity to evolve and adapt
effectively. In animals, it is often beneficial for appendages to co-evolve, and it has been

observed that fore-and hind-limbs share expression of Hox genes early in metazoan

n 1
development. 1 J Thus, changes in the regulatory patterns of these genes would effect the

development of both the fore- and hind-limbs, facilitating co-evolution.

See also

• Gene regulatory network

References

[1] Niehrs, C. and Pollet, Nicolas. Synexpression groups in eukaryotes. Nature 1999 December 2; 402: 483 - 487.
[2] Mai, B. et al. Characterization of the ECB binding complex responsible for the M/Gl-specific Transcription of
CLN3 and SW14. Molecular and Cell Biology 2002 Jan; 430-441.

Computational epigenetics

n l
Computational epigenetics 1 J uses bioinformatic methods to complement experimental

research in epigenetics. Due to the recent explosion of epigenome datasets, computational

methods play an increasing role in all areas of epigenetic research.

Definition

Research in computational epigenetics comprises the development and application of
bioinformatic methods for solving epigenetic questions, as well as computational data
analysis and theoretical modeling in the context of epigenetics.

Current research areas

Epigenetic data processing and analysis

Various experimental techniques have been developed for genome-wide mapping of
epigenetic information, the most widely used being ChlP-on-chip, ChlP-seq and bisulfite
sequencing. All of these methods generate large amounts of data and require efficient ways
of data processing and quality control by bioinformatic methods.

Epigenome prediction

A substantial amount of bioinformatic research has been devoted to the prediction of
epigenetic information from characteristics of the genome sequence. Such predictions
serve a dual purpose. First, accurate epigenome predictions can substitute for experimental
data, to some degree, which is particularly relevant for newly discovered epigenetic
mechanisms and for species other than human and mouse. Second, prediction algorithms
build statistical models of epigenetic information from training data and can therefore act
as a first step toward quantitative modeling of an epigenetic mechanism.

Computational epigenetics

292

Applications in cancer epigenetics

The important role of epigenetic defects for cancer opens up new opportunities for
improved diagnosis and therapy. These active areas of research give rise to two questions
that are particularly amenable to bioinformatic analysis. First, given a list of genomic
regions exhibiting epigenetic differences between tumor cells and controls (or between
different disease subtypes), can we detect common patterns or find evidence of a functional
relationship of these regions to cancer? Second, can we use bioinformatic methods in order
to improve diagnosis and therapy by detecting and classifying important disease subtypes?

Emerging topics

The first wave of research in the field of computational epigenetics was driven by rapid
progress of experimental methods for data generation, which required adequate
computational methods for data processing and quality control, prompted epigenome
prediction studies as a means of understanding the genomic distribution of epigenetic
information, and provided the foundation for initial projects on cancer epigenetics. While
these topics will continue to be major areas of research and the mere quantity of epigenetic
data arising from epigenome projects poses a significant bioinformatic challenge, several
additional topics are currently emerging.

• Epigenetic regulatory circuitry: Reverse engineering the regulatory networks that read,
write and execute epigenetic codes.

• Population epigenetics: Distilling regulatory mechanisms from the integration of
epigenome data with gene expression profiles and haplotype maps for a large sample
from a heterogeneous population.

• Evolutionary epigenetics: Learning about epigenome regulation in human (and its
medical consequences) by cross-species comparisons.

• Theoretical modeling: Testing our mechanistic and quantitative understanding of
epigenetic mechanisms by in silico simulation.

• Statistical genome browsers: Developing a new blend of web services that enable
biologists to perform sophisticated genome and epigenome analysis within an easy-to-use
genome browser environment.

• Medical epigenetics: Searching for epigenetic mechanisms that play a role in diseases
other than cancer, as there is strong circumstantial evidence for epigenetic regulation
being involved in mental disorders, autoimmune diseases and other complex diseases.

Sources and further reading

The original version of this article was based on a review paper on computational
epigenetics that appeared in the January 2008 issue of the Bioinformatics journal: Bock, C.
and Lengauer, T. (2008) Computational epigenetics. Bioinformatics, 24, 1-10 . This
review paper provides >100 references to scientific papers and extensive background
information. It is published as open access and can be downloaded freely from the
publisher's web page: http://dx.doi.org/10.1093/bioinformatics/btm546 c .

Computational epigenetics

293

References

[1] Bock, C; and LengauerT (2008). "Computational epigenetics". Bioinformatics 24 (1): 1-10. doi

10.1093/bioinformatics/btm546 (http://dx.doi.org/10.1093/bioinformatics/btm546).
[2] http://dx.doi.org/10.1093/bioinformatics/btm546

Protein-protein interaction

Protein-protein interactions involve not only the direct-contact association of protein
molecules but also longer range interactions through the electrolyte, aqueous solution
medium surrounding neighbor hydrated proteins over distances from less than one
nanometer to distances of several tens of nanometers. Furthermore, such protein-protein

interactions are thermodynamically linked functions of dynamically bound ions and water
that exchange rapidly with the surrounding solution by comparison with the molecular
tumbling rate (or correlation times) of the interacting proteins. Protein associations are also
studied from the perspectives of biochemistry, quantum chemistry, molecular dynamics,
signal transduction and other metabolic or genetic/epigenetic networks. Indeed,
protein-protein interactions are at the core of the entire Interactomics system of any living
cell.

The interactions between proteins are important for very numerous— if not all— biological
functions. For example, signals from the exterior of a cell are mediated to the inside of that
cell by protein-protein interactions of the signaling molecules. This process, called signal
transduction, plays a fundamental role in many biological processes and in many diseases
(e.g. cancers). Proteins might interact for a long time to form part of a protein complex, a
protein may be carrying another protein (for example, from cytoplasm to nucleus or vice
versa in the case of the nuclear pore importins), or a protein may interact briefly with
another protein just to modify it (for example, a protein kinase will add a phosphate to a
target protein). This modification of proteins can itself change protein-protein interactions.
For example, some proteins with SH2 domains only bind to other proteins when they are
phosphorylated on the amino acid tyrosine while bromodomains specifically recognise
acetylated lysines. In conclusion, protein-protein interactions are of central importance for
virtually every process in a living cell. Information about these interactions improves our
understanding of diseases and can provide the basis for new therapeutic approaches.

Methods to investigate protein-protein interactions

Biochemical methods

As protein-protein interactions are so important there are a multitude of methods to detect
them. Each of the approaches has its own strengths and weaknesses, especially with regard
to the sensitivity and specificity of the method. A high sensitivity means that many of the
interactions that occur in reality are detected by the screen. A high specificity indicates
that most of the interactions detected by the screen are also occurring in reality.

Co-immunoprecipitation is considered to be the gold standard assay for protein-protein
interactions, especially when it is performed with endogenous (not overexpressed and
not tagged) proteins. The protein of interest is isolated with a specific antibody.
Interaction partners which stick to this protein are subsequently identified by western

Protein-protein interaction

294

blotting. Interactions detected by this approach are considered to be real. However, this
method can only verify interactions between suspected interaction partners. Thus, it is
not a screening approach. A note of caution also is that immunoprecipitation experiments
reveal direct and indirect interactions. Thus, positive results may indicate that two
proteins interact directly or may interact via a bridging protein.

Bimolecular Fluorescence Complementation (BiFC) is a new technique in observing the

interactions of proteins. Combining with other new techniques, this method can be used

to screen protein-protein interactions and their modulators c * .

Affinity electrophoresis as used for estimation of binding constants, as for instance in

lectin affinity electrophoresis or characterization of molecules with specific features like

glycan content or ligand binding.

Pull-down assays are a common variation of immunoprecipitation and

immunoelectrophoresis and are used identically, although this approach is more

amenable to an initial screen for interacting proteins.

Label transfer can be used for screening or confirmation of protein interactions and can

provide information about the interface where the interaction takes place. Label transfer

can also detect weak or transient interactions that are difficult to capture using other in

vitro detection strategies. In a label transfer reaction, a known protein is tagged with a

detectable label. The label is then passed to an interacting protein, which can then be

identified by the presence of the label.

The yeast two-hybrid screen investigates the interaction between artificial fusion

proteins inside the nucleus of yeast. This approach can identify binding partners of a

protein in an unbiased manner. However, the method has a notorious high false-positive

rate which makes it necessary to verify the identified interactions by

co-immunoprecipitation.

In-vivo crosslinking of protein complexes using photo-reactive amino acid analogs was

roi

introduced in 2005 by researchers from the Max Planck Institute In this method, cells
are grown with photoreactive diazirine analogs to leucine and methionine, which are
incorporated into proteins. Upon exposure to ultraviolet light, the diazirines are activated
and bind to interacting proteins that are within a few angstroms of the photo-reactive
amino acid analog.

Tandem affinity purification (TAP) method allows high throughput identification of
protein interactions. In contrast to Y2H approach accuracy of the method can be
compared to those of small-scale experiments (Collins et al., 2007) and the interactions
are detected within the correct cellular environment as by co-immunoprecipitation.
However, the TAP tag method requires two successive steps of protein purification and
consequently it can not readily detect transient protein-protein interactions. Recent
genome-wide TAP experiments were performed by Krogan et al., 2006 and Gavin et al.,
2006 providing updated protein interaction data for yeast organism.

Chemical crosslinking is often used to "fix" protein interactions in place before trying to
isolate/identify interacting proteins. Common crosslinkers for this application include the
non-cleavable NHS-ester crosslinker, bzs-sulfosuccinimidyl suberate (BS3); a cleavable
version of BS3, dithiobis(sulfosuccinimidyl propionate) (DTSSP); and the imidoester
crosslinker dimethyl dithiobispropionimidate (DTBP) that is popular for fixing
interactions in ChIP assays.

Chemical crosslinking followed by high mass MALDI mass spectrometry can be used to
analyze intact protein interactions in place before trying to isolate/identify interacting

Protein-protein interaction

295

proteins. This method detects interactions among non-tagged proteins and is available
from CovalX.

SPINE (Strep-protein interaction experiment) [ ^ uses a combination of reversible
crosslinking with formaldehyde and an incorporation of an affinity tag to detect
interaction partners in vivo.

Quantitative immunoprecipitation combined with knock-down (QUICK) relies on
co-immunoprecipitation, quantitative mass spectrometry (SILAC) and RNA interference
(RNAi). This method detects interactions among endogenous non-tagged proteins^ ^ .
Thus, it has the same high confidence as co-immunoprecipitation. However, this method
also depends on the availability of suitable antibodies.

Physical/Biophysical and Theoretical methods

• Dual Polarisation Interferometry (DPI) can be used to measure protein-protein
interactions. DPI provides real-time, high-resolution measurements of molecular size,
density and mass. While tagging is not necessary, one of the protein species must be
immobilized on the surface of a waveguide. As well as kinetics and affinity,
conformational changes during interaction can also be quantified.

• Static Light scattering (SLS) measures changes in the Rayleigh scattering of protein
complexes in solution and can non-destructively characterize both weak and strong
interactions without tagging or immobilization of the protein. The measurement consists
of mixing a series of aliquots of different concentrations or compositions with the anylate,
measuring the effect of the changes in light scattering as a result of the interaction, and
fitting the correlated light scattering changes with concentration to a model. Weak,
non-specific interactions are typically characterized via the second virial coefficient. This
type of analysis can determine the equilibrium association constant for associated
complexes. . Additional light scattering methods for protein activity determination
were previously developed by Timasheff. More recent Dynamic Light scattering (DLS)
methods for proteins were reported by H. Chou that are also applicable at high protein
concentrations and in protein gels; DLS may thus also be applicable for in vivo
cytoplasmic observations of various protein-protein interactions.

• Surface plasmon resonance can be used to measure protein-protein interaction.

• With Fluorescence correlation spectroscopy, one protein is labeled with a fluorescent dye
and the other is left unlabeled. The two proteins are then mixed and the data outputs the
fraction of the labeled protein that is unbound and bound to the other protein, allowing
you to get a measure of K D and binding affinity. You can also take time-course
measurements to characterize binding kinetics. FCS also tells you the size of the formed
complexes so you can measure the stoichiometry of binding. A more powerful methods is
[[fluorescence cross-correlation spectroscopy (FCCS) that employs double labeling
techniques and cross-correlation resulting in vastly improved signal-to-noise ratios over
FCS. Furthermore, the two-photon and three-photon excitation practically eliminates
photobleaching effects and provide ultra-fast recording of FCCS or FCS data.

• Fluorescence resonance energy transfer (FRET) is a common technique when observing
the interactions of only two different proteins .

• Protein activity determination by NMR multi-nuclear relaxation measurements, or 2D-FT
NMR spectroscopy in solutions, combined with nonlinear regression analysis of NMR
relaxation or 2D-FT spectroscopy data sets. Whereas the concept of water activity is
widely known and utilized in the applied biosciences, its complement-the protein activity

Protein-protein interaction

296

which quantitates protein-protein interactions- is much less familiar to bioscientists as it
is more difficult to determine in dilute solutions of proteins; protein activity is also much
harder to determine for concentrated protein solutions when protein aggregation, not
merely transient protein association, is often the dominant process^ J .

Theoretical modeling of protein-protein interactions involves a detailed physical
chemistry/thermodynamic understanding of several effects involved, such as
intermolecular forces, ion-binding, proton fluctuations and proton exchange. The theory
of thermodynamically linked functions is one such example in which ion-binding and
protein-protein interactions are treated as linked processes; this treatment is especially
important for proteins that have enzymatic activity which depends on cofactor ions
dynamically bound at the enzyme active site, as for example, in the case of
oxygen-evolving enzyme system (OES) in photosythetic biosystems where the oxygen
molecule binding is linked to the chloride anion binding as well as the linked state
transition of the manganese ions present at the active site in Photosystem II(PSII).
Another example of thermodynamically linked functions of ions and protein activity is
that of divalent calcium and magnesium cations to myosin in mechanical energy
transduction in muscle. Last-but-not least, chloride ion and oxygen binding to hemoglobin
(from several mammalian sources, including human) is a very well-known example of
such thermodynamically linked functions for which a detailed and precise theory has
been already developed.

Molecular dynamics (MD) computations of protein-protein interactions.
Protein-protein docking, the prediction of protein-protein interactions based only on the
three-dimensional protein structures from X-ray diffraction of protein crystals might not
be satisfactory. [9] [10]

Network visualization of protein-protein interactions

Visualization of protein-protein interaction networks is a popular application of scientific
visualization techniques. Although protein interaction diagrams are common in textbooks,
diagrams of whole cell protein interaction networks were not as common since the level of
complexity made them difficult to generate. One example of a manually produced molecular
interaction map is Kurt Kohn's 1999 map of cell cycle control. Drawing on Kohn's map,
in 2000 Schwikowski, Uetz, and Fields published a paper on protein-protein interactions in
yeast, linking together 1,548 interacting proteins determined by two-hybrid testing. They
used a force-directed (Sugiyama) graph drawing algorithm to automatically generate an
image of their network. [12] [13] [14] .

An experimental view of Kurt Kohn's 1999 map gmap L J . Image was merged via gimp
2.2.17 and then uploaded to maplib.net

Protein-protein interaction

297

See also

Interactomics

Signal transduction

Biophysical techniques

Biochemistry methods

Genomics

Complex systems biology

Complex systems

Immunoprecipitation

Protein-protein interaction prediction

Protein-protein interaction screening

BioGRID, a public repository for protein and genetic interactions

Database of Interacting Proteins (DIP)

NCIBI National Center for Integrative Biomedical Informatics

Biotechnology

Protein nuclear magnetic resonance spectroscopy

2D-FT NMRI and Spectroscopy

Fluorescence correlation spectroscopy

Fluorescence cross-correlation spectroscopy

Light scattering

ConsensusPathDB

References

[I] Kinetic Linked-Function Analysis of the Multiligand Interactions on Mg2+ -Activated Yeast Pyruvate Kinase.
Thomas J. Bollenbach and Thomas Nowak., Biochemistry, 2001, 40 (43), pp. 13097-13106

[2] Lu JP, Beatty LK, Pinthus JH. (2008). "Dual expression recombinase based (DERB) single vector system for

high throughput screening and verification of protein interactions in living cells.". Nature Precedings

<http://hdl.handle.net/10101/npre.2008. 1550. 2>.
[3] Suchanek, M., Radzikowska, A., and Thiele, C. (2005). "Photo-leucine and photo-methionine allow

identification of protein-protein interactions in living cells". Nature Methods 2: 261-268. doi:

10.1038/nmeth752 (http://dx.doi.org/10.1038/nmeth752). PMID 15782218.
[4] Herzberg C., Weidinger LA., Dorrbecker B., Hiibner S., Stiilke J. and Commichau FM. (2007). "SPINE: A

method for the rapid detection and analysis of protein-protein interactions in vivo". Proteomics 7(22):

4032-4035. doi: 10.1002/pmic.200700491 (http://dx.doi.org/10.1002/pmic.200700491). PMID 17994626.
[5] Selbach, M., Mann, M. (2006). "Protein interaction screening by quantitative immunoprecipitation combined

with knockdown (QUICK)". Nature Methods 3: 981-983. doi: 10.1038/nmeth972 (http://dx.doi.org/10.1038/

nmeth972). PMID 17072306.
[6] Arun K. Attri and Allen P. Minton (2005). "Composition gradient static light scattering: A new technique for

rapid detection and quantitative characterization of reversible macromolecular hetero-associations in solution".

Analytical Biochemistry 346: 132-138. doi: 10.1016/j.ab.2005.08.013 (http://dx.doi.Org/10.1016/j.ab.2005.

08.013). PMID 16188220.
[7] GadellaTWJr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN 978-0-08-054958-3. (2008) 560 pages.
[8] #Baianu, I.C.; Kumosinski, Thomas (August 1993). "NMR Principles and Applications to Protein Structure,

Activity and Hydration.,". Ch.9 in Physical Chemistry of Food Processes: Advanced Techniques and

Applications. (New York: Van Nostrand-Reinhold) 2: 338-420. ISBN 0-442-00582-2.
[9] Bonvin AM (2006). "Flexible protein-protein docking". Current Opinion in Structural Biology 16: 194-200. doi:

10.1016/j.sbi.2006.02.002 (http://dx.doi.Org/10.1016/j.sbi.2006.02.002). PMID 16488145.
[10] Gray JJ (2006). "High-resolution protein-protein docking". Current Opinion in Structural Biology 16: 183-193

doi: 10.1016/j.sbi.2006.03.003 (http://dx.doi.Org/10.1016/j.sbi.2006.03.003). PMID 16546374.

[II] KurtW. Kohn (1999).
"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid= 1043602 3 |Molecular
Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems". Molecular Biology of the Cell

Protein-protein interaction

298

10 (8): 2703-2734. PMID 10436023. http://www.pubmedcentral.nih. gov/articlerender.fcgi?tool=pubmed&
pubmedid=l 0436023.

[12] Benno Schwikowskil, Peter Uetz, and Stanley Fields (2000).

"http://igtmvl . fzk.de/www/itg/uetz/publications/Schwikowski2000. pdf|A network of protein-protein
interactions in yeast". Nature Biotechnology 18: 1257-1261. doi: 10.1038/82360 (http://dx.doi.org/10.1038/
82360). PMID 11101803. http://igtmvl.fzk.de/www/itg/uetz/publications/Schwikowski2000.pdf.

[13] Rigaut G, Shevchenko A, Rutz B, Wilm M, Mann M, Seraphin B (1999) A generic protein purification method
for protein complex characterization and proteome exploration. Nat Biotechnol. 17:1030-2.

[14] Prieto C, De Las Rivas J (2006). APID: Agile Protein Interaction DataAnalyzer. Nucleic Acids Res.

34:W298-302.
[15] http://www.maplib. net/map. php?id=1700&lat=-52.67138590320257&lng=34.3817138671875&z=9

Further reading

1. Gadella TW Jr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN
978-0-08-054958-3. (2008) 560 pages

2. Langel FD, et al., Multiple protein domains mediate interaction between BcllO and
Maltl, J. Biol. Chem., (2008) 283(47):32419-31

3. Clayton AH. , The polarized AB plot for the frequency-domain analysis and
representation of fluorophore rotation and resonance energy homotransfer. J Microscopy.
(2008) 232(2):306-12

4. Clayton AH, et al.. Predominance of activated EGFR higher-order oligomers on the cell
surface. Growth Factors (2008) 20:1

5. Plowman et al., Electrostatic Interactions Positively Regulate K-Ras Nanocluster
Formation and Function. Molecular and Cellular Biology (2008) 4377-4385

6. Belanis L, et al., Galectin-1 Is a Novel Structural Component and a Major Regulator of
H-Ras Nanoclusters. Molecular Biology of the Cell (2008) 19:1404-1414

7. Van Manen HJ, Refractive index sensing of green fluorescent proteins in living cells
using fluorescence lifetime imaging microscopy. Biophys J. (2008) 94(8):L67-9

8. Van der Krogt GNM, et al., A Comparison of Donor-Acceptor Pairs for Genetically
Encoded FRET Sensors: Application to the Epac cAMP Sensor as an Example, PLoS ONE,
(2008) 3(4):el916

9. Dai X, et al., Fluorescence intensity and lifetime imaging of free and
micellar-encapsulated doxorubicin in living cells. Nanomedicine. (2008) 4(l):49-56.

10. Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by
fluorescence correlation spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.

11. Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical
Imaging and High Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds,
Somatic Embryos and Single Cells., Baianu, I.C. et al. 2004., In Oil Extraction and
Analysis., D. Luthria, Editor pp. 241-273, AOCS Press., Champaign, IL

12. Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT)
Spectroscopy. Nobel Lecture, on December 9, 1992.

13. Baianu, I.C; Kumosinski, Thomas (August 1993). "NMR Principles and Applications to
Protein Structure, Activity and Hydration.,". Ch.9 in Physical Chemistry of Food
Processes: Advanced Techniques and Applications. (New York: Van Nostrand-Reinhold)
2: 338-420. ISBN 0-442-00582-2.

14. Kurt Wuthrich in 1982-1986 : 2D-FT NMR of solutions (http://en.wikipedia.org/wiki/
Nuclear_magnetic_resonance#Nuclear_spin_and_magnets)

15. Charles P. Slichter.1996. Principles of Magnetic Resonance., Springer: Berlin and New
York, Third Edition., 651pp. ISBN 0-387-50157-6.

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299

16. Kurt Wiithrich. Protein structure determination in solution by NMR spectroscopy . J
BiolChem. 1990, December 25;265(36):22059-62.

External links

• National Center for Integrative Biomedical Informatics (NCIBI) (http://portal.ncibi.org/
gateway/)

• Proteins and Enzymes (http://www.dmoz.org/Science/Biology/
BiochemistryandMolecularBiology/Biomolecules/ProteinsandEnzymes/) at the
Open Directory Project

• FLIM Applications (http://www.nikoninstruments.com/infocenter.php?n=FLIM) FLIM
is also often used in microspectroscopic/ chemical imaging, or microscopic, studies to
monitor spatial and temporal protein-protein interactions, properties of membranes and
interactions with nucleic acids in living cells.

• Arabidopsis thaliana protein interaction network (http://bioinfo.esalq.usp.br/atpin)

Interactomics

Interactomics is a discipline at the intersection of bioinformatics and biology that deals
with studying both the interactions and the consequences of those interactions between

and among proteins, and other molecules within a cell 1 J . The network of all such
interactions is called the Interactome. Interactomics thus aims to compare such networks of
interactions (i.e., interactomes) between and within species in order to find how the traits
of such networks are either preserved or varied. From a mathematical, or mathematical
biology viewpoint an interactome network is a graph or a category representing the most
important interactions pertinent to the normal physiological functions of a cell or organism.

Interactomics is an example of "top-down" systems biology, which takes an overhead, as
well as overall, view of a biosystem or organism. Large sets of genome-wide and proteomic
data are collected, and correlations between different molecules are inferred. From the
data new hypotheses are formulated about feedbacks between these molecules. These
hypotheses can then be tested by new experiments J .

Through the study of the interaction of all of the molecules in a cell the field looks to gain a
deeper understanding of genome function and evolution than just examining an individual

genome in isolation 1 J . Interactomics goes beyond cellular proteomics in that it not only
attempts to characterize the interaction between proteins, but between all molecules in the
cell.

Interactomics

300

These

Methods of interactomics

The study of the interactome requires the collection of large amounts of data by way of high
throughput experiments. Through these experiments a large number of data points are
collected from a single organism under a small number of perturbations
experiments include:

• Two-hybrid screening

• Tandem Affinity Purification

• X-ray tomography

• Optical fluorescence microscopy

Recent developments

The field of interactomics is currently rapidly expanding and developing. While no
biological interactomes have been fully characterized. Over 90% of proteins in
Saccharomyces cerevisiae have been screened and their interactions characterized, making

it the first interactome to be nearly fully specified c ^ .

n 1
Also there have been recent systematic attempts to explore the human interactome 1 J and

[4]

VENOM

LIFE

Metabolic Network Model for Escherichia coli.

Other species whose interactomes have been studied in some detail include Caenorhabditis
elegans and Drosophila melanogaster.

Interactomics

301

Criticisms and concerns

Kiemer and Cesarenr J raise the following concerns with the current state of the field:

• The experimental procedures associated with the field are error prone leading to "noisy
results". This leads to 30% of all reported interactions being artifacts. In fact, two groups
using the same techniques on the same organism found less than 30% interactions in
common.

• Techniques may be biased, i.e. the technique determines which interactions are found.

• Ineractomes are not nearly complete with perhaps the exception of S. cerivisiae.

• While genomes are stable, interactomes may vary between tissues and developmental
stages.

• Genomics compares amino acids, and nucleotides which are in a sense unchangeable, but
interactomics compares proteins and other molecules which are subject to mutation and
evolution.

• It is difficult to match evolutionarily related proteins in distantly related species.

See also

Interaction network
Proteomics
Metabolic network
Metabolic network modelling
Metabolic pathway
Genomics

Mathematical biology
Systems biology

References

[1] Kiemer, L; G Cesareni (2007). "Comparative interactomics: comparing apples and pears?". TRENDS in

Biochemistry 25: 448-454. doi: 10.1016/j.tibtech.2007.08.002 (http://dx.doi.Org/10.1016/j.tibtech.2007.

08.002).
[2] Bruggeman, F J; H V Westerhoff (2006). "The nature of systems biology". TRENDS in Microbiology 15: 45-50

doi: 10. 1016/j.tim.2006. 11.003 (http://dx.doi.Org/10.1016/j.tim.2006.ll.003).
[3] Krogan, NJ; et al. (2006). "Global landscape of protein complexes in the yeast Saccharomyeses Cerivisiae ".

Nature 440: 637-643. doi: 10.1038/nature04670 (http://dx.doi.org/10.1038/nature04670).
[4] further citation needed

External links

• Interactomics.org (http://interactomics.org). A dedicated interactomics web site
operated under BioLicense.

• Interactome.org (http://interactome.org). An interactome wiki site.

• PSIbase (http://psibase.kobic.re.kr) Structural Interactome Map of all Proteins.

• Omics.org (http://omics.org). An omics portal site that is openfree (under BioLicense)

• Genomics.org (http://genomics.org). A Genomics wiki site.

• Comparative Interactomics analysis of protein family interaction networks using PSIMAP
(protein structural interactome map) (http://bioinformatics.oxfordjournals.org/cgi/
content/full/2 1/1 5/3234)

• Interaction interfaces in proteins via the Voronoi diagram of atoms (http://www.
sciencedirect.com/science? ob=ArticleURL& udi=B6TYR-4KXVD30-2& user=10&

Interactomics

302

_coverDate=l 1/30/2 006&_rdoc = l&_fmt=&_orig=search&_sort=d&view=c&

_acct=C000050221&_version=l&_urlVersion=0&_userid=10&

md5 = 8361bf3fe7834b4642cdda3b979de8bb)

Using convex hulls to extract interaction interfaces from known structures. Panos Dafas,

Dan Bolser, Jacek Gomoluch, Jong Park, and Michael Schroeder. Bioinformatics 2004 20:

1486-1490.

PSIbase: a database of Protein Structural Interactome map (PSIMAP). Sungsam Gong,

Giseok Yoon, Insoo Jang Bioinformatics 2005.

Mapping Protein Family Interactions : Intramolecular and Intermolecular Protein Family

Interaction Repertoires in the PDB and Yeast, Jong Park, Michael Lappe & Sarah A.

TeichmannJ.M.B (2001).

Semantic Systems Biology (http://www.semantic-systems-biology.org)

Developmental biology

Developmental biology is the

study of the process by which
organisms grow and develop.
Modern developmental biology
studies the genetic control of cell
growth,

differentiation

and

"morphogenesis," which is the
process that gives rise to tissues,

organs

and

anatomy.

Developmental biology is that
branch of life science, which deals
with the study of the process by
which
develop.

organisms

grow

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"Views of a Fetus in the Womb", Leonardo da Vinci, ca.
1510-1512. The subject of prenatal development is a major

subset of developmental biology.

Related fields of study

Embryology is a subfield, the study

of organisms between the one-cell

stage (generally, the zygote) and

the end of the embryonic stage.

Embryology was originally a more

descriptive science until the 20th

century. Embryology and developmental biology today deal with the various steps

necessary for the correct and complete formation of the body of a living organism.

The related field of evolutionary developmental biology was formed largely in the 1990s and
is a synthesis of findings from molecular developmental biology and evolutionary biology
which considers the diversity of organismal form in an evolutionary context.

Developmental biology

303

Perspectives

Animal development is a spectacular process and represents a masterpiece of temporal and
spatial control of gene expression. Developmental genetics is a very helpful process. It
studies the effect that genes have in a phenotype. The findings of developmental biology
can help to understand developmental malfunctions such as chromosomal aberrations, for
example, Down syndrome. An understanding of the specialization of cells during
embryogenesis may yield information on how to specialize stem cells to specific tissues and
organs, which could lead to the specific cloning of organs for medical purposes. Another
biologically important process that occurs during development is apoptosis - programmed
cell death or "suicide". For this reason, many developmental models are used to elucidate
the physiology and molecular basis of this cellular process. Similarly, a deeper
understanding of developmental biology can foster greater progress in the treatment of
congenital disorders and diseases, e.g. studying human sex determination can lead to
treatment for disorders such as congenital adrenal hyperplasia.

Developmental model organisms

Often used model organisms in developmental biology include the following
• Vertebrates

Zebrafish Danio rerio
Medakafish Oryzias latipes
Fugu (pufferfish) Takifugu rubripes
Frog Xenopus laevis, Xenopus tropicalis^ 2 *
Chicken Gallus gallus

Mouse Mus musculus (Mammalian embryogenesisr
nvertebrates

Lancelet Branchiostoma lanceolatum
Ascidian Ciona intestinalis
Sea urchin Strongylocentrotus purpuratus
Roundworm Caenorhabditis elegans

Fruit fly Drosophila melanogaster (Drosophila embryogenesis)
Plants (Plant embryogenesis)

Arabidopsis thaliana
Maize

Snapdragon Antirrhinum majus
Other

• Slime mold Dictyostelium discoideum

Studied phenomena

Cell differentiation

Differentiation is the formation of cell types, from what is originally one cell - the zygote or
spore. The formation of cell types like nerve cells occurs with a number of intermediary,
less differentiated cell types. A cell stays a certain cell type by maintaining a particular
pattern of gene expression. This depends on regulatory genes, e.g. for transcription
factors and signaling proteins. These can take part in self-perpetuating circuits in the gene

Developmental biology

304

regulatory network, circuits that can involve several cells that communicate with each
other. J External signals can alter gene expression by activating a receptor, which triggers
a signaling cascade that affects transcription factors. For example, the withdrawal of
growth factors from myoblasts causes them to stop dividing and instead differentiate into
muscle cells. ]

Embryonal development

Embryogenesis is the step in the life cycle after fertilisation - the development of the
embryo, starting from the zygote (fertilised egg). Organisms can differ drastically in the
how embryo develops, especially when belong to different phyla. For example, embryonal
development in placental mammals starts with cleavage of the zygote into eight
uncommited cells, which then form a ball (morula). The outer cells become the
trophectoderm which will form the fetal part of the placenta, while inner cells become the
inner cell mass that will form all other organs. In contrast, the fruit fly zygote first forms a
sausage-shaped syncytium, which is still one cell but with many cell nuclei.

Patterning is important for determining which cells develop which organs. This is mediated
by signaling between adjacent cells by proteins on their surfaces, and by gradients of
signaling molecules. An example is retinoic acid, which forms a gradient in the head to
tail direction in animals. Retinoic acid enters cells and activates Hox genes in a
concentration-dependent manner - Hox genes differ in how much retinoic acid they require
for activation. As Hox genes code for transcription factors, this causes discrete segments in
the head to tail direction. J This is important for e.g. the segmentation of the spine in
vertebrates.

Embryonal development does not always go right, and errors can result in birth defects or
miscarriage. Often the reason is genetic (mutation or chromosome abnormality), but there
can be environmental influence (teratogens). Abnormal development is also of

evolutionary interest as it provides a mechanism for changes in body plan (see evolutionary
developmental biology).

Growth

Growth is the enlargement of a tissue or organism. Growth continues after the embryonal
stage, and occurs through cell proliferation, enlargement of cells or accumulation of
extracellular material. In plants, growth results in an adult organism that is strikingly
different from the embryo. The proliferating cells tend to be distinct from differentiated
cells (see stem cell and progenitor cell). In some tissues proliferating cells are restricted to

ri2i

specialised areas, such as the growth plates of bones. 1 But some stem cells migrate to
where they are needed, such as mesenchymal stem cells which can migate from the bone
marrow to form e.g. muscle, bone or adipose tissue. The size of an organ frequently
determines its growth, as in the case of the liver which grows back to its previous size if a
part is removed. Growth factors, such as fibroblast growth factors in the animal embryo and

n 21

growth hormone in juvenile mammals, also control the extent of growth. 1 J

Developmental biology

305

Metamorphosis

Most animals have a larval stage, with a body plan different from that of the adult
organism. The larva abrubtly develops into an adult in a process called metamorphosis. For
example, butterfly larvae (caterpillars) are specilised for feeding whereas adult butterflies
(imagos) are specilised for flight and reproduction. When the caterpillar has grown enough,
it turns into an immobile pupa. Here, the imago develops from imaginal discs found inside
the larva. [14]

Regeneration

Regeneration is the reactivation of development so that a missing body part grows back.
This phenomenon has been studied particularly in salamanders, where the adults can
reconstruct a whole limb after it has been amputated. ^ Researchers hope to one day be
able to induce regeneration in humans (see regenerative medicine). There is little
spontaneous regeneration in adult humans, although the liver is a notable exception. Like
for salamanders, the regeneration of the liver involves dedifferentiation of some cells to a
more embryonal state. ]

Developmental systems biology

Computer simulation of multicellular development is a research methodology to understand
the function of the very complex processes involved in the development of organisms. This
includes simulation of cell signaling, multicell interactions and regulatory genomic
networks in development of multicellular structures and processes (see French flag model
or Biological Physics of the Developing Embryo for literature). Minimal genomes for
minimal multicellular organisms may pave the way to understand such complex processes
in vivo.

See also

Altricial and Precocial

Auxology

Body plan

Cell signaling

Embryogenesis

Embryology

Evolutionary developmental biology

Plant evolutionary developmental biology

Fertilization

Fish development

Cell signaling networks

Developmental noise

Enhancer

Enhanceosome

Gene regulatory network

Promoter

Signal transduction

Transcription factor

Developmental biology

306

References

[I] Haffter P, Niisslein-Volhard C (1996). "http://www.intjdevbiol.com/paper.php?doi=8735932|Large scale
genetics in a small vertebrate, the zebrafish". Int. J. Dev. Biol. 40: 221-7. PMID 8735932. http://www.
intjdevbiol.com/paper.php?doi=8735932.

[2] AmayaE (2005). "http://genome.cshlp.org/content/15/12/1683.longlXenomics". Genome Res. 15 (12): 1683-91.

PMID 16339366. http://genome.cshlp.org/content/15/12/1683.long.
[3] Keller G (2005). "http://genesdev.cshlp.org/content/19/10/1129.longlEmbryonic stem cell differentiation:

emergence of a new era in biology and medicine". Genes Dev. 19 (10): 1129-55. PMID 15905405. http://

genesdev.cshlp.org/content/19/10/1129.long.
[4] Wolpert L, Beddington R, Jessell T, Lawrence P, Meyerowitz E, Smith J (2002). Principles of development (2nd

ed.). Oxford university press, pp. 293-295. ISBN 0-19-879291-3.
[5] Ben-Tabou de-Leon S, Davidson EH (2007). "Gene regulation: gene control network in development". Annu Rev

Biophys Biomol Struct 36: 191. doi: 10. 1146/annurev.biophys. 35. 040405. 102002 (http://dx.doi.org/10.1146/

annurev.biophys. 35.040405. 102002). PMID 17291181.
[6] Wolpert L, Beddington R, Jessell T, Lawrence P, Meyerowitz E, Smith J (2002). Principles of development (2nd

ed.). Oxford university press, pp. 304-307. ISBN 0-19-879291-3.
[7] Wolpert L, Beddington R, Jessell T, Lawrence P, Meyerowitz E, Smith J (2002). Principles of development (2nd

ed.). Oxford university press, pp. 41-50, 493. ISBN 0-19-879291-3.
[8] Christ B, Schmidt C, Huang R, Wilting J, Brand-Saberi B (January 1998).

"http://link.springer.de/link/service/journals/00429/bibs/7197001/71970001.htmlSegmentationofthevertebra

body". Anat. Embryol. 197 (1): 1-8. PMID 9462855. http://link.springer.de/link/service/journals/00429/

bibs/7197001/71970001. htm.
[9] Marshall H, Morrison A, Studer M, Popperl H, Krumlauf R (July 1996).

"http://www.fasebj.org/cgi/pmidlookup?view=long&pmid=8801179|Retinoids and Hox genes". FASEBJ. 10 (9):

969-78. PMID 8801179. http://www.fasebj.org/cgi/pmidlookup?view=long&pmid= 880 1179.
[10] Holtzman NA, Khoury MJ (1986). "Monitoring for congenital malformations". Annu Rev Public Health 7:

237-66. doi: 10. 1146/annurev.pu. 07. 050186. 001321 (http://dx.doi.org/10.1146/annurev.pu.07.050186.

001321). PMID 3521645.

[II] Fujimoto K, Ishihara S, Kaneko K (2008).
"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=246471 1 |Network evolution of
body plans". PLoS ONE 3 (7): e2772. doi: 10. 1371/journal.pone. 0002772 (http://dx.doi.org/10.1371/journal.
pone.0002772). PMID 18648662.

[12] Wolpert L, Beddington R, Jessell T, Lawrence P, Meyerowitz E, Smith J (2002). Principles of development

(2nd ed.). Oxford university press, pp. 467-482. ISBN 0-19-879291-3.
[13] Chamberlain G, Fox J, Ashton B, Middleton J (November 2007). "Concise review: mesenchymal stem cells:

their phenotype, differentiation capacity, immunological features, and potential for homing". Stem Cells 25

(11): 2739-49. doi: 10.1634/stemcells.2007-0197 (http://dx.doi.org/10.1634/stemcells.2007-0197). PMID

17656645.
[14] Gilbert SF (2003). Developmental biology (7th ed.). Sinauer. pp. 575-585. ISBN 0-87893-258-5.
[15] Gilbert SF (2003). Developmental biology (7th ed.). Sinauer. pp. 592-601. ISBN 0-87893-258-5.
[16] Stocum DL (December 2002). "Development. A tail of transdifferentiation". Science 298 (5600): 1901-3. doi:

10. 1126/science. 1079853 (http://dx.doi.org/10.1126/science.1079853). PMID 12471238.

External links

• Developmental Biology of Plants and Animals (http://developmentalbiology.de/en/)

• Developmental Biology - 8th Edition (http://8e.devbio.com) by Scott Gilbert (online
textbook)

Cellular differentiation

307

Cellular differentiation

developmental biology,

cellular differentiation is

the process by which a less
specialized cell becomes a
more specialized cell type.

Differentiation

occurs

numerous times during the
development of a multicellular
organism as the organism
changes from a single zygote
to a complex system of tissues
and cell types. Differentiation
is a common process in adults
as well: adult stem cells divide
and create fully-differentiated
daughter cells during tissue
repair and during normal cell

turnover.

Differentiation

dramatically changes a cell's

size,

shape,

membrane

Skin Cells

Epidermis

Neuron
of Brain

Pigment
Cell

Ectoderm

(External Layer)

Gastrula

Germ
Celts

Zygote

Blastocyst

Mesoderm
{Middle 8 Layer]

Cardiac
Muscle

Skeletal

Muscle

Cells

Tubule Red Blood
Cell of Cells
the Kid nay

Smooth
Muscle
(in Gut)

-Ended trm-

f, Internal Layer]

• #

Lung Cell
Alveolar

oil)

Thyroid

Cell

Pancreatic
Cell

In the center of the diagram the early steps in the development of a
mammal. On the top and bottom are some of the fully-differentiated

cell types that will eventually form in the adult.

potential, metabolic activity,

and responsiveness to signals.

These changes are largely due to highly-controlled modifications in gene expression. With a

few exceptions, cellular differentiation almost never involves a change in the DNA sequence

itself. Thus, different cells can have very different physical characteristics despite having

the same genome.

A cell that is able to differentiate into many cell types is known as pluripotent. Such cells
are called stem cells in animals and meristematic cells in higher plants. A cell that is able to
differentiate into all cell types is known as totipotent. In mammals, only the zygote and
early embryonic cells are totipotent, while in plants many differentiated cells can become
totipotent with simple laboratory techniques. In cytopathology, the level of cellular
differentiation is used as a measure of cancer progression. "Grade" is a marker of how
differentiated a cell in a tumor is.

Mammalian cell types

Three basic categories of cells make up the mammalian body: germ cells, somatic cells, and
stem cells. Each of the approximately 100,000,000,000,000 (10 ) cells in an adult human
has its own copy or copies of the genome except certain cell types, such as red blood cells,
that lack nuclei in their fully differentiated state. Most cells are diploid; they have two
copies of each chromosome. Such cells, called somatic cells, make up most of the human
body, such as skin and muscle cells. Cells differentiate to specialize for different functions.

Germ line cells are any line of cells that give rise to gametes— eggs and sperm— and thus
are continuous through the generations. Stem cells, on the other hand, have the ability to

Cellular differentiation

308

divide for indefinite periods and to give rise to specialized cells. They are best described in
the context of normal human development.

Development begins when a sperm fertilizes an egg and creates a single cell that has the
potential to form an entire organism. In the first hours after fertilization, this cell divides
into identical cells. In humans, approximately four days after fertilization and after several
cycles of cell division, these cells begin to specialize, forming a hollow sphere of cells,
called a blastocyst. The blastocyst has an outer layer of cells, and inside this hollow sphere,
there is a cluster of cells called the inner cell mass. The cells of the inner cell mass will go
on to form virtually all of the tissues of the human body. Although the cells of the inner cell
mass can form virtually every type of cell found in the human body, they cannot form an
organism. These cells are referred to as pluripotent.

Pluripotent stem cells undergo further specialization into multipotent progenitor cells that
then give rise to functional cells. Examples of stem and progenitor cells include:

• Hematopoietic stem cells (adult stem cells) from the bone marrow that give rise to red
blood cells, white blood cells, and platelets

• Mesenchymal stem cells (adult stem cells) from the bone marrow that give rise to stromal
cells, fat cells, and types of bone cells

• Epithelial stem cells (progenitor cells) that give rise to the various types of skin cells

• Muscle satellite cells (progenitor cells) that contribute to differentiated muscle tissue

Dedifferentiation

Dedifferentiation is a cellular process often seen in more basal life forms such as worms
and amphibians in which a partially or terminally differentiated cell reverts to an earlier

rn r2i

developmental stage, usually as part of a regenerative process. 1 Dedifferentiation also

roi

occurs in plants . Cells in cell culture can lose properties they originally had, such as
protein expression, or change shape. This process is also termed dedifferentiation c ] .

Some believe dedifferentiation is an aberration of the normal development cycle that
results in cancer/ J whereas others believe it to be a natural part of the immune response
lost by humans at some point as a result of evolution.

A small molecule dubbed reversine, a purine analog, has been discovered that has proven
to induce dedifferentiation in myotubes. These dedifferentiated cells were then able to
redifferentiate into osteoblasts and adipocytes.

Mechanisms

Each specialized cell type in an organism expresses a subset of all the genes that constitute
the genome of that species. Each cell type is defined by its particular pattern of regulated
gene expression. Cell differentiation is thus a transition of a cell from one cell type to
another and it involves a switch from one pattern of gene expression to another. Cellular
differentiation during development can be understood as the result of a gene regulatory
network. A regulatory gene and its cis-regulatory modules are nodes in a gene regulatory

T71

network; they receive input and create output elsewhere in the network L J . The systems
biology approach to developmental biology emphasizes the importance of investigating how
developmental mechanisms interact to produce predictable patterns (morphogenesis).

A few evolutionarily conserved types of molecular processes are often involved in the
cellular mechanisms that control these switches. The major types of molecular processes

Cellular differentiation

309

that control cellular differentiation involve cell signaling. Many of the signal molecules that
convey information from cell to cell during the control of cellular differentiation are called
growth factors. Although the details of specific signal transduction pathways vary, these
pathways often share the following general steps. A ligand produced by one cell binds to a
receptor in the extracellular region of another cell, inducing a conformational change in the
receptor. The shape of the cytoplasmic domain of the receptor changes, and the receptor
acquires enzymatic activity. The receptor then catalyzes reactions that phosphorylate other
proteins, activating them. A cascade of phosphorylation reactions eventually activates a
dormant transcription factor or cytoskeletal protein, thus contributing to the differentiation
process in the target cell . Cells and tissues can vary in competence, their ability to
respond to external signals [ ] .

Induction refers to cascades of signaling events, during which a cell or tissue signals to
another cell or tissue to influence its developmental fate . Yamamoto and Jeffery L J
investigated the role of the lens in eye formation in cave- and surface-dwelling fish, a
striking example of induction^ J . Through reciprocal transplants, Yamamoto and Jeffery J
found that the lens vesicle of surface fish can induce other parts of the eye to develop in
cave- and surface-dwelling fish, while the lens vesicle of the cave-dwelling fish cannot .

Other important mechanisms fall under the category of asymmetric cell divisions, divisions
which give rise to daughter cells with distinct developmental fates. Asymmetric cell
divisions can occur because of segregation of cytoplasmic determinants or because of
signaling *- * . In the former mechanism, distinct daughter cells are created during
cytokinesis because of an uneven distribution of regulatory molecules in the parent cell; the
distinct cytoplasm that each daughter cell inherits results in a distinct pattern of
differentiation for each daughter cell. A well-studied example of pattern formation by
asymmetric divisions is body axis patterning in Drosophila. RNA molecules are an important
type of intracellular differentiation control signal. The molecular and genetic basis of
asymmetric cell divisions has also been studied in green algae of the genus Volvox, a model
system for studying how unicellular organisms can evolve into multicellular organisms .
In Volvox carteri, the 16 cells in the anterior hemisphere of a 32-celled embryo divide
asymmetrically, each producing one large and one small daughter cell. The size of the cell
at the end of all cell divisions determines whether it will become a specialized germ or
somatic cell [9] [11] .

See also

• Morphogenesis

• Multipotent

• Germ layer

• Cell fate determination

References

[1] Stocum DL; Amphibian regeneration and stem cells (http://www.ncbi.nlm.nih.gov/sites/

entrez?db=pubmed&uid=14594207&cmd=showdetailview&indexed=google); Curr Top Microbiol Immunol.

2004;280:1-70. PMID: 14594207

[2] CM Casimir, PB Gates, RK Patient and JP Brockes; Evidence for dedifferentiation and metaplasia in amphibian
limb regeneration from inheritance of DNA methylation (http://dev.biologists.org/cgi/content/abstract/104/
4/657); Development Vol 104, Issue 4 657-668

Cellular differentiation

310

[3] Dedifferentiation and Regeneration in Bryophytes: A Selective Review (http://www.rsnz.org/publish/nzjb/

1971/47.php), K.L. Giles, New Zealand Journal of Botany 9: 689-94
[4] Dedifferentiation-associated changes in morphology and gene expression in primary human articular

chondrocytes in cell culture (http://www.ncbi. nlm.nih.gov/entrez/ query. fcgi?cmd=Retrieve&

db=PubMed&list_uids=11795984&dopt=Citation), M. Schnabel et al., Osteoarthritis and Cartilage, Volume

10, Issue 1 , January 2002, Pages 62-70.
[5] Stewart Sell; Cellular Origin of Cancer - Dedifferentiation or Stem Cell Maturation Arrest? (http://www.jstor

org/view/00916765/ap060112/06a00040/0); Environmental Health Perspectives, 1993
[6] Panagiotis A. Tsonis; Stem Cells from Differentiated Cells (http://www.ncbi.nlm.nih.gov/entrez/query.

fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=l 5087480); Molecular Interventions 4:81-83,

(2004)
[7] DeLeon SBT, EH Davidson; Gene regulation: Gene control network in development. Annual Review of

Biophysics and Biomolecular Structure 36:191-212, 2007
[8] Gilbert; Developmental Biology, eighth edition. Sinaur Associates, Inc., p. 147, 2006

[9] Rudel and Sommer; The evolution of developmental mechanisms. Developmental Biology 264, 15-37, 2003
[10] Yamamoto Y and WR Jeffery; Central role for the lens in cave fish eye degeneration. Science 289 (5479),

631-633, 2000
[11] Kirk MM, A Ransick, SE Mcrae, DL Kirk; The relationship between cell size and cell fate in Volvox carteri.

Journal of Cell Biology 123, 191-208, 1993

Morphogenesis

Morphogenesis (from the Greek morphe shape and genesis creation, literally, "beginning
of the shape"), is the biological process that causes an organism to develop its shape. It is
one of three fundamental aspects of developmental biology along with the control of cell
growth and cellular differentiation. The process controls the organized spatial distribution
of cells during the embryonic development of an organism. Morphogenetic responses may
be induced in organisms by hormones, by environmental chemicals ranging from
substances produced by other organisms to toxic chemicals or radionuclides released as
pollutants, and other plants, or by mechanical stresses induced by spatial patterning of the
cells. Morphogenesis can take place in an embyro, a mature organism, in cell culture or
inside tumor cell masses.

Morphogenesis also describes the development of unicellular life forms that do not have an
embryonic stage in their life cycle, or describes the evolution of a body structure within a
taxonomic group.

History

Some of the earliest ideas on how physical and mathematical processes and constraints
affect biological growth were written by D'Arcy Wentworth Thompson and Alan Turing.
These works postulated the presence of chemical signals and physico-chemical processes
such as diffusion, activation, and deactivation in cellular and organismic growth. The fuller
understanding of the mechanisms involved in actual organisms required the discovery of
DNA and the development of molecular biology and biochemistry.

Morphogenesis

311

Molecular basis

Several types of molecules are particularly important during morphogenesis. Morphogens
are soluble molecules that can diffuse and carry signals that control cell differentiation
decisions in a concentration-dependent fashion. Morphogens typically act through binding
to specific protein receptors. An important class of molecules involved in morphogenesis
are transcription factor proteins that determine the fate of cells by interacting with DNA.
These can be coded for by master regulatory genes and either activate or deactivate the
transcription of other genes; in turn, these secondary gene products can regulate the
expression of still other genes in a regulatory cascade. Another class of molecules involved
in morphogenesis are molecules that control cell adhesion. For example, during
gastrulation, clumps of stem cells switch off their cell-to-cell adhesion, become migratory,
and take up new positions within an embryo where they again activate specific cell
adhesion proteins and form new tissues and organs. Several examples that illustrate the
roles of morphogens, transcription factors and cell adhesion molecules in morphogenesis
are discussed below.

Cellular basis

Morphogenesis arises because of changes in
the cellular structure or how cells interact in

n 1

tissues 1 J . Certain cell types "sort out". Cell
"sorting out" means that when the cells
physically interact they move so as to sort into
clusters that maximize contact between cells of
the same type. The ability of cells to do this
comes from differential cell adhesion. Two
well-studied types of cells that sort out are
epithelial cells and mesenchymal cells. During
embryonic development there are some cellular

differentiation

events

during

which

mesenchymal cells become epithelial cells and
at other times epithelial cells differentiate into
mesenchymal

cells

(see

Epithelial-mesenchymal transition). Following
epithelial-mesenchymal transition, cells can
migrate away from an epithelium and then
associate with other similar cells in a new
location.

' l " "1

ffc^

■' '■

^H •*. ** i

""■■I ■

• t

■ - J

^^"* "" m u

J* ^

•*

Too

microns

■

& 1

* i

^^^HB m-

Example of cell sorting out with cultured PI 9

embryonal carcinoma cells. Live cells were

stained with either Dil (red) or DiO (green). The

red cells were genetically altered and express

higher levels of E-cadherin than the green cells.

After labeling, the two populations of cells were

mixed and cultured together allowing the cells to

form large multi-cellular mixed aggregates.

Individual cells are less than 10 micrometres in

diameter. The image was captured by scanning

confocal microscopy.

Adhesion

During embryonic development, cells sort out
in different layers due to differential adhesion. Cells that share the same cell-to-cell
adhesion molecules separate from cells that have different adhesion molecules. Cells sort
based upon differences in adhesion between the cells, so even two populations of cells with
different levels of the same adhesion molecule can sort out. In cell culture cells that have
the strongest adhesion move to the center of a mixed aggregates of cells.

Morphogenesis

312

The molecules responsible for adhesion are called cell adhesion molecules (CAMs).

Several types of cell adhesion molecules are known and one major class of these molecules
are cadherins. There are dozens of different cadherins that are expressed on different cell
types. Cadherins bind to other cadherins in a like-to-like manner: E-cadherin (found on
many epithelial cells) binds preferentially to other E-cadherin molecules. Mesenchymal
cells usually express other cadherin types such as N-cadherin.

Extracellular Matrix

The extracellular matrix (ECM) is involved with separating tissues, providing structural
support or providing a structure for cells to migrate on. Collagen, laminin, and fibronectin
are major ECM molecules that are secreted and assembled into sheets, fibers, and gels.
Multisubunit transmembrane receptors called integrins are used to bind to the ECM.
Integrins bind extracellularly to fibronectin, laminin, or other ECM components, and
intracellularly to microfilament-binding proteins oc-actinin and talin to link the cytoskeleton
with the outside. Integrins also serve as receptors to trigger signal transduction cascades
when binding to the ECM. A well-studied example of morphogenesis that involves ECM is
mammary gland ductal branching^ , .

See also

Embryogenesis

Pattern formation

French flag model

Reaction-diffusion

Neurulation

Gastrulation

Axon guidance

Eye development

Polycystic kidney disease 2

Drosophila embryogenesis

Manuel DeLanda

References

[1] Gilbert, Scott F. (2000).

http://www.ncbi.nlm. nih.gov/books/bv.fcgi?highlight=morphogenesis&rid=dbio. section. 372 1 ''Morphogenesis
and Cell Adhesion". Developmental biology (6th ed.). Sunderland, Mass: Sinauer Associates. ISBN
0-87893-243-7.

[2] Fata JE, Werb Z, Bissell MJ (2004).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=31 4442 1 Regulation of mammary
gland branching morphogenesis by the extracellular matrix and its remodeling enzymes". Breast Cancer Res. 6
(1): 1-11. doi: 10.1186/bcr634 (http://dx.doi.org/10.1186/bcr634). PMID 14680479.

[3] Sternlicht MD (2006). "http://breast-cancer-research.eom/content/8/l/201 |Key stages in mammary gland
development: the cues that regulate ductal branching morphogenesis". Breast Cancer Res. 8 (1): 201. doi:
10.1186/bcrl368 (http://dx.doi.org/10.1186/bcrl368). PMID 16524451. PMC: 1413974 (http://www.
pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid= 141 3974). http://breast-cancer-research.
com/content/8/1/201.

Morphogenesis

313

External links

• Artificial Life model of multicellular morphogenesis with autonomously generated
gradients for positional information (http://panmental.de/ALifeXIflag)

Nuclear medicine

Nuclear medicine is a branch of medicine and medical imaging that uses radioactive
isotopes (radionuclides) in the diagnosis and treatment of disease. Nuclear medicine thus
relies on the process of radioactive decay. Molecular imaging may employ nuclear medical
techniques when it uses radioisotopes to produce images that reflect biological processes
that take place at the cellular and sub cellular level.

Nuclear medicine procedures use pharmaceuticals that have been labeled with
radionuclides (radiopharmaceuticals). In diagnosis, radioactive substances are
administered to patients and the radiation emitted is detected. The diagnostic tests involve
the formation of an image using a gamma camera or positron emission tomography,
invented by Hal O. Anger, and sometimes called an Anger gamma camera, as well as single
photon emission tomography SPECT. Imaging may also be referred to as radionuclide
imaging or nuclear scintigraphy. Other diagnostic tests use probes to acquire
measurements from parts of the body, or counters for the measurement of samples taken
from the patient.

In therapeutic use, radionuclides may be administered to treat disease, or provide palliative
pain relief. To a large extent therapeutic nuclear medicine is an emerging field, although a

few isotopes, such as iodine-131 have long been used therapeutically. 1 . Use of radiation
from radioisotopes (such as cobalt-60) external to the body has merged with the practice of
radiotherapy (Radiation therapy medicine), where these radionuclides are used by
practioners who also employ other sources of radiation. See radiotherapy for discussion of
the therapeutic use of external radioisotopes. Finally, the use of implanted capsules of
isotopes (brachytherapy) may be handled by nuclear medicine or radiation therapy
medicine.

Nuclear medicinal tests differ from most other imaging modalities in that diagnostic tests
primarily show the physiological function of the system being investigated as opposed to
traditional anatomical imaging such as CT or MRI. In some centers, the nuclear medicine
images can be superimposed, using software or hybrid cameras, on images from modalities
such as CT or MRI to highlight the part of the body in which the radiopharmaceutical is
concentrated. This practice is often referred to as image fusion or co-registration.

Nuclear medicine diagnostic tests are usually provided by a dedicated department within a
hospital and may include facilities for the preparation of radiopharmaceuticals. The specific
name of a department can vary from hospital to hospital, with the most common names
being the nuclear medicine department and the radioisotope department. Nuclear medicine
is a technologically embedded speciality that requires collaboration of not only physicians
(nuclear medicine physicians or radiologists), technologists, and support personnel, but
also medical physicists, engineers, radiochemists, radiopharmacists, radiobiologists, and
instrument manufacturers.

Nuclear medicine

314

Source of radioisotopes

About two thirds of the world's supply of medical isotopes are produced at the Chalk River
Laboratories in Chalk River, Ontario, Canada. The Canadian Nuclear Safety Commission
ordered the NRU reactor to be shut down on November 18, 2007 for regularly scheduled
maintenance and an upgrade of the safety systems to modern standards. The upgrade took
longer than expected and in December 2007 a critical shortage of medical isotopes
occurred. The Canadian government unanimously passed emergency legislation, allowing
the reactor to re-start on 16 December 2007, and production of medical isotopes to
continue.

The Chalk River reactor is used to irradiate materials with neutrons which are produced in
great quantity during the fission of U-235. These neutrons change the nucleus of the
irradiated material by adding a neutron. For example, the second most commonly used
radionuclide is Tc-99m, following the most commonly used radionuclide, F-18 (which is
produced by accelerator bombardment of 0-18 with protons. The 0-18 constitutes about
0.20% of ordinary oxygen (mostly 0-16), from which it is extracted; see FDG).

In a reactor, one of the fission products of uranium is Molybdenum-99 which is extracted
and shipped to radiopharmaceutical houses all over North America. The Mo-99
radioactively beta decays with a half-life of 2.7 days, turning initially into Tc-99m, which is
then extracted (milked) from a "Moly cow" (see technetium-99m generator). The Tc-99m
then further decays, while inside a patient, releasing a gamma photon which is detected by
the gamma camera. It decays to its ground state of Tc-99, which is relatively
non-radioactive compared to Tc-99m.

Diagnostic testing

Diagnostic tests in nuclear medicine exploit the way that the body handles substances
differently when there is disease or pathology present. The radionuclide introduced into the
body is often chemically bound to a complex that acts characteristically within the body;
this is commonly known as a tracer. In the presence of disease, a tracer will often be
distributed around the body and/or processed differently. For example, the ligand
methylene-diphosphonate (MDP) can be preferentially taken up by bone. By chemically
attaching technetium-99m to MDP, radioactivity can be transported and attached to bone
via the hydroxy apatite for imaging. Any increased physiological function, such as due to a
fracture in the bone, will usually mean increased concentration of the tracer. This often
results in the appearance of a 'hot-spot' which is a focal increase in radio-accumulation, or
a general increase in radio-accumulation throughout the physiological system. Some
disease processes result in the exclusion of a tracer, resulting in the appearance of a
'cold-spot'. Many tracer complexes have been developed in order to image or treat many
different organs, glands, and physiological processes. The types of tests can be split into
two broad groups: zn-vzvo and in-vitro:

Nuclear medicine

315

Types of diagnostic studies

Common isotopes used in nuclear medicine

isotope

symbol

1/2

decay

photons

Imaging:

fluorine- 18

18 F

110 m

p +

511 (193%)

0.664 (97%o)

gallium- 6 7

67 Ga

3.26 d

93 (39%>),
185 (21%>),
300 (17%)

krypton-81m

81m Kr

13.1 s

190 (68%o)

rubidium-82

82 Rb

1.27m

P +

511 (191%o)

3.379 (95%)

technetium-99m

99m T

6.01 h

140 (89%o)

—

indium-Ill

m In

2.80 d

171 (90%),
245 (94%)

iodine-123

123x

13.3 h

159 (83%o)

—

xenon- 133

133 Xe

5.24 d

81 (31%o)

0.364 (99%)

thallium-201

201 T ,

3.04 d

69-83* (94%),
167 (10%)

Therapy:

yttrium-90

90y

2.67 d

2.280 (100%)

iodine-131

131t

8.02 d

364 (81%))

0.807 (100%)

Z = atomic number, the number of protons; T = half-life; decay = mode of decay
photons = principle photon energies in kilo-electron volts, keV, (abundance/decay)
p = beta maximum energy in mega-electron volts, MeV, (abundance/decay)
p + = p + decay; p" = p" decay; IT = isomeric transition; ec = electron capture
* X-rays from progeny, mercury, Hg

A typical nuclear medicine study involves administration of a radionuclide into the body by
intravenous injection in liquid or aggregate form, ingestion while combined with food,
inhalation as a gas or aerosol, or rarely, injection of a radionuclide that has undergone
micro-encapsulation. Some studies require the labeling of a patient's own blood cells with a
radionuclide (leukocyte scintigraphy and red blood cell scintigraphy). Most diagnostic
radionuclides emit gamma rays, while the cell-damaging properties of beta particles are
used in therapeutic applications. Refined radionuclides for use in nuclear medicine are
derived from fission or fusion processes in nuclear reactors, which produce radioisotopes
with longer half-lives, or cyclotrons, which produce radioisotopes with shorter half-lives, or
take advantage of natural decay processes in dedicated generators, i.e.
molybdenum/technetium or strontium/rubidium.

The most commonly used intravenous radionuclides are:

• Technetium-99m (technetium-99m)

• Iodine-123 and 131

• Thallium-201

• Gallium-67

Nuclear medicine

316

• Fluorine-18 Fluorodeoxyglucose

• Indium-Ill Labeled Leukocytes

The most commonly used gaseous/aerosol radionuclides are:

• Xenon-133

• Krypton-81m

• Technetium-99m Technegas

• Technetium-99m DTPA

Analysis

The end result of the nuclear medicine imaging process is a "dataset" comprising one or
more images. In multi-image datasets the array of images may represent a time sequence
(ie. cine or movie) often called a "dynamic" dataset, a cardiac gated time sequence, or a
spatial sequence where the gamma-camera is moved relative to the patient. SPECT (single
photon emission computed tomography) is the process by which images acquired from a
rotating gamma-camera are reconstructed to produce an image of a "slice" through the
patient at a particular position. A collection of parallel slices form a slice-stack, a
three-dimensional representation of the distribution of radionuclide in the patient.

The nuclear medicine computer may require millions of lines of source code to provide
quantitative analysis packages for each of the specific imaging techniques available in
nuclear medicine.

Time sequences can be further analysed using kinetic models such as multi-compartment
models or a Patlak plot.

Radiation dose

A patient undergoing a nuclear medicine procedure will receive a radiation dose. Under
present international guidelines it is assumed that any radiation dose, however small,
presents a risk. The radiation doses delivered to a patient in a nuclear medicine
investigation present a very small risk of inducing cancer. In this respect it is similar to the
risk from X-ray investigations except that the dose is delivered internally rather than from
an external source such as an X-ray machine.

The radiation dose from a nuclear medicine investigation is expressed as an effective dose
with units of sieverts (usually given in millisieverts, mSv). The effective dose resulting from
an investigation is influenced by the amount of radioactivity administered in
megabecquerels (MBq), the physical properties of the radiopharmaceutical used, its
distribution in the body and its rate of clearance from the body.

Effective doses can range from 6 ]xSv (0.006 mSv) for a 3 MBq chromium-51 EDTA
measurement of glomerular filtration rate to 37 mSv for a 150 MBq thallium-201
non-specific tumour imaging procedure. The common bone scan with 600 MBq of
technetium-99m-MDP has an effective dose of 3 mSv (1).

Formerly, units of measurement were the curie (Ci), being 3.7E10 Bq, and also 1.0 grams of
Radium (Ra-226); the rad (radiation absorbed dose), now replaced by the gray; and the rem
(Rontgen equivalent man), now replaced with the sievert. The rad and rem are essentially
equivalent for almost all nuclear medicine procedures, and only alpha radiation will
produce a higher Rem or Sv value, due to its much higher Relative Biological Effectiveness
(RBE). Alpha emitters are nowadays rarely used in nuclear medicine, but were used

Nuclear medicine

317

extensively before the advent of nuclear reactor and accelerator produced radioisotopes.
The concepts involved in radiation exposure to humans is covered by the field of Health
Physics.

Notes

[1] http://www.radiomedix.com/RD_AboutTNM.htm
[2] http://jcsmr.anu.edu.au/technegas/home.html

Further reading

• Patient's guide to nuclear medicine

• Mas JC: A Patient's Guide to Nuclear Medicine Procedures: English-Spanish. Society of
Nuclear Medicine, 2008. ISBN 978-0972647892

• Physician's guides to nuclear medicine

• Taylor A, Schuster DM, Naomi Alazraki N: A Clinicians' Guide to Nuclear Medicine,
2nd edition. Society of Nuclear Medicine, 2000. ISBN 978-0932004727

• Mark J. Shumate MJ, Kooby DA, Alazraki NP: A Clinician's Guide to Nuclear Oncology:
Practical Molecular Imaging and Radionuclide Therapies. Society of Nuclear Medicine,
January 2007. ISBN 978-0972647885

• Textbook of nuclear medicine

• Ell P, Gambhir S: Nuclear Medicine in Clinical Diagnosis and Treatment. Churchill
Livingstone, 2004. (1950 pages) ISBN 978-0443073120

• Wikibook

• physics of nuclear medicine (http://en.wikibooks.org/wiki/
Basic_Physics_of_Nuclear_Medicine|Basic)

External links

• International Atomic Energy Agency (IAEA), Division of Human Health, Nuclear Medicine
(http://www-naweb.iaea.org/nahu/nm/default.asp)

• RADAR Medical Procedure Radiation Dose Calculator and Consent Language Generator
(http://www.doseinfo-radar.com/RADARDoseRiskCalc.html)

• Society of Nuclear Medicine (http://www.snm.org/)

• Brochure: What is Nuclear Medicine? (http://interactive.snm.org/docs/
whatisnucmed.pdf)

• Resource center: information about nuclear medicine (http://interactive.snm.org/
index.cfm?PageID=6309&RPID = 1089)

Radionuclide

318

Radionuclide

A radionuclide is an atom with an unstable nucleus, which is a nucleus characterized by
excess energy which is available to be imparted either to a newly-created radiation particle
within the nucleus, or else to an atomic electron (see internal conversion) . The
radionuclide, in this process, undergoes radioactive decay, and emits a gamma ray(s)
and/or subatomic particles. These particles constitute ionizing radiation. Radionuclides may
occur naturally, but can also be artificially produced.

Radionuclides are often referred to by chemists and physicists as radioactive isotopes or
radioisotopes, and play an important part in the technologies that provide us with food,
water and good health. However, they can also constitute real or perceived dangers.

Origin

Naturally occurring radionuclides fall into three categories: primordial radionuclides,
secondary radionuclides and cosmogenic radionuclides. Primordial radionuclides originate
mainly from the interiors of stars and, like uranium and thorium, are still present because
their half-lives are so long that they have not yet completely decayed. Secondary
radionuclides are radiogenic isotopes derived from the decay of primordial radionuclides.
They have shorter half-lives than primordial radionuclides. Cosmogenic isotopes, such as
carbon-14, are present because they are continually being formed in the atmosphere due to
cosmic rays.

Artificially produced radionuclides can be produced by nuclear reactors, particle
accelerators or by radionuclide generators:

• Radioisotopes produced with nuclear reactors exploit the high flux of neutrons present.
The neutrons activate elements placed within the reactor. A typical product from a
nuclear reactor is thallium-201 and iridium-192. The elements that have a large
propensity to take up the neutrons in the reactor have a high Barnes Number.

• Particle accelerators such as cyclotrons accelerate particles to bombard a target to
produce radionuclides. Cyclotrons accelerate protons at a target to produce positron
emitting radioisotopes e.g. fluorine-18.

• Radionuclide generators contain a parent isotope that decays to produce a radioisotope.
The parent is usually produced in a nuclear reactor. A typical example is the
technetium-99m generator used in nuclear medicine. The parent produced in the reactor
is molybdenum-99.

Trace radionuclides are those that occur in tiny amounts in nature either due to inherent
rarity, or to half-lives that are significantly shorter than the age of the Earth. Synthetic
isotopes are inherently not naturally occurring on Earth, but can be created by nuclear
reactions.

Uses

Radionuclides are used in two major ways: for their chemical properties and as sources of
radiation. Radionuclides of familiar elements such as carbon can serve as tracers because
they are chemically very similar to the non-radioactive nuclides, so most chemical,
biological, and ecological processes treat them in a near identical way. One can then
examine the result with a radiation detector, such as a geiger counter, to determine where

Radionuclide

319

the provided atoms ended up. For example, one might culture plants in an environment in
which the carbon dioxide contained radioactive carbon; then the parts of the plant that had
laid down atmospheric carbon would be radioactive.

In nuclear medicine, radioisotopes are used for diagnosis, treatment, and research.
Radioactive chemical tracers emitting gamma rays or positrons can provide diagnostic
information about a person's internal anatomy and the functioning of specific organs. This
is used in some forms of tomography: single photon emission computed tomography and
positron emission tomography scanning.

Radioisotopes are also a promising method of treatment in hemopoietic forms of tumors,
while the success for treatment of solid tumors has been limited so far. More powerful
gamma sources sterilise syringes and other medical equipment. About one in two people in
Western countries are likely to experience the benefits of nuclear medicine in their lifetime.

In biochemistry and genetics, radionuclides label molecules and allow tracing chemical and
physiological processes occurring in living organisms, such as DNA replication or amino
acid transport.

In food preservation, radiation is used to stop the sprouting of root crops after harvesting,
to kill parasites and pests, and to control the ripening of stored fruit and vegetables.

In agriculture and animal husbandry, radionuclides also play an important role. They
produce high intake of crops, disease and weather resistant varieties of crops, to study how
fertilisers and insecticides work, and to improve the production and health of domestic
animals.

Industrially, and in mining, radionuclides examine welds, to detect leaks, to study the rate
of wear, erosion and corrosion of metals, and for on-stream analysis of a wide range of
minerals and fuels.

Most household smoke detectors contain the radionuclide americium formed in nuclear
reactors, saving many lives.

Radionuclides trace and analyze pollutants, to study the movement of surface water, and to
measure water runoffs from rain and snow, as well as the flow rates of streams and rivers.
Natural radionuclides are used in geology, archaeology, and paleontology to measure ages
of rocks, minerals, and fossil materials.

Dangers

If radionuclides are released into the environment, through accident, poor disposal, or
other means, they can potentially cause harmful effects of radioactive contamination. They
can also cause damage if they are excessively used during treatment or in other ways
applied to living beings. This is called radiation poisoning. Radionuclides can also cause
malfunction of some electrical devices.

Radionuclide

320

See also

• Hyperaccumulators table - 3

• Radioactivity in biology

• Radiometric dating

• Radionuclide cisternogram

References

• Carlsson J et al.: "Tumour therapy with radionuclides: assessment of progress and
problems". Radiotherapy and Oncology, Volume 66, Issue 2, February 2003, Pages
107-117. PMID 12648782. Available online as full text.

• Radioisotopes in Industry L , World Nuclear Association.

External links

T21

• EPA - Radionuclides - EPA's Radiation Protection Program: Information.

• Interactive Chart of Nuclides L J - A chart of all nuclides

References

[1] http
[2] http
[3] http

//world-nuclear, org/info/inf 5 6. html

//www. epa.gov/rpdwebOO/radionuclides/index. html

//www. nndc.bnl.gov/chart/

321

Advanced Experimental
Techniques and Methods

Positron emission tomography

(PET) is a nuclear medicine
imaging technique which produces
a three-dimensional image or
picture of functional processes in
the body. The system detects pairs
of gamma rays emitted indirectly
by a positron-emitting radionuclide
(tracer), which is introduced into
the body on a biologically active

molecule.

Images

tracer

concentration in 3-dimensional
space within the body are then

reconstructed

computer

analysis. In modern scanners, this

reconstruction

often

accomplished with the aid of a CT X-ray scan performed on the patient during the same
session, in the same machine.

If the biologically active molecule chosen for PET is FDG, an analogue of glucose, the
concentrations of tracer imaged then give tissue metabolic activity, in terms of regional
glucose uptake. Although use of this tracer results in the most common type of PET scan,
other tracer molecules are used in PET to image the tissue concentration of many other
types of molecules of interest.

Description

Operation

To conduct the scan, a short-lived radioactive tracer
isotope, is injected into the living subject (usually into

chemically

blood circulation) .

The

tracer

incorporated into a biologically active molecule. There
is a waiting period while the active molecule becomes
concentrated in tissues of interest; then the research
subject or patient is placed in the imaging scanner. The

Photo multiplier

Scintillator ^^

Crystals

Detector Black

Schematic view of a detector block and

ring of a PET scanner

Positron emission tomography

322

Coincidence
Processing Unit

Sinogram/
Listmode Data

molecule most commonly used for this purpose is fluorodeoxyglucose (FDG), a sugar, for
which the waiting period is typically an hour. During the scan a record of tissue
concentration is made as the tracer decays.

As the radioisotope undergoes positron emission

decay (also known as positive beta decay), it emits a

positron, an antiparticle of the electron with

opposite charge. After travelling up to a few

millimeters the positron encounters and annihilates

with an electron, producing a pair of annihilation

(gamma) photons moving in opposite directions.

These are detected when they reach a scintillator in

the scanning device, creating a burst of light which

is detected by photomultiplier tubes or silicon

avalanche photodiodes (Si APD). The technique

depends on simultaneous or coincident detection of the pair of photons moving in

approximately opposite direction (it would be exactly opposite in their center of mass

frame, but the scanner has no way to know this, and so has a built-in slight direction-error

tolerance). Photons which do not arrive in temporal "pairs" (i.e. within a timing-window of

few nanoseconds) are ignored.

Annihilation

Image Reconstruction

Schema of a PET acquisition process

Localization of the positron annihilation event

The most significant fraction of electron-positron decays result in two 511 keV gamma
photons being emitted at almost 180 degrees to each other; hence it is possible to localize
their source along a straight line of coincidence (also called formally the line of response
or LOR). In practice the LOR has a finite width as the emitted photons are not exactly 180
degrees apart. If the recovery time of detectors is about 1 picosecond rather than about 10
nanoseconds, it is possible to localize the event to a segment of a cord, whose length is
determined by the detector timing resolution. As the timing resolution improves, the
signal-to-noise ratio (SNR) of the image will improve, requiring fewer events to achieve the
same image quality. This technology is not yet common, but it is available on some new
systems [1].

Image reconstruction using coincidence statistics

More commonly, a technique much like the reconstruction of computed tomography (CT)
and single photon emission computed tomography (SPECT) data is used, although the data
set collected in PET is much poorer than CT, so reconstruction techniques are more difficult
(see Image reconstruction of PET).

Using statistics collected from tens-of-thousands of coincidence events, a set of
simultaneous equations for the total activity of each parcel of tissue along many LORs can
be solved by a number of techniques, and thus a map of radioactivities as a function of
location for parcels or bits of tissue (also called voxels), may be constructed and plotted.
The resulting map shows the tissues in which the molecular probe has become
concentrated, and can be interpreted by a nuclear medicine physician or radiologist in the
context of the patient's diagnosis and treatment plan.

Positron emission tomography

323

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Combination of PET with CT and MRI

PET scans are increasingly read alongside CT or
magnetic resonance imaging (MRI) scans, the
combination ("co-registration") giving both anatomic
and metabolic information (i.e., what the structure
is, and what it is doing biochemically). Because PET
imaging is most useful in combination with
anatomical imaging, such as CT, modern PET
scanners are now available with integrated high-end
multi-detector-row CT scanners. Because the two
scans can be performed in immediate sequence
during the same session, with the patient not
changing position between the two types of scans,
the two sets of images are more-precisely
registered, so that areas of abnormality on the PET
imaging can be more perfectly correlated with
anatomy on the CT images. This is very useful in
showing detailed views of moving organs or
structures with higher anatomical variation, which
is more common outside the brain.

PET-MRI: At the Julich Institute of Neurosciences
and Biophysics, the world largest PET/MRI device
will begin operation in April 2009: a 9.4-tesla
magnetic resonance tomograph (MRT) combined with a positron emission tomograph
(PET). Presently, only the head and brain can be imaged at these high magnetic field
strengths.

Radioisotopes

Radionuclides used in PET scanning are typically isotopes with short half lives such as
carbon-11 (-20 min), nitrogen-13 (-10 min), oxygen-15 (-2 min), and fluorine-18 (-110
min). These radionuclides are incorporated either into compounds normally used by the
body such as glucose (or glucose analogues), water or ammonia, or into molecules that bind
to receptors or other sites of drug action. Such labelled compounds are known as
radiotracers. It is important to recognize that PET technology can be used to trace the
biologic pathway of any compound in living humans (and many other species as well),
provided it can be radiolabeled with a PET isotope. Thus the specific processes that can be
probed with PET are virtually limitless, and radiotracers for new target molecules and
processes are being synthesized all the time; as of this writing there are already dozens in
clinical use and hundreds applied in research. Due to the short half lives of most
radioisotopes, the radiotracers must be produced using a cyclotron and radiochemistry
laboratory that are in close proximity to the PET imaging facility. The half life of fluorine-18
is long enough such that fluorine-18 labeled radiotracers can be manufactured
commercially at an offsite location.

Positron emission tomography

324

Limitations

The minimization of radiation dose to the subject is an attractive feature of the use of
short-lived radionuclides. Besides its established role as a diagnostic technique, PET has an
expanding role as a method to assess the response to therapy, in particular, cancer
therapy, where the risk to the patient from lack of knowledge about disease progress is
much greater than the risk from the test radiation.

Limitations to the widespread use of PET arise from the high costs of cyclotrons needed to
produce the short-lived radionuclides for PET scanning and the need for specially adapted
on-site chemical synthesis apparatus to produce the radiopharmaceuticals. Few hospitals
and universities are capable of maintaining such systems, and most clinical PET is
supported by third-party suppliers of radiotracers which can supply many sites
simultaneously. This limitation restricts clinical PET primarily to the use of tracers labelled
with F-18, which has a half life of 110 minutes and can be transported a reasonable
distance before use, or to rubidium-82, which can be created in a portable generator and is
used for myocardial perfusion studies. Nevertheless, in recent years a few on-site
cyclotrons with integrated shielding and hot labs have begun to accompany PET units to
remote hospitals. The presence of the small on-site cyclotron promises to expand in the
future as the cyclotrons shrink in response to the high cost of isotope transportation to
remote PET machines L

Because the half-life of F-18 is about two hours, the prepared dose of a radiopharmaceutical
bearing this radionuclide will undergo multiple half-lives of decay during the working day.
This necessitates frequent recalibration of the remaining dose (determination of activity per
unit volume) and careful planning with respect to patient scheduling.

Image reconstruction

The raw data collected by a PET scanner are a list of 'coincidence events' representing
near-simultaneous detection of annihilation photons by a pair of detectors. Each
coincidence event represents a line in space connecting the two detectors along which the
positron emission occurred. Modern systems with a high time resolution also use a
technique (called "Time-of-flight") where they more precisely decide the difference in time
between the detection of the two photons and can thus limit the length of the earlier
mentioned line to around 10 cm.

Coincidence events can be grouped into projections images, called sinograms. The
sinograms are sorted by the angle of each view and tilt, the latter in 3D case images. The
sinogram images are analogous to the projections captured by computed tomography (CT)
scanners, and can be reconstructed in a similar way. However, the statistics of the data is
much worse than those obtained through transmission tomography. A normal PET data set
has millions of counts for the whole acquisition, while the CT can reach a few billion counts.
As such, PET data suffer from scatter and random events much more dramatically than CT
data does.

In practice, considerable pre-processing of the data is required - correction for random
coincidences, estimation and subtraction of scattered photons, detector dead-time
correction (after the detection of a photon, the detector must "cool down" again) and
detector-sensitivity correction (for both inherent detector sensitivity and changes in
sensitivity due to angle of incidence).

Positron emission tomography

325

Filtered back projection (FBP) has been frequently used to reconstruct images from the
projections. This algorithm has the advantage of being simple while having a low
requirement for computing resources. However, shot noise in the raw data is prominent in
the reconstructed images and areas of high tracer uptake tend to form streaks across the
image.

Iterative expectation-maximization algorithms are now the preferred method of
reconstruction. The advantage is a better noise profile and resistance to the streak artifacts
common with FBP, but the disadvantage is higher computer resource requirements.

Attenuation correction: As different LORs must traverse different thicknesses of tissue,
the photons are attenuated differentially. The result is that structures deep in the body are
reconstructed as having falsely low tracer uptake. Contemporary scanners can estimate
attenuation using integrated x-ray CT equipment, however earlier equipment offered a
crude form of CT using a gamma ray (positron emitting) source and the PET detectors.

While attenuation corrected images are generally more faithful representations, the
correction process is itself susceptible to significant artifacts. As a result, both corrected
and uncorrected images are always reconstructed and read together.

2D/3D reconstruction: Early PET scanners had only a single ring of detectors, hence the
acquisition of data and subsequent reconstruction was restricted to a single transverse
plane. More modern scanners now include multiple rings, essentially forming a cylinder of
detectors.

There are two approaches to reconstructing data from such a scanner: 1) treat each ring as
a separate entity, so that only coincidences within a ring are detected, the image from each
ring can then be reconstructed individually (2D reconstruction), or 2) allow coincidences to
be detected between rings as well as within rings, then reconstruct the entire volume
together (3D).

3D techniques have better sensitivity (because more coincidences are detected and used)
and therefore less noise, but are more sensitive to the effects of scatter and random
coincidences, as well as requiring correspondingly greater computer resources. The advent
of sub-nanosecond timing resolution detectors affords better random coincidence rejection,
thus favoring 3D image reconstruction.

History

The concept of emission and transmission tomography was introduced by David Kuhl and
Roy Edwards in the late 1950s. Their work later led to the design and construction of
several tomographic instruments at the University of Pennsylvania. Tomographic imaging
techniques were further developed by Michel Ter-Pogossian, Michael E. Phelps and others
at the Washington University School of Medicine.

Work by Gordon Brownell, Charles Burnham and their associates at the Massachusetts
General Hospital beginning in the 1950s contributed significantly to the development of
PET technology and included the first demonstration of annihilation radiation for medical
imaging^ J . Their innovations, including the use of light pipes, and volumetric analysis have
been important in the deployment of PET imaging.

In the 1970s, Tatsuo Ido at the Brookhaven National Laboratory was the first to describe
the synthesis of 18F-FDG, the most commonly used PET scanning isotope carrier. The
compound was first administered to two normal human volunteers by Abass Alavi in August

Positron emission tomography

326

1976 at the University of Pennsylvania. Brain images obtained with an ordinary (non-PET)
nuclear scanner demonstrated the concentration of FDG in that organ. Later, the substance
was used in dedicated positron tomographic scanners, to yield the modern procedure.

Applications

PET is both a medical and research tool. It is used
heavily in clinical oncology (medical imaging of tumors
and the search for metastases), and for clinical
diagnosis of certain diffuse brain diseases such as those
causing various types of dementias. PET is also an
important research tool to map normal human brain
and heart function.

PET is also used in pre-clinical studies using animals,
where it allows repeated investigations into the same
subjects. This is particularly valuable in cancer
research, as it results in an increase in the statistical
quality of the data (subjects can act as their own
control) and substantially reduces the numbers of
animals required for a given study.

Alternative methods of scanning include x-ray
computed tomography (CT), magnetic resonance
imaging (MRI) and functional magnetic resonance
imaging (fMRI), ultrasound and single photon emission
computed tomography (SPECT).

While some imaging scans such as CT and MRI isolate

organic anatomic changes in the body, PET and SPECT

are capable of detecting areas of molecular biology

detail (even prior to anatomic change). PET scanning

does this using radiolabeled molecular probes that have different rates of uptake

depending on the type and function of tissue involved. Changing of regional blood flow in

various anatomic structures (as a measure of the injected positron emitter) can be

visualized and relatively quantified with a PET scan.

PET imaging is best performed using a dedicated PET scanner. However, it is possible to
acquire PET images using a conventional dual-head gamma camera fitted with a
coincidence detector. The quality of gamma-camera PET is considerably lower, and
acquisition is slower. However, for institutions with low demand for PET, this may allow
on-site imaging, instead of referring patients to another center, or relying on a visit by a
mobile scanner.

PET is a valuable technique for some diseases and disorders, because it is possible to target
the radio-chemicals used for particular bodily functions.

1. Oncology: PET scanning with the tracer fluorine-18 (F-18) fluorodeoxyglucose (FDG),
called FDG-PET, is widely used in clinical oncology. This tracer is a glucose analog that is
taken up by glucose-using cells and phosphorylated by hexokinase (whose mitochondrial
form is greatly elevated in rapidly-growing malignant tumours). A typical dose of FDG
used in an oncological scan is 200-400 MBq for an adult human. Because the oxygen

Maximum intensity projection (MIP) of

a F-18 FDG wholebody PET

acquisition, showing abnormal focal

uptake in the liver. Normal isotope

levels are seen in the brain, renal

collection systems, and bladder. Image

is rotating clockwise.

Positron emission tomography

327

atom which is replaced by F-18 to generate FDG is required for the next step in glucose
metabolism in all cells, no further reactions occur in FDG. Furthermore, most tissues
(with the notable exception of liver and kidneys) cannot remove the phosphate added by
hexokinase. This means that FDG is trapped in any cell which takes it up, until it decays,
since phosphorylated sugars, due to their ionic charge, cannot exit from the cell. This
results in intense radiolabeling of tissues with high glucose uptake, such as the brain, the
liver, and most cancers. As a result, FDG-PET can be used for diagnosis, staging, and
monitoring treatment of cancers, particularly in Hodgkin's disease, non Hodgkin's
lymphoma, and lung cancer. Many other types of solid tumors will be found to be very
highly labeled on a case-by-case basis- a fact which becomes especially useful in
searching for tumor metastasis, or for recurrence after a known highly-active primary
tumor is removed. Because individual PET scans are more expensive than "conventional"
imaging with computed tomography (CT) and magnetic resonance imaging (MRI),
expansion of FDG-PET in cost-constrained health services will depend on proper health
technology assessment; this problem is a difficult one because structural and functional
imaging often cannot be directly compared, as they provide different information.
Oncology scans using FDG make up over 90% of all PET scans in current practice.
Neurology: PET neuroimaging is based on an
assumption that areas of high radioactivity are
associated with brain activity. What is actually
measured indirectly is the flow of blood to
different parts of the brain, which is generally
believed to be correlated, and has been measured
using the tracer oxygen-15. However, because of
its 2-minute half-life 0-15 must be piped directly
from a medical cyclotron for such uses, and this is
difficult. In practice, since the brain is normally a
rapid user of glucose, and since brain pathologies
such as Alzheimer's disease greatly decrease
brain metabolism of both glucose and oxygen in
tandem, standard FDG-PET of the brain, which
measures regional glucose use, may also be

successfully used to differentiate Alzheimer's disease from other dementing processes,
and also to make early diagnosis of Alzheimer's disease. The advantage of FDG-PET for
these uses is its much wider availability. PET imaging with FDG can also be used for
localization of seizure focus: A seizure focus will appear as hypometabolic during an
interictal scan. Several radiotracers (i.e. radioligands) have been developed for PET that
are ligands for specific neuroreceptor subtypes such as [ C] raclopride and [ F]
fallypride for dopamine D2/D3 receptors, [ 1:L C]McN 5652 and [ n C]DASB for serotonin
transporters, or enzyme substrates (e.g. 6-FDOPA for the AADC enzyme). These agents
permit the visualization of neuroreceptor pools in the context of a plurality of
neuropsychiatric and neurologic illnesses. A novel probe developed at the University of
Pittsburgh termed PIB (Pittsburgh Compound-B) permits the visualization of amyloid
plaques in the brains of Alzheimer's patients. This technology could assist clinicians in
making a positive clinical diagnosis of AD pre-mortem and aid in the development of
novel anti-amyloid therapies.

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328

3. Cardiology, atherosclerosis and vascular disease study: In clinical cardiology, FDG-PET
can identify so-called "hibernating myocardium", but its cost-effectiveness in this role
versus SPECT is unclear. Recently, a role has been suggested for FDG-PET imaging of
atherosclerosis to detect patients at risk of stroke [8].

4. Neuropsychology / Cognitive neuroscience: To examine links between specific
psychological processes or disorders and brain activity.

5. Psychiatry: Numerous compounds that bind selectively to neuroreceptors of interest in
biological psychiatry have been radiolabeled with C-ll or F-18. Radioligands that bind to
dopamine receptors (D1,D2, reuptake transporter), serotonin receptors (5HT1A, 5HT2A,
reuptake transporter) opioid receptors (mu) and other sites have been used successfully
in studies with human subjects. Studies have been performed examining the state of
these receptors in patients compared to healthy controls in schizophrenia, substance
abuse, mood disorders and other psychiatric conditions.

6. Pharmacology: In pre-clinical trials, it is possible to radiolabel a new drug and inject it
into animals. Such scans are referred to as biodistribution studies. The uptake of the
drug, the tissues in which it concentrates, and its eventual elimination, can be monitored
far more quickly and cost effectively than the older technique of killing and dissecting the
animals to discover the same information. Much more commonly, however, drug
occupancy at a purported site of action can be inferred indirectly by competition studies
between unlabeled drug and radiolabeled compounds known apriori to bind with
specificity to the site. A single radioligand can be used this way to test many potential
drug candidates for the same target. A related technique involves scanning with
radioligands that compete with an endogenous (naturally occurring) substance at a given
receptor to demonstrate that a drug causes the release of the natural substance.

7. PET technology for small animal imaging: A miniature PET tomograph has been
constructed that is small enough for a fully conscious and mobile rat to wear on its head
while walking around [9]. This RatCAP (Rat Conscious Animal PET) allows animals to be
scanned without the confounding effects of anesthesia. PET scanners designed
specifically for imaging rodents microPET or other scanners for small primates are
marketed for academic and pharmaceutical research.

Safety

PET scanning is non-invasive, but it does involve exposure to ionizing radiation. The total
dose of radiation is small, however, usually around 7 mSv. This can be compared to 2.2 mSv
average annual background radiation in the UK, 0.02 mSv for a chest x-ray, up to 8 mSv for
a CT scan of the chest, according to the UK National Radiological Protection Board. A
policy change suggested by the IFALPA member associations in year 1999 mentioned that
an aircrew member is likely to receive a radiation dose of 4-9 mSv per year. 1 J

Positron emission tomography

329

See also

• Diffuse optical imaging

• Hot cell (Equipment used to produce the radiopharmaceuticals used in PET)

• Molecular Imaging

References

[I] http://www.uphs.upenn.edu/news/News_Releases/jun06/PETCTITC.htm

[2] http://www.fz-juelich.de/portal/index.php?index=1172|"A Close Look Into the Brain". Julich Research Centre.

29 April 2009. http://www.fz-juelich.de/portal/index.php?index=1172. Retrieved on 2009-04-29.
[3] Young H, Baum R, Cremerius U, et al. (1999). "Measurement of clinical and subclinical tumour response using

[18F]-fluorodeoxyglucose and positron emission tomography: review and 1999 EORTC recommendations.".

European Journal of Cancer 35 (13): 1773-1782. doi: 10.1016/S0959-8049(99)00229-4 (http://dx.doi.org/10.

1016/S0959-8049(99)00229-4).
[4] Technology | July 2003: Trends in MRI | Medical Imaging (http://www.medicalimagingmag.com/issues/

articles/2 003-0 70 5 . asp)
[5] Ter-Pogossian, M.M.; M.E. Phelps, E.J. Hoffman (1975).

"http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4251398| A positron-emission transaxial

tomograph for nuclear imaging (PET)". Radiology 114 (1): 89-98. http://www.osti.gov/energycitations/

product.biblio.jsp?osti_id=4251398.
[6] Phelps, M.E.; E.J. Hoffman, N.A. Mullani, M.M. Ter-Pogossian (01 Mar 1975).

"http://jnm.snmjournals.Org/cgi/content/abstract/l 6/3/210| Application of annihilation coincidence detection to

transaxial reconstruction tomography". Journal of Nuclear Medicine 16 (3): 210-224. PMID 1113170. http://

jnm.snmj ournals.org/cgi/content/ abstract/ 1 6/3/2 10.
[7] Sweet, W.H.; G.L. Brownell (1953). "Localization of brain tumors with positron emitters". Nucleonics 11:

40-45.
[8] http://circ.ahajournals.org/cgi/content/abstract/105/23/2708
[9] http ://www. chemistry. bnl. gov/ratcap/gallery.html
[10] Patient Dose information (http://www.hpa. org. uk/web/HPAweb&HPAwebStandard/HPAweb_C/

1195733826941), Health Protection Agency, 4 September 2008.

[II] Air crew radiation exposure— An overview (http://www.ans.org/pubs/magazines/nn/docs/2000-l-3.pdf),
Susan Bailey, Nuclear News (a publication of American Nuclear Society), January 2000.

Further reading

• Bustamante E. and Pedersen P.L. (1977). "High aerobic glycolysis of rat hepatoma cells
in culture: role of mitochondrial hexokinase.". Proceedings of the National Academy of
Sciences USA 74 (9): 3735-3739. doi: 10.1073/pnas.74.9.3735 (http://dx.doi.org/10.
1073/pnas. 74.9. 3735).

• Klunk WE, Engler H, Nordberg A, Wang Y, Blomqvist G, Holt DP, Bergstrom M,
Savitcheva I, Huang GF, Estrada S, Ausen B, Debnath ML, Barletta J, Price JC, Sandell J,
Lopresti BJ, Wall A, Koivisto P, Antoni G, Mathis CA, and Langstrom B. (2004). "Imaging
brain amyloid in Alzheimer's disease with Pittsburgh Compound-B.". Annals of Neurology
55 (3): 306-319. doi: 10.1002/ana.20009 (http://dx.doi.org/10.1002/ana.20009).

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External links

• PET Images (http://rad.usuhs.edu/medpix/master.php3?mode=image_finder&
action=search&srchstr=&srch_type=all&labels=&details=2&no_filter=2&
plane_id=&capt_id=-4&filter_m=modality&filter_o=&acr_pre=&filter_p=&
acr_post=#top) Search MedPix(r)

• Seeing is believing: In vivo functional real-time imaging of transplanted islets using
positron emission tomography (PET)(a protocol) (http://www.natureprotocols.com/
2006/1 2/2 l/seeing_is_believing_in_vivo_fu_l.php)

• The nuclear medicine and molecular medicine podcast (http://nuccast.com) - Podcast

• Positron emmission particle tracking (http://www.np.ph.bham.ac.uk/pic/pept.htm)
(PEPT) - engineering analysis tool based on PET that is able to track single particles in
3D within mixing systems or fluidised beds. Developed at the University of Birmingham,
UK.

• CMS coverage of PET scans (http://www.hematologytimes.com/ht/p_article.
do?id=948)

2D-FT NMRI and Spectroscopy

2D-FT Nuclear magnetic resonance imaging (2D-FT NMRI), or Two-dimensional
Fourier transform nuclear magnetic resonance imaging (NMRI), is primarily a
non— invasive imaging technique most commonly used in biomedical research and medical
radiology/nuclear medicine/MRI to visualize structures and functions of the living systems
and single cells. For example it can provides fairly detailed images of a human body in any
selected cross-sectional plane, such as longitudinal, transversal, sagital, etc. The basic

NMR phenomenon or physical principle is essentially the same in N(MRI), nuclear
magnetic resonance/FT (NMR) spectroscopy, topical NMR, or even in Electron Spin
Resonance /EPR; however, the details are significantly different at present for EPR, as only
in the early days of NMR the static magnetic field was scanned for obtaining spectra, as it
is still the case in many EPR or ESR spectrometers. NMRI, on the other hand, often utilizes
a linear magnetic field gradient to obtain an image that combines the visualization of
molecular structure and dynamics. It is this dynamic aspect of NMRI, as well as its highest
sensitivity for the H nucleus that distinguishes it very dramatically from X-ray CAT
scanning that 'misses' hydrogens because of their very low X-ray scattering factor.

Thus, NMRI provides much greater contrast especially for the different soft tissues of the
body than computed tomography (CT) as its most sensitive option observes the nuclear spin
distribution and dynamics of highly mobile molecules that contain the naturally abundant,
stable hydrogen isotope H as in plasma water molecules, blood, disolved metabolites and
fats. This approach makes it most useful in cardiovascular, oncological (cancer),
neurological (brain), musculoskeletal, and cartilage imaging. Unlike CT, it uses no ionizing
radiation, and also unlike nuclear imaging it does not employ any radioactive isotopes.
Some of the first MRI images reported were published in 1973 c ^ and the first study
performed on a human took place on July 3, 1977. L J Earlier papers were also published by
Sir Peter Mansfield [4] in UK (Nobel Laureate in 2003), and R. Damadian in the USA [5] ,
(together with an approved patent for 'fonar', or magnetic imaging). The detailed physical
theory of NMRI was published by Peter Mansfield in 1973 c ^ . Unpublished 'high-resolution'
(50 micron resolution) images of other living systems, such as hydrated wheat grains, were

2D-FT NMRI and Spectroscopy

331

also obtained and communicated in UK in 1977-1979, and were subsequently confirmed by
articles published in Nature by Peter Callaghan.

NMR Principle

Certain nuclei such as H
nuclei, or "fermions 1 have
spin-1/2, because there are
two spin states, referred to as
"up" and "down" states. The
nuclear magnetic resonance

absorption
occurs

when

phenomenon
samples

containing such nuclear spins
are placed in a static magnetic
field and a very short

radiofrequency

pulse

applied with a center, or
carrier, frequency matching
that of the transition between
the up and down states of the

1 T71

spin-1/2 H nuclei that were polarized by the static magnetic field. Very low field
schemes have also been recently reported. - 1

Advanced 4.7 T clinical diagnostics and biomedical research NMR

Imaging instrument.

Chemical Shifts

NMR is a very useful family of techniques for chemical and biochemical research because
of the chemical shift; this effect consists in a frequency shift of the nuclear magnetic
resonance for specific chemical groups or atoms as a result of the partial shielding of the
corresponding nuclei from the applied, static external magnetic field by the electron
orbitals (or molecular orbitals) surrounding such nuclei present in the chemical groups.
Thus, the higher the electron density surrounding a specific nucleus the larger the chemical
shift will be. The resulting magnetic field at the nucleus is thus lower than the applied
external magnetic field and the resonance frequencies observed as a result of such
shielding are lower than the value that would be observed in the absence of any electronic
orbital shielding. Furthermore, in order to obtain a chemical shift value independent of the
strength of the applied magnetic field and allow for the direct comparison of spectra
obtained at different magnetic field values, the chemical shift is defined by the ratio of the
strength of the local magnetic field value at the observed (electron orbital-shielded) nucleus
by the external magnetic field strength, H, / H . The first NMR observations of the

1 Q

chemical shift, with the correct physical chemistry interpretation, were reported for F
containing compounds in the early 1950s by Herbert S. Gutowsky and Charles P. Slichter
from the University of Illinois at Urbana (USA).

A related effect in metals is called the Knight shift, which is due only to the conduction
electrons. Such conduction electrons present in metals induce an "additional" local field at
the nuclear site, due to the spin re-orientation of the conduction electrons in the presence
of the applied (constant), external magnetic field. This is only broadly "similar 1 to the

2D-FT NMRI and Spectroscopy

332

chemical shift in either solutions or diamagnetic solids.

NMR Imaging Principles

A number of methods have been devised for combining magnetic field gradients and
radiofrequency pulsed excitation to obtain an image. Two major maethods involve either 2D
-FT or 3D-FT L J reconstruction from projections, somewhat similar to Computed
Tomography, with the exception of the image interpretation that in the former case must
include dynamic and relaxation/contrast enhancement information as well. Other schemes
involve building the NMR image either point-by-point or line-by-line. Some schemes use
instead gradients in the rf field rather than in the static magnetic field. The majority of
NMR images routinely obtained are either by the Two-Dimensional Fourier Transform
(2D-FT) technique (with slice selection), or by the Three-Dimensional Fourier Transform
(3D— FT) techniques that are however much more time consuming at present. 2D-FT NMRI
is sometime called in common parlance a "spin-warp". An NMR image corresponds to a
spectrum consisting of a number of "spatial frequencies' at different locations in the sample
investigated, or in a patient. A two-dimensional Fourier transformation of such a "real"
image may be considered as a representation of such "real waves" by a matrix of spatial
frequencies known as the k-space. We shall see next in some mathematical detail how the
2D-FT computation works to obtain 2D-FT NMR images.

Two-dimensional Fourier transform imaging and
spectroscopy

A two-dimensional Fourier transform (2D-FT) is computed numerically or carried out in two
stages, both involving "standard 1 , one-dimensional Fourier transforms. However, the
second stage Fourier transform is not the inverse Fourier transform (which would result in
the original function that was transformed at the first stage), but a Fourier transform in a
second variable— which is "shifted 1 in value— relative to that involved in the result of the
first Fourier transform. Such 2D-FT analysis is a very powerful method for both NMRI and

ri2i

two-dimensional nuclear magnetic resonance spectroscopy (2D-FT NMRS) that allows
the three-dimensional reconstruction of polymer and biopolymer structures at atomic

MO]

resolution. 1 J for molecular weights (Mw) of dissolved biopolymers in aqueous solutions
(for example) up to about 50,000 Mw. For larger biopolymers or polymers, more complex
methods have been developed to obtain limited structural resolution needed for partial
3D-reconstructions of higher molecular structures, e.g. for up 900,000 Mw or even oriented
microcrystals in aqueous suspensions or single crystals; such methods have also been
reported for in vivo 2D-FT NMR spectroscopic studies of algae, bacteria, yeast and certain
mammalian cells, including human ones. The 2D-FT method is also widely utilized in optical
spectroscopy, such as 2D-FT NIR hyperspectral imaging (2D-FT NIR-HS), or in MRI
imaging for research and clinical, diagnostic applications in Medicine. In the latter case,
2D-FT NIR-HS has recently allowed the identification of single, malignant cancer cells
surrounded by healthy human breast tissue at about 1 micron resolution, well-beyond the
resolution obtainable by 2D-FT NMRI for such systems in the limited time available for such
diagnostic investigations (and also in magnetic fields up to the FDA approved magnetic
field strength H of 4.7 T, as shown in the top image of the state-of-the-art NMRI
instrument). A more precise mathematical definition of the "double 1 (2D) Fourier transform
involved in both 2D NMRI and 2D-FT NMRS is specified next, and a precise example

2D-FT NMRI and Spectroscopy

333

follows this generally accepted definition.

2D-FT Definition

A 2D-FT, or two-dimensional Fourier transform, is a standard Fourier transformation of a
function of two variables, f(x , x ), carried first in the first variable x , followed by the
Fourier transform in the second variable x 2 of the resulting function F(s r x 2 ). Note that in
the case of both 2D-FT NMRI and 2D-FT NMRS the two independent variables in this
definition are in the time domain, whereas the results of the two successive Fourier
transforms have, of course, frequencies as the independent variable in the NMRS, and
ultimately spatial coordinates for both 2D NMRI and 2D-FT NMRS following computer
structural recontructions based on special algorithms that are different from FT or 2D-FT.
Moreover, such structural algorithms are different for 2D NMRI and 2D-FT NMRS: in the
former case they involve macroscopic, or anatomical structure detrmination, whereas in the
latter case of 2D-FT NMRS the atomic structure reconstruction algorithms are based on the
quantum theory of a microphysical (quantum) process such as nuclear Overhauser
enhancement NOE, or specific magnetic dipole-dipole interactions between neighbor
nuclei.

Example 1

A 2D Fourier transformation and phase correction is applied to a set of 2D NMR (FID)
signals: s(t,.,t ) yielding a real 2D-FT NMR "spectrum 1 (collection of ID FT-NMR spectra)
represented by a matrix S whose elements are

S Oi,/A>) = Re / /co5(i/iti)eicp c "^ t2) 5(i l5 t2)dtidf2

where : ^land : ^2 denote the discrete indirect double-quantum and
single-quantum(detection) axes, respectively, in the 2D NMR experiments. Next, the
covariance matrix is calculated in the frequency domain according to the following equation

c (*4, v%) = S T S = J» 1? vQSfa, ^)L with s ^ ^ taking all possible

single-quantum frequency values and with the summation carried out over all discrete,
double quantum frequencies : v \.

Example 2

MCI

Atomic Structure from 2D-FT STEM Images of electron distributions in a

high-temperature cuprate superconductor "paracrystal' reveal both the domains (or
"location') and the local symmetry of the 'pseudo-gap' in the electron-pair correlation band
responsible for the high— temperature superconductivity effect (obtained at Cornell
University). So far there have been three Nobel prizes awarded for 2D-FT NMR/MRI during
1992-2003, and an additional, earlier Nobel prize for 2D-FT of X-ray data ("CAT scans');
recently the advanced possibilities of 2D-FT techniques in Chemistry, Physiology and
Medicine c ^ received very significant recognition. ]

2D-FT NMRI and Spectroscopy

334

Brief explanation of NMRI diagnostic uses in Pathology

As an example, a diseased tissue such as a malign tumor, can be detected by 2D-FT NMRI
because the hydrogen nuclei of molecules in different tissues return to their equilibrium
spin state at different relaxation rates, and also because of the manner in which a malign
tumor spreads and grows rapidly along the blood vessels adjacent to the tumor, also
inducing further vascularization to occur. By changing the pulse delays in the RF pulse
sequence employed, and/or the RF pulse sequence itself, one may obtain a
"relaxation— based contrast', or contrast enhancement between different types of body
tissue, such as normal vs. diseased tissue cells for example. Excluded from such diagnostic
observations by NMRI are all patients with ferromagnetic metal implants, (e.g., cochlear
implants), and all cardiac pacemaker patients who cannot undergo any NMRI scan because
of the very intense magnetic and RF fields employed in NMRI which would strongly
interfere with the correct functioning of such pacemakers. It is, however, conceivable that
future developments may also include along with the NMRI diagnostic treatments with
special techniques involving applied magnetic fields and very high frequency RF. Already,
surgery with special tools is being experimented on in the presence of NMR imaging of
subjects. Thus, NMRI is used to image almost every part of the body, and is especially useful
for diagnosis in neurological conditions, disorders of the muscles and joints, for evaluating
tumors, such as in lung or skin cancers, abnormalities in the heart (especially in children

r I 01

with hereditary disorders), blood vessels, CAD, atherosclerosis and cardiac infarcts J
(courtesy of Dr. Robert R. Edelman)

See also

Nuclear magnetic resonance (NMR)

Edward Mills Purcell

Felix Bloch

Medical imaging

Paul C. Lauterbur

Magnetic resonance microscopy

Peter Mansfield

Computed tomography (CT)

FT-NIRS (NIR)

Magnetic resonance elastography

Solid-state NMR

Knight shift

John Hasbrouck Van Vleck

Chemical shift

Herbert S. Gutowsky
John S. Waugh

Charles Pence Slichter

Protein nuclear magnetic resonance spectroscopy
Kurt Wuthrich

Nuclear Overhauser effect

Fourier transform spectroscopy(FTS)
Jean Jeneer

Richard R. Ernst

Relaxation

Earth's field NMR (EFNMR)

Robinson oscillator

2D-FT NMRI and Spectroscopy

335

Footnotes

[I] Antoine Abragam. 1968. Principles of Nuclear Magnetic Resonance., 895 pp., Cambridge University Press:
Cambridge, UK.

[2] Lauterbur, P.C., Nobel Laureate in 2003 (1973). "Image Formation by Induced Local Interactions: Examples of
Employing Nuclear Magnetic Resonance". Nature 242: 190-1. doi: 10.1038/242190a0 (http://dx.doi.org/10.
1038/242190a0).

[3] Howstuffworks "How MRI Works" (http://www.howstuffworks.com/mri.htm/printable)

[4] Peter Mansfield. 2003. Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI (http://www.
parteqinnovations.com/pdf-doc/fandr-Gazl006.pdf)

[5] Damadian, R. V. "Tumor Detection by Nuclear Magnetic Resonance," Science, 171 (March 19, 1971):
1151-1153 (http://www.sciencemag.org/cgi/content/abstract/171/3976/1151)

[6] NMR 'diffraction' in solids? P. Mansfield et al. 1973 J. Phys. C: Solid State Phys. 6 L422-L426 doi:
10.1088/0022-3719 (http://www.iop.Org/EJ/article/0022-3719/6/22/007/jcv6i22pL422.pdf)

[7] Antoine Abragam. 1968. Principles of Nuclear Magnetic Resonance., 895 pp., Cambridge University Press:
Cambridge, UK.

[8] Raftery D (August 2006).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=l 568902 |MRI without the
magnet". Proc Natl Acad Sci USA. 103 (34): 12657-8. doi: 10. 1073/pnas. 0605625103 (http://dx.doi.org/10.
1073/pnas. 0605625103). PMID 16912110.

[9] Wu Y, Chesler DA, Glimcher MJ, et al (February 1999).

"http://www.pnas.org/cgi/pmidlookup?view=long&pmid=9990066|Multinuclear solid-state three-dimensional

MRI of bone and synthetic calcium phosphates". Proc. Natl. Acad. Sci. U.SA. 96 (4): 1574-8. doi:

10. 1073/pnas. 96.4. 1574 (http://dx.doi.Org/10.1073/pnas.96.4.1574). PMID 9990066. PMC: 15521 (http://

www.pubmedcentral.nih. gov/articlerender.fcgi?tool=pmcentrez&artid= 15521). http://www.pnas.org/cgi/

pmidlookup?view=long&pmid=9990066.

[10] http://www.math.cuhk.edu.hk/course/mat2071a/lecl_08.ppt

[II] *Haacke, E Mark; Brown, Robert F; Thompson, Michael; Venkatesan, Ramesh (1999). Magnetic resonance
imaging: physical principles and sequence design. New York: J. Wiley & Sons. ISBN 0-471-35128-8.

[12] Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT) Spectroscopy. Nobel
Lecture (http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf), on December 9,
1992.

[13] http://en.wikipedia.0rg/wiki/Nuclear_magnetic_res0nance#Nuclear_spin_and_magnets Kurt Wuthrich in
1982-1986 : 2D-FT NMR of solutions

[14] Charles P. Slichter.1996. Principles of Magnetic Resonance. Springer: Berlin and New York, Third Edition.,
651pp. ISBN 0-387-50157-6.

[15] http://www.physorg.com/newsl29395045.html

[16] http://nobelprize.org/nobel_prizes/chemistry/laureates/1991/ernst-lecture.pdf

[17] Protein structure determination in solution by NMR spectroscopy (http://www.ncbi.nlm.nih.gov/entrez/
query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=2266107&query_hl=33&
itool=pubmed_docsum) Kurt Wuthrich. J Biol Chem. 1990 December 25;265(36):22059-62.

[18] http://www.mr-tip.com/servl. php?type=img&img=Cardiac%20Infarct%20Short%20Axis%20Cine%204

References

• Antoine Abragam. 1968. Principles of Nuclear Magnetic Resonance., 895 pp., Cambridge
University Press: Cambridge, UK.

• Charles P. Slichter.1996. Principles of Magnetic Resonance. Springer: Berlin and New
York, Third Edition., 651pp. ISBN 0-387-50157-6.

• Kurt Wuthrich. 1986, NMR of Proteins and Nucleic Acids., J. Wiley and Sons: New York,
Chichester, Brisbane, Toronto, Singapore. ( Nobel Laureate in 2002 for 2D-FT NMR
Studies of Structure and Function of Biological Macromolecules (http://nobelprize.org/
nobel_prizes/chemistry/laureates/2002/wutrich-lecture.pdf)

• Protein structure determination in solution by NMR spectroscopy (http://www.ncbi.
nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt= Abstracts
list_uids=2266107&query_hl=33&itool=pubmed_docsum) Kurt Wuthrich. J Biol Chem.

2D-FT NMRI and Spectroscopy

336

1990 December 25;265(36):22059-62

2D-FT NMRI Instrument image: A JPG color image of a 2D-FT NMRI "monster 1
Instrument (http://upload.wikimedia.Org/wikipedia/en/b/bf/HWB-NMRv900.jpg).

Richard R. Ernst. 1992. Nuclear Magnetic Resonance Fourier Transform (2D-FT)
Spectroscopy. Nobel Lecture (http://nobelprize.org/nobel_prizes/chemistry/laureates/
1991/ernst-lecture.pdf), on December 9, 1992.

Peter Mansfield. 2003. Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI
(http://www.parteqinnovations.com/pdf-doc/fandr-Gazl006.pdf)

D. Benett. 2007. PhD Thesis. Worcester Polytechnic Institute. PDF of 2D-FT Imaging
Applications to NMRI in Medical Research. (http://www.wpi.edu/Pubs/ETD/Available/
etd-081707-080430/unrestricted/ dbennett.pdf) Worcester Polytechnic Institute.
(Includes many 2D-FT NMR images of human brains.)

Paul Lauterbur. 2003. Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI.
(http://nobelprize.org/nobel_prizes/medicine/laureates/2003/)

Jean Jeener. 1971. Two-dimensional Fourier Transform NMR, presented at an Ampere
International Summer School, Basko Polje, unpublished. A verbatim quote follows from
Richard R. Ernst's Nobel Laureate Lecture delivered on December 2, 1992, "A new
approach to measure two-dimensional (2D) spectra." has been proposed by Jean Jeener at
an Ampere Summer School in Basko Polje, Yugoslavia, 1971 (Jean Jeneer,1971)). He
suggested a 2D Fourier transform experiment consisting of two $\pi/2$ pulses with a
variable time $t_l$ between the pulses and the time variable $t_2$ measuring the time
elapsed after the second pulse as shown in Fig. 6 that expands the principles of Fig. 1.
Measuring the response $s(t_l,t_2)$ of the two-pulse sequence and
Fourier-transformation with respect to both time variables produces a two-dimensional
spectrum $S(0_1,0_2)$ of the desired form. This two-pulse experiment by Jean Jeener is
the forefather of a whole class of $2D$ experiments that can also easily be expanded to
multidimensional spectroscopy.

Dudley, Robert, L (1993). "High-Field NMR Instrumentation". Ch. 10 in Physical
Chemistry of Food Processes (New York: Van Nostrand-Reinhold) 2: 421-30. ISBN
0-442-00582-2.

Baianu, I.C.; Kumosinski, Thomas (August 1993). "NMR Principles and Applications to
Structure and Hydration,". Ch.9 in Physical Chemistry of Food Processes (New York: Van
Nostrand-Reinhold) 2: 338-420. ISBN 0-442-00582-2.

Haacke, E Mark; Brown, Robert F; Thompson, Michael; Venkatesan, Ramesh (1999).
Magnetic resonance imaging: physical principles and sequence design. New York: J.
Wiley & Sons. ISBN 0-471-35128-8.

Raftery D (August 2006).

"http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=l 568902 |MRI

without the magnet". Proc Natl Acad Sci USA. 103 (34): 12657-8. doi:

10. 1073/pnas. 0605625103 (http://dx.doi.org/10.1073/pnas.0605625103). PMID

16912110.

Wu Y, Chesler DA, Glimcher MJ, et al. (February 1999).

"http://www.pnas.org/cgi/pmidlookup?view=long&pmid= 9990066 |Multinuclear
solid-state three-dimensional MRI of bone and synthetic calcium phosphates". Proc. Natl.
Acad. Sci. U.SA. 96 (4): 1574-8. doi: 10. 1073/pnas. 96.4. 1574 (http://dx.doi.org/10.

2D-FT NMRI and Spectroscopy

337

1073/pnas.96.4.1574). PMID 9990066. PMC: 15521 (http://www.pubmedcentral.nih
gov/articlerender.fcgi?tool=pmcentrez&artid= 15521). http://www.pnas.org/cgi/
pmidlookup?view=long&pmid= 9990066.

External links

• Cardiac Infarct or "heart attack" Imaged in Real Time by 2D-FT NMRI (http://www.
mr-tip . com/examgif s/cardiac_infarct_short_axis_cine_6 . gif )

• Interactive Flash Animation on MRI (http://www.e-mri.org) - Online Magnetic
Resonance Imaging physics and technique course

• Herbert S. Gutowsky

• Jiri Jonas and Charles P. Slichter: NMR Memoires at NAS about Herbert Sander
Gutowsky; NAS = National Academy of Sciences, USA, (http://books.nap.edu/html/
biomems/hguto wsky . pdf )

• 3D Animation Movie about MRI Exam (http://www.patiencys.com/MRI/)

• International Society for Magnetic Resonance in Medicine (http://www.ismrm.org)

• Danger of objects flying into the scanner (http://www.simplyphysics.com/
flying_obj e cts . html)

Related Wikipedia websites

Medical imaging

Computed tomography

Magnetic resonance microscopy

Fourier transform spectroscopy

FT-NIRS

Chemical imaging

Magnetic resonance elastography

Nuclear magnetic resonance (NMR)

Chemical shift

Relaxation

Robinson oscillator

Earth's field NMR (EFNMR)

Rabi cycle

This article incorporates material by the original author from 2D-FT MR- Imaging and
related Nobel awards (http://planetphysics.org/encyclopedia/2DFTImaging.html) on
PlanetPhysics (http://planetphysics.org/), which is licensed under the GFDL.

NMR spectroscopy

338

NMR spectroscopy

Nuclear

magnetic

resonance

spectroscopy, most commonly known
as NMR spectroscopy, is the name
given to a technique which exploits the
magnetic properties of certain nuclei.
This phenomenon and its origins are
detailed in a separate section on nuclear
magnetic

resonance.

The

most

important applications for the organic
chemist are proton NMR and carbon-13
NMR spectroscopy. In principle, NMR is
applicable to any nucleus possessing
spin.

Many types of information can be
obtained from an NMR spectrum. Much
like using infrared spectroscopy to
identify functional groups, analysis of a
ID NMR spectrum provides information
on the number and type of chemical
entities in a molecule. However, NMR
provides much more information than
IR.

A 900MHz NMR instrument with a 21.2 T magnet at
HWB-NMR, Birmingham, UK, being loaded with a sample

The impact of NMR spectroscopy on the natural sciences has been substantial. It can,
among other things, be used to study mixtures of analytes, to understand dynamic effects
such as change in temperature and reaction mechanisms, and is an invaluable tool in
understanding protein and nucleic acid structure and function. It can be applied to a wide
variety of samples, both in the solution and the solid state.

NMR spectroscopy

339

Basic NMR techniques

When placed in a magnetic field, NMR active nuclei

(such as H or

C) absorb at a frequency

characteristic of the isotope. The resonant
frequency, energy of the absorption and the
intensity of the signal are proportional to the
strength of the magnetic field. For example, in a 21
tesla magnetic field, protons resonate at 900 MHz.
It is common to refer to a 21 T magnet as a 900
MHz magnet, although different nuclei resonate at a
different frequency at this field strength.

In the Earth's magnetic field the same nuclei
resonate at audio frequencies. This effect is used in
Earth's field NMR spectrometers and other
instruments. Because these instruments are
portable and inexpensive, they are often used for
teaching and field work.

Chemical shift

The NMR sample is prepared in a
thin-walled glass tube - an NMR tube

Depending on the local chemical environment, different protons in a molecule resonate at
slightly different frequencies. Since both this frequency shift and the fundamental resonant
frequency are directly proportional to the strength of the magnetic field, the shift is
converted into a field -independent dimensionless value known as the chemical shift. The
chemical shift is reported as a relative measure from some reference resonance frequency.

1 1 ^ 2Q

(For the nuclei H, C, and Si, TMS (tetramethylsilane) is commonly used as a
reference.) This difference between the frequency of the signal and the frequency of the
reference is divided by frequency of the reference signal to give the chemical shift. The
frequency shifts are extremely small in comparison to the fundamental NMR frequency. A
typical frequency shift might be 100 Hz, compared to a fundamental NMR frequency of 100

MHz, so the chemical shift is generally expressed in parts per million (ppm). L J

By understanding different chemical environments, the chemical shift can be used to obtain

some structural information about the molecule in a sample. The conversion of the raw data

i
to this information is called assigning the spectrum. For example, for the H-NMR spectrum

for ethanol (CH CH OH), one would expect three specific signals at three specific chemical

shifts: one for the CH group, one for the CH group and one for the OH group. A typical

CH group has a shift around 1 ppm, a CH attached to an OH has a shift of around 4 ppm

and an OH has a shift around 2-3 ppm depending on the solvent used.

Because of molecular motion at room temperature, the three methyl protons average out
during the course of the NMR experiment (which typically requires a few ms). These
protons become degenerate and form a peak at the same chemical shift.

The shape and size of peaks are indicators of chemical structure too. In the example
above— the proton spectrum of ethanol— the CH peak would be three times as large as the
OH. Similarly the CH peak would be twice the size of the OH peak but only 2/3 the size of
the CH peak.

NMR spectroscopy

340

Modern analysis software allows analysis of the size of peaks to understand how many
protons give rise to the peak. This is known as integration— a mathematical process which
calculates the area under a graph (essentially what a spectrum is). The analyst must
integrate the peak and not measure its height because the peaks also have width— and thus
its size is dependent on its area not its height. However, it should be mentioned that the
number of protons, or any other observed nucleus, is only proportional to the intensity, or
the integral, of the NMR signal, in the very simplest one-dimensional NMR experiments. In
more elaborate experiments, for instance, experiments typically used to obtain carbon- 13
NMR spectra, the integral of the signals depends on the relaxation rate of the nucleus, and
its scalar and dipolar coupling constants. Very often these factors are poorly understood -
therefore, the integral of the NMR signal is very difficult to interpret in more complicated
NMR experiments.

J-coupling

Multiplicity

Intensity Ratio

Singlet (s)

Doublet (d)

1:1

Triplet (t)

1:2:1

Quartet (q)

1:3:3:1

Quintet

1:4:6:4:1

Sextet

1:5:10:10:5:1

Septet

1:6:15:20:15:6:1

Some of the most useful information for structure determination in a one-dimensional NMR
spectrum comes from J-coupling or scalar coupling (a special case of spin-spin coupling)
between NMR active nuclei. This coupling arises from the interaction of different spin
states through the chemical bonds of a molecule and results in the splitting of NMR signals.
These splitting patterns can be complex or simple and, likewise, can be straightforwardly
interpretable or deceptive. This coupling provides detailed insight into the connectivity of
atoms in a molecule.

Coupling to n equivalent (spin Vi) nuclei splits the signal into a n + 1 multiplet with
intensity ratios following Pascal's triangle as described on the right. Coupling to additional
spins will lead to further splittings of each component of the multiplet e.g. coupling to two
different spin Vi nuclei with significantly different coupling constants will lead to a doublet
of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically
equivalent (that is, have the same chemical shift) has no effect of the NMR spectra and
couplings between nuclei that are distant (usually more than 3 bonds apart for protons in
flexible molecules) are usually too small to cause observable splittings. Long-range
couplings over more than three bonds can often be observed in cyclic and aromatic
compounds, leading to more complex splitting patterns.

For example, in the proton spectrum for ethanol described above, the CH group is split
into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH 2 protons. Similarly,
the CH is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring
CH 3 protons. In principle, the two CH 2 protons would also be split again into a doublet to
form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of the

NMR spectroscopy

341

acidic hydroxyl proton often results in a loss of coupling information.

Coupling to any spin V2 nuclei such as phosphorus-31 or fluorine- 19 works in this fashion
(although the magnitudes of the coupling constants may be very different). But the splitting
patterns differ from those described above for nuclei with spin greater than V2 because the
spin quantum number has more than two possible values. For instance, coupling to
deuterium (a spin 1 nucleus) splits the signal into a 1:1:1 triplet because the spin 1 has
three spin states. Similarly, a spin 3/2 nucleus splits a signal into a 1:1:1:1 quartet and so
on.

Coupling combined with the chemical shift (and the integration for protons) tells us not only
about the chemical environment of the nuclei, but also the number of neighboring NMR
active nuclei within the molecule. In more complex spectra with multiple peaks at similar
chemical shifts or in spectra of nuclei other than hydrogen, coupling is often the only way
to distinguish different nuclei.

Second-order (or strong) coupling

The above description assumes that the coupling constant is small in comparison with the
difference in NMR frequencies between the inequivalent spins. If the shift separation
decreases (or the coupling strength increases), the multiplet intensity patterns are first
distorted, and then become more complex and less easily analyzed (especially if more than
two spins are involved). Intensification of some peaks in a multiplet is achieved at the
expense of the remainder, which sometimes almost disappear in the background noise,
although the integrated area under the peaks remains constant. In most high-field NMR,
however, the distortions are usually modest and the characteristic distortions (roofing) can
in fact help to identify related peaks.

Second-order effects decrease as the frequency difference between multiplets increases, so
that high-field (i.e. high-frequency) NMR spectra display less distortion than lower
frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra
from later machines typically operating at frequencies at 200 MHz or above.

Magnetic inequivalence

More subtle effects can occur if chemically equivalent spins (i.e. nuclei related by symmetry
and so having the same NMR frequency) have different coupling relationships to external
spins. Spins that are chemically equivalent but are not indistinguishable (based on their
coupling relationships) are termed magnetically inequivalent. For example, the 4 H sites of
1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an
individual member of one of the pairs has different couplings to the spins making up the
other pair. Magnetic inequivalence can lead to highly complex spectra which can only be
analyzed by computational modeling. Such effects are more common in NMR spectra of
aromatic and other non-flexible systems, while conformational averaging about C-C bonds
in flexible molecules tends to equalize the couplings between protons on adjacent carbons,
reducing problems with magnetic inequivalence.

NMR spectroscopy

342

Correlation spectroscopy

Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic
resonance (NMR) spectroscopy. This type of NMR experiment is best known by its
acronym, COSY. Other types of two-dimensional NMR include J-spectroscopy, exchange
spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation
spectroscopy (TOCSY) and heteronuclear correlation experiments, such as HSQC, HMQC,
and HMBC. Two-dimensional NMR spectra provide more information about a molecule than
one-dimensional NMR spectra and are especially useful in determining the structure of a
molecule, particularly for molecules that are too complicated to work with using
one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean
Jeener, a professor at Universite Libre de Bruxelles, in 1971. This experiment was later
implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst, who published their
work in 1976. [2]

Solid-state nuclear magnetic resonance

A variety of physical circumstances does not allow molecules to be studied in solution, and
at the same time not by other spectroscopic techniques to an atomic level, either. In
solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions,
etc., it is in particular the dipolar coupling and chemical shift anisotropy that become
dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR
spectroscopy, these additional interactions would lead to a significant broadening of
spectral lines. A variety of techniques allows to establish high-resolution conditions, that
can, at least for C spectra, be comparable to solution-state NMR spectra.

Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation
of possible molecular orientation by sample orientation, and the reduction of anisotropic
nuclear magnetic interactions by sample spinning. Of the latter approach, fast spinning
around the magic angle is a very prominent method, when the system comprises spin 1/2
nuclei. A number of intermediate techniques, with samples of partial alignment or reduced
mobility, is currently being used in NMR spectroscopy.

Applications in which solid-state NMR effects occur are often related to structure
investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical
analysis in inorganic chemistry, but also include "exotic" applications like the plant leaves
and fuel cells.

NMR spectroscopy applied to proteins

Much of the recent innovation within NMR spectroscopy has been within the field of protein
NMR, which has become a very important technique in structural biology. One common
goal of these investigations is to obtain high resolution 3-dimensional structures of the
protein, similar to what can be achieved by X-ray crystallography. In contrast to X-ray
crystallography, NMR is primarily limited to relatively small proteins, usually smaller than
35 kDa, though technical advances allow ever larger structures to be solved. NMR
spectroscopy is often the only way to obtain high resolution information on partially or
wholly intrinsically unstructured proteins.

Proteins are orders of magnitude larger than the small organic molecules discussed earlier
in this article, but the same NMR theory applies. Because of the increased number of each

NMR spectroscopy

343

element present in the molecule, the basic ID spectra become crowded with overlapping
signals to an extent where analysis is impossible. Therefore, multidimensional (2, 3 or 4D)
experiments have been devised to deal with this problem. To facilitate these experiments, it

1 o 1 c

is desirable to isotopically label the protein with C and N because the predominant

1 2

naturally occurring isotope C is not NMR-active, whereas the nuclear quadrupole moment
of the predominant naturally occurring N isotope prevents high resolution information to
be obtained from this nitrogen isotope. The most important method used for structure
determination of proteins utilizes NOE experiments to measure distances between pairs of
atoms within the molecule. Subsequently, the obtained distances are used to generate a 3D
structure of the molecule using a computer program.

See also

In vivo magnetic resonance spectroscopy

Low field NMR

Magnetic Resonance Imaging

Nuclear Magnetic Resonance

NMR spectra database

NMR tube - includes sample preparation

Protein nuclear magnetic resonance spectroscopy

References

[1] James Keeler. http://www-keeler.ch.cam.ac.uk/lectures/Irvine/chapter2.pdfl "Chapter 2: NMR and energy
levels" (reprinted at University of Cambridge). Understanding NMR Spectroscopy. University of California,
Irvine. http://www-keeler.ch.cam.ac.uk/lectures/Irvine/chapter2.pdf. Retrieved on 2007-05-11.

[2] Martin, G.E; Zekter, A.S., Two-Dimensional NMR Methods for Establishing Molecular Connectivity; VCH
Publishers, Inc: New York, 1988 (p. 59)

External links

• Protein NMR- A Practical Guide (http://www.protein-nmr.org.uk) Practical guide to
NMR, in particular protein NMR assignment

• James Keeler. http://www-keeler.ch. cam. ac.uk/lectures/Irvine/|"Understanding NMR
Spectroscopy" (reprinted at University of Cambridge). University of California, Irvine.
http://www-keeler.ch.cam.ac.uk/lectures/Irvine/. Retrieved on 2007-05-11.

• The Basics of NMR (http://www.cis.rit.edu/htbooks/nmr/) - A non-technical overview

of NMR theory, equipment, and techniques by Dr. Joseph Hornak, Professor of Chemistry
atRIT

• NMRWiki.ORG (http://nmrwiki.org) project, a Wiki dedicated to NMR, MRI, and EPR.

• NMR spectroscopy for organic chemistry (http://www.organicworldwide.net/nmr.
html)

• The Spectral Game (http://spectralgame.com) NMR spectroscopy game.

Free NMR processing, analysis and simulation software

• WINDNMR-Pro (http://www.chem.wisc.edu/areas/reich/plt/windnmr.htm) -
simulation software for interactive calculation of first and second-order spin-coupled
multiplets and a variety of DNMR lineshapes.

• CARA (http://www.nmr.ch) - resonance assignment software developed at the Wiithrich
group

NMR spectroscopy

344

NMRShiftDB (http://www.nmrshiftdb.org) - open database and NMR prediction

website

Spinworks (http://www.umanitoba.ca/chemistry/nmr/spinworks/)

Fourier transform spectroscopy

Fourier transform spectroscopy is a measurement technique whereby spectra are
collected based on measurements of the temporal coherence of a radiative source, using
time-domain measurements of the electromagnetic radiation or other type of radiation. It
can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared
spectroscopy (FT IR, FT-NIRS), Fourier transform (FT) nuclear magnetic resonance ,
mass spectrometry and electron spin resonance spectroscopy. There are several methods
for measuring the temporal coherence of the light, including the continuous wave
Michelson or Fourier transform spectrometer and the pulsed Fourier transform
spectrograph (which is more sensitive and has a much shorter sampling time than
conventional spectroscopic techniques, but is only applicable in a laboratory environment).

Continuous wave Michelson or Fourier transform
spectrograph

The Michelson spectrograph is similar to

the

instrument

used

the

Michelson-Morley experiment. Light from
the source is split into two beams by a
half-silvered mirror, one is reflected off a
fixed mirror and one off a moving mirror
which introduces a time delay -- the Fourier
transform spectrometer is just a Michelson
interferometer with a movable mirror. The
beams interfere, allowing the temporal
coherence of the light to be measured at

each

different

time

delay

setting,

effectively converting the time domain into

spatial

coordinate.

making

measurements of the signal at many
discrete positions of the moving mirror, the
spectrum can be reconstructed using a
Fourier transform of the temporal

coherence

of the

light.

Michelson

mirror

coherent
light source

detector

The Fourier transform spectrometer is just a

Michelson interferometer but one of the two

fully-reflecting mirrors is movable, allowing a variable

delay (in the travel-time of the light) to be included in

one of the beams.

spectrographs are capable of very high spectral resolution observations of very bright
sources. The Michelson or Fourier transform spectrograph was popular for infra-red
applications at a time when infra-red astronomy only had single pixel detectors. Imaging
Michelson spectrometers are a possibility, but in general have been supplanted by imaging
Fabry-Perot instruments which are easier to construct.

Fourier transform spectroscopy

345

Pulsed Fourier transform spectrometer

A pulsed Fourier transform spectrometer does not employ transmittance techniques. In the
most general description of pulsed FT spectrometry, a sample is exposed to an energizing
event which causes a periodic response. The frequency of the periodic response, as
governed by the field conditions in the spectrometer, is indicative of the measured
properties of the analyte.

Examples of Pulsed Fourier transform spectrometry

In magnetic spectroscopy (EPR, NMR), an RF pulse in a strong ambient magnetic field is
used as the energizing event. This turns the magnetic particles at an angle to the ambient
field, resulting in gyration. The gyrating spins then induce a periodic current in a detector
coil. Each spin exhibits a characteristic frequency of gyration (relative to the field strength)
which reveals information about the analyte.

In FT-mass spectrometry, the energizing event is the injection of the charged sample into
the strong electromagnetic field of a cyclotron. These particles travel in circles, inducing a
current in a fixed coil on one point in their circle. Each traveling particle exhibits a
characteristic cyclotron frequency-field ratio revealing the masses in the sample.

The Free Induction Decay

Pulsed FT spectrometry gives the advantage of requiring a single, time-dependent
measurement which can easily deconvolute a set of similar but distinct signals. The
resulting composite signal, is called a free induction decay, because typically the signal will
decay due to inhomogeneities in sample frequency, or simply unrecoverable loss of signal
due to entropic loss of the property being measured.

Fellgett Advantage

One of the most important advantages of Fourier transform spectroscopy was shown by
P.B. Fellgett, an early advocate of the method. The Fellgett advantage, also known as the
multiplex principle, states that a multiplex spectrometer such as the Fourier transform
spectroscopy will produce a gain of the order of the square root of m in the signal-to-noise
ratio of the resulting spectrum, when compared with an equivalent scanning
monochromator, where m is the number of elements comprising the resulting spectrum
when the measurement noise is dominated by detector noise.

Converting spectra from time domain to frequency domain

— ii/27vt

S(t) = / I(v)e- mm du

The sum is performed over all contributing frequencies to give a signal S(t) in the time
domain.

2£iri/t

I{v) = 2Re f S{t)e m dt

J — CO

gives non-zero value when S(t) contains a component that matches the oscillating function.
Remember that

e w = cos 2: + zsin#

Fourier transform spectroscopy

346

See also

• Applied spectroscopy

• 2D-FT NMRI and Spectroscopy

• Forensic chemistry

• Forensic polymer engineering

• nuclear magnetic resonance

• Infra-red spectroscopy

References and notes

[1] Antoine Abragam. 1968. Principles of Nuclear Magnetic Resonance., 895 pp., Cambridge University Press
Cambridge, UK.

Further reading

• Ellis, D.I. and Goodacre, R. (2006). "Metabolic fingerprinting in disease diagnosis:

biomedical applications of infrared and Raman spectroscopy". The Analyst 131: 875-885.
doi: 10.1039/b602376m (http://dx.doi.org/10.1039/b602376m).

External links

• Description of how a Fourier transform spectrometer works (http://scienceworld.
wolfram.com/physics/FourierTransformSpectrometer.html)

• The Michelson or Fourier transform spectrograph (http://www.astro.livjm.ac.uk/
courses/phys362/notes/)

• Internet Journal of Vibrational Spectroscopy - How FTIR works (http://www.ijvs.com/
volume5/edition5/sectionl.html#Feature)

• Fourier Transform Spectroscopy Topical Meeting and Tabletop Exhibit (http://www.osa.
org/meetings/topicalmeetings/fts/default.aspx)

Nuclear Magnetic resonance imaging

347

Nuclear Magnetic resonance imaging

Magnetic Resonance Imaging (MRI), or nuclear
magnetic resonance imaging (NMRI), is primarily a
medical imaging technique most commonly used in
radiology to visualize the internal structure and
function of the body. MRI provides much greater
contrast between the different soft tissues of the body
than computed tomography (CT) does, making it

especially

useful

neurological

(brain),

musculoskeletal, cardiovascular, and oncological

(cancer) imaging. Unlike CT, it uses no ionizing

radiation, but uses a powerful magnetic field to align

the nuclear magnetization of (usually) hydrogen atoms

in water in the body. Radio frequency (RF) fields are

used to systematically alter the alignment of this

magnetization, causing the hydrogen nuclei to produce

a rotating magnetic field detectable by the scanner. This signal can be manipulated by

additional magnetic fields to build up enough information to construct an image of the

body. [1] :36

Para-sagittal MRI of the head, with
aliasing artifacts (nose and forehead in

the back of the head)

Magnetic Resonance Imaging is a relatively new technology. The first MR image was
published in 1973 and the first study performed on a human took place on July 3, 1977. L J

[4]

By comparison, the first human X-ray image was taken in 1895.

Magnetic Resonance Imaging was developed from knowledge gained in the study of nuclear
magnetic resonance. In its early years the technique was referred to as nuclear magnetic
resonance imaging (NMRI). However, as the word nuclear was associated in the public
mind with ionizing radiation exposure it is generally now referred to simply as MRI.
Scientists still use the term NMRI when discussing non-medical devices operating on the
same principles. The term Magnetic Resonance Tomography (MRT) is also sometimes used.

How MRI works

The body is mainly composed of water molecules which each contain two hydrogen nuclei
or protons. When a person goes inside the powerful magnetic field of the scanner, these
protons align with the direction of the field.

A radio frequency electromagnetic field is then briefly turned on causing the protons to
absorb some of its energy. When this field is turned off the protons release this energy at a
resonance radio frequency which can be detected by the scanner. The frequency of the
emitted signal depends on the strength of the magnetic field. The position of protons in the
body can be determined by applying additional magnetic fields during the scan which
allows an image of the body to be built up. These are created by turning gradients coils on
and off which creates the knocking sounds heard during an MR scan.

Diseased tissue, such as tumors, can be detected because the protons in different tissues
return to their equilibrium state at different rates. By changing the parameters on the
scanner this effect is used to create contrast between different types of body tissue.

Nuclear Magnetic resonance imaging

348

Contrast agents may be injected intravenously to enhance the appearance of blood vessels,
tumors or inflammation. Contrast agents may also be directly injected into a joint in the
case of arthrograms, MR images of joints. Unlike CT, scanning MRI uses no ionizing
radiation and is generally a very safe procedure. Patients with some metal implants,
cochlear implants, and cardiac pacemakers are prevented from having an MRI scan due to
effects of the strong magnetic field and powerful radio frequency pulses.

MRI is used to image every part of the body, and is particularly useful for neurological
conditions, for disorders of the muscles and joints, for evaluating tumors, and for showing
abnormalities in the heart and blood vessels.

Physics principles

Nuclear magnetism

Subatomic particles such as

protons have the quantum

mechanical property of spin.

Certain nuclei such as H

(protons), 2 H, 3 He, 23 Na or

P, have a non-zero spin and

therefore a magnetic moment.

In the case of the so-called

1
spin-1/2 nuclei, such as H,

there are two spin states,

sometimes referred to as "up"

and "down". Nuclei such as

12
C have no unpaired neutrons

or protons, and no net spin;

however, the isotope

(referred to as "carbon 13")
does.

Modern 3 tesla clinical MRI scanner

When these spins are placed in a strong external magnetic field they precess around an axis
along the direction of the field. Protons align in two energy "eigenstates" (the "Zeeman
effect"): one low-energy and one high-energy, which are separated by a certain splitting
energy.

Resonance and relaxation

In the static magnetic fields commonly used in MRI, the energy difference between the
nuclear spin states corresponds to a photon at radio frequency wavelengths. Resonant
absorption of energy by the protons due to an external oscillating magnetic field will occur
at the Larmor frequency for the particular nucleus.

The net magnetization vector has two components. The longitudinal magnetization is due to
a tiny excess of protons in the lower energy state. This gives a net polarization parallel to
the external field. Application of an RF pulse can destroy (with a so-called 90° pulse) or
even reverse (with a so-called 180° pulse) this polarization vector. The transverse
magnetization is due to coherences forming between the two proton energy states following
an RF pulse typically of 90°. This gives a net polarization perpendicular to the external field

Nuclear Magnetic resonance imaging

349

in the transverse plane. The recovery of longitudinal magnetization is called longitudinal or
Xi relaxation and occurs exponentially with a time constant 7\. The loss of phase coherence
in the transverse plane is called transverse or T% relaxation. 7\is thus associated with the
enthalpy of the spin system (the number of nuclei with parallel versus anti-parallel spin)
while T^is associated with its entropy (the number of nuclei in phase).

When the radio frequency pulse is turned off, the transverse vector component produces an
oscillating magnetic field which induces a small current in the receiver coil. This signal is
called the free induction decay (FID). In an idealized nuclear magnetic resonance
experiment, the FID decays approximately exponentially with a time constant T%, but in
practical MRI small differences in the static magnetic field at different spatial locations
("inhomogeneities") cause the Larmor frequency to vary across the body creating
destructive interference which shortens the FID. The time constant for the observed decay
of the FID is called the T2* ("T 2 star") relaxation time, and is always shorter than T3.
Also, when the radio frequency pulse is turned off, the longitudinal magnetization starts to
recover exponentially with a time constant I\.

In MRI, the static magnetic field is caused to vary across the body (a field gradient), so that
different spatial locations become associated with different precession frequencies. Usually
these field gradients are pulsed, and it is the almost infinite variety of RF and gradient
pulse sequences that gives MRI its versatility. Application of field gradient destroys the FID
signal, but this can be recovered and measured by a refocusing gradient (to create a
so-called "gradient echo"), or by a radio frequency pulse (to create a so-called "spin-echo").
The whole process can be repeated when some Ti -relaxation has occurred and the thermal
equilibrium of the spins has been more or less restored.

Typically in soft tissues 7\is around one second while Tgand T%* are a few tens of
milliseconds, but these values vary widely between different tissues (and different external
magnetic fields), giving MRI its tremendous soft tissue contrast.

Contrast agents work by altering (shortening) the relaxation parameters, especially Jl.

Imaging

A number of schemes have been devised for combining field gradients and radio frequency
excitation to create an image:

• 2D or 3D reconstruction from projections, much as in Computed Tomography.

• Building the image point-by-point or line-by-line.

• Gradients in the RF field rather than the static field.

Although each of these schemes is occasionally used in specialist applications, the majority
of MR Images today are created either by the Two-Dimensional Fourier Transform (2DFT)
technique with slice selection, or by the Three-Dimensional Fourier Transform (3DFT)
technique. Another name for 2DFT is spin-warp. What follows here is a description of the
2DFT technique with slice selection.

The 3DFT technique is rather similar except that there is no slice selection and
phase-encoding is performed in two separate directions.

Another scheme which is sometimes used, especially in brain scanning or where images are
needed very rapidly, is called echo-planar imaging (EPI): In this case, each RF excitation is
followed by a train of gradient echoes with different spatial encoding.

Nuclear Magnetic resonance imaging

350

Image contrast and contrast enhancement

Image contrast is created by differences in the strength of the NMR signal recovered from
different locations within the sample. This depends upon the relative density of excited
nuclei (usually water protons), on differences in relaxation times ( 7\, Tgand T%*) of those
nuclei after the pulse sequence, and often on other parameters discussed under specialized
MR scans. Contrast in most MR images is actually a mixture of all these effects, but careful
design of the imaging pulse sequence allows one contrast mechanism to be emphasized
while the others are minimized. The ability to choose different contrast mechanisms gives
MRI tremendous flexibility. In the brain, Ti -weighting causes the nerve connections of
white matter to appear white, and the congregations of neurons of gray matter to appear
gray, while cerebrospinal fluid (CSF) appears dark. The contrast of white matter, gray
matter and cerebrospinal fluid is reversed using T2or T2* imaging, whereas
proton-density-weighted imaging provides little contrast in healthy subjects. Additionally,
functional parameters such as cerebral blood flow (CBF), cerebral blood volume (CBV) or
blood oxygenation can affect T\, T2and I2* and so can be encoded with suitable pulse
sequences.

In some situations it is not possible to generate enough image contrast to adequately show
the anatomy or pathology of interest by adjusting the imaging parameters alone, in which
case a contrast agent may be administered. This can be as simple as water, taken orally, for
imaging the stomach and small bowel. However, most contrast agents used in MRI are
selected for their specific magnetic properties. Most commonly, a paramagnetic contrast
agent (usually a gadolinium compound ) is given. Gadolinium-enhanced tissues and

fluids appear extremely bright on Xj. -weighted images. This provides high sensitivity for
detection of vascular tissues {e.g., tumors) and permits assessment of brain perfusion {e.g.,
in stroke). There have been concerns raised recently regarding the toxicity of
gadolinium-based contrast agents and their impact on persons with impaired kidney
function. The American College of Radiology released screening criteria for patients

T71

intended to be given gadolinium-based contrast agents to identify potential risk factors
for negative reactions. Special actions may be taken, such as hemodialysis following a
contrast MRI scan for renally-impaired patients.

More recently, superparamagnetic contrast agents, e.g., iron oxide nanoparticles ,

have become available. These agents appear very dark on T9*-weighted images and may
be used for liver imaging, as normal liver tissue retains the agent, but abnormal areas {e.g.,
scars, tumors) do not. They can also be taken orally, to improve visualization of the
gastrointestinal tract, and to prevent water in the gastrointestinal tract from obscuring
other organs {e.g., the pancreas). Diamagnetic agents such as barium sulfate have also
been studied for potential use in the gastrointestinal tract, but are less frequently used.

K-space

formalism

technique that proved invaluable in unifying different MR imaging techniques. They showed
that the demodulated MR signal S{t) generated by freely precessing nuclear spins in the
presence of a linear magnetic field gradient G equals the Fourier transform of the effective
spin density, i.e.

S(t) = p eS (k(t)) = / dx p(x) ■ e 2 <" **>■*

Nuclear Magnetic resonance imaging

351

where:

*(*) =

In other words, as time progresses the signal traces out a trajectory in k-space with the
velocity vector of the trajectory proportional to the vector of the applied magnetic field
gradient. By the term effective spin density we mean the true spin density p[x) corrected
for the effects of I\ preparation, Tg decay, dephasing due to field inhomogeneity, flow,
diffusion, etc. and any other phenomena that affect that amount of transverse
magnetization available to induce signal in the RF probe.

From the basic k-space formula, it follows immediately that we reconstruct an image I(S)
simply by taking the inverse Fourier transform of the sampled data, viz.

m =fs sm .^ *■

Using the k-space formalism, a number of seemingly complex ideas became simple. For
example, it becomes very easy to understand the role of phase encoding (the so-called
spin-warp method). In a standard spin echo or gradient echo scan, where the readout (or
view) gradient is constant (e.g. G x ), a single line of k-space is scanned per RF excitation.
When the phase encoding gradient is zero, the line scanned is the fe^axis. When a non-zero
phase-encoding pulse is added in between the RF excitation and the commencement of the
readout gradient, this line moves up or down in k-space, i.e., we scan the line Mj= constant.

The k-space formalism also makes it very easy to compare different scanning techniques. In
single-shot EPI, all of k-space is scanned in a single shot, following either a sinusoidal or
zig-zag trajectory. Since alternating lines of k-space are scanned in opposite directions, this
must be taken into account in the reconstruction. Multi-shot EPI and fast spin echo
techniques acquire only part of k-space per excitation. In each shot, a different interleaved
segment is acquired, and the shots are repeated until k-space is sufficiently well-covered.
Since the data at the center of k-space represent lower spatial frequencies than the data at
the edges of k-space, the revalue for the center of k-space determines the image's Ti
contrast.

The importance of the center of k-space in determining image contrast can be exploited in
more advanced imaging techniques. One such technique is spiral acquisition - a rotating
magnetic field gradient is applied, causing the trajectory in k-space to spiral out from the
center to the edge. Due to T2and T 2 * decay the signal is greatest at the start of the
acquisition, hence acquiring the center of k-space first improves contrast to noise ratio
(CNR) when compared to conventional zig-zag acquisitions, especially in the presence of
rapid movement.

Since x and k are conjugate variables (with respect to the Fourier transform) we can use
the Nyquist theorem to show that the step in k-space determines the field of view of the
image (maximum frequency that is correctly sampled) and the maximum value of k sampled
determines the resolution, i.e.

FOV oc — j Resolution oc |fc max
(these relationships apply to each axis [X, Y, and Z] independently).

Nuclear Magnetic resonance imaging

352

Example of a pulse sequence

transmit

receive -

' l "FE

I !

"PE

Simplified timing diagram for two-dimensional-Fourier-transform

(2DFT) Spin Echo (SE) pulse sequence

In the timing diagram, the
horizontal axis represents

time.

The

vertical
(top

axis
row)

represents:

amplitude of radio frequency

pulses;

(middle

rows)

amplitudes of the three

orthogonal magnetic

field

gradient pulses; and (bottom
row) receiver analog-to-digital

converter

(ADC).

Radio

frequencies are transmitted at
the Larmor frequency of the
nuclide to be imaged. For
example, for H in a magnetic
field of IT, a frequency of

42.5781

MHz would be

employed. The three field
gradients are labeled G v (typically corresponding to a patient's Left-to-Right direction and
colored red in diagram), G (typically corresponding to a patient's Front-to-Back direction
and colored green in diagram), and G (typically corresponding to a patient's Head-to-Toe
direction and colored blue in diagram). Where negative-going gradient pulses are shown,
they represent reversal of the gradient direction, i.e., Right-to-Left, Back-to-Front or
Toe-to-Head. For human scanning, gradient strengths of 1-100 mT/m are employed: Higher
gradient strengths permit better resolution and faster imaging. The pulse sequence shown
here would produce a transverse (axial) image.

The first part of the pulse sequence, SS, achieves Slice Selection. A shaped pulse (shown
here with a sine modulation) causes a 90° (n/2 radian) nutation of longitudinal nuclear
magnetization within a slab, or slice, creating transverse magnetization. The second part of
the pulse sequence, PE, imparts a phase shift upon the slice-selected nuclear
magnetization, varying with its location in the Y direction. The third part of the pulse
sequence, another Slice Selection (of the same slice) uses another shaped pulse to cause a
180° (n radian) rotation of transverse nuclear magnetization within the slice. This
transverse magnetisation refocuses to form a spin echo at a time TE. During the spin echo,
a frequency-encoding (FE) or readout gradient is applied, making the resonant frequency of
the nuclear magnetization vary with its location in the X direction. The signal is sampled
n times by the ADC during this period, as represented by the vertical lines. Typically n
of between 128 and 512 samples are taken.

The longitudinal relaxation is then allowed to recover somewhat and after a time TR the
whole sequence is repeated n times, but with the phase-encoding gradient incremented
(indicated by the horizontal hatching in the green gradient block). Typically n pE of between
128 and 512 repetitions are made.

The negative-going lobes in G v and G 7 are imposed to ensure that, at time TE (the spin echo
maximum), phase only encodes spatial location in the Y direction.

Nuclear Magnetic resonance imaging

353

Typically TE is between 5 ms and 100 ms, while TR is between 100 ms and 2000 ms.

After the two-dimensional matrix (typical dimension between 128x128 and 512x512) has
been acquired, producing the so-called K-space data, a two-dimensional Fourier transform
is performed to provide the familiar MR image. Either the magnitude or phase of the
Fourier transform can be taken, the former being far more common.

Scanner construction and operation

The major components of an MRI scanner are: the main
magnet, which polarizes the sample, the shim coils for
correcting inhomogeneities in the main magnetic field,
the gradient system which is used to localize the MR
signal and the RF system, which excites the sample and
detects the resulting NMR signal. The whole system is
controlled by one or more computers.

mri scanner cross £#tTictn

Service connections

(including emergency cryostat vent pipe}

Thermal Insulation

Cryostat filled with
liquid helium

Supfl rcon d u cti ng
p rirnory c I retro m o g n
coil

Magnetic gradient
coils

RFtransTitcci

Scanner bore

Body port specific
receive coll

Longitudinal section

Scanner table

Schematic of construction of a
cylindrical superconducting MR

scanner

Magnet

The magnet is the largest and most expensive
component of the scanner, and the remainder of the
scanner is built around it. The strength of the magnet is
measured in tesla (T). Clinical magnets generally have a
field strength in the range 0.1—3.0 T, with research
systems available up to 9.4 T for human use and 21 T
for animal systems J .

Just as important as the strength of the main magnet is

its precision. The straightness of the magnetic lines

within the center (or, as it is technically known, the

iso-center) of the magnet needs to be near-perfect. This is known as homogeneity.

Fluctuations (inhomogeneities in the field strength) within the scan region should be less

than three parts per million (3 ppm). Three types of magnets have been used:

• Permanent magnet: Conventional magnets made from ferromagnetic materials (e.g., steel
alloys containing rare earth elements such as neodymium) can be used to provide the
static magnetic field. A permanent magnet that is powerful enough to be used in an MRI
will be extremely large and bulky; they can weigh over 100 tonnes. Permanent magnet
MRIs are very inexpensive to maintain; this cannot be said of the other types of MRI
magnets, but there are significant drawbacks to using permanent magnets. They are only
capable of achieving weak field strengths compared to other MRI magnets (usually less
than 0.4 T) and they are of limited precision and stability. Permanent magnets also
present special safety issues; since their magnetic fields cannot be "turned off,"
ferromagnetic objects are virtually impossible to remove from them once they come into
direct contact. Permanent magnets also require special care when they are being
brought to their site of installation.

• Resistive electromagnet: A solenoid wound from copper wire is an alternative to a
permanent magnet. An advantage is low initial cost, but field strength and stability are
limited. The electromagnet requires considerable electrical energy during operation
which can make it expensive to operate. This design is essentially obsolete.

Nuclear Magnetic resonance imaging

354

• Superconducting electromagnet: When a niobium-titanium or niobium-tin alloy is cooled
by liquid helium to 4K (-269°C / -452°F) it becomes a superconductor, losing resistance
to flow of electrical current. An electromagnet constructed with superconductors can
have extremely high field strengths, with very high stability. The construction of such
magnets is extremely costly, and the cryogenic helium is expensive and difficult to
handle. However, despite their cost, helium cooled superconducting magnets are the
most common type found in MRI scanners today.

Most superconducting magnets have their coils of superconductive wire immersed in liquid
helium, inside a vessel called a cryostat. Despite thermal insulation, ambient heat causes
the helium to slowly boil off. Such magnets, therefore, require regular topping-up with
liquid helium. Generally a cryocooler, also known as a coldhead, is used to recondense
some helium vapor back into the liquid helium bath. Several manufacturers now offer
'cryogenless' scanners, where instead of being immersed in liquid helium the magnet wire
is cooled directly by a cryocooler.

Magnets are available in a variety of shapes. However, permanent magnets are most
frequently 'C shaped, and superconducting magnets most frequently cylindrical. However,
C-shaped superconducting magnets and box-shaped permanent magnets have also been
used.

Magnetic field strength is an important factor in determining image quality. Higher
magnetic fields increase signal-to-noise ratio, permitting higher resolution or faster
scanning. However, higher field strengths require more costly magnets with higher
maintenance costs, and have increased safety concerns. A field strength of 1.0 - 1.5 T is a
good compromise between cost and performance for general medical use. However, for
certain specialist uses (e.g., brain imaging) higher field strengths are desirable, with some
hospitals now using 3.0 T scanners.

Shims

When a sample is placed into the scanner, the main
magnetic field is distorted by susceptibility boundaries
within that sample, causing signal dropout (regions
showing no signal) and spatial distortions in acquired
images. For humans or animals the effect is particularly
pronounced at air-tissue boundaries such as the sinuses
(due to paramagnetic oxygen in air) making, for
example, the frontal lobes of the brain difficult image.
To restore field homogeneity a set of shim coils are
included in the scanner. These are resistive coils,
usually at room temperature, capable of producing field corrections distributed as several

ri q]

orders of spherical harmonics.

FID signal from a badly shimmed
sample has a complex envelope.

After placing the sample in the scanner, the BO field is 'shimmed' by adjusting currents in
the shim coils. Field homogeneity is measured by examining an FID signal in the absence of

field

gradients.

The

FID

from

poorly

Nuclear Magnetic resonance imaging

355

shimmed sample will show a complex decay envelope,
often with many humps. Shim currents are then
adjusted to produce a large amplitude exponentially
decaying FID, indicating a homogeneous BO field. The
process is usually automated.

FID signal from a well shimmed
sample, showing a pure exponential

decay.

Gradients

Gradient coils are used to spatially encode the positions of protons by varying the magnetic
field linearly across the imaging volume. The Larmor frequency will then vary as a function
of position in the x, y and z-axes.

Gradient coils are usually resistive electromagnets powered by sophisticated amplifiers
which permit rapid and precise adjustments to their field strength and direction. Typical
gradient systems are capable of producing gradients from 20 mT/m to 100 mT/m (i.e., in a
1.5 T magnet, when a maximal z-axis gradient is applied, the field strength may be 1.45 T at
one end of a 1 m long bore and 1.55 T at the other 1 J ). It is the magnetic gradients that
determine the plane of imaging - because the orthogonal gradients can be combined freely,
any plane can be selected for imaging.

Scan speed is dependent on performance of the gradient system. Stronger gradients allow
for faster imaging, or for higher resolution; similarly, gradients systems capable of faster
switching can also permit faster scanning. However, gradient performance is limited by
safety concerns over nerve stimulation.

Some important characteristic of gradient amplifiers and gradient coil are slew rate and
gradient strength. As mentioned earlier, a gradient coil will create an additional, linearly
varying magnetic field that adds or subtracts from the main magnetic field. This additional
magnetic field will have components in all 3 directions, viz. X, Y and Z; however, only the
component along the magnetic field (usually called the Z-axis, hence denoted G z ) is useful
for imaging. Along any given axis, the gradient will add to the magnetic field on one side of
the zero position and subtract from it on the other side. Since the additional field is a
gradient, it has units of gauss per cm or millitesla (mT) per meter. High performance
gradient coils used in MRI are typically capable of producing a gradient magnetic field of
approximate 30 mT per meter or higher for a 1.5 T MRI. The slew rate of a gradient system
is a measure of how quickly the gradients can be ramped on or off. Typical higher
performance gradients have a slew rate of up to 100-200 tesla per meter per second. The
slew rate depends both on the gradient coil (it takes more time to ramp up or down a large
coil than a small coil) and on the performance of the gradient amplifier (it takes a lot of
voltage to overcome the inductance of the coil) and has adequate influence on image
quality.

Nuclear Magnetic resonance imaging

356

Radio frequency system

The radio frequency (RF) transmission system consists of an RF synthesizer, power
amplifier and transmitting coil. This is usually built into the body of the scanner. The power
of the transmitter is variable, but high-end scanners may have a peak output power of up to
35 kW, and be capable of sustaining average power of 1 kW. The receiver consists of the
coil, pre-amplifier and signal processing system. While it is possible to scan using the
integrated coil for RF transmission and MR signal reception, if a small region is being
imaged, then better image quality (i.e., signal-to-noise ratio) is obtained by using a
close-fitting smaller coil. A variety of coils are available which fit closely around parts of the
body, e.g., the head, knee, wrist, breast, or internally, e.g., the rectum.

A recent development in MRI technology has been the development of sophisticated
multi-element phased array coils which are capable of acquiring multiple channels of
data in parallel. This 'parallel imaging 1 technique uses unique acquisition schemes that
allow for accelerated imaging, by replacing some of the spatial coding originating from the
magnetic gradients with the spatial sensitivity of the different coil elements. However, the
increased acceleration also reduces the signal-to-noise ratio and can create residual
artifacts in the image reconstruction. Two frequently used parallel acquisition and
reconstruction schemes are known as SENSE L J and GRAPPA. J A detailed review of
parallel imaging techniques can be found here: C ^

Applications

In clinical practice, MRI is used to distinguish pathologic tissue (such as a brain tumor)
from normal tissue. One advantage of an MRI scan is that it is harmless to the patient. It
uses strong magnetic fields and non-ionizing radiation in the radio frequency range.
Compare this to CT scans and traditional X-rays which involve doses of ionizing radiation
and may increase the risk of malignancy, especially in a fetus.

While CT provides good spatial resolution (the ability to distinguish two structures an
arbitrarily small distance from each other as separate), MRI provides comparable
resolution with far better contrast resolution (the ability to distinguish the differences
between two arbitrarily similar but not identical tissues). The basis of this ability is the
complex library of pulse sequences that the modern medical MRI scanner includes, each of
which is optimized to provide image contrast based on the chemical sensitivity of MRI.

For example, with particular values of the echo time (TE) and the repetition time (TR),
which are basic parameters of image acquisition, a sequence will take on the property of Tg
-weighting. On a T% -weighted scan, water- and fluid-containing tissues are bright (most
modern T% sequences are actually fast resequences) and fat-containing tissues are dark.
The reverse is true for 71 -weighted images. Damaged tissue tends to develop edema,
which makes a T% -weighted sequence sensitive for pathology, and generally able to
distinguish pathologic tissue from normal tissue. With the addition of an additional radio
frequency pulse and additional manipulation of the magnetic gradients, a T% -weighted
sequence can be converted to a FLAIR sequence, in which free water is now dark, but
edematous tissues remain bright. This sequence in particular is currently the most sensitive
way to evaluate the brain for demyelinating diseases, such as multiple sclerosis.

The typical MRI examination consists of 5-20 sequences, each of which are chosen to
provide a particular type of information about the subject tissues. This information is then
synthesized by the interpreting physician.

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Basic MRI scans

Comparison of Different Types of MR Contrast

math>T_2</math
weighting

math>T_2</math>*
weighting

weighting with
gadolinium contrast

T\ -weighted MRI

7\ -weighted scans use a gradient echo (GRE) sequence, with short TE and short TR. This is
one of the basic types of MR contrast and is a commonly run clinical scan. The I\ weighting
can be increased (improving contrast) with the use of an inversion pulse as in an MP-RAGE
sequence. Due to the short repetition time (TR) this scan can be run very fast allowing the
collection of high resolution 3D datasets. A Tj. reducing gadolinium contrast agent is also
commonly used, with a Tuscan being collected before and after administration of contrast
agent to compare the difference. In the brain 7\ -weighted scans provide good gray
matter/white matter contrast.

T>2 -weighted MRI

T2-weighted scans use a spin echo (SE) sequence, with long TE and long TR. They have
long been the clinical workhorse as the spin echo sequence is less susceptible to
inhomogeneities in the magnetic field. They are particularly well suited to edema as they
are sensitive to water content (edema is characterized by increased water content).

T 2 *-weighted MRI

T9* (pronounced "T 2 star") weighted scans use a gradient echo (GRE) sequence, with long
TE and long TR. The gradient echo sequence used does not have the extra refocusing pulse
used in spin echo so it is subject to additional losses above the normal Tgdecay (referred to
as T^), these taken together are called T2*. This also makes it more prone to
susceptibility losses at air/tissue boundaries, but can increase contrast for certain types of
tissue, such as venous blood.

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Spin density weighted MRI

Spin density, also called proton density, weighted scans try to have no contrast from either
X2 or Ti decay, the only signal change coming from differences in the amount of available
spins. It uses a spin echo or sometimes a gradient echo sequence, with short TE and long
TR.

Specialized MRI scans

Diffusion MRI

Diffusion MRI measures the diffusion of water molecules in
biological tissues. In an isotropic medium (inside a glass
of water for example) water molecules naturally move
randomly according to Brownian motion. In biological
tissues however, the diffusion may be anisotropic. For
example a molecule inside the axon of a neuron has a low
probability of crossing the myelin membrane. Therefore the
molecule will move principally along the axis of the neural
fiber. If we know that molecules in a particular voxel diffuse
principally in one direction we can make the assumption
that the majority of the fibers in this area are going parallel
to that direction.

The recent development of diffusion tensor imaging (DTI)

enables diffusion to be measured in multiple directions and

the fractional anisotropy in each direction to be calculated for each voxel. This enables

researchers to make brain maps of fiber directions to examine the connectivity of different

regions in the brain (using tractography) or to examine areas of neural degeneration and

demyelination in diseases like Multiple Sclerosis.

Another application of diffusion MRI is diffusion-weighted imaging (DWI). Following an
ischemic stroke, DWI is highly sensitive to the changes occurring in the lesion. J It is
speculated that increases in restriction (barriers) to water diffusion, as a result of cytotoxic
edema (cellular swelling), is responsible for the increase in signal on a DWI scan. The DWI
enhancement appears within 5-10 minutes of the onset of stroke symptoms (as compared
with computed tomography, which often does not detect changes of acute infarct for up to
4-6 hours) and remains for up to two weeks. Coupled with imaging of cerebral perfusion,
researchers can highlight regions of "perfusion/diffusion mismatch" that may indicate
regions capable of salvage by reperfusion therapy.

Like many other specialized applications, this technique is usually coupled with a fast
image acquisition sequence, such as echo planar imaging sequence.

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Magnetization Transfer MRI

Magnetization transfer (MT) refers to the transfer of longitudinal magnetization from free
water protons to hydration water protons in NMR and MRI.

In magnetic resonance imaging of molecular solutions, such as protein solutions, two types
of water molecules, free (bulk) and hydration, are found. Free water protons have faster
average rotational frequency and hence less fixed water molecules that may cause local
field inhomogeneity. Because of this uniformity, most free water protons have resonance
frequency lying narrowly around the normal proton resonance frequency of 63 MHz (at 1.5
tesla). This also results in slower transverse magnetization dephasing and hence longer T?.
Conversely, hydration water molecules are slowed down by interaction with solute
molecules and hence create field inhomogeneities that lead to wider resonance frequency
spectrum.

Fluid attenuated inversion recovery (FLAIR)

Fluid Attenuated Inversion Recovery (FLAIR) c , is an inversion-recovery pulse sequence
used to null signal from fluids. For example, it can be used in brain imaging to suppress
Cerebrospinal fluid (CSF) so as to bring out the periventricular hyperintense lesions, such
as multiple sclerosis (MS) plaques. By carefully choosing the inversion time TI (the time
between the inversion and excitation pulses), signal from any particular tissue can be
suppressed.

Magnetic resonance angiography

Magnetic resonance angiography (MRA) is used to

generate pictures of the arteries in order to evaluate

them for stenosis (abnormal narrowing) or

aneurysms (vessel wall dilatations, at risk of

rupture). MRA is often used to evaluate the arteries

of the neck and brain, the thoracic and abdominal

aorta, the renal arteries, and the legs (called a

"run-off"). A variety of techniques can be used to

generate the pictures, such as administration of a

paramagnetic contrast agent (gadolinium) or using

a technique known as "flow-related enhancement"

(e.g. 2D and 3D time-of-flight sequences), where

most of the signal on an image is due to blood which

has recently moved into that plane, see also FLASH

MRI. Techniques involving phase accumulation

(known as phase contrast angiography) can also be used to generate flow velocity maps

easily and accurately. Magnetic resonance venography (MRV) is a similar procedure that is

used to image veins. In this method the tissue is now excited inferiorly while signal is

gathered in the plane immediately superior to the excitation plane, and thus imaging the

venous blood which has recently moved from the excited plane.

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Magnetic Resonance Gated Intracranial CSF Dynamics (MR-GILD)

Magnetic resonance gated intracranial cerebrospinal fluid (CSF)or liquor dynamics
(MR-GILD) technique is an MR sequence based on bipolar gradient pulse used to
demonstrate CSF pulsatile flow in ventricles, cisterns, aqueduct of Sylvius and entire
intracranial CSF pathway. It is a method for analyzing CSF circulatory system dynamics in
patients with CSF obstructive lesions such as normal pressure hydrocephalus. It also allows
visualization of both arterial and venous pulsatile blood flow in vessels without use of
contrast agents. [23] [24] .

Diastolic time data acquisition (DTD A).

Systolic time data acquisition (STDA).

Magnetic resonance spectroscopy

Magnetic resonance spectroscopy is used to measure the levels of different metabolites in
body tissues. The MR signal produces a spectrum of resonances that correspond to
different molecular arrangements of the isotope being "excited". This signature is used to
diagnose certain metabolic disorders, especially those affecting the brain, as well as to
provide information on tumor metabolism. J

Magnetic resonance spectroscopic imaging (MRSI) combines both spectroscopic and
imaging methods to produce spatially localized spectra from within the sample or patient.
The spatial resolution is much lower (limited by the available SNR), but the spectra in each
voxel contains information about many metabolites. Because the available signal is used to
encode spatial and spectral information, MRSI requires high SNR achievable only at higher
field strengths (1.5T and above).

Functional MRI

Functional MRI (fMRI) measures signal changes in the
brain that are due to changing neural activity. The
brain is scanned at low resolution but at a rapid rate
(typically once every 2-3 seconds). Increases in neural
activity cause changes in the MR signal via

To*

[97]

changes; this mechanism is referred to as the BOLD
(blood-oxygen-level dependent) effect. Increased neural
activity causes an increased demand for oxygen, and
the vascular system actually overcompensates for this,
increasing the amount of oxygenated hemoglobin
relative to deoxygenated hemoglobin. Because
deoxygenated hemoglobin attenuates the MR signal,

A fMRI scan showing regions of
activation in orange, including the
primary visual cortex (VI, BA17).

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the vascular response leads to a signal increase that is related to the neural activity. The
precise nature of the relationship between neural activity and the BOLD signal is a subject
of current research. The BOLD effect also allows for the generation of high resolution 3D
maps of the venous vasculature within neural tissue.

While BOLD signal is the most common method employed for neuroscience studies in
human subjects, the flexible nature of MR imaging provides means to sensitize the signal to
other aspects of the blood supply. Alternative techniques employ arterial spin labeling
(ASL) or weight the MRI signal by cerebral blood flow (CBF) and cerebral blood volume
(CBV). The CBV method requires injection of a class of MRI contrast agents that are now in
human clinical trials. Because this method has been shown to be far more sensitive than the
BOLD technique in preclinical studies, it may potentially expand the role of fMRI in clinical
applications. The CBF method provides more quantitative information than the BOLD
signal, albeit at a significant loss of detection sensitivity.

Interventional MRI

The lack of harmful effects on the patient and the operator make MRI well-suited for
"interventional radiology", where the images produced by a MRI scanner are used to guide
minimally-invasive procedures. Of course, such procedures must be done without any
ferromagnetic instruments.

A specialized growing subset of interventional MRI is that of intraoperative MRI in which
the MRI is used in the surgical process. Some specialized MRI systems have been
developed that allow imaging concurrent with the surgical procedure. More typical,
however, is that the surgical procedure is temporarily interrupted so that MR images can
be acquired to verify the success of the procedure or guide subsequent surgical work.

Radiation therapy simulation

Because of MRI's superior imaging of soft tissues, it is now being utilized to specifically
locate tumors within the body in preparation for radiation therapy treatments. For therapy
simulation, a patient is placed in specific, reproducible, body position and scanned. The
MRI system then computes the precise location, shape and orientation of the tumor mass,
correcting for any spatial distortion inherent in the system. The patient is then marked or
tattooed with points which, when combined with the specific body position, will permit
precise triangulation for radiation therapy.

Current density imaging

Current density imaging (CDI) endeavors to use the phase information from images to
reconstruct current densities within a subject. Current density imaging works because
electrical currents generate magnetic fields, which in turn affect the phase of the magnetic
dipoles during an imaging sequence. To date no successful CDI has been performed using
biological currents, but several studies have been published which involve applied currents
through a pair of electrodes.

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Magnetic resonance guided focused ultrasound

In MRgFUS therapy, ultrasound beams are focused on a tissue - guided and controlled
using MR thermal imaging - and due to the significant energy deposition at the focus,
temperature within the tissue rises to more than 65 °C, completely destroying it. This
technology can achieve precise "ablation" of diseased tissue. MR imaging provides a
three-dimensional view of the target tissue, allowing for precise focusing of ultrasound
energy. The MR imaging provides quantitative, real-time, thermal images of the treated
area. This allows the physician to ensure that the temperature generated during each cycle
of ultrasound energy is sufficient to cause thermal ablation within the desired tissue and if
not, to adapt the parameters to ensure effective treatment.

Multinuclear imaging

Hydrogen is the most frequently imaged nucleus in MRI because it is present in biological
tissues in great abundance. However, any nucleus which has a net nuclear spin could
potentially be imaged with MRI. Such nuclei include helium-3, carbon-13, fluorine-19,
oxygen-17, sodium-23, phosphorus-31 and xenon-129. Na and P are naturally abundant

o 129

in the body, so can be imaged directly. Gaseous isotopes such as He or Xe must be
hyperpolarized and then inhaled as their nuclear density is too low to yield a useful signal

17 13 19

under normal conditions. O, C and F can be administered in sufficient quantities in
liquid form (e.g. 7 0-water, C-glucose solutions or perfluorocarbons) that

hyperpolarization is not a necessity.

Multinuclear imaging is primarily a research technique at present. However, potential
applications include functional imaging and imaging of organs poorly seen on H MRI (e.g.

lungs and bones) or as alternative contrast agents. Inhaled hyperpolarized He can be used

1 3
to image the distribution of air spaces within the lungs. Injectable solutions containing C

1 29

or stabilized bubbles of hyperpolarized Xe have been studied as contrast agents for
angiography and perfusion imaging. P can potentially provide information on bone
density and structure, as well as functional imaging of the brain.

Susceptibility weighted imaging (SWI)

Susceptibility weighted imaging (SWI), is a new type of contrast in MRI different from spin
density, 7\, or Ti imaging. This method exploits the susceptibility differences between
tissues and uses a fully velocity compensated, three dimensional, RF spoiled,
high-resolution, 3D gradient echo scan. This special data acquisition and image processing
produces an enhanced contrast magnitude image very sensitive to venous blood,
hemorrhage and iron storage. It is used to enhance the detection and diagnosis of tumors,
vascular and neurovascular diseases (stroke and hemorrhage, multiple sclerosis,
Alzheimer's), and also detects traumatic brain injuries that may not be diagnosed using
other methods. ]

Other specialized MRI techniques

MRI is a new and active field of research and new methods and variants are often published
when they are able to get better results in specific fields. Examples of these recent
improvements are T2*-weighted turbo spin-echo ( T2TSE MRI), Double inversion recovery
MRI (DIR-MRI) or Phase-sensitive inversion recovery MRI (PSIR-MRI), all of them able to
improve imaging of the brain lesions L . Another example is MP-RAGE

(magnetization-prepared rapid acquisition with gradient echor , which improves images

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of multiple sclerosis cortical lesions^ ]

Portable instruments

Portable magnetic resonance instruments are available for use in education and field
research. Using the principles of Earth's field NMR, they have no powerful polarizing
magnet, so that such instruments can be small and relatively inexpensive. Some can be
used for both EFNMR spectroscopy and MRI imaging 1 J . The low strength of the Earth's
field results in poor signal to noise ratios, requiring relatively long scan times to capture
spectroscopic data or build up MRI images.

Research with atomic magnetometers have discussed the possibility for cheap and portable
MRI instruments without the large magnet.

MRI versus CT

A computed tomography (CT) scanner uses X-rays, a type of ionizing radiation, to acquire
its images, making it a good tool for examining tissue composed of elements of a higher
atomic number than the tissue surrounding them, such as bone and calcifications (calcium
based) within the body (carbon based flesh), or of structures (vessels, bowel). MRI, on the
other hand, uses non-ionizing radio frequency (RF) signals to acquire its images and is best
suited for non-calcified tissue, though MR images can also be acquired from bones and
teeth [36] as well as fossils. [37]

CT may be enhanced by use of contrast agents containing elements of a higher atomic
number than the surrounding flesh such as iodine or barium. Contrast agents for MRI are
those which have paramagnetic properties, e.g. gadolinium and manganese.

Both CT and MRI scanners can generate multiple two-dimensional cross-sections (slices) of
tissue and three-dimensional reconstructions. Unlike CT, which uses only X-ray attenuation
to generate image contrast, MRI has a long list of properties that may be used to generate
image contrast. By variation of scanning parameters, tissue contrast can be altered and
enhanced in various ways to detect different features. (See Applications above.)

MRI can generate cross-sectional images in any plane (including oblique planes). In the
past, CT was limited to acquiring images in the axial (or near axial) plane. The scans used
to be called Computed Axial Tomography scans (CAT scans). However, the development of
multi-detector CT scanners with near-isotropic resolution, allows the CT scanner to produce
data that can be retrospectively reconstructed in any plane with minimal loss of image
quality.

For purposes of tumor detection and identification in the brain, MRI is generally
superior. J I J L J However, in the case of solid tumors of the abdomen and chest, CT is
often preferred due to less motion artifact. Furthermore, CT usually is more widely
available, faster, much less expensive, and may be less likely to require the person to be
sedated or anesthetized.

MRI is also best suited for cases when a patient is to undergo the exam several times
successively in the short term, because, unlike CT, it does not expose the patient to the
hazards of ionizing radiation.

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Economics of MRI

MRI equipment is expensive. 1.5 tesla scanners often cost between $1 million and $1.5
million USD. 3.0 tesla scanners often cost between $2 million and $2.3 million USD.
Construction of MRI suites can cost up to $500,000 USD, or more, depending on project
scope.

MRI scanners have been significant sources of revenue for healthcare providers in the US.
This is because of favorable reimbursement rates from insurers and federal government
programs. Insurance reimbursement is provided in two components, an equipment charge
for the actual performance of the MRI scan and professional charge for the radiologist's
review of the images and/or data. In the US Northeast, an equipment charge might be
$3,500 and a professional charge might be $350. Some insurance companies require
preapproval of an MRI procedure as a condition for coverage.

In the US, the 2007 Deficit Reduction Act (DRA) significantly reduced reimbursement rates
paid by federal insurance programs for the equipment component of many scans, shifting
the economic landscape. Many private insurers have followed suit.

Safety

Death and injuries have occurred from projectiles created by the magnetic field, although
relatively few compared to the millions of examinations administered. J L J MRI makes
use of powerful magnetic fields which, though they have not been demonstrated to cause
direct biological damage, can interfere with metallic and electromechanical devices.
Additional (small) risks are presented by the radio frequency systems, components or
elements of the MRI system's operation, elements of the scanning procedure and
medications that may be administered to facilitate MRI imaging.

There are many steps that the MRI patient and referring physician can take to help reduce
the remaining risks, including providing a full, accurate and thorough medical history to the
MRI provider.

Several of the specific MRI safety considerations are identified below:

Implants and foreign bodies

Pacemakers are generally considered an absolute contraindication towards MRI scanning,
though highly specialized protocols have been developed to permit scanning of select
pacing devices. Several cases of arrhythmia or death have been reported in patients with
pacemakers who have undergone MRI scanning without appropriate precautions. Notably,
the Medtronic company has received FDA approval for the first-ever clinical trial for a
MR-Conditional pacemaker device, which has already received regulatory approval in
Europe. Other electronic implants have varying contraindications, depending upon scanner
technology, and implant properties, scanning protocols and anatomy being imaged.

Many other forms of medical or biostimulation implants may be contraindicated for MRI
scans. These may include vagus nerve stimulators, implantable cardioverter-defibrillators,
loop recorders, insulin pumps, cochlear implants, deep brain stimulators, and many others.
Medical device patients should always present complete information (manufacturer, model,
serial number and date of implantation) about all implants to both the referring physician
and to the radiologist or technologist before entering the room for the MRI scan.

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While these implants pose a current problem, scientists and manufacturers are working on
improved designs which will further minimize the risks that MRI scans pose to medical
device operations. One such development in the works is a nano-coating for implants
intended to screen them from the radio frequency waves, helping to make MRI exams
available to patients currently prohibited from receiving them. The current article c ^ for
this is from New Scientist.

Ferromagnetic foreign bodies (e.g. shell fragments), or metallic implants (e.g. surgical
prostheses, aneurysm clips) are also potential risks, and safety aspects need to be
considered on an individual basis. Interaction of the magnetic and radio frequency fields
with such objects can lead to trauma due to movement of the object in the magnetic field,
thermal injury from radio-frequency induction heating of the object, or failure of an
implanted device. These issues are especially problematic when dealing with the eye. Most
MRI centers require an orbital x-ray to be performed on anyone suspected of having metal
fragments in their eyes, something not uncommon in metalworking.

Because of its non-ferromagnetic nature and poor electrical conductivity, titanium and its
alloys are useful for long term implants and surgical instruments intended for use in
image-guided surgery. In particular, not only is titanium safe from movement from the
magnetic field, but artifacts around the implant are less frequent and less severe than with
more ferromagnetic materials e.g. stainless steel. Artifacts from metal frequently appear as
regions of empty space around the implant - frequently called 'black-hole artifact' e.g. a
3mm titanium alloy coronary stent may appear as a 5mm diameter region of empty space
on MRI, whereas around a stainless steel stent, the artifact may extend for 10-20 mm or
more.

In 2006, a new classification system for implants and ancillary clinical devices has been
developed by ASTM International and is now the standard supported by the US Food and
Drug Administration:

MR-Safe — The device or implant is completely non-magnetic,
non-electrically conductive, and non-RF reactive, eliminating all of
the primary potential threats during an MRI procedure.

MR-Conditional — A device or implant that may contain magnetic,
electrically conductive or RF-reactive components that is safe for
operations in proximity to the MRI, provided the conditions for
safe operation are defined and observed (such as 'tested safe to
1.5 teslas' or 'safe in magnetic fields below 500 gauss in
strength').

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MR-Unsafe — Nearly self-explanatory, this category is reserved
for objects that are significantly ferromagnetic and pose a clear
and direct threat to persons and equipment within the magnet
room.

Though the current classification system was originally developed
for regulatory-approved medical devices, it is being applied to all
manner of items, appliances and equipment intended for use in the
MR environment.

In the case of pacemakers, the risk is thought to be primarily RF

induction in the pacing electrodes/wires causing inappropriate pacing of the heart, rather
than the magnetic field affecting the pacemaker itself. Much research and development is
being undertaken, and many tools are being developed in order to predict the effects of the
RF fields inside the body.

Patients who have been prescribed MRI exams who are concerned about safety may be
interested in the 10 Questions To Ask Your MRI Provider L .

MRI providers who wish to measure the degree to which they have effectively addressed
the safety issues for patients and staff may be interested in the MRI Suite Safety Calculator
L J provided through a radiology website.

Projectile or missile effect

As a result of the very high strength of the magnetic field needed to produce scans
(frequently up to 60,000 times the earth's own magnetic field effects), there are several
incidental safety issues addressed in MRI facilities. Missile-effect accidents, where
ferromagnetic objects are attracted to the center of the magnet, have resulted in injury and
death. J L J A video simulation of a fatal projectile effect accident L J illustrates the
extreme power that contemporary MRI equipment can exert on ferromagnetic objects.

In order to help reduce the risks of projectile accidents, ferromagnetic objects and devices
are typically prohibited in proximity to the MRI scanner, with non-ferromagnetic versions of
many tools and devices typically retained by the scanning facility. Patients undergoing MRI
examinations are required to remove all metallic objects, often by changing into a gown or
scrubs.

New ferromagnetic-only detection devices are proving highly effective in supplementing
conventional screening techniques in many leading hospitals and imaging centers and are
now recommended by the American College of Radiology's Guidance Document for Safe MR
Practices: 2007 L , the United States' Veterans Administration's Design Guide L and the

[521

Joint Commission's Sentinel Event Alert #38 .

The magnetic field and the associated risk of missile-effect accidents remains a permanent
hazard — as superconductive MRI magnets retain their magnetic field, even in the event of
a power outage.

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Radio frequency energy

A powerful radio transmitter is needed for excitation of proton spins. This can heat the body
to the point of risk of hyperthermia in patients, particularly in obese patients or those with
thermoregulation disorders. Several countries have issued restrictions on the maximum
specific absorption rate that a scanner may produce.

Peripheral nerve stimulation (PNS)

The rapid switching on and off of the magnetic field gradients is capable of causing nerve
stimulation. Volunteers report a twitching sensation when exposed to rapidly switched
fields, particularly in their extremities. The reason the peripheral nerves are stimulated is
that the changing field increases with distance from the center of the gradient coils (which
more or less coincides with the center of the magnet). Note however that when imaging the
head, the heart is far off-center and induction of even a tiny current into the heart must be
avoided at all costs. Although PNS was not a problem for the slow, weak gradients used in
the early days of MRI, the strong, rapidly-switched gradients used in techniques such as
EPI, fMRI, diffusion MRI, etc. are indeed capable of inducing PNS. American and European
regulatory agencies insist that manufacturers stay below specified dB/dt limits (dB/dt is the
change in field per unit time) or else prove that no PNS is induced for any imaging
sequence. As a result of dB/dt limitation, commercial MRI systems cannot use the full rated
power of their gradient amplifiers.

Acoustic noise

Switching of field gradients causes a change in the Lorentz force experienced by the
gradient coils, producing minute expansions and contractions of the coil itself. As the
switching is typically in the audible frequency range, the resulting vibration produces loud
noises (clicking or beeping). This is most marked with high-field machines and
rapid-imaging techniques in which sound intensity can reach 120 dB(A) (equivalent to a jet
engine at take-off) [53] .

Appropriate use of ear protection is essential for anyone inside the MRI scanner room
during the examination. J

Cryogens

As described above in 'Scanner Construction And Operation', many MRI scanners rely on
cryogenic liquids to enable superconducting capabilities of the electromagnetic coils within.
Though the cryogenic liquids most frequently used are non-toxic, their physical properties
present specific hazards.

An emergency shut-down of a superconducting electromagnet, an operation known as
"quenching", involves the rapid boiling of liquid helium from the device. If the rapidly
expanding helium cannot be dissipated through an external vent, sometimes referred to as
'quench pipe', it may be released into the scanner room where it may cause displacement of

[55]

the oxygen and present a risk of asphyxiation. 1 J

Liquid helium, the most commonly used cryogen in MRI, undergoes near explosive
expansion as it changes from liquid to a gaseous state. Rooms built in support of
superconducting MRI equipment should be equipped with pressure relief mechanisms
and an exhaust fan, in addition to the required quench pipe.

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Since a quench results in rapid loss of all cryogens in the magnet, recommissioning the
magnet is extremely expensive and time-consuming. Spontaneous quenches are uncommon,
but may also be triggered by equipment malfunction, improper cryogen fill technique,
contaminates inside the cryostat, or extreme magnetic or vibrational disturbances.

Contrast agents

The most commonly used intravenous contrast agents are based on chelates of gadolinium.
In general, these agents have proved safer than the iodinated contrast agents used in X-ray
radiography or CT. Anaphylactoid reactions are rare, occurring in approx. 0.03-0.1%. Of
particular interest is the lower incidence of nephrotoxicity, compared with iodinated
agents, when given at usual doses— this has made contrast-enhanced MRI scanning an
option for patients with renal impairment, who would otherwise not be able to undergo
contrast-enhanced CT. J

Although gadolinium agents have proved useful for patients with renal impairment, in
patients with severe renal failure requiring dialysis there is a risk of a rare but serious
illness, nephrogenic systemic fibrosis, that may be linked to the use of certain
gadolinium-containing agents. The most frequently linked is gadodiamide, but other agents
have been linked too. Although a causal link has not been definitively established,
current guidelines in the United States are that dialysis patients should only receive
gadolinium agents where essential, and that dialysis should be performed as soon as
possible after the scan is complete, in order to remove the agent from the body
promptly. In Europe where more gadolinium-containing agents are available, a

classification of agents according to potential risks has been released. J L J

Pregnancy

No effects of MRI on the fetus have been demonstrated. In particular, MRI avoids the
use of ionizing radiation, to which the fetus is particularly sensitive. However, as a
precaution, current guidelines recommend that pregnant women undergo MRI only when
essential. This is particularly the case during the first trimester of pregnancy, as
organogenesis takes place during this period. The concerns in pregnancy are the same as
for MRI in general, but the fetus may be more sensitive to the effects— particularly to
heating and to noise. However, one additional concern is the use of contrast agents;
gadolinium compounds are known to cross the placenta and enter the fetal bloodstream,
and it is recommended that their use be avoided.

Despite these concerns, MRI is rapidly growing in importance as a way of diagnosing and
monitoring congenital defects of the fetus because it can provide more diagnostic
information than ultrasound and it lacks the ionizing radiation of CT. MRI without contrast
agents is the imaging mode of choice for pre-surgical, in-utero diagnosis and evaluation of
fetal tumors, primarily teratomas, facilitating open fetal surgery, other fetal interventions,
and planning for procedures (such as the EXIT procedure) to safely deliver and treat babies
whose defects would otherwise be fatal.

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Claustrophobia and discomfort

Due to the construction of some MRI scanners, they can be potentially unpleasant to lie in.
Older models of closed bore MRI systems feature a fairly long tube or tunnel. The part of
the body being imaged needs to lie at the center of the magnet which is at the absolute
center of the tunnel. Because scan times on these older scanners may be long (occasionally
up to 40 minutes for the entire procedure), people with even mild claustrophobia are
sometimes unable to tolerate an MRI scan without management. Modern scanners may
have larger bores (up to 70 cm) and scan times are shorter. This means that claustrophobia
is less of an issue, and many patients now find MRI an innocuous and easily tolerated
procedure.

Nervous patients may still find the following strategies helpful:

• Advance preparation

• visiting the scanner to see the room and practice lying on the table

• visualization techniques

• chemical sedation

• general anesthesia

• Coping while inside the scanner

• holding a "panic button"

• closing eyes as well as covering them (e.g. washcloth, eye mask)

• listening to music on headphones or watching a movie with a Head-mounted display
while in the machine

• Scan Rooms with lighting, sound and images on the wall. Some rooms come with
images on the walls or ceiling.

Alternative scanner designs, such as open or upright systems, can also be helpful where
these are available. Though open scanners have increased in popularity, they produce
inferior scan quality because they operate at lower magnetic fields than closed scanners.
However, commercial 1.5 Tesla open systems have recently become available, providing
much better image quality than previous lower field strength open models .

For babies and young children chemical sedation or general anesthesia are the norm, as
these subjects cannot be instructed to hold still during the scanning session. Obese patients
and pregnant women may find the MRI machine to be a tight fit. Pregnant women may also
have difficulty lying on their backs for an hour or more without moving.

Acoustic noise associated with the operation of an MRI scanner can also exacerbate the
discomfort associated with the procedure.

Nephrogenic systemic fibrosis (NSF) or Nephrogenic fibrosing dermopathy is a rare and
serious syndrome that involves fibrosis of skin, joints, eyes, and internal organs. Its cause is
not fully understood, but it seems to be associated with exposure to gadolinium (which is
frequently used as a contrast substance for MRIs) in patients with severe kidney failure.

Guidance

Safety issues, including the potential for biostimulation device interference, movement of
ferromagnetic bodies, and incidental localized heating, have been addressed in the
American College of Radiology's White Paper on MR Safety which was originally published
in 2002 and expanded in 2004. The ACR White Paper on MR Safety has been rewritten and
was released early in 2007 under the new title ACR Guidance Document for Safe MR

Nuclear Magnetic resonance imaging

370

Practices [50] .

In December 2007, the Medicines in Healthcare product Regulation Agency (MHRA), a UK

healthcare regulatory body, issued their Safety Guidelines for Magnetic Resonance Imaging

Equipment in Clinical Use .

In February 2008, the Joint Commission, a US healthcare accrediting organization, issued a

Sentinel Event Alert #38 L J , their highest patient safety advisory, on MRI safety issues.

In July 2008, the United States Veterans Administration, a federal governmental agency

serving the healthcare needs of former military personnel, issued a substantial revision to

their MRI Design Guide c ] which includes physical or facility safety considerations.

The European Physical Agents Directive

The European Physical Agents (Electromagnetic Fields) Directive is legislation adopted in
European legislature. Originally scheduled to be required by the end of 2008, each
individual state within the European Union must include this directive in its own law by the
end of 2012. Some member nations passed complying legislation and are now attempting to
repeal their state laws in expectation that the final version of the EU Physical Agents
Directive will be substantially revised prior to the revised adoption date.

The directive applies to occupational exposure to electromagnetic fields (not medical
exposure) and was intended to limit workers' acute exposure to strong electromagnetic
fields, as may be found near electricity substations, radio or television transmitters or
industrial equipment. However, the regulations impact significantly on MRI, with separate
sections of the regulations limiting exposure to static magnetic fields, changing magnetic
fields and radio frequency energy. Field strength limits are given which may not be
exceeded for any period of time. An employer may commit a criminal offense by allowing a
worker to exceed an exposure limit if that is how the Directive is implemented in a
particular Member State.

The Directive is based on the international consensus of established effects of exposure to
electromagnetic fields, and in particular the advice of the European Commissions's advisor,
the International Commission on Non-Ionizing Radiation Protection (ICNIRP). The aims of
the Directive, and the ICNIRP guidelines upon which it is based, are to prevent exposure to
potentially harmful fields. The actual limits in the Directive are very similar to the limits
advised by the Institute of Electrical and Electronics Engineers, with the exception of the
frequencies produced by the gradient coils, where the IEEE limits are significantly higher.

Many Member States of the EU already have either specific EMF regulations or (as in the
UK) a general requirement under workplace health and safety legislation to protect
workers against electromagnetic fields. In almost all cases the existing regulations are
aligned with the ICNIRP limits so that the Directive should, in theory, have little impact on
any employer already meeting their legal responsibilities.

The introduction of the Directive has brought to light an existing potential issue with
occupational exposures to MRI fields. There are at present very few data on the number or
types of MRI practice that might lead to exposures in excess of the levels of the
Directive. J There is a justifiable concern amongst MRI practitioners that if the

Directive were to be enforced more vigorously than existing legislation, the use of MRI
might be restricted, or working practices of MRI personnel might have to change.

In the initial draft a limit of static field strength to 2 T was given. This has since been
removed from the regulations, and whilst it is unlikely to be restored as it was without a

Nuclear Magnetic resonance imaging

371

strong justification, some restriction on static fields may be reintroduced after the matter
has been considered more fully by ICNIRP. The effect of such a limit might be to restrict
the installation, operation and maintenance of MRI scanners with magnets of 2 T and
stronger. As the increase in field strength has been instrumental in developing higher
resolution and higher performance scanners, this would be a significant step back. This is
why it is unlikely to happen without strong justification.

Individual government agencies and the European Commission have now formed a working
group to examine the implications on MRI and to try to address the issue of occupational
exposures to electromagnetic fields from MRI.

2003 Nobel Prize

Reflecting the fundamental importance and applicability of MRI in the medical field, Paul
Lauterbur of the University of Illinois at Urbana-Champaign and Sir Peter Mansfield of the
University of Nottingham were awarded the 2003 Nobel Prize in Physiology or Medicine for
their "discoveries concerning magnetic resonance imaging". The Nobel Prize committee
acknowledged Lauterbur' s insight of using magnetic field gradients to introduce spatial
localization, a discovery that allowed rapid acquisition of 2D images. Sir Peter Mansfield
was credited with introducing the mathematical formalism and developing techniques for
efficient gradient utilization and fast imaging. The actual research by Paul Lauterbur was
done almost 30 years ago at Stony Brook University in Stony Brook, NY.

The award was vigorously protested by Raymond Vahan Damadian, founder of FONAR
Corporation, who claimed that he was the inventor of MRI, and that Lauterbur and
Mansfield had merely refined the technology. An ad hoc group, called "The Friends of
Raymond Damadian", took out full-page advertisements in the New York Times and The
Washington Post entitled "The Shameful Wrong That Must Be Righted", demanding that he
be awarded at least a share of the Nobel Prize . Also, in a letter to Physics Today,

Herman Carr pointed out his own early use of field gradients for one-dimensional MR

[70]

imaging 1 J .

See also

Earth's field NMR (EFNMR)
Electron-spin resonance (spin physics)
History of brain imaging
Medical imaging
Magnetic immunoassay

Nuclear magnetic resonance (NMR)

Relaxation

Robinson oscillator

Rabi cycle

Magnetic resonance microscopy
Magnetic Particle Imaging (MPI)
Magnetic resonance elastography
Neuroimaging software
Nephrogenic fibrosing dermopathy

Nobel Prize controversies

Nuclear Magnetic resonance imaging

372

Footnotes

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External links

BIGS-animation (http://www.bigs.de/BLH/en/index.php?option=com_content&

view=category&layout=blog&id=100&Itemid=268) - Physics of MRI like spin,

modification of spin or pulse sequences

MDCT (http://www.mdct.com.au) - Free Radiology Resource For Radiographers,

Radiologists and Technical Assistants

A Guided Tour of MRI: An introduction for laypeople (http://www.magnet.fsu.edu/

education/tutorials/magnetacademy/mri/) National High Magnetic Field Laboratory

Joseph P. Hornak, Ph.D. The Basics of MRI (http://www.cis.rit.edu/htbooks/mri/).

Underlying physics and technical aspects.

Video: What to Expect During Your MRI Exam (http://www.imrser.org/PatientVideo.

html) from the Institute for Magnetic Resonance Safety, Education, and Research

(IMRSER)

3D Animation Movie about MRI Exam (http://www.patiencys.com/MRI/)

Interactive Flash Animation on MRI (http://www.e-mri.org) - Online Magnetic

Resonance Imaging physics and technique course

International Society for Magnetic Resonance in Medicine (http://www.ismrm.org)

Article on helium scarcity and potential effects on NMR and MRI communities (http://

www. ebyte.it/stan/blog. html#08Feb29)

Danger of objects flying into the scanner (http://www.simplyphysics.com/

flyingobj e cts . html)

Video compiled of MRI scans showing arachnoid cyst (http://www.youtube.com/

watch?v=PF_mDsdxSsg)

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Neuroimaging

Neuroimaging includes the use of various techniques
to either directly or indirectly image the structure,
function/pharmacology of the brain. It is a relatively

new

discipline

within

medicine

and

neuroscience/psychology.

Overview

Neuroimaging falls into two broad categories:

• Structural imaging, which deals with the structure of
the brain and the diagnosis of gross (large scale)
intracranial disease (such as tumor), and injury, and

• functional imaging, which is used to diagnose
metabolic diseases and lesions on a finer scale (such
as Alzheimer's disease) and also for neurological and
cognitive psychology research and building
brain-computer interfaces.

Functional imaging enables, for example, the
processing of information by centers in the brain to be
visualized directly. Such processing causes the involved
area of the brain to increase metabolism and "light up"
on the scan.

Para-sagittal MRI of the head in a
patient with benign familial

macrocephaly.

History

In 1918 the American neurosurgeon Walter Dandy

introduced the technique of ventriculography. X-ray

images of the ventricular system within the brain were

obtained by injection of filtered air directly into one or

both lateral ventricles of the brain. Dandy also observed that air introduced into the

subarachnoid space via lumbar spinal puncture could enter the cerebral ventricles and also

demonstrate the cerebrospinal fluid compartments around the base of the brain and over

its surface. This technique was called pneumoencephalography.

In 1927 Egas Moniz, professor of neurology in Lisbon and recipient of the Nobel Prize for
Physiology or Medicine in 1949, introduced cerebral angiography, whereby both normal
and abnormal blood vessels in and around the brain could be visualized with great
accuracy.

In the early 1970s, Allan McLeod Cormack and Godfrey Newbold Hounsfield introduced
computerized axial tomography (CAT or CT scanning), and ever more detailed anatomic
images of the brain became available for diagnostic and research purposes. Cormack and
Hounsfield won the 1979 Nobel Prize for Physiology or Medicine for their work. Soon after
the introduction of CAT in the early 1980s, the development of radioligands allowed single
photon emission computed tomography (SPECT) and positron emission tomography (PET)

Neuroimaging

377

of the brain.

More or less concurrently, magnetic resonance imaging (MRI or MR scanning) was
developed by researchers including Peter Mansfield and Paul Lauterbur, who were
awarded the Nobel Prize for Physiology or Medicine in 2003. In the early 1980s MRI was
introduced clinically, and during the 1980s a veritable explosion of technical refinements
and diagnostic MR applications took place. Scientists soon learned that the large blood flow
changes measured by PET could also be imaged by the correct type of MRI. Functional
magnetic resonance imaging (fMRI) was born, and since the 1990s, fMRI has come to
dominate the brain mapping field due to its low invasiveness, lack of radiation exposure,
and relatively wide availability. As noted above fMRI is also beginning to dominate the field
of stroke treatment.

In early 2000s the field of neuroimaging reached the stage where limited practical
applications of functional brain imaging have become feasible. The main application area is
crude forms of brain-computer interface.

Brain imaging techniques

Computed Axial Tomography

Computed Tomography (CT) or Computed Axial Tomography (CAT) scanning uses a series
of x-rays of the head taken from many different directions. Typically used for quickly
viewing brain injuries, CT scanning uses a computer program that performs a numerical
integral calculation (the inverse Radon transform) on the measured x-ray series to estimate
how much of an x-ray beam is absorbed in a small volume of the brain. Typically the

information is presented as cross sections of the brain. 1 J

In approximation, the denser a material is, the whiter a volume of it will appear on the scan
(just as in the more familiar "flat" X-rays). CT scans are primarily used for evaluating
swelling from tissue damage in the brain and in assessment of ventricle size. Modern CT
scanning can provide reasonably good images in a matter of minutes.

Diffuse Optical Imaging

Diffuse Optical Imaging (DOI) or Diffuse Optical Tomography (DOT) is a medical imaging
modality which uses near infrared light to generate images of the body. The technique
measures the optical absorption of haemoglobin, and relies on the absorption spectrum of
haemoglobin varying with its oxygenation status.

Event Related Optical Signal

Event Related Optical Signal (EROS) is a brain-scanning technique which uses infrared
light through optical fibers to measure changes in optical properties of active areas of the
cerebral cortex. Whereas techniques such as diffuse optical imaging (DOT) and near
infrared spectroscopy (NIRS) measure optical absorption of haemoglobin, and thus are
based on blood flow, EROS takes advantage of the scattering properties of the neurons
themselves, and thus provides a much more direct measure of cellular activity. EROS can
pinpoint activity in the brain within millimeters (spatially) and within milliseconds
(temporally). Its biggest downside is the inability to detect activity more than a few
centimeters deep. EROS is a new, relatively inexpensive technique that is non-invasive to
the test subject. It was developed at the University of Illinois at Urbana-Champaign where

Neuroimaging

378

it is now used in the Cognitive Neuroimaging Laboratory of Dr. Gabriele Gratton and Dr
Monica Fabiani.

Magnetic Resonance Imaging

Magnetic Resonance Imaging (MRI) uses magnetic
fields and radio waves to produce high quality two- or
three-dimensional images of brain structures without
use of ionizing radiation (X-rays) or radioactive tracers.
During an MRI, a large cylindrical magnet creates a
magnetic field around the head of the patient through
which radio waves are sent. When the magnetic field is
imposed, each point in space has a unique radio
frequency at which the signal is received and
transmitted (Preuss). Sensors read the frequencies and
a computer uses the information to construct an image.
The detection mechanisms are so precise that changes
in structures over time can be detected.

Using MRI, scientists can create images of both surface
and subsurface structures with a high degree of anatomical detail. MRI scans can produce
cross sectional images in any direction from top to bottom, side to side, or front to back.
The problem with original MRI technology was that while it provides a detailed assessment
of the physical appearance, water content, and many kinds of subtle derangements of
structure of the brain (such as inflammation or bleeding), it fails to provide information
about the metabolism of the brain (i.e. how actively it is functioning) at the time of imaging.
A distinction is therefore made between "MRI imaging" and "functional MRI imaging"
(fMRI), where MRI provides only structural information on the brain while fMRI yields both
structural and functional data.

Neuroimaging

379

Functional Magnetic Resonance Imaging

Functional Magnetic Resonance Imaging (fMRI) relies
on the paramagnetic properties of oxygenated and
deoxygenated hemoglobin to see images of changing
blood flow in the brain associated with neural activity.
This allows images to be generated that reflect which
brain structures are activated (and how) during
performance of different tasks.

Most fMRI scanners allow subjects to be presented with

different visual images, sounds and touch stimuli, and

to make different actions such as pressing a button or

moving a joystick. Consequently, fMRI can be used to

reveal brain structures and processes associated with

perception, thought and action. The resolution of fMRI

is about 2-3 millimeters at present, limited by the

spatial spread of the hemodynamic response to neural

activity. It has largely superseded PET for the study of

brain activation patterns. PET, however, retains the

significant advantage of being able to identify specific

brain receptors (or transporters) associated with particular neurotransmitters through its

ability to image radiolabeled receptor "ligands" (receptor ligands are any chemicals that

stick to receptors).

Axial MRI slice at the level of the basal

ganglia, showing fMRI BOLD signal

changes overlayed in red (increase)

and blue (decrease) tones.

As well as research on healthy subjects, fMRI is increasingly used for the medical diagnosis
of disease. Because fMRI is exquisitely sensitive to blood flow, it is extremely sensitive to
early changes in the brain resulting from ischemia (abnormally low blood flow), such as the
changes which follow stroke. Early diagnosis of certain types of stroke is increasingly
important in neurology, since substances which dissolve blood clots may be used in the first
few hours after certain types of stroke occur, but are dangerous to use afterwards. Brain
changes seen on fMRI may help to make the decision to treat with these agents. With
between 72% and 90% accuracy where chance would achieve 0.8%, fMRI techniques can

roi

decide which of a set of known images the subject is viewing. 1 J

MagnetoEncephaloGraphy

Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic
fields produced by electrical activity in the brain via extremely sensitive devices such as
superconducting quantum interference devices (SQUIDs). MEG offers a very direct
measurement neural electrical activity (compared to fMRI for example) with very high
temporal resolution but relatively low spatial resolution. The advantage of measuring the
magnetic fields produced by neural activity is that they are not distorted by surrounding
tissue, unlike the electric fields measured by EEG (particularly the skull and scalp).

There are many uses for the MEG, including assisting surgeons in localizing a pathology,
assisting researchers in determining the function of various parts of the brain,
neurofeedback, and others.

Neuroimaging

380

Positron Emission Tomography

Positron Emission Tomography (PET) measures
emissions from radioactively labeled metabolically
active chemicals that have been injected into the

bloodstream.

The

emission

data

are

computer-processed to produce 2- or 3-dimensional

images of the distribution of the chemicals throughout

the brain. L J The positron emitting radioisotopes used

are produced by a cyclotron, and chemicals are labeled

with these radioactive atoms. The labeled compound,

called a radiotracer, is injected into the bloodstream

and eventually makes its way to the brain. Sensors in

the PET scanner detect the radioactivity as the

compound accumulates in various regions of the brain.

A computer uses the data gathered by the sensors to

create multicolored 2- or 3-dimensional images that

show where the compound acts in the brain. Especially useful are a wide array of ligands

used to map different aspects of neurotransmitter activity, with by far the most commonly

used PET tracer being a labeled form of glucose (see FDG).

The greatest benefit of PET scanning is that different compounds can show blood flow and
oxygen and glucose metabolism in the tissues of the working brain. These measurements
reflect the amount of brain activity in the various regions of the brain and allow to learn
more about how the brain works. PET scans were superior to all other metabolic imaging
methods in terms of resolution and speed of completion (as little as 30 seconds), when they
first became available. The improved resolution permitted better study to be made as to the
area of the brain activated by a particular task. The biggest drawback of PET scanning is
that because the radioactivity decays rapidly, it is limited to monitoring short tasks. c ^
Before fMRI technology came online, PET scanning was the preferred method of functional
(as opposed to structural) brain imaging, and it still continues to make large contributions
to neuroscience.

PET scanning is also used for diagnosis of brain disease, most notably because brain
tumors, strokes, and neuron-damaging diseases which cause dementia (such as Alzheimer's
disease) all cause great changes in brain metabolism, which in turn causes easily detectable
changes in PET scans. PET is probably most useful in early cases of certain dementias (with
classic examples being Alzheimer's disease and Pick's disease) where the early damage is
too diffuse and makes too little difference in brain volume and gross structure to change CT
and standard MRI images enough to be able to reliably differentiate it from the "normal"
range of cortical atrophy which occurs with aging (in many but not all) persons, and which
does not cause clinical dementia.

Neuroimaging

381

Single Photon Emission Computed Tomography

Single Photon Emission Computed Tomography (SPECT) is similar to PET and uses gamma
ray emitting radioisotopes and a gamma camera to record data that a computer uses to
construct two- or three-dimensional images of active brain regions SPECT relies on an
injection of radioactive tracer, which is rapidly taken up by the brain but does not
redistribute. Uptake of SPECT agent is nearly 100% complete within 30 - 60s, reflecting
cerebral blood flow (CBF) at the time of injection. These properties of SPECT make it
particularly well suited for epilepsy imaging, which is usually made difficult by problems
with patient movement and variable seizure types. SPECT provides a "snapshot" of cerebral
blood flow since scans can be acquired after seizure termination (so long as the radioactive
tracer was injected at the time of the seizure). A significant limitation of SPECT is its poor
resolution (about 1 cm) compared to that of MRI.

Like PET, SPECT also can be used to differentiate different kinds of disease processes
which produce dementia, and it is increasingly used for this purpose. Neuro-PET has a
disadvantage of requiring use of tracers with half-lives of at most 110 minutes, such as
FDG. These must be made in a cyclotron, and are expensive or even unavailable if
necessary transport times are prolonged more than a few half-lives. SPECT, however, is
able to make use of tracers with much longer half-lives, such as technetium-99m, and as a
result, is far more widely available.

See also

Brain mapping
Functional neuroimaging

functional near-infrared imaging
History of brain imaging
Human Cognome Project
Magnetic resonance imaging
Magnetoencephalography
Medical imaging
Neuroimaging software
Statistical parametric mapping
Transcranial magnetic stimulation
Voxel-based morphometry
Physioscan

References

[1] Jeeves, p. 21

[2] Smith, Kerri (March 5, 2008).

"http://www.nature.com/news/2008/080305/full/news. 2008. 650. html | Mind-reading with a brain scan". Nature

News (Nature Publishing Group), http://www.nature.com/news/2008/080305/full/news.2008.650.html.

Retrieved on 2008-03-05.
[3] Keim, Brandon (March 5, 2008). "http://www.wired.com/science/discoveries/news/2008/03/mri_visionlBrain

Scanner Can Tell What You're Looking At". Wired News (CondeNet). http://www.wired.com/science/

discoveries/news/2008/03/mri_vision. Retrieved on 2008-03-05.
[4] Nilsson, page 57
[5] Nilson, pg. 60
[6] Philip Ball Brain Imaging Explained

Neuroimaging

382

Further reading

Philip Ball. Brain Imaging Explained '.

J. Graham Beaumont (1983). Introduction to Neuropsychology. New York: The Guilford

Press.

Jean-Pierre Changeux (1985). Neuronal Man: The Biology of Mind. New York: Oxford

University Press.

Malcom Jeeves (1994). Mind Fields: Reflections on the Science of Mind and Brain. Grand

Rapids, MI: Baker Books.

Richard G. Lister and Herbert J. Weingartner (1991). Perspectives on Cognitive

Neuroscience. New York: Oxford University Press.

James Mattson and Merrill Simon (1996). The Pioneers ofNMR and Magnetic Resonance

in Medicine. United States: Dean Books Company.

Lars-Goran Nilsson and Hans J. Markowitsch (1999). Cognitive Neuroscience of Memory.

Seattle: Hogrefe & Huber Publishers.

Donald A. Norman (1981). Perspectives on Cognitive Science. New Jersey: Ablex

Publishing Corporation.

Brenda Rapp (2001). The Handbook of Cognitive Neuropsychology. Ann Arbor, MI:

Psychology Press.

External links

• The Whole Brain Atlas @ Harvard (http://www.med.harvard.edu/AANLIB/home.html)

• The McConnell Brain Imaging Center, McGill University (http://www2.bic. mni.mcgill.
ca/)

• The American Society of Neuroimaging (ASN) (http://www.asnweb.org/).

• UCLA Neuroimaging Training Program (http://www.brainmapping.org/NITP).

• Laboratory of Neuro Imaging (http://www.loni.ucla.edu/) at UCLA

• A Neuroimaging portal (http://www.mri-tutorial.com/)

• BrainMapping.org, a free BrainMapping community information portal (http://www.
brainmapping.org/)

• Lecture notes on mathematical aspects of neuroimaging (http://www.fil.ion.ucl.ac.uk/
~wpenny/mbi/) by Will Penny, University College London

• "Transcranial Magnetic Stimulation" (http://www.ai.mit.edu/projects/medical-vision/
surgery/tms.html). by Michael Leventon in association with MIT AI Lab.

• Foundations offMRI (http://www.ee.duke.edu/~jshorey/MRIHomepage/MRImain.
html) by Jamie Shorey.

• International Society for Neuroimaging in Psychiatry (ISNIP) (http://www.isnip.org/)

Computed tomography

383

Computed tomography

]Computed
tomography
(CT) is

medical

imaging

method

employing

tomography.

Digital

geometry

processing is

used to

generate

three-dimensional

A Multislice CT Scanner:

[http://www.toshiba-medical.eu/upload/CT/AquilionONE/System%20Images/AQlEnlarge.jpg

image of the

inside of an

object from a

large series of two-dimensional X-ray images taken around a single axis of rotation. The

word "tomography" is derived from the Greek tomos (slice) and graphein (to write).

Computed tomography was originally known as the "EMI scan" as it was developed at a

research branch of EMI, a company best known today for its music and recording business.

It was later known as computed axial tomography (CAT or CT scan) and body section

rontgenography.

CT produces a volume of data which can be manipulated, through a process known as
"windowing", in order to demonstrate various bodily structures based on their ability to
block the X-ray/R6ntgen beam. Although historically the images generated were in the axial
or transverse plane, orthogonal to the long axis of the body, modern scanners allow this
volume of data to be reformatted in various planes or even as volumetric (3D)
representations of structures. Although most common in medicine, CT is also used in other
fields, such as nondestructive materials testing. Another example is the DigiMorph project
at the University of Texas at Austin which uses a CT scanner to study biological and
paleontological specimens.

History

In the early 1900s, the Italian radiologist Alessandro Vallebona proposed a method to
represent a single slice of the body on the radiographic film. This method was known as
tomography. The idea is based on simple principles of projective geometry: moving
synchronously and in opposite directions the X-ray tube and the film, which are connected
together by a rod whose pivot point is the focus; the image created by the points on the
focal plane appears sharper, while the images of the other points annihilate as noise. This is

only marginally effective, as blurring occurs only in the

"x"

plane. There are also more

complex devices which can move in more than one plane and perform more effective
blurring.

Computed tomography

384

Tomography had been one of the pillars of radiologic diagnostics until the late 1970s, when
the availability of minicomputers and of the transverse axial scanning method, this last due
to the work of Godfrey Hounsfield and South African born Allan McLeod Cormack,
gradually supplanted it as the modality of CT.

The first commercially viable CT scanner was invented by Sir Godfrey Hounsfield in Hayes,
United Kingdom at EMI Central Research Laboratories using X-rays. Hounsfield conceived

his idea in 1967/ J and it was publicly announced in 1972. Allan McLeod Cormack of Tufts
University in Massachusetts independently invented a similar process, and both Hounsfield
and Cormack shared the 1979 Nobel Prize in Medicine.

The original 1971 prototype took 160
parallel readings through 180 angles, each
1° apart, with each scan taking a little over
five minutes. The images from these scans

took 2.5 hours to be processed by algebraic
reconstruction techniques on a large
computer. The scanner had a single
photomultiplier detector, and operated on
the Translate/Rotate principle.

It has been claimed that thanks to the
success of The Beatles, EMI could fund
research and build early models for medical
use. The first production X-ray CT
machine (in fact called the "EMI-Scanner")

was limited to making tomographic sections of the brain, but acquired the image data in
about 4 minutes (scanning two adjacent slices), and the computation time (using a Data
General Nova minicomputer) was about 7 minutes per picture. This scanner required the
use of a water-filled Perspex tank with a pre-shaped rubber "head-cap" at the front, which
enclosed the patient's head. The water-tank was used to reduce the dynamic range of the
radiation reaching the detectors (between scanning outside the head compared with
scanning through the bone of the skull). The images were relatively low resolution, being
composed of a matrix of only 80 x 80 pixels. The first EMI-Scanner was installed in Atkinson
Morley Hospital in Wimbledon, England, and the first patient brain-scan was made with it
in 1972.

Computed tomography

385

In the U.S., the first installation was at the
Mayo Clinic. As a tribute to the impact of
this system on medical imaging the Mayo
Clinic has an EMI scanner on display in the
Radiology Department.

The first CT system that could make images

of any part of the body and did not require

the "water tank" was the ACTA (Automatic

Computerized Transverse Axial) scanner

Georgetown University. This machine had

30 photomultiplier tubes as detectors and

completed a scan in only 9 translate/rotate

cycles, much faster than the EMI-scanner.

It used a DEC PDP11/34 minicomputer both to operate the servo-mechanisms and to

acquire and process the images. The Pfizer drug company acquired the prototype from the

university, along with rights to manufacture it. Pfizer then began making copies of the

prototype, calling it the "200FS" (FS meaning Fast Scan), which were selling as fast as they

could make them. This unit produced images in a 256x256 matrix, with much better

definition than the EMI-Scanner's 80x80

Previous studies

Tomography

A form of tomography can be performed by moving the X-ray source and detector during an
exposure. Anatomy at the target level remains sharp, while structures at different levels are
blurred. By varying the extent and path of motion, a variety of effects can be obtained, with
variable depth of field and different degrees of blurring of 'out of plane 1 structures. J :

Although largely obsolete, conventional tomography is still used in specific situations such
as dental imaging (orthopantomography) or in intravenous urography.

Tomosynthesis

Digital tomosynthesis combines digital image capture and processing with simple
tube/detector motion as used in conventional radiographic tomography. Although there are
some similarities to CT, it is a separate technique. In CT, the source/detector makes a
complete 360-degree rotation about the subject obtaining a complete set of data from
which images may be reconstructed. In digital tomosynthesis, only a small rotation angle
(e.g., 40 degrees) with a small number of discrete exposures (e.g., 10) are used. This
incomplete set of data can be digitally processed to yield images similar to conventional
tomography with a limited depth of field. However, because the image processing is digital,
a series of slices at different depths and with different thicknesses can be reconstructed
from the same acquisition, saving both time and radiation exposure.

Because the data acquired is incomplete, tomosynthesis is unable to offer the extremely
narrow slice widths that CT offers. However, higher resolution detectors can be used,
allowing very-high in-plane resolution, even if the Z-axis resolution is poor. The primary

Computed tomography

386

interest in tomosynthesis is in breast imaging, as an extension to mammography, where it
may offer better detection rates with little extra increase in radiation exposure.

Reconstruction algorithms for tomosynthesis are significantly different from conventional
CT, because the conventional filtered back projection algorithm requires a complete set of
data. Iterative algorithms based upon expectation maximization are most commonly used,
but are extremely computationally intensive. Some manufacturers have produced practical
systems using off-the-shelf GPUs to perform the reconstruction.

Diagnostic use

Since its introduction in the 1970s, CT has become an important tool in medical imaging to
supplement X-rays and medical ultrasonography. Although it is still quite expensive, it is the
gold standard in the diagnosis of a large number of different disease entities. It has more
recently begun to also be used for preventive medicine or screening for disease, for
example CT colonography for patients with a high risk of colon cancer. Although a number
of institutions offer full-body scans for the general population, this practice remains
controversial due to its lack of proven benefit, cost, radiation exposure, and the risk of
finding 'incidental' abnormalities that may trigger additional investigations.

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typically used to detect:

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fractures

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patient with a sudden severe
headache

3. a blood clot or bleeding within
the brain shortly after a patient
exhibits symptoms of a stroke

4. a stroke

5. brain tumors

6. enlarged brain cavities in
patients with hydrocephalus

7. diseases/malformations of the
skull

8. evaluate the extent of bone and
soft tissue damage in patients
with facial trauma, and planning
surgical reconstruction

9. diagnose diseases of the
temporal bone on the side of the
skull, which may be causing
hearing problems

10. determine whether inflammation or other changes are present in the paranasal sinuses

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A head CT showing displacement of the ventricles (the dark

structures) which are normally in the midline.

Computed tomography

387

12. guide the passage of a needle used to obtain a tissue sample (biopsy) from the brain

13. assess aneurysms or arteriovenous malformations

Chest

CT can be used for detecting both acute and chronic changes in the lung parenchyma, that
is, the internals of the lungs. It is particularly relevant here because normal two
dimensional x-rays do not show such defects. A variety of different techniques are used
depending on the suspected abnormality. For evaluation of chronic interstitial processes
(emphysema, fibrosis, and so forth), thin sections with high spatial frequency
reconstructions are used - often scans are performed both in inspiration and expiration.
This special technique is called High Resolution CT (HRCT). HRCT is normally done with
thin section with skipped areas between the thin sections. Therefore it produces a sampling
of the lung and not continuous images. Continuous images are provided in a standard CT of
the chest.

For detection of airspace disease (such as pneumonia) or cancer, relatively thick sections
and general purpose image reconstruction techniques may be adequate. IV contrast may
also be used as it clarifies the anatomy and boundaries of the great vessels and improves
assessment of the mediastinum and hilar regions for lymphadenopathy; this is particularly
important for accurate assessment of cancer.

CT angiography of the chest is also becoming the primary method for detecting pulmonary
embolism (PE) and aortic dissection, and requires accurately timed rapid injections of
contrast (Bolus Tracking) and high-speed helical scanners. CT is the standard method of
evaluating abnormalities seen on chest X-ray and of following findings of uncertain acute
significance.

More than 62 million scans are ordered each year, according to the 2007 New England
Journal of Medicine study. 31% of 62 million (19,2 million) is used for lung CT's.

Pulmonary angiogram

CT pulmonary angiogram (CTPA) is a medical diagnostic test used to diagnose
pulmonary embolism (PE). It employs computed tomography to obtain an image of the
pulmonary arteries.

It is a preferred choice of imaging in the diagnosis of PE due to its minimally invasive
nature for the patient, whose only requirement for the scan is a cannula (usually a 20G).

MDCT (multi detector CT) scanners give the optimum resolution and image quality for this
test. Images are usually taken on a 0.625 mm slice thickness, although 2 mm is sufficient.
50-100 mis of contrast is given to the patient at a rate of 4 ml/s. The tracker/locator is
placed at the level of the Pulmonary Arteries, which sit roughly at the level of the carina.
Images are acquired with the maximum intensity of radio-opaque contrast in the Pulmonary
Arteries. This is done using bolus tracking.

CT machines are now so sophisticated that the test can be done with a patient visit of 5
minutes with an approximate scan time of only 5 seconds or less.

Computed tomography

388

A normal CTPA scan will show the
contrast filling the pulmonary
vessels, looking bright white.
Ideally the aorta should be empty
of contrast to reduce any partial
volume artifact which may result
in a false positive. Any mass filling
defects, such as an embolus, will
appear dark in place of the
contrast, filling / blocking the
space where blood should be
flowing into the lungs.

Cardiac

Example of a CTPA, demonstrating a saddle embolus (dark
horizontal line) occluding the pulmonary arteries (bright white

triangle)

With the advent of subsecond
rotation combined with multi-slice
CT (up to 64-slice), high resolution
and high speed can be obtained at
the same time, allowing excellent imaging of the coronary arteries (cardiac CT
angiography). Images with an even higher temporal resolution can be formed using
retrospective ECG gating. In this technique, each portion of the heart is imaged more than
once while an ECG trace is recorded. The ECG is then used to correlate the CT data with
their corresponding phases of cardiac contraction. Once this correlation is complete, all
data that were recorded while the heart was in motion (systole) can be ignored and images
can be made from the remaining data that happened to be acquired while the heart was at
rest (diastole). In this way, individual frames in a cardiac CT investigation have a better
temporal resolution than the shortest tube rotation time.

Because the heart is effectively imaged more than once (as described above), cardiac CT
angiography results in a relatively high radiation exposure around 12 mSv. For the sake of
comparison, a chest X-ray carries a dose of approximately 0.02 L J to 0.2 mSv and natural
background radiation exposure is around 0.01 mSv/day. Thus, cardiac CTA is equivalent to
approximately 100-600 chest X-rays or over 3 years worth of natural background radiation.
Methods are available to decrease this exposure, however, such as prospectively
decreasing radiation output based on the concurrently acquired ECG (aka tube current
modulation.) This can result in a significant decrease in radiation exposure, at the risk of
compromising image quality if there is any arrhythmia during the acquisition. The
significance of radiation doses in the diagnostic imaging range has not been proven,
although the possibility of inducing an increased cancer risk across a population is a source
of significant concern. This potential risk must be weighed against the competing risk of not
performing a test and potentially not diagnosing a significant health problem such as
coronary artery disease.

It is uncertain whether this modality will replace invasive coronary catheterization.
Currently, it appears that the greatest utility of cardiac CT lies in ruling out coronary artery
disease rather than ruling it in. This is because the test has a high sensitivity (greater than
90%) and thus a negative test result means that a patient is very unlikely to have coronary
artery disease and can be worked up for other causes of their chest symptoms. This is

Computed tomography

389

termed a high negative predictive value. A positive result is less conclusive and often will
be confirmed (and possibly treated) with subsequent invasive angiography. The positive
predictive value of cardiac CTA is estimated at approximately 82% and the negative
predictive value is around 93%.

Dual Source CT scanners, introduced in 2005, allow higher temporal resolution by
acquiring a full CT slice in only half a rotation, thus reducing motion blurring at high heart
rates and potentially allowing for shorter breath-hold time. This is particularly useful for ill
patients who have difficulty holding their breath or who are unable to take heart-rate
lowering medication.

The speed advantages of 64-slice MSCT have rapidly established it as the minimum
standard for newly installed CT scanners intended for cardiac scanning. Manufacturers are
now actively developing 256-slice and true 'volumetric' scanners, primarily for their
improved cardiac scanning performance.

The latest MSCT scanners acquire images only at 70-80% of the R-R interval (late diastole).
This prospective gating can reduce effective dose from 10-15mSv to as little as 1.2mSv in
follow-up patients acquiring at 75% of the R-R interval. Effective doses at a centre with well
trained staff doing coronary imaging can average less than the doses for conventional
coronary angiography.

Abdominal and pelvic

CT is a sensitive method for diagnosis of abdominal diseases. It is used frequently to
determine stage of cancer and to follow progress. It is also a useful test to investigate acute
abdominal pain (especially of the lower quadrants, whereas ultrasound is the preferred first
line investigation for right upper quadrant pain). Renal stones, appendicitis, pancreatitis,
diverticulitis, abdominal aortic aneurysm, and bowel obstruction are conditions that are
readily diagnosed and assessed with CT. CT is also the first line for detecting solid organ
injury after trauma.

Oral and/or rectal contrast may be used depending on the indications for the scan. A dilute
(2% w/v) suspension of barium sulfate is most commonly used. The concentrated barium
sulfate preparations used for fluoroscopy e.g. barium enema are too dense and cause
severe artifacts on CT. Iodinated contrast agents may be used if barium is contraindicated
(for example, suspicion of bowel injury). Other agents may be required to optimize the
imaging of specific organs, such as rectally administered gas (air or carbon dioxide) or fluid
(water) for a colon study, or oral water for a stomach study.

CT has limited application in the evaluation of the pelvis. For the female pelvis in
particular, ultrasound and MRI are the imaging modalities of choice. Nevertheless, it may
be part of abdominal scanning (e.g. for tumors), and has uses in assessing fractures.

CT is also used in osteoporosis studies and research alongside dual energy X-ray
absorptiometry (DXA). Both CT and DXA can be used to assess bone mineral density (BMD)
which is used to indicate bone strength, however CT results do not correlate exactly with
DXA (the gold standard of BMD measurement). CT is far more expensive, and subjects
patients to much higher levels of ionizing radiation, so it is used infrequently.

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390

Extremities

CT is often used to image complex fractures, especially ones around joints, because of its
ability to reconstruct the area of interest in multiple planes. Fractures, ligamentous injuries
and dislocations can easily be recognised with a 0.2 mm resolution.

Advantages and hazards

Advantages over traditional radiography

There are several advantages that CT has over traditional 2D medical radiography. First,
CT completely eliminates the superimposition of images of structures outside the area of
interest. Second, because of the inherent high-contrast resolution of CT, differences
between tissues that differ in physical density by less than 1% can be distinguished. Finally,
data from a single CT imaging procedure consisting of either multiple contiguous or one
helical scan can be viewed as images in the axial, coronal, or sagittal planes, depending on
the diagnostic task. This is referred to as multiplanar reformatted imaging.

CT is regarded as a moderate to high radiation diagnostic technique. While technical
advances have improved radiation efficiency, there has been simultaneous pressure to
obtain higher-resolution imaging and use more complex scan techniques, both of which
require higher doses of radiation. The improved resolution of CT has permitted the
development of new investigations, which may have advantages; compared to conventional
angiography for example, CT angiography avoids the invasive insertion of an arterial
catheter and guidewire; CT colonography (also known as virtual colonoscopy or VC for
short) may be as useful as a barium enema for detection of tumors, but may use a lower
radiation dose. CT VC is increasingly being used in the UK as a diagnostic test for bowel
cancer and can negate the need for a colonoscopy.

The greatly increased availability of CT, together with its value for an increasing number of
conditions, has been responsible for a large rise in popularity. So large has been this rise
that, in the most recent comprehensive survey in the United Kingdom, CT scans constituted
7% of all radiologic examinations, but contributed 47% of the total collective dose from
medical X-ray examinations in 2000/2001. Increased CT usage has led to an overall rise in
the total amount of medical radiation used, despite reductions in other areas. In the United
States and Japan for example, there were 26 and 64 CT scanners per 1 million population in
1996. In the U.S., there were about 3 million CT scans performed in 1980, compared to an
estimated 62 million scans in 2006.

The radiation dose for a particular study depends on multiple factors: volume scanned,
patient build, number and type of scan sequences, and desired resolution and image
quality. Additionally, two helical CT scanning parameters that can be adjusted easily and
that have a profound effect on radiation dose are tube current and pitch. J

The increased use of CT scans has been the greatest in two fields: screening of adults
(screening CT of the lung in smokers, virtual colonoscopy, CT cardiac screening and
whole-body CT in asymptomatic patients) and CT imaging of children. Shortening of the
scanning time to around one second, eliminating the strict need for subject to remain still
or be sedated, is one of the main reasons for large increase in the pediatric population
(especially for the diagnosis of appendicitis). CT scans of children have been estimated to
produce non-negligible increases in the probability of lifetime cancer mortality leading to
calls for the use of reduced current settings for CT scans of children. J These calculations

Computed tomography

391

are based on the assumption of a linear relationship between radiation dose and cancer
risk; this claim is controversial, as some but not all evidence shows that smaller radiation
doses are less harmful. ] Estimated lifetime cancer mortality risks attributable to the
radiation exposure from a CT in a 1-year-old are 0.18% (abdominal) and 0.07% (head)— an
order of magnitude higher than for adults— although those figures still represent a small
increase in cancer mortality over the background rate. In the United States, of
approximately 600,000 abdominal and head CT examinations annually performed in
children under the age of 15 years, a rough estimate is that 500 of these individuals might
ultimately die from cancer attributable to the CT radiation . ^ The additional risk is still
very low (0.35%) compared to the background risk of dying from cancer (23%).
However, if these statistics are extrapolated to the current number of CT scans, the
additional rise in cancer mortality could be 1.5 to 2%. Furthermore, certain conditions can
require children to be exposed to multiple CT scans. Again, these calculations can be

T71

problematic because the assumptions underlying them could overestimate the risk. 1 J

CT scans can be performed with different settings for lower exposure in children, although
these techniques are often not employed. Surveys have suggested that currently, many CT
scans are performed unnecessarily. Ultrasound scanning or magnetic resonance imaging
are alternatives (for example, in appendicitis or brain imaging) without the risk of radiation
exposure. Although CT scans come with an additional risk of cancer, especially in children,
the benefits that stem from their use outweighs the risk in many cases. ^ Studies support
informing parents of the risks of pediatric CT scanning. J

Typical scan doses

Examination

Typical effective dose (mSv)

(milli rem)

Chest X-ray

0.1

Head CT

1.5 [12]

150

Screening mammography

3 [7]

300

Abdomen CT

5.3 [12]

530

Chest CT

5.8 [12]

580

Chest, Abdomen and Pelvis CT

9.9 [12]

990

CT colonography (virtual colonoscopy)

3.6- 8.8

360 -880

Cardiac CT angiogram

6.7-13 [13]

670 - 1300

Barium enema

15 [7]

1500

Neonatal abdominal CT

20 [7]

2000

For purposes of comparison the average background exposure in the UK is 1-3 mSv per

annum.

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392

Adverse reactions to contrast agents

Because contrast CT scans rely on intravenously administered contrast agents in order to
provide superior image quality, there is a low but non-negligible level of risk associated
with the contrast agents themselves. Many patients report nausea and discomfort,
including warmth in the crotch which mimics the sensation of wetting oneself. Certain
patients may experience severe and potentially life-threatening allergic reactions to the
contrast dye.

The contrast agent may also induce kidney damage. The risk of this is increased with
patients who have preexisting renal insufficiency, preexisting diabetes, or reduced
intravascular volume. In general, if a patient has normal kidney function, then the risks of
contrast nephropathy are negligible. Patients with mild kidney impairment are usually
advised to ensure full hydration for several hours before and after the injection. For
moderate kidney failure, the use of iodinated contrast should be avoided; this may mean
using an alternative technique instead of CT e.g. MRI. Perhaps paradoxically, patients with
severe renal failure requiring dialysis do not require special precautions, as their kidneys
have so little function remaining that any further damage would not be noticeable and the
dialysis will remove the contrast agent.

Low-Dose CT Scan

The main issue within radiology today is how to reduce the radiation dose during CT
examinations without compromising the image quality. Generally, a high radiation dose
results in high-quality images. A lower dose leads to increased image noise and results in
unsharp images. Unfortunately, as the radiation dose increases, so does the associated risk
of radiation induced cancer - even though this is extremely small. A radiation exposure of
around 1200 mrem (similar to a 4-view mammogram) carried a radiation-induced cancer
risk of about a million to one. However, there are several methods that can be used in order
to lower the exposure to ionizing radiation during a CT scan.

1. New software technology can significantly reduce the radiation dose. The software
works as a filter that reduces random noise and enhances structures. In this way, it is
possible to get high-quality images and at the same time lower the dose by as much as 30
to 70 percent.

2. Individualize the examination and adjust the radiation dose to the body type and body
organ examined. Different body types and organs require different amounts of radiation.

3. Prior to every CT examination, evaluate the appropriateness of the exam whether it is
motivated or if another type of examination is more suitable.

Computed Tomography versus MRI

See the entries or paragraphs of the same name in the MRI and 2D-FT NMRI and
Spectroscopy articles. The basic mathematics of the 2D-Fourier transform in CT
reconstruction is very similar to the 2D-FT NMRI, but the computer data processing in CT
does differ in detail, as for example in the case of the volume rendering or the artifacts
elimination algorithms that are specific to CT.

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393

Process

X-ray slice data is generated using an X-ray source that

rotates around the object; X-ray sensors are positioned

on the opposite side of the circle from the X-ray source.

The earliest sensors were scintillation detectors, with

photomultiplier tubes excited by (typically) cesium

iodide crystals. Cesium iodide was replaced during the

eighties by ion chambers containing high pressure

Xenon gas. These systems were in turn replaced by

scintillation systems based on photo diodes instead of

photomultipliers and modern scintillation materials

with more desirable characteristics. Many data scans

are progressively taken as the object is gradually

passed through the gantry. They are combined together

by the mathematical procedures known as tomographic

reconstruction. The data are arranged in a matrix in memory, and each data point is

convolved with its neighbours according with a seed algorithm using Fast Fourier

Transform techniques. This dramatically increases the resolution of each Voxel (volume

element). Then a process known as Back Projection essentially reverses the acquisition

geometry and stores the result in another memory array. This data can then be displayed,

photographed, or used as input for further processing, such as multi-planar reconstruction.

Newer machines with faster computer systems and newer software strategies can process
not only individual cross sections but continuously changing cross sections as the gantry,
with the object to be imaged, is slowly and smoothly slid through the X-ray circle. These are
called helical or spiral CT machines. Their computer systems integrate the data of the
moving individual slices to generate three dimensional volumetric information (3D-CT
scan), in turn viewable from multiple different perspectives on attached CT workstation
monitors. This type of data acquisition requires enormous processing power, as the data are
arriving in a continuous stream and must be processed in real-time.

In conventional CT machines, an X-ray tube and detector are physically rotated behind a
circular shroud (see the image above right); in the electron beam tomography (EBT) the
tube is far larger and higher power to support the high temporal resolution. The electron
beam is deflected in a hollow funnel shaped vacuum chamber. X-rays are generated when
the beam hits the stationary target. The detector is also stationary. This arrangement can
result in very fast scans, but is extremely expensive.

The data stream representing the varying radiographic intensity sensed at the detectors on
the opposite side of the circle during each sweep is then computer processed to calculate
cross-sectional estimations of the radiographic density, expressed in Hounsfield units.
Sweeps cover 360 or just over 180 degrees in conventional machines, 220 degrees in EBT.

Computed tomography

394

CT scanner with cover removed to
show the principle of operation

CT is used in medicine as a diagnostic tool and as a
guide for interventional procedures. Sometimes
contrast materials such as intravenous iodinated
contrast are used. This is useful to highlight structures
such as blood vessels that otherwise would be difficult
to delineate from their surroundings. Using contrast
material can also help to obtain functional information
about tissues.

Pixels in an image obtained by CT scanning are
displayed in terms of relative radiodensity. The pixel
itself is displayed according to the mean attenuation of
the tissue(s) that it corresponds to on a scale from
+ 3071 (most attenuating) to -1024 (least attenuating)
on the Hounsfield scale. Pixel is a two dimensional unit

based on the matrix size and the field of view. When the CT slice thickness is also factored
in, the unit is known as a Voxel, which is a three dimensional unit. The phenomenon that
one part of the detector cannot differentiate between different tissues is called the "Partial
Volume Effect". That means that a big amount of cartilage and a thin layer of compact bone
can cause the same attenuation in a voxel as hyperdense cartilage alone. Water has an
attenuation of Hounsfield units (HU) while air is -1000 HU, cancellous bone is typically
+400 HU, cranial bone can reach 2000 HU or more (os temporale) and can cause artifacts.
The attenuation of metallic implants depends on atomic number of the element used:
Titanium usually has an amount of +1000 HU, iron steel can completely extinguish the
X-ray and is therefore responsible for well-known line-artifacts in computed tomograms.
Artifacts are caused by abrupt transitions between low- and high-density materials, which
results in data values that exceed the dynamic range of the processing electronics.

Windowing

Windowing is the process of using the calculated Hounsfield units to make an image. A
typical display device can only resolve 256 shades of gray, some specialty medical displays
can resolve up to 1024 shades of gray. These shades of gray can be distributed over a wide
range of HU values to get an overview of structures that attenuate the beam to widely
varying degrees. Alternatively, these shades of gray can be distributed over a narrow range
of HU values (called a "narrow window") centered over the average HU value of a
particular structure to be evaluated. In this way, subtle variations in the internal makeup of
the structure can be discerned. This is a commonly used image processing technique known
as contrast compression. For example, to evaluate the abdomen in order to find subtle
masses in the liver, one might use liver windows. Choosing 70 HU as an average HU value
for liver, the shades of gray can be distributed over a narrow window or range. One could
use 170 HU as the narrow window, with 85 HU above the 70 HU average value; 85 HU
below it. Therefore the liver window would extend from -15 HU to +155 HU. All the shades
of gray for the image would be distributed in this range of Hounsfield values. Any HU value
below -15 would be pure black, and any HU value above 155 HU would be pure white in
this example. Using this same logic, bone windows would use a "wide window" (to evaluate
everything from fat-containing medullary bone that contains the marrow, to the dense
cortical bone), and the center or level would be a value in the hundreds of Hounsfield units.

Computed tomography

395

To an untrained person, these window controls would correspond to the more familiar
"Brightness" (Window Level) and "Contrast" (Window Width).

Artifacts

Although CT is a relatively accurate test it is liable to produce artifacts, such as the
following.

• Aliasing Artifact or Streaks

These appear as dark lines which radiate away from
sharp corners. It occurs because it is impossible for the
scanner to 'sample' or take enough projections of the
object, which is usually metallic. It can also occur when
an insufficient X-ray tube current is selected, and
insufficient penetration of the x-ray occurs. These
artifacts are also closely tied to motion during a scan.
This type of artifact commonly occurs in head images around the pituitary fossa area.

• Partial Volume Effect

This appears as 'blurring' over sharp edges. It is due to the scanner being unable to
differentiate between a small amount of high-density material (e.g. bone) and a larger
amount of lower density (e.g. cartilage). The processor tries to average out the two
densities or structures, and information is lost. This can be partially overcome by scanning
using thinner slices.

• Ring Artifact

Probably the most common mechanical artifact, the image of one or many 'rings' appears
within an image. This is usually due to a detector fault.

• Noise Artifact

This appears as graining on the image and is caused by a low signal to noise ratio. This
occurs more commonly when a thin slice thickness is used. It can also occur when the
power supplied to the X-ray tube is insufficient to penetrate the anatomy.

• Motion Artifact

This is seen as blurring and/or streaking which is caused by movement of the object being
imaged.

• Windmill

Streaking appearances can occur when the detectors intersect the reconstruction plane.
This can be reduced with filters or a reduction in pitch.

• Beam Hardening

This can give a 'cupped appearance'. It occurs when there is more attenuation in the center
of the object than around the edge. This is easily corrected by filtration and software.

Computed tomography

396

Three-dimensional (3D) image reconstruction

The principle

Because contemporary CT scanners offer isotropic, or near isotropic, resolution, display of
images does not need to be restricted to the conventional axial images. Instead, it is
possible for a software program to build a volume by 'stacking' the individual slices one on
top of the other. The program may then display the volume in an alternative manner.

Multiplanar reconstruction

Multiplanar reconstruction (MPR) is the simplest
method of reconstruction. A volume is built by stacking
the axial slices. The software then cuts slices through
the volume in a different plane (usually orthogonal).
Optionally, a special projection method, such as

maximum-intensity

projection

(MIP)

Typical screen layout for diagnostic
software, showing one 3D and three

MPR views

minimum-intensity projection (mlP), can be used to
build the reconstructed slices.

MPR is frequently used for examining the spine. Axial
images through the spine will only show one vertebral
body at a time and cannot reliably show the
intervertebral discs. By reformatting the volume, it
becomes much easier to visualise the position of one
vertebral body in relation to the others.

Modern software allows reconstruction in non-orthogonal (oblique) planes so that the
optimal plane can be chosen to display an anatomical structure. This may be particularly
useful for visualising the structure of the bronchi as these do not lie orthogonal to the
direction of the scan.

For vascular imaging, curved-plane reconstruction can be performed. This allows bends in a
vessel to be 'straightened' so that the entire length can be visualised on one image, or a
short series of images. Once a vessel has been 'straightened' in this way, quantitative
measurements of length and cross sectional area can be made, so that surgery or
interventional treatment can be planned.

MIP reconstructions enhance areas of high radiodensity, and so are useful for angiographic
studies. mlP reconstructions tend to enhance air spaces so are useful for assessing lung
structure.

3D rendering techniques

Surface rendering

A threshold value of radiodensity is chosen by the operator (e.g. a level that
corresponds to bone). A threshold level is set, using edge detection image processing
algorithms. From this, a 3-dimensional model can be constructed and displayed on
screen. Multiple models can be constructed from various different thresholds, allowing
different colors to represent each anatomical component such as bone, muscle, and
cartilage. However, the interior structure of each element is not visible in this mode of
operation.

Computed tomography

397

Volume rendering

Surface rendering is limited in that it will only display surfaces which meet a threshold
density, and will only display the surface that is closest to the imaginary viewer. In
volume rendering, transparency and colors are used to allow a better representation of
the volume to be shown in a single image - e.g. the bones of the pelvis could be
displayed as semi-transparent, so that even at an oblique angle, one part of the image
does not conceal another.

Image segmentation

Where different structures have similar radiodensity, it can become impossible to separate
them simply by adjusting volume rendering parameters. The solution is called
segmentation, a manual or automatic procedure that can remove the unwanted structures
from the image.

Example

Some slices of a cranial CT scan are shown below. The bones are whiter than the
surrounding area. (Whiter means higher attenuation.) Note the blood vessels (arrowed)
showing brightly due to the injection of an iodine-based contrast agent.

A volume rendering of this volume clearly shows the high density bones.

Computed tomography

398

After using a segmentation tool to remove the bone, the previously concealed vessels can
now be demonstrated.

Brain vessels reconstructed in 3D after
bone has been removed by

segmentation

See also

• Xenon-enhanced CT scanning

Notes

[1] Richmond, Caroline (September 18, 2004). "http://www.bmj.com/cgi/content/full/329/7467/687IObituary- Sir

Godfrey Hounsfield". BMJ (London, UK: BMJ Group) 2004:329:687 (18 Sept 2004). http://www.bmj.com/cgi/

content/full/329/7467/687. Retrieved on Sept 12, 2008.
[2] Filler, AG (2009): The history, development, and impact of computed imaging in neurological diagnosis and

neurosurgery: CT, MRI, DTI: Nature Precedings DOI: 10.1038/npre.2009.3267.2 (http://precedings. nature.

com/documents/32 6 7/version/2 ) .
[3] http://www.whittington.nhs.uk/default.asp?c=2804&t=l|"The Beatles greatest gift... is to science".

Whittington Hospital NHS Trust. http://www.whittington.nhs.uk/default.asp?c=2804&t=l. Retrieved on

2007-05-07.
[4] Novelline, Robert. Squire's Fundamentals of Radiology. Harvard University Press. 5th edition. 1997. ISBN

0674833392.
[5] Hart, D; Wall B F (2002).

"http://www.hpa.org.uk/radiation/publications/w_series_reports/2002/nrpb_w4.pdflRadiation exposure of the UK

population from Medical and Dental X-ray examinations" (- Scholar search (http://scholar.google.co.uk/

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399

scholar?hl=en&lr=&q=author:Hart+intitle:Radiation+exposure+of+the+UK+population+from+
Medical+and+Dental+X-ray+examinations&as_publication=NRPB+report+W-4&as_ylo=2002&
as_yhi=2002&btnG = Search)). NRPB report W-4. http://www.hpa.org.uk/radiation/publications/
w_series_reports/2002/nrpb_w4.pdf.

[6] Hart D. ; Wall (2004). "http://linkinghub.elsevier.com/retrieve/pii/S0720048X03001785IUKpopulation dose
from medical X-ray examinations". European Journal of Radiology 50 (3): 285-291. doi:
10.1016/S0720-048X(03)00178-5 (http://dx.doi.org/10. 1016/S0720-048X(03)001 78-5). http://linkinghub.
elsevier.com/retrieve/pii/S0720048X03001785.

[7] Brenner DJ, Hall EJ (November 2007).

"http://content.nejm.org/cgi/pmidlookup?view=short&pmid=l 804603 l&promo=ONFLNSl 9 |Computed
tomography--an increasing source of radiation exposure". N. Engl. J. Med. 357 (22): 2277-84. doi:
10.1056/NEJMra072149 (http://dx.doi.org/10.1056/NEJMra072149). PMID 18046031. http://content.
nejm.org/cgi/pmidlookup?view=short&pmid=l 804603 l&promo=ONFLNSl 9.

[8] Donnelly, Lane F.; et al (01 February 2001). "http://www.ajronline.Org/cgi/reprint/l 76/2/303 1 Minimizing
Radiation Dose for Pediatric Body Applications of Single-Detector Helical CT". American Journal of
Roentgenology 176 (2): 303-6. http://www.ajronline.Org/cgi/reprint/176/2/303.

[9] Brenner, David J.; et al. (01 Feb 2001). "http://www.ajronline.org/cgi/content/abstract/176/2/289|Estimated
Risks of Radiation-Induced Fatal Cancer from Pediatric CT". American Journal of Roentgenology 176 (176):
289-296. PMID 11159059. http://www.ajronline.Org/cgi/content/abstract/176/2/289.

[10] Brenner D, Elliston C, Hall E, Berdon W (February 2001).

"http://www.ajronline.org/cgi/pmidlookup?view=long&pmid=ll 159059|Estimated risks of radiation-induced
fatal cancer from pediatric CT" . AJR Am J Roentgenol 176 (2): 289-96. PMID 11159059. http://www.ajronline.
org/cgi/pmidlookup?view=long&pmid= 1 1 159059.

[11] Larson DB, Rader SB, Forman HP, Fenton LZ (August 2007).

"http://www.ajronline.org/cgi/pmidlookup?view=long&pmid=17646450|Informing parents about CT radiation
exposure in children: it's OK to tell them". AJR Am J Roentgenol 189 (2): 271-5. doi: 10.2214/AJR.07.2248
(http://dx.doi.org/10.2214/AJR.07.2248). PMID 17646450. http://www.ajronline.org/cgi/
pmidlookup?view=long&pmid= 1 7646450.

[12] Shrimpton, P.C; Miller, H.C; Lewis, M.A; Dunn, M. Doses from Computed Tomography (CT) examinations in
the UK- 2003 Review (http://www.hpa.org.uk/web/HPAwebFile/HPAweb_C/1194947420292)

[13] Radiation Exposure during Cardiac CT: Effective Doses at Multi-Detector Row CT and Electron-Beam CT
(http://radiology.rsnajnls.Org/cgi/content/abstract/226/l/145)

External links

• Open-source computed tomography simulator with educational tracing displays (http://
ctsim.org)

• idoimaging.com: Free software for viewing CT and other medical imaging files (http://
www.idoimaging.com)

• CT Artefacts (http://www.impactscan.org/slides/impactcourse/artefacts/imgO.html)
by David Platten

• DigiMorph (http://digimorph.org/) A library of 3D imagery based on CT scans of the
internal and external structure of living and extinct plants and animals.

• MicroCT and calcified tissues (http://www.med.univ-angers.fr/discipline/lab_histo/
page_microCT.htm) A website dedicated to microCT in the microscopic analysis of
calcified tissues.

• Free Radiology Resource for Radiologists, Radiographers, and Technical Assistance
(http://www.mdct.com.au:)

• Radiation Risk Calculator (http://www.xrayrisk.com) Calculate cancer risk from CT
scans and xrays.

Chemical imaging

400

Chemical imaging

Chemical imaging is the simultaneous measurement of spectra (chemical information)
and images or pictures (spatial informations ^ c ] The technique is most often applied to
either solid or gel samples, and has applications in chemistry, biology^ J L J L J L J L J L J ^
medicine^ ] c , pharmacy^ ^ (see also for example: Chemical Imaging Without Dyeing

m 9i ri3i ri4i

L J )/ food science, biotechnology , agriculture and industry (see for example:NIR

Chemical Imaging in Pharmaceutical Industry ^ ] and Pharmaceutical Process Analytical
Technology: ). NIR, IR and Raman chemical imaging is also referred to as hyperspectral,
spectroscopic, spectral or multispectral imaging (also see microspectroscopy). However,
other ultra-sensitive and selective, chemical imaging techniques are also in use that involve

either UV-visible or fluorescence microspectroscopy. Chemical imaging techniques can be

n 71 n 8i
used to analyze samples of all sizes, from the single molecule to the cellular level in

biology and medicine^ ^ c ] c , and to images of planetary systems in astronomy, but

different instrumentation is employed for making observations on such widely different

systems.

Chemical imaging instrumentation is composed of three components: a radiation source to
illuminate the sample, a spectrally selective element, and usually a detector array (the
camera) to collect the images. When many stacked spectral channels (wavelengths) are
collected for different locations of the microspectrometer focus on a line or planar array in
the focal plane, the data is called hyperspectral; fewer wavelength data sets are called
multispectral. The data format is called a hypercube. The data set may be visualized as a
three-dimensional block of data spanning two spatial dimensions (x and y), with a series of
wavelengths (lambda) making up the third (spectral) axis. The hypercube can be visually
and mathematically treated as a series of spectrally resolved images (each image plane
corresponding to the image at one wavelength) or a series of spatially resolved spectra. The
analyst may choose to view the spectrum measured at a particular spatial location; this is
useful for chemical identification. Alternatively, selecting an image plane at a particular
wavelength can highlight the spatial distribution of sample components, provided that their
spectral signatures are different at the selected wavelength.

Many materials, both manufactured and naturally occurring, derive their functionality from
the spatial distribution of sample components. For example, extended release
pharmaceutical formulations can be achieved by using a coating that acts as a barrier layer.
The release of active ingredient is controlled by the presence of this barrier, and
imperfections in the coating, such as discontinuities, may result in altered performance. In
the semi-conductor industry, irregularities or contaminants in silicon wafers or printed
micro-circuits can lead to failure of these components. The functionality of biological
systems is also dependent upon chemical gradients - a single cell, tissue, and even whole
organs function because of the very specific arrangement of components. It has been shown
that even small changes in chemical composition and distribution may be an early indicator
of disease.

Any material that depends on chemical gradients for functionality may be amenable to
study by an analytical technique that couples spatial and chemical characterization. To
efficiently and effectively design and manufacture such materials, the 'what' and the
'where' must both be measured. The demand for this type of analysis is increasing as
manufactured materials become more complex. Chemical imaging techniques not only

Chemical imaging

401

permit visualization of the spatially resolved chemical information that is critical to
understanding modern manufactured products, but it is also a non-destructive technique so
that samples are preserved for further testing.

History

Commercially available laboratory-based chemical imaging systems emerged in the early
1990s (ref. 1-5). In addition to economic factors, such as the need for sophisticated
electronics and extremely high-end computers, a significant barrier to commercialization of
infrared imaging was that the focal plane array (FPA) needed to read IR images were not
readily available as commercial items. As high-speed electronics and sophisticated
computers became more commonplace, and infrared cameras became readily commercially
available, laboratory chemical imaging systems were introduced.

Initially used for novel research in specialized laboratories, chemical imaging became a
more commonplace analytical technique used for general R&D, quality assurance (QA) and
quality control (QC) in less than a decade. The rapid acceptance of the technology in a
variety of industries (pharmaceutical, polymers, semiconductors, security, forensics and
agriculture) rests in the wealth of information characterizing both chemical composition
and morphology. The parallel nature of chemical imaging data makes it possible to analyze
multiple samples simultaneously for applications that require high throughput analysis in
addition to characterizing a single sample.

Principles

Chemical imaging shares the fundamentals of vibrational spectroscopic techniques, but
provides additional information by way of the simultaneous acquisition of spatially resolved
spectra. It combines the advantages of digital imaging with the attributes of spectroscopic
measurements. Briefly, vibrational spectroscopy measures the interaction of light with
matter. Photons that interact with a sample are either absorbed or scattered; photons of
specific energy are absorbed, and the pattern of absorption provides information, or a
fingerprint, on the molecules that are present in the sample.

On the other hand, in terms of the observation setup, chemical imaging can be carried out
in one of the following modes: (optical) absorption, emission (fluorescence), (optical)
transmission or scattering (Raman). A consensus currently exists that the fluorescence
(emission) and Raman scattering modes are the most sensitive and powerful, but also the
most expensive.

In a transmission measurement, the radiation goes through a sample and is measured by a
detector placed on the far side of the sample. The energy transferred from the incoming
radiation to the molecule(s) can be calculated as the difference between the quantity of
photons that were emitted by the source and the quantity that is measured by the detector.
In a diffuse reflectance measurement, the same energy difference measurement is made,
but the source and detector are located on the same side of the sample, and the photons
that are measured have re-emerged from the illuminated side of the sample rather than
passed through it. The energy may be measured at one or multiple wavelengths; when a
series of measurements are made, the response curve is called a spectrum.

A key element in acquiring spectra is that the radiation must somehow be energy selected -
either before or after interacting with the sample. Wavelength selection can be

Chemical imaging

402

accomplished with a fixed filter, tunable filter, spectrograph, an interferometer, or other
devices. For a fixed filter approach, it is not efficient to collect a significant number of
wavelengths, and multispectral data are usually collected. Interferometer-based chemical
imaging requires that entire spectral ranges be collected, and therefore results in
hyperspectral data. Tunable filters have the flexibility to provide either multi- or
hyperspectral data, depending on analytical requirements.

Spectra may be measured one point at a time using a single element detector (single-point
mapping), as a line-image using a linear array detector (typically 16 to 28 pixels) (linear
array mapping), or as a two-dimensional image using a Focal Plane Array (FPA) (typically
256 to 16,384 pixels) (FPA imaging). For single-point the sample is moved in the x and y
directions point-by-point using a computer-controlled stage. With linear array mapping, the
sample is moved line-by-line with a computer-controlled stage. FPA imaging data are
collected with a two-dimensional FPA detector, hence capturing the full desired
field-of-view at one time for each individual wavelength, without having to move the
sample. FPA imaging, with its ability to collected tens of thousands of spectra
simultaneously is orders of magnitude faster than linear arrays which are can typically
collect 16 to 28 spectra simultaneously, which are in turn much faster than single-point
mapping.

Terminology

Some words common in spectroscopy, optical microscopy and photography have been
adapted or their scope modified for their use in chemical imaging. They include: resolution,
field of view and magnification. There are two types of resolution in chemical imaging. The
spectral resolution refers to the ability to resolve small energy differences; it applies to the
spectral axis. The spatial resolution is the minimum distance between two objects that is
required for them to be detected as distinct objects. The spatial resolution is influenced by
the field of view, a physical measure of the size of the area probed by the analysis. In
imaging, the field of view is a product of the magnification and the number of pixels in the
detector array. The magnification is a ratio of the physical area of the detector array
divided by the area of the sample field of view. Higher magnifications for the same detector
image a smaller area of the sample.

Types of vibrational chemical imaging instruments

Chemical imaging has been implemented for mid-infrared, near-infrared spectroscopy and
Raman spectroscopy. As with their bulk spectroscopy counterparts, each imaging technique
has particular strengths and weaknesses, and are best suited to fulfill different needs.

Mid-infrared chemical imaging

Mid-infrared (MIR) spectroscopy probes fundamental molecular vibrations, which arise in

the spectral range 2,500-25,000 nm. Commercial imaging implementations in the MIR

region typically employ Fourier Transform Infrared (FT-IR) interferometers and the range is

more commonly presented in wavenumber, 4,000 - 400 cm . The MIR absorption bands
tend to be relatively narrow and well-resolved; direct spectral interpretation is often
possible by an experienced spectroscopist. MIR spectroscopy can distinguish subtle
changes in chemistry and structure, and is often used for the identification of unknown
materials. The absorptions in this spectral range are relatively strong; for this reason,
sample presentation is important to limit the amount of material interacting with the

Chemical imaging

403

incoming radiation in the MIR region. Most data collected in this range is collected in
transmission mode through thin sections (~10 micrometres) of material. Water is a very
strong absorber of MIR radiation and wet samples often require advanced sampling
procedures (such as attenuated total reflectance). Commercial instruments include point
and line mapping, and imaging. All employ an FT-IR interferometer as wavelength selective
element and light source.

For types of MIR microscope, see
Microscopy#infrared microscopy.

Atmospheric windows in the

infrared

spectrum

are

also

employed to perform chemical

imaging remotely.

these

spectral regions the atmospheric
gases (mainly water and

co 2 )

Remote chemical imaqinq of a simultaneous release of SF and
NH at 1.5km using the FIRST imaging spectrometer

•3

present low absorption and allow

infrared viewing over kilometer

distances. Target molecules can then be viewed using the selective absorption/emission

processes described above. An example of the chemical imaging of a simultaneous release

of SF 6 and NFL is shown in the image.

Near-infrared chemical imaging

The analytical near infrared (NIR) region spans the range from approximately 700-2,500
nm. The absorption bands seen in this spectral range arise from overtones and combination
bands of O-H, N-H, C-H and S-H stretching and bending vibrations. Absorption is one to two
orders of magnitude smaller in the NIR compared to the MIR; this phenomenon eliminates
the need for extensive sample preparation. Thick and thin samples can be analyzed without
any sample preparation, it is possible to acquire NIR chemical images through some
packaging materials, and the technique can be used to examine hydrated samples, within
limits. Intact samples can be imaged in transmittance or diffuse reflectance.

The lineshapes for overtone and combination bands tend to be much broader and more
overlapped than for the fundamental bands seen in the MIR. Often, multivariate methods
are used to separate spectral signatures of sample components. NIR chemical imaging is
particularly useful for performing rapid, reproducible and non-destructive analyses of
known materials . NIR imaging instruments are typically based on one of two

platforms: imaging using a tunable filter and broad band illumination, and line mapping
employing an FT-IR interferometer as the wavelength filter and light source.

Raman chemical imaging

The Raman shift chemical imaging spectral range spans from approximately 50 to 4,000

i
cm ; the actual spectral range over which a particular Raman measurement is made is a

function of the laser excitation frequency. The basic principle behind Raman spectroscopy

differs from the MIR and NIR in that the x-axis of the Raman spectrum is measured as a

function of energy shift (in cm ) relative to the frequency of the laser used as the source of
radiation. Briefly, the Raman spectrum arises from inelastic scattering of incident photons,
which requires a change in polarizability with vibration, as opposed to infrared absorption,
which requires a change in dipole moment with vibration. The end result is spectral

Chemical imaging

404

information that is similar and in many cases complementary to the MIR. The Raman effect

is weak - only about one in 10 photons incident to the sample undergoes Raman scattering.
Both organic and inorganic materials possess a Raman spectrum; they generally produce
sharp bands that are chemically specific. Fluorescence is a competing phenomenon and,
depending on the sample, can overwhelm the Raman signal, for both bulk spectroscopy and
imaging implementations.

Raman chemical imaging requires little or no sample preparation. However, physical
sample sectioning may be used to expose the surface of interest, with care taken to obtain a
surface that is as flat as possible. The conditions required for a particular measurement
dictate the level of invasiveness of the technique, and samples that are sensitive to high
power laser radiation may be damaged during analysis. It is relatively insensitive to the
presence of water in the sample and is therefore useful for imaging samples that contain
water such as biological material.

Fluorescence imaging (visible and NIR)

This emission microspectroscopy mode is the most sensitive in both visible and FT-NIR
microspectroscopy, and has therefore numerous biomedical, biotechnological and
agricultural applications. There are several powerful, highly specific and sensitive
fluorescence techniques that are currently in use, or still being developed; among the
former are FLIM, FRAP, FRET and FLIM-FRET; among the latter are NIR fluorescence and
probe-sensitivity enhanced NIR fluorescence microspectroscopy and nanospectroscopy
techniques (see "Further reading" section).

Sampling and samples

The value of imaging lies in the ability to resolve spatial heterogeneities in solid-state or
gel/gel-like samples. Imaging a liquid or even a suspension has limited use as constant
sample motion serves to average spatial information, unless ultra-fast recording techniques
are employed as in fluorescence correlation microspectroscopy or FLIM obsevations where
a single molecule may be monitored at extremely high (photon) detection speed.
High-throughput experiments (such as imaging multi-well plates) of liquid samples can
however provide valuable information. In this case, the parallel acquisition of thousands of
spectra can be used to compare differences between samples, rather than the more
common implementation of exploring spatial heterogeneity within a single sample.

Similarly, there is no benefit in imaging a truly homogeneous sample, as a single point
spectrometer will generate the same spectral information. Of course the definition of
homogeneity is dependent on the spatial resolution of the imaging system employed. For
MIR imaging, where wavelengths span from 3-10 micrometres, objects on the order of 5
micrometres may theoretically be resolved. The sampled areas are limited by current
experimental implementations because illumination is provided by the interferometer.
Raman imaging may be able to resolve particles less than 1 micrometre in size, but the
sample area that can be illuminated is severely limited. With Raman imaging, it is
considered impractical to image large areas and, consequently, large samples. FT-NIR
chemical/hyperspectral imaging usually resolves only larger objects (>10 micrometres),
and is better suited for large samples because illumination sources are readily available.
However, FT-NIR microspectroscopy was recently reported to be capable of about 1.2
micron (micrometer) resolution in biological samples Furthermore, two-photon

Chemical imaging

405

excitation FCS experiments were reported to have attained 15 nanometer resolution on
biomembrane thin films with a special coincidence photon-counting setup.

Detection limit

The concept of the detection limit for chemical imaging is quite different than for bulk
spectroscopy, as it depends on the sample itself. Because a bulk spectrum represents an
average of the materials present the spectral signatures of trace components are simply
overwhelmed by dilution. In imaging however, each pixel has a corresponding spectrum. If
the physical size of the trace contaminant is on the order of the pixel size imaged on the
sample, its spectral signature will likely be detectable. If however, the trace component is
dispersed homogeneously (relative to pixel image size) throughout a sample, it will not be
detectable. Therefore, detection limits of chemical imaging techniques are strongly
influenced by particle size, the chemical and spatial heterogeneity of the sample, and the
spatial resolution of the image.

Data analysis

Data analysis methods for chemical imaging data sets typically employ mathematical
algorithms common to single point spectroscopy or to image analysis. The reasoning is that
the spectrum acquired by each detector is equivalent to a single point spectrum; therefore
pre-processing, chemometrics and pattern recognition techniques are utilized with the
similar goal to separate chemical and physical effects and perform a qualitative or
quantitative characterization of individual sample components. In the spatial dimension,
each chemical image is equivalent to a digital image and standard image analysis and
robust statistical analysis can be used for feature extraction.

See also

• Multispectral image

• Microspectroscopy

• Imaging spectroscopy

References

[1] http://www.imaging.net/chemical-imaging/Chemical imaging

[2] http://www.malvern.com/LabEng/products/sdi/bibliography/sdi_bibliography.htm E. N. Lewis, E. Lee and

L. H. Kidder, Combining Imaging and Spectroscopy: Solving Problems with Near-Infrared Chemical Imaging.

Microscopy Today, Volume 12, No. 6, 11/2004.
[3] C.L. Evans and X.S. Xie.2008. Coherent Anti- Stokes Raman Scattering Microscopy: Chemical Imaging for

Biology and Medicine., doi:10.1146/annurev.anchem. 1.031207. 112754 Annual Review of Analytical Chemistry,

1: 883-909.

[4] Diaspro, A., and Robello, M. (1999). Multi-photon Excitation Microscopy to Study Biosystems. European

Microscopy and Analysis., 5:5-7.
[5] D.S. Mantus and G. H. Morrison. 1991. Chemical imaging in biology and medicine using ion microscopy.,

Microchimica Acta, 104, (1-6) January 1991, doi: 10.1007/BF01245536
[6] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in

giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.
[7] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by

fluorescence correlation spectroscopy with one- and two-photon excitation. Biophysical Journal,

77(10):2251-2265.

[8] l.Lee, S. C. et al., (2001). One Micrometer Resolution NMR Microscopy. J. Magn. Res., 150: 207-213.

Chemical imaging

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[9] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[10] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann and S. S. Korban,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[11] J. Dubois, G. Sando, E. N. Lewis, Near-Infrared Chemical Imaging, A Valuable Tool for the Pharmaceutical

Industry, G.I.T. Laboratory Journal Europe, No. 1-2, 2007.
[12] http ://witec . de/en/download/Raman/ImagingMicroscopy04 . pdf

[13] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY.
[14] Applications of Novel Techniques to Health Foods, Medical and Agricultural Biotechnology. (June 2004) I. C.

Baianu, P. R. Lozano, V. I. Prisecaru and H. C. Lin q-bio/0406047 (http://arxiv.org/abs/q-bio/0406047)
[15] http://www.spectroscopyeurope.com/NIR_14_3.pdf
[16] http://www.fda.gov/cder/OPS/PAT.htm
[17] Eigen, M., and Rigler, R. (1994). Sorting single molecules: Applications to diagnostics and evolutionary

biotechnology, Proc. Natl. Acad. Sci. USA 91:5740.
[18] Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by fluorescence correlation

spectroscopy, BioScience (Ed. Klinge & Owman) p. 180.
[19] Single Cancer Cell Detection by Near Infrared Microspectroscopy, Infrared Chemical Imaging and

Fluorescence Microspectroscopy.2004.I. C. Baianu, D. Costescu, N. E. Hofmann, S. S. Korban and et al.,

q-bio/0407006 (July 2004) (http://arxiv.org/abs/q-bio/0407006)
[20] Oehlenschlager F., Schwille P. and Eigen M. (1996). Detection of HIV-1 RNA by nucleic acid sequence-based

amplification combined with fluorescence correlation spectroscopy, Proc. Natl. Acad. Sci. USA 93:1281.
[21] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
[22] M. Chamberland, V. Farley, A. Vallieres, L. Belhumeur, A. Villemaire, J. Giroux et J. Legault,

High-Performance Field-Portable Imaging Radiometric Spectrometer Technology For Hyperspectral imaging

Applications, Proc. SPIE 5994, 59940N, September 2005.
[23] Novel Techniques for Microspectroscopy and Chemical Imaging Analysis of Soybean Seeds and

Embryos. (2002). Baianu, I.C, Costescu, D.M., and You, T. Soy2002 Conference, Urbana, Illinois.
[24] Near Infrared Microspectroscopy, Chemical Imaging and NMR Analysis of Oil in Developing and

Mutagenized Soybean Embryos in Culture. (2003). Baianu, I.C, Costescu, D.M., Hofmann, N., and Korban, S.S.

AOCS Meeting, Analytical Division.
[25] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.

Further reading

1. E.N. Lewis, P. J. Treado, I. W. Levin, Near-Infrared and Raman Spectroscopic Imaging,
American Laboratory, 06/1994:16 (1994)

2. E. N. Lewis, P.J. Treado, R. C. Reeder, G. M. Story, A. E. Dowrey, C. Marcott, I. W.
Levin, FTIR spectroscopic imaging using an infrared focal-plane array detector,
Analytical Chemistry, 67:3377 (1995)

3. P. Colarusso, L. H. Kidder, I. W. Levin, J. C. Fraser, E. N. Lewis Infrared Spectroscopic
Imaging: from Planetary to Cellular Systems, Applied Spectroscopy, 52 (3):106A (1998)

4. P. J. Treado I. W. Levin, E. N. Lewis, Near-Infrared Spectroscopic Imaging Microscopy of
Biological Materials Using an Infrared Focal-Plane Array and an Acousto-Optic Tunable
Filter (AOTF), Applied Spectroscopy, 48:5 (1994)

5. Hammond, S.V., Clarke, F. C, Near-infrared microspectroscopy. In: Handbook of
Vibrational Spectroscopy, Vol. 2, J.M. Chalmers and P.R. Griffiths Eds. John Wiley and
Sons, West Sussex, UK, 2002, p. 1405-1418

Chemical imaging

407

6. L.H. Kidder, A.S. Haka, E.N. Lewis, Instrumentation for FT-IR Imaging. In: Handbook of
Vibrational Spectroscopy, Vol. 2, J.M. Chalmers and P.R. Griffiths Eds. John Wiley and
Sons, West Sussex, UK, 2002, pp.1386-1404

7. J. Zhang; A. O'Connor; J. F. Turner II, Cosine Histogram Analysis for Spectral Image
Data Classification,Applied Spectroscopy, Volume 58, Number 11, November 2004, pp.
1318-1324(7)

8. J. F. Turner II; J. Zhang; A. O'Connor, A Spectral Identity Mapper for Chemical Image
Analysis, Applied Spectroscopy, Volume 58, Number 11, November 2004, pp.
1308-1317(10)

9. H. R. MORRIS, J. F. TURNER II, B. MUNRO, R. A. RYNTZ, P. J. TREADO, Chemical
imaging of thermoplastic olefin (TPO) surface architecture, Langmuir, 1999, vol. 15, no8,
pp. 2961-2972

10. J. F. Turner II, Chemical imaging and spectroscopy using tunable filters:
Instrumentation, methodology, and multivariate analysis, Thesis (PhD). UNIVERSITY OF
PITTSBURGH, Source DAI-B 59/09, p. 4782, Mar 1999, 286 pages.

11. P. Schwille.(2001). in Fluorescence Correlation Spectroscopy. Theory and applications.
R. Rigler & E.S. Elson, eds., p. 360. Springer Verlag: Berlin.

12. Schwille P., Oehlenschlager F. and Walter N. (1996). Analysis of RNA-DNA
hybridization kinetics by fluorescence correlation spectroscopy, Biochemistry 35:10182.

13. FLIM | Fluorescence Lifetime Imaging Microscopy: Fluorescence, fluorophore chemical
imaging, confocal emission microspectroscopy, FRET, cross-correlation fluorescence
microspectroscopy (http://www.nikoninstruments.com/infocenter.php?n=FLIM).

14. FLIM Applications: (http://www.nikoninstruments.com/infocenter.php?n=FLIM)
"FLIM is able to discriminate between fluorescence emanating from different
fluorophores and autoflorescing molecules in a specimen, even if their emission spectra
are similar. It is, therefore, ideal for identifying fluorophores in multi-label studies. FLIM
can also be used to measure intracellular ion concentrations without extensive
calibration procedures (for example, Calcium Green) and to obtain information about the
local environment of a fluorophore based on changes in its lifetime." FLIM is also often
used in microspectroscopic/chemical imaging, or microscopic, studies to monitor spatial
and temporal protein-protein interactions, properties of membranes and interactions with
nucleic acids in living cells.

15. Gadella TW Jr., FRET and FLIM techniques, 33. Imprint: Elsevier, ISBN
978-0-08-054958-3. (2008) 560 pages

16. Langel FD, et al., Multiple protein domains mediate interaction between BcllO and

is and

Maltl, J. Biol. Chem., (2008) 283(47):32419-31

17. Clayton AH. , The polarized AB plot for the frequency-domain analysi
representation of fluorophore rotation and resonance energy homotransfer. J Microscopy.

(2008) 232(2):306-12

18. Clayton AH, et al., Predominance of activated EGFR higher-order oligomers on the cell
surface. Growth Factors (2008) 20:1

19. Plowman et al., Electrostatic Interactions Positively Regulate K-Ras Nanocluster
Formation and Function. Molecular and Cellular Biology (2008) 4377-4385

20. Belanis L, et al., Galectin-1 Is a Novel Structural Component and a Major Regulator of
H-Ras Nanoclusters. Molecular Biology of the Cell (2008) 19:1404-1414

21. Van Manen HJ, Refractive index sensing of green fluorescent proteins in living cells
using fluorescence lifetime imaging microscopy. Biophys J. (2008) 94(8):L67-9

Chemical imaging

408

22. Van der Krogt GNM, et al., A Comparison of Donor-Acceptor Pairs for Genetically
Encoded FRET Sensors: Application to the Epac cAMP Sensor as an Example, PLoS ONE,
(2008) 3(4):el916

23. Dai X, et al., Fluorescence intensity and lifetime imaging of free and
micellar-encapsulated doxorubicin in living cells. Nanomedicine. (2008) 4(l):49-56.

External links

• NIR Chemical Imaging in Pharmaceutical Industry (http://www.spectroscopyeurope.
com/NIR_l 4_3.pdf)

• Pharmaceutical Process Analytical Technology: (http://www.fda.gov/cder/OPS/PAT.
htm)

• NIR Chemical Imaging for Counterfeit Pharmaceutical Product Analysis (http://www.
spectroscopymag.com/spectroscopy/Near-IR+ Spectroscopy/

NIR-Chemical-Imaging-for-Counterfeit-Pharmaceutica/ArticleStandard/ Article/detail/
406629)

• Chemical Imaging: Potential New Crime Busting Tool (http://www.sciencedaily.com/
releases/2007/08/070802103435. htm)

• Chemical Imaging Without Dyeing (http://witec.de/en/download/Raman/
ImagingMicroscopy04.pdf) - Chemical Imaging Without Dyeing

Hyperspectral imaging

Hyperspectral imaging collects and processes information from across the
electromagnetic spectrum. Unlike the human eye, which just sees visible light,
hyperspectral imaging is more like the eyes of the mantis shrimp, which can see visible
light as well as from the ultraviolet to infrared. Hyperspectral capabilities enable the
mantis shrimp to recognize different types of coral, prey, or predators, all which may
appear as the same color to the human eye.

Humans build sensors and processing systems to provide the same type of capability for
application in agriculture, mineralogy, physics, and surveillance. Hyperspectral sensors
look at objects using a vast portion of the electromagnetic spectrum. Certain objects leave
unique 'fingerprints' across the electromagnetic spectrum. These 'fingerprints' are known
as spectral signatures and enable identification of the materials that make up a scanned
object. For example, having the spectral signature for oil helps mineralogists find new oil
fields.

Hyperspectral imaging

409

Acquisition and Analysis

Hyperspectral sensors collect information as a set of
images'. Each image represents a range of the
electromagnetic spectrum and is also known as a
spectral band. These 'images' are then combined and
form a three dimensional hyperspectral cube for
processing and analysis.

Hyperspectral cubes are generated from airborne
sensors like the NASA's Airborne Visible/Infrared
Imaging Spectrometer (AVIRIS), or from satellites like

NASA's Hyperion. 1 J However, for many development
and validation studies handheld sensors are used.

The precision of these sensors is typically measured in
spectral resolution, which is the width of each band of
the spectrum that is captured. If the scanner picks up on a large number of fairly narrow
frequency bands, it is possible to identify objects even if said objects are only captured in a
handful of pixels. However, spatial resolution is a factor in addition to spectral resolution. If
the pixels are too large, then multiple objects are captured in the same pixel and become
difficult to identify. If the pixels are too small, then the energy captured by each sensor-cell
is low, and the decreased signal-to-noise ratio reduces the reliability of measured features.

MicroMSI, Opticks and Envi are three remote sensing applications that support the
processing and analysis of hyperspectral data. The acquisition and processing of
hyperspectral images is also referred to as imaging spectroscopy.

Multispectral/
Hyperspectral Comparison

Differences between Hyperspectral and Multispectral

Hyperspectral Imaging is part of a class of techniques
commonly referred to as spectral imaging or spectral
analysis. Hyperspectral Imaging is related to
multispectral imaging. The distinction between
hyperspectral and multispectral is usually defined as
the number of spectral bands. Multispectral data
contains from tens to hundreds of bands. Hyperspectral
data contains hundreds to thousands of bands.
However, hyperspectral imaging may be best defined
by the manner in which the data is collected.
Hyperspectral data is a set of contiguous bands (usually
by one sensor). Multispectral is a set of optimally
chosen spectral bands that are typically not contiguous
and can be collected from multiple sensors.

Hyperspectral and Multispectral

Differences.

Hyperspectral imaging

410

Applications

Hyperspectral remote sensing is used in a wide array of real-life applications. Although
originally developed for mining and geology (The ability of hyperspectral imaging to
identify various minerals makes it ideal for the mining and oil industries, where it can be
used to look for ore and oil it has now spread into fields as wide-spread as ecology and

surveillance, as well as historical manuscript research such as the imaging of the
Archimedes Palimpsest. This technology is continually becoming more available to the
public, and has been used in a wide variety of ways. Organizations such as NASA and the
USGS have catalogues of various minerals and their spectral signatures, and have posted
them online to make them readily available for researchers.

Agriculture

Although the costs of acquiring hyperspectral images is typically high, for specific crops
and in specific climates hyperspectral remote sensing is used more and more for
monitoring the development and health of crops. In Australia work is underway to use
imaging spectrometers to detect grape variety, and develop an early warning system for
disease outbreaks. Furthermore work is underway to use hyperspectral data to detect the
chemical composition of plants which can be used to detect the nutrient and water status
of wheat in irrigated systems

Mineralogy

The original field of development for hyperspectral remote sensing, hyperspectral sensing
of minerals is now well developed. Many minerals can be identified from images, and their
relation to the presence of valuable minerals such as gold and diamonds is well understood.
Currently the move is towards understanding the relation between oil and gas leakages
from pipelines and natural wells; their effect on the vegetation and the spectral signatures.
Recent work includes the PhD dissertations of Werfr J and Noomen 1 J .

Physics

Physicists use an electron microscopy technique that involves microanalysis using either
Energy dispersive X-ray spectroscopy (EDS), Electron energy loss spectroscopy (EELS),
Infrared Spectroscopy(IR), Raman Spectroscopy, or cathodoluminescence (CL)
spectroscopy, in which the entire spectrum measured at each point is recorded. EELS
hyperspectral imaging is performed in a scanning transmission electron microscope
(STEM); EDS and CL mapping can be performed in STEM as well, or in a scanning electron
microscope or electron probe microanalyzer (EPMA). Often, multiple techniques (EDS,
EELS, CL) are used simultaneously.

In a "normal" mapping experiment, an image of the sample will be made that is simply the
intensity of a particular emission mapped in an XY raster. For example, an EDS map could
be made of a steel sample, in which iron x-ray intensity is used for the intensity grayscale of
the image. Dark areas in the image would indicate not-iron-bearing impurities. This could
potentially give misleading results; if the steel contained tungsten inclusions, for example,
the high atomic number of tungsten could result in bremsstrahlung radiation that made the
iron-free areas appear to be rich in iron.

By hyperspectral mapping, instead, the entire spectrum at each mapping point is acquired,
and a quantitative analysis can be performed by computer post-processing of the data, and

Hyperspectral imaging

411

a quantitative map of iron content produced. This would show which areas contained no
iron, despite the anomalous x-ray counts caused by bremsstrahlung. Because EELS
core-loss edges are small signals on top of a large background, hyperspectral imaging
allows large improvements to the quality of EELS chemical maps.

Similarly, in CL mapping, small shifts in the peak emission energy could be mapped, which
would give information regarding slight chemical composition changes or changes in the
stress state of a sample.

Surveillance

Hyperspectral surveillance is the implementation of hyperspectral scanning technology for
surveillance purposes. Hyperspectral imaging is particularly useful in military surveillance
because of measures that military entities now take to avoid airborne surveillance. Airborne
surveillance has been in effect since soldiers used tethered balloons to spy on troops during
the American Civil War, and since that time we have learned not only to hide from the
naked eye, but to mask our heat signature to blend in to the surroundings and avoid
infrared scanning, as well. The idea that drives hyperspectral surveillance is that
hyperspectral scanning draws information from such a large portion of the light spectrum
that any given object should have unique spectral signature in at least a few of the many

bands that get scanned.

Advantages and Disadvantages

The primary advantages to hyperspectral imaging is that, because an entire spectrum is
acquired at each point, the operator needs no a priori knowledge of the sample, and
post-processing allows all available information from the dataset to be mined.

The primary disadvantages are cost and complexity. Fast computers, sensitive detectors,
and large data storage capacities are needed for analyzing hyperspectral data. Significant
data storage capacity is necessary since hyperspectral cubes are large multi-dimensional
datasets, potentially exceeding hundreds of megabytes. All of these factors greatly increase
the cost of acquiring and processing hyperspectral data. Also, one of the hurdles that
researchers have had to face is finding ways to program hyperspectral satellites to sort
through data on their own and transmit only the most important images, as both

transmission and storage of that much data could prove difficult and costly. As a
relatively new analytical technique, the full potential of hyperspectral imaging has not yet
been realized.

See also

• Airborne Real-time Cueing Hyperspectral Enhanced Reconnaissance

• Full Spectral Imaging

• Multi-spectral image

• Chemical imaging

• Remote Sensing

• Sensor fusion

Hyperspectral imaging

412

External Links

ITT Visual Information Solutions - ENVI Hyperspectral Image Processing Software

References

[1] Schurmer, J.H., (Dec 2003) Hyperspectral imaging from space (http://www.afrlhorizons.com/Briefs/Dec03/

VS0302.html), Air Force Research Laboratories Technology Horizons
[2] Ellis, J., (Jan 2001) Searching for oil seeps and oil-impacted soil with hyperspectral imagery (http://www.

eomonline.com/Common/currentissues/Jan01/ellis.htm), Earth Observation Magazine.
[3] Smith, R.B. (July 14, 2006), Introduction to hyperspectral imaging with TMIPS (http://www. microimages.

com/getstart/pdf/hyp rspec.pdf), Microimages Tutorial Web site
[4] Lacar, F.M., et al., Use of hyperspectral imagery for mapping grape varieties in the Barossa Valley, South

Australia (http://hdl.handle.net/2440/39292), Geoscience and remote sensing symposium (IGARSS'01) -

IEEE 2001 International, vol.6 2875-2877p. doi: 10. 1109/IGARSS. 2001. 978191 (http://dx.doi.org/10.1109/

IGARSS. 2001. 978191)
[5] Ferwerda, J.G. (2005), Charting the quality of forage: measuring and mapping the variation of chemical

components in foliage with hyperspectral remote sensing (http://www.itc.nl/library/Papers_2005/phd/

ferwerda.pdf), Wageningen University, ITC Dissertation 126, 166p. ISBN 90-8504-209-7
[6] Tilling, A.K., et al., (2006) Remote sensing to detect nitrogen and water stress in wheat (http://www. regional

org.au/au/asa/2006/plenary/technology/4584_tillingak.htm), The Australian Society of Agronomy
[7] Werff H. (2006), Knowledge based remote sensing of complex objects: recognition of spectral and spatial

patterns resulting from natural hydrocarbon seepages (http://www.itc.nl/library/papers_2006/phd/vdwerff.

pdf), Utrecht University, ITC Dissertation 131, 138p. ISBN 90-6164-238-8
[8] Noomen, M.F. (2007), Hyperspectral reflectance of vegetation affected by underground hydrocarbon gas

seepage (http://www.itc.nl/library/papers_2007/phd/noomen.pdf), Enschede, ITC 151p. ISBN

978-90-8504-671-4.
[9] http://www.ittvis.com/ProductServices/ENVI.aspx

M ultispectral imaging

1. Redirect Multi-spectral image

Electron Microscopy

413

Electron Microscopy

1. redirect electron microscope

This is a subject of study.

Rory sees this as a potential money-maker in his bid for pron domination

Atomic force microscope

The atomic force microscope (AFM) or
scanning force microscope (SFM) is a very
high-resolution type of scanning probe
microscopy, with demonstrated resolution
of fractions of a nanometer, more than
1000 times better than the optical
diffraction limit. The precursor to the AFM,
the scanning tunneling microscope, was
developed by Gerd Binnig and Heinrich
Rohrer in the early 1980s, a development
that earned them the Nobel Prize for
Physics in 1986. Binnig, Quate and Gerber
invented the first AFM in 1986. The AFM is
one of the foremost tools for imaging,
measuring and manipulating matter at the
nanoscale. The information is gathered by
"feeling" the surface with a mechanical
probe. Piezoelectric elements that facilitate
tiny but accurate and precise movements
on (electronic) command enable the very
precise scanning.

5.0 |im/d isj

ptm/div
0.14

.0 pim/div

Topographic scan of a glass surface

Atomic force microscope

414

Basic principle

Part of a series of articles on

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Atomic force microscope
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Detector and

Feedback

Electronics

Photodiode

Sample Surface

Cantilever &Tip

PZT Scanner

Block Diagram of Atomic Force

Microscope

The AFM consists of a microscale cantilever with a
sharp tip (probe) at its end that is used to scan the
specimen surface. The cantilever is typically silicon or
silicon nitride with a tip radius of curvature on the
order of nanometers. When the tip is brought into
proximity of a sample surface, forces between the tip
and the sample lead to a deflection of the cantilever
according to Hooke's law. Depending on the situation,
forces that are measured in AFM include mechanical
contact force, Van der Waals forces, capillary forces,
chemical bonding, electrostatic forces, magnetic forces
(see Magnetic force microscope (MFM)), Casimir
forces, solvation forces etc. As well as force, additional
quantities may simultaneously be measured through the

Atomic force microscope

415

xlOOO

AFM cantilever (after use) in the
Scanning Electron Microscope,
magnification 1,000 x (image width

100 micrometers)

use of specialised types of probe (see Scanning thermal
microscopy, photothermal microspectroscopy, etc.).
Typically, the deflection is measured using a laser spot
reflected from the top surface of the cantilever into an
array of photodiodes. Other methods that are used
include optical interferometry, capacitive sensing or
piezoresistive AFM cantilevers. These cantilevers are
fabricated with piezoresistive elements that act as a
strain gauge. Using a Wheatstone bridge, strain in the
AFM cantilever due to deflection can be measured, but
this method is not as sensitive as laser deflection or
interferometry.

If the tip was scanned at a constant height, a risk would
exist that the tip collides with the surface, causing
damage. Hence, in most cases a feedback mechanism is
employed to adjust the tip-to-sample distance to
maintain a constant force between the tip and the
sample. Traditionally, the sample is mounted on a
piezoelectric tube, that can move the sample in the z
direction for maintaining a constant force, and the x
and y directions for scanning the sample. Alternatively
a 'tripod' configuration of three piezo crystals may be
employed, with each responsible for scanning in the x,y
and z directions. This eliminates some of the distortion
effects seen with a tube scanner. In newer designs, the
tip is mounted on a vertical piezo scanner while the
sample is being scanned in X and Y using another piezo
block. The resulting map of the area s = f(x,y) represents the topography of the sample.

X3000 lOpm i —

8kU

AFM cantilever (after use) in the
Scanning Electron Microscope,
magnification 3,000 x (image width

30 micrometers)

The AFM can be operated in a number of modes, depending on the application. In general,
possible imaging modes are divided into static (also called Contact) modes and a variety of
dynamic (or non-contact) modes where the cantilever is vibrated.

Imaging modes

The primary modes of operation are static (contact) mode and dynamic mode. In the static
mode operation, the static tip deflection is used as a feedback signal. Because the
measurement of a static signal is prone to noise and drift, low stiffness cantilevers are used
to boost the deflection signal. However, close to the surface of the sample, attractive forces
can be quite strong, causing the tip to 'snap-in' to the surface. Thus static mode AFM is
almost always done in contact where the overall force is repulsive. Consequently, this
technique is typically called 'contact mode'. In contact mode, the force between the tip and
the surface is kept constant during scanning by maintaining a constant deflection.

In the dynamic mode, the cantilever is externally oscillated at or close to its fundamental
resonance frequency or a harmonic. The oscillation amplitude, phase and resonance
frequency are modified by tip-sample interaction forces; these changes in oscillation with
respect to the external reference oscillation provide information about the sample's

Atomic force microscope

416

characteristics. Schemes for dynamic mode operation include frequency modulation and the
more common amplitude modulation. In frequency modulation, changes in the oscillation
frequency provide information about tip-sample interactions. Frequency can be measured
with very high sensitivity and thus the frequency modulation mode allows for the use of
very stiff cantilevers. Stiff cantilevers provide stability very close to the surface and, as a
result, this technique was the first AFM technique to provide true atomic resolution in
ultra-high vacuum conditions (Giessibl).

In amplitude modulation, changes in the oscillation amplitude or phase provide the
feedback signal for imaging. In amplitude modulation, changes in the phase of oscillation
can be used to discriminate between different types of materials on the surface. Amplitude
modulation can be operated either in the non-contact or in the intermittent contact regime.
In ambient conditions, most samples develop a liquid meniscus layer. Because of this,
keeping the probe tip close enough to the sample for short-range forces to become
detectable while preventing the tip from sticking to the surface presents a major hurdle for
the non-contact dynamic mode in ambient conditions. Dynamic contact mode (also called
intermittent contact or tapping mode) was developed to bypass this problem (Zhong et al.).
In dynamic contact mode, the cantilever is oscillated such that the separation distance
between the cantilever tip and the sample surface is modulated.

Amplitude modulation has also been used in the non-contact regime to image with atomic
resolution by using very stiff cantilevers and small amplitudes in an ultra-high vacuum
environment.

pH 3.89

25 nm

Tapping Mode

In tapping mode the cantilever is driven to oscillate

up and down at near its resonance frequency by a

small piezoelectric element mounted in the AFM tip

holder. The amplitude of this oscillation is greater

than 10 nm, typically 100 to 200 nm. Due to the

interaction of forces acting on the cantilever when

the tip comes close to the surface, Van der Waals

force or dipole-dipole interaction, electrostatic

forces, etc cause the amplitude of this oscillation to

decrease as the tip gets closer to the sample. An

electronic servo uses the piezoelectric actuator to

control the height of the cantilever above the

sample. The servo adjusts the height to maintain a

set cantilever oscillation amplitude as the cantilever

is scanned over the sample. A Tapping AFM image

is therefore produced by imaging the force of the

oscillating contacts of the tip with the sample

surface. This is an improvement on conventional

contact AFM, in which the cantilever just drags

across the surface at constant force and can result in surface damage. Tapping mode is

gentle enough even for the visualization of supported lipid bilayers or adsorbed single

pH 4.24

Single polymer chains (0.4 nm thick)
recorded in a tapping mode under aqueous
media with different pH. Green locations of
the two-chains-superposition correspond to
0.8 nm thickness (Roiter and Minko, 2005).

Atomic force microscope

417

polymer molecules (for instance, 0.4 nm thick chains of synthetic polyelectrolytes) under
liquid medium. At the application of proper scanning parameters, the conformation of
single molecules remains unchanged for hours (Roiter and Minko, 2005).

Non-Contact Mode

Here the tip of the cantilever does not contact the sample surface. The cantilever is instead
oscillated at a frequency slightly above its resonance frequency where the amplitude of
oscillation is typically a few nanometers (<10nm). The van der Waals forces, which are
strongest from lnm to lOnm above the surface, or any other long range force which
extends above the surface acts to decrease the resonance frequency of the cantilever. This
decrease in resonance frequency combined with the feedback loop system maintains a
constant oscillation amplitude or frequency by adjusting the average tip-to-sample distance.
Measuring the tip-to-sample distance at each (x,y) data point allows the scanning software
to construct a topographic image of the sample surface.

Non-contact mode AFM does not suffer from tip or sample degradation effects that are
sometimes observed after taking numerous scans with contact AFM. This makes
non-contact AFM preferable to contact AFM for measuring soft samples. In the case of rigid
samples, contact and non-contact images may look the same. However, if a few monolayers
of adsorbed fluid are lying on the surface of a rigid sample, the images may look quite
different. An AFM operating in contact mode will penetrate the liquid layer to image the
underlying surface, whereas in non-contact mode an AFM will oscillates above the adsorbed
fluid layer to image both the liquid and surface.

AFM -Beam Deflection Detection

Laser

Detector

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PFiotodiod
Detector

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Laser light from a solid state diode is reflected off the

back of the cantilever and collected by a position

sensitive detector (PSD) consisting of two closely

spaced photodiodes whose output signal is collected by

a differential amplifier. Angular displacement of

cantilever results in one photodiode collecting more

light than the other photodiode, producing an output

signal (the difference between the photodiode signals

normalized by their sum) which is proportional to the

deflection of the cantilever. It detects cantilever

deflections <lA (thermal noise limited). A long beam path (several cm) amplifies changes in

beam angle.

FHBtJbHck Loop MainlHiriH Conxilanl
0*r:illaiinn Amplitude nr Frequency

Controller
Electronics

Cantilever & Tip

Sample

AFM - Non-Contact Mode

Atomic force microscope

418

Solid State Laser Diode

Output:

A-B
B+A

Spirt Photodiode Detector

Force spectroscopy

Another major application of AFM (besides imaging) is

force spectroscopy, the measurement of force-distance

curves. For this method, the AFM tip is extended

towards and retracted from the surface as the static

deflection of the cantilever is monitored as a function of

piezoelectric displacement. These measurements have

been used to measure nanoscale contacts, atomic

bonding, Van der Waals forces, and Casimir forces,

dissolution forces in liquids and single molecule stretching and rupture forces (Hinterdorfer

& Dufrene). Forces of the order of a few pico-Newton can now be routinely measured with a

vertical distance resolution of better than 0.1 nanometer.

Cantilever and Tip

AFM Beam Deflection Detection

Problems with the technique include no direct measurement of the tip-sample separation
and the common need for low stiffness cantilevers which tend to 'snap' to the surface. The
snap-in can be reduced by measuring in liquids or by using stiffer cantilevers, but in the
latter case a more sensitive deflection sensor is needed. By applying a small dither to the
tip, the stiffness (force gradient) of the bond can be measured as well (Hoffmann et al.).

Identification of individual surface atoms

The AFM can be used to image and manipulate atoms
and structures on a variety of surfaces. The atom at the

individual atoms on the

"senses"

apex of the tip

underlying surface when it forms incipient chemical
bonds with each atom. Because these chemical
interactions subtly alter the tip's vibration frequency,
they can be detected and mapped.

Physicist Oscar Custance (Osaka University, Graduate
School of Engineering, Osaka, Japan) and his team used
this principle to distinguish between atoms of silicon,
tin and lead on an alloy surface (Nature 2007, 446, 64).

The trick is to first measure these forces precisely for
each type of atom expected in the sample. The team
found that the tip interacted most strongly with silicon
atoms, and interacted 23% and 41% less strongly with
tin and lead atoms, respectively. Thus, each different
type of atom can be identified in the matrix as the tip is moved across the surface.

Such a technique has been used now in biology and extended recently to cell biology.
Forces corresponding to (i) the unbinding of receptor ligand couples (ii) unfolding of
proteins (iii) cell adhesion at single cell scale have been gathered.

The atoms of a Sodium Chloride crystal
viewed with an Atomic Force

Microscope

Atomic force microscope

419

Advantages and disadvantages

The AFM has several advantages over the scanning
electron microscope (SEM). Unlike the electron

microscope which provides

two-dimensional

projection or a two-dimensional image of a sample, the

AFM provides a true three-dimensional surface profile.

Additionally, samples viewed by AFM do not require

any special treatments (such as metal/carbon coatings)

that would irreversibly change or damage the sample.

While an electron microscope needs an expensive

vacuum environment for proper operation, most AFM

modes can work perfectly well in ambient air or even a

liquid environment. This makes it possible to study

biological macromolecules and even living organisms. In principle, AFM can provide higher

resolution than SEM. It has been shown to give true atomic resolution in ultra-high vacuum

(UHV) and, more recently, in liquid environments. High resolution AFM is comparable in

resolution to Scanning Tunneling Microscopy and Transmission Electron Microscopy.

The first Atomic Force Microscope

A disadvantage of AFM compared with the scanning electron microscope (SEM) is the
image size. The SEM can image an area on the order of millimetres by millimetres with a
depth of field on the order of millimetres. The AFM can only image a maximum height on
the order of micrometres and a maximum scanning area of around 150 by 150 micrometres.

Another inconvenience is that an incorrect choice of tip for the required resolution can lead
to image artifacts. Traditionally the AFM could not scan images as fast as an SEM,
requiring several minutes for a typical scan, while a SEM is capable of scanning at near
real-time (although at relatively low quality) after the chamber is evacuated. The relatively
slow rate of scanning during AFM imaging often leads to thermal drift in the image
(Lapshin, 2004, 2007), making the AFM microscope less suited for measuring accurate
distances between artifacts on the image. However, several fast-acting designs were
suggested to increase microscope scanning productivity (Lapshin and Obyedkov, 1993)
including what is being termed videoAFM (reasonable quality images are being obtained
with videoAFM at video rate - faster than the average SEM). To eliminate image distortions
induced by thermodrift, several methods were also proposed (Lapshin, 2004, 2007).

AFM images can also be affected by hysteresis of the piezoelectric material (Lapshin, 1995)
and cross-talk between the (x,y,z) axes that may require software enhancement and
filtering. Such filtering could "flatten" out real topographical features. However, newer
AFM use real-time correction software (for example, feature-oriented scanning, Lapshin,
2004, 2007) or closed-loop scanners which practically eliminate these problems. Some AFM
also use separated orthogonal scanners (as opposed to a single tube) which also serve to
eliminate cross-talk problems.

Due to the nature of AFM probes, they cannot normally measure steep walls or overhangs.
Specially made cantilevers can be modulated sideways as well as up and down (as with
dynamic contact and non-contact modes) to measure sidewalls, at the cost of more
expensive cantilevers and additional artifacts.

Atomic force microscope

420

Piezoelectric Scanners

AFM scanners are made from piezoelectric material, which expands and contracts
proportionally to an applied voltage. Whether they elongate or contract depends upon the
polarity of the voltage applied. The scanner is constructed by combining independently
operated piezo electrodes for X, Y, & Z into a single tube, forming a scanner which can
manipulate samples and probes with extreme precision in 3 dimensions.

Scanners are characterized by their sensitivity which is
the ratio of piezo movement to piezo voltage, i.e. by
how much the piezo material extends or contracts per
applied volt. Because of differences in material or size,
the sensitivity varies from scanner to scanner.

Typical scanner piezo tube and X-Y-Z configurations. AC Signals applied to conductive areas of
lie tube create piezo movement along the three major axes

Metal

Electrode

Piezoelectric
Material

GND

AC voltages applied to the different electrodes of the piezoelectric seamier produce a scanning
raster motion in X and Y There are two seements of the piezoelectnc crystal for X (X & X) and Y
(Y&Y).

Piezoelectric Scanner

Sensitivity varies non-linearly with respect to scan size.
Piezo scanners exhibit more sensitivity at the end than
at the beginning of a scan. This causes the forward and
reverse scans to behave differently and display
hysteresis between the two scan directions. This can be
corrected by applying a non-linear voltage to the piezo
electrodes to cause linear scanner movement and calibrating the scanner accordingly.

The sensitivity of piezoelectric materials decreases exponentially with time. This causes
most of the change in sensitivity to occur in the initial stages of the scanner's life.
Piezoelectric scanners are run for approximately 48 hours before they are shipped from the
factory so that they are past the point where we can expect large changes in sensitivity. As
the scanner ages, the sensitivity will change less with time and the scanner would seldom
require recalibration.

See also

• Interfacial force microscope

• Friction force microscope

• Scanning tunneling microscope

• Scanning probe microscopy

• Scanning voltage microscopy

References

• A. D L. Humphris, M. J. Miles, J. K. Hobbs, A mechanical microscope: High-speed atomic
force microscopy L , Applied Physics Letters 86, 034106 (2005).

• D. Sarid, Scanning Force Microscopy, Oxford Series in Optical and Imaging Sciences,
Oxford University Press, New York (1991)

• R. Dagani, Individual Surface Atoms Identified, Chemical & Engineering News, 5 March
2007, page 13. Published by American Chemical Society

• Q. Zhong, D. Inniss, K. Kjoller, V. B. Elings, Surf. Sci. Lett. 290, L688 (1993).

• V. J. Morris, A. R. Kirby, A. P. Gunning, Atomic Force Microscopy for Biologists. (Book)
(December 1999) Imperial College Press.

T21

• J. W. Cross SPM - Scanning Probe Microscopy Website

• P. Hinterdorfer, Y. F. Dufrene, Nature Methods, 3, 5 (2006)

Atomic force microscope

421

F. Giessibl, Advances in Atomic Force Microscopy, Reviews of Modern Physics 75 (3),

949-983 (2003).

R. H. Eibl, V.T. Moy, Atomic force microscopy measurements of protein-ligand

interactions on living cells. Methods Mol Biol. 305:439-50 (2005)

P. M. Hoffmann, A. Oral, R. A. Grimble, H. O. Ozer, S. Jeffery, J. B. Pethica, Proc. Royal

Soc. A 457, 1161 (2001).

R. V. Lapshin, O. V. Obyedkov, Fast-acting piezoactuator and digital feedback loop for

T31

scanning tunneling microscopes , Review of Scientific Instruments, vol. 64, no. 10, pp.

2883-2887, 1993.

R. V. Lapshin, Analytical model for the approximation of hysteresis loop and its

application to the scanning tunneling microscope c , Review of Scientific Instruments,

vol. 66, no. 9, pp. 4718-4730, 1995.

R. V. Lapshin, Feature-oriented scanning methodology for probe microscopy and

nanotechnology , Nanotechnology, vol. 15, iss. 9, pp. 1135-1151, 2004.

R. V. Lapshin, Automatic drift elimination in probe microscope images based on

techniques of counter-scanning and topography feature recognition L , Measurement

Science and Technology, vol. 18, iss. 3, pp. 907-927, 2007.

P. West, Introduction to Atomic Force Microscopy: Theory, Practice and Applications —

www.AFMUniversity.org

R. W. Carpick and M. Salmeron, Scratching the surface: Fundamental investigations of

tribology with atomic force microscopy [ , Chemical Reviews, vol. 97, iss. 4, pp.

1163-1194 (2007).

Y. Roiter and S. Minko, AFM Single Molecule Experiments at the Solid-Liquid Interface:

In Situ Conformation of Adsorbed Flexible Polyelectrolyte Chains , Journal of the

American Chemical Society, vol. 127, iss. 45, pp. 15688-15689 (2005).

References

[ 1 ] http ://www. infinite sima. com/downloads/ APL_paper.pdf

[2] http://www.mobot.org/jwcross/spm/

[3] http://www.nanoworld.Org/homepages/lapshin/publications.htm#fastl993

[4] http://www.nanoworld.Org/homepages/lapshin/publications.htm#analyticall995

[5] http://www.nanoworld.Org/homepages/lapshin/publications.htm#feature2004

[6] http://www.nanoworld.Org/homepages/lapshin/publications.htm#automatic2007

[7] http://dx.doi.org/10.1021/cr960068q

[8] http://dx.doi.org/10.1021/ja0558239

X-ray microscope

422

X-ray microscope

An X-ray microscope uses electromagnetic radiation in the soft X-ray band to produce
images of very small objects.

Unlike visible light, X-rays do not reflect or refract easily, and they are invisible to the
human eye. Therefore the basic process of an X-ray microscope is to expose film or use a
charge-coupled device (CCD) detector to detect X-rays that pass through the specimen. It is
a contrast imaging technology using the difference in absorption of soft x-ray in the water
window region (wavelength region: 2.3 - 4.4 nm, photon energy region: 0.28 - 0.53 keV) by
the carbon atom (main element composing the living cell) and the oxygen atom (main
element for water).

Early X-ray microscopes by Paul Kirkpatrick and Albert Baez used grazing-incidence
reflective optics to focus the X-rays, which grazed X-rays off parabolic curved mirrors at a
very high angle of incidence. An alternative method of focusing X-rays is to use a tiny
fresnel zone plate of concentric gold or nickel rings on a silicon dioxide substrate. Sir
Lawrence Bragg produced some of the first usable X-ray images with his apparatus in the
late 1940's.

In the 1950's Newberry produced a shadow X-ray
microscope which placed the specimen between the
source and a target plate, this became the basis for
the first commercial X-ray microscopes from the
General Electric Company.

The Advanced Light Source (ALS)[1] in Berkeley CA
is home to XM-1 (http://www.cxro.lbl.gov/BL612/
), a full field soft X-ray microscope operated by the
Center for X-ray Optics [2] and dedicated to various
applications in modern nanoscience, such as
nanomagnetic materials,

environmental

and

Indirect drive laser inertial confinement

fusion uses a "hohlraum" which is

irradiated with laser beam cones from

either side on it its inner surface to bathe a

fusion microcapsule inside with smooth

high intensity X-rays. The highest energy

X-rays which penetrate the hohlraum can

be visualized using an X-ray microscope

such as here, where X-radiation is

represented in orange/red.

materials sciences and biology. XM-1 uses an X-ray
lens to focus X-rays on a CCD, in a manner similar
to an optical microscope. XM-1 still holds the world
record in spatial resolution with Fresnel zone plates
down to 15nm and is able to combine high spatial
resolution with a sub-lOOps time resolution to study
e.g. ultrafast spin dynamics.

The ALS is also home to the world's first soft x-ray microscope designed for biological and
biomedical research. This new instrument, XM-2 was designed and built by scientists from
the National Center for X-ray Tomography (http:/ / next. lbl. gov). XM-2 is capable of
producing 3-Dimensional tomograms of cells.

Sources of soft X-rays suitable for microscopy, such as synchrotron radiation sources, have
fairly low brightness of the required wavelengths, so an alternative method of image
formation is scanning transmission soft X-ray microscopy. Here the X-rays are focused to a
point and the sample is mechanically scanned through the produced focal spot. At each
point the transmitted X-rays are recorded with a detector such as a proportional counter or
an avalanche photodiode. This type of Scanning Transmission X-ray Microscope (STXM)

X-ray microscope

423

was first developed by researchers at Stony Brook University and was employed at the
National Synchrotron Light Source at Brookhaven National Laboratory.

The resolution of X-ray microscopy lies between that of the optical microscope and the
electron microscope. It has an advantage over conventional electron microscopy in that it
can view biological samples in their natural state. Electron microscopy is widely used to
obtain images with nanometer level resolution but the relatively thick living cell cannot be
observed as the sample has to be chemically fixed, dehydrated, embedded in resin, then
sliced ultra thin. However, it should be mentioned that cryo-electron microscopy allows the
observation of biological specimens in their hydrated natural state. Until now, resolutions
of 30 nanometer are possible using the Fresnel zone plate lens which forms the image using
the soft x-rays emitted from a synchrotron. Recently, more researchers have begun to use
the soft x-rays emitted from laser-produced plasma rather than synchrotron radiation.

Additionally, X-rays cause fluorescence in most materials, and these emissions can be
analyzed to determine the chemical elements of an imaged object. Another use is to
generate diffraction patterns, a process used in X-ray crystallography. By analyzing the
internal reflections of a diffraction pattern (usually with a computer program), the
three-dimensional structure of a crystal can be determined down to the placement of
individual atoms within its molecules. X-ray microscopes are sometimes used for these
analyses because the samples are too small to be analyzed in any other way.

See also

Synchrotron X-ray tomographic
microscopy

External links

Application of X-ray microscopy in
analysis of living hydrated cells [ - 1

Hard X-ray microbeam experiments with
a sputtered-sliced Fresnel zone plate and
its applications

Scientific applications of soft x-ray

[4]

microscopy
Microarrays products

v 1 ^

<**!■■■.

A square beryllium foil mounted in a steel case to be
used as a window between a vacuum chamber and an
X-ray microscope. Beryllium, due to its low Z number

is highly transparent to X-rays.

X-ray microscope

424

References

[1] http://www-als.lbl.gov

[2] http://www.cxro.lbl.gov

[3] http://www.ncbi.nlm.nih. gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&

list_uids= 11 972376
[4] http://www.cxro.lbl. gov/BL612/index.php?content=research.html
[5] http://www.ibio.co.il/Products.aspx?level=2&prodID=17

Fluorescence microscope

A fluorescence microscope (colloquially synonymous
with epifluorescent microscope) is a light microscope
used to study properties of organic or inorganic
substances using the phenomena of fluorescence and
phosphorescence instead of, or in addition to, reflection

rn r 21

and absorption. 1 J L J

A fluorescent microscope (Olympus
BX61), coupled with a digital camera.

Fluorescence microscope

425

Technique

In most cases, a component of interest in the specimen
is specifically labeled with a fluorescent molecule called
a fluorophore (such as green fluorescent protein (GFP),
fluorescein or DyLight 488). ^ The specimen is
illuminated with light of a specific wavelength (or
wavelengths) which is absorbed by the fluorophores,
causing them to emit longer wavelengths of light (of a
different color than the absorbed light). The
illumination light is separated from the much weaker
emitted fluorescence through the use of an emission
filter. Typical components of a fluorescence microscope
are the light source (xenon arc lamp or mercury-vapor
lamp), the excitation filter, the dichroic mirror (or
dichromatic beamsplitter), and the emission filter (see
figure below). The filters and the dichroic are chosen to

match

the

spectral excitation

and

emission

An inverted fluorescent microscope
(Nikon TE2000). Note the orange plate

that allows the user to look at the
sample while protecting his eyes from

the excitation UV light.

characteristics of the fluorophore used to label the

n 1
specimen. 1 J In this manner, a single fluorophore (color)

is imaged at a time. Multi-color images of several

fluorophores must be composed by combining several single-color images. *

Most fluorescence microscopes in use are epifluorescence microscopes (i.e. excitation and
observation of the fluorescence are from above (epi-) the specimen). These microscopes
have become an important part in the field of biology, opening the doors for more advanced
microscope designs, such as the confocal laser scanning microscope and the total internal
reflection fluorescence microscope (TIRF). The Vertico SMI combining localisation
microscopy with spatially modulated illumination uses standard fluorescence dyes and
reaches an optical resolution below 10 nanometers (1 nanometer = 1 nm =

Fluorophores lose their ability to fluoresce as they are illuminated in a process called
photobleaching. Special care must be taken to prevent photobleaching through the use of
more robust fluorophores, by minimizing illumination, or by introducing a scavenger system
to reduce the rate of photobleaching.

1 x 10 9 m).

Fluorescence microscope

426

Epifluorescence microscopy

detector

ocuiar

emission filter

dichroic mirror

ight source

excitation filter

objective
J

Epifluorescence microscopy is a method of fluorescence
microscopy that is widely used in life sciences. The
excitatory light is passed from above (or, for inverted
microscopes, from below), through the objective and
then onto the specimen instead of passing it first
through the specimen. (In the latter case the
transmitted excitatory light reaches the objective
together with light emitted from the specimen). The
fluorescence in the specimen gives rise to emitted light
which is focused to the detector by the same objective
that is used for the excitation. A filter between the
objective and the detector filters out the excitation light
from fluorescent light. Since most of the excitatory light
is transmitted through the specimen, only reflected
excitatory light reaches the objective together with the
emitted light and this method therefore gives an improved signal to noise ratio. A common
use in biology is to apply fluorescent or fluorochrome stains to the specimen in order to
image a protein or other molecule of interest.

specimen

Schematic of a fluorescence

microscope.

Gallery

w-<57 w-528

w=617 Combined

•

-
<

- 5 5

Epifluorescent imaging of
the three components in a

dividing human cancer

cell. DNA is stained blue,

a protein called INCENP

is green, and the

microtubules are red.

Each fluorophore is

imaged separately using a

different combination of

excitation and emission

filters, and the images are

captured sequentially

using a digital CCD

camera, then overlaid to

give a complete image.

Endothelial cells under

the microscope. Nuclei

are stained blue with

DAPI, microtubules are

marked green by an

antibody bound to FITC

and actin filaments are

labelled red with

phalloidin bound to

TRITC. Bovine pulmonary

artery endothelial (BPAE)

cells

human lymphocyte

nucleus stained with DAPI

with chromosome 13

(green) and 21 (red)

centromere probes

hybrydized (Fluorescent

in situ hybridization

(FISH))

Yeast cell membrane

visualized by some

membrane proteins fused

with RFP and GFP

fluorescent markers.

Imposition of light from

both of markers results in

yellow colour.

Fluorescence microscope

427

See also

• Microscope

• Mercury-vapor lamp

• Xenon arc lamp

• Stokes shift

References

[1] Spring KR, Davidson MW.

http://www.microscopyu.com/articles/fluorescence/fluorescenceintro.htmll "Introduction to Fluorescence
Microscopy". Nikon MicroscopyU. http://www.microscopyu.com/articles/fluorescence/fluorescenceintro.
html. Retrieved on 2008-09-28.

[2] http://nobelprize.org/educational_games/physics/microscopes/fluorescence/! "The Fluorescence Microscope"
Microscopes— Help Scientists Explore Hidden Worlds. The Nobel Foundation, http://nobelprize.org/
educationalgames/physics/microscopes/fluorescence/. Retrieved on 2008-09-28.

Further reading

• Bradbury, S. and Evennett, P., Fluorescence microscopy., Contrast Techniques in Light
Microscopy., BIOS Scientific Publishers, Ltd., Oxford, United Kingdom (1996).

• Rost, F., Quantitative fluorescence microscopy. Cambridge University Press, Cambridge,
United Kingdom (1991).

• Rost, F., Fluorescence microscopy. Vol. I. Cambridge University Press, Cambridge,
United Kingdom (1992). Reprinted with update, 1996.

• Rost, F., Fluorescence microscopy. Vol. II. Cambridge University Press, Cambridge,
United Kingdom (1995).

• Rost, F. and Oldfield, R., Fluorescence microscopy., Photography with a Microscope,
Cambridge University Press, Cambridge, United Kingdom (2000).

External links

• WikiScope (http://wikiscope.org)

• Fluorophores.org (http://www.fluorophores.org) - Database of fluorescent dyes.

Fluorescence correlation spectroscopy

428

Fluorescence correlation
spectroscopy

Fluorescence correlation spectroscopy (FCS) is a common technique used by physicists,
chemists, and biologists to experimentally characterize the dynamics of fluorescent species
(e.g. single fluorescent dye molecules in nanostructured materials, autofluorescent proteins
in living cells, etc.). Although the name indicates a specific link to fluorescence, the method
is used today also for exploring other forms of luminescence (like reflections, luminescence
from gold-beads or quantum dots or phosphorescent species). The "spectroscopy" in the
name is not readily found as in common usage a spectrum is generally understood to be a
frequency spectrum. The autocorrelation is a genuine form of spectrum, however: It is the
time-spectrum generated from the power spectrum (via inverse fourier transform).

Commonly, FCS is employed in the context of optical microscopy, in particular confocal or
two photon microscopy. In these techniques light is focused on a sample and the measured
fluorescence intensity fluctuations (due to diffusion, physical or chemical reactions,
aggregation, etc.) are analyzed using the temporal autocorrelation. Because the measured
property is essentially related to the magnitude and/or the amount of fluctuations, there is
an optimum measurement regime at the level when individual species enter or exit the
observation volume (or turn on and off in the volume). When too many entities are
measured at the same time the overall fluctuations are small in comparison to the total
signal and may not be resolvable - in the other direction, if the individual fluctuation-events
are too sparse in time, one measurement may take prohibitively too long. FCS is in a way
the fluorescent counterpart to dynamic light scattering, which uses coherent light
scattering, instead of (incoherent) fluorescence.

When an appropriate model is known, FCS can be used to obtain quantitative information
such as

• diffusion coefficients

• hydrodynamic radii

• average concentrations

• kinetic chemical reaction rates

• singlet-triplet dynamics

Because fluorescent markers come in a variety of colors and can be specifically bound to a
particular molecule (e.g. proteins, polymers, metal-complexes, etc.), it is possible to study
the behavior of individual molecules (in rapid succession in composite solutions). With the
development of sensitive detectors such as avalanche photodiodes the detection of the
fluorescence signal coming from individual molecules in highly dilute samples has become
practical. With this emerged the possibility to conduct FCS experiments in a wide variety of
specimens, ranging from materials science to biology. The advent of engineered cells with
genetically tagged proteins (like green fluorescent protein) has made FCS a common tool
for studying molecular dynamics in living cells.

Fluorescence correlation spectroscopy

429

History

Signal-correlation techniques have first been experimentally applied to fluorescence in

1972 by Magde, Elson, and Webb L J , who are therefore commonly credited as the
"inventors" of FCS. The technique was further developed in a group of papers by these and
other authors soon after, establishing the theoretical foundations and types of
applications. See Thompson (1991) for a review of that period.

Beginning in 1993 , a number of improvements in the measurement techniques-notably
using confocal microscopy, and then two photon microscopy-to better define the
measurement volume and reject background greatly improved the signal-to-noise and
allowed single molecule sensitivity. Since then, there has been a renewed interest in

FCS, and as of August 2007 there has been over 3,000 papers using FCS found in Web of
Science. See Krichevsky and Bonnet for a recent review. In addition, there has been a
flurry of activity extending FCS in various ways, for instance to laser scanning and spinning
disk confocal microscopy (from a stationary, single point measurement), in using
cross-correlation (FCCS) between two fluorescent channels instead of autocorrelation, and
in using Forster Resonance Energy Transfer (FRET) instead of fluorescence.

Typical FCS setup

The typical FCS setup consists of a laser line (wavelengths ranging typically from 405 - 633
nm (cw), and from 690 - 1100 nm (pulsed)), which is reflected into a microscope objective
by a dichroic mirror. The laser beam is focused in the sample, which contains fluorescent
particles (molecules) in such high dilution, that only few are within the focal spot (usually 1
- 100 molecules in one fL). When the particles cross the focal volume, they fluoresce. This
light is collected by the same objective and, because it is red-shifted with respect to the
excitation light it passes the dichroic reaching a detector, typically a photomultiplier tube
or avalanche photodiode detector. The resulting electronic signal can be stored either
directly as an intensity versus time trace to be analyzed at a later point, or, computed to
generate the autocorrelation directly (which requires special acquisition cards). The FCS
curve by itself only represents a time-spectrum. Conclusions on physical phenomena have
to be extracted from there with appropriate models. The parameters of interest are found
after fitting the autocorrelation curve to modeled functional forms. c ^ The setup is shown
in Figure 1 .

The Measurement Volume

The measurement volume is a convolution of illumination (excitation) and detection
geometries, which result from the optical elements involved. The resulting volume is
described mathematically by the point spread function (or PSF), it is essentially the image
of a point source. The PSF is often described as an ellipsoid (with unsharp boundaries) of
few hundred nanometers in focus diameter, and almost one micrometre along the optical
axis. The shape varies significantly (and has a large impact on the resulting FCS curves)
depending on the quality of the optical elements (it is crucial to avoid astigmatism and to
check the real shape of the PSF on the instrument). In the case of confocal microscopy, and
for small pinholes (around one Airy unit), the PSF is well approximated by Gaussians:

Fluorescence correlation spectroscopy

430

where Jo is the peak intensity, r and z are radial and axial position, and ^^and ^are the
radial and axial radii, and ^z ^ w a». This Gaussian form is assumed in deriving the
functional form of the autocorrelation.

Typically ^xyis 200-300 nm, and ^zis 2-6 times larger. J One common way of calibrating
the measurement volume parameters is to perform FCS on a species with known diffusion
coefficient and concentration (see below). Diffusion coefficients for common fluorophores in
water are given in a later section.

The Gaussian approximation works to varying degrees depending on the optical details, and
corrections can sometimes be applied to offset the errors in approximation. ]

Autocorrelation Function

The (temporal) autocorrelation function is the correlation of a time series with itself shifted
by time T, as a function of 7":

{SI(t)SI(t + t)) (I(t)I(t + r)) _

where SI(t) = I(t) — (I(t)) is the deviation from the mean intensity. The normalization
(denominator) here is the most commonly used for FCS, because then the correlation at
r = 0, G(0), is related to the average number of particles in the measurement volume.

Interpreting the Autocorrelation Function

To extract quantities of interest, the autocorrelation data can be fitted, typically using a
nonlinear least squares algorithm. The fit's functional form depends on the type of
dynamics (and the optical geometry in question).

Normal Diffusion

The fluorescent particles used in FCS are small and thus experience thermal motions in
solution. The simplest FCS experiment is thus normal 3D diffusion, for which the
autocorrelation is:

G(T) - G(0 \l + (T/T D mi + a-*<r/T D) y» + G <°°>

where & = uJ z /UJ X yis the ratio of axial to radial e~ 2 radii of the measurement volume, and

T £?is the characteristic residence time. This form was derived assuming a Gaussian

measurement volume. Typically, the fit would have three free parameters--G(O), C?(oo), and

r D --from which the diffusion coefficient and fluorophore concentration can be obtained.
With the normalization used in the previous section, G(0) gives the mean number of

diffusers in the volume <N>, or equivalently-with knowledge of the observation volume

size-the mean concentration:

< N > V eff <C>'

where the effective volume is found from integrating the Gaussian form of the
measurement volume and is given by:

T/ _3/2 2 . ,

Veff = K W^W*-

r D gives the diffusion coefficient: D = uj" xy jAro-

Fluorescence correlation spectroscopy

431

Anomalous diffusion

If the diffusing particles are hindered by obstacles or pushed by a force (molecular motors,
flow, etc.) the dynamics is often not sufficiently well-described by the normal diffusion
model, where the mean squared displacement (MSD) grows linearly with time. Instead the
diffusion may be better described as anomalous diffusion, where the temporal dependenc of
the MSD is non-linear as in the power-law:

MSD = 6D a t a

where D a is an anomalous diffusion coefficient. "Anomalous diffusion" commonly refers

only to this very generic model, and not the many other possibilities that might be

described as anomalous. Also, a power law is, in a strict sense, the expected form only for a

narrow range of rigorously defined systems, for instance when the distribution of obstacles

is fractal. Nonetheless a power law can be a useful approximation for a wider range of

systems.

The FCS autocorrelation function for anomalous diffusion is:

GW - G(0) (1 + (r/^-Xl + a-Hr/r D} ^ + G <°°> -

where the anomalous exponent a is the same as above, and becomes a free parameter in
the fitting.

Using FCS, the anomalous exponent has been shown to be an indication of the degree of
molecular crowding (it is less than one and smaller for greater degrees of crowding) 1 J .

Polydisperse diffusion

If there are diffusing particles with different sizes (diffusion coefficients), it is common to fit
to a function that is the sum of single component forms:

G(t) = G*(0) £ Tl , ,_,_ , w * __.„_,_ , v[n + G(co)

(l + {rfriv))(l + a-*{T/r D d)W

where the sum is over the number different sizes of particle, indexed by i, and Q i gives the
weighting, which is related to the quantum yield and concentration of each type. This
introduces new parameters, which makes the fitting more difficult as a higher dimensional
space must be searched. Nonlinear least square fitting typically becomes unstable with
even a small number of T A*s. A more robust fitting scheme, especially useful for
polydisperse samples, is the Maximum Entropy Method^ J .

Diffusion with flow

With diffusion together with a uniform flow with velocity t'in the lateral direction, the
autocorrelation is :

G(T) - ^(ITFMlW^"^-^''^ 1 ^ 001

where t v = uj X yf vis the average residence time if there is only a flow (no diffusion).

Fluorescence correlation spectroscopy

432

Chemical relaxation

A wide range of possible FCS experiments involve chemical reactions that continually
fluctuate from equilibrium because of thermal motions (and then "relax"). In contrast to
diffusion, which is also a relaxation process, the fluctuations cause changes between states
of different energies. One very simple system showing chemical relaxation would be a
stationary binding site in the measurement volume, where particles only produce signal
when bound (e.g. by FRET, or if the diffusion time is much faster than the sampling
interval). In this case the autocorrelation is:

G(t) = G(0) exp(-r/r B ) + G(oo)

where

-l

TB = {km + Kff)

is the relaxation time and depends on the reaction kinetics (on and off rates), and:
G(0) = 7^^- = t^tK

K > (N) k aff (N)

is related to the equilibrium constant K.

Most systems with chemical relaxation also show measureable diffusion as well, and the
autocorrelation function will depend on the details of the system. If the diffusion and
chemical reaction are decoupled, the combined autocorrelation is the product of the
chemical and diffusive autocorrelations.

Triplet State Correction

The autocorrelations above assume that the fluctuations are not due to changes in the
fluorescent properties of the particles. However, for the majority of (bio)organic
fluorophores--e.g. green fluorescent protein, rhodamine, Cy3 and Alexa Fluor dyes-some
fraction of illuminated particles are excited to a triplet state (or other non-radiative
decaying states) and then do not emit photons for a characteristic relaxation time T F.
Typically r f'is on the order of microseconds, which is usually smaller than the dynamics of
interest (e.g. T D) but large enough to be measured. A multiplicative term is added to the
autocorrelation account for the triplet state. For normal diffusion:

where Fis the fraction of particles that have entered the triplet state and T P\s the
corresponding triplet state relaxation time. If the dynamics of interest are much slower
than the triplet state relaxation, the short time component of the autocorrelation can simply
be truncated and the triplet term is unnecessary.

Common fluorescent probes

The fluorescent species used in FCS is typically a biomolecule of interest that has been
tagged with a fluorophore (using immunohistochemistry for instance), or is a naked
fluorophore that is used to probe some environment of interest (e.g. the cytoskeleton of a
cell). The following table gives diffusion coefficients of some common fluorophores in water
at room temperature, and their excitation wavelengths.

Fluorescent dye

D (xlO 10 m 2 s 1 )

Excitation
wavelength (nni)

Reference

Fluorescence correlation spectroscopy

433

Rhodamine 6G

2.8, 3.0, 4.14 ± 0.05 @ 25.00 °C

514

[16] [17] [18]

t t

Rhodamine 110

2.7

488

[19]

Tetramethyl rhodamine

2.6

543

Cy3

2.8

543

Cy5

2.5, 3.7 ± 0.15 @ 25.00 °C

633

[20] [21]

carboxyfluorescein

3.2

488

Alexa-488

1.96

488

[22]

Atto655-maleimide

4.07 ± 0.1 @ 25.00 °C

663

[23]

Atto655-carboxylicacid

4.26 ± 0.08 @ 25.00 °C

663

[24]

2Q, 7Q-difluorofluorescein
(Oregon Green488)

4.11 ± 0.06 @ 25.00 °C

498

[25]

Variations of FCS

FCS almost always refers to the single point single channel, temporal autocorrelation
measurement, although the term "fluorescence correlation spectroscopy" out of its
historical scientific context implies no such restriction. FCS has been extended in a number
of variations by different researchers, with each extension generating another name
(usually an acronym).

Fluorescence Cross-Correlation Spectroscopy (FCCS)

FCS is sometimes used to study molecular interactions using differences in diffusion times
(e.g. the product of an association reaction will be larger and thus have larger diffusion
times than the reactants individually); however, FCS is relatively insensitive to molecular
mass as can be seen from the following equation relating molecular mass to the diffusion
time of globular particles (e.g. proteins):

2kT K }

where 7 ?is the viscosity of the sample and Mis the molecular mass of the fluorescent
species. In practice, the diffusion times need to be sufficiently different-a factor of at least
1.6-which means the molecular masses must differ by a factor of 4. J Dual color
fluorescence cross-correlation spectroscopy (FCCS) measures interactions by
cross-correlating two or more fluorescent channels (one channel for each reactant), which
distinguishes interactions more sensitively than FCS, particularly when the mass change in
the reaction is small.

Fluorescence correlation spectroscopy

434

Two- and three- photon FCS excitation

Several advantages in both spatial resolution and minimizing photodamage/photobleaching
in organic and/or biological samples are obtained by two-photon or three-photon excitation

FCS [27] [28] [29] [30] [31]

FRET-FCS

Another FCS based approach to studying molecular interactions uses fluorescence
resonance energy transfer (FRET) instead of fluorescence, and is called FRET-FCS. J With
FRET, there are two types of probes, as with FCCS; however, there is only one channel and
light is only detected when the two probes are very close-close enough to ensure an
interaction. The FRET signal is weaker than with fluorescence, but has the advantage that
there is only signal during a reaction (aside from autofluorescence).

Image Correlation Spectroscopy (ICS)

When the motion is slow (in biology, for example, diffusion in a membrane), getting
adequate statistics from a single-point FCS experiment may take a prohibitively long time.
More data can be obtained by performing the experiment in multiple spatial points in
parallel, using a laser scanning confocal microscope. This approach has been called Image

rooi

Correlation Spectroscopy (ICS) . The measurements can then be averaged together.

Another variation of ICS performs a spatial autocorrelation on images, which gives
information about the concentration of particles^ ^ . The correlation is then averaged in
time.

A natural extension of the temporal and spatial correlation versions is spatio-temporal ICS
(STICS) c . In STICS there is no explicit averaging in space or time (only the averaging
inherent in correlation). In systems with non-isotropic motion (e.g. directed flow,
asymmetric diffusion), STICS can extract the directional information. A variation that is
closely related to STICS (by the Fourier transform) is k-space Image Correlation
Spectroscopy (kICS). [36]

There are cross-correlation versions of ICS as well. ]

Scanning FCS variations

Some variations of FCS are only applicable to serial scanning laser microscopes. Image
Correlation Spectroscopy and its variations all were implemented on a scanning confocal or
scanning two photon microscope, but transfer to other microscopes, like a spinning disk
confocal microscope. Raster ICS (RICS) [37] , and position sensitive FCS (PSFCS) [38]
incorporate the time delay between parts of the image scan into the analysis. Also, low
dimensional scans (e.g. a circular ringr -only possible on a scanning system-can access
time scales between single point and full image measurements. Scanning path has also
been made to adaptive ly follow particles.

Fluorescence correlation spectroscopy

435

Spinning disk FCS, and spatial mapping

Any of the image correlation spectroscopy methods can also be performed on a spinning
disk confocal microscope, which in practice can obtain faster imaging speeds compared to a
laser scanning confocal microscope. This approach has recently been applied to diffusion in
a spatially varying complex environment, producing a pixel resolution map of diffusion
coefficient. . The spatial mapping of diffusion with FCS has subsequently been extended
to TIRF system. J Spatial mapping of dynamics using correlation techniques had been
applied before, but only at sparse points or at coarse resolution^ J .

Total internal reflection FCS

Total internal reflection fluorescence (TIRF) is a microscopy approach that is only sensitive
to a thin layer near the surface of a coverslip, which greatly minimizes background
fluorscence. FCS has been extended to that type of microscope, and is called TIR-FCS C
Because the fluorescence intensity in TIRF falls off exponentially with distance from the
coverslip (instead of as a Gaussian with a confocal), the autocorrelation function is
different.

Other fluorescent dynamical approaches

There are two main non-correlation alternatives to FCS that are widely used to study the
dynamics of fluorescent species.

Fluorescence recovery after photobleaching (FRAP)

In FRAP, a region is briefly exposed to intense light, irrecoverably photobleaching
fluorophores, and the fluorescence recovery due to diffusion of nearby (non-bleached)
fluorophores is imaged. A primary advantage of FRAP over FCS is the ease of interpreting
qualitative experiments common in cell biology. Differences between cell lines, or regions
of a cell, or before and after application of drug, can often be characterized by simple
inspection of movies. FCS experiments require a level of processing and are more sensitive
to potentially confounding influences like: rotational diffusion, vibrations, photobleaching,
dependence on illumination and fluorescence color, inadequate statistics, etc. It is much
easier to change the measurement volume in FRAP, which allows greater control. In
practice, the volumes are typically larger than in FCS. While FRAP experiments are
typically more qualitative, some researchers are studying FRAP quantitatively and including
binding dynamics. ^ A disadvantage of FRAP in cell biology is the free radical perturbation
of the cell caused by the photobleaching. It is also less versatile, as it cannot measure
concentration or rotational diffusion, or co-localization. FRAP requires a significantly higher
concentration of fluorophores than FCS.

Particle tracking

In particle tracking, the trajectories of a set of particles are measured, typically by applying
particle tracking algorithms to movies. [46] Particle tracking has the advantage that all the
dynamical information is maintained in the measurement, unlike FCS where correlation
averages the dynamics to a single smooth curve. The advantage is apparent in systems
showing complex diffusion, where directly computing the mean squared displacement
allows straightforward comparison to normal or power law diffusion. To apply particle
tracking, the particles have to be distinguishable and thus at lower concentration than

Fluorescence correlation spectroscopy

436

required of FCS. Also, particle tracking is more sensitive to noise, which can sometimes
affect the results unpredictably.

References

[I] Magde, D., Elson, E. L., Webb, W. W. Thermodynamic fluctuations in a reacting system: Measurement by
fluorescence correlation spectroscopy, (1972) Phys Rev Lett, 29,705-708.

[2] Ehrenberg, M., Rigler, R. Rotational brownian motion and fluorescence intensity fluctuations, (1974) Chem

Phys, 4,390-401.
[3] Elson, E. L., Magde, D. Fluorescence correlation spectroscopy I. Conceptual basis and theory,(1974)

Biopolymers, 13,1-27.
[4] Magde, D., Elson, E. L., Webb, W. W. Fluorescence correlation spectroscopy II. An experimental

realization^ 1974) Biopolymers, 13,29-61.
[5] Thompson N L 1991 Topics in Fluorescence Spectroscopy Techniques vol 1, ed J R Lakowicz (New York:

Plenum) pp 337-78
[6] Rigler, R, U. Metsl, J. Widengren and P. Kask. Fluorescence correlation spectroscopy with high count rate and

low background: analysis of translational diffusion. European Biophysics Journal (1993) 22(3), 159.
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biotechnology, (1994) Proc. Natl. Acad. Sci. USA, 91,5740-5747.
[8] Rigler, M. Fluorescence correlations, single molecule detection and large number screening. Applications in

biotechnology,(1995) J. Biotechnol, 41,177-186.
[9] O. Krichevsky, G. Bonnet, "Fluorescence correlation spectroscopy: the technique and its applications," Rep.

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molecules in biology, (2 00 2 )BioEssays, 24,758-764.

[II] Mayboroda, O. A., van Remoortere, A., Tanke H. J., Hokke, C. H., Deelder, A. M., A new approach for
fluorescence correlation spectroscopy (FCS) based immunoassays, (2003), J. Biotechnol., 107, 185-192.

[12] Hess, S.T., and W.W. Webb. 2002. Focal volume optics and experimental artifacts in confocal fluorescence

correlation spectroscopy. Biophys. J. 83:2300-2317.
[13] Banks, D. S., and C. Fradin. 2005. Anomalous diffusion of proteins due to molecular crowding. Biophys. J.

89:2960-2971.

[14] Sengupta, P., K. Garai, J. Balaji, N. Periasamy, and S. Maiti. 2003. Measuring Size Distribution in Highly

Heterogeneous Systems with Fluorescence Correlation Spectroscopy. Biophys. J. 84(3):1977-1984.
[15] Kohler, R.H., P. Schwille, W.W. Webb, and M.R. Hanson. 2000. Active protein transport through plastid

tubules: velocity quantified by fluorescence correlation spectroscopy. J Cell Sci 113(22):3921-3930
[16] Magde, D., Elson, E. L., Webb, W. W. Fluorescence correlation spectroscopy II. An experimental

realization^ 19 74) Biopolymers, 13,29-61.
[17] Berland, K. M. Detection of specific DNA sequences using dual-color two-photon fluorescence correlation

spectroscopy. (2 004) J. Biotech nol ,108(2), 127-136.
[18] Muller, C.B., Loman, A., Pacheco, V., Koberling, F., Willbold, D., Richtering, W., Enderlein, J. Precise

measurement of diffusion by multi-color dual-focus fluorescence correlation spectroscopy (2008), EPL, 83,

46001.
[19] Pristinski, D., Kozlovskaya, V., Sukhishvili, S. A. Fluorescence correlation spectroscopy studies of diffusion of

a weak polyelectrolyte in aqueous solutions. (2005), J. Chem. Phys., 122, 014907.
[20] Widengren, J., Schwille, P., Characterization of photoinduced isomerization and back-isomerization of the

cyanine dye Cy5 by fluorescence correlation spectroscopy. (2000), J. Phys. Chem. A, 104, 6416-6428.
[21] Loman, A., Dertinger, T., Koberling, F., Enderlein, J. Comparison of optical saturation effects in conventional

and dual-focus fluorescence correlation spectroscopy (2008), Chem. Phys. Lett., 459, 18-21.
[22] Pristinski, D., Kozlovskaya, V., Sukhishvili, S. A. Fluorescence correlation spectroscopy studies of diffusion of

a weak polyelectrolyte in aqueous solutions. (2005), J. Chem. Phys., 122, 014907.
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46001.
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46001.
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Fluorescence correlation spectroscopy

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[26] Meseth, U., Wohland, T., Rigler, R., Vogel, H. Resolution of fluorescence correlation measurements. (1999)

Biophys.J., 76, 1619-1631.
[27] Diaspro, A., and Robello, M. (1999). Multi-photon Excitation Microscopy to Study Biosystems. European

Microscopy and Analysis., 5:5-7.
[28] Bagatolli, L.A., and Gratton, E. (2000). Two-photon fluorescence microscopy of coexisting lipid domains in

giant unilamellar vesicles of binary phospholipid mixtures. Biophys J., 78:290-305.
[29] Schwille, P., Haupts, U., Maiti, S., and Webb. W.(1999). Molecular dynamics in living cells observed by

fluorescence correlation spectroscopy with one- and two- photon excitation. Biophysical Journal,

77(10):2251-2265.

[30] Near Infrared Microspectroscopy, Fluorescence Microspectroscopy, Infrared Chemical Imaging and High

Resolution Nuclear Magnetic Resonance Analysis of Soybean Seeds, Somatic Embryos and Single Cells.,

Baianu, I.C. et al. 2004., In Oil Extraction and Analysis., D. Luthria, Editor pp. 241-273, AOCS Press.,

Champaign, IL.
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259-271.
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[36] Kolin, D.L., D. Ronis, and P.W. Wiseman. 2006. k-Space Image Correlation Spectroscopy: A Method for
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[37] Digman, M.A., P. Sengupta, P.W. Wiseman, CM. Brown, A.R. Horwitz, and E. Gratton. 2005. Fluctuation
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88(5):L33-36.

[38] Skinner, J. P., Y. Chen, and J.D. Mueller. 2005. Position-Sensitive Scanning Fluorescence Correlation

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[39] Ruan, Q., M.A. Cheng, M. Levi, E. Gratton, and W.W. Mantulin. 2004. Spatial-temporal studies of membrane

dynamics: scanning fluorescence correlation spectroscopy (SFCS). Biophys.J. 87:1260-1267.
[40] A. Berglund and H. Mabuchi, "Tracking-FCS: Fluorescence correlation spectroscopy of individual particles,"

Opt. Express 13, 8069-8082 (2005).
[41] Sisan, D.R., R. Arevalo, C. Graves, R. McAllister, and J.S. Urbach. 2006. Spatially resolved fluorescence

correlation spectroscopy using a spinning disk confocal microscope. Biophysical Journal 91(ll):4241-4252.
[42] Kannan, B., L. Guo, T. Sudhaharan, S. Ahmed, I. Maruyama, and T. Wohland. 2007. Spatially resolved total

internal reflection fluorescence correlation microscopy using an electron multiplying charge-coupled device

camera. Analytical Chemistry 79(12):4463-4470
[43] Wachsmuth, M., W. Waldeck, and J. Langowski. 2000. Anomalous diffusion of fluorescent probes inside living

cell nuclei investigated by spatially-resolved fluorescence correlation spectroscopy. J. Mol. Biol. 298(4):677-689
[44] Lieto, A.M., and N.L. Thompson. 2004. Total Internal Reflection with Fluorescence Correlation Spectroscopy:

Nonfluorescent Competitors. Biophys.J. 87(2):1268-1278.
[45] Sprague, B.L., and J.G. McNally. 2005. FRAP analysis of binding: proper and fitting. Trends in Cell Biology

15(2):84-91.

[46] http://www.physics.emory.edu/~weeks/idl/

Fluorescence correlation spectroscopy

438

See also

• Confocal microscopy

• Fluorescence cross-correlation spectroscopy

• FRET

• Dynamic light scattering

• Diffusion coefficient

External links

• Single-molecule spectroscopic methods (http://dx.doi.Org/10.1016/j.sbi.2004.09.
004)

• FCS Classroom (http://www.fcsxpert.com/classroom)

Fluorescence cross-correlation
spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS) was introduced by Eigen and
Rigler in 1994 and experimentally realized by Schwille in 1997. It extends the fluorescence
correlation spectroscopy (FCS) procedure by introducing high sensitivity for distinguishing
fluorescent particles which have a similar diffusion coefficient. FCCS uses two species
which are independently labelled with two spectrally separated fluorescent probes. These
fluorescent probes are excited and detected by two different laser light sources and
detectors commonly known as green and red respectively. Both laser light beams are
focused into the sample and tuned so that they overlap to form a superimposed confocal
observation volume.

The normalized cross-correlation function is defined for two fluorescent species G and R
which are independent green, G and red, R channels as follows:

M < SI G (t)SI R (t + r) > < I G (t)I R (t + r) >

>QK{T) + < /c(t) y< /fl(t) > < ^^ ><; lR{t) >

where differential fluorescent signals SI G at a specific time, t and &Ir at a delay time, t
later is correlated with each other.

Modeling

Cross-correlation curves are modeled according to a slightly more complicated
mathematical function than applied in FCS. First of all, the effective superimposed
observation volume in which the G and R channels form a single observation volume,
v'eff.RG in the solution:

V effRG = ^ 2 « G + <*)« G + <*) 1/2 /2 3/2

2 2

where w^g and k^../? are radial parameters and ^^and ^-Rare the axial parameters

for the G and R channels respectively.

The diffusion time, T D t GR for a doubly (G and R) fluorescent species is therefore described

as follows:

Fluorescence cross-correlation spectroscopy

439

T Di GR - — —

where Dgr is the diffusion coefficient of the doubly fluorescent particle.

The cross-correlation curve generated from diffusing doubly labelled fluorescent particles

can be modelled in separate channels as follows:

r n = (< Cg > Diff k (r)+ < Can > Differ))

G{T) V efftGR {<C a > + <C GR >)*

r n = (< C R > Diff k (r)+ < C GR > Differ))
R{ ' } V eff>GR (<C R > + <C GR >)2

In the ideal case, the cross-correlation function is proportional to the concentration of the
doubly labeled fluorescent complex:

G gr (t) = 1 +

Difft

ff>

V eff (< C G > + < C GR >)(< C R > + < C GR >)

(l + -^)(l+a- 2 (^)V2

Contrary to FCS 7 the intercept of the cross-correlation curve does not yield information
about the doubly labelled fluorescent particles in solution.

See also

• Fluorescence correlation spectroscopy

• Dynamic light scattering

• Fluorescence spectroscopy

• Diffusion coefficient

External links

• FCS Classroom [1]

References

[ 1 ] http ://www.fcsxpert. com/classroom

Forster resonance energy transfer

440

Forster resonance energy transfer

1. REDIRECT Forster resonance energy transfer

Neutron scattering

Neutron scattering encompasses all scientific techniques whereby the deflection of
neutron radiation is used as a scientific probe. Neutrons readily interact with atomic nuclei
and magnetic fields from unpaired electrons, making a useful probe of both structure and
magnetic order. Neutron Scattering falls into two basic categories - elastic and inelastic.
Elastic scattering is when a neutron interacts with a nucleus or electronic magnetic field
but does not leave it in an excited state, meaning the emitted neutron has the same energy
as the injected neutron. Scattering processes that involve an energetic excitation or
relaxation by the neutron are inelastic: the injected neutron's energy is used or increased to
create an excitation or by absorbing the excess energy from a relaxation, and consequently
the emitted neutron's energy is reduced or increased respectively.

For several good reasons, moderated neutrons provide an ideal tool for the study of almost
all forms of condensed matter. Firstly, they are readily produced at a nuclear research
reactor or a spallation source. Normally in such processes neutrons are however produced
with much higher energies than are needed. Therefore moderators are generally used
which slow the neutrons down and therefore produce wavelengths that are comparable to
the atomic spacing in solids and liquids, and kinetic energies that are comparable to those
of dynamic processes in materials. Moderators can be made from Aluminium and filled with
liquid hydrogen (for very long wavelength neutrons) or liquid methane (for shorter

7 ft

wavelength neutrons). Fluxes of 10 /s - 10 /s are not atypical in most neutron sources from
any given moderator.

The neutrons cause pronounced interference and energy transfer effects in scattering
experiments. Unlike an x-ray photon with a similar wavelength, which interacts with the
electron cloud surrounding the nucleus, neutrons interact with the nucleus itself. Because
the neutron is an electrically neutral particle, it is deeply penetrating, and is therefore more
able to probe the bulk material. Consequently, it enables the use of a wide range of sample
environments that are difficult to use with synchrotron x-ray sources. It also has the
advantage that the cross sections for interaction do not increase with atomic number as
they do with radiation from a synchrotron x-ray source. Thus neutrons can be used to
analyse materials with low atomic numbers like proteins and surfactants. This can be done
at synchrotron sources but very high intensities are needed which may cause the structures
to change. Moreover, the nucleus provides a very short range, isotropic potential varying
randomly from isotope to isotope, making it possible to tune the nuclear scattering contrast
to suit the experiment:

The neutron has an additional advantage over the x-ray photon in the study of condensed
matter. It readily interacts with internal magnetic fields in the sample. In fact, the strength
of the magnetic scattering signal is often very similar to that of the nuclear scattering
signal in many materials, which allows the simultaneous exploration of both nuclear and
magnetic structure. Because the neutron scattering amplitude can be measured in absolute
units, both the structural and magnetic properties as measured by neutrons can be

Neutron scattering

441

compared quantitatively with the results of other characterisation techniques

See also

• Neutron diffraction

• Small angle neutron scattering

• Neutron Reflectometry

• Inelastic neutron scattering

• neutron triple-axis spectrometry

• neutron time-of-flight scattering

• neutron backscattering

• neutron spin echo

• neutron resonance spin echo

• Neutron scattering facilities

External links

rn r2i

• Neutron Scattering - A primer L J (LANL-hosted black and white version L J ) - An
introductory article written by Roger Pynn (Los Alamos National Laboratory)

References

[1] http://knocknick.files.wordpress.com/2008/04/neutrons-a-primer-by-rogen-pynn.pdf
[2] http://library.lanl.gov/cgi-bin/getfile700326651.pdf

Synchrotron

A synchrotron is a particular type
of cyclic particle accelerator in
which the magnetic field (to turn
the particles so they circulate) and
the electric field (to accelerate the

particles)

are

carefully

synchronized with the travelling

particle

beam.

The

synchrotron

conceived

01iphant [1]

was

Sir

proton

originally

Marcus

The honour of the

first to publish the idea belongs to
Vladimir Veksler, and the first

electron
constructed

synchrotron

was

Oliphant's

supervisor Edwin McMillan.

Here, the synchrotron is the circular track, off which the

beamlines branch.

Synchrotron

442

Characteristics

While a cyclotron uses a constant magnetic field and a constant-frequency applied electric
field (one of these is varied in the synchrocyclotron), both of these fields are varied in the
synchrotron. By increasing these parameters appropriately as the particles gain energy,
their path can be held constant as they are accelerated. This allows the vacuum chamber
for the particles to be a large thin torus. In reality it is easier to use some straight sections
between the bending magnets and some bent sections within the magnets giving the torus
the shape of a round-cornered polygon. A path of large effective radius may thus be
constructed using simple straight and curved pipe segments, unlike the disc-shaped
chamber of the cyclotron type devices. The shape also allows and requires the use of
multiple magnets to bend the particle beams. Straight sections are required at spacings
around a ring for both radiofrequency cavities, and in third generation light sources allow
space for insertion devices such as wigglers and undulators.

The maximum energy that a cyclic accelerator can impart is typically limited by the
strength of the magnetic field(s) and the minimum radius (maximum curvature) of the
particle path.

In a cyclotron the maximum
radius is quite limited as the
particles start at the center

and spiral outward, thus the
entire path must be a

self-supporting

disc-shaped

The interior of the Australian Synchrotron facility. Dominating the

image is the storage ring, showing the optical diagnostic beamline at

front right. In the middle of the storage ring is the booster

synchrotron and linac

evacuated chamber. Since the

radius is limited, the power of

the machine becomes limited

by the strength of the

magnetic field. In the case of

an ordinary electromagnet the

field strength is limited by the saturation of the core (when all magnetic domains are

aligned the field may not be further increased to any practical extent). The arrangement of

the single pair of magnets the full width of the device also limits the economic size of the

device.

Synchrotrons overcome these limitations, using a narrow beam pipe which can be
surrounded by much smaller and more tightly focusing magnets. The ability of this device
to accelerate particles is limited by the fact that the particles must be charged to be
accelerated at all, but charged particles under acceleration emit photons (light), thereby
losing energy. The limiting beam energy is reached when the energy lost to the lateral
acceleration required to maintain the beam path in a circle equals the energy added each
cycle. More powerful accelerators are built by using large radius paths and by using more
numerous and more powerful microwave cavities to accelerate the particle beam between
corners. Lighter particles (such as electrons) lose a larger fraction of their energy when
turning. Practically speaking, the energy of electron/positron accelerators is limited by this
radiation loss, while it does not play a significant role in the dynamics of proton or ion
accelerators. The energy of those is limited strictly by the strength of magnets and by the
cost.

Synchrotron

443

Design and operation

Particles are injected into the main ring at substantial energies by either a linear
accelerator or by an intermediate synchrotron which is in turn fed by a linear accelerator.
The "linac" is in turn fed by particles accelerated to intermediate energy by a simple high
voltage power supply, typically a Cockcroft-Walton generator.

Starting from an appropriate initial value determined by the injection velocity the magnetic
field is then increased. The particles pass through an electrostatic accelerator driven by a
high alternating voltage. At particle speeds not close to the speed of light the frequency of
the accelerating voltage can be made roughly proportional to the current in the bending
magnets. A finer control of the frequency is performed by a servo loop which responds to
the detection of the passing of the traveling group of particles. At particle speeds
approaching light speed the frequency becomes more nearly constant, while the current in
the bending magnets continues to increase. The maximum energy that can be applied to the
particles (for a given ring size and magnet count) is determined by the saturation of the
cores of the bending magnets (the point at which increasing current does not produce
additional magnetic field). One way to obtain additional power is to make the torus larger
and add additional bending magnets. This allows the amount of particle redirection at
saturation to be less and so the particles can be more energetic. Another means of
obtaining higher power is to use superconducting magnets, these not being limited by core
saturation.

Large synchrotrons

One

the

early

large

synchrotrons, now retired, is the
Bevatron, constructed in 1950 at

Berkeley

the

Lawrence

Laboratory. The name of this

proton accelerator comes from its

power, in the range of 6.3 GeV

(then called BeV for billion

electron volts; the name predates

the adoption of the SI prefix giga-).

A number of heavy elements,

unseen in the natural world, were

first created with this machine.

This site is also the location of one

of the first large bubble chambers used to examine the results of the atomic collisions

produced here.

Modern industrial-scale synchrotrons can be very large (here,

Soleil near Paris)

Another early large synchrotron is the Cosmotron built at Brookhaven National Laboratory
which reached 3.3 GeV in 1953. [2]

Until August 2008, the highest energy synchrotron in the world was the Tevatron, at the
Fermi National Accelerator Laboratory, in the United States. It accelerates protons and
antiprotons to slightly less than 1 TeV of kinetic energy and collides them together. The
Large Hadron Collider (LHC), which has been built at the European Laboratory for High
Energy Physics (CERN), has roughly seven times this energy. It is housed in the 27 km

Synchrotron

444

tunnel which formerly housed the Large Electron Positron (LEP) collider, so it will maintain
the claim as the largest scientific device ever built. The LHC will also accelerate heavy ions
(such as lead) up to an energy of 1.15 PeV.

The largest device of this type seriously proposed was the Superconducting Super Collider
(SSC), which was to be built in the United States. This design, like others, used
superconducting magnets which allow more intense magnetic fields to be created without
the limitations of core saturation. While construction was begun, the project was cancelled
in 1994, citing excessive budget overruns —

this was due to naive cost estimation and

economic management issues rather than any basic engineering flaws. It can also be
argued that the end of the Cold War resulted in a change of scientific funding priorities that
contributed to its ultimate cancellation.

While there is still potential for yet more powerful proton and heavy particle cyclic
accelerators, it appears that the next step up in electron beam energy must avoid losses
due to synchrotron radiation. This will require a return to the linear accelerator, but with
devices significantly longer than those currently in use. There is at present a major effort to
design and build the International Linear Collider (ILC), which will consist of two opposing
linear accelerators, one for electrons and one for positrons. These will collide at a total
center of mass energy of 0.5 TeV.

However, synchrotron radiation also has a wide range of applications (see synchrotron
light) and many 2nd and 3rd generation synchrotrons have been built especially to harness
it. The largest of those 3rd generation synchrotron light sources are the European
Synchrotron Radiation Facility (ESRF) in Grenoble, France, the Advanced Photon Source
(APS) near Chicago, USA, and SPring-8 in Japan, accelerating electrons up to 6, 7 and 8
GeV, respectively.

Synchrotrons which are useful for cutting edge research are large machines, costing tens
or hundreds of millions of dollars to construct, and each beamline (there may be 20 to 50 at
a large synchrotron) costs another two or three million dollars on average. These
installations are mostly built by the science funding agencies of governments of developed
countries, or by collaborations between several countries in a region, and operated as
infrastructure facilities available to scientists from universities and research organisations
throughout the country, region, or world. More compact models, however, have been
developed, such as the Compact Light Source.

List of installations

Synchrotron

Location & Country

Energy
(GeV)

Circumference
(m)

Commissioned

Decommissioned

Advanced Photon
Source (APS)

Argonne National
Laboratory, USA

7.0

1104

1995

ISIS

Rutherford Appleton
Laboratory, UK

0.8

163

1985

Australian
Synchrotron

Melbourne, Australia

216

2006

LNLS

Campinas, Brazil

1.37

93.2

1997

SESAME

Allaan, Jordan

2.5

125

Under Design

Synchrotron

445

Bevatron

Lawrence Berkeley
Laboratory, USA

114

1954

1993

Advanced Light
Source

Lawrence Berkeley
Laboratory, USA

1.9

196.8

1993

Cosmotron

Brookhaven National
Laboratory, USA

1953

1968

Nimrod

Rutherford Appleton
Laboratory, UK

1957

1978

Alternating Gradient
Synchrotron (AGS)

Brookhaven National
Laboratory, USA

800

1960

Stanford
Synchrotron
Radiation
Lightsource

SLAC National
Accelerator
Laboratory, USA

234

1973

Cornell High Energy
Synchrotron Source
(CHESS)

Cornell University,

USA

5.5

768

1979

Soleil

Paris, France

354

2006

Shanghai
Synchrotron
Radiation Facility
(SSRF)

Shanghai, China

3.5

432

2007

Proton Synchrotron

CERN, Switzerland

628.3

1959

Tevatron

Fermi National
Accelerator
Laboratory, USA

1000

6300

1983

Swiss Light Source

Paul Scherrer Institute,
Switzerland

2.8

288

2001

Large Hadron
Collider (LHC)

CERN, Switzerland

7000

26659

2008

BESSY II

Helmholtz-Zentrum
Berlin in Berlin,
Germany

1.7

240

1998

European
Synchrotron
Radiation Facility
(ESRF)

Grenoble, France

844

1988

MAX-I

MAX-lab, Sweden

0.55

1986

MAX-II

MAX-lab, Sweden

1.5

1997

MAX-III

MAX-lab, Sweden

0.7

2008

ELETTRA

Trieste, Italy

2-2.4

260

1993

Diamond Light
Source

Oxfordshire, UK

561.6

2002

DORIS III

DESY, Germany

4.5

289

1980

PETRA II

DESY, Germany

2304

1995

2007

Canadian Light
Source

University of
Saskatchewan, Canada

2.9

171

2002

Synchrotron

446

SPring-8

RIKEN, Japan

1436

1997

Taiwanese National
Synchrotron
Radiation Research
Center

Hsinchu Science Park,
Taiwan

3.3

518.4

2008

Synchrotron Light
Research Institute
(SLRI)

Nakhon Ratchasima,
Thailand

1.2

81.4

2004

Indus 1

Raja Ramanna Centre
for Advanced
Technology, Indore,
India

0.45

1999

Indus 2

Raja Ramanna Centre
for Advanced
Technology, Indore,
India

2.5

2005

Synchrophasotron

JINR, Dubna, USSR

180

1957

2005

U-70

IHEP, Protvino, USSR

1967

CAMD

LSU, Louisiana, US

1.5

Note: in the case of colliders, the quoted power is often double what is shown here. The
above table shows the power of one beam but if two opposing beams collide head on, the
effective power is doubled.

Applications

Life sciences: protein and large molecule crystallography

Drug discovery and research

"Burning" computer chip designs into metal wafers

Studying molecule shapes and protein crystals

Analyzing chemicals to determine their composition

Observing the reaction of living cells to drugs

Inorganic material crystallography and microanalysis

Fluorescence studies

Semiconductor material analysis and structural studies

Geological material analysis

Medical imaging

Proton therapy to treat some forms of cancer

Synchrotron

447

See also

• List of synchrotron radiation facilities

• Synchrotron X-ray tomographic microscopy

• Energy amplifier

• Superconducting Radio Frequency

References

[1] Nature 407, 468 (28 September 2000) (http://www.nature.com/nature/journal/v407/n6803/full/

407468a0.html).
[2] The Cosmotron (http://www.bnl.gov/bnlweb/history/cosmotron.asp)

External links

• Australian Synchrotron (http://www.synchrotron.org.au)

• Diamond UK Synchrotron (http://www.diamond.ac.uk)

• Lightsources.org (http://www.lightsources.org/cms/)

• CERN Large Hadron Collider (http://lhc-new-homepage.web.cern.ch/
lhc-new-homepage)

• Synchrotron Light Sources of the World (http://www-als.lbl.gov/als/
synchrotron_sources.html)

• A Miniature Synchrotron: (http://www.technologyreview.com/Biotech/20149/)
room-size synchrotron offers scientists a new way to perform high-quality x-ray
experiments in their own labs, Technology Review, February 04, 2008

• Brazilian Synchrotron Light Laboratory (http://www.lnls.br/lnls/cgi/cgilua.exe/sys/
start. htm?UserActiveTemplate=lnls_2007_english&tpl=home)

• Podcast interview (http://omegataupodcast.net/2009/03/28/
11-synchrotron-radiation-science-at-esrf/) with a scientist at the European Synchrotron
Radiation Facility

ISIS neutron source

448

ISIS neutron source

ISIS is a world leading pulsed
neutron and muon source. It is
situated at
Appleton

the

Rutherford

Laboratory

Oxfordshire, United Kingdom and
is part of the Science and
Technology Facilities Council . It

uses

the

techniques
and

muon
neutron

spectroscopy

scattering to probe the structure

and dynamics of condensed matter

on a microscopic scale ranging

from the subatomic to the

macromolecular.

Hundreds of experiments are
performed annually at ISIS by
visiting researchers from around
the world, in diverse science areas
including physics, chemistry,

materials

engineering,

earth

sciences, biology and archaeology.

Neutrons and muons

Neutrons

are

uncharged

ISIS experimental hall for Target Station 1

constituents of atoms and penetrate materials well, deflecting only from the nuclei of
atoms. The statistical accumulation of deflected neutrons at different positions beyond the
sample can be used to find the structure of a material, and the loss or gain of energy by
neutrons can reveal the dynamic behaviour of parts of a sample, for example diffusive
processes in solids. At ISIS the neutrons are created by accelerating 'bunches' of protons in
a synchrotron, then colliding these with a heavy tantalum metal target, under a constant
cooling load to dissipate the heat from the 160 kW proton beam. The tantulum atoms
slough off neutrons, and these are channelled through guides, or beamlines, to about 20
instruments, individually optimised for the study of different types of matter. The target
station and most of the instruments are set in a large hall. The penetrating neutrons are a
dangerous form of radiation so the target and beamlines are heavily shielded with concrete.

ISIS produces muons by colliding a fraction of the proton beam with a graphite target,
producing pions which decay rapidly into muons, delivered in a spin-polarised beam to
sample stations.

ISIS neutron source

449

Science at ISIS

ISIS is administered and operated
by the Science and Technology

(previously

Facilities

Council

CCLRC). Experimental time is
open to academic users from
funding countries and is applied
for through a twice-yearly 'call for
proposals'. Research allocation, or

'beam-time',

allotted

applicants via a peer-review process. Users and their parent institutions do not pay for the
running costs of the facility, which are as much as £11,000 per instrument per day. Their
transport and living costs are also refunded whilst carrying out the experiment. Most users
stay in Ridgeway House, a hotel near the site, or at Cosener's House, an STFC-run
conference centre in Abingdon. Over 600 experiments by 1600 users are completed every
year.

A large number of support staff operate the facility, aid users, and carry out research, the
control room is staffed 24 hours a day, every day of the year. Instrument scientists oversee
the running of each instrument and liaise with users, and other divisions provide sample
environment, data analysis and computing expertise, maintain the accelerator, and run
education programmes.

Among the important and pioneering work carried out was the discovery of the structure of
high-temperature superconductors and the solid phase of buckminster-fullerene.

Construction for a second target station started in 2003, and the first neutrons were

delivered to the target on December 14 2007 L J . It will use low-energy neutrons to study
soft condensed matter, biological systems, advanced composites and nanomaterials. To
supply the extra protons for this, the accelerator is being upgraded.

History and background of ISIS

The source was approved in 1977 for the RAL site on the Harwell campus and recycled
components from earlier UK science programmes including the accelerator hall which had
previously been occupied by the Nimrod accelerator. The first beam was produced in 1984,
and the facility was formally opened by the then Prime Minister Margaret Thatcher in
October 1985. [2]

The name ISIS is not an acronym: it refers to the Ancient Egyptian goddess and the local
name for the River Thames. The name was selected for the official opening of the facility in
1985, prior to this it was known as the SNS, or Spallation Neutron Source. The name was
considered appropriate as Isis was a goddess who could restore life to the dead, and ISIS
made use of equipment previously constructed for the Nimrod and Nina accelerators^ J .

ISIS neutron source

450

External links

• ISIS facility [22]

• ISIS Second Target Station [4]

• The Science and Technology Facilities Council

References

[1] ISIS Second Target Station Project (http://ts-2.isis.rl.ac.uk/)

[2] Linacs at the Rutherford Appleton Laboratory (http://epubs.cclrc.ac.uk/bitstream/692/linacplahistory.pdf)

[3] Explanation of the name of ISIS (http://www.isis.rl.ac.uk/aboutIsis/index.htm)

[4] http://ts-2.isis.rl.ac.uk/

[5] http://www.stfc.ac.uk

Geographical coordinates: 51°34D18DN 1°19D12[]W

Article Sources and Contributors

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DRider, Dacb, DeadEyeArrow, Demus Wiesbaden, Dicklyon, Dietmar.paschek, DragonflySixtyseven, Drswenson, Ebuchol, Ehdr, Gentgeen, Giftlite,
Huckit, Itamblyn, Itub, JWSchmidt, Jerome Charles Potts, Jorgenumata, Jugander, Kaihsu, Karol Langner, Katherine Folsom, Kennylam, Kevyn,
Kjaergaard, Knordlun, Laurentl979, Lexor, LiDaobing, Linas, Lomenoldur, Ludx, Maduixa, Marchuta, Marx Gomes, Mateusz Galuszka, Mattopia, Md
Arshad Iqbal, Mihoopes, Mr Marie Weaver, Msuzen, Nicolasbock, Oiramrasec, Opabinia regalis, Ossi, P99am, Paul.raymond.brenner, Pedrito, Pelister,
PhCOOH, Pksach, PrometheusX303, Raviwiki4, Rob Hooft, Rool812, Sandycx, Shura58, Smoe, Smremde, Stewartadcock, Sudiarta, TStein,
Themfromspace, Thorwald, Utcursch, Van helsing, Whanrott, Wikimcmd, Wittgenstein77, Wiz9999, Xavier andrade, Yrtgm, 200 anonymous edits

Computer model Source: http://en.wikipedia.org/windex.php?oldid= 16233838 Contributors: -

Quantum Monte Carlo Source: http://en.wikipedia.org/windex.php?oldid=297714926 Contributors: Acipsen, Amyoungil, Bci2, Conscious, Henry
Delforn, Isilanes, Jheriko, Karol Langner, Lucaskw, Mdt26a, Melcombe, Michael Hardy, NNemec, Pablomme, Paulcardan, Rbonvall, Rich Farmbrough,
Rjwilmsi, Sagaciousuk, Supersion77, TestPilot, Trigger hippie77, UkPaolo, Veinor, Vgy7ujm, Vyznev Xnebara, WilliamDParker, WirawanO, 43 anonymous
edits

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Chemistrannik, Chenmengen, CzarB, Dcrjsr, Dreftymac, Edguy99, Edward, EranHodis, Fvasconcellos, Harryboyles, Icep, JLSussman, Jweissll, Karol
Langner, Linforest, McVities, Mdd, Mobius, Mrug2, NapoliRoma, NicoV, Ohnoitsjamie, Outriggr, P99am, PBarak, Petermr, Provelt, Rjwilmsi, Rogerb67,
SchuminWeb, Shura58, Sjoerd de Vries, SkyWalker, Thumperward, Timrollpickering, Vizbi, Vriend, Walkerma, WikiDan61, 16 anonymous edits

Theoretical physics Source: http://en.wikipedia.org/windex.php?oldid=2971 56048 Contributors: Acecrack, AdrianW. Elder, Alton, Ancheta Wis, Andrei
Stroe, AndrewHowse, Antandrus, Aravindashwin, Arne Saknussemm, Atzatzatz, Autocracy, Bci2, Bevo, Bjorn.kallen, Bobol92, Boojum, Brianjd, BryanD,
CDN99, Canadian-Bacon, CanadianLinuxUser, Censusgray, Cmichael, Coolbho3000, Crazytales, Cronholml44, Crowsnest, D, D6, DBishopl984,
DarkFalls, Darthveda, David Shear, Derek f am, Deville, Discospinster, Djr32, Doublestein, Drilnoth, Ducarmont, Edcolins, Eep 2 , Ellywa, Emote, Equendil,
Etale, Everyking, Fieldworld, Firestorm, Francine Rogers, GT5162, Giftlite, Gnfl, Gogo Dodo, Googl, Gregbard, Grendelkhan, H2g2bob, Headbomb,
Husond, IMNTU, Impreziv, Introvert, Ironboyll, Jagged 85, Jeff Nixon, JerrySteal, Jheald, Jok2000, Joshua Davis, Jpod2, Jules.lt, Karada, Karol Langner,
Kbh3rd, Kigalil, Kjkolb, Knowledge Seeker, Ktsordia, Lexor, Loodog, LordtzerO, LoveMed, LovesMacs, Lumidek, Materialscientist, Mathforms05, Matt
Deres, Matt489, Maurice Carbonaro, Member, Michael Hardy, Micheal54, MidwestGeek, Mike Doughney, Mipadi, Moink, Moonaysl, Mor, MrOllie,
Msuzen, Nate-sama, NawlinWiki, Neonblak, Nnp, Not Ross Almighty, Ntmatter, Ohnoitsjamie, Oleg Alexandrov, Ottokar, Pat Payne, Pearle, Phils, Piano
non troppo, Pizzal512, Ractogon, Ragesoss, Ranveig, Rbarreira, Rbellin, Reddi, Reyk, Rknasc, SD6-Agent, SS2005, ST47, Sadi Carnot, Sailorl889,
Salgueiro, SchfiftyThree, ScienceApologist, SiliconSlick.J.Shmoove, Silly rabbit, Silvonen, SimonP, Sjakkalle, Soldarat, Sreekanthv, Steve Pucci,
Stevemidgley, Stevenmattern, TakuyaMurata, Tamtamar, Tasudrty, The Anome, The-G-Unit-Boss, Theoryinpractice, Thisisbossi, Totorotroll, Truthnlove,
Tyler Bronfstein, Tzustrategy, Unyoyega, Uugedsaz, Versus22, Vina, Vivek Vyas, Voyajer, Waldir, XJamRastafire, Yhr, Yill577, Yndurain, Yttire, Zundark,
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Aleksandar Guzijan, Altenmann, AntOnTrack, Ap, Athkalani, AxelBoldt, Bluemoose, Brazzouk, CX, Caesium, Charles Matthews, Chetvorno,
Chopchopwhitey, ComplexOl, Complexica, Cumi, Cutler, Daniele.tampieri, Dino, Dmharvey, Dysprosia, EPM, El C, Epbrl23, Epolk, Everyking,
Evilphoenix, Filemon, Filur, Finn-Zoltan, Fredrik, Gandalf61, Giftlite, Headbomb, Hesam7, Highlightened, Hve, Hydroli, Jabernal, Jay Gatsby, Jeff3000,
Jeffrey Smith, JerrySteal, Jitse Niesen, JocK, Jugander, K-UNIT, KYPark, Karol Langner, Kayvan45622, Kenneth M Burke, Kotepho, Kzzl, Lakinekaki,
Lightmouse, Linas, ManiacK, Marj Tiefert, MathMartin, Mathmanta, Met mht, Mdd, Meersan, Michael Hardy, Milly.mortimer, Msh210, Neelix,
Nnl23645, Noeckel, Oleg Alexandrov, Orange Death, OrgasGirl, Patrickdepinguin, PetaRZ, Pgan002, Phys, PlatypeanArchcow, RedWolf, Reddi,
Reinderien, Revolver, Rhythmiccycle, Rich Farmbrough, Rintrah, Sadi Carnot, Salgueiro, Salix alba, Sam Korn, Samuelbf85, SilverSurfer314, Snoyes,
Solace098, Sverdrup, Template namespace initialisation script, The Anome, The wub, Tobias Hoevekamp, Tomisti, Tommyjs, Tosha, Volfy, Voretus,
Waitati, WaysToEscape, WhiteC, WillowW, XJamRastafire, XaosBits, Zsniew, 120 anonymous edits

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Bifurcation diagram Source: http://en.wikipedia.org/windex.php?oldid=288103420 Contributors: 4pqlinjbok, A5b, Aarktica, Adam majewski, Ap,
AxelBoldt, Damian Yerrick, Deeptrivia, Dmharvey, El C, Enigmal2345 / Giftlite, Gknor, Here, Japanese Searobin, Jugander, Kpmkpm, Lakinekaki, Lenthe,
Linas, Mathmoclaire, Matthewsim, Meelar, Nabinkm, PAR, Paul Matthews, Pengo, PierreAbbat, Qef, Roadrunner, Sverdrup, 21 anonymous edits

Phase space Source: http://en.wikipedia.org/windex.php?oldid=261513456 Contributors: Adam majewski, BMF81, Beowulf333, Bovlb, Charles
Matthews, Complexica, Cuzkatzimhut, Danman3459, Deville, Edsanville, ErNa, Evilphoenix, Galaksiafervojo, Giftlite, Gpvos, Jheald, Jmath666, K-UNIT,
KasugaHuang, Linas, Linuxlad, Lowellian, Marasmusine, Met mht, Meisam, Mernst, Michael Hardy, Oleg Alexandrov, Paddles, Ploncomi, Sadi Carnot,
Shoeofdeath, SigmaAlgebra, Srleffler, ThorinMuglindir, TimBentley, Ulner, Viriditas, Vugluskr, XaosBits, 46 anonymous edits

Phase portrait Source: http://en.wikipedia.org/windex.php?oldid=286002201 Contributors: Adam majewski, Arcfrk, Arthena, Ashraful,
Captaintancredi, Deeptrivia, Kevin, Lechatjaune, Pethrus, Stepa, 3 anonymous edits

Bifurcation theory Source: http://en.wikipedia.org/windex.php?oldid=288854389 Contributors: Amitkashwar, Anandhan, Arthur Rubin, Athkalani,
Cat2020, Deeptrivia, Dharma6662000, Dmr2, Giftlite, Guckurev, Harriv, Headbomb, Hesacon, JanSuchy, Jheald, Jugander, K-UNIT, Kenneth M Burke,
Linas, Mathmoclaire, Mmernex, Paul Matthews, Pizzal512, Pt, Rhythmiccycle, Saziel, Squidonius, Stefankroon, Sviemeister, Voretus, Zanaq, Zsniew, 33
anonymous edits

Relation algebra Source: http://en.wikipedia.org/windex.php?oldid=296506302 Contributors: Balder ten Cate, Charles Matthews, Charvest,
Concerned cynic, D6, David Eppstein, Elwikipedista, Hans Adler, Irmy, Jon Awbrey, King Bee, Koavf, Lambiam, Lethe, Linelor, Mboverload, Mets501,
Mhss, Michael Hardy, Nbarth, Physis, Plasticup, QuadrivialMind, Ramsey2006, Sam Staton, The Tetrast, Tillmo, Tobias Bergemann, Vaughan Pratt, 107
anonymous edits

Category theory Source: http://en.wikipedia.org/windex.php?oldid=297655633 Contributors: 0, 63.162.153.xxx, 7.239, APH, Alexwright, Anonymous
Dissident, Archelon, AxelBoldt, Azrael ezra, Balrivo, Barnaby dawson, Bci2, Bevo, Blaisorblade, Brentt, Bryan Derksen, CBM, CSTAR, Calculuslover,
Cambyses, Campani, Cbcarlson, Cenarium, Ceyockey, Chalst, Charles Matthews, Chas zzz brown, Choni, Chris Pressey, Conversion script, Creidieki,
Cyde, David Sneek, Davin, DesolateReality, Dominus, Dysprosia, Elwikipedista, Erik Zachte, Fotino, Fropuff, Gandalf61, Gdr, Giftlite, Go for it!,
Goclenius, Grubber, Gzhanstong, Hadal, Hairy Dude, Hans Adler, Hesam7, Htamas, Inkling, JeffreyYasskin, Jiang, Jimp, Jmabel, John Z, Jon Awbrey,
Julian Mendez, LC, Lambiam, Laurentius, Lethe, Linas, Lotte Monz, Loupeter, Lupin, Luqui, Lysdexia, Magmi, Marco Krohn, MarkSweep, Markus
Krotzsch, Marudubshinki, Mat cross, Matt Crypto, Maurice Carbonaro, Michael Hardy, Mikeblas, Mikolt, Msh210, Nbarth, Oliverkroll, Palnot, Paul
August, Phils, Phys, Physis, Point-set topologist, Popx, Pred, Rec syn, Revolver, Roadrunner, Robertbyrne, Ryan Reich, Salix alba, Sam Staton,
SamStokes, Selvakumar.sarangan, Semorrison, SixWingedSeraph, Smimram, Szquirrel, TakuyaMurata, TeH nOmlnAtOr, Template namespace
initialisation script, Tkeu, Tlepp, Tobias Bergemann, Toby, Toby Bartels, Topology Expert, Tzanko Matev, Unyoyega, Wik, WikiWizard, XudongGuan,
Youandme, Zhaoway, Zundark, 138 anonymous edits

Algebraic topology Source: http://en.wikipedia.org/windex.php?oldid=297484042 Contributors: APH, Aaeamdar, Agiieybana, Akriasas, Alansohn,
Alodyne, Archgoon, AxelBoldt, Banus, Bci2, B14ck54bb4th, Charles Matthews, Chas zzz brown, ChazYork, Cyc, Cicero, D stankov, Dave Foley, David
Eppstein, Delaszk, Dysprosia, Father Christmastime, Fropuff, Gauge, Giftlite, Gtrmp, Haiviet, Horoball, Icairns, Katzmik, Kubigula, Lethe, Linas, Lupin,
MathMartin, Matt Hellige, Michael Hardy, Michael Slone, Msh210, Newone, Obradovic Goran, Phys, Plclark, Polyrhythm, Revolver, Rich Farmbrough,
Rjwilmsi, Sam Staton, Smimram, TakuyaMurata, Template namespace initialisation script, TimothyRias, Timwi, Tinyde Evenstar, Youandme, Zundark, 37
anonymous edits

Algebraic logic Source: http://en.wikipedia.org/windex. php?oldid=295384025 Contributors: CBM, Chalst, Charles Matthews, Elwikipedista, EmilJ,
Giftlite, Gregbard, Hmains, Jitse Niesen, Mhss, Michael Hardy, PWilkinson, Palnot, Strangename, The Tetrast, Trovatore, 11 anonymous edits

Quantum logic Source: http://en.wikipedia.org/windex.php?oldid=297664527 Contributors: Andris, Angela, Archelon, Aster Rainbow, BD2412, Bci2,
CSTAR, Charles Matthews, Cybercobra, DJIndica, David edwards, Dcoetzee, Dmr2, Dysprosia, Edward, EpsilonO, GTBacchus, Gaius Cornelius, Gene
Ward Smith, Giftlite, GordonRoss, Hairy Dude, Headbomb, Icairns, Ilan770, Jengod, John Baez, Kimberlyg, KnightRider, Kuratowski's Ghost, Kzollman,
Lethe, Linas, Lucidish, Met mht, Mhss, Michael Hardy, Modify, Oerjan, Parkyere, RsimmondsOl, Sheliak, Shlomi Hillel, Stevenjohnston, Stevertigo, T=0,
Trovatore, V79, Zumbo, ^^s, 36 anonymous edits

Lukasiewicz logic Source: http://en.wikipedia.org/windex.php?oldid=127640345 Contributors: -

MV-algebra Source: http://en.wikipedia.org/windex.php?oldid=292604365 Contributors: Charles Matthews, Charvest, Dismas, Eequor, GTBacchus,
Hans Adler, Julian Mendez, Kjkolb, LBehounek, Mhss, Pgallert, Riverofdreams, Salix alba, Smmurphy, Ululuca, 13 anonymous edits

Molecular evolution Source: http://en.wikipedia.org/windex.php?oldid=294465595 Contributors: lOoutoflOdie, 168..., A.bit, AdamRetchless, Aranae,
Aunt Entropy, AxelBoldt, Ben Tillman, Borgx, Bornhj, Debresser, Duncharris, Emw2012, Etxrge, Eugene van der Pijll, Ewen, GSlicer, Gaius Cornelius,
GeoMor, Kosigrim, Lexor, Lindosland, M stone, MER-C, Marooned Morlock, Mewl 139, Neutrality, Nonsuch, Northfox, Notreallydavid, OnBeyondZebrax,
Owenman, PDH, PhDP, Ragesoss, Rigadoun, Ryulong, Sadi Carnot, Samsara, Seglea, Shyamal, Steinsky, Stirling Newberry, StormBlade, Swpb, Template
namespace initialisation script, That Guy, From That Show!, The Anome, Theuser, Thue, Timwi, Vsmith, Wavesmikey, Whatiguana, 52 anonymous edits

Radiobiology Source: http://en.wikipedia.org/windex.php?oldid=280558628 Contributors: Altenmann, Beland, Biscuittin, CDN99, Clicketyclack,
Cobaltbluetony, DV8 2XL, Dart evader, Eleassar777, KnightRider, Mion, Myomindr, NawlinWiki, Oldnoah, Rbrus, Rsabbatini, Squidonius, Topazg,
Zereshk, 10 anonymous edits

Photosynthesis Source: http://en.wikipedia.org/windex. php?oldid=297930077 Contributors: (jarbarf), *drew, --April, 678910, @pple, AJRM,
ASKingquestions, ATMarsden, Abu-Fool Danyal ibn Amir al-Makhiri, Academic Challenger, Accuruss, Adashiel, Ahoerstemeier, Aitias, Alansohn,
Alexius08, Ali, Ali Salter, Alksub, AmiDaniel, Andris, AndyZ, Angam, Angela, Angr, AnonMoos, Anonymi, Ans, Antandrus, AnthonyQBachler, Antony2,
Apokryltaros, Arcadian, ArjunOl, Art LaPella, Atrian, Autl221, AxelBoldt, B820, BGFMSM, Bailey654, BanyanTree, Batemanl234, Bayerischermann,
Bbatsell, Beetstra, Ben-Zin, Bencherlite, Bendzh, Bergsten, Bertiethecat, Bfahome, Bhadani, Blahed768, Bobol92, Boghog2, Bongwarrior,
Bookandcoffee, Bowlhover, Brainmachine, Bryan Derksen, Burnhamd, CQJ, CWY2190, Cacycle, Call me Bubba, Caltas, Camw, Can't sleep, clown will eat
me, CanadianLinuxUser, Canterbury Tail, CardinalDan, Cassius987, Causa sui, Cayte, Cbrownl023, Celarnor, CerealKiller, Ceyockey, Chamal N, Chao,
Chasingsol, Cheesy Yeast, Chepry, Chirpy7, Chlor, Chodorkovskiy, Chrislk02, Chun-hian, Cimex, Ciphergoth, Ckatz, Clicketyclack, ClockworkSoul,
ClockworkTroll, Closedmouth, Clubjuggle, ClydelOrace, Cmdrjameson, Coching, Cohesion, Collegedegree, Color probe, ComCat, Commander, Condem,
Consequencefree, Conversion script, Corrigen, Crazytales, Creidieki, Crittens, Crystallina, Cyde, Cyrius, DVD R W, Da monster under your bed, DaGizza,
Dacrycarpus, Daharde, Dandv, Daniel233, Daniel5127, DanielCD, Danny B-), Dar-Ape, Darekun, Darklilac, David D., David Wahler, DavidDidwin,
DavidWBrooks, Daycd, Db099221, Dbenbenn, Dbrett480, Debresser, Decltype, Delfigolo, Delta G, Demi s96, Demiurge, Deor, DerHexer, Dfrg.msc,
Dienamight, Dina, Dinsdalea, Discospinster, Dj Capricorn, Domminico, Doniago, Dori, DotComCairney, Dr. Mandellez, Drdaveng, Dreadstar, Dreg743,
Drini, Drphilharmonic, Dsinghs, Dullhunk, Dungodung, Dweller, Dwmyers, EScribe, ESkog, Eaglestrikell7, EarthPerson, EconoPhysicist, Ed, Eeekster,
Eleassar, Elmer Clark, Epbrl23, Eric Kvaalen, Etacarll, Etxrge, Evercat, Everyking, Evil Monkey, Excirial, Fahadsadah, Faithlessthewonderboy, Feezo,
Feniouk, Fenteany, Fermion, Fgbhrgthnrtgnb, FocalPoint, Fox6453, Fram, Freakofnurture, Fredrik, FreplySpang, Frymaster, Fullmetall23321,
Funnybunny, Funper, Fvw, G2sai, GHe, GTBacchus, Gachal, Gadfium, Gaff, Gary King, Geejo, GeeOh, Gekedo, Gene Nygaard, Germen, Gggh, Ghewgill,
Giftlite, Gilliam, GinkgolOO, Glenn, Goatmanl2, Govindjee, GregAsche, GregMinton, Gregturn, Gruzd, Guettarda, Gwernol, HBNayr, HLHJ, Hadal,
Haham hanuka, Hao21ian, Hawaiian717, Hdt83, Hello32020, Henrik, Heron, Hgrenbor, Hil 12233, Hometown, Hordaland, Hpfreak26, Hul2, Hunrizzo8,
Hydrogen Iodide, II MusLiM HyBRiD II, ITOD, Iapetus, Icseaturtles, Ihopel27, Imanoob69, Imi2012, Imogen89, InNuce, Indon, Init, Irishguy, Iron
Dragon91, Ixfd64, J.delanoy, JDnCoke, JForget, JWSchmidt, JYolkowski, Jaknouse, JamesR777, JamibOy, Jasonphollinger, Jaxl, Jazzy211, Jecar, Jeffq,
Jennavecia, Jfg284, Jklin, Jlittlet, Jni, Joanjoc, JoaoRicardo, Johann Wolfgang, John254, JohnalOO, Jondel, Josh Grosse, Joshjoshjoshl, JoshuaZ, Jpoelmal3,
Jrbouldin, Jtdirl, Jugger90, Juhwade, Jusjih, K-UNIT, KFP, Kaabi, Kablammo, Kamal Chid, Kasper90, Kazvorpal, Kbh3rd, Kcordina, Keilana, Kevyn, Kim
Bruning, King Toadsworth, King of Hearts, Kingpinl3, Kopid03, Korg, Kungfuadam, Kungming2, Kupirijo, Kuru, L'Aquatique, LOL, La goutte de pluie,
Lanoitarus, Larryorr, Laur2ro, Laurentl979, Lawrenceuniversityl, Lemchesvej, Li-sung, Lightmouse, Lights, Likeabird, Lilyl5, Logan, Looxix, Lord 1284,
Lord.lucan, Luna Santin, Lupin, MER-C, MNAdam, MPF, Magnus Manske, Makemi, Malcolm, Malcolm Farmer, Malkinann, Malljaja, Malo,
Malomaboy06, Manil, ManuelGR, Marj Tiefert, Marlith, Marysunshine, Master Jay, Mat-C, Mattbr, Matthuxtable, MattieTK, Mav, Maxim, Mboverload,

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Modster, Modulatum, Molybdenumblue, Momusufan, Mrg024, Mrmonsterman, Mrrhum, Munita Prasad, Munyanah, Mwarren us, Mygerardromance,
Myrryam, NMChico24, Nakon, Name b, Narayanese, Natalie Erin, Nehrams2020, NewEnglandYankee, Neyne, Nibls, Nicholasink, Nick, Nickl25, Nik42,
NinaStarry, Nisadaninisa, Nivix, Nonagonal Spider, Nonluddite, Norrello, Nuno Tavares, Nuvitauy07, Nv8200p, OMGHeHasAGim, Ocatecir, Oggie
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POOlOOp, PDH, PaePae, Paine Ellsworth, Pajast, Patrickdavidson, Paul August, Pavel Vozenilek, Peipei, Pekaje, Pentawing, Persian Poet Gal,
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PoeticX, Polyhedron, PontifexlOl, Postdlf, Postglock, Primal400, Prince Godfather, Pro crast in a tor, Procrastinator, Prodego, Proguitarboy, Quadpus,
Quiddity, Quintote, Qwerqwerqwer, Qxz, R Calve te, RJASE1, RJHall, RMFanl, Ram-Man, Ramcy, Randomnotice, Raven4x4x, Raymondwinn, Reaper X,
Red Herring, RedWordSmith, RexNL, Rgamble, Rhysboy, RiaderO, Rich Farmbrough, Rje, Rjwilmsi, Rob Hooft, Robchurch, Robsavoie, Rock2e, RoyBoy,
Rozzychan, Ryanrs, Ryulong, Salsb, Samballance, Samsara, Samtux, Sangol23, Sannse, Sarinl23, Saseigel, Scarian, Sceptre, SchfiftyThree, Schlice,
Scohoust, Sdornan, Search4Lancer, SebastianHelm, Selket, Sengkang, Shafei, Shanel, Shenme, Shiningstarrl997, Shotwell, Simpsons contributor,
Sjakkalle, Skizzik, Slashme, SlimVirgin, Smartse, Smith609, Smokizzy, Snigbrook, Someguyl221, Sonett72, SonicAD, Soumyasch, SparrowsWing,
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SweetNeo85, Swmcd, THEN WHO WAS PHONE?, Tackyleprechaun, Talrias, Tameeria, Tarquin, Tattoo275, Tawker, Tchaika, TedE, Teh wise one,
Tellyaddict, Tero, TestPilot, TexasAndroid, Thatotherdude, The Catfish, The wub, TheArmadillo, TheTito, Thingg, Tide rolls, TigerShark, Tikoo, Tim Q.
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CardinalDan, CflmOOl, Chasingsol, Citicat, Conversion script, CrashingWave, D6, DanlOO, Darklilac, Dave6, DeathFlamel31, Deicas, Delldot, DerHexer,
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Erick.Antezana, Erkenbrack, Everyking, Explodicle, FAGGOODIKIKICOO, Figma, Flamingspinach, Flyguy649, Foreveriamchangd, Forluvoft,
Frankenpuppy, Fratrep, Fritzpoll, GFP, Ghaly, Giftlite, GoodDamon, Graymornings, Hadal, Heathhunnicutt, Horselover Frost, Hughittl, II MusLiM
HyBRiD II, IW.HG, Ikiroid, Ilikepie2221, Ingolia, Intelligentsium, Iridescent, Isnow, J. delanoy, Jagbag2, Jake Wartenberg, Jan. Smolik, Jedi6, Jethero, John
Dalton, Johnuniq, Joyous!, Jujube, Karen Johnson, Kastor48252, Khoikhoi, Kittyes, KnoitallOO, Ktotam, Kuru, Kurykh, La goutte de pluie, Lameomclame,
Lave, Leafyplant, Lexor, Ling. Nut, Loupeter, Lunajurai, MONGO, MPerel, Magnus Manske, Maxi, Meekywiki, Mets501, Midgley, Mikael Haggstrom,
Mspraveen, Mumijary41, Mwfn, Mygerardromance, Naturespace, Nbauman, NewEnglandYankee, Nikki chan, Nikkirox69, Nona89, Omes, Onco p53,
Opabinia regalis, Openlander, Oskoreien, OttoTheFish, Palica, Penhaligon 5, Persian Poet Gal, Phe, PlumCrumbleAndCustard, Prashanthns, PrestonH,
Protox, Quantumobserver, Rawling, RexNL, Rjwilmsi, Robinatron, Rrburke, Samsara, SantanuRoy, Sarcasticidealist, Scientizzle, Serephine, Shinpahl,
Showmanl6, Sionus, Sjo, SI, SnekOl, Snowolf, Sodium, Squidonius, Srr712, Stevage, Svenskajohannes, Synchronism, T-borg, Tarotcards, Tcncv,
Thaerhashem, The Rambling Man, The Transhumanist, TimVickers, Time, Twooars, Until It Sleeps, VegaDark, Versus22, Vietbio, Vishnava, Walik,
Waster, Whosasking, Xcentaur, Yahel Guhan, Zephyris, Zidane tribal, j Jc >i*, 445 anonymous edits

DNA Source: http://en.wikipedia.org/windex. php?oldid=297347068 Contributors: (, (jarbarf), -Majestic-, 168.., 168..., 169, 17Drew, 3dscience, 4ule,
62. 253. 64. xxx, 7434be, 84user, A D 13, A bit iffy, A-giau, Aaaxlp, Aatomicl, Academic Challenger, Acer, Adam Bishop, Adambiswangerl, Adamstevenson,
Adashiel, Adenosine, Adrian. benko, Ahoerstemeier, Aitias, AJ123456, Alai, Alan Au, Aldaron, Aldie, Alegoo92, Alexandremas, Alkivar, Alphachimp,
Alzhaid, Amboo85, Anarchy on DNA, Ancheta Wis, AndonicO, Andre Engels, Andrew wilson, Andreww, Andrij Kursetsky, Andycjp, Anital988,
Anomalocaris, Antandrus, Ante Aikio, Anthere, Anthony, Anthony Appleyard, Antilived, Antony-22, Aquaplus, Aquilla34, ArazZeynili, Arcadian, Ardyn,
ArielGold, Armored Ear, Artichoker, Asbestos, Astrowob, Atlant, Aude, Autonova, Avala, AxelBoldt, AySz88, AzaToth, BD2412, BMF81, Banus, BaronLarf,
Bbatsell, Bci2, Bcorr, Ben Webber, Ben-Zin, BenBildstein, Benjah-bmm27, Bensaccount, Bernie Sanders' DNA, Bevo, Bhadani, BharlOOlOl, BiH, Bijee,
BikA06, Bill Nelson's DNA, Billmcgnl89, Biolinker, Biriwilg, Bjwebb, Blastwizard, Blondtraillite, Bmtbomb, Bobblewik, Bobol92, Bongwarrior, Borisblue,
Bornhj, Brian0918, Brighterorange, Briland, Brim, Brockett, Bryan, Bryan Derksen, CWY2190, Cacycle, Caerwine, Cainer91, Cal 1234, Calaschysm,
Can't sleep, clown will eat me, Canadaduane, Carbon-16, Carcharoth, Carlo. milanesi, Carlwev, Casliber, Cathalgarvey, CatherineMunro, CattleGirl,
Causa sui, Cburnett, Cerberus lord, Chanora, Chanting Fox, Chaojoker, Charm, Chill Pill Bill, Chino, Chodges, Chris 73, Chris84, Chuck Grassley's DNA,
Chuck02, Clivedelmonte, ClockworkSoul, CloudNine, Collins. mc, Colorajo, CommonsDelinker, Conversion script, Cool3, Coolawesome, Coredesat,
Cornacchial23, Cosmotron, Cradleloverl23, Crazycomputers, Crowstar, Crusadeonilliteracy, CryptoDerk, Crzrussian, Cubskrazy29, CupOBeans, Curps,
Cyan, Cyclonenim, Cyrius, D6, DIREKTOR, DJAX, DJRafe, DNA EDIT WAR, DNA is shyt, DVD R W, Daniel Olsen, Daniel987600, Danielkueh, Danny,
Danny B-), Danskil4, Darklilac, Darth Panda, Davegrupp, David D., David Eppstein, Davidbspalding, Daycd, Db099221, Dbabbitt, Dcoetzee,
DeAceShooter, DeadEyeArrow, Delldot, Delta G, Deltabeignet, DevastatorllC, Diberri, Dicklyon, Digger3000, Digitalme, Dina, Djml279, Dlohcierekim's
sock, Dmn, Docjames, Doctor Faust, Docu, Dogposter, DonSiano, Donarreiskoffer, Drdl2, Dr.Kerr, Drini, Dudewheresmywallet, Dullhunk,
Duncan. france, Dungodung, Dysmorodrepanis, E. Wayne, ERcheck, ESkog, Echo parkOO, Echuck215, Eddycrai, Editing DNA, Edwy, Efbfweborg, Egil,
ElTyrant, Elb2000, Eleassar777, EliasAlucard, ElinorD, Ellmist, Eloquence, Emoticon, Epingchris, Erik Zachte, Escape Artist Swyer, Esurnir, Etanol,
Ettrig, EurekaLott, Everyking, Evil Monkey, Ewawer, Execvator, FOTEMEH, Fabhcun, Factual, Fagstein, Fastfission, Fconaway, Fcrick, Fernando S.
Aldado, Ffirehorse, Figma, Figure, Firefoxman, Firetrap9254, Fishingpal99, Flavaflavl005, Florentino floro, Fnielsen, Forluvoft, Freakofnurture,
FreplySpang, Friendly Neighbour, Frostyservant, Fruge, Fvasconcellos, G3pro, GAThrawn22, GHe, GODhack, Gaara san, Galoubet, Gary King, Gatortpk,
Gazibara, Geejo, Gene Nygaard, GeoMor, Giftlite, Gilisa, Gilliam, Gimmetrow, Gjuggler, Glen Hunt's DNA, Glenn, Gmaxwell, GoEThe, Goatasaur, Gogo
Dodo, Golnazfotohabadi, GordonWatts, Gracenotes, Graeme Bartlett, GraemeL, Grafikm fr, Graft, Graham87, GrahamColm, Grandegrandegrande,
GregorB, Grover Cleveland, Gurko, Gustav von Humpelschmumpel, Gutza, Gwsrinme, Hadal, Hagerman, Hairchrm, Hairwheel, Hannes Rost, Harianto,
Heathhunnicutt, Hephaestos, Heron, Heyheyhack, Hockey21dude, Horatio, Hu, Hughdbrown, Hurricanehink, Hut 8.5, Hvn0413, I hate DNA, Iapetus,
Icairns, Ilia Kr., Impamiizgraa, InShaneee, Inge-Lyubov, Isilanes, Isis07, Itub, Ixfd64, Izehar, JHMM13, JWSchmidt, JWSurf, Jacek Kendysz, Jackrm,
JamesMLane, JamesMtl984, Janejellyroll, Jaxl, Jeka911, Jer ome, JeremyA, Jerzy, Jetsetpainter, Jh51681, Jiddisch, Jimriz, Jimwong, Jlh29, Jls043,
Jmccl50, Jo9100, JoanneB, Joconnol, Johanvs, JohnArmagh, Johntex, Johnuniq, Jojit fb, JonMoulton, Jonrunles, Jorvik, JoshuaZ, Josq, Jossi, Jstech, Julian
Diamond, Jumbo Snails, Junes, Jwrosenzweig, Kahlfin, Kapow, Karrmann, Kazkaskazkasako, Kbh3rd, Keegan, Keepweek, Keilana, Kelly Martin, Kemyou,
Kendrick7, Kerry077, Kevin Breitenstein, Kevmitch, Kghose, Kholdstare99, Kierano, KimvdLinde, King of Hearts, KingTT, Kingturtle, Kitch, Knaggs,
Knowledge Seeker, KnowledgeOfSelf, Koavf, KrakatoaKatie, Kums, Kungfuadam, Kuru, Kwamikagami, Kwekubo, KyNephi, LA2, La goutte de pluie,
Lascorz, Latka, Lavateraguy, Lee Daniel Crocker, Lemchesvej, Lerdsuwa, Leuko, Lexor, Lhenslee, Lia Todua, LightFlare, Lightmouse, Lightspeedchick,
Ligulem, Lincher, Lion Wilson, Lir, Llongland, Llull, Lockesdonkey, Logical2u, Loginbuddy, Looxix, Loren36, Loris, Luigi30, Luk, Lumos3, Luna Santin,
Luuva, MER-C, MKoltnow, MONGO, Mac, Madeleine Price Ball, Madhero88, Magadan, Magnus Manske, Majorly, Malcolm rowe, Malo, Mandyj61596,
Mantissal28, Marcus. aerlous, Marj Tiefert, MarvPaule, Master dingley, Mattbr, Mattbrundage, Mattjblythe, Mav, Max Baucus' DNA, Max Naylor,
McDogm, Medessec, Medos2, Melaen, Melchoir, Mentalmaniac07, Mgiganteusl, Mgtoohey, Mhking, Michael Devore, MichaelHa, MichaelaslO,
Michigan user, MidgleyDJ, Midnightblueowl, Midoriko, Mika293, Mike Rosoft, Mikker, Mikko Paananen, Mintmanl6, MisfitToys, Miszal3, Mithent,
Mjpieters, Mleefs7, Moink, Moorice, Mortene, Mr Bungle, Mr Meow Meow, Mr Stephen, MrErku, Mstislavl, Mstroeck, Mulad, Munita Prasad, Muro de
Aguas, Mwanner, Mxn, Nakon, Narayanese, Natalie Erin, Natarajanganesan, Nate 1028, NatureA16, Nauseam, Nbauman, Neckro, Netkinetic, Netoholic,
Neutrality, NewEnglandYankee, Nighthawk380, NighthawkJ, Nihiltres, Nirajrm, Nishkid64, Nitecrawler, Nitramrekcap, No Guru, NoIdeaNick,

Article Sources and Contributors

455

NochnoiDozor, Nohat, Northfox, NorwegianBlue, Nthornberry, Nunh-huh, OBloodyHell, OOODDD, Obli, Oblivious, Ocolon, Ojl, Omicronpersei8, Onco
p53, Opabinia regalis, Opelio, Orrin Hatch's DNA, Orthologist, Ortolan88, Ouishoebean, Outriggr, OwenX, P99am, PDH, PFHLai, PaePae, Pakaran,
Pascal666, PatrickOMoran, Patrick2480, Patstuart, Paul venter, Paulinho28 / Pcb21, Pde, Peak, Pedro, Persian Poet Gal, Peter Isotalo, Peter K., Peter
Winnberg, Pgan002, Philip Trueman, PhilipO, Phoenix Hacker, Pierceno, PierreAbbat, Pigman, Pigmietheclub, Pilotguy, Pkirlin, Poor Yorick,
Portugue6927, Potatoswatter, Preston47, Priscilla 95925, Pristontalelll, Pro crast in a tor, Prodego, Psora, PsyMar, Psymier, Pumpkingrower05,
Pyrospirit, Quebec99, Quickbeam, Qutezuce, Qxz, R'n'B, R. S. Shaw, RDBrown, RSido, Ragesoss, Rajwikil23, RandomP, Randomblue, Raul654, Raven in
Orbit, Ravidreams, Rdb, Rdsmith4, Red Director, Reddi, Rednblu, Redneckjimmy, Redquark, Retired username, Rettetast, RexNL, Rich Farmbrough,
RichG, Richard Durbin's DNA, Ricky81682, Rjwilmsi, Roadnottaken, Robdurbar, RobertG, Rocastelo, RoddyYoung, Rory096, Rotem Dan, Roy Brumback,
RoyBoy, RoyLaurie, Royalguardll, RunOrDie, Russ47025, RxS, RyanGerbillO, Ryulong, S77914767, SCEhardt, STAN SWANSON, SWAdair, Sabbre,
Safwan40, Sakkura, SallyForthl23, Sam Burne James, Samsara, Samuel, Samuel Blanning, SandyGeorgia, Sangol23, Sangwine, Savidan, Scarce,
Sceptre, Schutz, Sciencechick, Sciencemanl23, Scincesociety, Sciurinae, Scope creep, Scoterican, Sean William, SeanMack, Seans Potato Business,
SebastianHawes, Seldonl, Sentausa, Serephine, Shadowlynk, Shanes, ShaunL, Shekharsuman, Shizhao, Shmee47, Shoy, Silsor, SimonD, Sintaku,
Sir.Loin, Sjjupadhyay, Sjollema, Sloth monkey, Slrubenstein, Sly G, SmilesALot, Smithbrenon, Snowmanradio, Snowolf, Snurks, Solipsist, Someone else,
Sonett72, Sopoforic, Spaully, Spectrogram, Splette, Spondoolicks, Spongebobsqpants, SpuriousQ, Squidonius, SquirepantslOl, Statsone, Steel, Steinsky,
Stemonitis, Stephenb, SteveHopson, Stevertigo, Stevietheman, Stewartadcock, Stuart7m, Stuhacking, SupaStarGirl, Supspirit, Susvolans, Sverdrup,
Swid, Switchercat, T'Shael, Taco325i, Takometer, TakuyaMurata, Tariqabjotu, Tarret, Taulant23, Tavilis, Tazmaniacs, Ted Longstaffe, Tellyaddict,
TenOfAllTrades, Terraguy, Testl 00000, TestPilot, The Rambling Man, The WikiWhippet, TheAlphaWolf, TheChrisD, TheGrza, TheKMan, TheRanger,
Thorwald, ThreeDaysGraceFanlOl, Thue, Tiddly Tom, Tide rolls, TigerShark, TimVickers, Timewatcher, Timir2, Timl2k4, Timrollpickering, Timwi,
Tobogganoggin, Toby Bartels, TobyWilsonl992, Tom Allen, Tom Harkin's DNA, Tomgally, Toninu, Tonyl, Tonyrenploki, Trd300gt, Trent Lott's DNA,
Triwbe, Troels Arvin, Tstrobaugh, Tufflaw, Turnstep, Twilight Realm, Tyl46Tyl46, UBeR, Unint, Unukorno, Usergreatpower, Utcursch, Uthbrian,
Vaernnond, Vandelizer, Vanished user, Vary, Virtualphtn, Visium, Vividonset, VladimirKorablin, Vsmith, Vyasa, WAS 4.250, WAvegetarian, WHeimbigner,
WJBscribe, Wafulz, WarthogDemon, Wavelength, WelshMatt, West Brom 4ever, Where, Whosasking, Whoutz, Why My Fleece?, Wik, Wiki alf, Wiki emma
Johnson, Wikiborg, Wikipedia Administration, William Pietri, WillowW, Wimt, Wknight94, Wmahan, Wnt, Wobble, WolfmanSF, Wouterstomp, Wwwwolf,
Xy7, YOUR DNA, Yahel Guhan, Yamamoto Ichiro, Yamla, YanWong, Yansa, Yaser al-Nabriss, Yasha, Yomama9753, Younusporteous, Yurik, ZScout370,
Zahid Abdassabur, Zahiri, Zazou, Zell Miller's DNA, Zephyris, Zoicon5, Zouavman Le Zouave, Zsinj, Zven, 1329 anonymous edits

Molecular models of DNA Source: http://en. wikipedia. org/windex.php?oldid=297347366 Contributors: Bci2, Chris the speller, CommonsDelinker,
Oscarthecat, Until It Sleeps

DNA structure Source: http://en. wikipedia. org/windex.php?oldid=293141623 Contributors: Andreww, Antandrus, Bci2, CDN99, Chodges, DVD RW,
DabMachine, Dysmorodrepanis, Forluvoft, Gene Nygaard, Hannes Rost, Harold f, Joel7687, Josq, Luuva, Maikfr, Mr.Z-man, MrHaiku, Nasz,
PatrickOMoran, Rajan.kartik, Reinyday, Rich Farmbrough, Thorwald, TimVickers, Tomgally, Wknight94, Yahel Guhan, Zephyris, 23 anonymous edits

Paracrystalline Source: http://en.wikipedia.org/windex.php?oldid=29 1869326 Contributors: Bci2, CharlotteWebb, Furmanj, Giftlite, Sting au,
Venny85, Warut, 1 anonymous edits

DNA Dynamics Source: http://en. wikipedia. org/windex.php?oldid=296104632 Contributors: Auntof6, Bci2, CanderOOOO, Chris the speller,
CommonsDelinker, Ironholds, Potatoswatter

Genomics Source: http://en. wikipedia. org/windex.php?oldid=297056002 Contributors: *drew, 5dPZ, AdamRetchless, Adenosine, Alex naish, Andreadb,
Anthere, ApersOn, Aphextwin5678, AxelBoldt, Barrylb, Bill.albing, Braidwood, Branttudor, Brion VIBBER, Bryan Derksen, Calvinthel337, Ceyockey,
Combio, CommodiCast, DabMachine, Dave Nelson, David D., Dekisugi, Dicklyon, Dmb000006, DoctorDNA, Dolfin, Drgarden, El C, Eubulides, Eugene,
Fred Bradstadt, Gary King, Genometer, GeoMor, Ghostoroy, Giftlite, Gilliam, Habj, Hadal, Hbent, Heron, Jenks, Jethero, Jfdwolff, Joconnol, Joerg Kurt
Wegner, Johntex, Johnuniq, Jongbhak, Larssono, Lexor, Lightmouse, Lost-theory, Mariusz Biegacki, Marj Tiefert, Mav, Mike Lin, Natarajanganesan,
Nitwitpicker, Oleginger, Para, Peak, Pgan002, Pharmtao, Pion, Pvosta, Quizkajer, RandomP, Recury, Rein0299, Rich Farmbrough, Ronz, Rppgen,
Sairen42, Scewing, Shanes, SimonP, Sjjupadhyay, Spitfire ch, Springmn, Starshadow, Stonedhamlet, Syp, Template namespace initialisation script,
TheObtuseAngleOfDoom, Thkim75, Thorwald, Tiddly Tom, Toddstl, Touchstone42, Unyoyega, VashiDonsk, W09110900, Wavelength, Wayne530,
Williamb, Wmahan, Wuzzybaba, Xanthoptica, ZayZayEM, ZimZalaBim, 131 anonymous edits

Gene regulatory network Source: http://en.wikipedia.org/windex.php?oldid=295440342 Contributors: Adiel lo, BigHaz, BryanD, Carl T, Charles
Matthews, DanielYamins, Delaszk, FlorianMarkowetz, Frederickmercury, Gaius Cornelius, Jknabe, Jpbowen, Jugander, Kku, Lexor, Massbiotech, Mdd,
Memestream, Michael Hardy, Mortalsyn, Narayanese, Natelewis, Neurocompute, PFHLai, Peak, Ronz, Rverduzco, Slambeck, Stewartadcock,
Tekhnofiend, WAS 4.250, WriterHound, Wynand.winterbach, 85 anonymous edits

Computational genomics Source: http://en.wikipedia.org/windex.php?oldid=290928485 Contributors: Appraiser, Blastwizard, Bluemoose, Cbock, D6,
Jethero, Jongbhak, LeaveSleaves, Meredyth, Michael Hardy, Pearle, Tarinth, Tim@, Twooars, 8 anonymous edits

DNA nanotechnology Source: http://en.wikipedia.org/windex.php?oldid=294763628 Contributors: 0x38I9J*, Alnokta, Amaling, Anthonydelaware,
Antony-22, Cyfal, Epbrl23, Giftlite, Gioto, Pwkr, ShawnDouglas, Thorwald, Tolosthemagician, ZayZayEM, 30 anonymous edits

DNA computing Source: http://en.wikipedia.org/windex.php?oldid=294822698 Contributors: 4v410n42, Ahoerstemeier, Alan smithee, Alfalfahotshots,
Antony-22, Arthena, Arun.p.m, Atreyu42, Bdesham, Biomol, Ceros, Coconut99 99, DavidCary, Dcoetzee, Drunkasian, Eaglizard, Gdr, Giftlite, Gioto,
Henrygb, Ihopel27, Iluvcapra, Ixfd64, Jeff G., JohnLynch, JonHarder, Jsmaster24, Kaster, Kevmitch, Lexor, Lightofglory, Lovro, Lowellian, Luuva,
MagnaMopus, Matt489, Maurice Carbonaro, Maurreen, Medlakeguy, Memming, Michal Jurosz, Mintleaf, Morio, Ohnoitsjamie, POlyglut, PasswOrd,
Pharod42, Piet Delport, Pixelface, Pizza Puzzle, Powo, Racklever, Radagast83, Rahulr7, Ray Dassen, Rulesdoc, Rwwww, SCriBu, Seans Potato Business,
SebastianHelm, Shanes, Stratocracy, Suruena, TheoClarke, TheronllO, TimoSirainen, Tverbeek, Vagodin, Vivacissamamente, Wapcaplet, Wik,
WulfTheSaxon, Xeo, Ykhwong, Yonaa, Zfr, 73 anonymous edits

Synexpression Source: http://en.wikipedia.org/windex.php?oldid= 167705002 Contributors: Bwpach, Frederickmercury, Iamunknown, Joel7687,
Open2universe, 2 anonymous edits

Computational epigenetics Source: http://en.wikipedia.org/windex.php?oldid=285482504 Contributors: 2over0, Asasia, Cbock, D.M.N., Mr Adequate,
TastyPoutine, 3 anonymous edits

Protein- protein interaction Source: http://en.wikipedia.org/windex.php?oldid=296552319 Contributors: 56869kltaylor, 7bdl, A wandering 1,
Alboyle, Apfelsine, Ashcroft, Bci2, Biophys, Clicketyclack, Cpichardo, D-rew, DarkSaber2k, Delldot, Djstates, Dsome, FreeKill, Giftlite, GracelinTina,
Hendrik FuJS, Hotheartdog, Jeandre du Toit, Jkbioinfo, Jkwaran, Jn3vl6, Jongbhak, Keesiewonder, Kkmurray, Kuheli, Kyawtun, Lafw, Lemchesvej,
Lenticel, Longhair, Meb025, Michael Hardy, MichaelMcGuffin, Miguel Andrade, NickelShoe, Ninjagecko, Nnh, Rajah, Reb42, Riana, Ronz, Seans Potato
Business, Snowolf, TheParanoidOne, Thorwald, Uthbrian, Victor D, Wenzelr, Whosasking, Wintrag, 68 anonymous edits

Interactomics Source: http://en.wikipedia.org/windex.php?oldid=293358442 Contributors: Bci2, Bdevrees, Erick.Antezana, Erodium, Jong, Jongbhak,
Karthik.raman, Lexor, Llull, Niteowlneils, PDH, Pekaje, Rajah, Tucsontt, 8 anonymous edits

Developmental biology Source: http://en.wikipedia.org/windex.php?oldid=289544668 Contributors: 168..., 2005-01-21T13:57Z, 2005-01-31T01:24Z,
ABF, APH, AdamRetchless, Altenmann, Andre Engels, AnnaP, ArbitrarilyO, Arcadian, Arkuat, AxelBoldt, Ben Ram, Bobol92, Borgx, Cjmnyc, Conversion
script, Cryptic, Cyberix, Discospinster, Drgarden, Egfr, Electric goat, Epastore, Eperotao, Eubanks718, Evolauxia, Ferrylodge, Fplay, GetAgrippa,
Ginkgo 100, Habj, Husond, IlSoge, JWSchmidt, JaGa, Jasonlncarnate, Je at uwo, Jeebee, Jimmer, Jknabe, JoergenB, JonHarder, JonMoulton, Keenan
Pepper, Kevin Saff, KillerChihuahua, KrytenKoro, Kurykh, Lexor, Lightmouse, Looxix, Lysis rationale, Magnus Manske, Margacst, Marshman,
Memestream, Mietchen, Miguel de Servet, Mikael Haggstrom, Mild Bill Hiccup, Mxn, Narayanese, Nehrams2020, Otets, Phlebas, Pion, Polyparadigm,
Pro bug catcher, Redheylin, Rhys, Rich Farmbrough, Rjwilmsi, Romanm, Samsara, SebastianHelm, SpitfireOOO, StN, Takanjack, TheAlphaWolf,
TheLimbicOne, Tristanb, Tycho, Van helsing, WAS 4.250, WikiNoise, Woody, XJamRastafire, Zfr, Zocky, Zzuuzz, 89 anonymous edits

Article Sources and Contributors

456

Cellular differentiation Source: http://en.wikipedia.org/windex.php?oldid=292518593 Contributors: 12dstring, AMAGOOCH, AdamRetchless,
Ahoerstemeier, AkashAD, Alansohn, Arcadian, Avjoska, Betacommand, Bratko4223, Brim, Bsadowskil, CANTFLAME, Ciar, DES04, Delldot, DerHexer,
Dmr2 / Dr Aaron, Dreamafter, Dullhunk, El C, EncycloPetey, Epbrl23, Everyking, Forluvoft, Franamax, GBuilder, Hadal, Hadil362, Hydrogen Iodide,
JWSchmidt, JamesBWatson, Lexor, MDChanderson, MK8, Malcolm Farmer, Marshman, Miss Madeline, Mxn, Nehrams2020, NuclearWarfare, Paulmch,
Peter Znamenskiy, QuadrivialMind, Redheylin, Res2216firestar, Rich Farmbrough, RoyBoy, Sj, Srlasky, TPK, TheLimbicOne, Twooars, Uncle Dick,
Valich, Wapcaplet, 91 anonymous edits

Morphogenesis Source: http://en.wikipedia.org/windex.php?oldid=296167027 Contributors: 168..., Aciel, AdamRetchless, Alan Peakall, Andre Engels,
Anwormy, ArbitrarilyO, Arminius, Arrt-932, Attilios, AxelBoldt, BD2412, Bfinn, Cayte, Celefin, Chaos, Conversion script, DabMachine, Darklilac, Daycd,
Dmmdl23, Drdl2, Drphilharmonic, Dullhunk, Eddovar, Electric goat, Enchanter, Epbrl23, Eubanks718, Falco528, Fjellstad, Frazzydee, Gem, Gogo
Dodo, Habibkoite, Hede2000, Hgilbert, IronChris, Izvora, J. delanoy, JWSchmidt, Jknabe, Julien Tuerlinckx, Khatru2, Lauriec, Ledfloyd, Lexor, Lulu of the
Lotus-Eaters, Magnus Manske, Malcolm Farmer, Matty j, Mccready, MikeBaharmast, Moriane, Morphogenesis2008, Phantom mafia, RDBrown, Rhys,
Robofish, Romanm, Scentoni, Shyamal, Sjorford, Sricel3, Stepa, WellsPedia, Zocky, 32 anonymous edits

Nuclear medicine Source: http://en.wikipedia.org/windex.php?oldid=297402497 Contributors: ABF, APH, Acrabb, Acroterion, AdamJ-TRX, AjAldous,
Alex.tan, Ali@gwc.org.uk, Altenmann, AndreasJS, Andrei, Arostron, Barlow, Beavertank, Benjaminevans82, Blanchardb, Bobblewik, Bogey97, Btyner,
BusterNutBag, Calvin 1998, CanadianLinuxUser, Captain Zyrain, Centrx, ChillyMD, Chowbok, CiaPan, Clicketyclack, Csblackburn, Ctande, Cyfal, DV8
2XL, Damato, DanMS, Daveswagon, Davidruben, Delaroyas, Diberri, Dirac66, Discospinster, Disenraged, DrFOJr.Tn, Dspradau, Dwayne Reed, Elassint,
Enderwiki, Epbrl23, EpicDream86, Evil Monkey, Fizzy, Fnielsen, Formol, Frickeg, Galoubet, GangofOne, Gilliam, Graeme L, II MusLiM HyBRiD II,
Igoldste, Iorsh, J. delanoy, Jerry, Jfdwolff, Jjkusaf, Jmjanzen, Keereann, Kubanczyk, LMB, Laurens-af, Lcolson, Leafyplant, Levent, Li4kata, Luna Santin,
MER-C, Madhero88, Mco44, Meelar, Mefanch, Mercurous, Mion, Mygerardromance, NickW557, Nihiltres, Nukemedsb, Oldnoah, Paulc206, PeteVerdon,
Possum, Quinlan Vos, Raven in Orbit, RazorlCE, Robertvanl, Ronhjones, Rsabbatini, SKvalen, SWAdair, Saimhe, Salvadorjo, Saric, Sbharris, Sceptre,
Semperf, Simesa, Simonbayly, Social Climber, Stephenb, Tcb0667, Tmarlow, Tony46, Treuss, Ultimus, Venu62, Voyagerfan5761, Wasted Sapience,
Wouterstomp, Yoderj, Zereshk, 260 anonymous edits

Radionuclide Source: http://en.wikipedia.org/windex.php?oldid=297561884 Contributors: Aarchiba, Actarux, AdamWalker, Addshore, Ahoerstemeier,
AjAldous, Andres, Animum, Antandrus, AxelBoldt, Ayla, Bobol92, Borgx, Braindamagehurts, Breakyunit, Butros, CALR, CUSENZA Mario, Ciphers,
Citicat, DaGizza, Deberle, Dekisugi, Discospinster, DocWatson42, Donarreiskoffer, Drstuey, Eleassar777, Ems57fcva, Epbrl23, Essaregee, Fnielsen,
FocalPoint, Gentgeen, Gregisfat2, Gungasdindin, H.sandOl, Hamburgersl212, Herbee, Icairns, Isnow, JLD, Jclerman, Jeremycenus, Jessiehawkes,
Jketola, Joanjoc, Johndoe616, Jons63, Jordi Burguet Castell, Keenan Pepper, Keilana, Kkmurray, Kpjas, Kristof vt, Kukini, Lir, Looxix, Mav, Mlessard,
Nilfanion, Nuclearmedzors, Ojigiri, PGWG, Pdbailey, PetaRZ, Philip Trueman, Pjvpjv, Postoak, Rhenning007, Rogerrluo, ST47, Sam Hocevar, Sbharris,
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Positron emission tomography Source: http://en.wikipedia.org/windex.php?oldid=296963324 Contributors: A314268, Alex Spade, Alex.tan, Andre
Engels, Andrei, Andrew73, Andrewa, Astuishin, Atlant, AxelBoldt, Axl, Bdekker, Benjaminevans82, Bertrus, Bfong, BlueEvo2, Bobblewik,
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DMacks, Da Joe, Damato, David Martland, Db099221, Deglr6328, Delta G, Discospinster, DocWatson42, Dougher, Doulos Christos, Drgarden, Dricherby,
Duedilly, Epbrl23, Fivepints, Fizzy, Flapdragon, Fnielsen, Frederickhoyles, Gaius Cornelius, Galoubet, Graham87, GyroMagician, Harsh Stone White,
Headbomb, Hehkuviini, Hul2, Ilgiz, Improv, J. delanoy, JForget, JMumford, JamesMLane, Jascii, JdeJ, Jeremy Butler, Jiang, Jk91 185, Jsmit317, Junior
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Neparis, Neutrality, NikNakk, Nunquam Dormio, OlEnglish, Oliphaunt, P3d0, PETUSER, Patrick, Pernambuco, Pgk, Phdplayahatadegree, Phil Boswell,
Purple Paint, RTC, Recognizance, Riwiener, Rmhermen, RodC, Ropcat, Rsabbatini, Salsa Shark, Salvadorjo, Sayeth, Sbharris, Schneelocke, Sduncan53,
SeanMack, Sine Wave, Sjayanthi, Slakhan, Slakr, SnowflakeHolocaust, SoWhy, Spellmaster, Stevesg, T.j.chryssikos, Tekhnofiend, TenOfAllTrades, The
Anome, Tide rolls, Tito4000, Tony46, TonySt, Toolator, Vasil', Vaughan, Voyagerfan5761, Wikid, Wolfgangamadeus, Yeti7, Yhseo, Zereshk, 234
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2D-FT NMRI and Spectroscopy Source: http://en.wikipedia.org/windex.php?oldid=297239250 Contributors: Bci2, Ched Davis, Drilnoth, H
Padleckas, JaGa, Reedy, Rich Farmbrough, Rjwilmsi, Teeschmid, 2 anonymous edits

NMR spectroscopy Source: http://en.wikipedia.org/windex.php?oldid=280684865 Contributors: Aihre, Andy M. Wang, AxelBoldt, Bci2, Beetstra,
Benandjonice, Biophysik, Borisovav, Bruker, CaneryMBurns, Ceyockey, ChemistHans, Cryptophile, DMacks, Djdaedalus, Flogiston, Freestyle-69, G-W,
Geejo, Gehtnix, Gene Nygaard, Ghiles, Graeme Bartlett, Hammerl980, Headbomb, Jclerman, Jenpen, Jingxin, Jrizor8 504, Julesd, Kafziel, Kaiserkarll3,
Keraman, Kjaergaard, Kkmurray, La goutte de pluie, Lee-Jon, LinguisticDemographer, Linmhall, Mac Davis, Markjosephl25, Mboverload,
Measure4Measure, Mike. lifeguard, Neparis, OMCV, Oxymoron83, Pekaje, Quantockgoblin, RG2, Ribol, Rifleman 82, Runningonbrains, Salsb, Santiago
Dominguez, Shalom Yechiel, Shrew, Sikkema, Smokefoot, Spellmaster, Srnec, Stepa, Takometer, TenOfAllTrades, Tkircher, Troodon, V8rik, Walkerma,
Whatamldoing, Xenonice, Zosma, 55 anonymous edits

Fourier transform spectroscopy Source: http://en.wikipedia.org/windex.php?oldid=291868949 Contributors: AJim, Asterion, Bci2, Berserkerus,
BigFatBuddha, BobbylOll, Christopherlin, Damian Yerrick, Deglr6328, E104421, Epbrl23, Graeme Bartlett, Guillom, Hankwang, Harold f,
Haydarkustu, HelgeStenstrom, Jaraalbe, Jcwf, John. lindner, Jonathan F, Kcordina, Kingpinl3, Kkmurray, Martyjmch, Michael Hardy, Nikai, Nitrogenl5,
Peter, Peterlewis, Rifleman 82, Rnt20, Ronningt, Roybb95, Seidenstud, Skier Dude, Slapidus, Smeyerl, Stannered, Sverdrup, Thepretenders22,
Thinkinnng, Tim Starling, Veinor, Victorsong, 69 anonymous edits

Nuclear Magnetic resonance imaging Source: http://en.wikipedia.org/windex.php?oldid=297760922 Contributors: 01bambern77, 2T, 99Perfectos,
A314268, AFdeCH, Aarchiba, Abdullahkhurram, Abecedare, Achromatic, Acrabb, Acroterion, Adhanali, Aetheling, Afiller, Agateller, Ageekgal,
Ahmad. ghamdi. 24, Ahoerstemeier, AirdishStraus, Alaniaris, Alansohn, Albany NY, Aldaron, Alex.tan, Amberroom, AndonicO, Andre Engels, AndreasJS,
Andrewhartl, Angyal8, Animum, Antandrus, Anupam, Apollyon48, Appraiser, ArglebarglelV, Argon233, Artemis6234, Axl, BBerryhill, BaggiolO, Bandy,
Banus, Bartl33, Bci2, Beaumont, Bebenko, Benjaminevans82, Binksternet, Biomedl23, Blinking Spirit, Bmeguru, Bobol92, Bodnotbod, Boivie, Boris
Barowski, Bovineone, Brandongalbraith, Brewhaha@edmc.net, Brownturkey, Brysonborg, Btunell, Bugnot, Bulbeck, Butros, C.Bluck, Cachorrito,
Cajolingwilhelm, Calton, CanadianLinuxUser, Capricorn42, Caspian, Chantoke, Chet nc, Chris La Mantia, Chris the speller, Christopher Thomas,
ChumpusRex, Ck lostsword, ClickRick, Clicketyclack, Cmcnicoll, Cmdrjameson, Coachfortner, Cometstyles, Commode7x, ConradPino, Correogsk,
Cortjstr, CosineKitty, Cubbi, Cxrtrack, DHN, Da monster under your bed, Daniel. Cardenas, DanielCD, Darrien, David s graff, David. Monniaux, Dawtsf,
Deglr6328, Deli nk, Delldot, Deor, Dgbenn, DiamonDie, Diberri, Dick Bos, Dieselbub, Dirac66, Dj manton, Dlohcierekim's sock, DocWatson42, Dochar,
Doctormatt, Doczilla, Dodgethis, Dogcow, Doregan, Dowew, Dreish, Duncharris, Dwayne Reed, Ekotkie, El aprendelenguas, Eras-mus, Eric-Wester,
Euyyn, Evahala, Eykanal, Femto, Ferdinangus, Fernkes, Fig wright, FirstPrinciples, Fixed Phil, Flamebroil, Fleminra, Floppster, Fnielsen, Francis felix,
Friginator, G-W, G3pro, Gaius Cornelius, Garrickla, Gary Cziko, Gene Nygaard, Giftlite, GinaDana, Glennwells, Goalguard33, Gradientll, Graham87,
Graldensblud, Gramsaystuart, Gsmgm, Gtstricky, Gurchzilla, Gurukeng, GyroMagician, H2g2bob, Hadal, Haham hanuka, Hassaanq, Havaska, Heathd,
Hermoye, Heron, Hibana, Huggles41ife, Huitzil, Husond, Hydrargyrum, Hydrogen Iodide, ICAPTCHA, IbuprofenlOl, Icairns, IceUnshattered, Igoldste,
Ihealthbuzz, Ikiroid, ImLookingThruYou, Improv, Indium, Iridescent, Islander, Isntbrain, Ixfd64, J. delanoy, JForget, JVinocur, JaGa, Jagl 23, Jaganath,
James Kanjo, JamesMLane, Jan van Male, JdH, Je at uwo, Jeffrey O. Gustafson, Jfdwolff, Jfrahm, Jht4060, Jiang, Jimbobl, Jlewis, Jmjanzen, Jnothman,
JoeAnderson, Joema, John. d.van. horn, JohnOwens, Jonas2818, Jonathanlewney, JonboyOl, Jong pom chu, Jossi, Jpbowen, Jprawn, Jrockley, Js9530,
Jscott.trapp, Jtact, Juansempere, Jumping cheese, K Eliza Coyne, KDesk, Katieh5584, Keenan Pepper, Khalid hassani, Kilbad, King himself88, Kjkolb,
Kmarhef, Kmpatterson, KnowledgeOfSelf, Kostmo, Kowey, Kpmiyapuram, Kram9, Kshenoy06, Kslays, Kubanczyk, Kuru, Kwamikagami, Kyoko, Lcjohnso,
Lcolson, LeadSongDog, Leafyplant, Light current, Linas, Liverpool Scouse, Lostlntel, LostLeviathan, Luca Balbi, Lucamauri, Lzhang, MAGI,
MMcCallister, Macserv, Macy, MakVal, Manil, Mark83, Master of Puppets, Matrad6781, Mattabat, Maxxicum, Mco44, Mcsee, Medconn, Mgiganteusl,
Michael Hardy, Michaelbusch, Mietchen, Miquonranger03, Mmoneypenny, Mogk, MoraSique, Mossig, Mrs.meganmmc, Myanw, Naniwako, Nasukaren,
NeilUK, Neparis, Nephron, NerdyNSK, Nergaal, Nick Mks, Nigholith, Nightryder84, NonNegative, Nowa, Nulzilla, Nyctea, Ofirglazer, Omegatron,
Optiganl3, Osm agha, Oxymoron83, P g chris, PDH, PMJ, PTSE, Paintman, Pakaran, Papadopc, Paraphelion, Parker007, Pasboudin, Pascal666, Peaceful
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Rasmus Faber, Read-write-services, Reedy, Reisio, RelentlessRecusant, Remmus4 / Reuben, RexNL, Rich Farmbrough, Richard Arthur Norton (1958- ),
Richwil, Rickterp, Ridow, Rji, Rjwilmsi, Roadrunner, Robertwharvey, Romeu, Ronz, RoyBoy, Rstehr, S Roper, SBarnes, SDC, Salsb, Sam Hocevar,
SamSim, SanGatiche, Sandstein, Saravask, Savedthat, Sayeth, Schobeiri, Schulte, ScienceApologist, ScottAlanHill, Scottmsg, Sedoc, Sesquiculusl,
Sfahey, Shanes, Shavec, Shoeofdeath, Simoes, Sjschen, Skippyjones, Smartwords, Sneakygreek, Solipsist, Sorchah, Soundray, Spick And Span,
Spidermonkey, Stan Sykora, StaticGull, Stepa, StephanieM, Stevenfruitsmaak, Stone, Sturm br, Sumersethi, Sunborn, Suruena, SusanLesch, Taggard,
TantalumTelluride, TenOfAllTrades, Tgilk, The Anome, The Hybrid, The JPS, The Random Editor, The undertow, TheBrain, TheGlenlivet, Thisisnotapipe,
Thorpe, Threestain, Tide rolls, TimothyFreeman, Timtrent, Timwi, Titoxd, Togo, Tomattea, Tommytao, TomyDuby, Triddle, Triksox, Una Smith, Unschool,
Useight, Uvo, Valde.maximus, Valentinpl4, Van helsing, Vantey, VashiDonsk, Vaughan, Vespristiano, Vicarious, Vicki Rosenzweig, Voice of All,
Vonspringer, Vpdvpd, Vuo, Weregerbil, Wernher, Wetman, Widefox, Wiki alf, Wimt, Wolf530, Wolfmankurd, Wouterstomp, Writtenright, Wtmitchell,
Xiggelee, Ygavet, Ystar, Zaak, ZalleZack, Zandperl, Zephalis, Zereshk, Ziggyc, Zureks, Omer Cengiz Qelebi, 909 anonymous edits

Neuroimaging Source: http://en.wikipedia.org/windex.php?oldid=297742338 Contributors: A314268, Action potential, Aitias, AjAldous, AllyUnion,
Appraiser, Ascorbic, Aviados, Brinticus, BathoryPeter, Charles Matthews, Chris the speller, Chriss789, Chupper, Closedmouth, CommonsDelinker,
DCDuring, Dancter, Delldot, Dwayne Reed, Dysprosia, Erich gasboy, Erkan Yilmaz, FSHL, Fabrice. Rossi, Faradayplank, Foobar, Frajolex, Fresheneesz,
Friedrich K., Fryed-peach, Gcmarino, Genesisl2, Gfariello, Giftlite, GyroMagician, Hadal, Hydrogen Iodide, Ipigott, Jakebroadhurst, Jfdwolff,
John. d.van. horn, Jumbuck, Junior Brian, Karada, Khalid hassani, Kozuch, Kpmiyapuram, Kslays, Looie496, Louislemieux, Mai, Mandark, Marcoscramer,
MarkSCohen, Maxim, Mboverload, Mdd, Michael Hardy, Mietchen, Mygerardromance, Mykej, N.vanstrien, NeuronExMachina, Nilmerg, O lara o,
Omegatron, Paranoid, Ph. eyes, Pjacobi, Poocat, Raistlinjones, Redrocketboy, Ringbang, Rsabbatini, SanGatiche, Sardanaphalus, Sayeth, Sbharris,
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Makarov, Vaughan, Veinor, Warut, Wikiborg, Wouterstomp, Ze miguel, 91 anonymous edits

Computed tomography Source: http://en.wikipedia.org/windex.php?oldid=297755379 Contributors: 2D, 2T, A314268, Abomasnow, Abu yasif, Acrabb,
Acroterion, Action potential, AdjustShift, Adw2000, Afiller, Ahpook, Ainlina, Alex.tan, Alexius08, Altzinn, Ameliorate!, Andrew73, Andrewwl978,
Antandrus, Anuradhasridhar, ApersOn, Apoc2400, ArglebarglelV, Argon233, Arostron, Aspects, Avalyn, AxelBoldt, BaggiolO, BakashilO, Bci2, Bemoeial,
Ben-Zin, Benjaminevans82, Betamod, Bhaber602, Biezl, Billlion, Bjweeks, Blanchardb, Blehfu, Blowdart, Bluetetrahedron, Bmdavll, Bouncingmolar,
Bovineone, Bright, Brat32, BrianKnez, Burhan Ahmed, CALR, Cancun771, Casmith 789, Cburnett, Cfoure, Chasingsol, Chowbok, ChumpusRex,
Ciphergoth, Cobaltbluetony, Coffee joe, CommonsDelinker, Coneslayer, Corti, Cowtown, Crucis, Crum375, Dan Austin, Daniel Mahu, Darklilac,
Deamonator, Deepstratagem, Delengar, Deli nk, Delldot, Dentropy, Diberri, Discospinster, Doc Tropics, Doc4heart, Dopefishjustin, Douglasjryan,
Draeco, Dsl3, Dtl2, Dy yol, ERcheck, Ed Fitzgerald, Edward, Eleassar777, Enquire, Erickraus, Erik Sorensen, Ex-User777, Fireice, Firien, Fleminra,
Flightdoc2, Fnielsen, Freddyzdead, Furqan Tejani, Fuzzball!, Fvasconcellos, Fyyer, Gail, Gaius Cornelius, GargoyleMT, Gary King, Gary Peach, Gem,
Gdh, Gekritzl, Gene Nygaard, Gerv, Giftlite, Gioto, Glitzy queenOO, Gmackl, Gonzonoir, Gradientll, Gunjannpatel, Gurch, HIradFB, Hadams, Hektor,
Hydra Rider, Hegesippe Cormier, Ian Dunster, Ian Geoffrey Kennedy, Icez, Ikluft, ImLookingThruYou, Isnow, J.delanoy, JForget, JIP, JVinocur, Jackelfive,
Jake Wartenberg, Jarviskj3, Jason7825, Jasonssmith94, Jellyfisho, Jennavecia, Jesse. Schneider, Jfdwolff, Jftuga, Jjron, Jk5177, Joechao, Johannes
Mockenhaupt, Johntex, Jonas Viper, JorgeGG, Jubilee7, Kaiba, Kaobear, Kaszeta, Keilana, Kevin Rosenberg, Khalid hassani, Kilbad, Kmccoy, Kostmo,
Kraftlos, Kram, Kubanczyk, Kyoko, La Pianista, Lambyte, Lamshuwing, Landonl980, Latulla, Leo013, Leujohn, Levydav, Liftarn, Lipothymia, LiveAction,
Llywrch, Lou Sander, Luk, Luna Santin, MAlvis, MER-C, Mahboud, Malcolma, Marcairhart, Mario 64 Master, Mark Lewis Epstein, Matpe815, Matturn,
Max Naylor, Maxim Razin, McSly, Mco44, Mcstrother, Mentisock, MercolaOverMerck, Metju, MiG, Michael Hardy, MicooliolOl, Mikael Haggstrom,
MisfitToys, Mpulier, Mr Stephen, Mytildebang, Negron305, Neparis, Nevit, Nimur, Nlitement, Nv8200p, Obaeyens, Odie5533, Ois69, Optiganl3,
Orimlig, Otisjimmyl, Parttimer, Pavthraa, Pearle, PeterSymonds, Pharaoh of the Wizards, Philipcosson, Piano non troppo, Pibwl, Porqin, Pratx,
Professorial, Pt, Pyrobob, Quentar, Radagast83, Ratagonia, Ravedave, Red Thunder, Reedy, Rigadoun, Rjwilmsi, Robertwharvey, Roboconnell, Roisterer,
RoyBoy, S Roper, SFC9394, Sabry hassouna, SajmonDK, Sayeth, Scientific American, Scottandrewhutchins, Seabhcan, Seabifar, Selket, Shawnc,
Shoessss, Shri, Simonpage, Sjschen, Sloverlord, Snowmanradio, Soundray, SparksBoy, Splash, StevenDH, Stevenfruitsmaak, Sturm br, Sumersethi,
Sundar, Takeel, TenOfAllTrades, Terence, Terrek, TheRealNightRider, Thiseye, Tmarlow, Tobias Bergemann, TomTheHand, Tony K10, Toolator,
TwoOneTwo, Uijttenhout, Ulrichschwabe, Valde.maximus, Van helsing, VashiDonsk, Versed, Vhathafhak, Vicarious, Vilcxjo, Vsion, VxP, Waggers,
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ZiggyGT, Zippy, Zxc890, Hweizhel?, 642 anonymous edits

Chemical imaging Source: http://en.wikipedia.org/windex.php?oldid=290927658 Contributors: Alansohn, Andyphil, AngelOfSadness, Annabel, Banus,
Batykefer, Bci2, BierHerr, Chris the speller, Closedmouth, D6, Davewild, Editore99, Geejo, HYPN2457, Iridescent, JIP, Jim.henderson, Kkmurray, Mdd,
Mkansiz, Natalie Erin, Skysmith, Ultraexactzz, Wilson003, 38 anonymous edits

Hyperspectral imaging Source: http://en.wikipedia.org/windex.php?oldid=291759304 Contributors: Adoniscik, Andrew c, Bci2, Cm the p, Dhaluza,
Gcrisford, Geologicharka, Hankwang, Jprikkel, Lantonov, Moin95, Victorsong, 15 anonymous edits

Multispectral imaging Source: http://en.wikipedia.org/windex.php?oldid=243967330 Contributors: -

Electron Microscopy Source: http://en.wikipedia.org/windex.php?oldid=84692424 Contributors: -

Atomic force microscope Source: http://en.wikipedia.org/windex.php?oldid=297548215 Contributors: .:Ajvol:., Admartch, Ahram, Ahram-kim,
Alansohn, Allentchang, Alvestrand, Ambios, Ams627, Angela, Anthonydelaware, Antony-22, Arcfrk, Ase, Askewmind, Average Earthman, Bendzh,
Bfollinprm, Bibble, Biophys, Bobblewik, Bochica, Bryan Derksen, Canjth, Cdnc, Chuckiesdad, Chych, Creepin475, Crm2kmsu, Crystallina,
Cucumberslumber, Cyrus Grisham, Davidcastro, Dgrant, Doulos Christos, Edward, El C, Femto, Flipperinu, Fontissophy, Frosty0814snowman, Gaijinpl,
Gene Nygaard, Gene93k, Geodesic42, Graphene, Grmf, HYPN2457, Halibutt, Jatosado, Jaxl, Jcwf, Jni, Joechao, JoeyfoxlO, John, John Dalton, Kamukwam,
Kariteh, Keenan Pepper, KristianMolhave, LMB, Lauranrg, Leifisme, Maximus Rex, Mormegil, NanoMamaForReal, Nmnogueira, Oreo Priest,
Physicistjedi, Pieter Kuiper, Qef, Quadell, Qxz, Raymondwinn, Rhandleyl23, RoB, Rob Hooft, Ronz, Rostislav Lapshin, Ruder, SJP, Satish.murthy,
Sbyrnes321, SecretDisc, Seraphchoir, Shnikenl, Sisyphos happy man, Skier Dude, Switchsonic, Tai89ch, Think outside the box, Tim Starling, Uglygizmo,
Vfranceschi, Wiki alf, Wikiborg, XarBiogeek, Yapete, Yurko, Yyy, Zeamays, Zureks, 176 anonymous edits

X-ray microscope Source: http://en.wikipedia.org/windex.php?oldid=296734543 Contributors: AB, AndyBQ, Birge, Bouncingmolar, Can't sleep, clown
will eat me, Chamal N, Deglr6328, Discospinster, Dratman, EbozMoore, Heron, Icairns, JTN, Marshman, NHSavage, Ptfptf, Rl, RoyBoy, Sommacal
Alfonso, Stepp-Wulf, Stirling Newberry, The Anome, Tommh Hepa, 27 anonymous edits

Fluorescence microscope Source: http://en.wikipedia.org/windex.php?oldid=283782950 Contributors: Andy Nestl, Bwbrian, Ch'marr, Cnickelfr,
Coccyx Bloccyx, DO11.10, DerHexer, Ferh2os, Firehox, Gbleem, Graham87, Hetar, IlyaV, JSpung, Joechao, John, Kupirijo, Kymacpherson, Llbbl,
MarcoTolo, Mastermolch, Microscopist, Mysid, Nicolae Coman, Nmnogueira, OttoTheFish, Pjvpjv, Pvosta, Radagast83, Scrabbler, Stepa, SubwayEater,
Utbg2008, Will-moore-dundee, Zeldaoot, 42 anonymous edits

Fluorescence correlation spectroscopy Source: http://en.wikipedia.org/windex.php?oldid=291 763472 Contributors: Bci2, BenFrantzDale, Berky,
Danrs, Dkkim, Gogowitsch, Hbayat, Jcwf, John, Karol Langner, Lightmouse, Maartend8, ST47, Skier Dude, Tizeff, Wisdom89, 32 anonymous edits

Fluorescence cross- correlation spectroscopy Source: http://en.wikipedia.org/windex. php?oldid=274364772 Contributors: Clicketyclack,
Maartend8, 4 anonymous edits

Forster resonance energy transfer Source: http://en.wikipedia.org/windex.php?oldid=197657138 Contributors: -

Neutron scattering Source: http://en.wikipedia.org/windex.php?oldid=297360408 Contributors: Andyfaff, Anonymous Dissident, Calltl, Cardamon,
Chipmonker, EBlackburn, Grj23, Hellbus, J bellingham, Jdrewitt, Joachim Wuttke, Karol Langner, Kdliss, Kiyabg, Msiebuhr, NSR, Nitrous x, Paula
Pilcher, PhilBentley, PranksterTurtle, Qwerty Binary, Sam8, Sanders muc, Soarhead77, 12 anonymous edits

Synchrotron Source: http://en.wikipedia.org/windex.php?oldid=291 170914 Contributors: Alvinwc, Animum, Aottley, Benbest, Besselfunctions, Bevo,

Bewebste, Boris Barowski, Brockert, BrokenSegue, BryanD, Cantus, Casey56, Choochus, Cirejcon, ConradPino, DV8 2XL, DanlOO, Darkgecko,

David. Monniaux, Dee Earley, Dlenmn, Drakmyth, E2m, EdwardEMeyer, Emerson7, Enquire, Estel, Eubulides, Excirial, Fantasi, Fredrik, Gbleem, Gene

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Leonard G., Linas, Lokster, Macaddctl984, Mancune2001, MarkSweep, Mike Rosoft, Mjamja, Mjspel, Mongerhedron, Mrpeauk, Mullet, Nahum Reduta,
Nikai, Nunh-huh, Olee007@gmail.com, P71ejo, PRehse, Palfrey, Pizzal512, Pj.de.bruin, Ptomato, RoyBoy, Rufua, RupertMillard, SDC4004, SSRF CHINA,
SallyForthl23, Smithbrenon, Stevenj, TPK, Teddybearspicnic, TheMaster42, Thinko, Timo Honkasalo, TimothyPilgrim, Tpikonen, Uvainio, WLU, Whitt35,
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ISIS neutron source Source: http://en.wikipedia.org/windex.php?oldid=281693631 Contributors: 2over0, Andreww, Benjaminevans82, BigDukeSix,
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Image Sources, Licenses and
Contributors

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ImagerFat triglyceride shorthand formula.PNG Source: http://en.wikipedia.org/windex.php?title=File:Fat_triglyceride_shorthand_formula
License: Public Domain Contributors: Wolfgang Schaefer

Image :AminoAcidball.svg Source: http://en.wikipedia.org/windex.php?title=File:AminoAcidball.svg License: Public Domain Contributors:
user:YassineMrabet

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