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Biophysical Chemistry 
and Theoretica 


Principles, Theory and Experimenta 


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Biophysics and Related Fields 


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 



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 

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

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

• 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 

Topics in biophysics and related fields 

Theoretical biophysics 
Mathematical biophysics 
Systems biology 
Medical biophysics 
Origin of Life 

Molecular biophysics 

Biological membranes 

Cell membranes 


Channels, receptors and transporters 

Enzyme kinetics 

Molecular motors 




Supramolecular assemblies 

Nucleic acids 

Cellular biophysics 

Cell division 
Cell migration 
Cell signalling 
Dynamical systems 





Biochemical systems theory 

Metabolic control analysis 

Techniques used in biophysics 

Atomic force microscopy 


Biosensor and Bioelectronics 

Calcium imaging 


Circular Dichroism 


Dual polarisation interferometry 





Neutron spin echo spectroscopy 

Patch clamping 

Nuclear Magnetic Resonance Spectroscopy 

Spectroscopy, imaging, etc. 

x-ray crystallography 


Animal locomotion 

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



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 


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 



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 


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 

• Important publications in biophysics 




[3] Robert Rosen's Research and Biography 


• Perutz MF (1962). Proteins and Nucleic Acids: Structure and Function. Amsterdam 
Elsevier. ASIN B000TS8P4G ( 



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 


Hobbie RK, Roth BJ (2006). edu/~roth/hobbie.htm\Intermediate Physics for Medicine 

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


External links 

• Biophysical Society ( 

• Educational Resources from Biophysical Society ( 
education/resources. htm|) 

• The European Biophysical Societies Association ( 

• The Wellcome Trust Physiome Project ( - Links 

• Nasif Nahle, Biophysics ( 




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. 


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 



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 have monomers called monosaccharides. Some of 

these monosaccharides 

(C 6 H 12 6 ), 


include glucose (C H O ), 



< C 5 H 10°4>- 



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 


oHi — r °' n — v ch 2 oh 


A molecule of sucrose 

(glucose + fructose), a 



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). 




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 



5' end 

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


\ »IH--N 

O— H2N 

• \ 

o. jyi-— \ J I 


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. 


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. 


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 



(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 

CH 2 OH 




CH 2 OH 




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 


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). 



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 carbohydrate metabolism 

Glucose is the major energy source in most life forms. For instance, polysaccharides are 
broken down into their monomers (glycogen phosphorylase removes glucose residues from 
glycogen). Disaccharides like lactose or sucrose are cleaved into their two component 

Glycolysis (anaerobic) 

Glucose is mainly metabolized by a very important and ancient ten-step pathway called 
glycolysis, the net result of which is to break down one molecule of glucose into two 
molecules of pyruvate; this also produces a net two molecules of ATP, the energy currency 
of cells, along with two reducing equivalents in the form of converting NAD + to NADH. This 
does not require oxygen; if no oxygen is available (or the cell cannot use oxygen), the NAD 
is restored by converting the pyruvate to lactate (lactic acid) (e. g. in humans) or to ethanol 
plus carbon dioxide (e. g. in yeast). Other monosaccharides like galactose and fructose can 
be converted into intermediates of the glycolytic pathway. 


In aerobic cells with sufficient oxygen, like most human cells, the pyruvate is further 
metabolized. It is irreversibly converted to acetyl-CoA, giving off one carbon atom as the 
waste product carbon dioxide, generating another reducing equivalent as NADH. The two 
molecules acetyl-CoA (from one molecule of glucose) then enter the citric acid cycle, 
producing two more molecules of ATP, six more NADH molecules and two reduced 
(ubi)quinones (via FADH as enzyme-bound cofactor), and releasing the remaining carbon 
atoms as carbon dioxide. The produced NADH and quinol molecules then feed into the 
enzyme complexes of the respiratory chain, an electron transport system transferring the 
electrons ultimately to oxygen and conserving the released energy in the form of a proton 
gradient over a membrane (inner mitochondrial membrane in eukaryotes). Thereby, oxygen 
is reduced to water and the original electron acceptors NAD + and quinone are regenerated. 
This is why humans breathe in oxygen and breathe out carbon dioxide. The energy released 
from transferring the electrons from high-energy states in NADH and quinol is conserved 



first as proton gradient and converted to ATP via ATP synthase. This generates an 
additional 28 molecules of ATP (24 from the 8 NADH + 4 from the 2 quinols), totaling to 32 
molecules of ATP conserved per degraded glucose (two from glycolysis + two from the 
citrate cycle). It is clear that using oxygen to completely oxidize glucose provides an 
organism with far more energy than any oxygen-independent metabolic feature, and this is 
thought to be the reason why complex life appeared only after Earth's atmosphere 
accumulated large amounts of oxygen. 



In vertebrates, vigorously contracting skeletal muscles (during weightlifting or sprinting, 
for example) do not receive enough oxygen to meet the energy demand, and so they shift to 
anaerobic metabolism, converting glucose to lactate. The liver regenerates the gl 
using a process called gluconeogenesis. This process is not quite the opposite of glycolysis, 
and actually requires three times the amount of energy gained from glycolysis (six 
molecules of ATP are used, compared to the two gained in glycolysis). Analogous to the 
above reactions, the glucose produced can then undergo glycolysis in tissues that need 
energy, be stored as glycogen (or starch in plants), or be converted to other 
monosaccharides or joined into di- or oligosaccharides. The combined pathways of 
glycolysis during exercise, lactate's crossing via the bloodstream to the liver, subsequent 
gluconeogenesis and release of glucose into the bloodstream is called the Cori cycle. 


Like carbohydrates, some proteins perform largely structural 

roles. For instance, movements of the proteins actin and 

myosin ultimately are responsible for the contraction of 

skeletal muscle. One property many proteins have is that 

they specifically bind to a certain molecule or class of 

molecules— they may be extremely selective in what they 

bind. Antibodies are an example of proteins that attach to 

one specific type of molecule. In fact, the enzyme-linked 

immunosorbent assay (ELISA), which uses antibodies, is 

currently one of the most sensitive tests modern medicine 

uses to detect various biomolecules. Probably the most 

important proteins, however, are the enzymes. These 

molecules recognize specific reactant molecules called 

substrates; they then catalyze the reaction between them. By 

lowering the activation energy, the enzyme speeds up that reaction by a rate of 10 ±x or 

more: a reaction that would normally take over 3,000 years to complete spontaneously 

might take less than a second with an enzyme. The enzyme itself is not used up in the 

process, and is free to catalyze the same reaction with a new set of substrates. Using 

various modifiers, the activity of the enzyme can be regulated, enabling control of the 

biochemistry of the cell as a whole. 

In essence, proteins are chains of amino acids. An amino acid consists of a carbon atom 

A schematic of hemoglobin. The 
red and blue ribbons represent 

the protein globin; the green 
structures are the heme groups. 


bound to four groups. One is an amino group, 


NH , and one is a carboxylic acid group, 

— COOH (although these exist as — NH and —COO under physiologic conditions). The 
third is a simple hydrogen atom. The fourth is commonly denoted "— R" and is different for 








each amino acid. There are twenty standard amino acids. Some of these have functions by 
themselves or in a modified form; for instance, glutamate functions as an important 

Amino acids can be joined 
together via a peptide bond. In 
this dehydration synthesis, a 
water molecule is removed 
and the peptide bond connects 
the nitrogen of one amino 
acid's amino group to the 






H, N - lX C - C 




H,N + - *(]! - Cie 



H 3 N + 







Generic amino acids (1) in neutral form, (2) as they exist 
physiologically, and (3) joined together as a dipeptide. 

carboxylic acid group. The 

resulting molecule is called a dipeptide, and short stretches of amino acids (usually, fewer 

than around thirty) are called peptides or polypeptides. Longer stretches merit the title 

proteins. As an example, the important blood serum protein albumin contains 585 


acid residues. 

The structure of proteins is traditionally described in a hierarchy of four levels. The primary 
structure of a protein simply consists of its linear sequence of amino acids; for instance, 

'alanine-glycine-tryptophan-serine-glutamate-asparagine-glycine-lysine-. . . " . 


structure is concerned with local morphology. Some combinations of amino acids will tend 
to curl up in a coil called an a-helix or into a sheet called a (3-sheet; some oc-helixes can be 
seen in the hemoglobin schematic above. Tertiary structure is the entire three-dimensional 
shape of the protein. This shape is determined by the sequence of amino acids. In fact, a 
single change can change the entire structure. The alpha chain of hemoglobin contains 146 
amino acid residues; substitution of the glutamate residue at position 6 with a valine 
residue changes the behavior of hemoglobin so much that it results in sickle-cell disease. 
Finally quaternary structure is concerned with the structure of a protein with multiple 
peptide subunits, like hemoglobin with its four subunits. Not all proteins have more than 
one subunit. 

Ingested proteins are usually broken up into single amino acids or dipeptides in the small 
intestine, and then absorbed. They can then be joined together to make new proteins. 
Intermediate products of glycolysis, the citric acid cycle, and the pentose phosphate 
pathway can be used to make all twenty amino acids, and most bacteria and plants possess 
all the necessary enzymes to synthesize them. Humans and other mammals, however, can 
only synthesize half of them. They cannot synthesize isoleucine, leucine, lysine, methionine, 
phenylalanine, threonine, tryptophan, and valine. These are the essential amino acids, since 
it is essential to ingest them. Mammals do possess the enzymes to synthesize alanine, 
asparagine, aspartate, cysteine, glutamate, glutamine, glycine, proline, serine, and tyrosine, 
the nonessential amino acids. While they can synthesize arginine and histidine, they cannot 
produce it in sufficient amounts for young, growing animals, and so these are often 
considered essential amino acids. 

If the amino group is removed from an amino acid, it leaves behind a carbon skeleton called 
an oc-keto acid. Enzymes called transaminases can easily transfer the amino group from one 
amino acid (making it an oc-keto acid) to another oc-keto acid (making it an amino acid). This 
is important in the biosynthesis of amino acids, as for many of the pathways, intermediates 
from other biochemical pathways are converted to the oc-keto acid skeleton, and then an 



amino group is added, often via transamination. The amino acids may then be linked 
together to make a protein. 

A similar process is used to break down proteins. It is first hydrolyzed into its component 
amino acids. Free ammonia (NH ), existing as the ammonium ion (NH*) in blood, is toxic 
to life forms. A suitable method for excreting it must therefore exist. Different strategies 
have evolved in different animals, depending on the animals' needs. Unicellular organisms, 
of course, simply release the ammonia into the environment. Similarly, bony fish can 
release the ammonia into the water where it is quickly diluted. In general, mammals 
convert the ammonia into urea, via the urea cycle. 


The term lipid comprises a diverse range of molecules and to some extent is a catchall for 
relatively water-insoluble or nonpolar compounds of biological origin, including waxes, fatty 
acids, fatty-acid derived phospholipids, sphingolipids, glycolipids and terpenoids (eg. 
retinoids and steroids). Some lipids are linear aliphatic molecules, while others have ring 
structures. Some are aromatic, while others are not. Some are flexible, while others are 

Most lipids have some polar character in addition to being largely nonpolar. Generally, the 
bulk of their structure is nonpolar or hydrophobic ("water-fearing"), meaning that it does 
not interact well with polar solvents like water. Another part of their structure is polar or 
hydrophilic ("water-loving") and will tend to associate with polar solvents like water. This 
makes them amphiphilic molecules (having both hydrophobic and hydrophilic portions). In 
the case of cholesterol, the polar group is a mere -OH (hydroxyl or alcohol). In the case of 
phospholipids, the polar groups are considerably larger and more polar, as described 

Lipids are an integral part of our daily diet. Most oils and milk products that we use for 
cooking and eating like butter, cheese, ghee etc, are comprised of fats. Vegetable oils are 
rich in various polyunsaturated fatty acids (PUFA). Lipid-containing foods undergo 
digestion within the body and are broken into fatty acids and glycerol, which are the final 
degradation products of fats and lipids. 

Nucleic acids 

A nucleic acid is a complex, high-molecular-weight biochemical macromolecule composed 
of nucleotide chains that convey genetic information. The most common nucleic acids are 
deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). Nucleic acids are found in all 
living cells and viruses. Aside from the genetic material of the cell, nucleic acids often play 
a role as second messengers, as well as forming the base molecule for adenosine 
triphosphate, the primary energy-carrier molecule found in all living organisms. 

Nucleic acid, so called because of its prevalence in cellular nuclei, is the generic name of 
the family of biopolymers. The monomers are called nucleotides, and each consists of three 
components: a nitrogenous heterocyclic base (either a purine or a pyrimidine), a pentose 
sugar, and a phosphate group. Different nucleic acid types differ in the specific sugar found 
in their chain (e.g. DNA or deoxyribonucleic acid contains 2-deoxyriboses). Also, the 
nitrogenous bases possible in the two nucleic acids are different: adenine, cytosine, and 
guanine occur in both RNA and DNA, while thymine occurs only in DNA and uracil occurs 



in RNA. 


Relationship to other "molecular-scale" biological sciences 

Researchers in biochemistry use specific 
techniques native to biochemistry, but 
increasingly combine these with techniques 
and ideas from genetics, molecular biology 
and biophysics. There has never been a 
hard-line between these disciplines in 
terms of content and technique, but 
members of each discipline have in the past 
been very territorial; today the terms 
molecular biology and biochemistry are 
nearly interchangeable. The following 
figure is a schematic that depicts one 
possible view of the relationship between 
the fields: 



Schematic relationship between biochemistry, 

genetics and molecular biology 

Chemical basis of 



- Oxytocin 

- Vasopressin 



- Testosterone 

- Estrogen 


and loss of 
appetite and 

- Dopamine 

- Norepinephrine 

- Serotonin 

- Nerve growth factor 

Increased heart rate 
Other physical effects 

Simplistic overview of the chemical basis of love, 
one of many applications that may be described in 

terms of biochemistry. 

such "knock-out" studies. 

Biochemistry is the study of the chemical 
substances and vital processes occurring in 
living organisms. Biochemists focus heavily 
on the role, function, and structure of 
biomolecules. The study of the chemistry 
behind biological processes and the 
synthesis of biologically active molecules are 
examples of biochemistry. 

Genetics is the study of the effect of genetic 
differences on organisms. Often this can be 
inferred by the absence of a normal 
component (e.g. one gene). The study of 
"mutants" - organisms which lack one or 
more functional components with respect to 
the so-called "wild type" or normal 
phenotype. Genetic interactions (epistasis) 
can often confound simple interpretations of 

Molecular biology is the study of molecular underpinnings of the process of replication, 
transcription and translation of the genetic material. The central dogma of molecular 
biology where genetic material is transcribed into RNA and then translated into protein, 
despite being an oversimplified picture of molecular biology, still provides a good starting 
point for understanding the field. This picture, however, is undergoing revision in light of 
emerging novel roles for RNA. 



Chemical Biology seeks to develop new tools based on small molecules that allow 
minimal perturbation of biological systems while providing detailed information about 
their function. Further, chemical biology employs biological systems to create 
non-natural hybrids between biomolecules and synthetic devices (for example emptied 
viral capsids that can deliver gene therapy or drug molecules). 

See also 


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) 

Related topics 

Biological psychiatry 


Chemical ecology 

Computational biomodeling 

EC number 

Hypothetical types of biochemistry 

International Union of Biochemistry and Molecular Biology 



Molecular biology 

Molecular medicine 
Plant biochemistry 
Structural biology 
Small molecule 


[1] Campbell, Neil A.; Brad Williamson; Robin J. Heyden (2006). 

http://www. html\Biology: Exploring Life. Boston, Massachusetts: Pearson Prentice 

Hall. ISBN 0-13-250882-6. 
[2] Smith E, Morowitz H (2004). 

" 53401 53|Universality in 

intermediary metabolism". Proc Natl Acad Sci USA 101 (36): 13168-73. doi: 10. 1073/pnas. 0404922101 (http:// PMID 15340153. 

articlerender.fcgi?tool=pubmed&pubmedid= 153401 53. 
[3] Romano A, Conway T (1996). "Evolution of carbohydrate metabolic pathways". Res Microbiol 147 (6-7): 

448-55. doi: 10.1016/0923-2508(96)83998-2 ( 1016/0923-2508(96)83998-2). PMID 




[4] Wohler, F. (1828). "Ueber kiinstliche Bildung des Harnstoffs". Ann. Phys. Chem. 12: 253-256. 

[5] Kauffman, G. B. and Chooljian, S.H. (2001). "Friedrich Wohler (1800-1882), on the Bicentennial of His Birth". 

The Chemical Educator 6 (2): 121-133. doi: 10.1007/s00897010444a ( 


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 
( + 191848148+44187710). 

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

External links 

• The Virtual Library of Biochemistry and Cell Biology ( 

• 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. ( Full text of 
Garrett and Grisham. 

• Biochemistry Animation ( (Narrated Flash 

• - The Swiss Initiative in Systems Biology ( 

Major families of biochemicals 

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


Quantum biocehmistry 


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. 


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 

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 

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 


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 . 


[1] Chemistry" 

The NIH Guide to Molecular Modeling. National Institutes of Health, 
guidedocuments/quantummechanicsdocument.html. Retrieved on 2007-09-08. 

External links 

• The Sherrill Group - Notes ( 

• ChemViz Curriculum Support Resources ( 

• 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 ( 

• Rudolph Marcus' Nobel lecture ( 

• Robert Mulliken's Nobel lecture ( 

• Linus Pauling's Nobel lecture ( 

• John Pople's Nobel lecture ( 

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. 


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 

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. 


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 


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 


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 

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 

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 ° 



[2] http ://www. 





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


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

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


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. 


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 


• 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 ] 


• A mechanochemical theory of morphogenesis 

• Biological pattern formation^ ^ 

• Spatial distribution modeling using plot samples 1 ] 


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 







i . 



S io 

■ 1 - 



M 10 

-?. ■ 





F/xed PoMs 

siarUng -area 



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} 


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 

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 

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] 



Biologically inspired computing 


Cellular automata [45] 

Coalescent theory 

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

Computational biology 

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


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 

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 

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 


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

• 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), " 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. 

• Scudo, F M (1971), " Volterra and 
theoretical ecology.", Theoretical population biology 2 (1): 1-23, 1971 Mar, 

• 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 

• 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 


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


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 


Lists of references 

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


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 


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


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. 


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


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. 


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 


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? 
?op=getobj&from=objects&id= 10921 



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




[8] "Research in Mathematical Biology". Retrieved on 2008-09-10. 
[9] 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 


Mathematical biology 


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

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

[14] Modern Cellular Automata by Kendall Preston and M.J. B. Duff 



[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 



[22] "Research in Mathematical Biology". Retrieved on 2008-09-10. 


Transformations 10770 








Currently available for download as an updated PDF: 

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

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

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

CO%3B2-S&size=LARGE&origin=JSTOR-enlargePage Lab.html|"The JJ Tyson Lab". Virginia Tech. 

Tyson%20Lab.html. Retrieved on 2008-09-10. 
[41]! "The Molecular Network Dynamics Research Group". Budapest University of 

Technology and Economics, 
[42 ] http ://www. kli. ac . at/theorylab/ALists/Authors_R. html 
[44] http://www. kli. 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. 



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


Mathematical biology 





http ://cogprints. org/3829/ 

Organisms as Super-complex Systems 10890 

http :// 10921 



Publications list for Robert Rosen 

External links 

• Theoretical and mathematical biology website ( 

• Complexity Discussion Group ( 

• Integrative cancer biology modeling and Complex systems biology (http://fs512.fshn. 

• UCLA Biocybernetics Laboratory ( 

• TUCS Computational Biomodelling Laboratory ( 

• Nagoya University Division of Biomodeling ( 

• Technische Universiteit Biomodeling and Informatics ( 

• BioCybernetics Wiki, a vertical wiki on biomedical cybernetics and systems biology (http:/ 

• Society for Mathematical Biology ( 

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

• European Society for Mathematical and Theoretical Biology ( 

• Journal of Mathematical Biology ( 

• Biomathematics Research Centre at University of Canterbury (http://www.math. 

• Centre for Mathematical Biology at Oxford University ( 

Mathematical biology 


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

nimr . mrc . ac . uk/) 

Institute for Medical BioMathematics ( 

Mathematical Biology Systems of Differential Equations ( 

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

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

The Collection of Biostatistics Research Archive ( 


Statistical Applications in Genetics and Molecular Biology ( 


The International Journal of Biostatistics ( 

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

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 


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 
Biological Theory L J 
BioSystems [6] 


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


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 


• 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 



[ 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+ 

[3] http://www.springerlink. com/link. asp?id= 102835 
[ 5 ] http ://www. mitpressj ournals . org/loi/biot/ 
[6] http ://www. elsevier. com/locate/biosystems 
[7] http://www.springerlink.eom/content/l 19979/ 


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. tilgher . it/biologiae . html 

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. maths, soton. 

http ://www. esmtb . org/ 

http ://www. tibs. org/ 

http ://www. isemna. org/ 

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

http ://www. siam . org/ 

http ://www. smb . org/ 

http ://www. biosemiotics. org/ 

Complex Systems Biology 


Complex Systems Biology 




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

in biological 


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 








Clean up the 


Produce ond 
use energy 








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



Many prolein 
machines interact 

through complex,, 

poihwoys. Analyzing 

iheie dynamic processei 

will lead :o models of lifo 


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. 


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. 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 

• 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). 


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 


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. intertfrukms. 

s&rotonrrv. etc.) 



Growth Factor* 
e.g.TGFu. EGF) 

<e g.. EPC>" 

Death factors, 
(eg Fasl.Tnf) 

Overview of signal transduction pathways 





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 

• 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 

• 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 

Complex systems 
Complex systems 
Biological network 
Biological systems 
Biomedical cybernetics 
Theoretical Biophysics 
Relational Biology 
Translational Research 
Computational biology 
Computational systems 

Synthetic biology 
Systems biology 
Systems ecology 
Systems immunology 

Related terms 


Artificial life 

Gene regulatory network 

Metabolic network modelling 

Living systems theory 

Network Theory of Aging 


Systems Biology Markup Language 



Viable System Model 


Systems biologists 

• Category: Systems biologists 

• 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 


[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] "Systems 

Biology - the 21st Century Science". 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 ( PMID 17463274. 
[4] Denis Noble (2006). The Music of Life: Biology beyond the genome. Oxford University Press. ISBN 

978-0199295739. p21 
[5] "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 ( 
[9] Noble D (1960). "Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations". Nature 

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

[II] " Means Toward a New Holism". Science 161 
(3836): 34-35. doi: 10. 1126/science. 161. 3836. 34 ( http:// 

the Systems", 

Complex Systems Biology 


[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. 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 ( 

PMID 15765094. 
[15] such as Gaggle (, SBW (, or commercial suits, e.g., 

MetaCore ( and MetaDrug ( 


Further reading 


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


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


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 


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


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:// 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. ( ISBN 


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


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). 

" systems go" 

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


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

Medicine" Medical Information Science Reference, October 2008 ISBN 

Complex Systems Biology 




• BMC Systems Biology ( - open access 
journal on systems biology 

• Molecular Systems Biology ( - open access journal on 
systems biology 

• IET Systems Biology ( - not open access journal on 
systems biology 


• 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 ( 
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:// 


• ( - 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 ( 

• 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 ( 

• Katia Basso, Adam A Margolin, Gustavo Stolovitzky, Ulf Klein, Riccardo Dalla-Favera, 
Andrea Califano, (2005) "Reverse engineering of regulatory networks in human B cells" 
( 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. - a 
review from the Science Creative Quarterly, 2005 

• Johnjoe McFadden, ( 
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:// Retrieved Jan, 15 2008. 

WTEC Panel Report on International Research and Development in Systems Biology 

( (2005) 

E. Werner, "The Future and Limits of Systems Biology", Science STKE (http://stke. 2005, pel6 (2005). 

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


E. Werner, "All systems go" ( 

446493a.pdf), "Nature" ( 

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., 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." ( 

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

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

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 - ( 

• Systems Biology Portal ( - administered by the 
Systems Biology Institute 

• Semantic Systems Biology ( 

• ( - The Swiss Initiative in Systems Biology 

• Systems Biology at the Pacific Northwest National Laboratory ( 





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. 

complexity vs. 

One of the problems in 
addressing complexity issues 




conceptually between 


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

elements in systems where 




'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 



variations from element independence 



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. 


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 

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. 


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 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. 



• 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 



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 

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. 



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 


Model of hierarchical complexity 

Occam's razor 

Process architecture 

Programming Complexity 

Sociology and complexity science 

Systems theory 

Variety (cybernetics) 


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

[2] Weaver, Warren (1948), " 947b. htm| Science and 

Complexity", American Scientist 36: 536 (Retrieved on 2007-11-21.), 

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]" '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 
( National Defense 
University. ISBN 9781579060466. 

• Czerwinski, Tom (1998). Coping with the Bounds: Speculations on Nonlinearity in 
Military Affairs ( CCRP. ISBN 
9781414503158 (from Pavilion Press, 2004). 



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. CCRP. ISBN 9781893723115. 

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

Operations ( CCRP. ISBN 


Heylighen, Francis (2008), " Complexity and Self-Organization ( 

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, 


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 


External links 

• Quantifying Complexity Theory ( - 
classification of complex systems 

• Complexity Measures ( 
complexity-measures.html) - an article about the abundance of not-that-useful complexity 

• UC Four Campus Complexity Videoconferences ( 
center/cac.html) - Human Sciences and Complexity 

• Complexity Digest ( - networking the complexity community 

• The Santa Fe Institute ( - engages in research in complexity 
related topics 

Complex adaptive system 


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. 


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. 


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 



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




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






adaptive agents. Complex 








Adoptive Behavior 






^^9e/7 C| 




Simple Self -Organized 
Local Relationships 




Complex Adaptive System 

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

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 




complexity is hard to quantify in 
biology, evolution has produced 




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. 






Passive trend 







Active trend 






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 

Enterprise systems 

Generative sciences 

Santa Fe Institute 

Complex adaptive system 


Cognitive Science 

Command and Control Research Program 

Simulated reality 
Sociology and complexity 


Computational Sociology 

Swarm Development Group 


[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 ( 

[3] Complexity in Social Science glossary (http://www. 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 ( 
[6] Carroll SB (2001). "Chance and necessity: the evolution of morphological complexity and diversity". Nature 

409 (6823): 1102-9. doi: 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 ( PMID 

[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 ( 

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

" 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 ( PMID 15253349. 
[10] Whitman W, Coleman D, Wiebe W (1998). " the 

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

10. 1073/pnas. 95. 12. 6578). PMID 9618454. 

[II] Schloss P, Handelsman J (2004). " 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:/ 
/ 4. 686-691. 2004). PMID 15590780. PMC: 539005 (http://www. 539005). 
pmidlookup?view=long&pmid= 1 5590780. 



• Ahmed E, Elgazzar AS, Hegazi AS (28 June 2005). " 
overview of complex adaptive systems". MansouraJ. Math 32. arXiv:nlin/0506059vl 

• Bullock S, Cliff D (2004). 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. 

ComplexityandEmergentBehaviour.asp) by the UK government's Foresight Programme 

• 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). of control: the new biology of machines, 

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

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

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

homepage. pharoah/) Retrieved Jan, 15 2008. 

External links 

• Complexity Digest ( comprehensive digest of latest CAS 
related news and research. 

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

• A description ( of complex adaptive systems on 
the Principia Cybernetica Web. 

• Quick reference ( 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 ( 

• The Open Agent-Based Modeling Consortium ( 




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. 



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 



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 



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 


[1] Charles T. Munger (2003-10-03). pdf| "Academic Economics 

Strengths and Faults After Considering Interdisciplinary Needs", 

[2] "Spotlight: application of quantitative 

concepts and techniques in undergraduate biology". 


External links 

• The International Biometric Society ( 

• The Collection of Biostatistics Research Archive ( 

• Guide to Biostatistics ( ( 

• Biostatistician ( 


• Statistical Applications in Genetics and Molecular Biology ( 

• Statistics in Medicine ( 

• The International Journal of Biostatistics ( 

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

• Journal of Biopharmaceutical Statistics ( 
10543406. asp) 

• Biostatistics ( 

• Biometrics ( 

• Biometrika ( 

• Biometrical Journal ( 

• Genetics Selection Evolution ( 




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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 


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. 


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 


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: 



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 



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 




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 . 



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 



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 

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 



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 

Related topics 


Bioinformatics companies 

Biologically inspired computing 

Biomedical informatics 

Computational biology 

Computational biomodeling 

Computational genomics 

DNA sequencing theory 

Dot plot (bioinformatics) 

Dry lab 

Margaret Oakley Dayhoff 

Metabolic network modelling 

Molecular Design software 


Natural computation 

Pharmaceutical company 

Protein-protein interaction prediction 

List of nucleic acid simulation software 

List of numerical analysis software 

List of protein structure prediction software 

List of scientific journals in bioinformatics 



Related fields 

Applied mathematics 

Artificial intelligence 




Comparative genomics 

Computational biology 

Computational epigenetics 

Computational science 

Computer science 





Information theory 

Mathematical biology 

Molecular modelling 



Pervasive adaptation 

Scientific computing 


Structural biology 

Systems biology 

Theoretical biology 

Veterinary informatics 


[1] Important projects: Species 2000 project (; uBio Project (; 
Partnership for Biodiversity Informatics ( 

• Achuthsankar S Nair Computational Biology & Bioinformatics - A gentle Overview (http:/ 
/print. 0CSI07.pdf), Communications of 
Computer Society of India, January 2007 

• Aluru, Srinivas, ed. Handbook of Computational Molecular Biology. Chapman & Hall/Crc, 
2006. ISBN 1584884061 (Chapman & Hall/Crc Computer and Information Science 

• Baldi, P and Brunak, S, Bioinformatics: The Machine Learning Approach, 2nd edition. 
MIT Press, 2001. ISBN 0-262-02506-X 

• Barnes, M.R. and Gray, I.C., eds., Bioinformatics for Geneticists, first edition. Wiley, 
2003. ISBN 0-470-84394-2 

• Baxevanis, A.D. and Ouellette, B.F.F., eds., Bioinformatics: A Practical Guide to the 
Analysis of Genes and Proteins, third edition. Wiley, 2005. ISBN 0-471-47878-4 

• Baxevanis, A.D., Petsko, G.A., Stein, L.D., and Stormo, G.D., eds., Current Protocols in 
Bioinformatics. Wiley, 2007. ISBN 0-471-25093-7 

• Claverie, J.M. and C. Notredame, Bioinformatics for Dummies. Wiley, 2003. ISBN 



Cristianini, N. and Hahn, M. Introduction to Computational Genomics (http://www., Cambridge University Press, 2006. (ISBN 

9780521671910 | ISBN 0521671914) 

Durbin, R., S. Eddy, A. Krogh and G. Mitchison, Biological sequence analysis. Cambridge 

University Press, 1998. ISBN 0-521-62971-3 

Gilbert, D. Bioinformatics software resources ( 

content/abstract/5/3/300). Briefings in Bioinformatics, Briefings in Bioinformatics, 

2004 5(3):300-304. 

Keedwell, E., Intelligent Bioinformatics: The Application of Artificial Intelligence 

Techniques to Bioinformatics Problems. Wiley, 2005. ISBN 0-470-02175-6 

Kohane, et al. Microarrays for an Integrative Genomics. The MIT Press, 2002. ISBN 


Lund, O. et al. Immunological Bioinformatics. The MIT Press, 2005. ISBN 0-262-12280-4 

Michael S. Waterman, Introduction to Computational Biology: Sequences, Maps and 

Genomes. CRC Press, 1995. ISBN 0-412-99391-0 

Mount, David W. Bioinformatics: Sequence and Genome Analysis Spring Harbor Press, 

May 2002. ISBN 0-87969-608-7 

Pachter, Lior and Sturmfels, Bernd. "Algebraic Statistics for Computational Biology" 

Cambridge University Press, 2005. ISBN 0-521-85700-7 

Pevzner, Pavel A. Computational Molecular Biology: An Algorithmic Approach The MIT 

Press, 2000. ISBN 0-262-16197-4 

Tisdall, James. "Beginning Perl for Bioinformatics" O'Reilly, 2001. ISBN 0-596-00080-4 

Dedicated issue of Philosophical Transactions B on Bioinformatics freely available (http:/ 


Catalyzing Inquiry at the Interface of Computing and Biology (2005) CSTB report (http:// 

Calculating the Secrets of Life: Contributions of the Mathematical Sciences and 

computing to Molecular Biology (1995) ( 

Foundations of Computational and Systems Biology MIT Course ( 


Computational Biology: Genomes, Networks, Evolution Free MIT Course (http://ocw. 


Algorithms for Computational Biology Free MIT Course ( 



Zhang, Z., Cheung, K.H. and Townsend, J. P. Bringing Web 2.0 to bioinformatics, Briefing 

in Bioinformatics. In press ( 



External links 

Major Organizations 

• Bioinformatics Organization (Bioinformatics. Org): The Open-Access Institute (http:// 
bioinformatics . org/) 
EMBnet ( 

European Bioinformatics Institute ( 
European Molecular Biology Laboratory ( 
The International Society for Computational Biology ( 
National Center for Biotechnology Information ( 
National Institutes of Health homepage ( 

Open Bioinformatics Foundation: umbrella non-profit organization supporting certain 
open-source projects in bioinformatics ( 
Swiss Institute of Bioinformatics 
Wellcome Trust Sanger Institute 

Major Journals 

Algorithms in Molecular Biology ( 

Bioinformatics (http ://bioinformatics . oupj ournals . org/) 

BMC Bioinformatics ( 

Briefings in Bioinformatics ( 

Journal of Advanced Research in Bioinformatics ( 

Evolutionary Bioinformatics ( 

Genome Research ( 

The International Journal of Biostatistics ( 

Journal of Computational Biology ( 


Cancer Informatics (http://la-press. com/journal. php?pa=description& 


Journal of the Royal Society Interface ( 


Molecular Systems Biology ( 

PLoS Computational Biology ( 

Statistical Applications in Genetic and Molecular Biology ( 


Transactions on Computational Biology and Bioinformatics - IEEE/ACM (http://www. 

computer, org/tcbb/) 

International Journal of Bioinformatics Research and Applications (http://www. ?journalcode=ijbra) 

List of Bioinformatics journals ( at 

EMBnet. News ( at 

International Journal of Computational Biology and Drug Design (IJCBDD) 

International Journal of Functional Informatics and Personalized Medicine (IJFIPM) 

Other sites 

• The exhaustive bioinformatics information resource directory including servers, tools, 
database links and bioinformatics companies ( 



• The Collection of Biostatistics Research Archive ( 

• Human Genome Project and Bioinformatics ( 

• List of Bioinformatics Research Groups ( 
php) at 

• List of Bioinformatics Research Groups ( 
Bioinformatics/ResearchGroups//) at the Open Directory Project 

• Tutorials / Resources / Primers 

• Bioinformatics - A Science Primer ( 
bioinformatics.html) — by NCBI 

• A bioinformatics directory ( 

See also 

• International Society of Intelligent Biological Medicine (ISIBM) 


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 

Biocybernetics as an abstract science is a part of theoretical biology, and based upon the 
principles of systemics. 


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 

Please heed this when you engage in an extensive search for information to assure access 
to a broad range of papers. 




• biocybernetics - the study of an entire living organism 

• neurocybernetics - cybernetics dealing with neurological models, (psycho-cybernetics 
was the title of a self-help book, and is not a scientific discipline) 

• molecular cybernetics - cybernetics dealing with molecular systems (e.g. molecular 
biology cybernetics) 

• cellular cybernetics - cybernetics dealing with cellular systems (e.g. information 
technology/cell phones,., or biological cells) 

• evolutionary cybernetics - study of the evolution of informational systems (See also 
evolutionary programming, evolutionary algorithm) 

• any distinct informational system within the realm of biology 

See also 

• Bioinformatics 

• Biosemiotics 

• Computational biology 

• Computational biomodeling 

• Medical cybernetics 


External links 


• Journal "Biological Cybernetics" 

• Scientific portal on biological cybernetics 


• UCLA Biocybernetics Laboratory 


[1] http://www.springerlink. com/link. asp?id= 100465 
[2 ] http :// www. biological-cybernetics . de 

Molecular dynamics 


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 





physicists, and this is reflected 
in differences in the jargon 
used by the different fields. In 
chemistry and biophysics, 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 

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 


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 

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 


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 

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 


• 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) 


ACEMD [27] (running on NVIDIA GPUs: heavily optimized with CUDA) 

ADUN [28] (classical, P2P database for simulations) 

AMBER (classical) 

Ascalaph (classical, GPU accelerated) 



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 


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 


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) 



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 

• 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 



[I] Alder, B. J.; T. E. Wainwright (1959). "Studies in Molecular Dynamics. I. General Method". J. Chem. Phys. 31 
(2): 459. doi: 10.1063/1.1730376 (http://dx.doi.Org/10.1063/l.1730376). 

[2] A. Rahman (1964). "Correlations in the Motion of Atoms in Liquid Argon". Phys Rev 136: A405-A411. doi: 

10.1103/PhysRev.l36.A405 ( 
[3] Bernal, J.D. (1964). "The Bakerian lecture, 1962: The structure of liquids". Proc. R. Soc. 280: 299-322. doi: 

10.1098/rspa.l964.0147 ( 
[4] Schlick, T. (1996). "Pursuing Laplace's Vision on Modern Computers", in J. P. Mesirov, K. Schulten and D. W. 

Sumners. Mathematical Applications to Biomolecular Structure and Dynamics, IMA Volumes in Mathematics 

and Its Applications. 82. New York: Springer-Verlag. pp. 218-247. ISBN 978-0387948386. 
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Paris, France: Gauthier-Villars. 
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(3): 639-648. doi: 10.1080/00268977800100471 ( 
[7] Tuckerman ME, Berne BJ, Martyna GJ (1991). "Molecular dynamics algorithm for multiple time scales: systems 

with long range forces". J Chem Phys 94 (10): 6811-6815. 
[8] Tuckerman ME, Berne BJ, Martyna GJ (1992). "Reversible multiple time scale molecular dynamics". J Chem 

Phys 97 (3): 1990-2001. doi: 10.1063/1.463137 (http://dx.doi.Org/10.1063/l.463137). 
[9] Sugita, Yuji; Yuko Okamoto (1999). "Replica-exchange molecular dynamics method for protein folding". Chem 

Phys Letters 314: 141-151. doi: 10.1016/S0009-2614(99)01123-9 ( 

S0009-2614(99)01 123-9). 
[10] Brenner, D. W. (1990). "Empirical potential for hydrocarbons for use in simulating the chemical vapor 

deposition of diamond films". Phys. Rev. B 42 (15): 9458. doi: 10.1 103/PhysRevB.42. 9458 ( 


[II] van Duin, A.; Siddharth Dasgupta, Francois Lorant and William A. Goddard III (2001). J. Phys. Chem. A 105: 

[12] Tersoff, J. (1989). ""Modeling solid-state chemistry: Interatomic potentials for multicomponent systems". 

Phys. Rev. B 39: 5566. doi: 10.1103/PhysRevB.39.5566 ( 
[13] Daw, M. S.; S. M. Foiles and M. I. Baskes (1993). "The embedded-atom method: a review of theory and 

applications". Mat. Sci. And Engr. Rep. 9: 251. doi: 10.1016/0920-2307(93)90001-U ( 

[14] Cleri, F.; V. Rosato (1993). "Tight-binding potentials for transition metals and alloys". Phys. Rev. B 48: 22. 

doi: 10.1103/PhysRevB.48.22 ( 
[15] Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD (2006). "A polarizable model of water for 

molecular dynamics simulations of biomolecules". Chem Phys Lett 418: 245-249. doi: 

10.1016/j.cplett.2005.10.135 (http://dx.doi.Org/10.1016/j.cplett.2005.10.135). 
[16] Patel, S. ; MacKerell, Jr. AD; Brooks III, Charles L (2004). "CHARMM fluctuating charge force field for 

proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic 

model" . J Comput Chem 25: 1504-1514. doi: 10. 1002/jcc. 20077 ( 
[17] Billeter, SR; SP Webb, PK Agarwal, T Iordanov, S Hammes-Schiffer (2001). "Hydride Transfer in Liver Alcohol 

Dehydrogenase: Quantum Dynamics, Kinetic Isotope Effects, and Role of Enzyme Motion". J Am Chem Soc 123: 

11262-11272. doi: 10.1021/ja011384b ( 
[18] Smith, A; CK Hall (2001). "Alpha-Helix Formation: Discontinuous Molecular Dynamics on an 

Intermediate-Resolution Protein Model". Proteins 44: 344-360. 
[19] Ding, F; JM Borreguero, SV Buldyrey, HE Stanley, NV Dokholyan (2003). "Mechanism for the alpha-helix to 

beta-hairpin transition". J Am Chem Soc 53: 220-228. doi: 10.1002/prot.l0468 ( 

prot. 10468). 
[20] Paci, E; M Vendruscolo, M Karplus (2002). "Validity of Go Models: Comparison with a Solvent-Shielded 

Empirical Energy Decomposition". Biophys J 83: 3032-3038. doi: 10.1016/S0006-3495(02)75308-3 (http://dx. 
[21] McCammon, J; JB Gelin, M Karplus (1977). "Dynamics of folded proteins". Nature 267: 585-590. doi: 

10.1038/267585a0 ( 
[22] Averback, R. S.; Diaz de la Rubia, T. (1998). "Displacement damage in irradiated metals and semiconductors". 

in H. Ehrenfest and F. Spaepen. Solid State Physics. 51. New York: Academic Press, p. 281-402. 
[23] R. Smith, ed (1997). Atomic & ion collisions in solids and at surfaces: theory, simulation and applications. 

Cambridge, UK: Cambridge University Press. 
[24] Freddolino P, Arkhipov A, Larson SB, McPherson A, Schulten K.! "Molecular dynamics simulation of the Satellite Tobacco Mosaic Virus 

Molecular dynamics 


(STMV)". Theoretical and Computational Biophysics Group. University of Illinois at Urbana Champaign, http:// 
[25] The Folding@Home Project ( and recent papers ( 

papers.html) published using trajectories from it. Vijay Pande Group. Stanford University 
[27] http://www.acellera. com/index. php?arg=acemd 

[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 

• 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 

• William Graham Hoover (1991) Computational Statistical Mechanics, Elsevier, ISBN 

Molecular dynamics 


External links 

• The Blue Gene Project ( (IBM) 

• D. E. Shaw Research ( (D. E. Shaw Research) 

• Molecular Physics ( 

• Statistical mechanics of Nonequilibrium Liquids ( 
~gary/book.html) Lecture Notes on non-equilibrium MD 

• Introductory Lecture on Classical Molecular Dynamics ( 
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. by Mark E. Tuckerman, 

New York University, USA 

• Introductory Lecture on Ab initio molecular dynamics: Theory and Implementation (http:/ 
/ 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 


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. 


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 


Gaussian quantum Monte Carlo 

See also 

Stochastic Green Function (SGF) algorithm 

Monte Carlo method 


Quantum chemistry 

Density matrix renormalization group 

Time-evolving block decimation 

Metropolis algorithm 

Wavefunction optimization 


ALPS [2] 
CHAMP [4] 
Monte Python [5] 
PIMC + + [6] 


pi-qmc J 
QMcBeaver [8] 
QmcMol [9] 
Qumax [11] 
Qwalk [12] 
TurboRVB [13] 
Zori [14] 


[ 1 ] http ://www. attaccalite . html 




[ 5 ] http ://code . google . com/p/montepython/ 


[7] http ://code . google . com/p/pi-qmc/ 



[10] http ://www. mcc .uiuc . edu/qmc/qmcpack/index. html 

[11] http ://attaccalite. altervista. org/qumax/index.php 




Quantum Monte Carlo 


V. G. Rousseau (May 2008). 

" Green Function (SGF) 

algorithm" (in English) (abstract). Phys. Rev. E 77: 056705. doi: 

10.1 103/PhysRevE. 77. 056705 ( Retrieved on 05/2008. 

Hammond, B.J.; W.A. Lester & P.J. Reynolds (1994) (in English). 70.html\Monte Carlo Methods in Ab Initio 

Quantum Chemistry. Singapore: World Scientific. ISBN 981-02-0321-7. OCLC 29594695 


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. 

0-7923-5552-0. Retrieved on 2007-01-18. 

W. M. C. Foulkes; L. Mitas, R. J. Needs and G. Rajagopal (5 January 2001). 

" Monte Carlo simulations of solids" (in 

English) (abstract). Rev. Mod. Phys. 73: 33-83. doi: 10.1103/RevModPhys.73.33 (http:// 

p33. Retrieved on 2007-01-18. 

Raimundo R. dos Santos (2003). " 

to Quantum Monte Carlo simulations for fermionic systems" (in English) (full text). Braz. 

J. Phys. 33: 36. Retrieved on 2007-01-18. 

External links 


• Joint DEMOCRITOS-ICTP School on Continuum Quantum Monte Carlo Methods (http:// 

• FreeScience Library -> Quantum Monte Carlo ( 

• UIUC 2007 Summer School on Computational Materials Science: Quantum Monte Carlo 
from Minerals and Materials to Molecules ( 

• Quantum Monte Carlo in the Apuan Alps V ( - 
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Molecular graphics 


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 = 


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. 


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 

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 


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 



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 


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. 


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 

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 


screen reflects a change of view or a change in the molecule or its reference frame. 


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, 
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 // 

xl = xOffset+atoml.getX()*scale; yl = yOff set+atoml.getY( )*scale // 


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 


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. 


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 


This table provides an incomplete chronology of molecular graphics advances. 






< 1960 


Crystal structures, with hidden atom 
and bond removal. Often clinographic 

Cyrus Levinthal, Bob 



First protein display on screen (Project 

Johnson, Motherwell 

ca 1970 

Pen plotter 

ORTEP, PLUTO. Very widely deployed 
for publishing crystal structures. 

Langridge, White, 

Late 1970s 

Departmental systems 
(PDP-11, Tektronix 
displays or DEC-VT11, e.g. 


Mixture of commodity computing with 
early displays. 

T. Alwyn Jones 



Crystallographic structure solution. 

Davies, Hubbard 



Laboratory systems with multicolor, 
raster and vector devices (Sigmex, 

Biosym, Tripos, Polygen 


PS300 and lower cost 
dumb terminals (VT200, 

Commercial integrated modelling and 
display packages. 

Silicon Graphics, Sun 

Late 1980s 


Commodity-priced single-user 
workstations with stereoscopic 


1989, 2000 

Machine independent 

Nearly free, multifunctional, still fully 
supported, many free servers 
based on it 

Molecular graphics 


Sayle, Richardson 

1992, 1993 

RasMol, Kinemage 

Platform-independent MG. 

MDL (van Vliet, Maffett, 
Adler, Holt) 



proprietary C++ ; free browser plugin 
for Mac (OS9) and PCs 



MarvinSketch [6] & 


MarvinSpace [8] (2005) 

proprietary Java applet or stand-alone 

Community efforts 


Jmol, PyMol, Protein 
Workshop ( 

Open-source Java applet or 
stand-alone application. 



NOC [9] 

Powerful and open source code 
molecular structure explorer 

LION Bioscience / EMBL 


SRS 3D [10] 

Free, open-source system based on 
Java3D. Integrates 3D structures with 
sequence and feature data (domains, 
SNPs, etc.). 

San Diego Supercomputer 



Free for academic/non-profit 

Weizmann Institute of 
Science - Community 



Collaborative, 3D wiki encyclopedia of 
proteins & other molecules 


[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 ( 

MT06970.html)". Compendium of Chemical Terminology Internet edition. 
[ 3 ] http ://www. scripps . edu/mb/goodsell/mgs_art/ 
[4] http :// swift. 

[6] http ://www. chemaxon. com/product/msketch. html 
[7] http ://www. chemaxon. com/product/mview. html 
[8] http ://www. chemaxon. com/product/mspace. html 

See also 

• List of Molecular Graphics Systems 

• Molecular Design software 

• Molecular model 

• Molecular modelling 

• Molecular geometry 

• Software for molecular mechanics modeling 

Molecular graphics 


External links 

The PyMOL Molecular Graphics System ( -- open source 

• PyMOLWiki ( -- community supported wiki for PyMOL 

History of Visualization of Biological Macromolecules ( 

microbio/rasmol/history.htm) by Eric Martz and Eric Francoeur. 

Brief History of Molecular Mechanics/Graphics ( 

7770-Lecture-l-intro.pdf) in LSU CHEM7770 lecture notes. 

Historical slides ( 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. ( 

The display looking down the axis of B-DNA has been likened to a rose window. 

Nelson Max's home page ( 

with links to 1982 classics. 

Jmol home page ( contains an applet with an automatic 

display of many features of molecular graphics including metaphors, scripting, 

annotation and animation. 

Richardson Lab ( includes Kinemage and 

molecular graphics images. 

History of RasMol. ( 

Molecule of the Month (http://www.rcsb. org/pdb/ 

moleculeofthemonth/index.html) at RCSB/PDB. 

xeo ( xeo is a free (GPL) open project management 

for nanostructures using Java 

Exhibitions of Molecular Graphics Art ( 

), 1994, 1998. 

NOCH home page ( A powerful, efficient and open source 

molecular graphics tool. 

eMovie ( a tool for creation of 

molecular animations with PyMOL. 

Proteopedia ( The collaborative, 3D encyclopedia of 

proteins and other molecules. 

Ascalaph Graphics ( 

html): a molecular viewer with some geometry editing capabilities. 

Molecular Graphics and Modelling Society, ( 

Journal of Molecular Graphics and Modelling ( 


_urlVersion=0&_userid=1495569&md5 = le86bcce088e98890cea52f6eda84b64) 

(formally Journal of Molecular Graphics). This journal is not open access. 


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. 


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 


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. 


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 

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 


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 


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- ) 
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. 


Black hole thermodynamics 
Classical mechanics 
Condensed matter physics 
Dark matter 
Field theory 
Fluid dynamics 
Solid mechanics 
General relativity 
Molecular modeling 
Particle physics 
Physical cosmology 
Quantum computers 
Quantum mechanics 

Theoretical physics 


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 


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. 


Causal Sets 

Dark energy or Einstein's Cosmological Constant 

Einstein-Rosen Bridge 


Grand unification theory 

Loop quantum gravity 


String theory 


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 



Dynamic theory of gravity 
Grand unification theory 
Luminiferous aether 
Steady state theory 
Theory of everything 

"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 


[1] See e.g. U. Krey, A. Owen, Basic Theoretical Physics -A Concise Overview, Berlin, Springer 2007 


• Note 1: Sometimes mathematical physics and theoretical physics are used synonymously 
to refer to the latter. 

External links 

• Timeline of Theoretical Physics ( 

• MIT Center for Theoretical Physics ( 

• Electronic Journal of Theoretical Physics (EJTP) ( 

• How to Become a Theoretical Physicist by a Nobel Laureate ( 

• Theory of longitudinal and transversal angular momentums ( 

Dynamical system 


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. 


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: 


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 


• 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 

• 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. 


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 


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). 


For a flow, the vector field &(x) is a linear function of the position in the phase space, that 


(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 


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 


A discrete-time, affine dynamical system has the form 


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 



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. 

Dynamical system 


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 


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 


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 


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 

People in systems and control 
Sarkovskii's theorem 
System dynamics 
Systems theory 


[ 1 ] http :// www. drchaos . net/drchaos/bb . html 

[2] webpage/index. html 

[ 3 ] http :// www. i-asr . org/ dynamic . 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 

• 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 

• Diederich Hinrichsen and Anthony J. Pritchard (2005). Mathematical Systems Theory I - 
Modelling, State Space Analysis, Stability and Robustness. Springer Verlag. ISBN 

Introductory texts with a unique perspective: 

• V. I. Arnold (1982). Mathematical methods of classical mechanics. Springer-Verlag. ISBN 

• Jacob Palis and Wellington de Melo (1982). Geometric theory of dynamical systems: an 
introduction. Springer-Verlag. ISBN 0-387-90668-1. 

Dynamical system 


• 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. 


• 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 

• 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 

External links 

• A collection of dynamic and non-linear system models and demo applets (http://vlab. (in Monash University's Virtual Lab) 

• Arxiv preprint server ( has daily 
submissions of (non-refereed) manuscripts in dynamical systems. 

• DSWeb ( provides up-to-date information on 
dynamical systems and its applications. 

• Encyclopedia of dynamical systems ( 
EncyclopediaofDynamicalSystems) A part of Scholarpedia — peer reviewed and 
written by invited experts. 

• Nonlinear Dynamics ( Models of 
bifurcation and chaos by Elmer G. Wiens 

• Oliver Knill ( has a series of examples of dynamical 
systems with explanations and interactive controls. 

• Sci. Nonlinear FAQ 2.0 (Sept 2003) ( 
faq-Contents.html) provides definitions, explanations and resources related to nonlinear 

Online books or lecture notes: 

• Geometrical theory of dynamical systems ( 
Nils Berglund's lecture notes for a course at ETH at the advanced undergraduate level. 

• Dynamical systems ( George D. Birkhoff s 
1927 book already takes a modern approach to dynamical systems. 

• Chaos: classical and quantum ( An introduction to dynamical 
systems from the periodic orbit point of view. 

Dynamical system 


Modeling Dynamic Systems ( 
An introduction to the development of mathematical models of dynamic systems. 
Learning Dynamical Systems ( 
tutorial/home. html). Tutorial on learning dynamical systems. 

Ordinary Differential Equations and Dynamical Systems ( 
~gerald/ftp/book-ode/). Lecture notes by Gerald Teschl 

Research groups: 

Dynamical Systems Group Groningen (, IWI, 

University of Groningen. 

Chaos @ UMD ( Concentrates on the applications of 

dynamical systems. 

Dynamical Systems (, SUNY Stony Brook. 

Lists of conferences, researchers, and some open problems. 

Center for Dynamics and Geometry (, Penn State. 

Control and Dynamical Systems (, Caltech. 

Laboratory of Nonlinear Systems (, Ecole Polytechnique 

Federale de Lausanne (EPFL). 

Center for Dynamical Systems (, 

University of Bremen 

Systems Analysis, Modelling and Prediction Group (, 

University of Oxford 

Non-Linear Dynamics Group (, Instituto Superior Tecnico, 

Technical University of Lisbon 

Dynamical Systems (, IMPA, Instituto Nacional de Matematica 

Pura e Aplicada. 

Nonlinear Dynamics Workgroup (, Institute of Computer 

Science, Czech Academy of Sciences. 

Simulation software based on Dynamical Systems approach: 

FyDiK ( 

Bifurcation diagram 


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; the code in MATLAB can be written as 

hold on 
while c < 4 

Bifurcation diagram 


for i=l:100; 

y = y.^2 -c; ^converge the iteration 


for 1=1:29 

y = y.^2 - c; 

plot(c,y, ' . ' ) ; % plot the converged points 




Symmetry breaking in bifurcation sets 

In a dynamical system such as 


Symmetry breaking in pitchfork bifurcation as the parameter 
epsilon is varied, epsilon = is the case of symmetric pitchfork 


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 


See also 

• Bifurcation theory 

• Phase portrait 


• 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. 


• The Logistic Map and Chaos 

• A small application for drawing the Logistic Map L J 


[1] http 
[2] http 
[3] http 



//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 







i r 

7 r 




-0,05 -- 



H h 

t r 

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 







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 


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 









diagrams from chaos theory are 





Mandelbrot set. 

Quantum mechanics 


quantum mechanics, 


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 


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 


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 


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. 









classifying the behaviour of 
systems by specifying when two 
different phase portraits represent 
the same qualitative dynamic 

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. 




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 


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 



• 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 

• Van der Pol oscillator see picture (right). 

• Bifurcation diagram 

• Mandelbrot set 

Phase portrait 


See also 

• Phase space 

• Phase plane 

• Phase plane method 


• 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 


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. 





described by maps rather than 
ODEs), this corresponds to a fixed 
point having a Floquet multiplier 
with modulus equal to one. In both 





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 : 


0.2 - 

-0.2 - 


-0.6 = 

-0.8 - 



a =-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 



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 


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 


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 

An example of a well-studied codimension-two bifurcation is the Bogdanov-Takens 

See also 

• Bifurcation diagram 

• Catastrophe theory 

• Feigenbaum constant 

• Phase portrait 


• Nonlinear dynamics 

• Bifurcations and Two Dimensional Flows by Elmer G. Wiens 

• Introduction to Bifurcation theory L J by John David Crawford 

Bifurcation theory 




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. 


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 



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 

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: 


R "*R < I 


(R surjective) 

R*R < I 


R is surjective and injective. 

Total or Connected 

I < RvR " 

Relation algebra 




R is functional and total. 

1-1 Function 

R *R = I and R*R "= I. R is total, functional, and injective. 


I < R 


R A I = 0. (0 = I") 


R*R <R 


R is reflexive and transitive. 


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. 


R = R " 


R*R "= R. R is a symmetric preorder. 


R * R " 


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 


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. 


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 


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 



• RelMICS / Relational Methods in Computer Science L J maintained by Wolfram Kahl L J 

• Carsten Sinz: ARA / An Automatic Theorem Prover for Relation Algebras 


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 


Logic of relatives 


Relation construction 

Relation reduction 


[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 

[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/ 


• Rudolf Carnap (1958) Introdution to Symbolic Logic and its Applications. Dover 

• 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 


Roger Maddux, 1991, " The Origin of Relation Algebras in the Development and 
Axiomatization of the Calculus of Relations, ( 
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. 
pub/staff/akama/repr . ps ) " 

• Richard Bird, Oege de Moor, Paul Hoogendijk, " Generic Programming with Relations 
and Functors, (" 

• R.P. de Freitas and Viana, " A Completeness Result for Relation Algebra with Binders. 

• Peter Jipsen ( 

• Relation algebras ( 
pdf). In Mathematical structures, ( If 
there are problems with LaTeX, see an old HTML version here. (http://math. 
chapman. edu/cgi-bin/ 

• " Foundations of Relations and Kleene Algebra, ( 

• " Computer Aided Investigations of Relation Algebras, ( 
-jipsen/ dissertation/)" 

• " A Gentzen System And Decidability For Residuated Lattices." ( 

• Vaughan Pratt: 

• " Origins of the Calculus of Binary Relations, ( 
pdf)" A historical treatment. 

• " The Second Calculus of Binary Relations, ( 

• Priss, Uta, " An FCA interpretation of Relation Algebra, ( 

• Kahl, Wolfram, ( and Schmidt, Gunther, (http:// " Exploring (Finite) Relation Algebras Using 
Tools Written in Haskell. ( 
2000-02/)" See homepage ( of 
the whole project. 

Category theory 


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. 


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 


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. 


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 


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 

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 



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 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 


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 


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 

• 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 


introduction to these ideas, see John Baez, 'A Tale of n-categories' (1996). 

Category theory 


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 



[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. 


Freely available online: 

• Adamek, Jifi, Herrlich, Horst, & Strecker, George E. (1990) Abstract and concrete 
categories ( John Wiley & Sons. 
ISBN 0-471-60922-6. 

• Freyd, Peter J. (1964) Abelian Categories, ( 
articles/3/tr3abs.html) New York: Harper and Row. 

• Michael Barr and Charles Wells (1999) Category Theory Lecture Notes. (http://folli. Based on their book Category Theory for 
Computing Science. 

• (2002) Toposes, triples and theories, ( 

pub/ttt.html) Revised and corrected translation of Grundlehren der mathematischen 
Wissenschaften (Springer-Verlag, 1983). 

• Leinster, Tom (2004) Higher operads, higher categories ( 
~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. ( Notes 

for a course offered as part of the MSc. in Mathematical Logic, Manchester University. 

• Turi, Daniele (1996-2001) Category Theory Lecture Notes, ( 
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 

• A. Martini, H. Ehrig, and D. Nunes (1996) Elements of Basic Category Theory (http:// (Technical Report 96-5, Technical 
University Berlin) 


Category theory 


Awodey, Steven (2006). Category Theory (Oxford Logic Guides 49). Oxford University 


Borceux, Francis (1994). Handbook of categorical algebra (Encyclopedia of Mathematics 

and its Applications 50-52). Cambridge Univ. Press. 

Freyd, Peter J. & Scedrov, Andre (, (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 


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 


Pierce, Benjamin (1991). Basic Category Theory for Computer Scientists. MIT Press. 

External links 

Chris Hillman, Categorical primer ( 


hillman01categorical.pdf), formal introduction to Category Theory. 

J. Adamek, H. Herrlich, G. Stecker, Abstract and Concrete Categories-The Joy of Cats 


Stanford Encyclopedia of Philosophy: " Category Theory ( 

entries/category- theory/)" ~ by Jean-Pierre Marquis. Extensive bibliography. 

Homepage of the Categories mailing list, ( 

html) with extensive resource list. 

Baez, John, 1996," The Tale of n-categories. ( 

html)" An informal introduction to higher order categories. 

The catsters (" a Youtube channel about 

category theory. 

Category Theory ( 

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 


Category theory 


Interactive Web page ( which 
generates examples of categorical constructions in the category of finite sets. Written by 
Jocelyn Paine ( 

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 

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 


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 


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 


Further reading 


• Allen Hatcher, Algebraic topology. (2002) Cambridge University Press, Cambridge, 
xii+544 pp. ISBN 052179160X and ISBN 0521795400 

• May, J. P. (1999), pdf]A 
Concise Course in Algebraic Topology, U. Chicago Press, Chicago, http://www.math., 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 


Lie groupoid 

Lie algebroid 

Grothendieck topology 

Serre spectral sequence 



Homotopy theory 

Fundamental group 

Homology theory 

Homological algebra 

Cohomology theory 


Algebraic K-theory 


Homotopy quantum field theory(HQFT) 

CW complex 

Simplicial complex 

Homology complex 


Exact sequence 

Algebraic topology 




[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.! 4/9/ 14-09. 

[5] Ronald Brown, Philip J. Higgins and Rafael Sivera. Nonabelian Algebraic Topology: Higher homotopy 

groupoids of filtered spaces. 512 pp, (Preprint 2009). 

[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. 

• 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),\Algebraic 
Topology, Cambridge: Cambridge University Press, ISBN 0-521-79540-0, http://www. A modern, geometrically flavored 
introduction to algebraic topology. 

Maunder, C.R.F. (1970), Algebraic Topology, London: Van Nostrand Reinhold, ISBN 

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. 

Ronald Brown, Higher dimensional group theory ( 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 
(, (vol. 2 in preparation); 
downloadable PDF: ( 
Van Kampen's theorem ( 
amp;id=3947) on PlanetMath 

Van Kampen's theorem result ( 
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. (Discusses generalized versions of 
van Kampen's theorem applied to topological spaces and simplicial sets). 

Algebraic logic 


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 

• 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 


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 



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 


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 


• Brady, Geraldine, 2000. From Peirce to Skolem: A neglected chapter in the history of 


logic. North-Holland/Elsevier Science BV: catalog page , Amsterdam, Netherlands, 625 

• Burris, Stanley, 2009. The Algebra of Logic Tradition L . Stanford Encyclopedia of 

• 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. 


[ 1 ] http :// www. philosophie . uni-osnabrueck. de/Publikationen%2 Lenzen/Lenzen%2 0Leibniz%2 OLogic . pdf 





[6] http ://plato. Stanford. edu/entries/consequence-algebraic/ 

Quantum logic 


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 



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 

• 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. 


Quantum logic 


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 


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 

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. 


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 

^(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 


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 

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; 


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 


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. 


• 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 


We see that a pure ensemble becomes a mixed ensemble after measurement. Measurement, 
as described above, is a special case of quantum operations. 


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] 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] 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 

[5] Georgescu, G. 2006, N-valued Logics and Lukasiewicz-Moisil Algebras, Axiomathes, 16 (1-2): 123- 
[7] http :// alessio. guglielmi. name/res/cos/crt.html#CQE 

Quantum logic 


See also 

• Mathematical formulation of quantum mechanics 

• Multi-valued logic 

• Quasi-set theory 

• HPO formalism (An approach to temporal quantum logic) 

• Quantum field theory 


• 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 

• 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, 

• 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 

• 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 

Lukasiewicz logic 


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. 


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 


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). 


• 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. 


[ 1 ] http ://plato. Stanford. edu/entries/logic-manyvalued/ 


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 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 


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 


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 

See also 

History of molecular evolution 

Chemical evolution 


Genetic drift 

E. coli long-term evolution experiment 

Evolutionary physiology 

Neutral theory of molecular evolution 

Nucleotide diversity 


Population genetics 


Genomic organization 
Horizontal gene transfer 

Human evolution 

Molecular clock 

Comparative phylogenetics 

Molecular evolution 


Further reading 

• Li, W.-H. (2006). Molecular Evolution. Sinauer. ISBN 0878934804. 

• Lynch, M. (2007). The Origins of Genome Architecture. Sinauer. ISBN 0878934847. 


[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 

[3] Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge. ISBN 

[4] Kimura, Motoo (1968). 

" Club/fall2006/Kimura_l 968_Nature.pdf (Evolutionary rate at the 

molecular level". Nature 217: 624-626. doi: 10.1038/217624a0 ( http:/ 

/www2. 968_Nature.pdf. 
[5] King, J.L. and Jukes, T.H. (1969). 

" Evolution". Science 164: 

788-798. doi: 10.1126/science.l64.3881.788 ( 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/ 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 ( PMID 

[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. 





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: 


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. 



See also 



Nuclear medicine 

Radioactivity in biology 


Cell survival curve 

Relative biological effectiveness 


• WikiMindMap [1] 


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 


• The Institute for Radiation Biology at the Helmholtz-Center for Environmental Health 




Photosynthesis LocJ is 

process that converts carbon 




compounds, especially sugars, 







sunlight. 1 J 
occurs in plants, algae, and 
many species of Bacteria, but 
not in Archaea. Photosynthetic 




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 


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 evolved early in the 
evolutionary history of life, when 
all forms of life on Earth were 

microorganisms . 



photosynthetic organisms probably 


evolved about 3500 


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 






Plants, algae, many bacteria 


Carbon dioxide 




Animals, fungi, 
many bacteria 


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). 


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. 






Light reactions 


Photosynthesis splits water to liberate 
O and fixes CO into sugar 



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, 


or bunched up 






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 




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 

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 



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 





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 



accessory pigments 


primary pigment reaction 
centre P700 or P680 


A Photosystem: A light-harvesting cluster of 
photosynthetic pigments present in the thylakoid 

membrane of chloroplasts. 











OxypcncvoKinj! i-omplH 


HHiCimytiL-ni II 

"Cytochrome Ivf complex 
vj \\ir ^^ PLivUievanin 

Membrane bourul iron Mil fur ptuicins 

m m ^ 2NAW-2IT 

■»», ■ 

2c NADP L rvJuwki^c 


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. 



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 



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 

Cental MeHlwfic Pathway* 


-j- ^ fiibulnwlrS-bbphoiphdTe 



Ribulose 5-phospKaie 


Cuban d I a rid* 


Phase 1: 

Carbon Fixation 

^ (-mulMflabolk Pathway* 



Phase 3: 

Regeneration of 

Phase 2: 


tjlyceraldehyde 3- phosphate 


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 






concentration in the leaves under these 

C. plants chemically fix carbon dioxide in 
the cells of the mesophyll by adding it to 

Carbon dioxide 

Phosphoenol pyruvate 

phyll Cell j 

Bundle Sheath Cell 


Calvin Cycle 

Carbon dioxide 

Inorganic Phosphate 

Overview of C4 carbon fixation 



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 


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 

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. 


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 




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. 



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. 


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 

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 




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. 


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 

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 



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 
Light-dependent reaction 
Photosynthetic reaction center 



Photosynthetically active radiation 

Quantum biology 

Red edge 

Jan Anderson (scientist) 


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. 


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(Mcgraw Hill Encyclopedia of Science and Technology). McGraw-Hill Professional, pp. vol 13 p. 470. ISBN 




Further reading 

Asimov, Isaac (1968). Photosynthesis. New York, London: Basic Books, Inc.. ISBN 


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 


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 


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) 


UC Berkeley video lecture ( 

photosynthesis-from-light-to-atp) on Photosynthesis 

In depth, advanced treatment of photosynthesis, also from Govindjee ( 

Science Aid: Photosynthesis ( 

photosynthesis.html) Article appropriate for high school science 

Liverpool John Moores University, Dr. David Wilkinson ( 

NewsCentre/6301 2.htm) 

Metabolism, Cellular Respiration and Photosynthesis - The Virtual Library of 

Biochemistry and Cell Biology ( 

Overall examination of Photosynthesis at an intermediate level (http://www.chemsoc. 


Overall Energetics of Photosynthesis ( 


Photosynthesis Discovery Milestones ( 

photosynthesisexperiments.html) - experiments and background 

Computational biology 


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 

• 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 


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. 





described by the Goldbeter-Koshland 



k 2 a 

A kinase Y and a phosphotase X that act on a protein 
Z; one possible application for the Goldbeter-Koshland 






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; 









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. 


Since we are looking at equilibrium properties we can write 



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 




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] 






+ (!■ 



Jl + (1 - 2) 



J<2 + 





with the constants 


[Z| ; Vl = fc,[X]; v 2 = h[Y]] Ji = &-= ■* 



j. ; 2 





If we thus solve the quadratic equation (1) for z we get: 





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 



Vi ) 

2(« 2 - t'i) 

B + v'B 2 - 4 (^ 




4(u 2 - ui)wi J 2 

I ■ I 

2(u 2 - vi) B + Y/^-^-t'iJuiJj 


B + V'B 2 - 4(i' 2 - i'i ) v 1 J 2 


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): 


G(v 1 ,v 2 ,J u J 2 ) 

2i'i J. 


B + y/'B 2 -i(y 2 -wi)i'iJ 2 


• Goldbeter A, Koshland DE (November 1981). 


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 


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 



Signalling pathway 

1. REDIRECT signal transduction 

Cell cycle 


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. 


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. 







G o 

A resting phase where the cell has left the cycle and has stopped 

Cell cycle 



Gap 1 

G i 

Cells increase in size in Gap 1. The G checkpoint control 
mechanism ensures that everything is ready for DNA 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 

Cell division 



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. 


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 


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 

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. 


Leland H. 

Regulation of cell cycle - Schematic 

Extracellular growth signal 


DNA damage by irradiation 

Cyclin D 


Cyclin D-CDK4 complex 



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 


Cyclin E-CDK2 complex 

| Cyclin A-CDK2 complex 

vjiimmiiMir "'■■■Mm 

Cell cycle 





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 


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 


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 



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 

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. 


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 

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 


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 


[I] Smith JA, Martin L (April 1973). 
,,|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 ( 

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). 

" 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). 

" 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 ( PMID 7575488. 
[6] "Press release". http:// 
[7] Spellman PT, Sherlock G, Zhang MQ, Iyer VR, Anders K, Eisen MB, Brown PO, Botstein D, Futcher B 

(December 1998). 


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 

[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). " 

Cycle Checkpoints: Preventing an Identity Crisis". Science 274 (5293): 1664-1672. doi: 

10. 1126/science.274. 5293. 1664 ( PMID 8939848. http:/ 


[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 

[12] Pedrali-Noy G, Spadari S, Miller-Faures A, Miller AO, Kruppa J, Koch G (January 1980). 

" 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 


[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 ( PMID 

[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:// 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 

External links 

• This article contains material from the Science Primer ( 
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, 

• Cell cycle and metabolic cycle regulated transcription in yeast (http://www.sceptrans. 

• Cell Cycle Animation ( Cycle/index. html) 

• Cell Cycle and Cytokinesis - The Virtual Library of Biochemistry and Cell Biology (http:// 

• Cell Cycle ( 

• Cell Cycle Portal ( 

• Fucci:Using GFP to visualize the cell-cycle ( 
GFP-ww/cooluses 1 9 .html) 

• Science Creative Quarterly's overview of the cell cycle ( 

• Cells alive ( 

• CCO ( The Cell-Cycle Ontology 

• KEGG - Human Cell Cycle ( 

• Cell cycle modeling ( 




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 

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. 




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 

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 


The backbone of the DNA 
strand is made from alternating 





5' end 

3' end 






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 



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. 


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. 



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 


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. 



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 

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 


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] 



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 


regulating gene expression through RNA-RNA base pairing. 1 J 

A few DNA sequences in prokaryotes and eukaryotes, and more in plasmids and viruses, 


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. 


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 





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 



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 




regions of DNA called telomeres. 
The main function of these regions 
is to allow the cell to replicate 
chromosome ends using 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. 



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 






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. 


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 






5-hydroxymethylcytosine in the brain, 1 J and the glycosylation of uracil to produce the 
"J-base" in kinetoplastids. [52] [53] 


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 



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 



T7 RNA polymerase (blue) producing a mRNA (green) from a 

DNA template (orange). 


and divergence. 

Some non-coding DNA sequences 







centromeres typically contain few 
genes, but are important for the 





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. 




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 





double-stranded structure of 

DNA provides 



replication. Here, the two 
strands are separated and 




DNA ligase 
DNA Polymerase (Pola) 

DNA primase 
RNA primer 




DNA Polymerase (P0I6) 


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 


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 



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. 


These binding proteins seem to stabilize 

single-stranded DNA and protect it from forming stem-loops or being degraded by 

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 


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 



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 



enters the bacterial cell, acting as part of the restriction modification system, 
technology, these sequence-specific nucleases are used in molecular cloning and DNA 

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. 




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 









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. 







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. 


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. 


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 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. 



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 




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 


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 





self-assembling branched DNA 




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 



lattices (both tile-based as well 
as using the "DNA origami" 
method) as 



three-dimensional structures 






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. * 



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. 


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 

Francis Crick 



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 ({tfttXUMie) 

barn iHim4 A. Atfffcam£ «**«SfM».c« 

Stone /« Mm«<v * Jta uttx ffruj . 

DNA Helix controversy 

In 1953 James D. Watson and Francis Crick suggested what is now accepted as the first 


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 


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. 



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 


X-ray crystallography 

Genetic disorder 

Junk DNA 

Nucleic acid analogues 

Nucleic acid methods 

Nucleic acid modeling 

Nucleic Acid Notations 



Polymerase chain reaction 

Proteopedia DNA [146] 

Southern blot 

Triple-stranded DNA 


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[136] Avery O, MacLeod C, McCarty M (1944). "http://www.jem.Org/cgi/reprint/l 49/2/2 97 1 Studies on the chemical 

nature of the substance inducing transformation of pneumococcal types. Inductions of transformation by a 

desoxyribonucleic acid fraction isolated from pneumococcus type III". J Exp Med 79 (2): 137-158. doi: 

10.1084/jem.79.2.137 (http://dx.doi.Org/10.1084/jem.79.2.137). 

[137] Hershey A, Chase M (1952). "http://www.jgp. org/cgi/reprint/36/l/39.pdf|Independent functions of viral 

protein and nucleic acid in growth of bacteriophage" (PDF). J Gen Physiol 36 (1): 39-56. doi: 

10.1085/jgp.36.1.39 (http://dx.doi.Org/10.1085/jgp.36.l.39). PMID 12981234. 

reprint/36/1/39. pdf. 
[138] The B-DNA X-ray pattern on the right of this linked image ( 

specialcollections/coll/pauling/dna/pictures/sci9.001.5.html) was obtained by Rosalind Franklin and 

Raymond Gosling in May 1952 at high hydration levels of DNA and it has been labeled as "Photo 51" 
[139] Nature Archives Double Helix of DNA: 50 Years ( 
[140] Original X-ray diffraction image ( 

[141] The Nobel Prize in Physiology or Medicine 1962 ( 

1962/) Nobelprize .org Accessed 22 December 06 
[142] Brenda Maddox (23 January 2003). " 

double helix and the 'wronged heroine'" (PDF). Nature 421: 407-408. doi: 10.1038/nature01399 (http://dx.doi. 

org/10. 1038/nature01399). PMID 12540909. 

[143] Crick, F.H.C. On degenerate templates and the adaptor hypothesis (PDF), ( 

uk/assets/wtx030893.pdf) (Lecture, 1955). Accessed 22 December 2006 
[144] Meselson M, Stahl F (1958). "The replication of DNA in Escherichia colV. Proc Natl Acad Sci USA 44 (7): 

671-82. doi: 10.1073/pnas.44.7.671 (http://dx.doi.Org/10.1073/pnas.44.7.671). PMID 16590258. 
[145] The Nobel Prize in Physiology or Medicine 1968 ( 

1968/) Accessed 22 December 06 

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 

• 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. 



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 ( 
Biomolecules/Nucleic_Acids/DNA//) at the Open Directory Project 
DNA binding site prediction on protein ( 
DNA coiling to form chromosomes ( education mac. htm) 
DNA from the Beginning ( 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. ( 
DNA the Double Helix Game ( 
dnadoublehelix/) From the official Nobel Prize web site 

DNA under electron microscope ( 

Dolan DNA Learning Center ( 

Double Helix: 50 years of DNA (, 

Double Helix 1953-2003 ( National Centre 
for Biotechnology Education 

Francis Crick and James Watson talking on the BBC in 1962, 1972, and 1974 (http:// 
Genetic Education Modules for Teachers ( — DNA 
from the Beginning Study Guide 

Guide to DNA cloning ( 

Olby R (January 2003). " 
debut for the double helix". Nature 421 (6921): 402-5. doi: 10.1038/nature01397 (http:// PMID 12540907. 

PDB Molecule of the Month pdb23_l ( 
Rosalind Franklin's contributions to the study of DNA ( 
- emoody/rfranklin. html) 

The Register of Francis Crick Personal Papers 1938 - 2007 ( 
speccoll/testing/html/mss0660a.html#abstract) at Mandeville Special Collections 
Library, Geisel Library, University of California, San Diego 

U.S. National DNA Day ( — watch videos and 
participate in real-time chat with top scientists 

" 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. 



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 


Spinning DNA 
generic model. 


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 


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 

Molecular models of DNA 




3' end 


deoxyribose "^'^ 


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Guanine 5- en d 

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CWA Polymerase (PoUr.i* 

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Molecular models of DNA 


Spacefilling model or CPK model - a molecule is represented by overlapping spheres 
representing the atoms. 

Images for DNA Structure Determination from X-Ray 

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 


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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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. 

K*v hi*. 

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DNA Helix controversy in 1952 

Molecular models of DNA 


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 

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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* each probe 25 nucleotides long 

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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 


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 


• 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 ■ 

* * * 








100 nm 

Detector and 




Sample Surface 

Cantilever & Tip 

PZT Scanner 


25 nm 

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Molecular models of DNA 


Mass spectrometry— Maldi informatics 


Data acquisition 

Mass spectrum 



Mass spectrum 
w/o background 

Peak detection 

List of peak 

Nucleic acid 

Peak integration 

mutations, etc 

List of peak 

Nudeic acid 


• 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 


• NMR constraints files for NAs in PDB format [3 ] 
NMR microscopy [ 2 ^ 
Microwave spectroscopy 

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 


Gallery: CARS (Raman spectroscopy), Fluorescence confocal 
microscopy, and Hyperspectral imaging 



Stokes shift 







virtuelle Zustande 








(a) S 

erspectral Comparison 

Beam splitter 

Light source 

Light detector 






dichroic mirror 


emission filter 

light source 

excitation filter 





'" i , 



w=617 Combined 


- *• 





Molecular models of DNA 


Enzymes and shell proteins 

Genomic and structural databases 

CBS Genome Atlas Database L J — contains examples of base skews. 


The Z curve database of 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 


[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 

[6] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953). 

" Structure of Deoxypentose Nucleic Acids" (PDF). 

Nature 111. 738-740. doi: 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): 

[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 

//www. phy . cam. ac . uk/research/bss/molbiophysics . php 

[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 ( 
[18] http://www.ncbi. 

[19] http ://ndbserver. rutgers . edu/atlas/xray/ index. html 

Molecular models of DNA 


[21] http ://ndb server. rutgers. edu/ftp/NDB/structure-f actors/ 



[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 ( ISSN 0002-7863 

[25] html/resources/01 general. php 

[27] ( obtaining dihedral angles from J coupling constants 
[28] ( files/ 

General_Karplus_Calculator.htm) Another Javascript-like NMR coupling constant to dihedral 
[29] http ://ndbserver. rutgers . edu/atlas/nmr/index. html 
[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) ( 
[35] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY. 
[36] imaging 
[37] 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 
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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) ( 
[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 ( 
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[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) ( 
[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 


[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, 


[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 ( 

[54] doi:10.1016/S0959-440X(00)00190-l ( 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] 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. 
[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. 
[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 


Applications of Novel Techniques to Health Foods, Medical and Agricultural 

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(1824), article 14. 

Sir Lawrence Bragg, FRS. The Crystalline State, A General survey. London: G. Bells and 

Sons, Ltd., vols. 1 and 2., 1966., 2024 pages. 

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, 

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Rigler R. and Widengren J. (1990). Ultrasensitive detection of single molecules by 

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Watson, James D. and Francis H.C. Crick. A structure for Deoxyribose Nucleic Acid 

( (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. 

Molecular models of DNA 


Wentworth, W.E. Physical Chemistry. A short course., Maiden (Mass.): Blackwell Science, 

Inc. 2000. 

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. 

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oxf ordj ournals . org/cgi/content/abstract/ 1 /4/2 9 5 ) 

Rothemund, Paul W. K.; Ekani-Nkodo, Axel; Papadakis, Nick; Kumar, Ashish; Fygenson, 

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Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun 

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Molecular models of DNA 


See also 


Molecular graphics 

DNA structure 

DNA Dynamics 

X-ray scattering 

Neutron scattering 


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 


DNA nanotechnology 


Atomic force microscopy 

X-ray microscopy 

Liquid crystal 



Sir Lawrence Bragg, FRS 

Sir John Randall 

James Watson 

Francis Crick 

Maurice Wilkins 

Herbert Wilson, FRS 

Alex Stokes 

Molecular models of DNA 


External links 

DNA the Double Helix Game ( 

dnadoublehelix/) From the official Nobel Prize web site 

MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. 


Double Helix 1953-2003 ( National Centre 

for Biotechnology Education 

DNA under electron microscope ( 


Ascalaph DNA ( — 

Commercial software for DNA modeling 

DNAlive: a web interface to compute DNA physical properties ( 

DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and 

DNA dynamics. 

DiProDB: Dinucleotide Property Database ( The database 

is designed to collect and analyse thermodynamic, structural and other dinucleotide 


Further details of mathematical and molecular analysis of DNA structure based on X-ray 

data ( 


Bessel functions corresponding to Fourier transforms of atomic or molecular helices. 

(http ://planetphy sics . org/?op = getobj &from = obj ec ts & 


Application of X-ray microscopy in analysis of living hydrated cells (http://www.ncbi. 

list_uids = 12379938) 

Characterization in nanotechnology some pdfs (http://nanocharacterization.sitesled. 


overview of STM/AFM/SNOM principles with educative videos ( 


SPM Image Gallery - AFM STM SEM MFM NSOM and More ( 

results/showcase. php) 

How SPM Works ( 

U.S. National DNA Day ( — watch videos and 

participate in real-time discussions with scientists. 

The Secret Life of DNA - DNA Music compositions ( 


DNA structure 


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] 


DNA structure 


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 : 





Propeller twist 

Rotation of one base with respect to the other in the same base pair. 


displacement along an axis in the base-pair plane perpendicular to the first, directed 
from the minor to the major groove. 


displacement along an axis in the plane of the base pair directed from one strand to 
the other. 


displacement along the helix axis. 


rotation around this axis 


rotation around this axis 


rotation around the helix axis. 

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 


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. 










axis of helix 
of Z-DNA 

The helix axis of A-, B-, and Z-DNA. 


Geometry attribute 




Helix sense 




Repeating unit 

1 bp 







Mean bp/turn 




Inclination of bp to axis 

+ 19° 



Rise/bp along axis 

2.3 A 

3.32 A 

3.8 A 

DNA structure 


Pitch/turn of helix 

24.6 A 

33.2 A 

45.6 A 

Mean propeller twist 

+ 18° 

+ 16° 


Glycosyl angle 



C: anti, 
G: syn 

Sugar pucker 



C: C2'-endo, 
G: C2'-exo 


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) 


Persistence Length 
/base pairs 






( CAG Wat 





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 


"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) 


Stacking AG 
/kcal mol" 

T A 


T G or C A 




A G or C T 


A A or T T 




G A or T C 




A C or G T 


G C 


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 


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 


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 

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 


The mechanical properties DNA under compression have not been characterized due to 
experimental difficulties in preventing the polymer from bending under the compressive 

DNA melting 

Melting stability of base steps (B DNA) 


Melting AG 
/Kcal mol" 1 

T A 


T G or C A 


C G 


A G or C T 


A A or T T 




G A or T C 




A C or G T 


G C 


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 


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 

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 


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 


Twist = -1, Writhe = 0. 

Twist = 0, Writhe = -1 


Twist = +1, Writhe = 0. 

Twist = 0. Writhe = +1 





Twist = -2, Writhe = 0. 

Twist = +2, Writhe = 0. 



Twist = 0, Writhe = -2. 

Twist = 0, Writhe = +2. 


(p\ 5§) Twist = 0, Writhe = -4. 



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. 



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 


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 


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 


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[24] Crick FH (1976). "Linking numbers and nucleosomes". Proc Natl Acad Sci USA 73 (8): 2639-43. doi: 

10.1073/pnas.73.8.2639 (http://dx.doi.Org/10.1073/pnas.73.8.2639). PMID 1066673. 
[25] Prunell A (1998). "A topological approach to nucleosome structure and dynamics: the linking number paradox 

and other issues". BiophysJ 74 (5): 2531-2544. PMID 9591679. 
[26] Luger K, Mader AW, Richmond RK, Sargent DF, Richmond TJ (1997). "Crystal structure of the nucleosome 

core particle at 2.8 A resolution". Nature 389 (6648): 251-260. doi: 10.1038/38444 ( 

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 ( PMID 12079350. 

External links 

• MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. 

• Ascalaph DNA ( — 
Commercial software for DNA modeling 

• DNAlive: a web interface to compute DNA physical properties ( 
DNAlive). Also allows cross-linking of the results with the UCSC Genome browser and 
DNA dynamics. 

• DiProDB: Dinucleotide Property Database ( The database 
is designed to collect and analyse thermodynamic, structural and other dinucleotide 




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 


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. 


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 

X-ray pattern of a B-DNA Paracrystal [10] 




[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 

[8] X-Ray Diffraction Patterns of Double-Helical Deoxyribonucleic Acid (DNA) Crystals and Paracrystalline Fibers 
[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 


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 

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 

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 


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DNA Dynamics 


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 


100 nm 


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DNA Dynamics 


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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• 11 probe-f eatures for each gene 

• each probe 25 nucleotides tong 

• lhouijnd& of gent* fprobe&vft) 

Reduced hybridisation signal doe lo polymorphism - wqnence variation 




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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 


Mass spectrometry— Maldi informatics 


Data acquisition 

Mass spectrum 



Mass spectrum 
w/o background 

Peak detection 

List of peak 

Peak integration 

List of peak 

Nucleic acid 

mutations, etc 

Nudeic acid 

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 


• NMR constraints files for NAs in PDB format [ ] 


NMR microscopy 

Vibrational circular dichroism (VCD) 

Microwave spectroscopy 


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 


Gallery: CARS (Raman spectroscopy), Fluorescence confocal 
microscopy, and Hyperspectral imaging 



Stokes shift 








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erspectral Comparison 



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Enzymos and shell proteins 

DNA Dynamics 


X-ray microscopy 

• Application of X-ray microscopy in the analysis of living hydrated cells 


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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Sample Surface 

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PZT Scanner 


[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 

[4] Wilkins M.H.F., A.R. Stokes A.R. & Wilson, H.R. (1953). 

" Structure of Deoxypentose Nucleic Acids" (PDF). 

Nature 111. 738-740. doi: 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): 

[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 


[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. 
[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] ( 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) ( 
[20] Raghavachari, R., Editor. 2001. Near-Infrared Applications in Biotechnology, Marcel-Dekker, New York, NY. 
[21] imaging 
[22] 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) ( 
[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 ( 
[28] Chemical Imaging Without Dyeing ( 
[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) ( 
[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 


[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, 


[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 ( 

[39] doi:10.1016/S0959-440X(00)00190-l ( 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] 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 ( ISSN 0002-7863 



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., 


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 

( (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. 

DNA Dynamics 


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 ( 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 ( ISSN 

0002-7863 ( 

Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun 

(November 2003). 

"; 302/5649/1 380 1 DNA-Templated 

Carbon Nanotube Field-Effect Transistor". Science 302 (6549): 1380-1382. doi: 

10.1 126/science. 1091 022 ( ISSN 

1095-9203 ( 


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 ( ISSN 1530-6984 (http:// 

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 ( 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 

( 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. 

DNA Dynamics 


See also 


Molecular modeling of DNA 


Signal transduction 




Molecular graphics 

Quantum computing 


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 


Crystal lattices 

Molecular geometry 


DNA nanotechnology 


Sirius visualization software 

DNA Dynamics 


Atomic force microscopy 

X-ray microscopy 

Liquid crystals 



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 ( 

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. 

list_uids = 12379938) 

DiProDB: Dinucleotide Property Database ( The database 

is designed to collect and analyse thermodynamic, structural and other dinucleotide 


DNA the Double Helix Game ( 

dnadoublehelix/) From the official Nobel Prize web site 

MDDNA: Structural Bioinformatics of DNA (http://humphry.chem. 


Double Helix 1953-2003 ( National Centre 

for Biotechnology Education 

DNA under electron microscope ( 


Further details of mathematical and molecular analysis of DNA structure based on X-ray 

data ( 


Bessel functions corresponding to Fourier transforms of atomic or molecular helices. 

(http ://planetphy sics . org/?op = getobj &from = obj ec ts & 


Characterization in nanotechnology some pdfs (http://nanocharacterization.sitesled. 


An overview of STM/AFM/SNOM principles with educative videos (http://www.ntmdt. 


SPM Image Gallery - AFM STM SEM MFM NSOM and More ( 

results/showcase. php) 

How SPM Works ( 

DNA Dynamics 


U.S. National DNA Day ( — watch videos and 

participate in real-time discussions with scientists. 

The Secret Life of DNA - DNA Music compositions ( 


Ascalaph DNA ( — 

Commercial software for DNA modeling 


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 


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 



Frederick Sanger in 1977. 


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 



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 


[I] EPA Interim Genomics Policy ( 

[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 ( 

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 ( 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 ( PMID 870828. 
[5] The Viral Genomes Resource, NCBI Friday, 14 September 2007 ( 

[6] Genome Project Statistic, NCBI Friday, 14 September 2007 ( 

[7] BBC article Human gene number slashed from Wednesday, 20 October 2004 ( 

[8] CBSE News, Thursday, 16 October 2003 ( 

index, shtml) 
[9] NHGRI, pressrelease of the publishing of the dog genome ( 
[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. 


[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. 



External links 

• Genomics Directory ( A one-stop biotechnology 
resource center for bioentrepreneurs, scientists, and students 

• Annual Review of Genomics and Human Genetics ( 

• BMC Genomics ( A BMC journal on 

• Genomics ( UK companies and 
laboratories* Genomics journal ( 

• ( An openfree wiki based Genomics portal 

• NHGRI ( US government's genome institute 

• Pharmacogenomics in Drug Discovery and Development ( 
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) ( 
One of the first undergraduate programs in the world 

• JCVI Comprehensive Microbial Resource ( 

• Pathema: A Clade Specific Bioinformatics Resource Center ( 

• ( The first Korean Genome published and 
the sequence is available freely. 

• GenomicsNetwork ( Looks at the development and use 
of the science and technologies of genomics. 

Gene regulatory network 


Gene regulatory network 

A gene regulatory network 




network (GRN) is a collection 
of DNA segments in a cell 
which interact with each other 
(indirectly through their RNA 




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 




accumulate at the cell-wall or 
within the cell to give it 
particular structural 




ixgfial A 

1 / 

* tK 

















facto A ^ 


jr™prt«i 0U1PUT 






Fl- idiom 


DNA i*%j*hC* 


RNA poJjnmcraie 



t w d b o c h 


Structure of a Gene Regulatory Network. 










outputs = 

Changed RNA 
and protein 





outputs = 

Changed cell 
behaviors and 

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. 


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 


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 


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 


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 


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. 


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 


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 


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 

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 


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 


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 


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 


connected, networks. These results suggest that a sparse, minimally connected, genetic 
architecture may be a fundamental design constraint shaping the evolution of gene network 

Gene regulatory network 


See also 

• Operon 

• Systems biology 

• Synexpression 

• Cis-regulatory module 

• Body plan 

• Morphogen 


[3] Kauffman, Stuart (1993). The Origins of Order. 

[4] Vohradsky, J. (2001). Neural model of the genetic network. The Journal of Biological Chemistry, 276, 

[5] Geard, N. and Wiles, J. A Gene Network Model for Developing Cell Lineages. In Artificial Life, 11 (3): 249-268, 

[6] Schilstra, M.J. and Bolouri, H. The Logic of Gene Regulation., 

[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:// 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.". 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 

Gene regulatory network 


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 (, Prioritizer software application 

S. A. Kauffman, "Metabolic stability and epigenesis in randomly constructed genetic 
nets", J. Theoret. Biol (1969) 22, 434-467 

External links 

• Gene Regulatory Networks ( 
generegulatorynetwork.shtml) — Short introduction 

• BIB: Yeast Biological Interaction Browser ( 

• Graphical Gaussian models for genome data ( 
— Inference of gene association networks with GGMs 

• A bibliography on learning causal networks of gene interactions (http://www.molgen. - regularly updated, contains hundreds of 
links to papers from bioinformatics, statistics, machine learning. 

• 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 ( 
GRNclocks) - Information page with model source code and Java applet. 

• Engineered Gene Networks ( 

• Tutorial: Genetic Algorithms and their Application to the Artificial Evolution of Genetic 
Regulatory Networks ( 

Computational genomics 


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. [ ] 


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 

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, 


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 


Contributions of computational genomics research to 


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 

• measure regions of genomes that have undergone unusually rapid evolution 

See also 



Computational biology 




Computational epigenetics 


[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 ( 
[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) ( 
[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:// 

• University of Bristol course in Computational Genomics, http://www. 

DNA nanotechnology 


DNA nanotechnology 

Part of a series of articles on 

Molecular self-assembly 

Self-assembled monolayer 

Supramolecular assembly 

DNA nanotechnology 

See also 

DNA nanotechnology is a subfield of nanotechnology which seeks to use the unique 
molecular recognition properties of DNA and other nucleic acids to create novel, 
controllable structures out of DNA. The DNA is thus used as a structural material rather 
than as a carrier of genetic information, making it an example of bionanotechnology. This 
has possible applications in molecular self-assembly and in DNA computing. 

Introduction: DNA crossover molecules 

Structure of the 4-arm junction. 


Left: A schematic. Right: A more realistic model. 

Each of the four separate DNA single strands are shown in different colors 

DNA nanotechnology 


DNA nanotechnology makes use of branched DNA structures to 
create DNA complexes with useful properties. DNA is normally a 
linear molecule, in that its axis is unbranched. However, DNA 
molecules containing junctions can also be made. For example, a 
four-arm junction can be made using four individual DNA strands 
which are complementary to each other in the correct pattern. Due to 
Watson-Crick base pairing, only portions of the strands which are 
complementary to each other will attach to each other to form duplex 
DNA. This four-arm junction is an immobile form of a Holliday 

Junctions can be used in more complex molecules. The most 
important of these is the "double-crossover" or DX motif. Here, two 
DNA duplexes lie next to each other, and share two junction points 
where strands cross from one duplex into the other. This molecule 
has the advantage that the junction points are now constrained to a 
single orientation as opposed to being flexible as in the four-arm 
junction. This makes the DX motif suitible as a structural building 
block for larger DNA complexes. 

A double-crossover 
(DX) molecule. This 
molecule consists of 

five DNA single 

strands which form 

two double-helical 

domains, on the left 

and the right in this 

image. There are two 

crossover points 

where the strands 

cross from one 

domain into the 

other. Image from 

Mao, 2004. [2] 

DNA nanotechnology 


Tile -based arrays 

Assembly of a DX array. Each bar 

represents a double-helical domain of DNA, 

with the shapes representing comlimentary 

sticky ends. The DX molecule at top will 

combine into the two-dimensional DNA 

array shown at bottom. Image from Mao, 

2004. [2] 

DX arrays 

DX, Double Crossover, molecules can be equipped 
with sticky ends in order to combine them into a 
two-dimenstional periodic lattice. Each DX molecule 
has four termini, one at each end of the two 
double-helical domains, and these can be equipped 
with sticky ends that program them to combine into 
a specific pattern. More than one type of DX can be 
used which can be made to arrange in rows or any 
other tessellated pattern. They thus form extended 
flat sheets which are essentially two-dimensional 
crystals of DNA. [4] 

DNA nanotubes 

In addition to flat sheets, DX arrays have been made 

to form hollow tubes of 4-20 nm diameter. These 

DNA nanotubes are somewhat similar in size and shape to carbon nanotubes, but the 

carbon nanotubes are stronger and better conductors, whereas the DNA nanotubes are 

more easily modified and connected to other structures. 

Other tile arrays 

Two-dimensional arrays have been made out of other motifs as well, including the Holliday 
junction rhombus array as well as various DX-based arrays in the shapes of triangles and 
hexagons. Another motif, the six-helix bundle, has the ability to form three-dimensional 
DNA arrays as well. ] 

DNA origami 

As an alternative to the tile-based approach, two-dimensional DNA structures can be made 
from a single, long DNA strand of arbitrary sequence which is folded into the desired shape 
by using shorter, "staple" strands. This allows the creation of two-dimensional shapes at the 
nanoscale using DNA. Demonstrated designs have included the smiley face and a coarse 
map of North America. DNA origami was the cover story of Nature on March 15, 2006. J 

DNA polyhedra 

A number of three-dimensional DNA molecules have been made which have the 
connectivity of a polyhedron such as an octahedron or cube. In other words, the DNA 
duplexes trace the edges of a polyhedron with a DNA junction at each vertex. The earliest 
demonstrations of DNA polyhedra involved multiple ligations and solid-phase synthesis 
steps to create catenated polyhedra. More recently, there have been demonstrations of a 
DNA truncated octahedron made from a long single strand designed to fold into the correct 
conformation, as well as a tetrahedron which can be produced from four DNA strands in a 
single step. 

DNA nanotechnology 


DNA nanomechanical devices 

DNA complexes have been made which change their conformation upon some stimulus. 
These are intended to have applications in nanorobotics. One of the first such devices, 
called "molecular tweezers/ 1 changes from an open to a closed state based upon the 
presence of control strands. 

DNA machines have also been made which show a twisting motion. One of these makes use 
of the transition between the B-DNA and Z-DNA forms to respond to a change in buffer 
conditions. Another relies on the presence of control strands to switch from a 
paranemic-crossover (PX) conformation to a double-junction (JX2) conformation. J 

Stem Loop Controllers 

A design called a stem loop, consisting of a single strand of DNA which has a loop at an 
end, are a dynamic structure that opens and closes when a piece of DNA bonds to the loop 

rm ri2i 

part. This effect has been exploited to create several logic gates. These logic gates 

have been used to create the computers MAYA I and MAYA II which can play tick-tac-toe to 
some extent. 1 J 


Algorithmic self-assembly 

DNA nanotechnology has been 
applied to the related field of DNA 
computing. A DX array has been 
demonstrated whose assembly 
encodes an XOR operation, which 






implement a cellular automaton 
which generates a fractal called 
the Sierpinski gasket. This shows 





incorporated into the assembly of 
DNA arrays, increasing its scope 
beyond simple periodic arrays. 

Note that DNA computing overlaps 
with, but is distinct from, DNA 
nanotechnology. The latter uses 
the specificity of Watson-Crick 
basepairing to 



DNA arrays that display a representation of the Sierpinski gasket 
on their surfaces. Click the image for further details. Image from 

Rothemund et ah, 2004. [14] 

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. 

DNA nanotechnology 


Nano architecture 

The idea of using DNA arrays to template the assembly of other functional molecules has 
been around for a while, but only recently has progress been made in reducing these kinds 
of schemes to practice. In 2006, researchers covalently attached gold nanoparticles to a 
DX-based tile and showed that self-assembly of the DNA structures also assembled the 
nanoparticles hosted on them. A non-covalent hosting scheme was shown in 2007, using 
Dervan polyamides on a DX array to arrange streptavidin proteins on specific kinds of tiles 
on the DNA array. [16] Previously in 2006 LaBean demonstrated the letters "D" "N" and "A" 


created on a 4x4 DX array using streptavidin. L J 

DNA has also been used to assemble a single walled carbon nanotube Field-effect 

n ri 
transistor. 1 J 

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] 


Note: Click on the doi to access the text of the referenced article. 

[1] Created from PDB 1M6G (http://www.rcsb. org/pdb/explore/ 

• Seeman, Nadrian C. (1 November 1999). "DNA Engineering and its Application to Nanotechnology". Trends 
in Biotechnology 17 (11): 437-443. doi: 10.1016/S0167-7799(99)01360-8 ( 
S0167-7799(99)01360-8). ISSN 0167-7799 ( 

• Seeman, Nadrian C. (January 2001). "DNA Nicks and Nodes and Nanotechnology". Nano Letters 1 (1): 
22-26. doi: 10. 1021/nl000182v ( ISSN 1530-6984 (http://worldcat. 
org/issn/1 530-6984). 

• Mao, Chengde (December 2004). "The Emergence of Complexity: Lessons from DNA". PLoS Biology 2 (12): 
2036-2038. doi: 10. 1371/journal.pbio. 0020431 ( ISSN 
1544-9173 ( 

• Kumara, Mudalige T. (July 2008). "Assembly pathway analysis of DNA nanostructures and the construction of 
parallel motifs". Nano Letters 8 (7): 1971-1977. doi: 10. 1021/nl800907y ( 

DNA nanotechnology 


nl800907y). ISSN . 

• Winfree, Erik; Liu, Furong; Wenzler, Lisa A. & Seeman, Nadrian C. (6 August 1998). "Design and 
self-assembly of two-dimensional DNA crystals". Nature 394: 529-544. doi: 10.1038/28998 (http://dx.doi. 
org/10.1038/28998). ISSN 0028-0836 ( 

• 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: 
10.1021/ja982824a ( ISSN 0002-7863 ( 

• 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 ( 
1021/ja0443191). ISSN 0002-7863 ( 

• 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 ( 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 ( 

• Mathieu, Frederick; Liao, Sniping; Kopatsch, Jens; Wang, Tong; Mao, Chengde & Seeman, Nadrian C. (April 
2005). "Six-Helix Bundles Designed from DNA". Nano Letters 5 (4): 661-665. doi: 10.1021/nl050084f (http:// ISSN 1530-6984 ( 

• Rothemund, Paul W. K. (2006). "Folding DNA to create nanoscale shapes and patterns". Nature 440: 
297-302. doi: 10.1038/nature04586 ( ISSN 0028-0836 (http:// 
worldcat. org/issn/002 8-0836). 

• Zhang, Yuwen; Seeman, Nadrian C. (1994). "Construction of a DNA-truncated octahedron". Journal of the 
American Chemical Society 116 (5): 1661-1669. doi: 10.1021/ja00084a006 ( 
ja00084a006). ISSN 0002-7863 ( 

• Shih, William M. ; Quispe, Joel D. ; Joyce, Gerald F. (12 February 2004). "A 1.7-kilobase single-stranded DNA 
that folds into a nanoscale octahedron". Nature 427: 618-621. doi: 10.1038/nature02307 (http://dx.doi. 
org/10. 1038/nature02307). ISSN 0028-0836 ( 

• Goodman, R.P.; Schaap, I.A.T.; Tardin, C.F.; Erben, CM.; Berry, R.M.; Schmidt, C.F.; Turberfield, A.J. (9 
December 2005). "Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication". 
Science 310 (5754): 1661-1665. doi: 10.1126/science.ll20367 ( 
1120367). ISSN 0036-8075 ( 

• Yurke, Bernard; Turberfield, Andrew J.; Mills, Allen P., Jr; Simmel, Friedrich C. & Neumann, Jennifer L. (10 
August 2000). "A DNA-fuelled molecular machine made of DNA". Nature 406: 605-609. doi: 
10.1038/35020524 ( ISSN 0028-0836 ( 

• Mao, Chengde; Sun, Weiqiong; Shen, Zhiyong & Seeman, Nadrian C. (14 January 1999). "A DNA 
Nanomechanical Device Based on the B-Z Transition". Nature 397: 144-146. doi: 10.1038/16437 (http://dx. 1038/16437). ISSN . 

• Yan, Hao; Zhang, Xiaoping; Shen, Zhiyong & Seeman, Nadrian C. (3 January 2002). "A robust DNA 
mechanical device controlled by hybridization topology". Nature 415: 62-65. doi: 10.1038/41 5062a (http:// ISSN . 

[11] DNA Logic Gates ( 
[12] ( 
[13] MAYA II ( 

• Rothemund, Paul W. K.; Papadakis, Nick & Winfree, Erik (December 2004). "Algorithmic Self-Assembly of 
DNA Sierpinski Triangles". PLoS Biology 2 (12): 2041-2053. doi: 10. 1371/journal.pbio. 0020424 (http://dx. ISSN 1544-9173 ( 

• 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. 

DNA nanotechnology 


org/issn/0269-2139). Link (http://peds.oxfordjournals.Org/cgi/content/abstract/l/4/295) 

• 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 ( 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 ( 

[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). 

", Fully Addressable DNA Tile 
Lattices Formed by Hierarchical Assembly Procedures". Angewandte Chemie 118 (40): 749-753. doi: 
10. 1002/ange. 200690141 ( ISSN 1521-3757 (http://worldcat. 
org/issn/1 52 1-3757). 

[18] Keren, K.; Kinneret Keren, Rotem S. Berman, Evgeny Buchstab, Uri Sivan, Erez Braun (November 2003). 
";302/5649/1380|DNA-Templated Carbon Nanotube 
Field-Effect Transistor". Science 302 (6549): 1380-1382. doi: 10. 1126/science. 1091022 ( 
1126/science. 1091022). ISSN 1095-9203 ( http://www.sciencemag. 







[25] http ://chemistry . asu . edu/faculty/haoyan . asp 



[28] http ://www. cs. duke. edu/~thl/ 






DNA computing 


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 


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. 


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 




• Computational Genes 

See also 

• Peptide computing 

• Parallel computing 

• Quantum computing 


[1] Leonard M. Adleman (1994-11-11). " 
Computation Of Solutions To Combinatorial Problems". Science (journal) 266 (11): 1021-1024. http://www. — 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). 

" the Computational Power of DNA". DAMATH: 
Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science 71. http:// — Describes a solution for the boolean satisfiability 

[3] Lila Kari, Greg Gloor, Sheng Yu (January 2000). " DNA to 
solve the Bounded Post Correspondence Problem". Theoretical Computer Science 231 (2): 192-203. http:// — Describes a solution for the bounded Post correspondence problem, 
a hard-on-average NP-complete problem. 

[4] Computer Made from DNA and Enzymes ( 

[5] Yaakov Benensonl, Binyamin Gil Uri Ben-Dor, Rivka Adar, Ehud Shapiro (2004-04-28). 

" autonomous molecular 
computer for logical control of gene expression". Nature (journal) 429: 423-429. http ://www. wisdom. 

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. 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 

• JB. Waldner (January 2007). Nanocomputers and Swarm Intelligence. ISTE. pp. 189. 
ISBN 2746215160. 

DNA computing 


External links 

• How Stuff Works explanation ( 

• Physics Web (http://physicsweb.Org/article/news/6/3/ll) 

• Ars Technica ( 

• A Bibliography of Molecular Computation and Splicing Systems ( 

• NY Times DNA Computer for detecting Cancer ( 

• Bringing DNA computers to life, in Scientific American ( 

• Japanese Researchers store information in bacteria DNA ( 
php?option=com_rsgallery2&page=inline&id= 1 97&catid= 1 &limitstart= 1 77) 

• International Meeting on DNA Computing ( s. 


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 

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. ^ 



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 


[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. 


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 


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: c . 

Computational epigenetics 



[1] Bock, C; and LengauerT (2008). "Computational epigenetics". Bioinformatics 24 (1): 1-10. doi 

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 

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 


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 


In-vivo crosslinking of protein complexes using photo-reactive amino acid analogs was 


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 


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 


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 

Protein-protein interaction 


See also 


Signal transduction 

Biophysical techniques 

Biochemistry methods 


Complex systems biology 

Complex systems 


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 


Protein nuclear magnetic resonance spectroscopy 

2D-FT NMRI and Spectroscopy 

Fluorescence correlation spectroscopy 

Fluorescence cross-correlation spectroscopy 

Light scattering 



[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 

< 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 ( 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 ( 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 ( 

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/ (http://dx.doi.Org/10.1016/ PMID 16488145. 
[10] Gray JJ (2006). "High-resolution protein-protein docking". Current Opinion in Structural Biology 16: 183-193 

doi: 10.1016/ (http://dx.doi.Org/10.1016/ PMID 16546374. 

[II] KurtW. Kohn (1999). 
" 1043602 3 |Molecular 
Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems". Molecular Biology of the Cell 

Protein-protein interaction 


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 . pdf|A network of protein-protein 
interactions in yeast". Nature Biotechnology 18: 1257-1261. doi: 10.1038/82360 ( 
82360). PMID 11101803. 

[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. 

[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 ( 

15. Charles P. Slichter.1996. Principles of Magnetic Resonance., Springer: Berlin and New 
York, Third Edition., 651pp. ISBN 0-387-50157-6. 

Protein-protein interaction 


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) ( 

• Proteins and Enzymes ( 
BiochemistryandMolecularBiology/Biomolecules/ProteinsandEnzymes/) at the 
Open Directory Project 

• FLIM Applications ( 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 ( 


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 




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 




Metabolic Network Model for Escherichia coli. 

Other species whose interactomes have been studied in some detail include Caenorhabditis 
elegans and Drosophila melanogaster. 



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 

• 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 

• 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 

• It is difficult to match evolutionarily related proteins in distantly related species. 

See also 

Interaction network 
Metabolic network 
Metabolic network modelling 
Metabolic pathway 

Mathematical biology 
Systems biology 


[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. 

[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 ( 
[4] further citation needed 

External links 

• ( A dedicated interactomics web site 
operated under BioLicense. 

• ( An interactome wiki site. 

• PSIbase ( Structural Interactome Map of all Proteins. 

• ( An omics portal site that is openfree (under BioLicense) 

• ( A Genomics wiki site. 

• Comparative Interactomics analysis of protein family interaction networks using PSIMAP 
(protein structural interactome map) ( 
content/full/2 1/1 5/3234) 

• Interaction interfaces in proteins via the Voronoi diagram of atoms (http://www. ob=ArticleURL& udi=B6TYR-4KXVD30-2& user=10& 



_coverDate=l 1/30/2 006&_rdoc = l&_fmt=&_orig=search&_sort=d&view=c& 


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: 


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 ( 

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 



"morphogenesis," which is the 
process that gives rise to tissues, 




Developmental biology is that 
branch of life science, which deals 
with the study of the process by 




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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 



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 

Lancelet Branchiostoma lanceolatum 
Ascidian Ciona intestinalis 
Sea urchin Strongylocentrotus purpuratus 
Roundworm Caenorhabditis elegans 

Fruit fly Drosophila melanogaster (Drosophila embryogenesis) 
Plants (Plant embryogenesis) 

Arabidopsis thaliana 

Snapdragon Antirrhinum majus 

• 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 


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 

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 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 


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 



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 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 


Body plan 

Cell signaling 



Evolutionary developmental biology 

Plant evolutionary developmental biology 


Fish development 

Cell signaling networks 

Developmental noise 



Gene regulatory network 


Signal transduction 

Transcription factor 

Developmental biology 



[I] Haffter P, Niisslein-Volhard C (1996). "|Large scale 
genetics in a small vertebrate, the zebrafish". Int. J. Dev. Biol. 40: 221-7. PMID 8735932. http://www. 

[2] AmayaE (2005). "". Genome Res. 15 (12): 1683-91. 

PMID 16339366. 
[3] Keller G (2005). " stem cell differentiation: 

emergence of a new era in biology and medicine". Genes Dev. 19 (10): 1129-55. PMID 15905405. http:// 
[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 ( 

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). 


body". Anat. Embryol. 197 (1): 1-8. PMID 9462855. 

bibs/7197001/71970001. htm. 
[9] Marshall H, Morrison A, Studer M, Popperl H, Krumlauf R (July 1996). 

"|Retinoids and Hox genes". FASEBJ. 10 (9): 

969-78. PMID 8801179. 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 ( 

001321). PMID 3521645. 

[II] Fujimoto K, Ishihara S, Kaneko K (2008). 
" 1 |Network evolution of 
body plans". PLoS ONE 3 (7): e2772. doi: 10. 1371/journal.pone. 0002772 ( 
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 ( PMID 

[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 ( PMID 12471238. 

External links 

• Developmental Biology of Plants and Animals ( 

• Developmental Biology - 8th Edition ( by Scott Gilbert (online 

Cellular differentiation 


Cellular differentiation 


developmental biology, 

cellular differentiation is 

the process by which a less 
specialized cell becomes a 
more specialized cell type. 



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 



dramatically changes a cell's 




Skin Cells 



of Brain 



(External Layer) 





{Middle 8 Layer] 





Tubule Red Blood 
Cell of Cells 
the Kid nay 

(in Gut) 

-Ended trm- 

f, Internal Layer] 

• # 


Lung 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 


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 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 


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. 


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 


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 


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 


[1] Stocum DL; Amphibian regeneration and stem cells ( 

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 ( 
4/657); Development Vol 104, Issue 4 657-668 

Cellular differentiation 


[3] Dedifferentiation and Regeneration in Bryophytes: A Selective Review ( 

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. 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 ( 

fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=l 5087480); Molecular Interventions 4:81-83, 

[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 (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. 


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. 



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 





mesenchymal cells become epithelial cells and 
at other times epithelial cells differentiate into 



Epithelial-mesenchymal transition). Following 
epithelial-mesenchymal transition, cells can 
migrate away from an epithelium and then 
associate with other similar cells in a new 

' l " "1 


■' '■ 

^H •*. ** i 


""■■I ■ 

• t 


■ - J 

^^"* "" m u 

J* ^ 





& 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. 


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. 



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 


Pattern formation 

French flag model 




Axon guidance 

Eye development 

Polycystic kidney disease 2 

Drosophila embryogenesis 

Manuel DeLanda 


[1] Gilbert, Scott F. (2000). 

http://www.ncbi.nlm. section. 372 1 ''Morphogenesis 
and Cell Adhesion". Developmental biology (6th ed.). Sunderland, Mass: Sinauer Associates. ISBN 

[2] Fata JE, Werb Z, Bissell MJ (2004). 

" 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 ( 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 ( PMID 16524451. PMC: 1413974 (http://www. 141 3974). http://breast-cancer-research. 



External links 

• Artificial Life model of multicellular morphogenesis with autonomously generated 
gradients for positional information ( 

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 

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 


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 

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 


Types of diagnostic studies 

Common isotopes used in nuclear medicine 










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%) 


81m Kr 


13.1 s 


190 (68%o) 



82 Rb 



P + 

511 (191%o) 

3.379 (95%) 


99m T 


6.01 h 


140 (89%o) 



m In 


2.80 d 


171 (90%), 
245 (94%) 




13.3 h 


159 (83%o) 


xenon- 133 

133 Xe 


5.24 d 


81 (31%o) 

0.364 (99%) 


201 T , 


3.04 d 


69-83* (94%), 
167 (10%) 





2.67 d 



2.280 (100%) 




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 


• 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 


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 


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 



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 ( 

External links 

• International Atomic Energy Agency (IAEA), Division of Human Health, Nuclear Medicine 

• RADAR Medical Procedure Radiation Dose Calculator and Consent Language Generator 

• Society of Nuclear Medicine ( 

• Brochure: What is Nuclear Medicine? ( 

• Resource center: information about nuclear medicine ( 
index.cfm?PageID=6309&RPID = 1089) 




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. 


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 


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 



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 

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. 


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. 



See also 

• Hyperaccumulators table - 3 

• Radioactivity in biology 

• Radiometric dating 

• Radionuclide cisternogram 


• 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 


• EPA - Radionuclides - EPA's Radiation Protection Program: Information. 

• Interactive Chart of Nuclides L J - A chart of all nuclides 


[1] http 
[2] http 
[3] http 

//world-nuclear, org/info/inf 5 6. html 

//www. html 



Advanced Experimental 
Techniques and Methods 

Positron emission tomography 

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 





concentration in 3-dimensional 
space within the body are then 




analysis. In modern scanners, this 




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. 



To conduct the scan, a short-lived radioactive tracer 
isotope, is injected into the living subject (usually into 


blood circulation) . 




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 ^^ 


Detector Black 

Schematic view of a detector block and 

ring of a PET scanner 

Positron emission tomography 


Processing Unit 

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. 


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 


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A Brain PET / MRI Fusion image 

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 


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 



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 


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 

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 

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. 


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 


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. 


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 


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. 

Positron emission tomography 


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. 


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 


See also 

• Diffuse optical imaging 

• Hot cell (Equipment used to produce the radiopharmaceuticals used in PET) 

• Molecular Imaging 



[2]|"A Close Look Into the Brain". Julich Research Centre. 

29 April 2009. 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 ( 

[4] Technology | July 2003: Trends in MRI | Medical Imaging ( 

articles/2 003-0 70 5 . asp) 
[5] Ter-Pogossian, M.M.; M.E. Phelps, E.J. Hoffman (1975). 

"| A positron-emission transaxial 

tomograph for nuclear imaging (PET)". Radiology 114 (1): 89-98. 

[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 abstract/ 1 6/3/2 10. 
[7] Sweet, W.H.; G.L. Brownell (1953). "Localization of brain tumors with positron emitters". Nucleonics 11: 

[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 (, 
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 ( 
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 ( 

Positron emission tomography 


External links 

• PET Images ( 
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) ( 
2006/1 2/2 l/seeing_is_believing_in_vivo_fu_l.php) 

• The nuclear medicine and molecular medicine podcast ( - Podcast 

• Positron emmission particle tracking ( 
(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, 

• CMS coverage of PET scans ( 

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 


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 




containing such nuclear spins 
are placed in a static magnetic 
field and a very short 




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 


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 

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 


two-dimensional nuclear magnetic resonance spectroscopy (2D-FT NMRS) that allows 
the three-dimensional reconstruction of polymer and biopolymer structures at atomic 


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 


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 

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 


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 


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) 


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 


Earth's field NMR (EFNMR) 

Robinson oscillator 

2D-FT NMRI and Spectroscopy 



[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 ( 

[3] Howstuffworks "How MRI Works" ( 

[4] Peter Mansfield. 2003. Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI (http://www. 

[5] Damadian, R. V. "Tumor Detection by Nuclear Magnetic Resonance," Science, 171 (March 19, 1971): 
1151-1153 ( 

[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). 

" 568902 |MRI without the 
magnet". Proc Natl Acad Sci USA. 103 (34): 12657-8. doi: 10. 1073/pnas. 0605625103 ( 
1073/pnas. 0605625103). PMID 16912110. 

[9] Wu Y, Chesler DA, Glimcher MJ, et al (February 1999). 

"|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). 



[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 (, on December 9, 

[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. 



[17] Protein structure determination in solution by NMR spectroscopy ( 
itool=pubmed_docsum) Kurt Wuthrich. J Biol Chem. 1990 December 25;265(36):22059-62. 

[18] php?type=img&img=Cardiac%20Infarct%20Short%20Axis%20Cine%204 


• 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 ( 

• Protein structure determination in solution by NMR spectroscopy (http://www.ncbi. Abstracts 
list_uids=2266107&query_hl=33&itool=pubmed_docsum) Kurt Wuthrich. J Biol Chem. 

2D-FT NMRI and Spectroscopy 


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 ( 
1991/ernst-lecture.pdf), on December 9, 1992. 

Peter Mansfield. 2003. Nobel Laureate in Physiology and Medicine for (2D and 3D) MRI 

D. Benett. 2007. PhD Thesis. Worcester Polytechnic Institute. PDF of 2D-FT Imaging 
Applications to NMRI in Medical Research. ( 
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. 

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 

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). 

" 568902 |MRI 

without the magnet". Proc Natl Acad Sci USA. 103 (34): 12657-8. doi: 

10. 1073/pnas. 0605625103 ( PMID 


Wu Y, Chesler DA, Glimcher MJ, et al. (February 1999). 

" 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 ( 

2D-FT NMRI and Spectroscopy 


1073/pnas.96.4.1574). PMID 9990066. PMC: 15521 (http://www.pubmedcentral.nih 
gov/articlerender.fcgi?tool=pmcentrez&artid= 15521). 
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 ( - 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, ( 
biomems/hguto wsky . pdf ) 

• 3D Animation Movie about MRI Exam ( 

• International Society for Magnetic Resonance in Medicine ( 

• Danger of objects flying into the scanner ( 
flying_obj e cts . html) 

Related Wikipedia websites 

Medical imaging 

Computed tomography 

Magnetic resonance microscopy 

Fourier transform spectroscopy 


Chemical imaging 

Magnetic resonance elastography 

Nuclear magnetic resonance (NMR) 

Chemical shift 


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 ( on 
PlanetPhysics (, which is licensed under the GFDL. 

NMR spectroscopy 


NMR spectroscopy 




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 




important applications for the organic 
chemist are proton NMR and carbon-13 
NMR spectroscopy. In principle, NMR is 
applicable to any nucleus possessing 

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 

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 


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 

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 


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. 



Intensity Ratio 

Singlet (s) 


Doublet (d) 


Triplet (t) 


Quartet (q) 








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 


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 

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 


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 


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 


[1] James Keeler. "Chapter 2: NMR and energy 
levels" (reprinted at University of Cambridge). Understanding NMR Spectroscopy. University of California, 
Irvine. 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 ( Practical guide to 
NMR, in particular protein NMR assignment 

• James Keeler. cam.|"Understanding NMR 
Spectroscopy" (reprinted at University of Cambridge). University of California, Irvine. Retrieved on 2007-05-11. 

• The Basics of NMR ( - A non-technical overview 

of NMR theory, equipment, and techniques by Dr. Joseph Hornak, Professor of Chemistry 

• NMRWiki.ORG ( project, a Wiki dedicated to NMR, MRI, and EPR. 

• NMR spectroscopy for organic chemistry ( 

• The Spectral Game ( NMR spectroscopy game. 

Free NMR processing, analysis and simulation software 

• WINDNMR-Pro ( - 
simulation software for interactive calculation of first and second-order spin-coupled 
multiplets and a variety of DNMR lineshapes. 

• CARA ( - resonance assignment software developed at the Wiithrich 

NMR spectroscopy 


NMRShiftDB ( - open database and NMR prediction 


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 

The Michelson spectrograph is similar to 






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 






effectively converting the time domain into 





measurements of the signal at many 
discrete positions of the moving mirror, the 
spectrum can be reconstructed using a 
Fourier transform of the temporal 


of the 




light source 



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 


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 


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 


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 ( 

External links 

• Description of how a Fourier transform spectrometer works (http://scienceworld. 

• The Michelson or Fourier transform spectrograph ( 

• Internet Journal of Vibrational Spectroscopy - How FTIR works ( 

• Fourier Transform Spectroscopy Topical Meeting and Tabletop Exhibit (http://www.osa. 

Nuclear Magnetic resonance imaging 


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 






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 


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 


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 

spin-1/2 nuclei, such as H, 

there are two spin states, 

sometimes referred to as "up" 

and "down". Nuclei such as 

C have no unpaired neutrons 

or protons, and no net spin; 

however, the isotope 



(referred to as "carbon 13") 

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 

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 


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. 


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 


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 

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 


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. 



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 



*(*) = 

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 

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 


Example of a pulse sequence 






receive - 










' l "FE 





I ! 



Simplified timing diagram for two-dimensional-Fourier-transform 

(2DFT) Spin Echo (SE) pulse sequence 

In the timing diagram, the 
horizontal axis represents 






amplitude of radio frequency 




amplitudes of the three 

orthogonal magnetic 


gradient pulses; and (bottom 
row) receiver analog-to-digital 




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 


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 


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 

Magnetic gradient 


Scanner bore 

Body port specific 
receive coll 

Longitudinal section 

Scanner table 

Schematic of construction of a 
cylindrical superconducting MR 



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 


• 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 

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. 



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 








Nuclear Magnetic resonance imaging 


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 



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 

Nuclear Magnetic resonance imaging 


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 ^ 


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. 

Nuclear Magnetic resonance imaging 


Basic MRI scans 

Comparison of Different Types of MR Contrast 



<math>T_l </math> 

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. 

Nuclear Magnetic resonance imaging 


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 

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. 

Nuclear Magnetic resonance imaging 


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 

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 

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. 

Nuclear Magnetic resonance imaging 


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 



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). 

Nuclear Magnetic resonance imaging 


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. 

Nuclear Magnetic resonance imaging 


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 

Nuclear Magnetic resonance imaging 


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 

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. 

Nuclear Magnetic resonance imaging 


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 

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. 


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. 

Nuclear Magnetic resonance imaging 


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 

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 

Nuclear Magnetic resonance imaging 


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 

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 

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 


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. 

Nuclear Magnetic resonance imaging 


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 


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 


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. 

Nuclear Magnetic resonance imaging 


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 


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. 

Nuclear Magnetic resonance imaging 


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 

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. 


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 


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 


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 


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) 


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 



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