I

p. '!/■

- p

*

l :3

.

-

.--';

"I

I

; :, $

y y %

itf

;

« $■

.

j

BIOPHYSICS

E. J. CASEY

A*

BIOPHYSICS

Concepts and Mechanisms

REINHOLD BOOKS IN THE BIOLOGICAL SCIENCES

Consulting Editor PROFESSOR PETER GRAY

Department oj Biological Sciences 1 niversity of Pittsburgh Pittsburgh, Pennsylvania

CONSULTING EDITOR'S STATEMENT

It is unfortunate that many students of biology regard biophysics as an esoteric and "•difficult" subject. The introduction of Professor Casey's "Biophysics: Concepts and Mechanisms'1 to the Reinhold Books in the Biological Sciences should do much to dispel this view. Certainly, if every premedical student had a course in biophysics — and certainly no better book than Casey's exists for that purpose today — he would find his subsequent struggles with physiology enormously simplified. This is not to suggest that Professor Casey either dilutes or oversimplifies his subject. The simplicity of this book lies in the transcendent clarity and utter logic of the presenta- tion. A brief introduction to the necessary mathematics starts the book. This leads to a discussion of the physical forces exemplified in man, of mat- ter waves, electromagnetic radiations, and radioactivity as they apply to biological research. The author then passes to big molecules, and through them to an introduction to bioenergetics and the speed of biological proc- esses. The chapter on biophysical studies on nerve and muscle that follows draws point to all that has come before. The chapters on ionizing radiations and biophysical control excellently round out the broad scope of the book. All this, it must again be emphasized, is couched in language intelligible to any interested science major. I feel confident that the physicist, clinician, and biologist will find this book an ideal synthesis of an exciting interdis- ciplinary science.

Peter Gray

Pittsburgh, Pennsylvania

October, 1962

c ■

BIOPHYSICS

Concepts and Mechanisms

\

E. J. CASEY

:

University of Ottawa

Head, Power Sources Section

Defence Research Chemical Laboratories

Ottawa, Canada

^

REINHOLD PUBLISHING CORPORATION, NEW YORK

Chapman & Hall, Ltd., London

Library of Congress Catalog Card Number 62-21000

Printed in the I 'mted States of America

TO

MY WIFE, MARY

MY PARENTS

and MY CHILDREN

Preface

This book is primarily intended to provide the student of biological sciences or of medicine with a substantial introduction into Biophysics. The subject matter, discussed in the Introduction, has been carefully chosen during ten years of teaching the subject. During this time the author has watched, in the literature, the subject begin to crystallize out from a rather nebulous mass of ideas and practices; and at the same time he has been able to observe what the students of this discipline require. Therefore, the book has been written with the needs of both student and teacher in mind, with the hope that this presentation of the choice of subject matter and the method of presenting it will be useful to others.

Three objectives have been kept in mind in the presentation: (1 ) to build up from the easy to the difficult; (2) to make the presentation interesting; and (3) to unify it. Accordingly, the book generally increases in difficulty from an oriented review with pertinent examples in the first part, through more difficult material in the middle and later parts. Occasional relaxations, which reduce the information rate and afford occasions for exemplification with biological material, are included. A rather vigorous insistence on dimensional analysis has been hidden in the presentation, in the attempt to make the concepts and definitions precise. Following early definition, different units and methods of expressing them are used, so that the reader will not be awed by them when he studies further elsewhere. Wherever possible, recent work is introduced.

Since the name "Biophysics" means so many different things to so many different people, the big difficulty has been to decide what not to write. In the interests of a unified presentation within a two-semester book, the limits chosen were concepts and mechanisms, with a minimizing of the method- ology which has already been treated in elegant fashion by others.

There are some novel features about this book. The author has found them useful in his classes and would be pleased to receive the reader's opinions. Although bioenergetics in the broad sense of the term permeates the major part of the book from Chapter 2 through Chapter 9, it reaches its peak of interest in Chapter 7 in a conceptual presentation where the

IX

x PREFACE

rigor of thermodynamics is sacrificed in favor of the development of a useful impression containing the necessary relationships: and these are illustrated. The electromagnetic spectrum (Chapter 4) and the matter wave spectrum (Chapter 3) are both surveyed, and stress is placed on those fractions which interact with (exchange energy with) biological material. The treatment of the effects of ionizing radiations (Chapter 9) surveys the hierarchy of struc- tures, from effects on simple molecules rrght up the scale to man. The unified treatment of speeds (Chapter 8) attempts to show similarities and differences of mechanisms among all rate processes: chemical reactions (catalyzed), fluid flow, diffusions, and electrical and heat conductance. The apparatus of physical control is described in Chapter 10; and in Chap- ter 11 the bases of control biophysics are introduced in terms which attempt to span the bridge between computer technology and brain mechanisms. The author has not hesitated to introduce a difficult concept if it would later serve a useful purpose, but has tried to get the reader through it in a simple manner.

Because the scope is so broad, depth in every part of the subject could not be achieved in a book of this size. However, the bibliography is substantial, and further reading is explicitly suggested in those cases where the proper direction is not obvious.

The chief inspiration for this work was the late Dr. Jean Ettori, Associate Professor at the Sorbonne and Professor of Biochemistry at the University of Ottawa. Known to his students as "the man who always had time," he died a hapless victim of cancer in 1961, at the age of 56. This man, who had gifts of vision in the biosciences as well as deep humility and love for his students, introduced the author to this subject and emphasized the need for what he called a "psychological presentation."

The following colleagues, all specialists in their own right — in chemistry, physics, or the biosciences — read parts of early drafts of the manuscript and made many helpful suggestions: Dr. C. E. Hubley, Prof. A. W. Lawson, Prof. L. L. Langley, Dr. J. F. Scaife, Prof. M. F. Ryan, Dr. S. T. Bayley, Mr. G. D. Kaye, Mr. G. T. Eake, and Dr. G. W. Mainwood. Several other close colleagues helped by catching flaws in the proof.

Mrs. Lydia (Mion) Labelle and Miss Nadine Sears struggled through the typing of a hand-written manuscript, Miss Sears in the important middle and late stages, and produced something which Mrs. Dorothy Donath of Reinhold could further mold into a finished text. The perceptive Miss Rosemary Maxwell turned out the best of the line drawings, and these in turn illustrate her talent.

The author has had the encouragement of Dr. J. J. Lussier, Dean of the Faculty of Medicine, University of Ottawa, and of Dr. H. Sheffer, Chief

PREFACE xi

Superintendent of the Defence Research Chemical Laboratories, Ottawa, where the author carries on a research program in the interests of National Defence.

E.J. Casey

Ottawa, Canada October, 1962

Contents

PREFACE ix

INTRODUCTION 1

Scope 1

Subject Matter — a classification 3

Method of Presentation 3

1. THE SYSTEMS CONCEPT AND TEN USEFUL PILLARS OF MATHEMAT-

ICAL EXPRESSION 6

The Systems Concept: introduced in general terms 6 The Ten Pillars: variable, function, limits, increments, instanta- neous rate of change; the differential and integral calculus; distribution of observations; expression of deviations; in- dices and logarithms; infinite series 8

2. SOME PHYSICAL FORCES EXEMPLIFIED IN MAN 26

Mechanical Forces: Newton's laws; units; levers; compressed

gas 27

Osmotic Force: properties; water balance 35

Electrical Forces: bioelectrics; colloids; intermolecular forces;

hydrogen bond 38

Generalized Force 44

3. MATTER WAVES; SOUND AND ULTRASOUND 47

Properties of Matter Waves: definition and illustration; absorp- tion 48 Sensitivity of a Detector and the Weber-Fechner Law 54 The Body's Detectors of Matter Waves: ear; mechanoreceptors 56 Speech 59 Noise 59 Physiological Effects of Intense Matter Waves: applications; therapy; neurosonic surgery 60

XIII

CONTENTS

ELECTROMAGNETIC RADIATIONS AND MATTER 67

The Structure of Matter: elementary particles; atomic structure; the nucleus; molecular structure and binding 68

Electromagnetic Radiation: nature; spectrum; absorption 76

Some Interactions of Electromagnetic Radiations and Living Matter: warming (infrared); visible (twilight and color vision); photochemical (ultraviolet); ionizing (X and gamma) 82

Microscopy: optical microscope (interference and phase con- trast); electron microscope 95

5. RADIOACTIVITY; BIOLOGICAL TRACERS 102

Ionization and Detection: positive ions; electrons; gamma rays;

neutrons 104

Disintegration (Decay): half-life; energy distribution; decay

products 112

Penetration of the Rays into Tissue 116

Uses as Biological Tracers: of molecular reactions; of fluid flow;

in metabolic studies; radioactive mapping 1 17

BIG MOLECULES— STRUCTURE OF MACROMOLECULES AND LIVING

MEMBRANES 125

Structure: crystalline macromolecules; dissolved macromole-

cules (static and dynamic methods); living membranes 126

Isomers and Multiplets: electron transitions and triplet states 143

Replication and Code-Scripts: DNA and RNA; coding theory 147

Mutations and Molecular Diseases: hemoglobins; others 156

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS 161

Laws (3) of Thermodynamics: statements; heat content of foods;

free energy; entropy 163 The Drive Toward Equilibrium: free energy released; role of

adenosine triphosphate, the mobile power supply 175 Redox Systems; Electron Transfer Processes: Nernst equation;

indicators and mediators 179

Measurement of A H, A F, and T A S 184

Concentration Cells; Membrane Potentials 185

Negative Entropy Change in Living Systems 187

CONTENTS xv

8. SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 192

General Principles: equilibrium us steady-state; rate-control- ling steps 193

Chemical Reaction Rates: effects of concentration and tempera- ture; the specific rate constant; catalysis by enzymes 195

Diffusion; Osmosis: diffusion coefficient; permeability con- stant 207

Fluid Flow: fluidity; laminar and turbulent flow; properties of plasma and of blood 212

Electrical Conductance: specific conductance; volume conduc- tor; EEG and EKG 219

Heat Conduction: heat production; heat loss 224

Formal Similarity and Integration of Five Rate Processes 230

Weightlessness 231

9. BIOLOGICAL EFFECTS OF IONIZING RADIATIONS 234

Dosimetry: dose units and measurement 236

Primary Effects: direct vs indirect; on molecules; oxygen effect 241

Biophysical Effects: coagulation; modification of transport prop- erties 245

Physiological Effects: sensitivity of cells; microirradiation of cells; irradiation of organs and tissues 247

Effects of Whole-Body Irradiation: present state of knowledge; therapy 254

10. BIOPHYSICAL STUDIES ON NERVE AND MUSCLE 262

Transient Bioelectrics in Nerve: historical review; tracer and voltage clamp techniques; cable and permeability theories; in central nervous system 262

Molecular Basis of Muscle Contraction: damped helical spring; energetics; structure; molecular kinetics of contraction 277

Effects of Environment on Control 290

11. THE LANGUAGE AND CONCEPTS OF CONTROL 295

The Systems Concept Redefined: information; entropy; measure- ment and noise; feedback; memory; implementation; control 296

Analogies: digital nature of nerve propagation; digital and analog computers 305

XVI

CONTENTS

The Computer in Biological Research: a study on the kinetics of iron metabolism 309

EPILOGUE— A PERSPECTIVE 315

TABLES OF COMMON LOGARITHMS AND EXPONENTIAL FUNC- TIONS 317

LIST OF SYMBOLS 319

INDEX 321

Introduction

SCOPE

Biophysics is today the youngest daughter of General Physiology, a sister to Biochemistry and Pharmacology. The subject matter is not yet very well defined, as the introduction to almost any of the recent essays on the subject quickly attests. Although the basic skeleton is clear enough — it being the engineering physicist's concept of a "system" suitably molded to describe the living thing — it may be many years before the dust has settled on dis- cussions of what appendages are proper to the skeletal framework of the subject.

Consider some of the pertinent disciplines in terms of Table 1. Biochem- istry and biophysics attempt to describe and interpret the chemical and physical processes of biological materials in terms of the principles of or- ganic chemistry, physical chemistry, and physics. Biophysics is concerned with questions about the physics of biological systems. It has the advantages of less complexity and more certainty than the biological subjects, but has the disadvantage of being limited to only specific aspects of the whole living system. For the human being, biophysics can be thought of as providing a description of his whole physical system from the particular view of physics. For medical research, for the highest forms of medical specialization, and for the general medical practitioner of the years to come, the requirement seems inevitably to be a strong background and experience in the medical arts, coupled with a thorough grounding in the scientific knowledge of medi- cine and the scientific approach to it. The same is true of the biosciences.

The scope of biophysics today is rather broad, if judged by the attitudes of authors of papers in several of the current journals, and in various essays. Yet the master, A. V. Hill, a Nobel prize winner who published his first paper in 1910 and is still active in research and physiology, has cautioned that the use of physical techniques or ideas alone for investigation of bio- logical problems does not of itself make biophysics. He defines the subject as: "the study of biological function, organization, and structure by physical and physiochemical ideas and methods," and then hastens to emphasize that he has put ideas first. He further expands* and drives home the key point as follows:

*From "Lectures on the Scientific Basis of Medicine," Vol. 4, Athlone Press, London, 1954-1955; reprinted inSdence, 124, 1233 (1956).

1

INTRODUCTION

There are people to whom physical intuitions come naturally, who can state a problem in physical terms, who can recognize physical relations when they turn up, who can express results in physical terms. These intellectual qualities more than any special facility with physical instruments and methods, are essential .... Equally essential, however, are the corresponding qualities, intuitions and experi- ence of the biologist .... The chief concern in the development of biophysics is that those [experimental] skills should be acquired by people who start with the right intellectual approach, both physical and biological.

On the question of scope of medical biophysics, Hill says:

... If biophysics is to make its contribution to medicine, it is necessary that most physicians should have some idea at least of what it is about, while some physicians should have a pretty good idea. The ideas and methods of physics and physical chemistry are being applied today and will increasingly be applied, not only directly to physical medicine and radiology, but to neurology, to the study of circulation, of respiration and excretion, and of the adjustment of the body to abnormal conditions of life and work. At longer range, moreover, they will be aimed at the fundamental problems of minute structure and organization, of the physical basis of growth and inheritance, of the ordered and organized sequence of chemical reactions in vital processes, of the means by which energy is supplied and directed to vital ends.

TABLE 1. Disciplines Surrounding Biophysics

o u

CL >.

> a.

.a. |

uUl

V TJ

-a «->

en

>> m

"3d a

C O

'35 £

re l— '

v

s_

<j

c

Clinical Studies

General Biology, Bacteriology, Immunology

Anatomy

Histology, Pathology

Pharmacology, Physiology

Biochemistry, Biophysics

Physical Chemistry, Physics

Mathematics, Philosophy

-a
o
-C

V
B	c
u	z
u=	" ~ ,

c <1>	c
	V
u t/1	—
u—	-a
o	V

	V ■—
-a
r/l	^™
03
(U
'-
u
c

Today, by the very nature of its origin, biophysics reaches into general physiology to some extent. Today, what subject matter is proper to bio- physics, and even more so to medical biophysics, is not unequivocally de- fined. Further, just as did biochemistry, it will probably take 25 to 50 years for the scope of biophysics to evolve into general acceptance.

SUBJECT MATTER

From recent and current literature, and within the scope discussed, it has been possible to arrive at a fair idea of the topics which are termed "Bio- physics."

Table 2, aided by Figure 1, is an attempt to classify the subject matter in a form which lends itself to an integrated presentation. One must realize, of course, that clear-cut distinctions cannot be made, and that each of these subjects must overlap the other to a greater or lesser extent — for all are parts of a system; and these parts interact.

TABLE 2. A Classification of Biophysics

Chapter I. Physical Biophysics ("True" Biophysics)

(a) Classical:

Mechanics, hydrostatics and hydrodynamics, optics and 2, 3 sound in man

(b) Modern:

Radiological physics, both electromagnetic and matter 4, 5, 9 waves; absorption; scatter; radioactive tracers II. Physicochemical Biophysics (Biophysical Chemistry)

(a) Structure of large molecules, colloids, and gels 6

(b) Energetics or thermodynamics:

Energy balance and energy transfer; temperature; food values; electrochemical control of and by redox systems

(c) Kinetics and mechanisms of physical biological processes:

Osmotic flow and water balance; incompressible flow in 8 circulatory systems; membrane differentiation

III. Physiological Biophysics (Physical Physiology)

(a) Classical:

Bioelectricity; brain and heart measurements; volume con- 7, 8, 10 duction; membrane potentials

(b) Modern:

Effects of high energy radiations; effect of physical and 9, 7 thermal shocks (radiation therapy, modern space medi- cine); system control; bioenergetics

IV. Mathematical Biophysics

Biostatistics; computers; cybernetics; growth rates and 1 1

cycles; the systems concept

METHOD OF PRESENTATION

After a review of useful and necessary mathematics, which the author has found to be a pragmatic need and a valuable teaching aid, two chapters

4 INTRODUCTION

have been devoted to Topic I (a) (see Table 2). These are followed by two chapters which introduce Topic I (b). Then after one chapter on Topic II (a), three chapters deal with Topics II (b), 11(c), and III (a), in an attempt to carry the important basic concepts through to useful applications. Syste- matic organization, so necessary in this era of specialization, demands a proper appreciation of the rather simple concepts which exist under the rather terrifying names!

The subject matter of biophysics (expressed as an "Area" of biolog- ical science).

Figure 1

Then the ninth chapter deals with biological effects of ionizing radiations, Topic 111(6), and the tenth with more complicated biophysical subjects which have arisen out of physiology and for which the biophysical approach provides a useful method of organization and investigation.

Of special interest may be Chapter 11, on concepts and mechanisms of control, in which an introduction is given to some of the important conse- quences of the use of the systems concept, principles of control, and informa- tion theory.

Although the purpose of the book is to give physicians, medical students, and students of the biosciences a readable introduction to the concepts of biophysics rather than to make biophysicists out of them, students and prac- titioners of pure science and engineering may relish the zest of a human biological flavor in the presentation.

Some simple, pertinent problems or exercises have been given at the end of each chapter.

References to introductory and time-proven texts, and to some late re- views, have been carefully selected with emphasis on clarity and imagina- tion in presentation; others have been selected for factual content only.

METHOD OF PRESENTATION 5

If the principles to follow are pondered at length, and reillustrated by the reader in other examples of his choice, the clarity of thought, and the true power and scope of the basic principle will become evident.

Conversely, it seems axiomatic, but it is often forgotten, that the serious reader should seek and expect to find in a book such as this a continuous thread of purpose in all the material contained between its covers.

CHAPTER 1

The Systems Concept, and

Ten Useful Pillars of Mathematical Expression

In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to explain new facts of the same kind.

The catch in this criterion lies in the word "simplest. " It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting.

The layman finds such a law as

dx/dt = kd2x/dy2

much less simple than "It oozes," (or "It diffuses," or "It flows"), of

which it is the mathematical statement.

The physicist reverses this judgement, and his statement is certainly the

more fruitful of the two so far as prediction is concerned.

(J. B.S. Haldane.)

THE "SYSTEMS" CONCEPT

In modern science and engineering an almost unbelievably broad and comprehensive use is made of the term "systems" and its various connota- tions. Chemists have long used the term to indicate the collection of chemi- cals— the chemical system — on which an experimenter was working. Biolo- gists have long used the term to indicate the group of materials and events

THE SYSTEMS CONCEPT 7

within the containing walls of the living thing: the biological system, or the living system. It was in the military campaign of ancient times that the idea or concept of control, within the military system, began to creep in. In mod- ern military systems, in educational, government, and business systems, the idea of organization and control by the central authority of the system has been developed. The concept has reached its highest state of definition and description in military defense systems — based principally on the extension of the use of electronic circuitry to other tasks than those performed by the simple oscillators of thirty years ago. Nevertheless, in those days a one-tube affair had all the elements of a modern system : a detector or source of in- formation fed a voltage signal into the grid of the vacuum tube; the signal modified the plate current by exercising a control over the direction of flow of electrons in the tube; the modified plate current passed through an ex- ternal load of resistors, the voltage drop across one of which was fed back into the input grid and exerted instantaneous control of the plate current; while the voltage drop across the rest of the load was used to perform the task assigned — in this case to feed the stable oscillating voltage into further circuitry.

The elements of this system are simple enough: a detector or source of in- formation (grid input), the transmission to a central authority (the grid), the control by the authority of expenditure of energy (in the plate circuit), and feed- back of part of the expended energy into the central authority so that the latter can know whether or not the energy is being expended in the desired manner and make corrections if necessary. One other element which the simple tube circuit does not have is the facility of being able to store informa- tion for use when required. A modern computer has this facility.

The living thing, and man especially, if a self-contained system (Figure 1-1) in this sense, having all the essential elements, with versatility and adaptability as well. The sensory organs (which enable one to see, touch, taste, smell, and hear) are the detectors of relevant information. Nerve is the transmis- sion line to the central authority, the brain, which stores information, ana- lyzes and abstracts the relevant part, decides what to do, and then dis- patches the necessary commands (electrochemical signals) to the nerve for transmission to the muscles (say) which expend energy in response to the command. Both a part of the muscle's expenditure and a continuous ob- servation by the sensory organs feed back information to the brain so that the central authority can know if the commands are being carried out. If not, corrective commands can be dispatched.

Each of the ten chapters to follow is concerned with some aspect of man's operation as a system. He is the most complex system we know, to be sure, and it is not always immediately obvious what is the relation between the detail which we must describe and the over-all systems concept. However,

THE SYSTEMS CONCEPT

detectors

"SYS TEM" Figure 1-1. The Parts of a System.

the reader should always have this organization in the back of his mind dur- ing study of the following pages.

Some of systems engineering can be reduced to mathematical description. Many details of medical physics can be reduced to simple arithmetical or algebraic expression. Hence, in this subject of biophysics, mathematical terminology is very useful, and in fact in some special cases quite necessary, if the length of the description of the subject matter is to be kept within reasonable limits.

INTRODUCTION TO THE TEN PILLARS

Mathematics has been defined as the concise, quantitative expression and development of ideas. It is in this sense that we shall use the material to follow.

Concise, quantitative description of natural phenomena is the goal of the physical scientists. Indeed, Lord Kelvin (1883) has written." "I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science." The approach made in this book introducing biophysics is to use the mathematical method of concise expression wherever possible without allowing the elegance to cloud the facts or ideas being discussed. Cumbersome manipulations have been omitted, and the methods have been used only when they serve in a simple manner to display clearly the material being discussed.

THE TEN PILLARS 9

For subsequent use in the introductory phases of biophysics we now de- fine ten conveniently grouped concepts. Since most of this is review, the presentation is cryptic. Since only the language and the logic, and not the operations, are necessary for future use in this book, we follow the principle so aptly stated by Lord Dunsany: "Logic, like whiskey, loses its beneficial effect when taken in too large quantities."

THE TEN PILLARS

1. The Variable

If so'me entity — it may be a physical property or some other combination of length, mass and time — changes under the influence of a force, that entity is called a variable. There are dependent and independent variables in nature. The value of the independent can be chosen at random, but any variable de- pendent upon that choice is thereby fixed in value.

The ideal gas law, PV = nRT, illustrates this. In a closed vessel of vol- ume V, containing n moles of gas, the independent variable (on the right- hand side of the equation by convention) is the temperature, T. The tem- perature can be chosen at will. However, once T has been fixed, the pres- sure, P, dependent upon T in this case for its value, has also been fixed.

2. The Function

Further, it can be said that P is proportional to T, or varies directly as 7", or P & T; that P vanes inversely as V, or is proportional to 1/F, or P <* \/V. The constant number, R, which serves to equalize the dimensions or units on the two sides, never varies with experimental conditions, contains all our further ignorance of this relationship expressing the equivalence of thermal and mechanical energy, and is one of the universal constants of nature, (7r, the value of the quotient of the circumference of a circle and its diameter is another example). There are constants other than the universal ones — they are simply variables held constant over the course of a particular changing situation. V in the preceding paragraph is an example. They are called "constants of the system."

A relationship between two variables, such that a choice of a value for one fixes the value of the other, is called a functional relationship. In general terms, if we do not know the exact relationship between two variables, y and x say, but we know that one exists, we can say y varies with x, or y is a junction of x, or in shorthand (ormy = f(x).

Nowjy = f(x) is so general that it could describe any functional relation- ship between y and x. In nature we find both rational and transcendental functions. Rationals can be expressed as a sum of simple terms, transcen- dental cannot. Three examples of the former functions are: (a) linear,

10 THE SYSTEMS CONCEPT

(b) parabolic, and (c) exponential. The periodic functions are transcenden- tal (see Figure 1-2).

Figure 1-2. The Graphical Shape of Some Important Functional Relationships Defined

in the Text.

(a) y = kx is a linear rational function and j> plotted against x is a straight line of the form y = mx + b, with b = 0. The ideal gas law, PV = nRT, again can be used as a pertinent example.

(b) y = mx2 -f b is a parabolic rational function. In the case of the area of a spherical cell, the value, A, increases faster than that of the radius, r, so that the plot of A( =y) vs r( =x) sweeps up rapidly in a curve toward higher values of A, as r is increased.

(c) N/N0 = e~kl is an exponential rational function, in this case a decay (minus sign) or lessening, as time / increases, of the fraction N/N0i where JV0 is the value of JV when t = 0; and A; is a proportionality con- stant. This function has less curvature than the parabolic. Radioac- tive decay is an example. The constant, k, can itself be negative. The weight of a growing baby is an example.

(c') y = log x is a cousin of (c), called the logarithmic function. It has the same curvature as (c) but a different node. An example is the voltage across the living cell's wall, a voltage which is dependent upon ratio of salt concentrations inside and outside the cell.

(d) y = k sin / is aperiodic function. The familiar sine wave of alternating current, the volume of the lungs as a function of time, and the pres- sure in the auricle of the heart as a function of time, are all examples.

Figure 1-2 illustrates the four functional relationships.

THE TEN PILLARS 11

These functions are all continuous; that is, at no point does the slope change suddenly from one value to another. It is probable that there are no discon- tinuous functions in nature, although the change in slope may be so sharp as to seem discontinuous in the first and cursory observation. Thus, phe- nomena involving the interface or juncture of two phases, as for example at the cell wall, are examples of rapidly changing continuous functions which at first sight appear to be discontinuous.

3. Limits

If a variable, changing in accordance with some assigned law, can be made to approach a fixed constant value as nearly as we wish without ever actually becoming equal to it, the constant is called the limiting value or limit of the variable under these circumstances.

A circus abounds with examples in which exceeding a limit in either dis- tance or time would mean a severe penalty. Consider the "hell drivers" who ride motorcycles inside a 40-ft cylinder, approaching the top — the limiting height — as closely as they dare, yet never suffering the disaster of actually reaching it. In other words, if y = /(*), and if, as x approaches a, y ap- proaches some value, b, then b is said to be the limit of/(x) when x equals a. In shorthand, for the functional relationship y = f(x), if x — * a as y — * b, then

Lim f(x) = b

x — '0

It is often useful to approach a limiting value and study its properties without having to suffer the embarassment sometimes associated with the limit itself. This concept was introduced by Leibnitz 300 years ago.

4. Increments

A small fraction of any quantity under observation is called an increment. Increment is thus exactly translated as "a little bit of." It is given a symbol, the Greek letter delta, A.

As the variable, x, increases (Figure 1-3) from zero to high values, that amount of x between A and B (i.e., x2 — xx) is "a little bit of" x, and is written in shorthand: \x.

!— *f

i

i r

0 A P B 40mph

Figure 1-3. Increments of Distance and Time, Ax and Af, used in defining velocity, Ax/Af, abouf point P, or dx/dr ai point P.

12 THE SYSTEMS CONCEPT

Increments may be as large or as small as we like. If we reduce the dis- tance between A and B, the value of Ax is reduced; this can continue until Ax is infinitesimally small (so small that we cannot think of anything smaller). Infinitely small increments are called infinitesimals, and are written in shorthand with the Arabic letter "d", i.e., d.v.

Combining the ideas of Sections 3 and 4, it is seen that as A and B ap- proach P, Ax gets smaller and smaller until, at the limit, Ax — ► dx, and it can be made infinitely small. This means that if we view the point, P, from B, we can move B in on P as closely as we please — in fact to an infinitely small distance away — and observe Pfrom as closely as we please. At the limit we observe Pfrom an infinitely small distance away, i.e., as A.v — > 0.

With the concepts of increments and limits we have implicitly intro- duced the concept of continuous number, as opposed to the discrete number which is familiar to us in our unitary, decimal, and fraction systems. Con- tinuous number admits of the possibility of continuous variation of x be- tween A and B; the number of steps can be infinite. Continuous number is involved when a car accelerates from 0 to 40 mph: the car passes through every conceivable velocity between 0 and 40, and not in the discrete jumps which our decimal and/or fraction systems would describe. At best, these latter are but very useful approximations, and can be considered as con- venient, regular stop-off points, or stations, along the path of continuously increasing number.

5. Instantaneous Rate of Change

Any living being is a complex system of interrelated physical and chemi- cal processes. Each of these processes in the "well" being is characterized by a particularly critical rate (speed or velocity) which enables it to fit into the complex system without either being too slow and holding all the other subsequent processes back, or too fast and allowing a runaway of certain subsequent processes. The study of the factors affecting the rates of processes is called "kinetics," and is discussed in detail for some biological processes, in Chapter 8.

Average rate or speed, over some time interval, is often useful; but it is the instantaneous rate, or the speed at any instant, that is most useful for an understanding of these complex, interrelated reactions.

If j; = f(x) and the function is continuous, we may be interested in how- fast y changes at any value of .v. In a diffusion process, for example, y would be a concentration and v the time. The question is: How much is the concen- tration in some particular volume changing per second at some particular second in time? The following three examples, one experimental, one graph- ical, and one analytical, illustrate the use of limits and increments to de- scribe this situation.

THE TEN PILLARS 13

(1) Experimental : To measure the instantaneous velocity of an automobile (refer again to Figure 1-3) requires measurements of distance and time be- tween two stations, A and B. Two observers with stop watches and a tape measure can easily do this. They measure a value of Ax/ At, which is the in- crement of distance covered in an increment of time. But the car is acceler- ating between A and B, and hence Ax/ At is only an average value between A and B, and may be quite different from the velocity as the car passes P. Better values can be obtained the closer the observers are to P, but of course no value can be obtained if both observers are at P because Ax = 0 and At = 0, and 0/0 is indeterminate, or can have any value from — « to + °°. The best value is obtained by taking observations at several values of A and B, at smaller and smaller values of Ax, until a good extrapolation to Ax = 0 can be made. Hence the limit of Ax /At as At approaches zero is the instantaneous velocity at the point, P. In shorthand notation, the instan- taneous velocity at PisLim Ax/ At.

A/— 0

This symbolic description is further simplified by use of the infinitesimal symbols: Lim Ax/ At = dx/dt. Conversely the previous statement is actu-

ally the definition of dx/dt. In other words, dx/dt is the instantaneous rate of change of x as t changes. A very simple experimental check on the method is to ride in a car and note the speedometer reading at point P.

Both of these methods of determining instantaneous rate are exemplified in biological processes.

(2) Graphical: A graph of the function which expresses the volume of the spherical cell, V = 4/37rr3, is shown in Figure 1-4. The question arises: How fast does the volume of the cell change with change in radius at a par- ticular value of the radius, r,? In other words, how "steep" is the slope of the curve, V vs r, at the point, r,?

Slope or gradient is defined by surveyors as "rise"/"run," where "rise" is the vertical height from the base to the top and "run" is the level, or hori- zontal distance from the foot of the hill to the top. The ratio "rise/run" de- fines the value (trigonometric function) of the tangent of the angle enclosed by the level direction and the direction toward the top.

The same is true in analytic geometry, the slope of the straight line join- ing P and P' being given by the ratio of the distances between P and P' as measured along the ordinate and along the abscissa. For example, slope

V2- F,

= AV/Ar.

r~, —

What we want to know is the value of the slope of the straight line which cuts the curve, V vs r, only once and at point P, that is, the slope of the tangent (geometrical figure) at P. This will give the instantaneous rate of change of Fas r changes, at P, or d V/dr at r,.

14

THE SYSTEMS CONCEPT

RADIUS, r

Figure 1-4. Volume of a Spherical Cell as a Function of its Radius. Determination of rate of change of V as r changes, i.e., dV/dr.

This case is now similar to (1) and need not be discussed in detail. A point, P', is chosen; a straight line joining P and P' is drawn, and the value of A V/Ar determined from the graph. At successive points closer and closer to .Pthe same thing is done, until it is more or less evident what will be the limiting value of A V/ A r as A r approaches zero. Once again, Lim A V/Ar =

d V/dr, the slope at P. It turns out that for this case d V/dr = Airr2.

(3) Analytical: A simple example* will illustrate one way in which this can be done algebraically.

The law established by Galileo at Padua governing the free fall of a body (Figure 1-5) toward earth, is expressed as S = 1/2 gt2, where S is the dis- tance fallen, t is the time of fall, and g is the value of acceleration due to gravity (32 ft per sec per sec.) This example is chosen not because of its specific relation to medical physics but because of its simplicity as an illus- tration of the algebraic determination of instantaneous rate of change by means of the method of increments. The experimental and graphical ex- amples, (1) and (2), are limited in that an extrapolation of incremental pro- portions is always necessary. In the algebraic method this is not necessary, but the limit still can be examined from as close in as it is possible to imagine.

*As an alternative one could have considered a child blowing up a balloon, and asked the question: How fast does the area of the balloon change as the radius changes? The area is given by A --= 4irr , also a parabolic function. Less easily conceived examples appear later.

THE TEN PILLARS

15

The question is: What is the velocity of the falling body at the instant it passes the point, S ?

At S, S = 1/2 gt2 -d-1)

At 5 + AS, S + AS = 1/2 g(t + A/)2. Multiplying out the square,

S + AS = 1/2 gt2 + gtAt + 1/2 gAt2 - -(1-2)

Between the two points, then, the value for AS is given by Eq. (1-2)- Eq. (1-1):

AS = gtAt + 1/2 gAt2 The average rate, over a small increment of time is:

AS/At = gt + 1/2 gAt Hence, the instantaneous rate is:

dS/dt = Lim AS/At = gt + 1/2 g x 0 = gt

A/— 0

That is, the instantaneous rate of change of distance with time (or velocity) at the point, S, is:

dS/dt = gt (1-3)

For example, 5 sec after free fall starts, Eq. (1-1) says that the distance fallen is 400 ft; and Eq. (1-3) says that the velocity as it passes the 400- ft mark is 160 ft per sec.

Maximum and minimum values of functions with changing slope and curvature must be given by the values of the function for which the instan- taneous rate of change, or slope, is zero. This can be visualized in the periodic function of Figure 1-2, for example.

6. The Differential and Integral Calculus

It has been seen that, given the explicit form of the "mother" function, it is possible by the method of increments to determine the explicit form of the

s

■ t

^

t + ^t

Figure 1-5. The Falling Body.

16 THE SYSTEMS CONCEPT

expression which describes the instantaneous rate of change-the "daugh- ter " or derived, function. A system of "operations" has also been devel- oped by which the same thing is accomplished. In this sense d/dx is an "operator," operating on y in a specific manner which accomplishes the same result as the method of increments gave us in Example (3) .

Conversely, if the rate of change is given (most often directly from the experiment), it is possible from the daughter equation to reverse the method of increments, and establish and examine the mother equation (Figure 1-6). The process is simply to sum the increments, under special conditions, when they are infinitesimally small. A system of operations has also been worked out for this process. The operator is symbolized as an elongated S , called the "integral sign," f, contrasted against the operator, "d", for the inverse

process.

.-. ^Pj^e_ntio t_i£n

rate of change

Figure 1-6. Definition of Differentiation and of Integration.

Described in the previous Sections 1 to 5 are the basic ideas of the calcu- lus The process of finding from the mother function, F{x), the daughter function, F'(x), which expresses rate of change, is called differentiation, or obtaining the derivative or derived function; the reverse process of summation of an infinite number of values of the derived function, F'(x), to give the mother function, F(x), is called integration or obtaining the integral.

Two more definitions in shorthand will prove to be useful, the second order derivative and the partial derivative. Both are actually quite simple concepts. We often run into a situation in which we wish to express how fast the speed is changing. (Consider the automobile example, given in Section 4, in which we are now interested in acceleration.) Since speed is dS/dt, the rate of change of speed is d/d«dS/dt), which is abbreviated d2S/dt2 with the operator "d," in the numerator squared and the whole differential in the denominator squared. It is obvious that the rate of change of acceleration would be expressed as d'S/dt\ and that higher orders exist, although they are not of common interest to us here.

THE TEN PILLARS 17

Sometimes one or more independent variables (y, z) are kept as constants of the system while another (x) is varied. The rate of change of the dependent variable, 0, as x changes, is expressed as an incomplete or partial derivative. To emphasize the partial character, a rounded operator, d, is used; and the constants of the system are stated as subscripts outside parentheses which enclose the partial derivative. Thus:

(d(f>/dx)y>i

expresses the rate at which 0 changes as x is changed, when y and z are kept constant.

The second-order partial derivative, the "acceleration," is expressed as before:

(d2<i>/dx2)M

This notation is used in all heat and mass transfer- considerations. For instance, note the Haldane quotation which introduced this chapter.

At this stage of development of biophysics (1962), the terminology of the calculus is being used in published work, hence the need for introduction to the bases and terminology of the subject. But explicit descriptions of most biophysical phenomena are very rare; hence there seems to be no need to in- troduce the operational calculus into an introductory book on biophysics at this time. Therefore no attempt has been made to display the actual opera- tions by which either differentiation or integration is accomplished. Opera- tional calculus is treated in detail in many standard textbooks.

7. Distribution of Observations

A great many biological phenomena lend themselves to statistical meth- ods of expression, i.e., age, height, weight, bloodcount, sugar analysis, etc. This is so true that the "average value" over a large number is considered the "normal" value, describing the "normal man." Hence it is instructive to examine some of the methods of statistical expression, and to discuss their reliability.

Statistics has come a long way since the publication in 1662 of John Graunt's "Natural and Political Observations Made upon the Bills of Mortality," a study based on the records kept during the Black Plague in London; and since Sir Edmund Halley (of "Comet" fame) wrote his basic paper on life insurance, which appeared 30 years later. In the 20th century statistical methods have penetrated nearly every field of learning in which numerical measurement is possible. Moroney's book4 gives a delightful in- troduction to the subject.

First of all, there are two factors which will result in a distribution in a number of observations. One is errors in measurement; the other is a real

18 THE SYSTEMS CONCEPT

distribution in what is being measured. Measuring the length of a room with a 12-in. ruler will result in a fairly wide error, and although the mean value of a number of observations should be close to fact, there may be a large uncertainty in an individual measurement. Besides such random errors, there may exist also constant errors which are sometimes very important but too rarely recognized. Suppose the ruler has been made 1/16 in. too short at the factory. If the room were 32 ft long, in addition to the random errors, every measurement would have been 2 in. short: even the mean value cannot be trusted in the presence of a constant error! It is revealing to read the temperatures on several of the thermometers in the laboratory thermometer drawer! Constant errors and the need for calibration become quite obvious. Even under the most carefully controlled experimental conditions, unknown constant errors creep in. In addition, personal bias is always with us, in reality if not in principle.

The variation in the quantity being measured is often called "biological variance." Consider the height of 80 people at a lecture — it usually has a distribution from about 5 ft, 0 in. to 6 ft, 3 in., with the average approxi- mately 5 ft, 7 in. Deviations from 5 ft, 7 in., however, could hardly be con- sidered as errors or abnormalities!

Constant errors are deadly and can result in gross misinterpretations. Analytical chemistry done without proper calibrations is an example. It has been shown to be prevalent even in routine analyses done day in and day out in the hospitals, with large variations in mean values being reported between them — each hospital apparently having its own constant errors! This is embarrassing, but it is a fact. Under these conditions, diagnoses made with reference to some published work from another hospital could easily be wrong. It is necessary continually to be on the alert against con- stant errors, or "biased [not personal] observations," as they are sometimes called.

Random errors and natural distribution in the variable measured can both be treated with statistical methods. The most reliable methods, and in fact the only reliable method in constant use, presuppose that the observa- tions distribute themselves about a mean or average value such that the density of points is greatest at the mean and progressively less and less as the deviation from the mean becomes larger. That is, it presumes a "normal" distribution in the observations. Figure 1-7 shows the normal distribution curve. It can be interpreted two ways:

(1) P represents the number of observations, N, which are Ax units less than the mean;

(2) P represents the probability that any measurement now being made will have a deviation less than Ax from the mean.

THE TEN PILLARS

19

It is axiomatic that any expression of confidence made in terms of normal distribution, presupposes normal distribution; and that any such expression concerning a distribution which is not normal is not only unwarranted, but also useless, and may be quite misleading. There are statistical methods for handling non-normal data, but they are not simple and are seldom used correctly. Mainland's book3 goes into some of these, using examples of medical interest.

-^x

+ ^y.

DEVIATION FROM MEAN VALUE

Figure 1-7. Normal Distribution of Observations. Solid Curve: Area under curve be- tween -a and +a includes 68 per cent of observations; between —2a and +2o, 94 per cent; and between -3a and +3o, greater than 99 per cent. Blocks: Typical Observa- tions of Heights of Thirty People at a Lecture.

8. Expressions of Deviations

The most common method of expressing a number of observations, x, of the same phenomenon is by the common average, or arithmetic mean, x. There are others, such as the median and the mode, which have some use in nearly normal distributions, but only the mean will be considered. Deviations Ax from the mean can easily be computed by subtraction, and then averaged, the result being expressed as the mean deviation Ax from the mean x.

A very common method of expressing the distribution is by the standard deviation, a, defined as the square root of the average of the deviations squared:

a = y/Ax2, or a = y^Ax2/n

20 THE SYSTEMS CONCEPT

Bessel's correction is introduced if the number, n, of samples is small (< 30); then

a = j/£ Ax2/(n - 1)

The most probable deviation, r, is that value of the deviation such that one- half the observations lies between the limits ±r.

The relative deviation, usually expressed as a per cent, is the fraction which the deviation is of the observed mean value, i.e., Ax/x.

Each of these has several names. In the case of random errors, "devia- tion" should read "error," of course; Ax is often called the absolute error of the measurement. Relative error is sometimes called per cent error or proportional error. These are discussed in detail, and examples are given, in Mainland's book.

Superposition of Errors. In the determination of a quantity, A, af(x, y, z) which requires measurement of x, y, and z, each with an absolute error, the errors must be superimposed one upon the other, or added; the reliability of the value obtained for A is no better than the sum of the errors in x, y and z- That is, the relative error in A is the sum of the relative errors in the meas- urements oix,y, andz-

9. Indices and Logarithms

In arithmetic the ancient Greeks devised and used a notation, now called that of indices, to express in shorthand the number of times a number is to be multiplied by itself. Thus, "2 multiplied by itself 5 times" (i.e., 2 x 2 x 2x2x2) = 32. This is written in shorthand as 25 = 32. The index, 5, is placed as a superscript to the base number 2.

A number of laws of indices can be shown to exist for the manipulation of such numbers. These laws were observed for cases in which the indices are whole numbers.

Now there is no reason to suppose that the rules would be different for fractional indices, although to multiply 2 by itself 5 1/2 times would really be tricky! Nevertheless, the rules are assumed to apply to fractional indices, as well as to whole-number ones, and further also to algebraic, unknown indices. In general, the laws of indices are as follows:

(\)am = axaxaxaxa m times

(2) ama" = am+n

(3) am/an = am-" if m > n

1 .. or am/a" = it n > m

THE TEN PILLARS 21

(4) (am)n = amn

(5) (ab)m = ambm

(6) {a/b)m = am/bm

Fractional indices are called roots. Thus, ai = y/a, the square root of a; and in general a'/"' = m\/~a, the mlh root of a.

(7) a" = 1

(8) a~" = 1/a"

(9) a" = °o

(10) a~' = 1/a" = 0

Logarithms

Let .4 = a". The index x, which tells how many times the base number a must be multiplied by itself to give A, is defined as the logarithm of A to the base a. In shorthand this statement is given by x = lbga A, where "to the base a" appears as a subscript to the abbreviated "logarithm."

Logarithms are indices and must obey the ten Laws of Indices, just as any other. For example:

log AB = log A + log B

log A/B = log A - log£

log Am = m log ,4

A change of base from base a to base b turns out to be analogous simply to a change of variable. In other words the logarithm to the base, a, is re- lated to the logarithm to the base, b, by a constant, \o%b a. One is a linear function of the other.

This can be shown as follows. Suppose A = a" and A = by, so that ax = by. Then loga A = loga b>, or x = y loga b.

There are two systems of logarithms in daily use in biophysics, as in all other science and technology:

(a) Common logarithms, to the base \0(y = \0" for example), used to simplify the manipulations of multiplication and division, based on rules (2) and (3). The abbreviation is log, or log l0.

(b) Natural logarithms, to the base e (y = ex for example), where e = 2.71828. . . . The base, e, and the functional relationship,}' = e", occur over and over again in man's description of nature, and therefore will be illustrated further. The abbreviation is In, or logf.

22 THE SYSTEMS CONCEPT

Conversion, as described above, is accomplished as follows:

log A = In A

2.303

where 2.303 = log, 10.

10. Infinite Series,- y = y0e ox

A series is any group of numbers, arithmetically related, which differ from each other in some regular and explicit manner. Thus

1+2 + 3 + 4 + 5 + n

is a series. This particular series is divergent, since the larger the n chosen, the greater the sum becomes. There are other series which are convergent, whose value approaches a limit as the number of terms is increased toward infinity. One such convergent series is

x x2 x 3 x 4

1 + — + + '■ + — +

1 2x1 3x2x1 4x3x2x1

This series, for a value of x = 1, simplifies to

1 l2 l3 l4

1 + — + + + +

1 2x1 3x2x1 4x3x2x1

which converges to the numerical value 2.71828 .... as more and more higher index terms are added. In shorthand ex is written for the first, and ex or e for the second series. Thus

X XL X3 X*

and

ex = 1 + — + — + ■ + ■ +

1 2x1 3x2x1 4x3x2x1

1 l2 l3

e = 1 + — + — + + = 2.71828

1 2x1 3x2x1

More generally, when x is preceded by a constant, k, kx is substituted for x :

, , kx (kx)2 (kxy (kxy

e** = 1 + h - — — + — + — +

1 2x1 3x2x1 4x3x2x1

The constant, k, simply tells how slowly the series converges for any particular value of x : the greater the value of k the greater the number of terms which will be necessary to define ekx to a chosen number of significant figures.

Now, when x is the variable, and k constant, we can call its evaluation proportional to jv and write

or y a ekx (1-4)

THE TEN PILLARS

23

The series typified by ekx is the only functional relationship in all of mathe- matics for which its instantaneous rate of change at a value of x is exactly proportional to itself. That is, it is the only function for which both

y a ekx (1-4)

and

dy/d.v « ekx (or « y) (1-5)

are true.

For completeness, if the proportionality constant in Eq. (1-4) is intro- duced,

y =y^ ---(1-4')

and

dy/dx = ky0ekx ,__(l-5')

or

dy/dx = ky

This, however, explains the importance of ex in mathematics. The im- portance in biophysics is that a great many naturally occurring phenomena are observed to behave according to Eq. (1-5'): many chemical reactions, growth, diffusion processes, radioactive decay, radiation absorption phe- nomena, etc. (Figure 1-8).

TIME

Figure 1-8. Two Exponential Relationships: Growth (positive k), and Decay (negative k).

For example, let y be the number of atoms of a given sample which give out a radioactive emanation (alpha, beta, or gamma ray), and x be the time. Eq. (1-4') says that the rate of emanation is always proportional to the num- ber of atoms which are left and are capable of disintegrating, a statement

24 THE SYSTEMS CONCEPT

which, if reflected upon, will become quite obvious because it is not only a "natural" law, an observed law of Nature, but also a logical deduction.

In our examples, most commonly a decay is involved, in this case the decay of a concentration. Thus k is a negative number. If the minus sign is taken out of the k and k replaced by — X, the expression becomes N = N0e~Xl, sometimes written N = N0 exp(-Xt), for radioactive decay, where JV0 is the number of particles present when t = 0.

Figure 1-8 shows the shape of the exponential curve for positive k values (growth), and for negative k values (decay). Note that the former increases to infinity, unless checked by the onset of some other law; and that the latter decays toward zero, reaching zero only after an infinitely long time, although it may be below the lowest measureable value within a very short time. The larger the value of k, the faster the growth curve sweeps upwards, and the sooner the decay curve approaches zero.

PROBLEMS

1-1 : (a) If a student must pass biochemistry, and John is a student, then . . . ?

(b) If y = 2x and Z = y, then what functional relationship exists between Z and*?

(c) Uy =/,(*) and £ = f2(x); and f2(x) = /, (x) -f3(x), then what is the rela- tionship between x andy?

(d) If A °c B, and B °c C, what is the relationship between A and C?

(e) If the weight of a given volume of gas is proportional to density, and if the density is proportional to its pressure, then what is the relationship between weight of a given volume and its pressure?

1-2: Choose at random, alphabetically for example, the heights in inches of 25 students.

(a) Is the distribution normal? Was the sample biased?

(b) What are the average deviation, Ax, and the standard deviation, a?

(c ) What fraction of the sample falls within the mean deviation from the mean?

(d) What fraction of the sample falls within one standard deviation from the mean? If the distribution had been normal, what would have been the fraction?

(e) What fractions of the sample fall with ±2 a and ±3 a? If the distribution had been normal, what would have been the fractions?

1-3: Make a table showing how the distance fallen, the speed, and the acceleration of a parachutist change in the first 5 sec before the chute opens. (Make the calculations for each second.)

Suppose he hits the earth at a velocity of 120 ft per sec without the chute opening. From what height did he jump?

1-4: The decay of Sr90 follows the exponential law N = JV0e~Xl, where N is the concentration of radiating material at any time, t; NQ is the concentration at some arbitrary zero of time; and X is the decay constant of Sr90, namely 0.028 years"1 (i.e., 0.028 is the fraction lost per year).

REFERENCES 25

(a) Make a table showing values of -Xl, e~Xl, and N0e~Xt for various values of / (years), assuming that N0 = 100% at/ = 0.

(b) From the results, make a plot of JV vs t, and estimate the half-life (the time, r, in years, when N = 50% of A0 ).

(c) Sketch decay curves for P32 (t = 14.3 days), I'31 (8 days), C'4 (5100 years), Co60 (5.3 years), Po210 (138 days), and Ra226 (1620 years), all on the same graph. Compare them.

REFERENCES

1. Petrie, P. A., et al., "Algebra — a Senior Course (for High Schools)," The Copp

Clark Publishing Co. Ltd., Toronto, 1960. (See p. 314jffor discussion on incre- ments.)

2. Thompson, Silvanus P., "Calculus Made Easy (Being a Very Simplest Introduc-

tion to Those Beautiful Methods of Reconing which are Generally called by the Terrifying Names of the Differential and Integral Calculus)," 3rd ed., MacMillan& Co. Ltd., London, 1948.

3. Mainland, D., "Elementary Medical Statistics," W. B. Saunders Co., Philadel-

phia, Pa., 1952.

4. Moroney, M. J., "Facts from Figures," 3rd ed., Penguin Books Ltd., Toronto,

1956.

CHAPTER 2

Some Physical Forces Exemplified

in Man

(Mechanical; Osmotic; Electrical)

All physical reality is a manifestation of what force does. On the ques- tion of what force is, science can do no better than to call it by other names. (Truth is a virtue, however inconvenient.)

INTRODUCTION

Force and energy, along with optics and acoustics, are the concerns of classical medical physics, and some of the principles have been understood for well over a hundred years. In this chapter the nature and the units of force are reviewed, and the relationship between force and energy discussed. The transfer of energy is reserved for Chapter 7.

The living system is in a state of continual exchange of force and energy with the environment. What is force? According to Newton (1687), it is vis impressa, an influence, measurable in both intensity and direction, operating on a body in such a manner as to produce an alteration of its state of rest or motion. Generically, force is the cause of a physical phenomenon. It is measured by its effect. Further penetration of the nature of force seems destined to remain a philosophical question, because the range of experi- ment stops at measurement of the effects.

By experiment it is possible to measure the effect of different forces on the same object, and devise a system of interconversion factors by which one kind of force is related to another (for example, mechanical to osmotic). Ef-

26

MECHANICAL FORCES 27

forts to penetrate the generic nature of the "force field" — to develop a uni- fied theory — received much impetus, without much success, during the life of Albert Einstein, but one notices now that efforts at unification are falling off as theorists drift into other problems. Hence the question most funda- mental to all science, biophysics included, viz: "What is force?", seems destined to remain unanswered for a long time yet. It is a more fundamental question even than "What is life?", for life is only one manifestation of force!

MECHANICAL FORCES

Newton's Three Laws of Motion

These three laws are the basic description of mechanical systems. From the simple statements can be inferred many properties of mass and inertia.

First Law: A body at rest tends to stay at rest, and a body in motion tends to continue moving in a straight line unless the body is acted upon by some unbalanced force (F). The property of the body by virtue of which this is true is given the name inertia. The measure of amount of inertia is called the mass (m).

Second Law: A body acted on by an unbalanced force will accelerate in the direction of the force; the acceleration (a) is directly proportional to the un- balanced force and inversely proportional to the mass of the body.

This second law describes the familiar experimentally derived relationship F a ma, or F = kma. If the dimensions of F are suitably defined, this be- comes F = ma. The need to choose the dimensions in this manner results from the fact, discussed earlier, that we really do not know what the nature of force is, but rather do we know only its effects. This is certainly true of the common forces of gravitation, electrostatics, and magnetism. Yet fric- tional force we are able to relate to physical interference of microrough- nesses and physical attraction of two surfaces — and thus have some idea of what this force is. The force exerted by the finger to push the pencil, or the force exerted by the thumb on a hypodermic needle drive home to us a meaning of mechanical force based on its effects.

Third Law: For every physical action there exists an equal and opposite reaction. The recoil of a rifle as the bullet is ejected, and the swinging arms which help man to maintain his balance while walking briskly, are examples.

Careful consideration of the statements themselves will enable the reader to appreciate the far-reaching consequences of these laws, consequences which range from suspension bridges to the molecular interactions of bio- chemistry, from the effects of high centrifugal forces on the pilot of a high- speed aircraft to the simple levers of which the human body in motion is a remarkably complex, though well coordinated, example.

28 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

Units and Dimensions

It is useful now to introduce definitions of certain quantities in mechanics. By the first law, a force is defined as anything which changes the state of rest or of motion in matter. The basic unit of force, in the centimeter-gram- second system, is called the dyne. This is the force which will produce an ac- celeration of 1 cm per sec each sec (1 cm sec-2) on a mass of 1 gram (1 g). All other forces (electrical, etc.) can be related by suitable experiments to this fundamental quantity of motion.

Force gives to mass an energy, a capability of doing work. In the system of mechanics, the amount of energy acquired by a mass under the influence of a force depends upon how long or over what distance the force acts. The energy imparted to 1 g of mass by a force sufficient to give the mass an ac- celeration of 1 cm sec-2 within the distance 1 cm, is called 1 erg. One erg = 1 dyne cm. This is an inconveniently small unit of energy, and a quantity often million (107) ergs has been defined as 1 joule (1 jou).

By contrast with this definition of energy units in the mechanical system, the unit of heat energy, the small calorie, has been defined as the amount of energy which it takes to raise the temperature of 1 g of water 1° C, between 4.5 and 5.5° C, where water is the most dense.* (As the temperature is lowered, water molecules begin to line up in "anticipation" of freezing, and the volume increases; as the temperature is raised, increased thermal energy tends to drive the molecules apart, and the volume also increases). Experi- mentally, by transformation of mechanical motion into heat in a water calorimeter, 1 cal has been found to equal 4.18 jou. One thousand cal, or 1 kilocalorie (1 kcal), has been defined 1 Cal, or large calorie. This is the unit used to describe the energy available from different foods.

Power is the rate at which energy is expended; that is, energy expended per unit time. The basic unit of power is the joule per second, called the watt (w). One-thousand watts is 1 kilowatt (1 kw). One horsepower (1 hp) is equivalent to 746 w or 3/4 kw.

Entergy exists in two general forms, kinetic and potential. Kinetic energy is that possessed by mass in motion. In mechanics potential energy is that possessed by a mass because of its position. In other disciplines potential energy assumes different forms: the energy stored in chemicals, or that stored in extended muscle, or in an electrostatic charge separation across a cell membrane, could be released to do useful work or provide heat.

Heat energy is all kinetic energy. It is the total energy of motion of all the molecules in the body under consideration. Temperature is an indicator of the amount of heat in a body, and can be considered to be the "force-like"

*The amount of heat required to raise 1 g of a substance 1°C is called the specific heat, c. It can be measured under constant pressure (cp) or under constant volume (cy ).

MECHANICAL FORCES 29

factor of heat energy. The accompanying capacitive factor in effect sums up the energies which can go into all the vibrations, rotations, and translations of each molecule. This capacitive factor is called entropy, S. Heat energy is therefore given as the product TS, and 5* must have the units calories per degree, since the product must be simply calories.

Heat energy was chosen over electrical, mechanical, or other forms for no other reason than that it is so common. All forms of energy can be factored into two parts, a potential part and a capacitative part: thus in addition to heat energy, we have force times distance for mechanical energy; voltage times charge for electrical energy; pressure times volume for the mechanical energy contained by a compressed gas; chemical potential times number of moles for chemical energy. Energy and its factors will be considered more fully in Chapter 7.

Kinetic energy of mass in motion is given by force x distance, which has the dimensions (g cm/sec2) cm, or g cm2/sec2. Kinetic energy of motion is also given by the familiar 1/2 mv2, with the same dimensions. Another familiar property of mass in motion is the momentum, M, defined as mv. Hence KE = 1/2 Mv.

Some of these quantities can be illustrated by the example of a 200-lb** football player running at full speed with the ball. His potential energy in the form of food has been reprocessed into glycogen, etc., and stored as po- tential energy. That part ready for rapid conversion is available in the form of the mobile chemical adenosine triphosphate (ATP), whose role as a mo- bile power supply is wondrously general throughout the living system. Dur- ing the motion this chemical energy is being transformed, at least in part, to the mechanical kinetic energy of motion. His KE amounts (speed 100 yds in 12 sec; 1 lb = 454 g) to about 26,000,000,000 (or 26 x 10") ergs, or 2600 jou, about 550 small calories. If he is stopped completely within 1 sec by collision, he will have transferred energy at an average rate during that second of 2600 jou per sec, 2600 w, or just over 3 hp. If that energy all went into heat, it could vaporize about 1 g of water. On the other hand this energy could have been transformed into electricity, and the power delivered could have lighted twenty-four 100-w light bulbs to full brilliance for a sec- ond! A further insight into the power expended in such collisions can be gained if it is remembered that the bulk of the energy is transferred in about 1/10 sec of contact, during which time the power is about 30 hp! It is obvious that, in spite of the delights attached to such athletic pursuits, from the point of view of pure physics alone, they are sheer waste of energy and power which could be used more efficiently to do other tasks. In fact even

** Weight, a force. Since F = ma: 1 lb force = 1 lb mass x 32 ft/ sec2, and 980 dynes force = 1 g force = 1 g mass x 980 cm/ sec2. (1 lb force is the force of attraction between the earth and 454 g mass.)

30 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

at its slowest, when no work is being done, basal metabolism amounts to about 0.1 hp. The human machine needs a minimum of 0.1 hp to keep it alive, and can put out continuously a maximum of about 0.01 hp of useful mechanical work, with occasional surges to several horsepower.

The football player's momentum just before collision was (200/32) x (300/12) = 154 lb sec. If this were transferred in 0.1 sec during collision, the impressed force, defined as rate of change of momentum, dM/dt, was 154/0.1 = 1540 lbs. This can be expressed as a "shock" (force per unit mass) of about 7.7 g, where g is the acceleration of all bodies due to gravita- tional attraction to the earth (32 ft/sec2, or 980 cm/sec2). The value 7.7 g is obtained directly from the second law, viz

J7I 154° 77

a = t m = = 7.7 g

200/g

By contrast, and as further illustration, the passengers on a modern com- mercial jet line experience about 2 g during take-off. The jet pilots for fighter aircraft and the astronauts have been tested up to 18 g. The famous right hand of boxer Joe Louis was said to impart up to 40 g to a stationary and nonelastic target. A laboratory centrifuge will provide a centrifugal acceleration of some thousands ofg; and the ultracentrifuge used in sedi- mentation experiments in which molecular weights of large molecules are obtained, develops up to 100,000 g. Centrifugal motion is convenient for varying at will the inertial mass of a body: e.g., in the human centrifuges in space-research laboratories.

As a machine, man is very versatile. However, he is quite inefficient be- cause of the continuous power being expended to keep him alive when he is not "in use." His highest purely physical role is that of a computer.

Two forces will now be considered: a mechanical force as applied to a lever, and the mechanical force of a compressed gas.

The Lever

A lever is one of a great number of machines — devices for doing work. This particular device permits mechanical energy to be factored into such values of force and distance that some desired mechanical result can be ac- complished. The lever does not create energy, of course, but simply makes the energy more available to do the particular job at hand. The familiar example of the crowbar to dislodge a large stone, using a log as a pry, is an example. In this case a relatively small force applied over a relatively large distance at the hands is transformed into a relatively large force applied over a relatively small distance at the stone. The mechanical advantage is the ratio of the two forces; it is inversely proportional to the ratio of the two dis- tances since Fid] must equal F2d2.

MECHANICAL FORCES

31

The three classes of levers, expressed in terms of the relative positions of applied force, Fa, resultant force, Fr , and fulcrum, with directions denoted by the arrows, are given in a classical example in Figure 2-1.

2nd class

weight of jaw

weight of body

weight of head

Figure 2-1. First-, Second-, and Third-Class Levers.

The muscular-skeletal system of the human body is a complex system of levers. The majority of these are third-class levers. A runner on tiptoe has a second-class lever in his foot: the ball is the fulcrum, Fa is at the heel, ap- plied by Achilles' tendon and the calf muscle, and FT is exerted near the instep. The jaw, the forearm, and the fingers of the hand are all third-class levers. However Jiu-jitsu is a study in first-class levers, and the arm and leg locks used in wrestling are almost invariably first-class levers. While doing push-ups the body is operating as a second-class lever. The pump of an old- fashioned well and a wheelbarrow are second-class levers, and there are countless other examples of each among man's tools. Simple levers were man's first machines.

Compressed Gas

Pressure is mechanical force per unit area (Figure 2-2). Atmospheric pressure is simply the weight force of a column of air 1 cm2 in area and of a height, h, equal to the effective height of air above the earth. From basic definitions P = p gh, where p is the average density over the height, h. The units of pressure are dynes cm-2, and of g, cm sec-2.

However, it is common practice, where differences or ratios of pressure are involved, to ignore the factor, g, which is constant at any particular spot on the earth's surface. The weight of the column of air is about 1 ,050 g or 1 5 lb above 1 in.2 The common unit is 15 lb (force) per sq in. (15 psi) = 1 at- mosphere (1 atm) at sea level.

32

SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

f .. pt +p2 + p3+p4 (pressure = force per unit area)

Figure 2-2. Pressure and Force.

It has been found that 15 psi can support a column of mercury about 30 in. (76 cm or 760 mm) high. That is, if a glass tube of any diameter (the larger the cross-sectional area the larger the force, since the pressure is 15 psi) is mounted vertically in a pool of mercury, and if the air in the tube above the mercury is exhausted substantially to zero pressure, the air pres- sure on the outside of the pool will force the mercury up the tube to a height of about 30 in. above the level in the pool. If the supporting pressure (dif- ference between air pressure on the mercury in the pool, open to air, and on the mercury in the column) is less than 15 psi, the height of the column is correspondingly less. Atmospheric pressure varies with the weather, from about 29 to 31 in. of mercury between very stormy, low-pressure weather and fine, high-pressure weather.

Living systems operate under this continuous pressure of 15 psi, but do not collapse for two reasons. Firstly tissue is about 80 per cent water by weight, and water is nearly incompressible. Secondly, air can pass fairly freely into those interior parts which are not solid or liquid, and the internal gas pressure is about the same as the external. A large reduction in pressure (e.g., 12 psi) over a small area of the skin surface can be tolerated for some minutes without ill effects. On the other hand, pressure-increases up to 327 psi at a new record depth in water of 726 ft were recently tolerated. The cur- rent skin-diving record is 378 ft, where the total pressure, P, is of the order of 12atm!

The total pressure (psi) is given by:

P = Patm + 0.43 D

where Palm = 14.8 psi, D is the depth in feet, and 0.43 is the weight, in pounds, of a column of water 1 in.2 in area and 1 ft high. At the record skin- diving depth, the total force on the body (20 sq ft) is about 270 tons!

The troubles start when pressure changes occur rapidly, such as during collisions or impact. Consider the skin diver equilibrated 200 ft below the

MECHANICAL FORCES 33

surface of the water. An extra amount of nitrogen will be dissolved in all the body fluids, including the blood stream. Henry's law describes how the amount of gas dissolved, w, increases linearly as pressure increases: i.e., w = HP, where H is the proportionality (Henry's) constant. This expresses the condition of the diver at equilibrium with his environment. If now, sud- denly, he rises to the surface, the nitrogen which has diffused into the blood stream is not able to diffuse out fast enough, and will come out of solution in the form of small gas bubbles, which rapidly coalesce to form larger ones. Under the conditions described, the bubbles so formed would be easily large enough to form "air locks" and prevent the flow through the blood capil- laries. This illustration simply shows the physical facts of the condition known as "bends": circulation ceases, waste products of muscle activity ac- cumulate, muscles cannot be reactivated; excruciating pain, paralysis, and death can result. The only treatment is to increase the pressure in a pressure tank in the hope that the nitrogen bubbles will redissolve.

A second problem, and often a more important one, illustrates another physical point. It is a fact that sometimes during fear the individual will hold his breath tightly as he pops to the surface from a considerable depth: since the opening at the epiglottis is small, only a small force by the muscles is necessary to apply the considerable pressure needed to keep this valve closed. Up from even 25 ft, for instance, the external pressure has dropped from 30 psi to 15, and if the extra gas is not exhaled, the excess pressure is a full atmosphere on the delicate walls of the lungs. Punctures, called air embolism, can occur, and cause a condition not unlike pneumonia, in which air-CO, exchange on the lung walls is retarded.

The results are similar in the case of a high-flying airman if he is ejected from the aircraft and is unprotected by a pressurized flying suit; or in the case of a space traveller whose pressurizing equipment fails. In these cases, in which the pressure is suddenly reduced from about 1 atm to (say) 0.01 atm, a second, more serious factor is introduced in addition to the first: the body fluids boil at pressures below about 25 mm Hg at 37°C.

Facts which the anesthetist should know about gases are expounded and illustrated beautifully by Macintosh et al.5; and aside from the ideal gas law, Henry's law, and recollections about thermal conductivity and resistance to flow through tubes — properties which are discussed briefly later — no further discussions on gases are presented in this book. The reader will have erred if he fails to consult Macintosh at this level of study.

Some Important Mechanical Properties

If a mechanical pressure (dynes cm-2) produces deformation, the pressure is called a stress. The amount of deformation, e.g., deformed length divided by the original, unstressed length, is called the strain.

34 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

Elasticity is the property by virtue of which a body resists and recovers from deformation produced by a force. If the elongation, s, is produced by a weight of mass, m, in a sample with cross-sectional area, A, and length, /, the modulus (Young's) for stretching is given by

stress mg /s mgl strain A/ I As

which has dimensions of a pressure, m is high for materials difficult to stretch.

The smallest value of the stress which produces a permanent alteration is called the elastic limit. Concussions, fractures, torn ligaments, and even bruises are examples of tissues having been forced beyond their elastic limit, usually during impact.

Impact resistance, or hardness, can only be measured relatively. It usually is done by dropping a hard steel sphere, or pointed instrument, on the ma- terial, then reading either the diameter of the deformation caused by the sphere, or the depth of penetration of the pointed instrument. Bone, teeth, and nail have yielded useful values for impact resistance.

Impulse is the product of pressure (stress) and time of application (con- sideration of the second law will show that impulse is also equal to momen- tum transferred per unit area). This is the physical description of the im- pact. Impulse measurements during impact applied directly to the brains of animals show that impulses composed of pressures of 30 to 90 psi acting for 1 millisecond (1 msec) or more cause physiological concussion (defined here as an immediate posttraumatic unconsciousness). Further, the impulse necessary to cause such damage increases rapidly with decreasing stress or pressure. There is a minimum time of application, of course, below which no damage is done.

Analysis of stress-strain patterns in the human being has been going on for many years, especially studies on bones in relation to how bones are formed, grow, and are broken; and on lumbar intervertebral discs. Strain in a bone is most accurately measured by an electric wire strain gauge; the electrical resistance of the wire changes with stress. By transverse loading of a femur, for instance, with stresses of ~1 ton/in.2, strains of the order of only 0.0001 in. /in. are found. The bone is remarkably rigid. On the other hand, the discs are relatively easily strained, as they must be if they are to do their job during spinal maneuvers. Strains per disc are of the order of 0.02 in.

On Hydro- (or Hemo-) Statics

It was indicated on page 30 that the gravitational force of attraction of a body to the earth is given by m g, where m is the mass in grams, and g is the acceleration (cm/sec2 ) or the force by which 1 gram mass is attracted to

THE OSMOTIC FORCE 35

the earth at sea level (980 dynes/g). Our goal now will be to show what problem is introduced by the simple facts that man's head is 6 ft away from his feet and he walks upright.

Two fluids circulate independently through the body: blood and lymph. Both move via a canal system. The former is a closed system driven by a pump; the latter is driven by muscle movement along the canals.

Because a column of air 6 ft high, of 1 in.2 cross-section, has negligible weight, there is no difference in the weight force of air at the head and feet. However, the weight of a column of water (or blood) of the same dimen- sions is 2.8 lb, quite an appreciable fraction (12 per cent) of 14.8 psi of at- mospheric pressure. In terms of the mercury manometer (1 atm, 14.8 psi, supports a column of mercury 30 in., or 760 mm high, remember?) this extra pressure at the feet due to the weight of the blood is 120 mm over 760. Hence the pump must force blood along against a 120-mm back-pressure. Add to this a small resistance to flow, mostly in the large arteries and veins in which the total area of flow is relatively small and the flow rate high.

The heart is a pulse pump. It distends, collecting a volume of blood freshly oxygenated in the lungs, closes its inlet valves, and contracts, forcing the blood out through the aorta. The aorta, like the rest of the circulating system, has elastic walls, which, in turn, distend under the hydraulic force impressed by the contracting heart muscles. The pressure-rise in the aorta, for a rather typical stroke-volume of 30 cc, may vary from 30 to 150 mm Hg pressure depending upon the reaction of the walls of the arterial system to the pulse and the physical position of the person. In the highly elastic walls of the young and healthy the value will be small; as the tissues become harder with age, or disease, it will rise.

The maximum value is called the systolic pressure, and is due directly to the factors outlined. It is usually of the order of 120 mm. The minimum value — reached after the walls of the aorta, distended by the stroke from the heart, have relaxed to the original diameter, having forced the blood along the artery-capillary system — is called the diastolic pressure. Typically in a healthy, adult male it is ~80 mm Hg. The mean value is about 100. The pulse period is about 1 sec. Because the veins in the legs are more easily distended than the arteries, most of the venous blood is stored there and re- called when needed. The center of gravity is thus lowered, and storage re- quires less work.

THE OSMOTIC FORCE

What Is It?

One of the most important forces at work in the living system is the os- motic (literally, Greek: "impulse") one. It is the force which drives the dif- fusion of water, nothing more, and is a property of a solution just as are

36

SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

freezing point, vapor pressure, and boiling point. All of these properties have a value which depends only upon the number of solute particles present in the solution. Thus, pure water has no osmotic pressure; and the greater the concentration (c) of alcohol, for instance, dissolved in water, the greater the osmotic pressure. In fact the osmotic pressure, ir, varies directly as the concentration (number of moles, n, per volume, V):

7T = —RT = cRT V

where R is the universal constant and Tthe absolute temperature. Note the analogy with the ideal gas law:

PV = nRT

Hence the former could be considered to be an ideal solution law.

Naturally, the higher the concentration, c, of solute the faster will such a solution diffuse into pure water. However, conversely, the lower the solute concentration the higher is the water concentration, until in the limit, the solution is pure water. Since the laws of diffusion are just the same for water as for any solute, water will diffuse from the solution of higher water con- centration to that of lower water concentration; that is, it will diffuse from the solution of lower salt concentration to the solution of higher salt concen- tration, or, in other words, from the solution of low osmotic pressure to that with high osmotic pressure (see Figure 2-3(a)). It will diffuse from pure water into any solution. The diffusion of water is called osmosis. The direc-

ts

(b)

high TT O

solute '

low TT

Olo ,

X>o °I°Q

o

oU

ola

solvent O

1°

° .net solvent flow

O

>L o ° r\

^■membrane _ O

0:6! o

hydro- static pressure

highTT

(ii)

lowTI0 ^^stretched ibrane

size

erythrocyte

membrane

Figure 2-3. Water Balance, (a) High and low osmotic pressures; (b) osmotic pressure difference balanced by applied mechanical pressure; (i) hydrostatic, (ii) elastic, restor- ing pressures.

THE OSMOTIC FORCE 37

tion of osmosis is determined by the osmotic pressure difference between the two solutions in contact, but otherwise there is no relationship between osmosis and osmotic pressure.

The osmotic pressure can be measured by determining the mechanical pressure which must be applied to the solution of high osmotic pressure so that osmosis ceases. The mechanical pressure might be a hydrostatic one (Figure 2-3 (b) i), an elastic restoring force per unit area (Figure 2-3 (b) ii), or some other.

Water Balance

In the body (mostly water) the balance among tissues is maintained by a curious assortment of mechanical and osmotic forces, dictated in large part by the physical characteristics of membranes which separate the fluids. All living membranes pass water with ease. It is the solute content which deter- mines the osmotic pressure difference between the two solutions separated by the membrane, and this is determined in part by the membrane itself. Some membranes pass everything— water, salts, molecules — excluding col- loids and larger particles; the large intestine is an example. Membranes in the kidney pass water, salts, and many small molecules readily and rapidly. The membrane which forms the cell wall of the red blood cell passes water and salts, and some small molecules readily. Nerve cell membrane passes water and Cl~ readily, but balks at most molecules (its metabolic rate is low), and lets K+ and Na+ through only with difficulty.

Since those species which can pass freely equalize their concentrations on opposite sides, only those which are restricted from passage can give rise to a difference in osmotic pressure. In the erythrocytes, water balance is thus controlled by the difference in soluble protein content between the cellular fluid and the plasma. Since the concentration is slightly greater inside than outside the cell, water runs in. As the cell walls become stretched, the re- storing pressure (the wall is elastic, like a balloon) applies a mechanical pressure on the liquid. An equilibrium is reached at which

7T, = 7T0 + PR

where the 7r's are osmotic pressures inside and outside the cell, and PR is the restoring pressure of the walls of the distended cell. Table 2-1 gives a quantitative illustration of this important point.

When membranes are ill-formed and cannot discriminate as they should, or when metabolic processes produce impenetrable species such as a protein whose concentration is different from the normal, the osmotic pressure dif- ference, 7r, — 7r0 , is not the same, and the powerful osmotic force differs from what it should be. The small mechanical compensation mechanisms (such as the restoring force in the erythrocyte wall) become strained, and edema

38 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

may result. These facts are the physical basis of the salt-free diets and other chemical attempts to control water balance.

TABLE 2-1. The Be	jlance Between Osmotic Pre	ssure Difference and Restoring
Pressu	re in Cell Walls.
Ion content of blood plasma (meq/1) :
Na+	138	ci-	105
K+	4.5	HC03-	25
Ca++	5.2	protein	16 Total: 149.7
Mg++	2.0	po4-3	2.2 /. 7r0 = 7.4 atm
		so4=	0.5
		remainder	1.0
Ion content of i	red blood cells (meq/1) :
Na+	16	ci-	55
K+	96	HCO3-	15 Total: 117
Ca++	0.5	other ions	47 .:. wt = 5.7 atm
Mg++	4.6
PR = 7T0 - IT,	= 1.7 atm	(25.5 psi) exerted by stretched walls of cell.
If cell radius	is 10m (10	"3 cm), total	force exerted by stretched cell wall is
only 0.00005 lb.

ELECTRICAL FORCES

Electrostatic Force

Like the gravitational and osmotic forces, we know little about the nature of electrical and magnetic forces either, but we can go a long way by study- ing and applying their effects.

The basic concept of electrostatics is that of the potential, ^ (psi), at a point. The potential is defined as the work required (hence it is an energy) to bring one positive charge from an infinite distance and place it at the point or position in question. The unit of potential is, therefore, joules/ coulomb.

Potential itself is impossible to measure, but differences in potential can be measured very accurately by the work they can do in the field or volume of space in which they exist — work of repulsion of pith balls, for example, or the work involved in deflecting the needle of a voltmeter or driving electric charges through some closed circuit. The potential difference, ^2 - ^ between two points is usually called " Fjou/cou, or volts."

The term "charge" should be amplified. It is the quantity or amount of electricity in a bundle — whatever electricity is. We know there are, for- mally, two kinds of electrical charge; they are called positive and negative.

ELECTRICAL FORCES

39

Positives repel; negatives repel; but positive attracts negative. Coulomb ob- served that the force of repulsion of like charges increases as the size of each, and decreases as the square of the distance. Thus

F =

ed2

where Fis the force in dynes, <7, and q2 are the charges in coulombs, d is the distance in centimeters, and e is the proportionality constant, called the di- electric constant (Figure 2-4). Unit charge is formally defined through Coulomb's facts: when two like charges are 1 cm apart and repel each other with a force of 1 dyne, each carries unit charge.

DISTANCE x

Figure 2-4. Interaction of Electrical Charges: (a) Coulomb's case; (b) field strength.

Bioelectric Potentials

At the microscopic level the most important potential differences in the living system arise from concentration differences (why they do will be seen later), and these occur almost without exception across living membranes. For example, in heart muscle cell the potential difference or voltage between the inside and outside of the cell, across the cell membrane, is about 85 mv, on the average, and cycles above and below this, as the heart beats.

40 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

The electric field strength (see Figure 2-4) is denned as the voltage gradient, X), dV/dx, i.e., the voltage change per centimeter of effective thickness of membrane across which the force acts. In cells it has been variously esti- mated that the effective part of the membrane is only about 100 angstroms (100 A), 100 x 10-8 cm, thick. The field strength across the membrane is therefore a phenomenal 85,000 v/cm, or over 200,000 v/in.!

Electric field strength enters many phases of biophysics, and will appear often throughout this book, e.g., whenever membranes or bioelectric phe- nomena, such as those which give rise to the electrocardiogram and en- cephalogram, are introduced.

The voltage gradient, TJ, (i.e., electric field strength) is the force which causes charge to flow — for positive charges, in the direction from higher to lower potential. The rate at which they flow (the current, i) is proportional to the forced. Thus

l oc

V

Since the potential difference acts over the same path as the charges flow, the path length can be taken into the proportionality constant, and the result becomes

i = AT amperes

where K is the current if the impressed voltage is 1 v. This is Ohm's law. Transfer of charge is discussed further in Chapter 8.

Colloids

At the microscopic level the most important electrostatic forces are those which help to stabilize colloids. Colloids are suspensions of liquid or solid particles in a liquid medium (water, in our case). The particles are of the order of microns (1/i = 10-4 cm) in diameter, and may be single macro- molecules, heavily hydrated, or collections or agglomerates of molecules. Characteristically, stable colloid particles (which do not agglutinate or precipitate) have excess like charge, and so repel each other. The repulsion promotes stability. The excess charge usually arises ultimately from the fact that the agglomerate contains acidic and basic chemical groups (e.g., — COO-, — NH3+, — P04=) whose extent of ionization at the tissue pH (~7) depends upon electrostatic interactions with other chemical groups nearby in the molecule. Since these interactions will differ from molecule to molecule, a chemical change in the colloid, an increased salt concentra- tion, or a shift in pH can weaken electrostatic repulsion and coagulate the colloid .... This is considered by some to be the mechanism by which anti- bodies work, and to be the reason why the blood groups are incompatible.

ELECTRICAL FORCES

41

Iniermolecular Forces

At the molecular level electrostatic interactions occur of such a profound nature that they are reflected all the way up to the physiology of the system. In this group we discuss not only charge-charge (ion-ion) forces, but also those arising from interactions involving dipoles, and even induced dipoles. With these concepts, along with that of electron dispersion in an atom-atom bond, we can then describe not only the "Coulombic forces" but also the so- called "London-van der Waals forces" operating between big molecules such as lipoproteins; and finally, with the concept of proton (H+) exchange between neighboring groups (two oxygens, for example), we can describe the extremely important "hydrogen bond."

For reasons which are reviewed in Chapter 4, in a molecule which is not symmetric, such as CO, one end accumulates more of the electronic charge than the other. In CO, the oxygen atom has the extra bit of negative charge, and the carbon is left slightly positive, by difference. The molecule has within it a permanent charge separation, and is called a permanent dipole. This and its weaker sister, the induced dipole, are shown in Figure 2-5.

8*

OS-

S'

permanent dipole

i pv i

0^ ^Osi.*NH3\

8*

-^B-

induced dipole

Figure 2-5. Electrostatic Charges in Molecules.

Water is a permanent dipole, its hydrogen ends being positive to the nega- tive oxygen. The — CONH — linkage between amino acids in proteins is also a permanent dipole, as are the — COOH groups of organic acids, and many others.

Although these are small charges, Coulomb's law applies to them, and fairly strong electrostatic forces can exist, firstly between permanent charges and permanent dipoles, and secondly between one permanent dipole and

42 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

another. Water molecules attract each other, dipole to dipole, and give to bulk water a structure of oriented dipoles. Ions attract one end of the dipole and repel the other, and the result is an array of water dipoles oriented radially outwards from a central ion. The dipoles on large molecules can be hydrated by attraction to water molecules. Big molecules can be attracted to each other, or indeed have one part folded back and attracted to another part where two dipoles fall in close proximity, or where one dipole falls close to a charged group. Thus the dipolar character helps to determine not only composition but also structure.

Still weaker forces exist between induced dipoles. Even if the molecule is symmetrical about an atom, a strong positive or negative charge can some- times induce the molecule's electrons to move a bit, so that the charge dis- tribution becomes distorted. Such induced charge separation is called an induced dipole. Interactions between the mutually induced dipoles of two molecules in close proximity are called the van der Waals forces. Further, it is postulated that the electron cloud of a molecule is in continuous motion, continually varying both the size and direction of its dipole. It induces a further dipole in its neighbor, and the new "dynamic" dipole interacts with the old static one in a manner which seems to confer an extra stability on the intermolecular "bond." The extra force of attraction is called the "dis- persion force," first postulated by London in 1930. Since one occurs when- ever the other does, today the mutually induced dipole and dispersion forces of attraction are referred to as the London-van der Waals forces. They are very weak by comparison with Coulombic forces, principally because the charges are not only small but deformable. However, in the absence of charged groups and when two molecules can come into close proximity (< 5 A) at a great many places over a fairly long distance (~15 carbon atoms in each molecular chain), considerable binding between the two has been shown to be accountable on the basis of London-van der Waals forces. Such is the case in lipoproteins in which a long hydrocarbon (and therefore with no polar groups and no permanent dipoles) chain becomes and remains intimately bonded to a polyamino acid or protein molecule. The strength and the sensitivity of this bond to interatomic spacings have been very evident in recent studies of lipoproteins in nerve cell membranes of the cen- tral nervous system. For example, one form of encephalitis is currently thought to be due to a change in binding which occurs as a result of inac- curate protein synthesis and poor binding to its lipid.

Whereas Coulombic forces are fairly long-range forces (al/a'2) the London-van der Waals forces are very short-range ( « \/d7) but become im- portant when the particles approach very close to one another (see Table 2-2).

ELECTRICAL FORCES

43

TABLE 2-2. Dependence of Force and Energy of Attraction Upon Distance Between Particles

Name

Interaction

Force Energy

Proportional to

Coulombic

London-van der Waals

London-van der Waals in long-chain molecular associations

ion-ion	\/d2	\/d
ion-dipole	\/d5	\/d*
dipole-dipole	\/d7	l/d6
dipole-induced dipole or
induced dipole-induced dipole	}/d7	\/d6
(as above)	\/d6	\/d5

The Hydrogen Bond

In the covalent bond two atoms are said to be held together by "shared pairs" of electrons, and the postulate that the electron of a pair can spend part of its time around each atom is thought to confer extra stability on the bond. This is the process known as "exchange." In a similar manner the hydrogen ion of an — OH group, if it finds itself in the vicinity of a second, somewhat negative oxygen, halogen, or nitrogen group may, by thermal agi- tation jump the gap to this second group. Ideally it may continuously os- cillate between the two, and on the average assume a position half-way be- tween them. When this occurs, the strong positive charge is equidistant from two negative charges, is attracted to them both, and so forms a bridge — a weak bond. This is the currently fashionable "hydrogen bond" (Fig- ure 2-6). It is very versatile in the sense that, in tissues especially, which are 80 per cent water, it can be credited with much of the secondary structure

,a^v

■0^

About 5 kcol needed to break I mole of hydrogen bonds I

Figure 2-6. Hydrogen Bond — a Shared Proton.

44 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

of big molecules — for instance, for the paracrystallinity of the regular molec- ular arrays so common in tissue, such as in muscle fiber and in the aqueous humor of the lens of the eye.

Electromagnetic Force

Although we live in the magnetic field of the earth, no information exists on the response of a man to large changes in magnetic-field strength. To small changes there is no response, as far as is known. Many molecular ef- fects are known, however, of which the recent exploitation of the so-called nuclear magnetic resonance phenomena, in which the location of a hydrogen atom in a molecule and the arrangement of atoms in molecular complexes can be learned, are exciting examples.

However, on biological systems the effects of magnetic fields are yet poorly understood. Small animals placed in fairly strong magnetic fields of ~4000 gauss (at $2/gauss, ' 1 lb> of electromagnet/ gauss) show inability to repro- duce. Cell division and growth are inhibited. Interference with the collec- tion of the mitotic apparatus in preparation for cell division is implicated. In this respect the effect of a magnetic field is similar to the effects of X or gamma rays.

The effects of electromagnetic forces — oscillating forces of unknown na- ture, which interact with both electric charges and magnetic poles, and with other electromagnetic forces — are better understood and are most important in the living system. In fact, the more the question is studied, the more it is realized in how many aspects of inanimate as well as animate subjects, electromagnetic forces play an important part.

Usually electromagnetic phenomena are described by their interaction energy, rather than force; this expedient enables us to by-pass their nature, and concentrate upon their effects. An "oscillating potential" permeates electromagnetic energy. It is a periodic function of time (see Figure 1-2). The amount of energy in a packet depends only upon its number of cycles per second.

Because of their importance, Chapter 4 is devoted almost completely to electromagnetic matters.

Yet will all this preoccupation with force, the physicist still is unable to cope with some really big ones, such as political "forces," and economic "pressures." In "The Razor's Edge" (1944), W. Somerset Maugham con- cludes: "Goodness is the greatest 'force' in the world!". . . . Unfortunately, we cannot measure it.

GENERALIZED FORCE

Although temperature is not usually thought of as a force, it is the driving force for heat-energy flow. Discussion on driving forces for several processes which occur in the living system is contained in Chapter 7.

PROBLEMS 45

All forces are, quite literally, ''factors of energy." Thus, a generalized driving force times a quantity yields energy. Some examples are:

Mechanical force x distance = mechanical energy or work

Gas pressure x volume of gas = mechanical energy or work

Osmotic pressure x molar volume = osmotic energy or work

Electrical potential x charge = electrical energy or work

Temperature x entropy = heat energy or work

Chemical potential x concentration = chemical energy or work

The inherent difficulties of considering both temperature in "degrees" (fractions of a length of a liquid metal along a tube!) and chemical poten- tial (actually an energy per unit concentration) as "forces," are expounded further in Chapter 7.

What happens to a biological system when the force responsible for the acceleration due to gravity (g) is removed — that is, becomes weightless — is critically important to future space travel. The meager information on the few human beings who have so far orbited the earth is reviewed in Chapter 8.

PROBLEMS

2-1 : A 200-lb football player is running full speed at a rate of 100 yd in 12 sec. Cal- culate his kinetic energy in ergs; in joules; in calories; in Calories or kilocalories. If he were stopped completely in 1 sec, what power would he deliver during that 1 sec (in watts; in horsepower; in Cal/hr)? Compare this with the basal metabolic rate of 0.1 hp, or 60 Cal/hr (1 lb = 454 g; 1 cal = 4.18 jou; 1 hp = 746 w; 1 jou/sec = 1 w).

2-2: Values of the solubility of nitrogen and oxygen in water are 0.001 50 and 0.00332 g of gas at 1 atm/100 g water, respectively. Approximately how many cubic centimeters of each gas are contained dissolved in the body fluids (200 lb, 80 per cent water) under 1 atm of air (20 per cent oxygen, 80 per cent nitrogen)? Neglect the fact that the solubility of gases is less in salt solutions than in pure water.

An anethetist may use a mixture up to 90 per cent oxygen, but he always re- tains about 5 per cent C02 in the inhaled gas. Why?

2-3: Assuming the total area of the adult human body to be 1 sq yd, calculate the total force due to the atmosphere (pressure 14.7 lb/in.2) on the body. In dynes; in tons force.

Calculate the total force on a skin diver at a depth of 450 ft. Why is he not crushed? What precautions must he take while coming up to the surface? Why?

2-4: Make two tables showing forces of repulsion — in dynes, of two like unit charges, each with 3 x 10"10 electrostatic units of charge — at distances 0.1, 1, 2, 5, and 25 A apart; one table for a medium of air or a vacuum (dielectric con- stant = 1), and the other for an aqueous solution (dielectric constant = 72). Plot the numbers, force vs distance, for each case.

46 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN

REFERENCES

1. Harrington, E. L., "General College Physics, " D. Van Nostrand Co., Inc., New

York, N. Y., 1952.

2. Randall, J. T., "Elements of Biophysics," the Year Book Publ., Inc., Chicago,

111., 1958.

3. Glasser, O., Ed., "Medical Physics," Vol. Ill, Year Book Publ., Inc., Chicago,

111., 1960; papers by Carter, Featherstone, Lipson, et al.

4. Moore, W.J., "Physical Chemistry," Prentice-Hall, Inc., New York, N. Y., 1950.

5. Macintosh, Sir R., Mushin, W. W., and Epstein, H. G., "Physics for the

Anesthetist," 2nd ed., Chas. C Thomas Publ. Co., Springfield, 111., 1960.

6. Robbins, S. L., "Textbook of Pathology With Clinical Applications," W. B.

Saunders Co., Philadelphia, Pa., 1957.

7. Wolf, A. V., "Body Water, " Sci. Amer., 199, 125 (1958).

CHAPTER 3

Matter Waves: Sound and Ultrasound

(On Music and Noise "from

CtoC,"

On Speech and Some Therapy)

According to Sir Richard Paget, human speech began by the performance of sequences of simple pantomimic gestures of the tongue, lips, etc. . . . Consider the word "hither. " The tongue makes the same beckoning gesture, while [one is] speaking this word, as is made with the hand.

(H. Fletcher.3)

INTRODUCTION

Our senses of touch and hearing reveal an environment which contains a bewildering array of matter waves: the breeze; falling raindrops; noise, speech, and music; earth tremors, shock, or blast waves; the vibrations en- countered when riding a horse, or when operating a jack-hammer. Bees and some other insects, and bats too, send and receive, and are guided in flight by very high-frequency matter waves.

Thus waves in matter have a great spectrum of manifestations, uses, and effects. It is the purpose of this chapter to illustrate them, for matter waves and electromagnetic radiations together comprise the most important method of man's continuous exchange of force and energy with his environ- ment. The latter are introduced in Chapter 4. They are fundamentally very different from matter waves, although often confused with them. In

47

48

MATTER WAVES: SOUND AND ULTRASOUND

matter waves the medium itself — solid, liquid, or gas — moves back and forth.

PROPERTIES OF MATTER WAVES

Definition

Matter waves are of two types, which differ only in the direction of the vibration relative to the direction of propagation. In transverse waves the vibration is perpendicular to the direction of propagation (a plucked violin string, for example). In longitudinal waves the vibration is parallel to the direction of propagation (the pressure waves from a blast, or in front of a piston, for example). Most of the matter waves which are of interest here are, like water waves, a combination of both.

The two basic properties are the pressure (force/unit area) of the wave and its rate of change with time. The former is usually called the ampli- tude, \p (dynes/cm2). The latter is usually expressed as the number of times the value of \p cycles back and forth per second, i.e., as the frequency (cycles/sec).

All matter waves, no matter what the shape, can be expressed as a super- position of simple, sinusoidal waves, of the type discussed in Chapter 1.

There are traveling waves and standing waves (Figure 3-1 (a) and (b)). A

<!> 0

biost,

shock,

water waves

auditory region (sound)

ultrasonic region

I I I

'(b)

I

20

21,000

.000,000

CYCLES PER SECOND

Figure 3-1. (a) Traveling Wave Such as Sound in Air; Standing Wave Such as On a Vibrating Violin String; (b) Range of Matter Waves.

PROPERTIES OF MATTER WAVES 49

sound wave moving through air travels from its source and imparts an energy to the receiver. This energy is primarily in the direction of propaga- tion, but with scattering some of it becomes transverse.

By contrast, the standing wave can impart no longitudinal energy — it has none. But it can impart transverse energy to the medium. The generation of the sound by the vibrating violin string is an example.

The intensity, /, of the matter wave is the power delivered by it per unit area. In. other words, / is the rate at which the wave expends energy. All traveling waves move at a certain velocity, v (cm/sec). Hence the product of amplitude (a pressure) times distance is the energy expended per unit area:

w = \p d (dynes/cm2 x cm = ergs/cm2)

The product of amplitude and velocity is the power expended per unit area:

I = \p v (dynes/cm2 x cm/ sec = ergs/cm2 sec)

The intensity or power expended per unit area by the traveling wave, is highest for those media having molecules with the greatest number of de- grees of freedom in which energy can be stored — gases for example. Both the range and speed of sound are highest in solids, somewhat less in liquids, far less in gases. However, for any medium of constant density, p, the ve- locity has a fixed value. This fact results in another useful relationship, that between amplitude (pressure) and intensity (power):

/ = Vlvp

which says simply that power delivered per unit area to any medium is pro- portional to the pressure squared, if velocity and density are held constant.* This (/ cc \^2) is a very useful rule-of-thumb, applicable, it turns out, to all field phenomena.

Useful also is the fact that, although low-frequency waves are easily re- flected and diffracted by air and hence are nondirectional (or will go around corners), high-frequency waves are only slightly scattered by air. Therefore, the latter can be beamed in a preferred direction from a source, and even focused on a particular spot by proper (saucer-like) design of the vibrating source.

*Dimensions:

3 sec cm

= ergs/cm sec

(Work it through.)

50 MATTER WAVES: SOUND AND ULTRASOUND

Illustrations

Frequency

Matter waves have a broad range of frequency, from zero up to the current practical upper limit of about 1,000,000 cycles per sec (cps) in use in some ultrasonic-therapy and submarine-detection studies (Figure 3-1 (c)). The human ear is most sensitive from ^50 to ^10,000 cps; the range of man's ear, however, may be from 20 to 21,000 cps. This, then, is the auditory or sound range. Speech requires 60 to 500 cps. The piano ranges from 27.2 to 4138.4 cps. The great basso profondo, Italo Tajo, could reach a minimum of ~60 cps; the diminutive coloratura soprano, Lili Pons, could hit 1300 cps on a good day. Of course, these are the basic frequencies, and it is understood that a basic frequency generated by any physical vibrator will contain over- tones, or harmonics, which are multiples (2x, 4x, even 8x) of the basic frequency. The quality of the tone is determined by the sum of all the com- ponents: the basic frequency plus its harmonics.

Training and youth combine to produce a receiver which can hear low- power sound up to 12,000 cps. Some musicians can detect overtones from their instruments up to 14,000 cps, but these are few. Most of us can detect frequencies up to 18,000 from a signal generator, if the signal is intense enough, and the odd person can detect up to 21,000 cps. Dogs do it with ease. Porpoises have a phenomenal sonic system in their heads which can sweep frequencies repetitively from a few cycles to many thousands of cycles — both send and receive.

Below and overlapping the auditory range for man is the range (0 to 50 cps) of blast and shock waves, earth tremors, water waves, and the like. The masseur will use vibrations 1 to 50 cps; a ship will roll at 0.1 cps. An air hammer operates at ~ 15 cps, and we hear the overtones.

Above the range of sound, from 20,000 up to > 1,000,000, lies the im- portant range of ultrasound, and the science and technology known as ultrasonics.

Velocity

The speed of matter waves depends sharply upon the medium, and in the case of a gas, its temperature and pressure. For instance, in air at 0°C and 1 atm pressure the speed is 331 meters/sec (mps) (730 miles/hr). In water and soft tissue it is 41 2 times higher than in air, and in solids it goes up to 5000 mps. The velocity of sound through fat is 1440, through muscle 1570, and through bone 3360 mps.

Velocity is independent of frequency; and it is probably just as well, other- wise the low tones of the organ might reach our ears later than the high tones of the same chord!

PROPERTIES OF MATTER WAVES

51

Amplitude and Intensity

There is a minimum pressure and power of matter waves below which the ear cannot detect the wave. This value is about 0.0002 dynes/cm2, an ex- tremely small value because the ear is very sensitive. The corresponding power or intensity limit is ~10 9 ergs/cm2 sec, i.e., ^lO"16 w/cm2! This value places its sensitivity very close to the threshold of the power in heat motion, and thus very close to the minimum background agitation of matter in our environment. The maximum amplitude the eardrum can stand, with- out certain irreparable damage resulting, is ~200 dynes/cm2. Therefore, the range of sensitivity of the ear is phenomenally high, one to a million. It is the most sensitive at 1,000 cps.

The sense of touch, particularly on the fingers and tongue, is not nearly so sensitive, but responds down to much lower frequencies.

To our knowledge, man has no detection apparatus for frequencies above about 20,000 cps. However, there is some evidence that ultrasound can penetrate to the brain and cause psychological aberrations, which may or may not be a result of organic damage.

One of the most convenient ways of generating matter waves of controlled frequency is by means of the vibrating crystal. Certain crystals are piezo- electric— that is, they expand or contract if an electric voltage is applied to contacts with two different crystal faces (Figure 3-2). The amount of the

(o)

£l_

+ V volts

crystol

(b)

applied voltage, V

(c)

time

radiating, vibrati ng surfoce

-target

beamed ultrasound

crystals

Figure 3-2. About Piezoelectric Crystals: (a) Voltage difference is applied between two opposite faces, (b) The length changes as the applied voltage is changed, (c) Varying volt- age, V, gives varying length, y. (d) Concave radiator concentrates matter waves on a target.

52 MATTER WAVES: SOUND AND ULTRASOUND

expansion or contraction increases with increasing applied voltage. Quartz and barium titanate are currently in wide use. If the applied voltage is varied, the crystal shape varies accordingly, or vibrates, and the matter wave so established is transmitted by contact with the medium. The ampli- tude of the vibration is higher the higher the vibrating voltage applied. The frequency of vibration follows that of the electrical signal, if the crystal is not too big. Figure 3-2 illustrates these points.

Apparatus with output which ranges from a few to a million cycles per second, and from next to nothing up to a few hundred watts per square centimeter of crystal, has been built and used.

Constructed with a concave radiating surface (Figure 3-2 (d)), an array of piezoelectric crystals, if properly oriented, can be made to focus an intense beam of matter waves at a point a few centimeters from the radiating sur- face. For example, in recent therapeutic work beams of 1 Mc (1,000,000 cps) were focused on a small target, and delivered energy at a rate (inten- sity) of 8 kw/cm2 of cross-section of the target !

Absorption

If waves are diverging, or being dissipated or scattered, the important gen- eral rule, called the "inverse square law," is obeyed. It says simply that the intensity, /, decreases as the distance from the source gets larger, in such a manner that if, for example, the distance between source and receiver is doubled, the intensity at the receiver falls to only one quarter. Quantita- tively,

I(x) oc \/x2

where I(x) is the intensity at any distance, x, away from the source. See Figure 3-3.

If a parallel beam of matter waves is absorbed by the medium, the rate of absorption at a point is proportional to the intensity at that point; or

dl/dx = -kl

which integrates (see Chapter 1) to

/ = I0e-*

if /0 is the value of / where x = 0.

For the case in which the waves are diverging and also being absorbed, a linear combination of the inverse square law and the absorption law applies. The energy absorbed from the matter-wave beam by the medium contri- butes to the thermal motion of the molecules of the medium. The absorp- tion coefficient, k, is intimately related to several physical properties of the medium.

PROPERTIES OF MATTER WAVES

53

Figure 3-3. Inverse Square Law. Radiation from source S diverges. Intensity (w/cm2) at distance, d, is four times the intensity at 2d because the same radiation is spread through four times the area by the time it reaches 2d.

However, there are two principal mechanisms of absorption of matter waves by tissue:

(a) Fnctional resistance: The momentum of the propagation, which is directional (Fig. 3-1 (a)), is passed to the molecules of the tissue, which be- come momentarily polarized by the pulse of pressure. The directed energy thus received quickly decays into random, nondirectional molecular motion. This mechanism can be called "molecular absorption." It is important at medium and high frequencies.

(b) Elastic reactance of the bulk tissue: Absorption occurs by movement of the bulk material; mass is displaced, and macro-oscillations result in sym- pathy with the impinging, oscillating pressure. Because the tissue is not perfectly elastic (i.e., the molecules will realign themselves so that they won't be polarized), the absorbed energy quickly dissipates in front of the pressure pulse as molecular motion or heat. This is the only method by which energy is absorbed at low frequencies — during earth tremors, train rumble, or massage, for example. This mechanism can be called "elastic absorption."

Reflection, due to the inertia of the tissue (its tendency to remain at rest unless forced to do otherwise — Newton's first law of motion), occurs at

54 MATTER WAVES: SOUND AND ULTRASOUND

high frequencies for soft tissue and even at low frequencies for dense tissue such as bone. Truly elastic tissues simply reflect incident matter waves.

The absorption coefficient for molecular absorption (k) is well known for air and water:

3vp

-> c_p °v jc

^ P ^ V

where /is the frequency (cps) of the impinging wave, v the velocity (cm/sec), p the density (g/cm3 ), rj the viscosity (dyne sec/cm2), A"7the heat conductiv- ity (cal/sec deg cm), and the c's are the specific heats (cal/deg g) at constant pressure, P, and constant volume, V. Hence the energy absorbed per centi- meter of penetration of the impinging wave increases linearly with the vis- cosity or "stickiness" of the medium and with its thermal conductivity; in- creases very rapidly with increasing frequency; but decreases with increas- ing density.

For water, which is a sufficiently good approximation to soft tissue for present purposes, k/f2 = 8.5 x 10"17 sec2/cm. For air the value is 1000 times higher, because although rj is 50 times smaller for air than for water, v is 4^2 times smaller and p is 1000 times smaller. For liquids only the first term (the frictional or viscous one) is important; for gases both are im- portant. Therefore it is useful to aerate a tissue before sonic therapy is ap- plied, because absorption is higher.

Since reflection increases with increasing frequency, the method of appli- cation is important. In the absence of reflection, the above expressions describe the situation well. Direct application of the vibrator to the tissue assures this. However, if the sound is beamed through air, the situation is quite different: reflection occurs.

Quantitative studies on tissues are only recent. The general rule which has emerged is as follows: Beamed through air, sound of high frequency suf- fers little absorption, and little damage results. The depth of penetration increases with increasing frequency. Most (>95 per cent) of the incident energy passes right through, or is reflected. Some of Von Gierke's figures (1950) are: 5 to 6 per cent absorbed at 100 cps; 0.2 to 4 per cent absorbed at 1000 cps; and <0.4 per cent absorbed at 10 kc. Beamed through liquid or solid, ultrasonic radiation is easily controlled and its absorption pre- dicted. More will be said about this later, in the section on therapy.

SENSITIVITY OF A DETECTOR, AND THE WEBER-FECHNER LAW

It is a fact that whether or not a receiver will detect a signal depends upon how much the signal differs from the background noise. The dependence is

SENSITIVITY OF A DETECTOR, AND THE WEBER-FECHNER LAW 55

not a simple proportionality, but rather a logarithmic one. Thus, the sensa- tion, or loudness, L, is given by

L oc log///°

where 1° is background intensity, and / is the intensity, over background, of the signal to be detected. This is the basic form of the Weber-Fechner law. It has many manifestations. For instance, if there are two signals equally strong, with different backgrounds, the resolution of (difference in loudness), L2 - L, , is related to the ratio of the intensities of the two backgrounds, 1° and I2°, as follows:

L2 — L{ oc log I°/I°

This is a law which has rather wide application, not only in the psycho- logical sensations but in detection of electromagnetic waves of many fre- quency ranges, from the radio to the infrared. Therefore its implications should be very thoroughly contemplated.

Because of this logarithmic law, it is convenient to express power ratios by a logarithmic unit, so that sensation becomes approximately linearly pro- portional to this unit. The unit is called the ^bel," (b) and is equal to the logarithm of the ratio of two sound intensities if they are in a ratio of 10 : 1. The number of bels then is given by

b = log 1/1°

For sound, the value 1° is arbitrarily chosen to be the lowest one which a human ear can detect (10-16 w/cm2; or, in pressure units, 0.0002 dynes/cm2, since the same conversion factor applies to numerator and denominator). The bel unit is too large for convenience, and the decibel, one tenth of a bel, has received wider use. Therefore, the number of decibels is:

db = io log i/r

Another form of the Weber-Fechner law, then, is

L « db

It holds true for all sensory receptors.

Some minimum discernible relative changes,** (/, - 7°)//° (where I, is threshold intensity), which man can detect are:

Brightness of light: 1 per cent

Lengths of lines: 2 per cent

Feeling of weight: 10 per cent

Loudness of sound: 30 per cent

** Remember relative error, defined in Chapter 1 ?

56

MATTER WAVES: SOUND AND ULTRASOUND

Sensitivity, S, of a detector, or discernment per decibel of signal over back- ground, is defined as

s = log r/Mt

where A I, = I, - 1° . Sensitivity is higher the smaller is the value of A/,. Usually when 6" is determined at different values of an independent variable, the result is expressed as the sensitivity relative to the maximum value taken as unity (S/Smax). The sensitivity of the ear is so expressed in Figure 3-4.

moximum sensitivity

0.01

10 100 1,000

FREQUENCY (cycles per second;

10,000

100,000

Figure 3-4. Sensitivity of Human Ear at Different Frequencies of Sound Waves. The indi vidual's sensitivity curve may differ markedly from this average curve.

THE BODY'S DETECTORS OF MATTER WAVES

Introduction

In this section are given an outline of the structure of the ear and a de- scription of the mechanism of the sense of touch. This sketch is meant to show the important general features, but does not penetrate into either the depths of the mechanism nor the psychology of the resulting sensations such as loudness and pitch. A very well written and concise display of the bio- physics of hearing is found in the book by Stacy et a/.6 An up-to-date survey of the physiology of hearing is given by Whitfield,7 and a masterful discus- sion of biological transducers (converters of mechanical to electrical stimuli) was recently given by Gray.8 To delve deeply into this aspect of the subject is, unfortunately, beyond our scope, although it is currently a very active part of biophysical research.

THE BODY'S DETECTORS OF MATTER WAVES 57

Notes on the Ear

The structure of the ear can be pictured, in simplest terms, as consisting of three main parts: the pinna (lobe) and external canal, the middle ear, and the cochlea. The canal and the middle ear are separated by the tym- panic membrane (ear drum) which covers and protects the latter. The middle-ear cavity contains a system of three bony levers, the ossicles (the malleus, incus, and stapes) whose main job seems to be to act as a matching device transmitting matter vibrations between the two fluids: the air outside in the external canal, and the perilymph inside the cochlea. The cochlea is a spiral canal within the bone of the skull. It is divided axially into three channels by membranous partitions. Into one of these, the scala vestibuli, is inserted the end of the stapes; this chamber, then, receives directly the transmitted vibrations. Through the membranes, vibrations are passed laterally into the other two canals, the scala media and the scala tympani. These two are separated by the basilar membrane, which receives the end- ings of the auditory nerve, and the cells of which are the transducers that convert the mechanical energy of vibration into the electrical energy trans- mitted along the nerve. Most recent work has been aimed at the mechanism of action of the region of the basilar membrane, the transducer. Some of the cells on the membrane have hair-like processes projecting from their upper ends and attached to the overhanging, tectorial membrane. Relative move- ment between the tectorial and basilar membranes distorts the cells of both. Note Figure 3-5.

The analogy with piezoelectric crystals is usefully drawn at this point: distortion of the shape of the transducer in both cases leads to change in the potential difference between two points on the surface of the transducer — in one case the surface potential of the crystal, in the other case the membrane potential of the cell.

An accumulation of evidence now exists — Von Bekesy13 received the 1961 Nobel Prize in Physiology and Medicine for this work, done at Harvard — that a traveling wave passes along the basilar membrane during excitation. The position at which the wave achieves its highest amplitude (think of the whip) is dependent upon the frequency of the wave being detected. Therefore, nerve signals from different tones arise at different spots, each spot associated with specific nerve endings. At low frequencies the whole basilar membrane vibrates in sympathy with the incoming matter wave.

The question of membrane potential change will be considered in Chap- ters 7 and 10, in reference to erythrocytes and nerve cells, upon which voltages have been directly measured in vivo.

Deformations in the structure, or failure of the ear to respond to matter waves, is the subject matter of the otologist. Corrections are applied some-

58

MATTER WAVES: SOUND AND ULTRASOUND

times simply by amplification of the signal reaching the tympanic mem- brane, sometimes, although less commonly, directly to the cochlea by stimu- lation of the bone structure which surrounds it. Surgery is often necessary to free the "frozen" lever system.

Reissner s membrane

bone

auditory ner ve

tec torial membrane

transducer cells

basilar membrane

COCHLEA

non-elastic oining f i ber s\

auditoi y nerve end ings

Figure 3-5. Schematic Drawing of Cross-section of the Cochlea, the Inner Ear. The three scalae are separated by deformable membranes. The transducers are fastened to the tectorial membrane by fibers. Relative motion between the tectorial membrane and the basilar membrane causes stretching of the transducer cells, resulting in change in membrane permeability, and therefore ionic composition and membrane potential. This change activates the nerve endings attached to the cells, and the impulse is carried down the auditory nerve to the brain.

The Sense of Touch And Other Mechanoreceptors

A magnificent array of mechanoreceptors (as well as photo-, chemo-, and thermal receptors) is displayed by the human body. These bring in informa- tion from the environment, and then provide a feedback of information con- cerning an action taken. The most sensitive transducers, other than those in the ear, are found on the tip of the tongue and on the tips of the fingers, although mechanoreceptors are located all over the body, so closely spaced that no pressure change on the surface, above some threshold value, goes undetected.

They all have three parts in common: (1) a mechanism for transmitting a pressure change to the receptor cell; (2) the deformable receptor cell, the deformation of which (apparently) changes its cell membrane potential at a point intimately associated with (3) a specialized ending of a nerve cell's

SPEECH 59

axon. Speculations are rampant on the mechanism of this transposition. Transduction through changing electrical potentials across the receptor cell wall is currently a very popular generalization; but reliable details of mech- anism, unfortunately, are too few.

SPEECH

Three resonators, or vibrating cavities, are responsible for the organized noise which we call speech. They are (1) the vocal chords, which close the exit used by air exhaled from the lungs; (2) the throat and the mouth; and (3) the nasal cavity. The vocal chords, the tongue, and the lips control the changes in vibration which are induced in the exhaling air stream and which are the sounds of speech. The combination of these three moving parts, each of which can take several different shapes, gives remarkable versatility in the production of sound.

The fundamental sounds of speech are divided into six classes: pure vowels, diphthongs, transitionals, semivowels, fricative consonants, and stop consonants. The subject of phonetics is well known, is heavily illustrated in any good dictionary, and needs no review here.

Amplitude and intensity are controlled mainly by the rate of expulsion of air, although secondary resonators such as the head and the chest play a small role.

Speech sounds have been analyzed on many people by the Bell Telephone Laboratories, for obvious reasons. Some of the results are contained in the classic book by Fletcher.3 For instance "oo" as in "pool" spoken by men (by women) has a mean fundamental frequency of 140 cps (270 cps), a mean low frequency of 411 (581 for women), scattered high frequency of 3700 (4412 for women). All speech sounds have been carefully recorded and ana- lyzed, and the sounds of the "average man" used for microphone design.

The fundamental speech sounds have a power. When one talks as loudly as possible without shouting, the average speech power is about 1000 micro- watts (1 nw = 0.000001 w) at the source. When one talks in as weak a voice as possible, without whispering, it drops to 0.1 fiw. A very soft whisper has a power of about 0.001 ^w. Very loud speech is ~20 db over average speech power; a soft whisper is ~40 db under average.

NOISE

High-intensity noise has become one of the most disturbing problems of the modern way of life. Noise is usually defined as any unwanted sound, and hence the classification is highly subjective. High-intensity noise is usually defined as any unwanted sound greater than 85 db (see Table 3-1).

60

MATTER WAVES: SOUND AND ULTRASOUND

Noise has many components — matter waves of many frequencies. The "buzz" from speech in a crowded room will center in the range 300 to 6000 cps. The noise generated by a wood planer has most of its energy between 200 and 2000 cps, while a power saw will emit noise from 50 to 6000 cps.

Only low-pitched or high-pitched voices can be clearly understood. This is the crux of the problem facing communication engineers and otologists alike: to provide a sufficient sound intensity level (over background noise) to the middle ear. This question is considered in more general terms in Chapter 11.

TABLE 3-1. Some Sources of Noise*

Location	Power (w/cm2)		Sound Power Level** (db)
50-hp siren	10"2		140
(100 ft away) Submarine engine room	io-5		110
(full speed) Factories	IO"4 to IO"8		76 to 128
Woodworking plants	10~4 to IO"8		80 to 114
Subway car	IO"7 to IO"8		80 to 90
Loud radio (2 ft away) Speech at 2 ft Speech at 1 2 ft Private office	IO"8 [ I0"12tol0-8 \| IO"'2	80 60 normal, 77 shouting 43 normal, 61 shouting 40
Average home	io-13		30
Library	10-h		20
"Silence"	IO"16		0

* After Neeley, K. K., "Noise — Some Implications for Aviation," Caw. Aeronaut. J., 3,312 (1957). ** Referred to 10-16 w/cm2, the threshold of hearing.

Exposure of man to high-intensity noise has several effects: change in hearing acuity, and mechanical or pathological damage to the cochlea; tem- porary blindness (>140 db); changes in ability to perform skilled and un- skilled tasks; feelings of fear, annoyance, dissatisfaction, and nausea. Dis- cussion of some of these effects follows in the next section.

PHYSIOLOGICAL EFFECTS OF INTENSE MATTER WAVES

The physicochemical basis of the physiological damage is fairly well understood. Five facts are important to the discussion:

(1) During the absorption of matter waves, a front of high pressure pre- cedes a front of reduced pressure through the tissue. There is therefore a differential pressure, or a pressure gradient, along the tissue which stretches and compresses it in sympathy with the incoming wave. If the amplitude is

PHYSIOLOGICAL EFFECTS OF INTENSE MATTER WAVES

61

such that the elastic limit is exceeded, tearing can result. Thus 160 db will rupture the eardrum itself, probably the toughest part of the soft tissue of the whole organ!

(2) At high frequencies, the compression occurs so fast that energy is passed from the matter wave to the recipient molecules so rapidly that it has no time to disperse through molecular vibrations. The molecule be- comes phenomenally "hot" or energetic, and may fly apart. Thus chemical bonds are broken (Figure 3-6 (a)). Water is decomposed to H2 and H202.

gas or steam

irradiator

metal pan

liquid making

contact with

brain through

hole in skull.

(a)

(b)

Figure 3-6. (a) Cavitation and Production of Broken Water Molecules by Ultra- sound. The OH fragment is a rapidly effective oxidizing agent, (b) Irradiation of a Small Locale in the Brain. (Success with Parkinson's disease reported.)

(3) During rarefaction (low-pressure part of the wave), any dissolved gas in the tissue may coalesce into bubbles; and in fact bubbles containing only water vapor may form, breaking molecular bonds as they form, and breaking more bonds as they collapse and release their high surface energy. This is called cavitation. It occurs in water at power levels as low as 140 db. This critical power level decreases with increasing frequency.

(4) With the breaking of bonds, free radicals are produced, which, for reasons to be discussed in Chapter 4, cause a (net) oxidation reaction to occur in most aqueous solutions. Three watts of power introduced at 500,000 cps, for example, will cause oxidation.

(5) Because of general absorption of energy within the volume irradiated with matter waves, a general temperature rise occurs. This upsets the metabolism of the tissue in a manner discussed later in Chapter 8. Irradia- tion by 1 megacycle (Mc) at a power of 50 w/cm2, for example, raises the temperature of water from 20 to 50° C in a few minutes.

Some specific observations of effects of sound waves on man are given in Table 3-2.

For obvious reasons, experiments using high-power sound are carefully and selectively done on man. However, an accumulation of experience is

62 MATTER WAVES: SOUND AND ULTRASOUND

being gained on animals, principally guinea pigs, rats, and mice. The in- vestigations have not been extensive enough to denote anything other than generalities. However, at 165 db, 500 to 400,000 cps, on guinea pigs, pathological changes occur in both the inner and middle ear; lesions appear in the organ of Corti, and it is ruptured from the basilar membrane. Hemor- rhages start where the malleus meets with the eardrum. Convulsions often result. The skin becomes blistered and reddened. Death is hastened by the damage.

TABLE 3-2. Effects of High-Intensity Sound on Man*

Frequency (cps) Level (db) Effect

stimulation of receptors in skin mild warming of body surfaces nausea, vomiting, dizziness; interference with touch

and muscle sense significant changes in pulse rate pain in middle ear changes in muscle tone; increase in tendon reflexes;

incoordination minor permanent damage if prolonged major permanent damage in short time vibration of muscles in arms and legs resonance in mouth, nasal cavities, and sinuses

♦Collected by Neeley, K. K., "Noise — Some Implications for Aviation," Can. Aeronaut. J., 3, 312 (1957).

SONIC AND ULTRASONIC THERAPY

Certain uses have already been demonstrated; others await discovery, for the technique is very new to medicine. The following applications are al- ready well known in principle, and are now being introduced in practice very cautiously — for the early 1950's saw the period of novelty wax strong, and then wane into a hard reappraisal in the mid-50's; and one now observes the gradual emergence of the place of vibrations in the medical arsenal. Details can be found in the reviews of two masters of the subject, R. F. Herrick10 and W.J. Fry1 and in the book edited by E. Kelly.2

Present Applications

(1) Subcutaneous lesions can be located by ultra high-frequency matter waves. They focus well at 1 Mc, and penetrate to a useful depth. The depth of penetration is a function of the power of the source. Since reflection of matter waves is greater the higher the density of the medium, tumors can be distinguished from normal tissue at a location deep below the surface.

100	110
2000 to 2500	>150
Jet engine	130 to 155
100 to 10,000	105
	140
	130 to 140
	~160
	~190
50	~120
700 to 1500	130

SONIC AND ULTRASONIC THERAPY 63

(2) Based on the same principle, the rate of blood flow through the ar- terial system can now be measured by reflected ultrasound, in a nondestruc- tive experiment in which all instrumentation is external to the body.

(3) Dentists have begun to apply sound to the ears of patients during drilling, because it has been found that the brain cannot perceive pain from the teeth and sound from the ear at the same time. The sound in this case acts as a local anesthetic.

(4) "Rapid massage" heat therapy is now quite common, with an assort- ment of low-frequency vibrator pads and belts available, and experimental models operating in the 12,000 to 50,000 cps region. For deep "massage" higher frequency ultrasound is used; it has the added advantage of comfort from noise.

(5) Certain skin diseases can be treated with beamed and focused ultra- sound. Thus viruses are destroyed (literally shaken into little bits!) by ultrasound, and a future in sterilization seems assured. In this application its competitor is soft X rays.

(6) "Neurosonic surgery" is now well advanced on animals, and has re- ceived some experimental evaluation on humans. The most spectacular suc- cess so far has been achieved in treatment of Parkinson's disease, the shaking palsy. Because of its future importance,*** some details will now be given.

"Neurosonic Surgery"

The ultrasonic radiation reaches the brain through a hole cut in the skull, and the matter waves are beamed and focused on that part, deep in the brain, in which involuntary movements are controlled (Figure 3-6 (b)). The energy dissipated by the beam is concentrated at the focus of the beam, and gently destroys the metabolic activity at the site (the substantia nigra). The method, when used carefully, has the advantage over all others that it pro- duces lesions at the focus of the ultrasonic energy without interfering with the normal blood flow from one part of the brain to another through the region irradiated. Of course this is a great advantage from the medical point of view. The techniques were worked out first on hundreds of cats and monkeys, and are now very cautiously being applied to man. Functional disruption of nervous conduction occurs within a few seconds of exposure to ultrasound of sufficient dosage to produce lesions: 980,000 cps, 1.8- to 3-sec duration, and particle velocity amplitude of 350 cm/sec, from a generator with the capability of 20 to 1000 w/cm2. From the therapeutic viewpoint it has been found possible to irradiate simultaneously the four small parts of the brain which are active with respect to Parkinsonism in the four limbs.

***In spite of the fact that Parkinsonism may be dying out. Thus the average age of these patients is steadily increasing, in North America, a trend which, if it continues, would indicate that the disease may have died out naturally by 1985.

64

MATTER WAVES: SOUND AND ULTRASOUND

Other conditions reported treated successfully by this method at this date include a case of cerebral palsy and one of phantom limb pain. The prin- ciple is simple enough: to produce lesions, without excessive damage, at the tiny spots in the brain which control the function which appears disordered. Conversely, using this tool to inhibit temporarily the various functions con- trolled by the brain, one not only can obtain a micromap, in three dimen- sions, of the control sites, but learn something of the mechanism of control as well.

The facts of microirradiation and selective absorption and damage, augur well for the future of "neurosonic therapy" as a strong competitor to the mechanical, electrical, and chemical techniques now in use in brain dis- orders.

Figure 3-7. Equipment for Clinical Ultrasonic Irradiation of a Patient with a Hyper- kinetic Mental Disorder. Upper right and insert: The multibeam irradiator itself. (Cour- tesy of W. J. Fry, University of Illinois Biophysics Research Laboratory.)

The Dunn-Fry Law

As the quotation from Lord Kelvin (Chapter 1) said, it is always com- forting to be able to state quantitatively an important fact. On animals it has been found that the time, t, of irradiation to a chosen physiological state — in this case to paralysis of the hind legs of young mice — is related to the intensity, / (power), of the irradiating ultrasound (982 kc/sec, hydrostatic

CONCLUSION

65

Q

UJ

or

300

250

200

co ~

-?-	E
UJ	o
h-	V
z
	•♦—
o	o *
-z.	*—
o
CO	III
<	z>
cr	CO
t-	CO

*- 100-

=5 h-

150

IRRADIATION TIME

t (seconds)

Figure 3-8. Threshold Energy for Paralysis as a Function of Ultrasonic Intensity, curve shows data of W. J. Fry and F. Dunn, 1956. Broken curve shows how the th is much higher than expected at very short irradiation times.

Solid reshold

pressure 1 atm, starting temperature 10° C) by the simple expression

t oc i/vTT

the Dunn-Fry law, which says simply that the time to paralysis is shorter the higher the intensity; but that the damage occurs relatively more slowly for large intensities than for small intensities.

This is one of the best rules-of-thumb so far worked out in biophysics of ultrasound therapy. It remains to be seen whether it is of general applica- bility. Intuitively one would think it should be. In any case it might be well to state the following memory aid: Probably because of general heating and of molecular excitation induced by absorbed ultrasound, metabolic, physio- logic, and histologic changes occur in tissues. In otner words, tissues Fry until Dunn!

CONCLUSION

"Like some other agents which have been introduced into the arma- mentarium of clinical medicine, medical ultrasonics passed through the early stages of enthusiasm, followed by a reactionary stage of pessimism, before it achieved the stature presently accorded it. Currently there are promising developments and interesting applications of ultrasound for medical diag- nosis, for therapy, and for biologic measurement." (J. F. Herrick.12)

The next ten years should be interesting ones from this point of view.

66 MATTER WAVES: SOUND AND ULTRASOUND

PROBLEMS

3- 1 : Express in decibels the sound which delivers 1 50 times the power of background

noise. 3-2: (a) Calculate the value of the absorption coefficient of sound in tissue at 50; 1000; 10,000; and 500,000 cycles per second (cps).

(b) Make a plot of intensity vs depth in tissue for each frequency. 3-3: How would you employ the inverse square law to "protect" yourself from an

intense source of noise? Suppose you wanted to reduce the noise level by

a factor often.

What could you learn about this problem from a = f(rj) as these terms are

defined in the text? 3-4: Two signals enter your ear: one at 500 cps, with intensities / and 7° equal to

10~I2and 10" l5 w/cm2, respectively; and the other at 6000 cps with intensities

/and 1° equal to 10 14 and 10~16 w/cm2. Which will seem the louder?

REFERENCES

1. Fry, W. J., Adv. in Biol, and Med. Phys., 6,281 (1959): a review, illustrated.

2. Kelly, E., Ed., "Ultrasound in Biology and Medicine," Amer. Inst, of Biol. Sciences,

Washington, D. C, 1957.

3. Fletcher, H., "Speech and Hearing," D. Van Nostrand Co., Inc., New York,

N.Y., 1946.

4. Ruch, T. C. and Fulton, J. F., Eds., "Medical Physiology and Biophysics,"

W. B. Saunders Co., Philadelphia, Pa., 1960.

5. Herzfeld, K. F. and Litovitz, T. A., "Absorption and Dispersion of Ultrasonic

Waves," Academic Press, New York, N. Y., 1959.

6. Stacy, R. W., Williams, D. T., Worden, R. E., and McMorris, R. O., "Essen-

tials of Biological and Medical Physics," McGraw-Hill Book Co., Inc., New York, N. Y., 1955.

7. Whitfield, I. C, "The Physiology of Hearing," in Progr. in Biophysics, 8, 1 (1957);

a review.

8. Gray, J. A. B., "Mechanical into Electrical Energy in Certain Mechano-

Receptors," Progr. in Biophysics, 9, 285 (1959); a review.

9. Neely, K. K., "Noise — Some Implications for Aviation," Can. Aeronaut. J., 3,

312(1957).

10. Herrick,J. F. and Anderson, J. A., "Circulatory System: Methods — Ultrasonic

Flow Meter," in "Medical Physics," Vol. Ill, O. Glasser, Ed., Yearbook Publ., Inc., Chicago, 111., 1960, p. 181.

11. Gardner, W. H., "Speech Pathology," ibid., p. 637.

12. Herrick, J. F., Proc. Inst. Radio Engineers, Nov., 1959, p. 1957.

13. Von Bekesy, G., "The Ear,"5W. Amer., Aug., 1957; a review.

CHAPTER 4

Electromagnetic Radiations and Matter

The next thing is striking: through the black carton container, which lets through no visible or ultraviolet rays of the sun, nor the electric arc light, an agent (X) goes through which has the property that it can produce a vivid fluorescence ....

We soon found that the agent penetrates all bodies, but to a very different degree. (W. C. Roentgen, Annalen der Physik und Chemie, 64, 1 (1898).)

INTRODUCTION

Within fifteen years, just before the turn of the century, complacent classi- cal physics received three rude shocks. The first was Julius Plucker's de- scription (circa 1890) of the electrical discharges which take place in gases under low pressure and high voltage (the embryo of the "neon" sign). The second was Henri Becquerel's discovery of natural radioactivity in 1895; and the third was Wilhelm Roentgen's discovery of X rays, reported in 1898. In the years since then, the three discoveries have collectively engendered in- tense investigation of: (1) the structure of molecules, atoms and nuclei; (2) arrangements of molecules in crystals and other, less well-defined molec- ular arrays; (3) the electromagnetic spectrum, from X rays through visible to infrared radiation; and (4) the interactions — and in fact interconversion! — of electromagnetic energy and matter. In this chapter a review is given of those facts and theories which are useful to an understanding of the bio- physics of the interactions of electromagnetic radiation and living matter.

67

68 ELECTROMAGNETIC RADIATIONS AND MATTER

THE STRUCTURE OF MATTER

The Elementary Particles and Atomic Architecture

Some of the key experimental facts accumulated within a few years of 1900 illustrate the bases upon which our knowledge of structure depends.

Roentgen found that his unknown, or "X," rays would cause fluorescence in zinc sulfide and barium platinocyanide; and further that they would ionize gases and darken a photographic plate. They were therefore easily detected by an electroscope, or by an increase in current through a gaseous discharge tube, or by photographic techniques. He studied penetration through paper, wood, and metals, and showed that difference in penetration is one of degree rather than of kind (cf. the quotation which opened this Chapter.)

A fluorescent screen on each end of a cylindrical gaseous discharge tube showed that particles, presumably charged, pass between the electrodes in each direction. By placing metal shields between positive and negative elec- trodes, and by impressing a voltage between horizontal plates placed with their plane parallel to the direction of flow, it was shown that the rays com- ing from the positive electrode bend toward the negative horizontal plate, and are therefore positively charged; and likewise the rays from the negative plate bend toward the positive plate, and are therefore negative. The nega- tive particles were called cathode rays, and positives canal rays.

In 1897, J. J. Thomson (not William Thomson, Lord Kelvin) measured the deviation of the (negative) cathode rays in an electric and magnetic field, and obtained a value for the quotient of the charge to mass, i.e., e/m. This value was found to be the same (1.757 x 10H cou/g) no matter what ma- terials were used. Cathode rays were therefore recognized as elementary particles of matter, and were called electrons. The (positive) canal rays, how- ever, were found to be different for different materials.

By an ingenious experiment in late 1897, Milliken was able to obtain an independent measure of e, the charge on the electron. One or two electrons were trapped on atomized oil particles, and the electrical force necessary to prevent each oil particle from falling under the influence of gravity was measured. Since the size of the particle could be determined from the rate of free fall, the charge absorbed by the particle could be evaluated. The smallest value obtained, 4.78 x 10~10 electrostatic units (1.600 x 10~19 cou), corresponded to one electron absorbed.

From Thomson's value of e/m, the mass could then be determined as 9 x 10"28 g. This was an astounding achievement, the fact that exact meas- urement of this mass was possible by these means, whereas the most sensi- tive chemical balance weighs to only approximately 10"6 g!

For the canal rays, e/m for H+ was found to be 1820 times smaller than for the electron. Faraday in 1830 had shown by electrolysis that the charge

THE STRUCTURE OF MATTER

69

on the hydrogen ion was equal and opposite to that on the electron (being simply the absence of an electron), and hence the mass of the H+ was deter- mined to be 1820 times the mass of the electron, i.e., approximately 2 x 10"24g.

In 1896 Becquerel reported that he had accidentally discovered a pene- trating emanation from uranium salts. Thus, his photographic plates, kept in a drawer, with a key in the drawer above, became exposed with the im- print of the key in the presence of some phosphorescent minerals — notably salts of uranium — lying on the top of the bench. These emanations were also found to ionize gases. The Curies, in 1898, extracted a concentrate from pitchblende which had high emissive power, and named it radium (hence the terms "■radium-active" or "radioactive" elements, and "radioactive emana- tion").

They measured the strength of the emission by means of an electroscope. This instrument is essentially a vertical metal rod with a thin gold leaf at- tached to it by one end. If the electroscope is charged, the free end of the gold leaf is held out from the main shaft by repulsion of the like electro- static charges. It falls to the shaft in the presence of ionizing radiation, at a rate which increases with the strength of the emitter, because the electro- static charge on the metal is neutralized by charged particles formed during the absorption of radiation. Today ionization chambers based on this prin- ciple have wide use: a burst of current due to ionizing radiation is ampli- fied and recorded. One pulse of current occurs for each bundle of emanation absorbed. Ionization chambers are discussed in Chapter 5.

In an experiment whose origin is obscure but which was refined and ex- panded by Rutherford (see Figure 4-1), three fractions emanating from a radioactive source such as radium were separated, and called alpha (a), beta (/3), and gamma (7) rays.

It was found that alpha rays are positively charged and are much heavier than the betas. They are completely stopped by thin paper or a few milli-

shields

rodioactive source

Figure 4-1 . Rutherford's Separation of Alpha, Beta, and Gamma Rays, by Means of an Electric Field Applied Between the Deflecting Plates. Tube is evacuated.

70

ELECTROMAGNETIC RADIATIONS AND MATTER

meters of air, and lose one half their intensity if directed through 0.005 mm aluminum foil. By contrast, the beta rays are negatively charged, only weakly ionize gases, can travel many centimeters through air, and lose one half their intensity only if passed through 0.5 mm of aluminum sheet. The gamma ray has no charge. It strongly ionizes gases and penetrates up to 4 in. of lead.

Careful determination of e/m showed the beta rays to be fast electrons, traveling at speeds up to 0.99 times the velocity of light (3 x 1010 cm/sec). Similar experiments, and actual collection of alpha rays in a lead box, showed that the alphas are helium ions, He++. Experiments on penetration and analogous properties indicated that the gammas are simply electromag- netic waves like light, except of very short wavelength, shorter (or "harder") and more energetic than X rays.

Rutherford's famous scattering experiments, performed about 1911, dis- closed the inner structure of the atom. Alpha rays were used as the bullets and metal foil as the target (Figure 4-2). He surrounded the target with a

photographic plate

0

nucleus

paths of	1 \ ©/
ulpliu * w
particles *■ scattered alphas -^^	'atom of Ni

©

Ni foil

Figure 4-2. Scattering of Alpha Rays by Nickel Nuclei. Definite scattering angles and

even back-scatter were observed. See text.

cylindrical photographic plate, and observed, in addition to dark spots re- sulting from direct penetration through the foil, dark spots at certain char- acteristic angles of scatter. Most important, though, was the observation of ia^-scattering, in which the incident radiation was reflected almost straight back, like a ball bouncing off a wall. In his own words, in a lecture delivered at Cambridge many years later, in 1936, Rutherford said:

On consideration, I realized that this scattering backwards must be the result of a single collision; and when I made calculations I saw it was impossible to get anything of that order of magnitude unless one took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus ....

The back-scatter requires such energy that the alphas must penetrate to within 1/10,000 of the center of the positive charge in the atom; this means that the positive charge is centered in a nucleus of diameter 1/10,000 that of

THE STRUCTURE OF MATTER

71

the whole atom. The atomic diameter calculated from Avogadro's number (6 x 1023 atoms per gram atomic weight) and the density of, say, nickel (8.9 g/cc) is found to be approximately 10~8 cm (1 A). Therefore the diam- eter of the nucleus is approximately 10 l2 cm. Of primary importance to an understanding of penetration of energetic radiation into tissue was the deduction: the total positive charge is centered at the nucleus, which con- tains also most of the weight of the atom. The negative charge, equal in magnitude to the positive but of negligible weight, is in the orbital electrons.

Atomic theory then developed rapidly, between 1910 and 1925. Max Planck suggested that light is emitted and absorbed in bundles of energy (quanta); and Niels Bohr postulated that the electrons are held in definite orbits or levels around the nucleus, bound to the nucleus by positive-negative attraction, yet held from each other by negative-negative repulsion, thus pre- serving a definite diameter for the whole atom.

It was in 1926 that Erwin Schroedinger proposed an expression relating energy to radius, which for the first time gave these qualitative ideas quan- titative expression. It describes a model of the atom in which the electrons exist in a series of levels or orbitals, given the names K, L, M, etc., the K-shell being next to the nucleus. Figure 4-3 illustrates the spherical and

Figure 4-3. Sommerfeld's Atom with Elliptical (p) and Spherical (s) Orbitals. Three p's are at right angles to one another. Each orbital can hold two electrons, whether both from the one atom or a "shared pair" in a bond. As drawn, this "atom" could accommodate 2 electrons in the K shell (Is) and 8 in the L shell (2-level). Thus it represents atoms from hydrogen (1 elec- tron) up to neon (10 electrons). The 3s, 3p, etc., orbitals, only slightly larger, and not shown, accommodate orbital electrons of elements higher in the periodic table.

72

ELECTROMAGNETIC RADIATIONS AND MATTER

ellipsoidal orbitals first envisioned by Sommerfeld and described by Schroedinger. Each orbital can accommodate two electrons only, according to Wolfgang Pauli's "exclusion principle." The quantitative theory has now been tested experimentally for 36 years, by observation of the "light" emitted by excited atoms, and it describes, with the most beautiful precision known in science today, the observed results (more about this later). The in- ference is that Bohr's guess was right. But nobody knows why!

Werner Heisenberg's introduction of the "uncertainty principle," and later his new formulation, called wave mechanics, in which all the elementary particles (and hence all matter) are considered to follow the undulations of electromagnetic waves, have only served to strengthen the grasp that this particular atomic model, or theory, has on science.

The model discloses that there are sublevels in which an electron may find itself within the electron cloud: the s, p, d, and / levels,* or orbitals, as they are called (Figure 4-4). In each of these the electron is confined within a certain spherical or cigar-shaped volume about the nucleus. The orbitals of the outermost electrons of the atom overlap with those of the neighboring atom, and form a "bond."

p-orbitol

s-orbito

schematic

de Broglie s standing waves

Figure 4-4. Schematic (exaggerated and distorted) s and p Orbitals with de Broglie's "Pilot Waves," Which are Thought to Guide the Electrons in Their Orbits.

Working from the inside to the outside, we discuss interatomic binding after a section in which we focus attention on the hard, heavy, positive core of the atom, the nucleus, knowledge about which is so important to the understanding of radioactivity and its biological effects.

*For sharp, principal, diffuse, and fundamental: descriptive codings used by spectroscopists to describe spectral lines.

THE STRUCTURE OF MATTER 73

The Atomic Nucleus

Since World War II much research has centered on the forces which hold the nucleus together. The nucleus carries all the positive charge and most of the mass of the atom. As a result of bombardment experiments (Fig- ure 4-2), especially on light nuclei, by 1930 it was known to be composed of two main particles, protons, p, (H+) or bare hydrogen nuclei, and neutrons, n, particles of the same weight as protons, but with no charge. Moseley showed in the year 1914 the correlation between atomic number and positive charge on the nucleus; and isolation and identification of isotopes (same atomic number, different atomic weight — i.e., more or fewer neutrons) fol- lowed at a fast pace, until today more than 600 isotopes of the 108 elements are known. Some nuclei are stable, but some are unstable, and fly apart spontaneously into fragments. These are the radioactive isotopes. Some un- stable isotopes do not exist in nature, but can be produced artificially by nuclear bombardment (by n, p, etc) techniques. They are called artificially- radioactive isotopes.

Experimental bombardment of the nucleus and examination of the prod- ucts by cloud chamber, ionization chamber, energy-balance studies, photo- graphic, and other techniques has disclosed about 20 new particles. First came the neutrino and the positive electron, or positron, then a number of new particles, at first all called mesons. Named after the great theoreticians, Bose and Fermi, these are now classified into:

Bosons (spin = 1)

(a) pions, or light mesons (t° : 264.2; tt±: 273.2)

(b) A;aons, or heavy mesons (k°: 965; k±: 966.5) Fermions (spin = 1/2)

(a) leptons, or light particles {n*: 206.77; e*: 1; neutrino)

(b) barions, or hyperons and nucleons (Xi*: 2585; 2*: 2330;

A°:2182; p*: 1836; n°: 1837)

The mass (in multiples of the electron mass) and charge (°, +, or " super- scripts) of these particles (ir, k, Xi, p, etc.) are given in parentheses. The bosons exist in the nucleus and contribute to its phenomenal binding energy. Isolated, all but the electron, proton, and neutrino are unstable. However, the neutron persists for about 20 minutes on the average. The others last only 10-6tol0-10sec.

Of some particular interest may be the muon (p*), well established as a cosmic-ray product in the atmosphere in which we live. It is ultimately pro- duced by the impact of a cosmic ray proton and an atomic nucleus in the upper atmosphere. A 7r-meson is first produced, which in turn decays

74

ELECTROMAGNETIC RADIATIONS AND MATTER

rapidly into the muon plus a gamma ray. The muon disintegrates into a fast, ionizing electron and two more gamma rays, at sea level.

The atom and its nucleus were recently detailed in delightful form by Gamov10, in a little book highly recommended for its simple, colorful de- scriptions of very complex phenomena.

Molecular Structure and Binding

It is the outer, or valence, electrons of the electron cloud which are evi- dently involved in binding atom to atom (Figure 4-4). Two distinct cases, and one intermediate case, have been studied thoroughly. First, the valence electron in "atom 1" can jump into an empty orbital of "atom 2," leaving atom 1 positive and making atom 2 negative. Strong electrostatic binding exists (Coulomb's law) because the charge separation is small. This is the case in all salts, both inorganic and organic. The bond is called ionic.

Secondly, the electron from atom 1 can simply exchange, or be "shared" with that of atom 2. For instance if each of the two valence electrons is in an s (spherical) orbital, and the orbitals can overlap so that exchange or sharing takes place, a "sigma" bond is formed. If both are in p ("probing") orbitals (cigar-shaped), and if they overlap, a so-called pi (7r) bond is formed (Figure 4-5). Indeed combinations of s and p, called "hybrids," are pos- sible. For example each of the four bonds made by a carbon atom is a hy- brid of one s and three/? valence electrons — imagine, in Figure 4-4, the 2s and 2p electron orbitals as distorted; it is a mixture, called an sp^ hybrid. The four are directed tetrahedrally from each other, like four long noses, each to form a bond (i.e., to share a pair of electrons) with a neighboring atom. In the case of water, each of the p orbitals of oxygen overlaps with s of hydrogen to form a bent (109°) molecule. The bond is called covalent.

TT-bond electrons

closed loop

(b)

TT bond electrons, open path, \ mobi le

carbon atoms

Figure 4-5. Diagrams of Overlapping it Bonds: (a) A closed loop to form a dough- nut of negative charge above the plane of a benzene ring; (b) on a protein with open and ringed molecular structures, in which 7r-bond electrons are somewhat mobile and can transfer charge from one end of the molecule to the other, if forced.

THE STRUCTURE OF MATTER 75

In between the ionic and covalent bond is the dative bond, in which the electron of atom 1 is partially given over to atom 2, although exchange and overlap still occur. Organic-phosphorus molecules are an important ex- ample (ATP, for instance, the "mobile power supply" in the living system). The oxygens of the phosphate assume a definite negative charge because of dative bonding.

Of special importance is the w bond, formed by the overlap of two p orbi- tals ("probosci"). It often forms the second bond in the "double bond" of conjugated organic molecules, and restricts the relative rotation of atoms 1 and 2 if joined by the it. But the most important property of the it bond is its position, directed parallel to, but not coaxial with, the atom — atom axis (Figure 5 (b)). Although it helps to bind atom 1 to atom 2, it is an ac- cumulation of negative charge outside the volume containing the two atoms. It therefore can form weak bonds (complexes) with positive ends of other molecules in the vicinity; but, most important, it can exchange electrons with other it bonds close by, and hence provide a pathway by which elec- trons can run along a molecule from a point of excess negative charge to a point of deficiency of charge. Hence some organic molecules in tissues are electronic conductors, a fact which only recently has been appreciated with respect to nerve conduction and photosynthesis. (This very important topic is pursued in Chapter 6.) Further, the possibility of different electronic states in molecules, with different types of bonds, has profound ramifications in interactions of the molecule (and the tissue of which it forms a part) with electromagnetic radiations. These very important topics are also discussed in Chapter 6.

It is obvious that the elementary particles are the building blocks of the living stuff. From the molecular point of view, however, it is not at all clear where the line is to be drawn between the living and nonliving. Usually the attributes of growth and reproduction are used to classify the living. Yet, in a supersaturated solution, copper sulfate crystals will "grow," layer upon layer; and if the temperature is allowed to fluctuate up and down with a frequency of one or two cycles per day, they will "reproduce" themselves, by "seeding," in the form of many crystallites on the walls of the container. In- deed, Teilhard de Chardin, in 1945, proposed that all the elementary par- ticles of matter are living, that they have the potency to do the things which living things can do, but that this potency is, to us, masked behind the gross behavior of large numbers. The gross behavior — statistical behavior — is all that our experimental techniques can today perceive in inanimate na- ture. Our techniques can examine the highlv organized individual man in which ~1028 particles are organized and controlled from within, although this inner FORCE is not amenable to physical examination as we know it today. From the point of view of elementary particles, the only difference be- tween living and nonliving matter is one of organization.

76 ELECTROMAGNETIC RADIATIONS AND MATTER

ELECTROMAGNETIC RADIATION; NATURE AND SPECTRUM

The electron clouds of atoms and molecules can be excited by various methods — by heat, bombardment by some charged particle, and by absorp- tion of incoming radiations. A simple example is the flame test for sodium: if a sodium salt is heated in a flame, it glows with a characteristic yellow glow. It is not burning (i.e., being oxidized by oxygen). Rather, the valence (outermost) electron gets excited (accepts energy) and "jumps" to a higher- energy orbital, from a 3s to a 3/?. Imagine the next set of orbitals around the nucleus in Figure 4-3. Its lifetime there is short, however, and it falls back to the original state ("ground state"), and emits the extra energy as electromagnetic radiation {light in this case) of such a wavelength (5893 A) that it excites the cone cells on the retina of the eye.

Biology is entering its electromagnetic age. Many parts of the electromag- netic spectrum are beginning to be used for diagnosis and therapy, as well as for studies which are leading to a better understanding of the roles of each of the parts in the systematized whole.

Nature of Electromagnetic Radiation

The exact nature of electromagnetic (em) radiation is unknown. What is known is that the wave has two component parts, an electric part and a mag- netic part, moving in phase, but in direction 90° from each other — much like two vibrating strings, one going up and down while the other goes back and forth — superimposed on each other. Each oscillates about an average value (zero) at a frequency which depends upon electronic vibrations in the source. The em waves travel in a straight line, and have energies inversely proportional to the wavelength, or directly proportional to the frequency (number of cycles per second). The wave carries no net electrical charge, and no net magnetic moment, but because of the components which can in- terfere or react with electric or magnetic fields, it can lose or gain energy (i.e., change frequency). All em waves travel at the velocity of "light." They have both wave properties (such as the capability of being reflected or diffracted) and particle properties (such as delivering their energy in bundles or quanta.). The unit bundle of electromagnetic energy is called the photon. Undulations in the electromagnetic field are described by the celebrated Maxwell equations (1873).

Electromagnetic radiations vary only in frequency, and through this, in energy. Therefore their use requires handling the energy contained in the radiation. For example, we know how to handle light with mirrors, lenses, microscopes, and prisms, and to detect it by photographic plates, photo- electric cells, the eye, etc. Handling, or making it serve a useful purpose, is simply a question of using equipment which does not absorb the light. Detec-

ELECTROMAGNETIC RADIATION; NATURE AND SPECTRUM 77

tion is simply a question of providing a medium which can absorb the light, or a medium with which the light can interact and be partially absorbed, to appear as another, more familiar form of energy.

Electromagnetic radiation propagates with undiminished energy through a vacuum, always at the speed of light no matter what the frequency.

The Electromagnetic Spectrum — A Survey

Table 4-1 gives some properties of interest for the whole spectrum of elec- tromagnetic radiations. Since the em radiation has both wave and particle properties, the wavelength range of the different sections is given, and the energy associated with an excitation in each section is given in electron volts (1 electron volt/molecule = 22,000 cal/mole). Common means of detecting and of handling the radiations are noted; and what happens during absorp- tion is indicated.

If one expects to gain insight into the interactions of electromagnetic radiations and matter, one must study the two Tables, 4-1 and 4-2, ex- haustively. There is no easier way. One will find, for example, from in- spection of the dimensions of the wavelength, A, and frequency, v, that they are related through the velocity, c, which for all electromagnetic radia- tions in vacuum, no matter what the wave length, is 3 x 1010 cm/sec (186,000 miles/sec). Thus

v = 3 x 10!0/A cycles/sec

Table 4-2 indicates some of the effects of the interaction of various "cuts" of the spectrum with matter. It is certainly true that radiation of short wave length (high frequency) carries more energy, is more penetrating, and can do more damage than that of long wave length. Thus, at wavelengths from 20,000 to 500,000 A, the radiation simply tickles the molecules into a rota- tional and vibrational frenzy (high heat energy;. Radiation of 4000 to 7800 A excites electrons in the pigment molecules of the retina of the eye, and is visible. (Maximum sensitivity of the eye is at about 6000 A.) Radia- tion of wavelength 2000 to 4000 A (ultraviolet) excites even the bonding elec- trons in a molecule, and so loosens up a bond that chemical reactions may take place which otherwise could not. Wavelengths below 2000 A, in the hard or vacuum ultraviolet, actually drive electrons out of a molecule, or ionize it; and as the wavelength gets shorter, and the radiation "harder," more and more ions are formed in the wake of the incoming radiation. In the X-ray region (X = 1 A) the electrons of even the K shell of the atom, the most tightly bound ones, can be excited or ejected; and in the gamma region (~0.01 A), even the nucleus can be penetrated by the radiation, al- though electrons in the atomic cloud are a more probable target.

78

E c

tt cu

cu Q

CU C bo co

a:

-a "o

53 J2 —

■ co o

be «u ^

CO " IU

E £\S

CJ —

<" -rl

-5 c

u CO

CO

U

bo _c

to t- bc

T3 <U

bD

— _ JS ^ N

2 CO

3 bD

CO

3

cr

u O

be

-a c

e -5

c/i pi CO co

3 J2 cr bo

&

u

u cu

a £ c £

"O cu "3

u o >• o

>, _Q CO j3

* C • C CO 3 CO

£.2E

3 _: 3 JZ

-

CU

JO

c

e

£0

CU JO

3

_o

6

to

cu 0"> O

S a- -t

cu

cO -C cu

C

_o to

N

'5 o

i u

x 9- CL

CO _ bD

cu cu

o

u3

3-

u

o

cu

§ 2

cu

3

CU CU

JZ

CU

-3 cu

.3-.

o S3

- ?

c E

«-> o

ci —

.- o

u rl ^ u

° " -£r °

« .S T3 «

cu O '

cu

CO s-

S g

-o -a

cu c

C •-

_Q

C

CO

cu

CO

3

3. "3 CU O

CU

3

b, "o -a

c

CO

E

3

3 cu

u

'cu

"3 CU

-3 c •- -C C

3 cu

-a

cu

c

3

3 0

r- T

>

cu

3,

o

T3 3 CO en 3 O

JZ

Cu >

O O

o

r-

o

CM

^1-

LO o

^ o o 2 - un

r- m

oo

o o

d

o

■<*■

o

^- d

I

O

o

O r-

~ I

<o O

o

'-' X

X 00

X

O o>

i- o ^

°"^

- x 2

X 00 <^

c

p

cu >-

cu

O O

o

cu

o

JU

"cu >^

o

o o o

o"

o o

cu

cu CO

bo

CU

0)

t

cu Q. O

o

u

E o

E

3 i_ ^« (J CU

a to

c a> o E o

iu

(U

CU

£ 0) 4)

cu <3> 4?

3 C «

cr o i)

« cc -

- 2r

cu o>

c o

c cu

D

i-

cu

3 O

O [_

Ou

in JO

O

CU

3

CO

"3 3 O CU

cu

CO

o

O =o O

o

X ro —

O O

O OJ

O )

* 2 2 o

X X (V) ,- c^ <^> I

©

O ©

o o

to

cu

cu ^

CO ^-v ©

M U O

CU ^ r—

E6o

CU

o un

©

LT)

CU >-

CU

3

•<

CU

u

CO

a.

© o

© ©

••< »<

•< o

o d

o © oo

©

o © ©

o

o ©

00

o

©

© ©

©

8° 8 N-

E

cu

©

LTl

O

r» cm

'-"" 2

2 •<

o o ©

©~

o

en

£

cu

o

E

cu

©

o

© ©

o

© o

CO

c

o

o ^5 o

-a

CO

-o

CO

<

CU

E

CO

O U

CO

E E

CO

O

X

CO		u CO	cu	cu >
cu	cu	3	cO	CO
^	»— i	3	O
XJ	u	M	>-,
u CO	in >	CO CU Z	U CO	cu

cr cu

be

CO

D

-3	-3
CO	CO
t_	5_
	t_t
cr	CO
CU	CO
Ih	CU
	-o
JZ	cO
bO	o

CQ

79

TABLE 4-2. The Electromagnetic Spectrum — Absorption

Radiation	Source	Absorbed by	Effects of Absorption
Cosmic	nuclear reactions	nucleus; electron	artificial radioac-
	on sun	cloud of atoms	tivity, fission, ex-
		and molecules	citation, ioni- zation
Gamma	radioactive elements	nucleus; electron	artificial radioac-
		cloud	tivity, excitation, ionization
X	metals hit by high-	electron cloud	excit. or eject, of K-
	speed electrons		shell electrons
Vacuum UV	sun; atoms hit by	electron cloud	excit. or eject, of L-
	med. speed elec-		or M-shell elec-
	trons		trons
Far and near UV	gas discharge tubes;	electron cloud	excit. of sub-shell
	sun*		and valence electrons
Visible	sun; thermally ex-	electron cloud	excit. of valence
	cited atoms		electrons
Near infrared	red-hot bodies (e.g.,	vibrating perma-	increased kinetic
	fireplace); sun	nent dipoles in	energy of vibrat.
		molecules	(incr. temp.)
Far infrared	red-hot carbon; sun	rotat. and vibr.	incr. kinet. energy
		perm, dipoles of	of rotat. and
		molecules	vibr. (incr. temp.)
Microwave	klystron radio tubes	rotation of perm.	incr. kinet. energy
(radar)		dipoles	of rotat. (incr. temp.)
Ultra high-freq.	tubes and tuned	reradiated by con-	unknown; interac-
radio	circuit	ductors (metals, the body, etc.)	tion with nerve?
High-freq. radio	tubes or transistors	reradiated by con-	unknown
	and tuned circuit	ductors (metals, the body, etc.)
Broadcast	tubes or transistors	reradiated by con-	unknown
	and tuned circuit	ductors (metals, the body, etc.)

* Estimates of the internal temperature of the sun go as high as a million degrees K. Spectroscopic meas- urements give the temperature of the incandescent gases surrounding the sun to be about 6000° K. A black body at 6000°K radiates some energy at nearly all wavelengths, but the maximum energy is radiated at about 5000 A, right in the middle of the range of wavelengths visible to man. This is no coincidence, of course, for man's senses are adapted to his environment.

After absorption of the damaging short-wavelength ionizing radiation by the upper atmosphere, the total energy reaching the surface of the earth on a clear day is ~ 1.25 cal/min cm1. However, above the a phere space travelers will have to be protected against the small amounts of ionizing radiation which extend right down to wavelengths in the X-ray region. The most prominent of these is the strong emission of excited hydrogen atoms, the"Lyman-alpha" line, at a wavelength of 1215 A.

80 ELECTROMAGNETIC RADIATIONS AND MATTER

Quantitative expression of these ideas followed Planck, who, in 1901, pro- posed that the energy, e, contained per photon in incoming electromagnetic radiation is proportional to the frequency, v, of the radiation. Thus

e = hv

where h is the proportionality (Planck's) constant, equal to 6.62 x 10"27 erg sec/photon (1 electron volt, ev, = 1.6 x 10 12 ergs).

Let w},w2, and w3 be the energies of binding of different atomic or molec- ular orbital states of the electron to the nucleus, and accept Bohr's as- sumption. If e = w}, w2, or w3, absorption of the incoming radiation will easily occur,accompanied by excitation of the electron from its "ground state," or orbital of lowest energy, to an excited state. If e ^ wy, w2, or w3, then absorption does not readily occur, although in favorable cases wx can be taken from a larger e, the electron excited to state 1, and the radiation pass on with reduced energy (e - w, = hv2) and lower frequency (longer wave- length). This is one aspect of the famous "Compton scattering."

If f is greater than some critical value, w, the ionization energy, the elec- tron can be ejected completely from the atom or molecule, and may have any kinetic energy up to and including e — w. Since the electron has a mass of 9 x 10_28g, the kinetic energy (1/2 mv2) is less than, or equal to, e — w. Now a negative particle of velocity v, just like any other member of the elec- tron cloud about a molecule, but moving with high velocity, is a very good ionizer itself. Hence the ionization process continues along a track through the tissue until all the incoming energy, e, has been dissipated either as heat or in producing ions.

The Laws of Absorption

In the tables of properties of em radiations, the bases of the techniques for handling them were implied. What happens when absorption takes place was also indicated. We consider now the extent of absorption, and its con- verse, the depth of penetration.

In brief and in summary, absorption of electromagnetic radiations is governed only by the laws of chance. The chance that a photon will be ab- sorbed depends only upon the number of target electrons and nuclei in its path. From the fact that the higher energy (shorter wave length) radiations penetrate deeper into any given material, it is inferred that they are more difficult to capture — have a "smaller capture cross-sectional area." Con- versely, the denser the target material the greater is the number of potential targets per centimeter of the photon's path, and hence the greater is the ab- sorption per unit length of path.

These ideas are expressed quantitatively in Lambert's law. The rate of

ELECTROMAGNETIC RADIATION; NATURE AND SPECTRUM 81

absorption is directly proportional to the amount to be absorbed; or

-dl/dx = k'l

where x is thickness and / is intensity, or number of photons passing 1 cm2 per sec. This is one of the natural functions (Chapter 1) for which / is ex- pressed explicitly as

/ = /,

-k'x

where I0 is the intensity when x = 0, just as the radiation enters the ab- sorbent; k' is a constant, characteristic of the absorbent (larger, the better the absorption capacity of the medium), called the absorption coefficient. The plot of / vs x is shown in Figure 1-2 (c).

Since In I0/I = k'x, conversion to common logarithms by dividing by 2.303 gives log I0/I = kx, where k' = 2.303 k, and k is called the "extinction coefficient."

Lambert's law is applicable over the whole electromagnetic spectrum, and, you will remember from Chapter 3, is useful also to describe the ab- sorption of matter waves. It is an obvious but very important point that the extinction coefficient of a substance will be different at different wave- lengths. From the far infrared, through to the near ultraviolet, the extinc- tion coefficient is large only for particular wavelengths. Such specificity is a property of molecular absorption. If these molecules are suspended or dis- solved in a medium, k will be directly proportional to the concentration, c (Beer's law). Thus k can now be factored into ac, where a is called the molec- ular extinction coefficient. Formally then:

log I0/I = acx (Beer-Lambert law)

The specificity for absorption of selected wavelengths disappears from the far ultraviolet through to gamma radiation — continuous absorption occurs accompanied by ionization — and the extinction coefficient decreases more or less linearly with decreasing wavelength (i.e., with increasing energy /photon). Thus ultraviolet light penetrates only a small fraction of an inch of tissue; and the k for tissue for near ultraviolet is very large. By contrast, soft X rays penetrate tissue with only a small amount of absorption per cm; and k is smaller. However, each photon of X rays absorbed carries roughly 1000 times more energy than each photon of near ultraviolet, and therefore only 1/1000 as much absorption is required to do the same damage. It is seen then that the important quantity is the energy absorbed per unit volume, because this determines the subsequent effect: warming of tissue, triggering of the optic nerve fiber, providing the energy for photochemical synthetic processes, or ionization and rupture of molecular bonds.

82 ELECTROMAGNETIC RADIATIONS AND MATTER

The molecular extinction coefficient is strongly dependent upon wave- length, as we shall soon see. The optical transmission is defined as 100 7//0 per cent. The optical density, often used, is defined as log (I0/I), and increases linearly as concentration of absorber is increased.

SOME INTERACTIONS OF ELECTROMAGNETIC RADIATIONS

AND LIVING MATTER

The parts of the spectrum which are of biophysical importance can be conveniently classified under four main titles: the warming region, the visible region, the photochemical region, and the ionizing region. Each of these is illus- trated below. Enough of the principles are given to introduce infrared and ultraviolet therapy. The visible region is considered in more detail, for obvious reasons. X and gamma rays, and hard ultraviolet too, are intro- duced here in principle only. Detection and absorption are discussed in Chapter 5, and Chapter 9 deals exclusively with biological effects of all the ionizing radiations.

The Warming Radiations (Infrared)

Electromagnetic radiation in the infrared range is always associated with heat energy of those molecules which contain permanent dipoles. Its ab- sorption results in increased rotations and vibrations, and therefore in in- creased temperature. Infrared radiations are then logically called "heat rays.

The penetration into tissue is appreciable, although the extinction coeffi- cient is large. The warming effect of absorption by the very outer layers of the skin can be felt beneath the surface because of the poor but substantial heat conduction of the tissue. Infrared-lamp therapy is based on this prin- ciple. Since the tissue is 85 per cent water, the strongest absorption would be expected to occur particularly near the strong water-absorption wave- lengths: (1) vibrations at 28,200 and 63,000 A, (2) rotations from 500,000 to 1,200,000 A, as well as (3) some absorption by mixed vibrations and ro- tations at nearly all wavelengths greater than about 8000 A. Intense infra- red electromagnetic radiation, when absorbed by tissue, causes gas and steam pockets which lead to lesions and blisters.

Infrared Spectra

The wavelengths absorbed often provide clues as to what rotation or vibration is absorbing the incoming radiation. In the instrument called the spectrometer a small slit of light from a continuously burning carbon arc — a good source of infrared radiation — passes through the absorbent and then on through a triangularly shaped crystal (prism) of KC1 or KBr; the trans- mitted radiation is broken up — the longer wavelengths will be bent sharply

SOME INTERACTIONS WITH LIVING MATTER 83

within the crystal, the shorter wavelengths less so — and the image of the slit will appear as darkening on a photographic plate, at positions proper to the wavelengths entering the slit. Thus the absorption bands of water corre-

O spond to O — H stretching vibrations and to H H bending vibrations.

This is true for any absorber with rotating or vibrating dipoles. Many thousands of spectra have been determined, principally in organic mole- cules, for purposes of learning what polar groups there are in the molecule, or for identification of a particular substance in a mixture. Continuous use is now being made of this technique in investigation and control of barbitu- ates and narcotics, for example. Each material has a characteristic spec- trum (plot of absorption vs wavelength), easily reproduced, in many cases easily identified. Figure 4-6 shows two examples, and gives an indication at the bottom of what rotations and vibrations within the molecule may be responsible for each absorption peak (pointing down).

Visible Radiations

This region is noteworthy for the sole reason that the animal body is equipped with a very sensitive set of living cells which can detect wave- lengths of 4000 to 7800 A coming in from excited molecules in the environ- ment. Molecules in the environment are excited by radiation which pours in from the sun at all frequencies proper to a hot body. The reradiated energy from the excited molecules of a tree, for example, outlines its shape; the exact composition of the reradiated energy defines its brightness and what we perceive as its color.

The eye is a device by which the energy of an electromagnetic radiation pattern is converted into the energy associated with the various nerve im- pulses which can traverse the optic nerve to part of the brain. It is a trans- ducer in the sense that it provides a mechanism by which electromagnetic radiation of wavelengths in the critical range can be received, focused, sorted out, and then converted into the chemical, thermal, and electrical energy which is necessary to trigger nerve propagation. In general, the energy car- ried by a nerve impulse is much greater than that of the light photons which trigger the propagation. This subject is considered in Chapter 10, and we confine ourselves here to what takes place before the nerve is triggered.

Architecture of the Eye

Figure 4-7 is a simplified sketch of the basic parts of the eye. It illustrates principally the roles of the lens, the retina, and the optic nerve. Light of intensity IQ ergs/cm2 from a light source falls on the cornea. About 96 per cent passes on through the lens, and about 4 per cent is reflected. The cornea, the aqueous humor, the lens, and the vitreous humor are essentially

84

-• \-

				*:			o <u
	o	,_ -D
	o	c ,_
	o:	0) !/>
	1 * °5	u a>c-
		o	•55 c
		cr	< 0)
o m	ac	X	to 'u
	»-	z	"E 2
	CO			<u t:
O ro	a: (to CO </>			E 2
	O 2 1 1				< £ _ O
O	o o				E 0
_J						£ £
					C 0
O					co 1/1
o					11
o				o z LU CD X o	■5 te <D = c O 11
o					I. 0 <^
to				£ •
i					"D 3
				c <-<
	o			D <"
	z Hi
o	CD
h-"	X			y ■£
H crcrz '
c a. \- 1-
O J- CO CO o » zo — ^ »* •<		^ c
E oo0		8 .2
	o				< 0
p i to <	>					^0 £ >
t				E -
<	1		■c °
«	a		S- 0
	»		CO •£
3	3	ec	7 2 2 E
		t-	0 *"
	CO
	X	— 3 U
o	g	5. 't
in	1	c a.
			>- 0
			Q.
o	Z X		»- O t 8.3
	CO o	-2 c I 3 O
	I		V \£ LU
	o		4> Q.
				S 0 <->

q			o	; JD O
		- •	O >.
lO			• ~ «> ,V 3 3 <J 0 a> X U
		3 0 ~ 01 °-==
in
cJ								IE 0 £

SOME INTERACTIONS WITH LIVING MATTER

85

point light source

(the object)

ornea aqueous humor

ciliary muscles

optic nerve Figure 4-7. Architecture of the Left Eye, Viewed from Above.

liquid crystal materials and are, of course, transparent. About 48 per cent of 70 reaches the retina. The iris acts as would the diaphragm of a camera, controlling the area of the pupil, and hence the total energy admitted.

The incoming light, which is usually divergent from the source, is focused on the retina by the lens. The distance, q, between the lens and the image (of the light-source) on the retina is constant, but the lens-to-object distance, p, may vary widely from about 4 in. to a mile. To be versatile, then the focal length, /, defined as

_L _L J_

/ ~ P + q

must be adjustable if objects at different distances are to have sharp images on the retina. Now the focal length depends upon the geometry of the lens: a thick lens will have a short focal length, and a thin lens a long focal length. Because the lens is a liquid crystal much like jelly, its shape can be changed by the tension exerted by the ciliary muscles. This tension is in turn con- trolled by a nervous signal fed back from the retina, the cells of which esti- mate the sharpness of the image. This process is known as accommodation.

Photosensitive Cells

The focused light falls on two types of cells on the retina, rod cells and cone cells, named because of their shape. The rod cells (scotopic vision) are the more sensitive to light, and distinguish for us light from dark when the intensity is very low (twilight vision). On the other hand the cone cells (photopic vision) are less sensitive, can resolve large amounts of light into its components, and therefore detect details of the image, such as shape and color.

The photosensitive cells are present in large numbers, estimated at 126,000 cells/mm2. Most of the cone cells are clustered close together about

86

ELECTROMAGNETIC RADIATIONS AND MATTER

a center called the fovea centralis. The distribution of rod cells is different (Figure 4-8) — practically none at the fovea, but otherwise distributed in great numbers over the whole area of the retina.

*

eg

2 2E

a.

UJ Cl

tf)

o

z <

O

I

CO

o o ce

u. O

160 -

120 -

80 -

40

HORIZONTAL ANGLE (DEGREES) FROM FOVEA CENTRALIS

Figure 4-8. The amount of rhodopsin and the number of rods per unit area have a similar dependence on angle bounded by the incoming light and the central meridian in which incoming light falls directly on the fovea. The optic disc, where the optic nerve enters, is about 16° to the nasal side, and there- fore a blind spot exists there. (Locate the blind spot in your right eye by first focusing the eye on the black dot, then turning the eye 16° to the left — i.e., about 4 in. if the dot is 10 in. from the eye.) (After Rushton.')

A brief discussion is now given of those molecules, known as pigments, which are not only the absorbers of the incoming radiation but also the transducers, the "machines" by which the incoming energy is trapped and "led across" into another form, not heat, which can trigger the optic nerve. Actually there are two separate subjects to discuss: twilight vision and color vision. Although much has been learned by direct experiment on animals, Rushton1 complained in his recent review: "Measurements upon human pig- ments have only just begun, and it is to be hoped that far better experiments will be made." We give here a summary of the present understanding of this

SOME INTERACTIONS WITH LIVING MATTER 87

important vital process, keeping pretty close to the facts, by-passing the theories.

Twilight Vision

As mentioned above, cells of two general shapes are found on the retina, rod and cone, the rod cells being responsible for the very sensitive detection of light from dark when it is almost dark. These cells distinguish the shape of the object, and although this is their primary role, they also permit us to dis- tinguish colors.

The pigment responsible for twilight vision is a molecule called rhodopsin, the classical "visual purple." It is a condensation product of the carotenoid, retinene, and a protein called opsin. Retinene is a 20-carbon, ringed com- pound, the aldehyde of vitamin A, and its structure is well known. How- ever, not very much is known about opsin. Another opsin has been identi- fied, attached to retinene in the pigment todopsin. Further, an isomer of retinene has been combined with the original opsin, and cyanopsin formed. However, only rhodopsin is active in twilight vision.

The extinction coefficient of rhodopsin, extracted in bile solution or in digitonin, has a maximum value at 5000 A. It drops off rapidly at both higher and lower wavelengths. Thus at 5500 A it is already down to about 25 per cent of the maximum, and at 5800 A is nearly zero; while at 4000 A it is also 25 per cent of the maximum value, but then remains about the same to wavelengths below those detected by the eye (smaller than 4000 A). The Beer-Lambert law is obeyed exactly for weak solutions of rhodopsin. Further, Figure 4-9 shows that the sensitivity of the human eye is deter- mined directly by the absorption of light by rhodopsin. To man's eye rhodopsin has a rose color; it absorbs strongly in the green (5000 to 5800 A) and yellow (5800 to 6000 A) regions and to a lesser extent in the blue (4200 to 5000 A), and reflects all the rest; it is this reflected light which falls on man's eye as he looks at the pigment, whether on the retina through an ophthalmoscope, or in solution. This is why it is "colored" rose.

It follows from the preceding paragraph that the fewest number of pho- tons which will trigger the nerve will be those of wavelength 5000 A, for it is here that the extinction coefficient is greatest. Incidentally, the unit of light energy falling on the retina is the troland. At this wavelength it amounts to about 100 quanta falling on a rod per second. However, the rhodopsin of a rod is half-bleached by about 0.03 trolands, or 3 quanta per rod. It happens that 1 troland is the retinal illumination when 0.1 millilambert (mL) is viewed through a pupil 2 mm in diameter; and 0.1 mL is the brightness of a white screen illuminated by 1 candle at a distance of 1 m.

Rhodopsin is "bleached" by white light. Its color fades rapidly through

88

ELECTROMAGNETIC RADIATIONS AND MATTER

yellowish to clear. In the dark, in vivo, the color is restored. The process can be summarized as follows:

photons + rhodopsin

k

A,

(bleaching) k2

bleached vitamin A -f energy

(to nerve endings)

+

retinene

+ energy (regeneration)

The scheme above indicates that the greater the intensity of the incoming light, the more will the rhodopsin be bleached. In twilight most of the pig- ment exists as rhodopsin, and the sensitivity is greatest. In daylight, most of it will be bleached, and the sensitivity least. "Dark-adaptation" is very familiar to us all; it is slow because the speed of regeneration of rhodopsin is

o

in

z

UJ Q

<

a. o

0.7 -

0.6 -

0.5 -

0.4 -

0.3 -

0.2 -

0. I -

250 300 350 400 450 500 550 3000 4000 5000

600 m M

o 6000 A

WAVELENGTH

Figure 4-9. The spectrum of human scotopic (twilight) vision sensitivity (crosses), and the absorption spectrum of rhodopsin (solid curve) are the same. (After Rushton.1)

SOME INTERACTIONS WITH LIVING MATTER 89

slow. The reader is invited to contemplate the expression of the Weber- Fechner law in this organ:

5" oc log r/M,

It says that the sensitivity, S, increases as the difference between the threshold intensity and that of the background decreases.

This photochemical description of twilight vision, although satisfactory in general, apparently needs revision, for serious troubles arise when quantita- tive description is attempted. It now seems likely that individual pigment molecules are attached to individual nerve endings, and the excitation of just one pigment molecule by incoming radiation is sufficient to trigger the nerve. Thus, although it takes upwards of half an hour for dark adaptation to oc- cur—that is, for the bulk rhodopsin to be regenerated in man after a bleach- ing— the minimum time during which the eye can recover enough from a flash to see another flash is about 0.01 sec.

Color Vision

The cone cells somehow distinguish between wavelengths, and thus dis- tinguish colors. The Young-Helmholtz theory, usually accepted, and now nearly 100 years old, suggested that three color-sensitive pigments exist, each one sensitive to one of the basic colors: red (6200 to 7800 A), green (5000 to 5800 A) and blue (4200 to 5000 A); and that various intensities mix to give the colors and qualities commonly referred to as hue, brightness, etc.

The Young-Helmholtz theory is based on the experimental fact that by a proper mixture of red, blue, and green light in an object, any shade of color can be matched. The theory is that the three pigments absorb definite frac- tions of the visible spectrum and overlap one another, and that the optic nerve can receive and transmit signals which correspond to any and all wavelengths of the spectrum. Apparently this theory now requires major modification as a result of the very recent (1959) work of E. H. Land.7 In some remarkable experiments he has shown in effect that the full range of colors can be recorded by the brain provided only that the proper mixtures of intensities of two wavelengths (one greater than, and one less than, 5880 A (yellow)), fall on the retina! It seems that the information about colors other than the two incoming wavelengths is developed in the retina. The possibility that the pigment molecules are in intimate contact in the cone cells, and dis- tribute the excitation energy among themselves in a manner controlled by the intensity pattern of the incoming light, immediately suggests itself. But more work is clearly needed following this surprising turn. Another recent surprise is that some evidence has been turned up that other molecules in the neurones, in the nerve pathway itself, contribute to the color perceived in human vision.

90 ELECTROMAGNETIC RADIATIONS AND MATTER

In spite of the credence placed in the Young-Helmholtz three-pigment theory of color vision, there is no direct evidence that three pigments exist in the cones. There is direct experimental evidence for two, however; this will now be recalled. Protanopes (color-blind people) cannot distinguish green from red. By measurement of the intensity of the light reflected from the retina as a function of incident wavelength on protanopes, it has been shown that a definite absorption by a pigment, given the name "chlorolabe," takes place with maximum at about 5400 A.

Now the protanope can see green, but not red. This fact means that a sec- ond pigment, given the name "erythrolabe," is missing in the protanope. Difference spectra (unreliable) of two pigments in the normal fovea (collec- tion of cone cells) show that the maximum absorption of the second, or miss- ing, pigment is about 6000 A. Thus there is good knowledge of one pig- ment, the chlorolabe, and knowledge of the existence of a second, erythro- labe. There is no experimental knowledge of a third in cones. But, of course, Land's new work indicates that only two are really necessary, one sensitive above and one sensitive below 5800 A. The two pigments discussed have these qualifications. Recall that the optical density maximum for rhodopsin is at 5000 A.

What the relation is between the excited pigment molecule and the color perceived is poorly known. Experimental approaches include that of meas- uring the electrical signals in the optic nerve (the electroretinogram, ERG) during stimulation by light, the reflection densitometry experiments men- tioned just above, studies of the rates of bleaching and recovery (adapta- tion), visual acuity, color perception, and Land's new work. However, since the excitation energy for electrons in large molecules is so dependent upon structure, it would not be surprising if rhodopsin, chlorolabe, and erythro- labe turn out to be very similar in composition. The answer will lie in knowledge of the structure of these molecules.

Incidentally, an important new fact, bearing upon acuity especially, is that the eyeball is never still, but rather is in a state of small, almost im- perceptible oscillations, such that the incoming light falls on a spot on the retina for only a few microseconds before it is deflected away. If the eyeball is fixed relative to the light source, color vision disappears.

Physical Defects of the Eye

If the lens is too thick or the eyeball elongated (myopia), the ciliary muscles are not able to make sufficient adjustment of the focal length to permit distant objects to be focused on the retina. The phenomenon is known as nearsightedness, and can be corrected with the aid of glasses with a concave lens of the proper focal length. If the length of the eyeball is too

SOME INTERACTIONS WITH LIVING MATTER 91

small, the condition is called hypermetropia, and can be corrected with a con- vex lens of proper focal length.

The lens of the eye often does not have the same curvature over all its sur- face, and light passing through the area of improper curvature will not be properly focused on the retina. The lens of such an eye is said to be astig- matic. A properly ground astigmatic glass lens can compensate.

Sometimes translucent or opaque tissue grows in or on the liquid crystal material of the lens and absorbs the incoming light before it reaches the retina. Such tissues are generally termed cataracts. Some can be removed by surgery; some are too extensive.

Depth Perception

Two detectors in different locations can inherently provide more informa- tion than one; and if relative information is recorded and interpreted from the two signals, more information is available from the two detectors than if each were interpreted separately. This is the reason sensory organs come in pairs. Typical of the relative information obtainable from two stations, in general, are direction and distance, or depth. Sound can be reflected, and hence the directional information provided by two stations is important. Light travels in a straight line to the eye, and therefore directional informa- tion is not important. However, the information derivable about distance or depth is important when we attempt to compare distances or develop a per- spective view. Ideally the eyes may each be rotated about 50° from a central line of vision. The two have to be in focus at the same time, on a near or a far object, and this requires a facility of minor individual adjustment. If the eyes cannot be made to focus (crossed eyes), sufficient correction can some- times be made with a suitable set of glass lenses, but often the cross must be corrected by shortening the lateral muscles or by suitable exercises designed to strengthen them.

Photochemical Radiations (Ultraviolet)

Photosynthesis

Subshell electrons are excited by the ultraviolet. The absorbed energy may be passed off to the vibrations or rotations of nearby molecules and ap- pear as heat energy; it may be re-emitted as ultraviolet; or it may excite the molecule and make it more susceptible to chemical attack by neighbor- ing molecules. Thus in the last case the ultraviolet may provide some or all of the activation energy needed for reaction to occur, and thereby increase the rate of reaction (treated later in Chapter 8). In fact, the photochemical mechanism is sometimes the only mechanism by which certain reactions can take place at a reasonable speed at biological temperature.

92 ELECTROMAGNETIC RADIATIONS AND MATTER

Because they carry more energy than photons in the visible region, the photons in the ultraviolet region are less likely to be absorbed. They pene- trate deeper into the absorbent and excite molecules at the point at which they are finally caught.

Of all the synthetic biological reactions whose rate is sensitive to ultra- violet light, probably the photosynthesis of simple organic sugars from C02 and 02 in plant leaves is the best understood; and yet the understanding of this basic process is not completely satisfactory. Of course if it were, we should be able to reproduce the syntheses in a test tube; but we cannot.

More important to present considerations is our knowledge of photo- catalyzed syntheses of the vitamins from basic components. Some of the vitamins have been purified, crystallized, and synthesized, and hence their chemical composition and structure are known. Consider the antirickets vitamin D2 (calciferol) for instance. Its structure is well known: two six- membered rings and a five-membered ring attached to an unsaturated aliphatic side chain of six carbon atoms, with a molecular weight of 393. This molecule is formed through the absorption of ultraviolet radiation of 2500 to 3000 A by ergosterol, a sterol molecule whose structure also is well known. The synthesis occurs in at least two steps. The absorption is con- sidered to take place at a carbon-carbon double bond, and the absorbed energy to go into excitation of the t electrons which form the bond. The opening of a benzene-like ring follows, and further rearrangements of the atoms and bonds give the biochemically active vitamin B2 structure. The re- action will not occur at all unless photolyzed.

This synthesis takes place in the human body at a location to which both the molecular components and ultraviolet radiation are accessible: that is, just beneath the surface of the skin in the living tissue serviced by the blood capillaries. Thus the principle upon which ultraviolet therapy is based, and the advantages of moderate exposure to sunlight, both become apparent.

Phototherapy

Prolonged sun bathing can damage skin pigments and can cause ery- thema. For instance, on the average it takes only 20 microwatts (/xw) of ultraviolet of wavelength 2537 A (from a mercury vapor lamp) falling upon the skin for 15 min to produce erythema. It is fortunate that the very in- tense ultraviolet radiation from the sun is attenuated (scattered, absorbed, converted into radiation of longer wavelength) by the ozone and nitrogen compounds in the upper atmosphere. Ultraviolet radiation would be a prob- lem in space travel if it were not so readily reflected by metallic surfaces. The effects on the eye are well known and have been implied in the discus- sion of the chemistry of the eye: the higher-energy photons of the ultraviolet in falling on the retina can keep the rod and cone cells devoid of rhodopsin

SOME INTERACTIONS WITH LIVING MATTER 93

and damage the color pigment molecules. Snow-blindness and "whiteouts" are the result. Further, ultraviolet has been attributed in some cases to promoting the growth of cataracts and photothalamia, or inflammation of the cornea. However, ordinary window glass absorbs all the dangerous ultraviolet, and colored inorganic materials can be added to filter out (or absorb) any undesired range of wave lengths. Therefore, protection is no problem, if properly sought.

Ultraviolet light has a lethal effect on primitive animal and plant life. This fact is used to good advantage in destroying the bacteria, eschenchia coli and bacteria coli, in foods or in our water supply. Each of these is killed by about 14 x 10"6 ergs per bacterium. Among the abnormalities successfully treated with ultraviolet light are conjunctivitis, fibrosis, acne, and surface in- fections of various kinds. Certain heavy metals (calcium, gold, silver, etc.) and certain highly absorptive molecules (methylene blue, quinine, etc.) sometimes increase the therapeutic value of the ultraviolet irradiation.

The shortest-wave, vacuum-ultraviolet radiation overlaps the X-ray re- gion. The principle difference between the two regions in the present classi- fication is whether ionization and bond rupture is the exception (ultraviolet) or the rule (X and gamma). The vacuum-ultraviolet will be discussed im- plicitly in the next section, for the differences between it and the X ray are of degree rather than of kind.

Ionizing Radiations (Mainly X and Gamma)

Principles

The only distinction between the radiations more and less energetic than that with a wavelength about 2000 A is one of excitation vs ionization. That is, at wavelength X greater than about 2000 A, excitation of electrons of the electron cloud takes place as the rule, and ionization takes place only in special circumstances; while at X less than about 2000 A the electrons can be knocked right out of the atom by the absorbed photon. As X decreases, the loosely held orbital electrons are the first to go, followed by the subshell elec- trons, and as X — » 1 A (X-ray region) the tightly bound K-shell electrons can be ejected.

A simple calculation will make this important point clear. It takes an in- put, w, of ~230 kcal to make 1 mole of ions out of 1 mole of atoms, i.e., 10 ev to make an ion out of an atom. (This is the energy carried by each photon of em radiation of wavelength 1200 A.) Now the gamma radiation of the radioactive isotope of cobalt of atomic weight 60 (referred to the hy- drogen atom as 1), Co60, used in deep radiation therapy for cancer, has an energy of about one million electron volts (1 mev/photon). Therefore, each photon would leave a wake of about 1 06/ 1 0 = 105 pairs of ions (or molecules which have been ionized) before it loses all its energy.

94 ELECTROMAGNETIC RADIATIONS AND MATTER

The electrons lost may have been valence, or bonding, electrons — active in holding the molecule together. In covalent bonding two paired electrons form the bond between carbon atoms, as in a sugar molecule for example. Ionization weakens the bond and perhaps breaks it; in any case the unpaired electron left is chemically very reactive and will make a new bond at any time or place. Cross-bonding of molecules, the synthesis of new molecules, polymerization of old ones, etc., all can occur. It is not hard to envisage how such reactions could adversely affect the tightly geared steady-state of normal living tissue.

It is convenient to reserve further discussion of the effects of ionizing radia- tions until the principles of radioactivity have been outlined. The radioac- tive emanations, alpha, beta, and the nucleons, are ionizing radiations, as are gamma and X, and the effects of all are conveniently discussed together.

Diagnosis by X Rays

The absorption of electromagnetic radiation increases with increasing density of the absorbent. Differentiation of diseased tissue from normal is based on this fact. The higher the speed of the electrons which impinge on the target metal, the harder the X rays so produced. Machines avail- able today produce X rays from electrons which have been accelerated by thousands to millions of volts. In general, the greater the voltage, the greater the energy of the X-ray photons, and the greater their penetrating power.

For example, at 40,000 v (i.e., 40 kilovolt potential (kvp), in radiation terminology) almost any tissue will stop some of the X radiation and cast a shadow on the fluorescent screen or photographic plate behind it. At 80 to 100 kvp, commonly used in medical diagnosis, the radiograph displays shadows which differentiate fat and other soft tissues from air space and from bone.

Whenever it is possible to insert molecules containing heavy metal atoms into a region of interest, differentiation of tissues in the region is enhanced (Figure 4-10). Thus barium sulfate solution is commonly administered as an enema so that the lower part of the intestines may be examined (by X radiation). Iodine in a variety of compounds is also widely used to increase differentiation. For instance, in iodophthalien it is preferentially taken up by the liver and stored in the gall bladder; thus gallstones, if present, are easily seen. Similarly, the kidneys, uterus, blood vessels, and even the heart can be made visible to X-radiography (see Figure 4-10 (b), for example). Location of broken bones, of swallowed pins, of stomach ulcers and of tumors is routine.

The use of X rays for diagnosis introduces the serious question of the ex- tent of the damage done by the rays absorbed. A complete fluoroscopic gastrointestinal examination with barium sulfate can be done by a competent physician with the dose to the region irradiated not exceeding 20 rads (the

MICROSCOPY

95

impinging x-rays 80 kvp

1.32

1.35

+ +

Co20

5.0

0.99 Four targets or absorbers

1.54

transmitted x- rays

photographic plates

Figure 4- 10a. Absorption of X Rays by Atoms. Energy of the incoming wave is trans- ferred to the electron cloud. Absorption is proportional to electron density, electrons per cubic A (bold numbers inside). Number of electrons (i.e., atomic number - valence) and atomic weight are given, as is atomic radius (at 7 o'clock). Note shift of both ampli- tude (number of photons per sec) and frequency (energy per photon).

unit is defined later — only relative numbers are of interest now), although electronic intensification of the image now permits one to reduce this dose by a factor of ten. Although immediately measurable damage appears only if the dose is hundreds of times higher, more subtle effects, such as malignant growths, may show up years or even generations later if the greatest caution is not exercised. The effects of absorbed radiation dose can be cumulative.

These questions are considered in more detail under "Therapy" in Chap- ter 9.

MICROSCOPY

A microscope is a device which throws a large image of a small object on the retina of the eye. It does this by passing definitive light through a sys- tem of lenses. A few useful notes are now given on the two most common types. All the necessary details are set out in a very useful, practical manner in the little book by Martin and Johnson entitled: "Practical Microscopy,"8 and in literature happily supplied by the optical companies.

96

ELECTROMAGNETIC RADIATIONS AND MATTER

Figure 4-10b(i). Absorption of X Rays by Tissues. Abdomen with Barium Sulfate in the Colon. Note the differences in absorption of X rays by skeleton (vertebrae, sacrum, ribs, etc.), soft tissue (bottom edge of kidney, psoas muscle, liver), and gas pockets in stomach and colon. Low contrast film.

Optical Microscope

The small object to be viewed is illuminated either from above or below. In the former case reflected light, and in the latter case transmitted light, is allowed to pass through a convex objective lens of short focal length. In passing through the objective, the rays (visible region) are sharply bent, so

MICROSCOPY

97

that a bright, but small image of the object exists within a few centimeters of the objective. About 10 cm away from the objective, and in line with the object, is the "eye-piece," or condenser, another convex lens with very short focal length, which throws an image of the objective's image on the retina if held about 2 cm away.

Figure 4-10b(ii). Absorption of X Rays by Tissues (Continued). Ab- domen with Iodine Metabolized into the Kidneys. Note the difference be- tween the normal calyces of the kidney (white "horse," upper left) and the defective one (upper right). High contrast film. (Courtesy of A. F. Crook, Ontario Cancer Foundation.)

Magnifications up to more than lOOOx are possible with the best instru- ments. The preparation of the lenses is the critical thing, for it is difficult and costly to grind a large lens which will not be astigmatic. If the lenses are perfect, the limit of resolution (the smallest distance by which two ob- jects can be separated and still be differentiated) is determined only by the wavelength of the light and the size of the aperture which admits the light.

98 ELECTROMAGNETIC RADIATIONS AND MATTER

For white light, with an average wavelength about 5000 A and a numerical aperture of unity, the resolving power is 10,000 A, or 10"4 cm, or 1 n. One can use monochromatic blue light to improve this somewhat; and the re- search use of ultraviolet (A = 2537 A from a mercury arc, for example) with fluorescent screens, is an attempt to push the resolution down to 0.1 ;u. In common practice, however, "good" microscopes used in schools and routine examination have a resolving power 5 to 20 /j..

The binocular microscope uses two microscopes in parallel, one for each eye. From this double input, one obtains depth perception.

Phase-contrast and interference features have been superimposed on the simple microscope, broadening its versatility by improving the contrast be- tween different parts of the object under study. Contrast occurs in the normal microscope because of differences in density. In phase and interfer- ence microscopes, used when the density is about the same throughout (soft tissue is ~90 per cent water), advantage is taken of the facts that the speed of light through materials, which determines their refractive index, and the amount to which the plane of polarized light can be rotated, often differ if the molecular composition of the materials is different, even though their density is the same. To take advantage of these facts, two methods are available. Both present a highly contrasted image to the eye, one in inten- sity, one in color.

The principles are really quite straightforward. The reader is referred to the trade literature for operating detail. Both are extensions of the normal bright-field transmission microscope; only the extensions will be noted here. In the phase microscope, an annular diaphragm is inserted in front of the con- denser lens and therefore before the light falls on the specimen, together with a phase plate composed of a thinly evaporated ring of dielectric on a background of thinly evaporated metal. Thus light passes at different speeds through different parts of the object to be viewed, and the emerging light waves are out of phase. At one point of emergence from the object the phase difference will be such that the waves cancel each other; at another they reinforce each other. The phase plate "fixes" these differences by retard- ing those which pass through the dielectric, and absorbing some of those which pass through the metal. Thus identification and analysis of the struc- ture of (unstained) living cells and tissues, the components of which are so similar in density that discrimination is impossible with the light microscope without killing and staining, is made possible. This instrument, invented by Zernicki in the Netherlands in 1932, is now an indispensible tool in clinical analyses — in bacteriological, histological, and, in particular, pathological studies of tumors and cancerous tissues. Note the contrast in Figure 4-11.

The interference microscope is a polarizing microscope, adapted so that part of the light passes through the object and part around it, the two then being

MICROSCOPY

99

Figure 4-11. Partially Crystalline Otoconiae (stones) of the Utricular Macula (bone) of the Organ of Balance in the Middle Ear: Sectioned, and in Negative Phase Contrast. Magnification 60 x . In addition to the sizes and shapes of the stones, note their darker center (glycoprotein) and the bright lamellar periph- ery (calcium carbonate). (Photograph courtesy of L F. Belanger, University of Ottawa Medical Faculty, and of J. Cytology and Cellular Comp.) .

recombined to interfere constructively or destructively (as in the case of phase, above), and to present to the eye enhanced differences in density or color. Before the light passes through the specimen it is plane-polarized by passing through a crystal in which the light in all but one plane is absorbed. The emerging, polarized light is split into two beams whose polarized planes are rotated at right angles to each other after one has passed through a sec- ond crystal (birefringent). One beam then passes through the specimen, and the other around it. The one which passes through is rotated, absorbed, and retarded in different places to an amount depending upon the arrange- ments of the molecules ( — the term is "different optical paths"). The dis- torted light is then recombined with that by-passed, and their interference presents the image in different colors to the eye. If monochromatic light is used, the image appears in the form of differences in intensity; if white light is used, the image appears in the form of differences in color. Although it is not as sensitive as the phase microscope to differences in structure, the inter- ference microscope affords a wider field of view, can show subtle differences as shades in color, and has permitted (optical) determination of the amount of a particular absorbing material in the field of view. Since its inception, in

100 ELECTROMAGNETIC RADIATIONS AND MATTER

the early 1950's, it has been used for quantitative studies of proteins in living muscle, growth rates of cells and parts of cells, and similar problems on living tissue which can be studied only with a nondestructive tool.

Electron Microscope

This development of the last twenty years has added a new dimension to the depth to which tissues can be viewed. After fixing and staining (e.g., permanganate, phosphotungstic acid, osmium oxide), a very thin cut to be examined is placed in high vacuum, and bombarded from below by electrons (from a hot filament) which have been accelerated through a small aperture. Some of the electrons hit dense parts of the object and are scattered and absorbed — the principle is the same as for X rays (Figure 4-10 (a)); others pass on through less dense parts and fall upon a fluorescent screen or photographic plate. Proper alignment permits, in today's machines, ampli- fications of 500 to 100,000 x , with resolution of a few angstroms.

One instrument, which can be considered typical for biological work,** gives a 15- A resolving power; 600 to 120,000x magnification; and accelera- tion voltages of 100, 75, or 50 kv, to give electron beams of equivalent wave- lengths of 0.037, 0.043, and 0.054 A. The "lenses" are electric voltages be- tween charged plates. The amplification can be increased to over 1 ,000,000 x by photographing the screen, and enlarging the photograph.

Others

The ultraviolet microscope and fluorescence microscope have been used and improved since the early 1900's. They have some specialized uses in biological research. X-ray microscopy is useful when the sections to be studied are opaque to visible and ultraviolet light. For example, in histo- logical sections on bone, soft (~5 kvp) X rays are absorbed by the mineral component, passed by the organic component.

Reflection microscopy, especially the slowly developing infrared reflection techniques, may find limited use in future studies on biological material.

PROBLEMS

4-1 : Draw the shapes of sigma and pi bonds.

4-2: If all 1028 atoms in a human being were lined up side by side, how long would

be the line, in miles? 4-3: It costs an input of about 105 kcal/mole to pull the first hydrogen off a water

molecule. "Light" of what wavelength will blast it off? (calculate it). 4-4: Sketch intensity vs distance for the penetration of electromagnetic radiation

into tissue, presuming concentration of absorbent of 0. 1 moles/1 and molecular

extinction coefficients of 0.1, 1.0, and 10.0.

**The limitations should be realized: the tissue sample is dead, dry, and thin while being viewed in the electron microscope.

REFERENCES 101

REFERENCES

1. Rushton, W. A. H., "Visual Pigments in Man and Animals and Their Relation

to Seeing," Prog, in Bwphys., 9, 239 (1959).

2. Stacy, R. W., et al., "Essentials of Biological and Medical Physics," McGraw-

Hill Book Co., Inc., New York, N. Y., 1955, p. 262.

3. Brindley, G. A., "Human Color Vision," in Prog, in Bwphys., 8,49 (1959).

4. Evans, R. M., "An Introduction to Color," John Wiley & Sons, Inc., New York,

N.Y., 1948.

5. Ruch, T. C. and Fulton, J. F., Eds., "Medical Physiology and Biophysics,"

W. B. Saunders Co., Philadelphia, Pa., 1960.

6. The Physics Staff, University of Pittsburgh, "Atomic Physics," 2nd ed., John

Wiley & Sons, Inc., New York, N. Y., 1944.

7. Land, E. H., "Color Vision and the Natural Image," Proc. Nat. Acad. Set., 45,

115 (1959); Sri. Amer., 200,84 (1959).

8. Martin, L. C. and Johnson, B. K., "Practical Microscopy," 3rd ed., Blackie &

Son, Ltd., London, 1958.

9. Shamos, M. H. and Murphy, G. M., "Recent Advances in Science," New York

Univ. Press and Interscience Pubis., Inc., New York, N. Y., 1956.

10. Gamov, G., "The Atom and its Nucleus," Prentice Hall, Inc., New York, N. Y.,

1961.

11. Richards, O. W., "Pioneer Phase and Interference Microscopes," N. T. State

J. Med., 61,430 (1961).

12. Bennett, A. H., Jupnik, H., Osterberg, H., and Richards, O. W., "Phase Micro-

scopy, "John Wiley & Sons, Inc., New York, N. Y., 1951.

13. Hale, A. J., "The Interference Microscope in Biological Research," Williams &

WilkinsCo., Baltimore, Md., 1958.

14. Pritchard, R. M., "Stabilized Images on the Retina," Sri. Amer., 204, 72 (1961).

15. Hall, C. E., "Introduction to Electron Microscopy," McGraw-Hill Book Co.,

New York, N. Y., 1953.

16. Szent-Gyorgyi, A., "Introduction to a Sub-Molecular Biology," Academic Press,

Inc., New York, N. Y., 1960.

CHAPTER 5

Radioactivity; Biological Tracers

Our sensory data, even with complex equipment, consists of flashes of light, of the rates of discharge of an electroscope, of audible clicks or totals from an automatic counter, of tracks of liquid particles in a small chamber, of the deposit of silver grains on a photographic film, of heat evolved, of certain color changes. From these simple observations scientists have al- ready created a complex and exciting description of particles far too small to be seen directly (Miner, Shackelton, and Watson.3)

INTRODUCTION

Properties of the Emanations

In 1897, we entered the golden age of nuclear physics. It was then that Becquerel, experimenting with pitchblende, which is fluorescent, acciden- tally discovered a new and exciting emanation from the material. The emanation was rather penetrating (through his desk-top), and darkened some photographic plates kept in a drawer below. The Curies extracted the element which gave rise to the activity — radium — and called the emanation "radium-activity/' from whdch we derive the modern name, radioactivity. Chapter 4 has already described how three components were isolated from one another by Rutherford, and named alpha, beta, and gamma rays. The relevant properties of each as determined from scattering experiments, etc., are gathered in Table 5- 1 .

It is the penetrating properties of these radiations with which we are now primarily concerned. However, to understand penetrating properties of radiations from any radioactive source, we must first understand their origin (i.e., in the atomic nucleus) and their absorption, as well as the methods used to detect them, to identify them, and to measure their energy.

102

INTRODUCTION

103

TABLE 5-1.	Physica	Properties of Nuclear Particles
Emanation	Symbols	Rest Mass (grams)	Charge	Nature	v/c	Source
Alpha	°.c§>	7.2 X 1(T24	+ 2	bare helium ions	0.001 to 0.1	unstable nuclei (u.n.)
Beta	ft •	9 X 1(T28	±1	electrons	0.1 to 0.9	u.n.; accel erators (ace.)
Gamma	'Y f /w^	(not appli- cable)	0	electromag- netic radia- tion	1.0	u.n.
Proton	P, o	1.8 x 1CT24	+ 1	bare hydrogen nucleus	0.01 to 0.2	u.n.; ace.
Neutron	n, O	1.8 x 10"24	0	same, neutra- lized	"fast," and "thermal" (slow)	u.n. ; fission
Deuteron	d,OQ	3.6 x 10"24	+ 1	n + p		u.n.; ace.

Note: Charge is the number of units of 4.8 x 10~ electrostatic units (esu) of charge.

Velocity is ;• ; and velocity of light, c, is 3 x 10 cm/sec. (The ratio v/c for protons in cosmic rays and in the Van Allen radiation belt above the earth's surface approaches 0.8 (or larger than that produced arti- ficially).

The Nucleus

As has already been seen (in Chapter 4), the size of the nucleus has been measured by means of scattering experiments and found to be 10"12 cm, or about 10"4 A. The nucleus carries all the positive charge and most of the weight of the atom. It is thus very dense.* The positive charge carried by such a dense particle is almost unimaginably high — for radium it is 88 times that of a hydrogen ion! — and it is therefore not surprising that the binding forces, whatever they may be, must be orders of magnitude stronger than those of the electron cloud of the atom; and even a minor reorganization or splitting must involve a mass-energy change. It is instructive for one to com- pare again (Table 4-1) the energy of visible light, ~ 1 electron volt/photon, with that of gamma rays, 1,000,000 electron volts/photon, which arise from nuclear rearrangements.

♦This can be illustrated by a calculation of the weight of a 1-cm cube of nuclei of nickel (Ni) atoms, for instance, it being presumed that the nuclei are close-packed, side by side. Sim e the diameter of each is ~10~12 cm, 1012 nuclei side by side would be 1 cm long; and the cube would contain 1036 nuclei. Each weighs 65 times as much as hydrogen, or 65 x : ! x 10~24 g. The weight of the 1-cc cube, then, is about 1014 g. or approximately 100,000,000 tons!

104 RADIOACTIVITY; BIOLOGICAL TRACERS

It is exactly this huge energy carried by the alpha or beta particle, or by the gamma photon (packet of light), which is responsible for its detection as well as the damage it does to the molecules of a tissue. Thus, as the emanation is absorbed by molecules of a gas, say, its energy is gradually dis- sipated by being passed over to the gas molecules; these in turn are at least excited, and many are ionized, a process which requires only a few electron- volts per molecule.

The number of protons in the nucleus determines its positive charge, and hence its position in the periodic table. Protons plus neutrons determine the weight of the nucleus. There may be several numbers of neutrons which can combine with a given number of protons, and thus there can be several weights of the same element. These different weights of the same elements are called "isotopes" (iso topos — in the same place in the periodic table). Some isotopes are quite stable, some spontaneously disintegrate. For ex- ample, carbon with 6 protons in the nucleus, may have 4 to 9 neutrons in the nucleus, to form C6!0, C6n, C612, C613, C614, C615. The isotope C612 is the basic carbon in nature, and is quite stable, whereas C6H is a long-lived beta emitter also found in nature. The others are short-lived, and are made artificially by bombardment of nuclei by the "bullets" listed in Table 5-1 .

IONIZATION AND DETECTION

Ionization

Positive Ions

The mechanism by which ionization takes place in the path of each emanation is important to considerations of penetration. Each mechanism is different from the others because the emanations differ so remarkably. The alpha (He24)++, the broton (H,1)+, and the deuteron (H,2)+ are very small, but dense; the alpha carries the positive charge of two protons. Upon collision with electron clouds of a target material, it easily ionizes the atoms by pulling the negative electrons after it, wasting a small fraction of its kinetic energy in the process. Since it is likely to tear at least one electron out of every atom through which it passes, it leaves a very dense wake of ionization (Figure 5-1). The alpha of radium (Ra) has a kinetic energy of 4.8 x 106 electron volts, which means that it leaves a wake of about 140,000 ionized atoms. Thus in air it can travel a few inches; in metal it can pene- trate only about 0.0001 cm; and in fact can be stopped by a piece of paper! Although its path is short, the radiation damage or ionization along the path is intense. Actually, theory shows that the energy transferred per centimeter of path (called the linear energy transfer, LET) increases with increasing charge, q, and decreases with increasing velocity, v, as follows:

LET cc q2/v2

IONIZATION AND DETECTION

105

absorption by the nucleus

decay of unstable nucleus

photoelectric absorption

Depth in Tissue

Figure 5-1. Schematic Representation of Tracks of a Neutron (n), and of Alpha (a), Beta (/?) and Gamma (7) Rays in Tissue. Note that the density of ionization increases as energy is lost from the impinging ray. The alpha trail of ionization is dense, the beta trail is spotty, and the gamma and neutron trails are composed of spurs.

From these considerations and the properties given in Table 5-1, one can understand that the differences among alphas, protons, and deuterons art- more those of degree than of kind. All are positive, heavy particles with high LET.

Electrons

The beta is a very small particle — a very fast electron. Its charge is either negative (as is the beta from P32) or positive (as is the beta from P30), al- though the negative is the more common among biologically interesting iso- topes. Because it is of light weight, with a mass only somewhat greater (rela- tively) than the mass of the electrons in the atom, a collision can result in energy transfer and a change in direction, similar to billiard balls in play. **] As a result the path traversed by the beta will be governed more or less by chance collision. It will have many changes of direction. Along the straight portions of the path, when the beta flies through the electron cloud of the

106 RADIOACTIVITY; BIOLOGICAL TRACERS

atom, excitation can occur, accompanied by loss of speed, and hence loss of energy ( = 1/2 mv2). The definite changes in direction result from collisions, and the energy and momentum transferred can cause ejection of the electron hit; i.e., ionization. When collisions are ''favorable," the trail of ionization, although sparse, may penetrate quite deeply into a tissue; but when unfavor- able, it will be very intense but very short. (See Figure 5-1.)

Very fast electrons may penetrate the atom as far as the nucleus, and by interaction with the field of force about the nucleus lose energy, with the production of secondary X rays. These X rays are called bremstrahlung. Hence a hard beta source may produce a secondary radiation which is much more penetrating than the impinging betas.

The initial velocities of betas from a source vary widely because the small neutral particle, the neutrino, is ejected from the nucleus along with the beta, and the energy of the disintegration is split between the two. It is the maximum energy of the betas which is usually given in tables of data. As a result of the energy distribution and the deflection of betas as they enter and lose energy in a target, the betas follow a nearly exponential law of penetration.

Gamma Rays

The gamma ray is electromagnetic radiation, like light, but of very short wavelength. Since it carries no charge, it is captured only by direct collision or wave-like interaction with a target: with the nucleus or the electrons of an atom. Some energy is transferred to the target electron and the gamma con- tinues on, usually in a modified direction, at reduced energy (e, = hvt) where v, is frequency and h is Planck's constant. The recoil electrons are relatively slow, and are therefore good ionizers (see Figure 5-1). Just as in the case of X rays (see Figure 4-10 (a)), then, absorption of gammas arises from essentially two processes: (1) "pair production": strong interaction with the nucleus and production of a pair of electrons (e+ and e~) — impor- tant in water only if energy of the y is above 3 Mev; and (2) "Compton ab- sorption": ejection of an electron at an angle, some of the energy of the gamma being lost, and the remainder ("Compton scattering") proceeding, usually in a changed direction, and always at lower frequency. The process (2) is repeated until, finally, the energy left from a succession of collisions is absorbed by the electron clouds of atoms (photoelectric absorption) and is ultimately dissipated as heat. At energies below about 0.2 Mev, elastic (Rayleigh) scattering reduces the absorption and increases the range of the gamma in water and soft tissues.

Neutrons

The neutron is as heavy as the proton, but carries no charge. Energy is lost only by collision with light nuclei, and hence it can penetrate as deeply

IONIZATION AND DETECTION 107

as X rays. The nuclei set in motion by bombardment by fast neutrons (0.1 to 15 Mev) have a high LET and leave a wake of intense ionization. Slow (thermal) neutrons are ultimately captured by nuclei; the product is nor- mally unstable, and, for light atoms, usually emits a gamma ray. A good billiard player will attest that maximum energy transfer can take place be- tween two neutral "particles" if they have the same weight. Therefore, neutrons are slowed down, or "moderated" best by materials containing much hydrogen — water, paraffin, etc. Thus, penetration into these ma- terials is slight, or in other words, the absorption coefficient is high.

Neutrons are by-products of nuclear fission, or of proton- or deuteron- bombardment of light nuclei; they have a half-life of the order of 20 min, can be quite destructive of living tissue, and are difficult to detect. The damage is caused by charged nuclei set in motion by the impact of the neutron, or from artificial radioactivity induced by capture of the neutron by the nucleus (Figure 5-1).

Defection

Ionizing radiation is detected by any one of four basic methods:

(1) Exposure of a Photographic Plate: i.e., reduction of silver halides to silver along the path of the photon or particle. If the plate is placed in contact with a section of tissue containing a radioactive tracer, the plate will be exposed where the activity is. This method of mapping is now known as "autoradi- ography."

Microradiography is another interesting technique in which a large shadow of a small object is allowed to fall on a photographic plate. This technique has been used for years with X rays as the source, and recently it has been demonstrated to be feasible and useful using alpha rays as the source. Figure 5-2 shows a micro X radiograph of a section of bone — the mineral content is clearly visible — and an alpha radiograph taken of the organic part after the mineral had been removed.

(2) Ionization of a Gas Contained Between Two Electrodes: As the photon or particle passes through the gas it leaves a wake of ion-pairs. If there is no potential difference between the electrodes, the ions will recombine. If a potential difference is applied (Figure 5-3 (a)), each ion will migrate toward an oppositely charged plate. Those which reach the plate before recombin- ing will be discharged and produce pulses of current in the external circuit. The higher the potential difference, the less is the recombination. Thus at an electric field strength of about 10^/cm almost all the ions produced are "collected" at the electrodes. This is called the "saturation" condition, and most ionization chamber systems operate in this region.

If the electric field strength is increased still further, the primary ions are given sufficient energy to produce secondary ionization of the s*as molecules, resulting in a multiplication of the original ionization. This is known as an

108

RADIOACTIVITY; BIOLOGICAL TRACERS

i

*•

**

M- f

(a)

(b)

Figure 5-2. Microradiography. (a)

X-ray microradiograph (5 kvp) of a sec- tion of natural compact bone (tibia). Note the large (black) osteonic canals and the (light) mineralized regions. Magnification 500 x. (b) Alpharadio- graph (source 2 mc/cm2 of Po210) of a section of the same bone demineralized. Note regions of low-density (dark) and high-density (light) organic material. Magnification 150x. Together (a) and (b) demonstrate directly the regions of growth of young bone around the osteonic canal: tissue mostly organic, only lightly mineralized. (c) Alpha- radiograph showing filiform papillae (top) of the human tongue. Note the dense fibrous collagen core of the papillae and of the supporting base of the epithelium, and observe the low- density (black) mucous-forming cells at the bottom of the picture. (Courtesy of L. F. Belanger, University of Ottawa Medical Faculty, and D. H. Copp, University of British Columbia Medical School.)

IONIZATION AND DETECTION

109

KZ3>

©-v

©

t

(a)

0>

' phot

00

photons

to • voltmeter

Geiger

threshold

saturation (s) region

Figure 5-3. Ionization Chamber: (a) sche- matic design — wire anode, A, and cylindrical cathode, K, filled with gas (e.g., Argon); (b) charge collected at A per pulse at different voltages. (See text.)

"avalanche" process. The multiplication factor may be as high as 103 or 104, so that the current pulse which is produced may be 103 or 104 times larger than the "saturation" pulse (Figure 5-3 (b)). Since the pulse size is propor- tional to the energy lost by the original photon or particle, a chamber oper- ated in this fashion is known as a "proportional" counter.

At higher voltages, the multiplication factor for large pulses tends to be smaller than that for small pulses, and all pulses are multiplied to a constant size regardless of initial strength. The voltage at which this gaseous dis- charge starts to occur is known as the "Geiger threshold."

Figure 5-3 shows an ion-chamber design from which the proportional counter and the Geiger counter may be developed. Figure 5-4 is a photo- graph of a typical unit.

(3) Fluorescence Induced in Solids and Liquids: The light emitted after the ab- sorption of ionizing radiation by a fluorescent solid is reflected on to the

110

RADIOACTIVITY; BIOLOGICAL TRACERS

Figure 5-4. Measurement of Radioactivity. Left: thin- walled Geiger tube for alpha- and gamma-ray detection. Right: a typical survey instrument with protected, detach- able detector tube. Typical ranges: 0 to 0.25 mr/hr; 0 to 2.5 mr/hr.

photocathode of a photomultiplier tube, causing the ejection of more elec- trons. These are multiplied in number by an internal secondary-emission system to produce a measurable current pulse for each scintillation. A typi- cal arrangement is shown in Figure 5-5. Certain organic liquids also fluoresce, and very sensitive liquid counters have recently been developed.

Each of the counters discussed in paragraphs (2) and (3) has specific uses, tor a radiation such as the l.Z-Mev gamma from Co60, for instance, the scintillation counter can have efficiencies as high as 15 per cent as compared to 1 per cent for a Geiger counter. Therefore, for medical tracer applica- tions of gamma in which the intensity is low, a scintillation counter would be preferred over a Geiger counter. However, if dosage is high, as it may be in radiation therapy, the extra sensitivity is not important. Figure 5-6

photons

scintillation phosphor

photocathode

0

JT

\

*fl

X

optical coupling to photocathode

pre-amplifier

T

photomultiplier assembly

pulse output to ammeter

Figure 5-5. Schematic Drawing of Scintillation Counter. (See text.)

IONIZATION AND DETECTION

111

shows a lead-collimated scintillation counter, useful, for instance, for ex- ploring the thyroid after radioactive iodine has been administered. External exploration of the organ for determination of size is known as scintography. Mechanical devices have been designed which control the exploration and print a map of the intensity of radiation from that area of the throat.

(4) Chemical Reactions Induced in Aqueous Solutions: Water is broken up into H and OH, and these very reactive products undergo reactions with solutes to produce new chemicals. Oxidations or reductions, molecular rearrange- ments, polymerization of plastics, and corrosion of metals have all been used as detectors. Important quantitative aspects of absorption of ionizing radia- tion by aqueous tissues are developed in Chapter 9.

Figure 5-6. Collimated Scintillation Counter. Top: disassembled to show photo- multiplier assembly. Bottom: assembled. With collimator (left) attached, the instrument can be used for scintography — tor detailed external mapping of the human body, above the liver for example, following internal administration of the appropriate radioactively-labeled chemicals. (Photographs courtesy of Burndepts Ltd., Erith, England.)

112 RADIOACTIVITY; BIOLOGICAL TRACERS

DISINTEGRATION (DECAY)

Rate of Decay; Half-Life

We have no control over the disintegration of individual nuclei: if a nucleus is unstable, it will decay at a time which is completely unpre- dictable. However it is possible to describe and predict the fraction of a large number of unstable nuclei which will decay within a given period; that is, AN/ At is easily measured. In fact the number of nuclei (J\ ) which do decay within a given time is proportional to the number present which are able to decay.

Thus

AN/ At oc N

or the instantaneous rate

dN/dt ex TV- Insertion of the proportionately constant — A (called the "decay con- stant") gives

-dN/dt = \N

After the summation in the fashion indicated in Chapter 1,

N = N0e~Xl

where N0 is the number present at any arbitrarily chosen zero of time.

This expression says simply that the number, N, of nuclei which are present at any time, t, is only a fraction of the number, N0, which were present at zero time — the fraction being e~Xt. Now, it is useful and instruc- tive to expand the fraction into the series it is, and write

e~Xi = l + + +

l 2x1 3x2x1

A2/2 A3;3 1 _ \t + +

The value of A differs for different radioactive elements. For Sr90 the value has been measured to be 0.028 yr '. After five years, for example,

.-* = 1 - (0.028 x 5) + (0-°28 X 5)2 - (°-°28 X 5)3 + ^0.87

2 6

Therefore N = 0.87 N0, or the fraction of N() left after five years is 87 per cent. Calculations for 10, 15, 25, 50 yr would span a time at which N is just 50 per cent of N0. For Sr90 this time is about 25 yr, and it is called the "half- life"— the time it takes active material to decay to 50 per cent of the original concentration, N0. Half-life, r - In 2/A = 0.693/A.

DISINTEGRATION (DECAY) 113

If two radioactive elements have been concentrated chemically to the same value of JV0, the one with the shorter half-life decays faster, has greater "ac- tivity" (higher dN/dt) at time zero, or delivers more emanations per second to the tissue being irradiated.

The unit of activity is the curie (c), that amount of radioactive material which provides 37 billion (i.e., 3.7 x 1010) disintegrations each second. Thus 1 g of pure Ra226 which gives off 4.8 Mev (average of 3) alphas, has a total activity of about 1 c. Sr3890, which gives off only a 0.6 Mev beta, decays faster and is less dense than radium; 1 g of pure Sr90 provides an activity of 147 c. However, since a pure radioactive substance is always contaminated by its daughter products, the activity per unit weight is deter- mined by the concentration of radioactive substance. Clearly 1 millicurie (mc) per gram might be usable in a medical application, whereas 1 mc per ton should be quite impractical. Specific activity is defined as the number of mc/g.

Figure 5-7 shows decay schemes for several radioactive isotopes of use as tracers in diagnosis and as irradiation sources in therapy.

Energy Distribution of the Emitted Rays

Before we come to the question of depth of penetration and extent of ionization of the rays from a radioactive source, we must consider two more factors: the energy distribution (spectrum) of the rays from any given pure source, and the number and kind of products of disintegration.

Both alphas and gammas are the result of a particular kind of fracture or rearrangement of unstable nuclei. One could consider the nuclei to be in excited states (think of an undulating water droplet), existing as such from the time of their formation (in the sun?) millions of years ago, and disinte- grating at a rate which we can measure but which we are not able to vary. Thus, although half the atoms of Ra226 in a sample will undergo alpha decay in a definite and reproducible time, we do not understand why the disinte- gration of Ra226 is always by loss of one alpha particle, a package of 2 pro- tons + 2 neutrons; and the most striking fact of all is that these alphas al- ways come off with the same velocity. The similarity of this quantum-like be- havior to the quantized absorption and radiation of light by the electron cloud of the atom, suggested to theoreticians that a Bohr-like model for the nucleus should be useful. Development of theory has proceeded along these lines, and has led at least to a quantitative description, if not an answer to the question "why?".

The alpha or the gamma radiation from a single elemental source occurs at discrete energies — alphas of single velocity, gammas of single frequency (Figure 5-8). However, with the beta is expelled a neutrino, a tiny neutral particle of variable velocity; and therefore the beta radiation from a single elemental source has a distribution of energies — low, corresponding to a

114

No,

24

sodium-24 0 I. 39mev

Mg

24

12

Co'

60 J27~

cobalt-60

Ni

60_ '28

15 hrs

K

42 (18%) (82%)

19

potossium-42

y 1.37

Co

42 20

/92.0

,yl.53

12.5 hrs

£3.6

y 2.76

. 59 (46%) (54%)

Fe„ 1 1 4 5 days

/30.46

yl 29 ^ rl.10

(43%) ^ (57%)

Sr

y

90_ 38

90

28yrs 32

0 0.54 15"

0 0.306

39 5.25yrs

7 I . I7mev

Zr

yl. 33mev

9o_ 40

phosphorus-32

j8 2.26

.32

14 2 days

0l.7lmev

carbon-14

.14

6~

4 1

C

N

H He

— 5568yrs

0O.I55mev

3 i

12.26 y rs

00.0 1 8 me v

tritium

lod ine-131

(3%) (9%) (87%)

00.33

/30.6lmev

(1%)

y0.64 <wy0.36 <-yO 28 ri(80%)r^-(5%)

00.87

■8 04 days

70.08 70.08

54 v stable

Figure 5-7. Decay Schemes for Several Radioactive Isotopes Used in Biological Research, and in Medical Diagnosis and Therapy.

DISINTEGRATION (DECAY)

115

fast neutrino; high, corresponding to a slow neutrino; and reaching the largest, or maximum value when the velocity of the ejected neutrino is zero. The spectra are represented in Fig. 5-8 for pure emitters. The areas under the curves for each type represent the total emission. Table 5-2 gives the energies of the emanations from some unstable isotopes of biological interest.

en

01

i

c o

alpha

gamma

Energy E

Figure 5-8. Energy Spectra of Three Emanations, Each from a Pure Source. Alphas and gammas are monoenergetic; betas come off with a range of energies (i.e., speeds).

Many biologically active chemical elements have unstable isotopes, of which the type, the speed, and the length of time over which the emanation is given off (i.e., the rate of decay) vary widely. There are now over six hundred isotopes known. Only about twenty of these satisfy the chemical, the energy, and the half-life requirements sufficiently well to be useful in biology. Of these, the uses of P32, I131, C14, and Co60 are the most advanced.

TABLE 5-2. Some Isotopes Used as Biological Tracers"

Isotope	Half-life	Ray Emitted	Energy (Mev)
H3	12 yr	beta"	0.0180
Cn	20 min.	beta+	0.97
C14	5100 yr	beta-	0.155
p32	14.3 days	beta"	1.71
,131	8.0 days	beta-	0.6
Co60	5.3 yr	beta-	0.31
		2 gammas	1.17, 1.33
Fe59	46 days	2 betas"	0.27,0.46
		2 gammas	1.1. 1.3
Cr51	28 days	s< condary X rays	0.75
Ra226	1620 yr	alpha	\ 8
		gamma	0.19

*From "Radiological Health Handbook," National Bureau -I Standards, Washington I > < '

116 RADIOACTIVITY; BIOLOGICAL TRACERS

"Daughter Products": Products of Radioactive Decay

Any radioactive source, before being administered for any good reason, should be examined for the radioactivity and the chemical properties of its disintegration products. Refer to Figure 5-7. Thus, loss of an alpha means

a shift downward of two places in the periodic table (e.g., radium — * radon);

and loss of a beta means a shift upward of one place (e.g., iodine I131 — > xenon131), because these charged particles (electrons) are ejected from the nucleus, and it is the charge on the nucleus which determines the position of the element in the periodic table. Loss of a gamma results in no shift, but is simply a loss of energy during a nuclear reorganization.

The daughter products often are unstable and give rise to further disin- tegration. Several steps may occur before a nucleus reaches a stable state. One of the simplest disintegrations is that of Na24, used in determining the role of sodium in a cell-membrane transfer. The scheme was seen depicted in Figure 5-7. The isotope Na24 gives off a 1.39 mev beta to become excited Mg24 (magnesium); but this in turn emits two hard gammas before reaching a stable product.

The Ra88226 nucleus and its daughters produce a total of eight alphas, eight betas, and eight gammas before reaching the stable isotope Pb82206 (lead). Three isotopes of polonium (Po84), two of bismuth (Bi83), one of thallium (Tl81) and three of lead take part in the disintegration scheme! Note that all the daughters except radon are solid elements. Although all have short half- lives, they take a fleeting part in the chemistry of the molecules in the vicin- ity in which they are formed.

By interesting contrast with radium (Ra), Po210 is a pure alpha emitter, and P32 (phosphorus) is a pure beta emitter. I131 and radio-gold, Au198, emit both betas and gammas. Decay schemes for some of these are given in Figure 5-7.

PENETRATION OF THE RAYS INTO TISSUE

It is preferable to discuss the penetration of the pure emanations and then to infer the effects of the mixed emission of mother and daughters.

The alpha (and also the proton and deuteron) penetrates in a straight line until it is stopped (Figure 5-1), provided of course that it does not "hit" a nucleus (Figure 4-2). Because both the a and the target nucleus are so small, the likelihood of collision is small. Since alphas are monoenergetic from a source, all penetrate to about the same depth.

Both beta-scattering and gamma-absorption are governed more or less by chance collisions in which energy is lost from the penetrating radiation. The intensity decays more or less exponentially with distance in each case (Figure 5-9). This is only true to a first approximation, however, because of scattering which is related to the geometry of the system.

PENETRATION OF THE RAYS INTO TISSUE

117

2 2

c

<u c ■o — 'o .c

^_ 0) O T3

c a> o c "*- !c

O o

o □

alphas

(0 001 mm)

(7 mm

(I mm)

gam mas

or neu t rons

(several feet)

Depth in tissue Figure 5-9. Penetration of 1 Mev Alphas, Betas, Gammas, and Neutrons into tissue

In simplest cases, the curve for gammas is truly exponential; that for betas has less curvature and reaches a maximum value, which is the depth of penetration of the fastest betas. Note that the area under each curve corre- sponds to 100 per cent of the impinging rays hitting the target. The depth of penetration is radically different for the three cases.

TABLE 5-3. Ranges of Various Types of Radiation in Soft Tissue.*

			Range of Radiation in Material
	Usual	Ionizing	of Low Atomic Number
Radiation	Energy Range (mev)	Particles in Tissue	Actual Range in Air, NTP (cm)	Equiv. Range in Watery Tissue (cm)
Beta rays	0.015 to 5	electrons	0.1 to 1000	0.0001 to 1.0
Electron beams	2 to 10	electrons	300 to 8000	0.4 to 10
X rays and	0.01	electrons	230	0.23
Gamma	0.10	electrons	25,000	4.0
rays**	1.0	electrons	23,000	10
L	10	electrons	34,000	34
Fast
neutrons**	0.1 to 10	protons	many meters	~10
Slow	less than	0.6-mev	0.8 (protons)	0.001
neutrons***	lOOev	protons
		+ 2.2-mev	400 (electrons)	0.5
		gammas
Proton
beamsj	5 to 400	protons	30 to 80,000	0.035 to 80
Alpha
raysf	5 to 10	alphas	4 to 14	0.003 to 0.01

*Krom "Radiological Health] [andbook," National Bureau of Standards Wa hington, D. C, I960

**Range for absorption of half the incident radiation.

***From "Safe Handling of Radioisotopes," Health Physics Addendum," < G Vppleton and I' N Krishnamoorthy. Eds., International Atomic Energy Agency, Vienna, I960

+From G. J. Hine and G. L. Brownell. "Radiation Dosimetry," Academii Press, [n< 1956 and W Whaling, "The Energy Loss of Charged Particles in Mattel " Handbuch der Physik, XXXI\

118 RADIOACTIVITY; BIOLOGICAL TRACERS

In review, the nature and properties of the four main types of emanation have been considered. Positive ions and electrons lose kinetic energy by charge interaction with the electron cloud of atoms in the path: the greater the electron density the greater the absorption. Gamma rays lose energy to the electron cloud principally by pair production or Compton scattering. A neutron must hit a nucleus to lose energy. When it does, either the nucleus (charged) recoils through the medium and ionizes as a positive ion, or the neutron is absorbed by the nucleus, usually to form an unstable iso- tope which decays with the expulsion of beta or gamma, proton or neutrons.

The data of Table 5-3 illustrate these important principles. Note par- ticularly the variation of the range in tissue for radiations of different type and energy. Protons are the ionizing particles in tissue which is under fast- neutron irradiation because hydrogen of water is the most plentiful target in the tissue. . . . This table should be thoroughly studied and understood.

USES AS BIOLOGICAL TRACERS

One of the simplest, and yet one of the most intriguing applications of the properties of radioactive substances has been in their use as tracers. The age of the earth, the authenticity of oil paintings, the courses of water and wind currents, have been probed simply by analyzing for the pertinent radioactive isotope in the proper place in the proper manner.

Three uses as tracers concern us here: (1) as an aid in determining the steps and paths by which molecular reactions occur, whether simple hydra- tions of ions, or the more complex syntheses and degradations of large bio- chemicals; (2) in plotting the course of fluid flow, through the blood capil- laries, across cell walls, etc.; (3) in plotting the time and space distribution of biologically active chemicals. Examples of each are now given to illustrate the principles. The book by Kamen,s now a classic in the subject of tracers, is highly recommended for further study.

Tracers of Molecular Reactions

The first use of isotopic tracers on a biological problem was reported by Hevesy in 1923; this was a study of lead metabolism in plants. When heavy water (D^O) became available in Urey's laboratory after the discovery of deuterium there in 1932, many biochemical problems were attacked: hydro- genations and dehydrogenations, cholesterol synthesis from smaller frag- ments, conversion of phenylalanine to tyrosine, etc. Then, by 1942, am- monium sulfate containing N715, instead of the more common N714, became available, and compounded the possibilities for biochemical investigations. Thanks to the nitrogen tracer, the fate of amino acids in protein synthesis could be followed. Probably the most important of all these investigations, from the point of view of biology, was the demonstration that protein mole-

USES AS BIOLOGICAL TRACERS 119

cules are in a dynamic equilibrium with their environment: they are not fixed end-items, but rather they are continually breaking apart here and there, accepting new amino acids and rejecting old. The same thing has now been found in lipid and carbohydrate metabolic reactions. Thus a dy- namic steady-state must now be considered well established in the biochem- istry of life, even at the molecular level, a fact which could be established only by this unique tool, the isotopic tracer.

To be useful as a tracer, the only requirement is that the isotope be present in an amount different from that occurring in nature. If the isotope is radioactive, its presence is easily detected by the ionization caused by its disintegration product. If it is not radioactive (deuterium, H,2, and nitro- gen-15, N7'\ are examples), it can be detected by two methods: (1) In the highly evacuated mass spectrograph, the atom is ionized by bombardment by electrons, and then, after the ion has been accelerated in an electric field to a prechosen velocity, it is allowed to enter the space between the poles of a strong magnet. It is deflected there by the magnetic field, by an amount determined by the weight of the flying particle: the heavier the particle the less the deflection. (2) By neutron activation: In some cases — N71S is an ex- ample— the nonradioactive isotopic tracer can be made active by bombard- ment with thermal neutrons, and then its quantity measured as the radio- activity of the product, N716 in this case, a hard beta and gamma emitter with a half-life of only a few seconds.

Tracers of Fluid Flow

The classical method of determining the flow pattern in the circulation system is to inject nitrous oxide, N20, at one point and then sample at vari- ous times and places after the injection.

The isotopic dilution technique, described under (1) and (2) above, has been used to map blood flow in the brain, advantage being taken of the fact that no new chemical reactions are introduced into the system in the ma- terials injected.

During the past five years, the radioactive isotope method has also been applied to the very difficult problem of measuring the rate of flow of blood through various parts of the brain, and although these experiments have not been done as yet on man, the work (mainly on cats) is interesting and in- structive, and illustrates the power of the method. The chemically inactive, freely diffusible gas, CF3I131, has (5 and y emanations well-suited to the de- tection techniques already described. For example, ~300 microcuries (fie) are administered, either by injection into the blood stream in about 10 cc of salt solution, or inhaled from a prepared air mixture. The blood can be shunted through a glass tube from one part of an artery to another, and the activity of the shunted blood determined with a counter attached to the glass.

120 RADIOACTIVITY; BIOLOGICAL TRACERS

Alternatively, autoradiographic techniques on deep-frozen sections of sacrificed animals can give quantitative information on blood flow at dif- ferent depths in the tissue and at different times. For example, through both superficial and deep cerebral structures the flow rate is about 1.2 cc/min per g of tissue — in all but the white matter, through which the rate of flow may be as low as 0.2. In the spinal cord the flow rate in the gray matter is 0.63 cc/min per g; in the white matter it is 0.14. Under light anesthesia these values are reduced about 25 per cent. All these values are given in terms of flow through 1 g of tissue, because there is just no good way to de- termine the number and dimensions of the blood capillaries in these tissues.

Studies on Metabolism: Time and Space Distribution of Biologically Active Chemicals

For information subsequently to be used in therapy of one sort or another, tracer studies on metabolism are probably the most important. Every tissue or organ has a definite turnover rate of its molecular components. Every substance which enters through the gastrointestinal tract or through the lungs into the blood stream, or is introduced directly into the body fluids through hypodermic needles, has one or more locations to which it goes, and a definite time (on the average) it stays there before being rejected in favor of new material. In practice, radioactive atoms are introduced into the molecules which compose the material to be studied.

Where this material goes, and how long it stays there, as well as in what form it is rejected, can all be answered by proper use of isotopic dilution or radioactive labeling technique. For example, studies have been made on the metabolism of proteins, such as the rate of protein synthesis and nitrogen (N15) transfer; on the intermediary carbohydrate metabolism (C14 and P32); on the intermediary metabolism of lipids — the pathways of fatty-acid oxida- tion and synthesis (H3); on healing of bone fractures; on iodine metabolism (I131) in the liver and in the thyroid; on turnover rate and growth rate of normal** and diseased tissue (C14, H2, O18, Fe59, Au198); on the metabolism and turnover in teeth (P32); and on blood circulation in the brain (I131)-

In more detail: the metabolism of nitrogen in the living system has been studied by the introduction of N'Mabeled glycine or other amino acids, ammonia, or nitrates, into food. Measurement of the N15 — by either activa- tion or mass spectrometry (since N15 is a stable isotope) — as it appears in the urine, as well as analysis of the molecules in which the nitrogen is con- tained, has shown that the cellular proteins and their constituent amino acids are in a state of ceaseless movement and renewal. The proteins and amino

**Other isotopes now in use in metabolic studies include: Cr , Na , S , CI , K , Ca , Mn54, Zn65, Br82, Rb86, I128.

USES AS BIOLOGICAL TRACERS

121

acids are continually being degraded, and being replaced by syntheses. That the rates of breakdown and resynthesis are the same is attested by the fact that the concentrations are maintained constant during life. About 60 per cent of N,5-containing protein has been shown to appear as glycine in the urine within 24 hr after a high-protein diet has been eaten; about 80 per cent appears within 60 hr. Liver, plasma, and intestinal-wall proteins are re- generated much faster than those of muscle and connective tissue.

The nitrogen that goes into ringed structures such as the porphyrins, which enter complexes with Fe+2 and Fe+3 to form the hemin of red-blood cells, turns over quite slowly: it takes 10 days for the hemin to be synthesized from isotopically tagged glycine, and then nearly 140 days before the deg- radation process (cell replacement in this case) reduces the concentration of tagged nitrogen to half the peak concentration (see Figure 5-10).

indirect

Time after oral administration

Figure 5-10. Radioactivity in a Particular Vol- ume of Tissue as a Function of Time After Administration. Time and height of the maxi- mum depend upon location of the volume, upon what chemical compound is given, its normal biochemistry, where it was introduced (direct or indirect), and the half-life of the isotope.

Other uses of radioactive tracers include the investigation of the effects of drugs and hormones on the turnover rate in particular tissues or organs. A subject of particular interest in recent years has been the role of insulin in the control of diabetes. In a diabetic, sugars are transported across the membrane and into the cell abnormally slowly, and they accumulate in the plasma, useless for supplying energy, via oxidation, inside the cell. Insulin, a medium-sized protein molecule whose structure has been well known since it was first synthesized in 1956, has been tagged with I131 and introduced into the blood stream. Within minutes, more than a third accumulates in the liver and the kidneys. However, a fraction adsorbs in a nonspecific man- ner on all membranes accessible to blood plasma and intracellular fluids. Cell walls are no exception; and the adsorption of insulin has been associ-

122 RADIOACTIVITY; BIOLOGICAL TRACERS

ated with an increase of the rate of sugar penetration (a process which itself has been followed by C14-tagged sugars). Whether the control exercised by insulin is simply by opening the access to pores, or whether it controls in a more subtle manner by increasing the activity of the enzyme (hexokinase) also thought to be adsorbed on the membrane, has not yet been settled. However, it can be seen that the use of radioactive tracers in such a phar- macological problem can make a valuable contribution to our knowledge of the processes involved.

The pioneering work of Huff and Judd on the quantitative analysis of the time and space distributions of Fe59 in blood plasma, will be discussed in Chapter 11 as a concrete example of how possible methods of action can be analyzed with a computer if it is fed reliable experimental measurements of where the Fe59 goes and how long it stays there. We learn a little about what the iron does, and also something about just what processes are interfered with during blood diseases.

Radioactive Mapping

Administration of compounds of I131, followed bv external measurements of beta-ray intensity in the thyroid region of the neck, has been introduced in some centers as a replacement test for determining whether the thyroid is normal, over-, or under-active. A hyperactive thyroid may absorb up to 80 per cent of the tagged iodine; a hypoactive gland may absorb as little as 15 per cent before normal biochemical turnover elsewhere in the body re- duces the concentration via excretion. Mapping of the thyroid by I131 scintography is common practice. Both the outline of the organ, and its turnover rate can be obtained from maps made at different time intervals after administration. The maximum activity of the emission is a direct measure of the uptake of iodine by the thyroid.

The flow of fluids through various critical parts of the system can also be mapped satisfactorily by dissolving in the fluid a small amount of gas which contains a radioactive emitter, and mapping from the outside with a col- limated scintillation counter (Figure 5-6).

Conclusion

A great many elementary biochemical reactions are being studied via the tracer technique, and a few physical processes also. Some of these will be found mentioned as examples in different parts of this book. The techniques are reliable and extremely sensitive, and have the unique advantage that the introduction of the radioactive element can be done in such a manner as not to upset the chemistry or the physics of the process in vivo. Already in ex- tensive use in biological research — in his review Kuzin12 was able to collect 358 references to new work published in 1959 alone!— now, led by successes

REFERENCES 123

with I131 and P32, radioactive tracer techniques have a wonderful future in medical diagnosis.

As it does in so many subjects, the National Bureau of Standards, in Washington, periodically publishes reliable definitions of terms, values of universal and experimental constants, and tables and graphs of collated data on radiologically important parameters. The ''Radiological Health Hand Book" is indispensible to further study of this subject, as a quantitative sup- plement to the classic work of Kamen.5

PROBLEMS

5- 1 : (a) What element is formed by the radioactive disintegration of: P~ £- 0'

P32 ^ Co60 ^ p30 1+

0- 8-

Na24 ^ Ra226 -^

a 8*

po210 _^ Na22 %

(b) Is the product radioactive too?

5-2: (a) Make a graph showing activity (counts per minute) against time, for up- take, utilization, and elimination of I !3! by the thyroid, (b) List five important reasons why I131 is used in irradiation-therapy of goiter.

5-3: The 1.70 mev /3-ray of P32 penetrates about 7 mm into tissue. The half-life is 14.3 days. A 1-millicurie (mc) source will deliver about 1 rad (radiation ab- sorbed dose) per minute.

How long would it take for a 1 mc of NaHP04 , composed of P32, taken orally as a solution in water, to administer 6000 rads to an organ in which it concen- trates?

REFERENCES

1. The Staff, Physics Dept., Univ. of Pittsburgh: "Atomic Physics," 2nd ed., John

Wiley & Sons, Inc., New York, N. Y., 1944.

2. "Atomic Radiation (Theory, Biological Hazards, Safety Measures, Treatment

of Injury)," RCA Service Co., Camden, N. J ., 1 959.

3. "Teaching with Radioisotopes," H. A. Miner, el al., Eds., U. S. Atomic Energy

Commission, Washington, D. C, 1959.

4. Scientific American, issue on "Ionizing Radiations," Vol. 201, September, 1959:

papers by S. Warren, p. 164, and R. L. Platzman, p. 74.

5. Kamen, M. D., "Tracer Techniques in Biology and Medicine," Academic Press,

New York, N. Y., 1960.

124 RADIOACTIVITY; BIOLOGICAL TRACERS

6. Glasser, O., Ed., "Medical Physics, Vol. Ill," Year Book Publishing Co.,

Chicago, 111., 1960: several short articles, p. 302-364. See especially: "Locali- zation of Brain Tumors with /^-Emitting Isotopes," by Silverstone and Robertson.

7. Kity, S. S., Methods in Med. Res., 1, 204 (1948).

8. Munck, O. and Lassen, N. A., Circulation Research, 5, 163 (1951).

9. Clarke, H. T., Urey, H. C, and 16 others, "The Use of Isotopes in Biology and

Medicine," in the Proceedings of a Symposium on the subject, The Univ. of Wisconsin Press, Madison, Wis., 1948.

10. Huff, R. L. and Judd, O. J., "Kinetics of Iron Metabolism," in Adv. in Biol, and

Med. Phys., 4,223 (1956).

11. Freygang, W. H. and Sokoloff, L., "Quantitative Measurement of Regional Cir-

culation in the Central Nervous System by the Use of Radioactive Inert Gas," Adv. in Biol, and Med. Phys., 6,263 (1958).

12. Kuzin, A. M., "The Application of Radioisotopes in Biology," Review Series,

No. 7, International Atomic Energy Agency, Vienna, 1960.

13. "Scintography — A collection of Scintigrams Illustrating the Modern Medical

Technique of in vivo Visualization of Radioisotope Distribution," R-C Scien- tific Co., Inc., Pasadena, Calif., 1955.

14. Cork, J. M., "Radioactivity and Nuclear Physics," 3rd ed., D. Van Nostrand,

Inc., New York, N. Y., 1957.

CHAPTER 6

Big Molecules

(Structure of Macromolecules and Living Membranes;

Isomers and Multiplets;

Codes and Molecular Diseases)

A score of diseases (including sickle cell anaemia and phenylketonuria) have so far been recognized as enzyme diseases, presumably resulting from the manufacture of abnormal molecules in place of active enzyme molecules. I think that it is not unlikely that there are hundreds or thousands of such diseases.

I foresee the day when many of these diseases will be treated by the use of artificial enzymes .... When our understanding of enzyme activity becomes great enough, it will be possible to synthesize a catalyst, etc

Thus did Linus Pauling emphasize to an international sym- posium of enzymologists in Chicago, in 1956, the relationship between the structure of the macromolecule and its chemical and physical roles in the living system.

INTRODUCTION

The structure of macromolecules and of arrays of them in living mem- branes and other tissues has occupied the attention of an important class of biophysicists for the past ten years. Using modern rapid-flow, quick-freeze- drying, and micromanipulation techniques, and armed with the phase and

125

126 BIG MOLECULES

interference microscopes, the X-ray diffraction camera, and the elertron microscope — the last now in such an advanced stage of development that, in proper hands, it can resolve or "see" small particles just a few atomic diameters apart — researchers have been able to gain new insight into the actual shape of the molecule in the tissue, and even into the positions of atoms and groups of atoms within the molecule.

Running concurrently with these physical researchers have been chemical studies which have finally solved the puzzle of the complete chemical composition of a few large, biologically important molecules. For example, although the hormone, insulin, has been known and used widely in the treat- ment of diabetes for nearly forty years, it was only in 1955 that Sanger and his colleagues at Cambridge were finally able to write down the complete structural formula. It contains 777 atoms! Since then, ribonuclease (RNAse), an enzyme containing 1876 atoms and which catalyzes the cleavage of ribonucleic acid, has also yielded the secret of its composition to the attack of persistent chemists. This completes the first big step toward knowing how this molecule works as a catalyst, although details of the struc- ture at and around the active site(s) are not yet known. This is the next big task, for if more than one of the chemical groups must exert their chemical effects on a specific part of the molecule whose hydrolysis is to be promoted, then their spatial arrangement must be very important. Not only must they be present, but they must be present at the proper positions in space if the catalytic activity of the site is to exist. In other words, if one of the players is out of position, the game is lost.

Table 6-1 gives a spectrum of biologically important organic molecules, small and large — some containing a metallic oxidizable and reducible ion which enters the chemical reactions of the molecule. Although some details are given in the following sections, the discussion is just an indication of the scope of the subject. There are excellent reference sources: for example, the recent book of Tanford.16

STRUCTURE

Our purpose, first, will be to outline the structure of two big molecules of critical biological importance, myoglobin and hemoglobin, learned in the recent work of the schools of Kendrew and Perutz, respectively. The method used was X-ray crystallography, and although the chemical com- position has not yet been fully worked out for these two molecules, X-ray crystallographic studies have completely outlined the form of the molecule in the dry crystalline state.

The second part of this section on structure is concerned with the cross- linked structure of liquid crystals, such as in the aqueous humor of the lens

STRUCTURE 127

of the eye, anH of membranes — those of the erythrocyte cell wall which are relatively homogeneous, and those patchy, mosaic membranes exemplified by the wall of the small intestine.

Crystalline Macromolecules

Diffraction of X rays by the regular arrays of the electron clouds which surround the atoms or ions of a crystalline substance was introduced in Chapter 4. The X rays diffracted from a single crystal interfere with one another in a manner which is determined solely by the position and electron density of the target atoms in the crystal. If the diffracted rays are allowed to fall upon a photographic plate, from the position and darkness of the spots on the plate, one can (at least in principle) locate the position and electron density of the diffracting atoms in the crystal. The position of the spot tells the angle, 9, of constructive scatter of the X rays of wavelength, A; and the Bragg interference equation, nX = 2d sin 0, relates these values, the "order" of interference, n, and the wavelength, A, to the spacing, d, within the crystal responsible for the scatter. The blackness of the spot gives the amplitude. The superposition of those waves which give rise to the one which emerges from the crystal, however, must be inferred from positions of the atoms in the crystal. This is done by a trial-and-error mathematical method involving superposition of infinite series, a method which will not be described here.

It was in 1951 that Pauling and Corey made the big break-through in our understanding of structure of proteins: they were able to determine from X-ray diffraction patterns that synthetic polypeptides formed of alpha amino acids all have a coiled, helical form. In other words, the back-bone of the polypeptide chain coils around and around, to form a cylindrically shaped molecular helix. This can be easily understood now, in retrospect, as follows. Since all the alpha amino acids have the structural formula

H R

I I N— C— COOH

H H

and since these condense through the — CONH-- linkage (Figure 6-1) in the form

H R O ! H R O

I llil I II

• • • -N-C-C-T-N-C-C- • • • 1 2\ 3 ' 4 5 1 6

h ; h

the atoms of the backbone of the chain, — N — C — C — , are repeated over and over again. The bonds can be bent around only so far, and, in the limit.

128

00

b/D

c

O

oc

o

c

o

c

co >~

t_ U

					CD
c	C			C	3 U	c
£	£			S	£
o	o			O	JJ	o
c	c			c	o s	c
_*	_*			_*	-c
„		CO	CO

CD	CD	(I)	CD	CJ	u	V
5	2	cd	CD	5	re ri	5
CO	CO	_	(-	CO	re	ro
		J	3
K3	re			re	D.	re
■*--		u	U	-w
co	CO	3	3	CO	^	CO
>-	>-	>.	re	>
s_	s-			t_	l_
CJ	U	CO	CO	CJ	OJ	(J

CO	CO
CO	CO
CD	CD

CD	CD
u	U
3	^

CD	CD
3	3

L	c
■	■ —
c	re
-	-C
w	CD
CD 1	~
L.	CD
	^:
CO

O
$

o

'c o en

u

c o t o

E

cd

3 o

c

O'

X

u

2

U

0

u

o

c o u

u

-a

CD

X! g

o 5

_2 re

U

vO

c

3

C

.5 o

br 3

\ /

CD

bfi >- c

£ -c S

t- bo -P

cd xr _

-z

3

be . ■- tj- x

b* ~ _ U

> re re q

c a. a. >

■sf re re

CI	c
i	!_
O	>>
CD	X
—	a.
3	l_
bn	o
Um	a.
	-o
	CD
c	"1

2 £-

CD

cj .3

o «

o

C

Si- £

CD

CD sO

co

<D C O

3 ■■ ~o

— . -Q CD

~ a. £

_g cj •£

-0 -i-i CD

1/1 & ■"

i be c

~ £ >-

3 u CO

3

oc

CJ

re o 3

CD

3

-a

a T3

o

a.

re

C 'cd

O

a,

CD

c

c o

CD

3

CD co

!-§

-c

CD <->

re cd

o ^ c «

c .£

O cj

o

CD CD

c

■z >?

CD T3

3 C

^ £

o

cj

CD«

C I

c .5

o

u O)

_o o bo

cu

CD

c

O

CD C O C

CD U U CJ r*1 +

C C C C + bC

O O O O <D — <D

C 3 3 C fc2U

+

o

<D	CD
3	C
O	o
c	3

O
(J	«
s- O	+ -a
	U
CN + c	O
N

c a

"5

E

CO

3 U

O $

CD

E o

c/>

<

_a>

_CL) 0

OC

CD

u-1 CO

						r^
o	LTl	^t"	o	CN	rO	lO
00	00	rg	<^;	un	O	m
— '	CN	m	LTl	o	oo	—

r~-	c3
ti-	^
O	LTl
en	-*■

re

c

CD

u

-a <

CL

CO

<

CD

3

2Uoi

CD C		^M
CD		Q. C
O	3	§6
re	C	w fTl
Cj	CD	-C .3
Q.	X	u >

a

o

CJ

c	o
o	CJ
bn	o
	c
CJ	CD
3	i_

c x £

C £ O

u O -3 O

2 < "3 £

129


T3
^	CU

Z>	jO
^	CQ
V)
	u
0	03
u	>
in
r	C
Q.	i-


	c
	jd
	c
	3

00
		1 3	3	e/T
T-^		re

<u		O	-3	C/5
u 'tTl		en u u •<	u -c
c		T3	en
2 o c	m	o	a	<U 13
.-■«;		c	—	• *"■
_>-	ve- il	o -a c	o	E
V	3 WD	C	t-
E	u.	o	c re 3
o		c

o • -

C s-

o u

o re

-2 ^

u <

3 9

U ^

C 3

2 3°

u a

KS —

3

- re u

3" o

-a 3

o

,<D

2 3

S <D 00 <J cfl -S vi ^

M Si

1-1 _™ . - <-j

CM

g ©

O

3

-C O 3

<u s- 3

be

3

O

3

(J 03

O

c

-c

3

o

•3 X

m

■ 2

IU ^* en Jj

■ ' O

3

O (J

'4-

N

3

OJ c

-3 3

o

3 <u

-

o I ra a. _* m

3 rs

en

_3

re ri Q. ~L

as-r

3 3 Q.

en O		CU C/5	^	-5		CU _y
"re		>	O 3	cu		CU _3
IU		n	^:	g;		c
3		re re	3 3	"o		^
3	3	>^	eu -3	V	?	— 0
cr	O	3	CU bo	"C	>
	3	~				0	"IT
en	_*	en	~~			—	X
OJ 3	>>	O	V	re	cu	?	—
u	O	~		E/3	(	T-	'J

■rr, r, ~ a >■ ~o. z -3

f 1^ "

cr u c

<u			4J
C		_*	Q.
u	„^	c
3	re u	£
>>	~S	C
Q.	X	re	t«
•n	re	<—	O
3	0	V	3
re <u	-a	re	T3 C
3		Q.	3-
•3	u	O	3
>>	re			L
n,	re	1		-^
		u		C /
y '3 re	ID re	O J2	3 IU -c	Z —

tin —

		IU 3	3		O	re
		0		3	c
O-.			^		11 — ■*	oj
t)	cn	rn	m	O	^i	i/)
r-	+	+	+	3	+
O	Oj	IU	<u	O	re
r-	b	tin	tin	C	•J>

<u 3

0

C IU ■r

tU

C o

o o o

cm"

c o

— (M

0

^

0 0

0

r-~"

0

CM

m

0 m

o

C3 O

3-

vo re

	<u
1—	^
	u
0	a>
	0
0)	?
J3
O

u

re _u

u

3

ZC

0
£ c sz	3 IS 0
0	bo
0	0
>-	>.
U	2

X
0	IU	c

be O p	_c	<u W) re

u	0	0
—	U	U

A_

		r~				en>
<u O			en 3	3 'C		en	C 'cj
>>	_y 0	< z	O O u 3.	a n	> c r..	- u CJ - en	0 u 3. O U
w	3 3	u	0	0	0	u 3

JOJ z

130

BIG MOLECULES

carbon 6 falls almost directly above nitrogen /, and the two are hydrogen bonded about 1.5 A apart. The diameter of the helix so formed is about 8 A. The helix has an open core, about 2 A across,. and the R-groups, or side chains to the main structure, jut out radially from the central axis of the cylinder.

Figure 6-1. The Planar -CONH — Linkage (boxed) Between Amino Acids in a Protein. Lengths in angstroms.

Since the helical shape is a property of poly alpha amino acids, it was given the name "alpha-helix, " and it is now probably the most famous structure of macromolecular physical chemistry. Figure 6-2 is a drawing, similar to the original disclosure, which shows the main chain (bold bonds) and the posi- tions of attached groups ( — R); and which indicates the positions of the hy- drogen bonds, the "bones" which give the helix rigidity.

It is now known to be the main structural component of «-keratin, hair, wool, nail, muscle, and connective tissue, etc. Recently it has been traced in muscle to the contractile enzyme, myosin itself. Because of the unique role of myosin, some of its physical and chemical properties are expounded in Chapter 10.

One protein, of unquestioned importance, which has intrigued biological investigators for years, is hemoglobin, the "oxygen carrier" of the respira- tory enzyme system, first crystallized and purified by Hoppe-Seyler in 1862. However, with a molecular weight of 67,000, its amino acid sequence and the physical structure of the molecule have only slowly yielded to persistent

STRUCTURE

131

Figure 6-2. Schematic Representation of the Alpha Helix of Protein. Three complete turns are shown. They start at the bottom C, wind out toward the reader through the next — N — C — , then back in through the plane of the paper, etc. (After Pauling and Corey, 1953.)

132 BIG MOLECULES

investigation. The X-ray diffraction pattern of even single crystals was too formidable for analysis until M. F. Perutz, about 1950, began to substitute heavy metals ions such as Hg+2 at particular spots on the molecule and to analyze the effects of these strong X-ray scatterers on the spectrum. With this technique, now known as the "method of isomorphous replacement," it was possible by 1960 to show the surprising result that the protein of the molecule at 6 angstroms' resolution looks like several intertwined worms, with the heme groups attached — not a regular array at all. Studies con- tinue on the amino acid sequence, and on the analysis of the X-ray diffrac- tion pattern, in an effort to get even better resolution of the detailed struc- ture of the hemoglobin molecule.

Inherently simpler, myoglobin (one Fe+2 ion only) has yielded not only to 6 A analysis (1956) but even to 1.5 A resolution (1958), work for which Kendrew and his team received a Nobel Prize in 1961. The main features of this molecule are depicted in the drawing shown in Figure 6-3. The a-helix

(flat) heme group

CH2

< „ p

CH,-/VV\

C-N N-C

HC (Fe) CH

0

XC-N N=C

/ I I \

HC-C C C C-

CH? XC C C

/ H |

CH3 CH3

protein (ferrous ion)

seqments

R= -CH2CH20H

I 1 1

30 A

Figure 6-3. Molecule of Myoglobin. (Drawn from the Model of Kendrew, 1958.)

hydrogen-bon(d)ed, forms the framework of the worm-like segments, sudden turns in which are thought to be associated with the proline groups — an amino acid residue of odd structural configuration. The heme group sits ex- posed, with the iron ion ready for oxidation or reduction, or, preferably, simply complexing with 02 picked up from air.

Although this is the configuration of crystalline myoglobin, the shape of the

STRUCTURE

133

molecule dissolved in salty water may be quite different — for example, one can readily imagine the legs of this molecular octopus unfolding in the blood stream.

Structural knowledge of many other big molecules is rapidly becoming available. This is a subject of intense interest. Straight chains and helices, some coiled into balls, some folded back and forth to form rods, others with randomly coiled shapes, are known or imagined. These forms are illustrated in Figure 6-4.

1 1 1 1 .)-

(I . . .

, , , , )-

C ■ ' i i j

random coil

helix

globe

rod

Figure 6-4. Some Molecular Shapes in Solution (schematic). Transitions one to another can be effected by change in pH, ionic composition, or temperature.

Receiving much attention in the hands of F. O. Schmitt and the MIT School has been collagen, the structural component of connective tissue, tendon, skin, cartilage, etc. (Figure 6-5). Formed of three interwound molecular helices of protein, with molecular dimensions approximately 3000 A long x 30 A in diameter, it cross-links end to end to form fibers, and then side to side to form either sheets (two dimensions) or blocks (three di- mensions) of connective tissue with very varied physical properties: for ex- ample, tensile strength up to 100,000 lbs/in2, equivalent to that of a steel wire of the same dimensions!

Now thought to be the basic information-carrier of the gene, and an ex- tremely important component of the nucleus of the cell, is desoxyribose- nucleic acid (DNA). At about 70 per cent relative humidity, it is an ex- tended, double-stranded helix, of molecular weight in the millions. Further discussion of the structure of DNA, and its sister nucleic acid, ribosenucleic acid (RNA), appears later in this chapter.

Now, the backbone of the helices of DNA and RNA is ribose, a sugar, polymerized through phosphate groups. Polymerized sugars are the second major structural component of living tissue — cellulose and chitin are ex- amples. Hyaluronic acid and glycogen are polysaccharides which take an integral part in the biochemistry of life. Thus glycogen is the form in which sugar is stored as an energy reserve in the liver. Polysaccharides, like proteins, take many forms in tissue. One which seems to be unique is the pleated sheet of cellulose.

134

BIG MOLECULES

€

I

':••-.

'<ft8*

m -

'■

*

Figure 6-5. Electron Micrograph of Collagen Fibers Carefully Lifted from Human Skin. Note how they are individually cross-segmented and collectively fused (Courtesy of J. Gross, Massachusetts General Hospital, and of Scientific American.)

Lipid molecules themselves are generally small, by comparison with the macromolecules discussed in this section (see Table 6-1). However, they condense with proteins to form macromolecular lipoproteins, and with cellulose to form lipocelluloses, and thus also play a primary role in the structure of tissue.

Metal-organic molecules are varied and important in living tissue (Table 6-1). The bright light from the point of view of our knowledge of structure

STRUCTURE

135

is vitamin BP, a substituted cyano-cobalt amide of molecular weight 1357, used in treating pernicious anemia, growth failure in children, etc. The complete chemical composition was disclosed in 1955, and culminated with X-ray diffraction analysis of structure three years later.

Dissolved Macromolecules

Unfortunately, when crystals such as those described in the previous sec- tion are dissolved in water, the molecules are subjected to a number of new and powerful forces of hydration and of polarization by ions, and the con- figurations of many molecules change. Since water has a diffuse diffraction pattern of its own, the X-ray technique used in crystals cannot be employed to advantage on solutions of these molecules, and other methods which indi- cate structure must be sought. All those to be described are useful, but each has its limitations.

The problem in solution is complicated by three other facts: (1) The molecule will not usually, unless it is globular-shaped, have a unique molec- ular weight; but rather will its molecular weight vary, some molecules in the solution having weights above, and some below an average value. The dis-

cs o o

o o

o

o o o

rO

o o o

»fr If) tD

I I I I 1 1 I I 1 1 I I 1 1 I

1 1 1 1 1 1 1

L ( Angstroms )

(b)

Number average 2450

Weight average 2820

Light scattering 3000

Flow birefringence 2600 — 2950

Intrinsic viscosity plus molecular weight 2970

Figure 6-6. Ichthyocol (a Protein Food Supplement from Fish): Direct Measure- ments of Molecular Size by Electron Micrographs, Compared with Results from Indirect Methods. Number (N) with length (L) multiplied by L gives total amount of protein with particles of length L Molecular weights, Mn and Mw, are derived from data plotted. (Data of Hall and Doty, J. Amer. Chem. Soc, 80, 1 269 ( 1 958).)

136 BIG MOLECULES

tribution shown in Figure 6-6 clearly shows this. Number-average, or weight-average molecular weights are obtained, depending upon whether the number of particles or their size is reflected by the measurement. (2) The configurations which the macromolecule can take in solution can vary, de- pending upon hydrogen ion concentration (pH), cation content, and other factors which imply strong electrical effects. (3) Many macromolecules are themselves polymers, and in turn may polymerize further in solution.

From this discussion it is easy to see that the elucidation of the exact size and shape, or structure, of a particular macromolecule in a particular solu- tion is probably still a long way off. Some physicochemical experiments which throw light on this vexing but important problem will now be outlined. We follow, in part, Paul Doty in this outline, and recommend highly his clearly written reviews5 of 1956 and 1960 to the reader who wishes to pursue the subject beyond the bare outline given here. The methods are divided conveniently into static (or equilibrium) and dynamic methods. All give molecular weight and/or dimensions.

Static Methods

Osmotic Pressure. This is the most sensitive property of dilute solutions of macromolecules, but since it is a colligative property it is strongly influenced by the presence of any molecules or ions other than the macromolecule being studied. The osmotic pressure, ir, as a function of concentration, c, can be expressed

7T \ B C

= — h c + c2 + ■■■

cRT Ad M2 M3

where M is the number-average molecular weight, B and C are constants related to molecular size and interactions, R is the gas constant, and T the absolute temperature. Measurements* of osmotic pressure at several concen- trations can be plotted as tt/cRTvs c, as is shown in Figure 6-7, Doty's 1960 data on collagen at 2°C. Extrapolation to zero concentration, where the polymer molecules have no influence on one another no matter how uncoiled they may be, gives the first term, \/M, the reciprocal of which is the num- ber-average molecular weight, M„, in this case 300,000. The parameters B and Care not zero because the macromolecules can physically coil around each other and, furthermore, interact with each other's electrically charged groups of atoms.

Light Scattering. We saw in Chapter 4 that light is scattered and absorbed by molecules in solution (Rayleigh scattering of light, and the Beer-Lambert law of light absorption). For macromolecules the loss is explicitly stated

*Referback to Figure 2-3 and the discussion on page 36. If c is expressed in g/1, it in atm, and R as 0.082 1 atm/deg. mol, M has units of g/mole.

STRUCTURE

137

6.0

(0

4.0 -

' 1	1 1 I 1
1	1 1 1 1

cr

2.0

0 0.2 0.4 0.6

Concentration g/IOOcc

Figure 6-7. Determination of Molecular Weight of Collagen by Osmotic Pressure (7r) Measure- ments. The intercept at c = 0 is equal to 1/Mn .

through a derivation due to Einstein and Debye. The resulting expression relates the intensity of the light scattered (Rw) at right angles (90°) to the incident light and the concentration of the scatterer in solution:

Kc_ R

90

M " M2

where A" is a constant depending upon the wavelength of the incoming light, the index of refraction of the solvent, and other factors, all of which can be measured. A plot of Kc/R90 vs c, then, has an intercept (value at c = 0) of 1/M, the reciprocal of which is the weight-average molecular weight.

Sedimentation Equilibrium. Perhaps the most versatile of them all, this method of measuring molecular weight can give a reliable value indepen- dently (almost) of the shape.

In the ultracentrifuge, which spins so rapidly that the centrifugal force can be higher even than 100,000 times that of the gravitational attraction to the earth when the suspension is at rest, a macromolecule can reach a stable position at which the centrifugal force is exacly balanced by a force in the opposite direction which is proportional to the number of buffeting mole- cules per cc (Brownian motion). Heavy molecules come to equilibrium at a position near the bottom of the centrifuge tube, light molecules toward the top.

After the solution has spun long enough for the macromolecules to assume their equilibrium distribution (usually some days for big molecules), the concentration, c, and concentration gradient dc/dx along the linear axis, x, of the tube (measured from the center of rotation), are measured, usually by a light-refraction technique. Use of the expression

(1 - p)u2xc \_ B RT dc/dx MM2

c +

138 BIG MOLECULES

at various concentrations and extrapolation to zero concentrations so that intermolecular interactions cannot interfere, gives the value of M, as before. Here p is the ratio of densities of solvent to solute, and a> the angular ve- locity of the centrifuge (radians/sec).

A more rapid method, used within the past few years, takes advantage of the fact that small volumes bounded by the top and the bottom of the tube reach equilibrium very rapidly; measurements of concentrations in these volumes can be made within a few hours, and an "average" molecular weight then evaluated.

Direct Measurement of Size and Shape via the Electron Microscope. For those polymers whose shape and weight are the same, dry or wet, the direct meas- urement by the electron microscope is possible. A comparison of the results of different methods on the globular molecule icthyocol is shown in Figure 6-6. The nonequilibrium methods will now be outlined.

Dynamic Methods

These are based on four transport processes which are discussed as a group in more detail in Chapter 8. The following outline sumcies here:

Diffusion under a concentration gradient and sedimentation under a centrif- ugal force can both be stated as the speed of the process under specific condi- tions, and these speeds expressed as D and s, respectively. An argument involving factional force offered by the water against movement of the macromolecules shows that the ratio of the two speeds, D/s, is related to the molecular weight, M, by

(1 ~ P) D _ J_ RT s M '

an expression originally derived by Svedberg. Measurements of D and s, and of the densities of solid and solute permit evaluation of molecular weight.

Intrinsic Viscosity. This property, /c as c — » 0 (where rj0 is the

Vo / viscosity of the solvent and r\ that of the solution), can be related to the vol- ume of the molecule and molecular weight by two expressions which in simplest form are:

(1) \r\\ = 2.5 V for spheres (7000 V for a big, randomly coiled molecule such as DNA) — here Fis cc/g; and

(2) [77] « Ma where a is an empirical constant, usually 0.5 to 1 .0. Although measurement of viscosity is easy enough, the proportionality

constants have an empirical character, and hence one always suspects the absolute values of size and shape so obtained. However, they are quite reli-

STRUCTURE

139

ably indicative of change in molecular shape as environment is changed, and it is in this manner that they are usually used.

Speed of rotation of a big molecule about an axis can be inferred by an opti- cal measurement calledy/oie» birefringence, and the result related to molecular weight. Both the optical technique involved and discussion of the propor- tionalities are beyond the scope of this outline, for they are very specialized.

Proper use of the techniques outlined have shown many interesting prop- erties about certain biologically active molecules. Compare now the results of the dynamic methods with those of. static methods. Table 6-2 gives aver- age weight and dimensions of collagen, measured by five different methods, and of erythrocyte DNA by two methods. Our well-worked illustration, Fig- ure 6-6, shows the results of the direct measurements of size of dried ichthyocol** rods by electron microscope techniques as compared with the indirect measurements by light scattering, flow birefringence, and intrinsic viscosity methods.

TABLE 6-2. Dimensions of Molecules of Collagen and DNA.

Molecule	Method	Mol Wt	Length	Diameter
Collagen*	Osmotic pressure	310,000	—	—
	Light scattering	345,000	3100A	13.0 A
	Intrinsic viscosity	—	2970	13.6
	Sedimentation and viscosity	300,000	—	12.8
	Flow birefringence and viscosity	350,000	2900	13.5
DNA**	Light scattering	4.7 to 6.2 million	—	—
	Sedimentation and viscosity	5.3 to 17.4 million	2030- 2350 A

* The chief constituent of connective tissue (cartilage, tendon, etc.). (After Doty, Oncley, etal., Eds. (19 "'Extracted from human erythrocytes. (After Butler, el al. (I960).)

These are particularly pleasing results, one result confirming the other. Such is often not the case for randomly coiled molecules for which the results of different methods may disagree violently with one another. Carbohy- drates are particularly perplexing from this viewpoint. Again, in solution DNA is a very large, randomly coiled molecule, an 'extended double- stranded helix, apt to polymerize and take any shape at all in response to its environment. Therefore the study of nucleic acid reproduction as a molec-

** As the name implies, ichthyocol is a collagen from fish, used as a food supplement, as are gelatin from animals and glutin from wheat.

140

BIG MOLECULES

ular reaction, like reactions of other randomly coiled molecules in solution, is made just that much more difficult. Some very fine X-ray diffraction work has been done On crystalline DNA, but even in crystalline form it may as- sume several structural arrangements, depending upon the humidity.

Molecular Structure of Living Membranes

There are two main subjects of interest in membrane biophysics: the structure of the membrane, and its penetration by small and large molecules and ions. They are closely interrelated. Thus there exist, in the human body, membranes which have every degree of specialization — frorn the quite nonspecific mosaic membrane of the small intestine to the highly specific membrane of nerve cells which not only can distinguish sodium ion from potassium ion (a trick which analytical chemists have only recently learned to do) but even change the rate at which it lets them through! We confine ourselves here to considerations of structure only. Penetration is discussed in Chapter 10.

From analytical and electron microscopic work, it has been found (Danielli and many others) over the past twenty-five years that most living mem- branes*** are laminar, composed of at least three, sometimes five, layers. The heart of the membrane is a bimolecular layer of lipid, flanked by thin layers of protein, or cellulose, or both (Figure 6-8 (a)). The cellulose, if pres-

cellulose ond/or protein layers

bimolecular fatty acid layer

Figure 6-8. Schematic Representation of Layers in the Living Membrane. For many membranes the total thickness is about 75A. (a) Note the position of the defect or pore, (b) Plan view of lipid film.

ent, seems to be there simply for structural reasons — to make the membrane mechanically strong. The protein layer can also provide strength. However, various metal ions and water form complexes with the protein, and some protein of most membranes has enzyme activity, a property which is cur-

*** For example, the cell wall, the endoplasmic reticulum within the cell, etc.

STRUCTURE 141

rently thought by some to be associated with control of the size of the holes through which penetration of ions and molecules occurs.

Although the membrane may have a total thickness of hundreds of ang- stroms, the hydrophobic lipid layer, probably continuous, (and certainly the well-protected center layer), is estimated to be only 75 A thick. Figure 6-9 is an electron micrograph of two membranes touching each other, from which the 75 A figure can be directly measured. This is a pattern which has been found in practically all the living membranes so photographed. The membrane is not perfectly symmetrical, as different staining methods have shown; and in some cases — the erythrocyte wall, for example — there is definitely an assymetry.

'-■•■>-,,* ■ --.■-■■ - .

-">'

-

^

Figure 6-9. Electron Micrograph of the Double Membrane of a Nerve. Osmic acid stains the outer protein layers (see also Figure 6-8), and scatters electrons (dark ridges), but does not absorb into the (light) lipid layer in between. Total distance across one membrane is about 75A. Magnification: 880,000 x. (Courtesy of J. D. Robertson, Harvard Medical School.)

When ones tries to penetrate deeper into the structure of the membrane, one runs into singularly difficult problems. Although it must be made up of macromolecules of protein, cellulose, and lipid, those molecules probably are distorted and stretched, or cross-linked into a planar structure. Neither the structure nor the properties of degraded or dissolved membrane mole- cules would therefore be expected to reflect those of the living membrane by conventional techniques of analysis. And yet not only are the complete membrane structures too thin to be studied in bulk, but also they degenerate when dried for X-ray or electron-microscopic study. In other words, good techniques for studying living membranes in vivo are still needed. Certain very specialized membranes, such as those enclosing nerve and muscle cells, and the rod and cone cells of the retina, can be studied through examina- tion of the details of their specialty. For instance, much progress has recently been made in elucidating the structure of the mitochondrion mem-

142 BIG MOLECULES

brane because of its unique function in electron transport in the step-wise oxidation of foods. But the general problem of direct knowledge of the struc- ture of living membranes probably awaits more knowledge of the structure of macromolecules in solution.

Indirect methods — i.e., studies of penetration of the living membrane by water, ions, and molecules — are proving to be very helpful to studies of structure, because from such studies one can infer some properties of the membrane in vivo: pore size, for example. An estimate of pore size (length and area) requires at least two independent experimental measurements, because there are two-dimensional parameters, area and length, to be evalu- ated. Both the rate of diffusion of a substance down a concentration gradi- ent and the rate of flow of a fluid under a mechanical pressure, should be larger the larger the area of the hole in the membrane and the shorter its length.

Although the rate of transport of water through the cell membrane of erythrocytes is very rapid, both rate of diffusion and rate of flow have re- cently been measured accurately enough to determine a value for average pore diameter in the erythrocyte wall in vivo. Diffusion rate of water was found by measuring the rate at which radioactively labeled water is picked up by the cells within a few milliseconds of being bathed in the labeled water. A fast-flow apparatus had to be used, the ingenious details of which are best described in the original papers.8 Then the rate of flow into the cell was measured by suddenly changing the osmotic pressure (salt concentra- tion) outside the cell, and following the change in cell diameter by means of a light-scattering technique.

From the results, an analysis gives about 7 A as the diameter of the pores in the erythrocyte wall. The beauty of this kind of experiment is that it is a measure of a physical property of the membrane while it is living and func- tioning normally. The limitation is that the analysis involves certain as- sumptions which may or may not turn out to be absolutely correct. In the next few years it will be supplemented by the so-called "differential osmotic pressure" approach of Staverman, in which pore size can be inferred by the "ieakiness" of the membrane to certain ions; and by the molecular- or ionic- sieve approach, in which a large number of ions of various sizes are tested for their penetration. The diameter of the largest one which can penetrate the membrane is the effective diameter of the pore.

Further support for the pore theory comes from examination of mono- molecular layers of large fatty acids and lipids. The lipid is spread out on water in a pan with a moveable boom (the so-called "Langmuir trough"). The boom is then made to reduce the area which the spread lipid must cover, and the force required to move the boom is measured on a sensitive torsion balance. When the layer has closed in completely, the resistance to

ISOMERS AND MULTIPLETS 143

movement of the boom increases sharply, and thus the continuous mono- molecular layer is formed. By means of electron microscopic examination it has been found that the molecules assume a two-dimensional crystal struc- ture, with many crystallites. Where these meet there is indication of defects or dislocations which could be the precursor of pores in the membrane- see Figure 6-8, (a) and (b).

All these approaches presume that pores really exist, and ignore Beutner's old (1911) idea that the membrane's lipid layer is a continuous barrier through which ions and molecules penetrate by either chemical reaction or solution in the lipid layer. This idea still has much appeal, especially in view of what is now known about the changes in transport mechanisms through a film across which a large electrical voltage exists. Thus a typical membrane potential of 100 mv across a membrane whose thickness is 100 A, would exert an electrical field of 100,000 v per cm across the membrane, and nobody knows yet what that would do to a continuous lipid layer. Perhaps acidic and basic organic molecules are formed by electrical discharge, simi- lar to the reactions known in organic transformer oils, to give the layer more of an ionic character so that water and ions can more easily dissolve.

Structure within the living membrane is a treacherous problem for study; but no problem is more intriguing, and none in biophysics more important.

ISOMERS AND MULTIPLETS

This section is concerned with (a) the stereoisomerism which is expected to occur in macro-organic molecules as well as in classical organic molecules; and with (b) excited states which one supposes to exist in macromolecules, by analogy with the properties of smaller ones. These subjects have a bearing on the physical structure of the molecules and their chemical reactivity; but the current practical interest is in their relationship to inherited characteris- tics, to disease, and to benign (passive) and malignant (invasive) tumors. Unfortunately this subject is, experimentally, still in its infancy, although the general principles had been discussed at some length by Delbriick and Schroedinger6 by 1944. Since the principles are fairly straightforward, and the experimental work by contrast very complicated and as yet not too definitive, we outline first the principles, and relate them to a model, or working hypothesis.

Isomers

Stereoisomerism — the existence of two or more chemicals with the same composition and differing only in the arrangement of the atoms — has been known in organic chemistry for a hundred years. Such isomers are truly different compounds, having differing physical and chemical properties. The propyl alcohols will illustrate this basic point. Thus normal propyl

144 BIG MOLECULES

alcohol has the following atomic arrangement:

H H H

I I I H— C— C— C— OH

I I I H H H

However, in isopropyl alcohol the OH group is attached to the central car- bon atom instead:

H OHH

I I I H— C— C— C— H

I I I H H H

"Normal" melts at -127° and boils at 98° C, while "iso" melts at -89° and boils at 82° C. Normal chlorinates slowly in PC13, iso chlorinates rapidly.

Not all isomers are so obvious. Consider adrenaline, which has the struc- tural formula

HO HO< >— C HOH CH2 NH CH3

Two forms exist, which differ only in the arrangement of the groups of atoms attached to the tetrahedral carbon atom starred. The two forms differ in optical rotation. One is physiologically active; the other is not.

As we proceed through the higher alcohols— for example, those with four carbon atoms or more and two OH groups— the stereoisomeric possibilities mount. In the sugars and celluloses in which rings of carbon atoms are linked to one another to form long chains, each carbon having an OH group, physical interference with free rotation about an interatomic bond adds further to the number of possibilities. In molecules of the size of nucleic acid molecules, the number of structurally different possibilities is enormous.

Thus (the example is Schroedinger's) the two characters of the Morse code, dot and dash, can be arranged in groups of four-character letters in 30 different ways. If, however, we have a system of even five characters, and if five copies of each of the five characters are arranged into linear code- scripts of 25 characters, the total number of possible 25-character code- scripts is an astronomical 63 x 1012— that is, 63 million millions! Note that even though the total number of characters chosen to define uniquely the "isomer" is only 25, the number of possibilities is hard to envisage; and indeed this number does not count any arrangements with either side-chains or rings, and is limited even further in that it excludes anything but five

ISOMERS AND MULTIPLETS 145

copies of each character to make up the 25! Of course, not just any arrange- ment of atoms gives a stable molecule; but on the other hand the number of chemical groups of which a macromolecule is composed ( — CH2, — NH, — CO, — C — S — , etc.) is certainly far more than five! .... One concludes that the number of stable isomers of a macromolecule must be huge, but at this stage of knowledge one really has no idea how many there are. Each must have a unique set of physical and chemical properties. Just as in the case of the simple alcohols, each must be a stable molecular entity.

Excited States

No molecule, even if anchored at some point, must be completely quiet if T > 0°K. Indeed, in an environment at 98°F (37°C) such a molecule, even if initially at rest, or quiet — i.e., in its vibrational and rotational "ground state" as it is called — will soon be buffeted into motion by neigh- boring molecules of gas, liquid, or solid, until its energy level or tempera- ture is, on the average, that of the environment. Heat energy enters the molecule as the energy of rotation or vibration if the molecule is anchored, and enters also as the kinetic energy of translation (linear motion) if the molecule is free. The vibrations and rotations may be thought of as standing or traveling matter waves moving across the molecule. Parts of the mole- cule can be fixed and immobile; other parts can be free. The distribution of energy within the molecule will be continuously changing.

Macromolecules accept and give up energy to the surroundings in discrete bursts or bunches or quanta, if the quantum theory applies here as it is known to apply to 2- and 3-atom molecules. However, the energy differ- ences between mechanically excited states must be very small — so small that almost a continuous exchange of energy must be possible.

The important point is that all of the configurations which result from heat exchange are configurations proper to one isomer; in principle the isomer may assume many shapes. Consider the random coil configuration of protein as an example. The one chemical entity may assume many shapes simply as a result of thermal exchange.

Electronically excited states also exist but these are different. It was seen in Chapter 4 that electrons which make the bonds of molecules can absorb and re-emit electromagnetic radiation, and that some excited states can be reached by the absorption of such small amounts of energy that even local heat energy sometimes will do the trick. It is a general rule-of-thumb that whenever a bonding electron accepts energy of any kind and becomes itself "excited," the bond is weakened. Once weakened, it is more susceptible to thermal buffeting and to chemical attack. Its "defense" is to rid itself of the extra energy and get back into the bond; this it does by reradiation, or by transfer of energy into the mechanical motion of the molecule.

146 BIG MOLECULES

The salient point is the following: If the extra energy in the molecule is large enough, quite by chance it may collect at a critical bond and loosen it sufficiently so that a rearrangement of groups within the molecule can occur, and thus produce a dif- ferent isomer. When this occurs in the DNA molecule of the gene, a mutation is the result.

There are many other biological processes which seem to involve excited electronic states of molecules: oxidations seem to be in a class by themselves because of the number of reactions of molecule + 02 + hght which have been demonstrated. In some reactions light is absorbed, and then im- mediately (within 10~12 sec) re-emitted, at least in part (fluorescence); in others the absorbed energy is retained for some appreciable time, perhaps a few seconds (phosphorescence). However, the extra energy to excite elec- trons in a molecule may also be derived from chemical reactions in the metabolism, for there is plenty of it there! This obviously occurs in some bacteria (pseudomonas, vibrio, etc.), some crustaceans, the elaterid beetle, and the firefly, for these animals are chemiluminescent.

That human beings are not luminescent may be a subtle reminder of two important facts: (a) in man the energy-producing metabolic reactions are more carefully delineated by enzymes, constrained to occur in many small steps, each one linked intimately with an energy-consuming metabolic process; and (b) there are electron and proton transfer reactions along large molecules, transfer mechanisms which can conduct the "energy" to where it can be used. In other words, in humans, because of the extra complexity of the system, the extra energy of excitation of molecules need not be radi- ated and lost; there is a mechanism provided by which it can be used.

This can be illustrated further. Although most proteins in vitro have no phosphorescence at room temperature where molecular mechanical motion is relatively large, at low temperature (77° K) all the following proteins, plus at least 18 amino acids, show phosphorescence: fibrinogen, y2 globulin, keratin, gelatin, zein, and bovine serum albumin, as well as egg albumin and silk fibroin. Aromatic rings with it (Pi) bonds in the molecules are a neces- sary condition for the phosphorescence.

In some simple organic molecules (certain ketones, for example) the extra energy has been found to excite one of the unshared pair or nonbonding (n) electrons on the oxygen atom. Its excited position is one of the so-called 7r positions or orbitals of the molecule. The transition is called an "/? — ir" transition (Figure 6-10). The energy absorbed during an n - w transition is about 80 kcal/mole, and can be produced by ultraviolet light of wave length about 3000 A.

The unshared pair of electrons form no bond, but they are paired in the sense that they have opposite "spins." The molecule which contains only paired electrons is said to be in a "singlet"1 state (S = In + 1,' where n is

REPLICATION AND CODE-SCRIPTS

147

jverlappin it electron above the plane of the atoms

Structural r,

formu la with conjugated double bonds q

//

\ //

n-T excitation

2 s electrons an unshared pair (non bonding)

Figure 6-10. The n-7r Electronic Transition (schematic).

the number of unshared electrons). When excited, however, the promoted electron, now in a formerly empty ir orbital, is unpaired; S = 3, and the molecule is said to be in a "triplet1' state. Triplet states are important be- cause they sometimes retain the extra energy, without radiating it, for rela- tively long periods of time. Thus molecules in the triplet state sometimes have time to collide with others which are similarly excited, and the total energy of the collision may be sufficient to cause the isomeric or mutation reaction.

Based on the work of M. Kasha, Reid10 has listed a few types of molecules (containing N, O, P, S) whose n — it transition and the subsequent triplet states probably are energy carriers in biological processes:

Amides Aldehydes and

ketones Amides Quinones Thioketones

Pyridines Diazines and

triazines Azo- and

diazo-compounds Nitroso-compounds Pyrimidines

possibly

Carbonates

Nitrates

Nitro-compounds

The mechanism of some isomeric reactions in which a triplet excited state is an intermediate is now fairly well understood. For large macromolecules, however, pertinent information remains for the future. Nevertheless the direction and importance of such work is now clear.

REPLICATION AND CODE-SCRIPTS

There are now four types of experiment which support the contention thai genetic information is carried by the nucleic acids, DNA and RNA. There is still little direct evidence from any species higher than virus or bacterium.

148 BIG MOLECULES

The celebrated French work on the transplanting of DNA in ducks seems to open the doorway to studies on higher animals. The long extrapolation to humans may turn out to be correct, although it is certainly not yet justified, for this will take generations to prove.

Bacterial transformation: If pure DNA, extracted from a suspension of bac- teria of one type (A) is added to a suspension of another type (B), the progeny of the thus-infected B type have characteristics of A.

Virus reproduction: Bacteriophage T2, a virus, which can reproduce only after it has entered into a living bacterial cell, can be split — the protein part from the nucleic acid part (DNA). The DNA, shorn of its protein, can enter the bacterial cell and rapidly reproduce the intact T2 phage particles again.

Virus "synthesis'''': Tobacco mosaic virus can be split chemically into pro- tein + RNA. One can then reconstitute the virus, using protein of strain A and RNA of strain B. The progeny are of strain B only, having resnythesized their original protein.

Genetic recombination of bacteria: In fertile strains of bacteria, in which DNA can be passed from the donor to recipient cells, the extent of the appearance of the characteristics of the donor in the progeny is proportional to the amount of DNA transferred.

Some Properties of DNA and RNA

These "nucleic" acids (found in the cell nucleus and in the cytoplasm) are substituted sugar molecules which are polymerized through phosphate linkages. In DNA the sugar is desoxyribose; in RNA it is ribose. Both have 5-carbon rings. The substituent groups on the sugar molecules are organic nitrogen bases. These are ringed compounds with two nitrogen atoms in the ring, and are four in number: adenine, guanine, cytosine, and thymine (in DNA) or uracil (in RNA). Linkages, etc., are shown in Table 6-3.

From X-ray diffraction studies it is known that DNA is a helical molecule with 10 sugar residues per turn of the helix. In the "dry" (70 per cent RH) crystalline state two helices are found interlocked (Figure 6-11), each with its phosphate-sugar chain facing to the outside, and the purine and pyrimi- dine bases, hydrogen-bonded together, facing to the inside. f

At cell division, the two interlocking helices separate, and each repro- duces, probably by a process analogous to crystal growth, as though each helix, separated, acts as a template or a die for the "casting" operation which forms the new molecule. That this occurs at mitosis, suggests that the helices are pulled apart by a force which exists only at mitosis. For instance if two ends, one from each helix, are attached to the membrane which encloses the nucleus, in the expansion before division (25 per cent by one measurement) the DNA helices could be pulled apart; then if each template reproduces its opposite by "condensation," two DNA molecules

| A single-stranded DNA is known, in phage <pX 174.

149

TABLE 6-3: Components of the Nucleic Acids (Linkage at *]

"Bases" (B)

Purines

NH2

A: adenine y NH

G: guanine

OH

N K

Pyrimidines NH,

C: cytosine N

o n; h

o

U: uracil HN

°V

O

T: thymine H*f

oA<

H*

CH

		"Sugars'	'(S)
Ribose		Deoxyribose	Phosphate link (P)
C 4	H2OH	I l	5C 4	H2OH /O.	I	1 i	S \ O OH 1/
1	l\H HA	)H	h	[\H	H/OH H	P /\
	\|3 \|2 OH OH		l3 OH	HO O-S

Carbons 3 and 5 link to phosphates; carbon 1 links to the base.

Nucleic Acid Backbone

Single Helix

Double Helix

P P P

\/\/\/\/ v

s s s s s

P P P P \/ \/ \/ \

s s s s

B B B B hydrogen- _ J j

bonded bases "j"

1 1

t c; T c

! ; i

A C A G

1 |

s

s s s s

/\y\/\/\

p p p p

150

BIG MOLECULES

will exist, one for each daughter cell after mitosis. There is now some evi- dence that the condensation reaction is enzyme-controlled, and, current with the times, someone has humorously suggested that an enzyme called "un- twisterase^ controls the uncoupling of the two DNA strands. The reaction is quite sensitive to salts and to pH, which usually indicates that strong elec- trical forces along the structure are important. There is also some evidence that RNA is formed by condensation around the two-stranded DNA, as a third party. DNA itself is not only synthesized by an enzyme, but is also degraded by one called DNAse.

8A small

base-access grooves

large

sugar-phosphate outside ring

ISA-

Figure 6-11. Schematic Drawing of Twin- Coiled DNA Molecule. (Refer to Table 6-3 for detailed structure.)

Much has been learned within the past eight years about .these important molecules. However, more than what has been said is beyond our scope here. It is currently a very active and popular phase of the study of big molecules. They are big, too: molecular weight 5 to 125 million! If uncoiled, the DNA of a human cell would stretch out to a full length of about 1 mm.

Coding Theory

The manner in which DNA and RNA molecules can carry genetic in- formation and control the sizes, shapes, and functioning of all the parts of the complete living system is still a mystery, although some progress has been made in understanding how this is done.

The coding problem is simply enough stated as follows: Since there are only four different pyridine and pyrimidine bases in the nucleic acid mole- cule, and vet there are 20 or more amino acids which must be arranged in

REPLICATION AND CODC-SCRIPTS 151

the proper order if the correct protein is to result, in what way can the four be arranged so that they carry, and can transfer, information on how the 20 amino acids should be organized to form such a great variety of proteins?

The answer to the question is not so simple. There are several theori< s, but just a tew definitive facts, and information is accumulating. The evi- dence is now that it is RNA which actually acts as the template or die lor protein synthesis. The RNA in turn obtains its exact configuration, before its job, by contact with the code-bearing DNA molecule. Its structure lias to be well fixed, for it must guide without error the condensation or linking of (of the order of) 100 amino-acid residues in even a smallish protein mole- cule of molecular weight ~1000. For if one of the components falls into the wrong slot, the whole molecule may be biochemically useless to the living system — a "bad molecule." There are many pitfalls, for the number of possible arrangements in a chain of even 100 units made up of 20 different kinds is enormous.

During protein synthesis the RNA is located in the cytoplasm primarily in the microsomes (ribosomes) (see Figure 6-12), and it is here that the bulk of the protein synthesis take place. Energy for the synthesis is provided by the adsorption on RNA of the amino acids, the "mobile power supply," ATP, and an enzyme, there being one specific enzyme (site) for each amino acid.

The replication process is supposed to go as follows: Sometime in the late stages of the period between cell divisions, during the early part of the prophase when the mitotic apparatus is collecting in preparation for division of the cell, the DNA molecules — which have been depolymerized and dis- persed throughout the cell and are presumably attending to the business of synthesis of big molecules — begin to polymerize and collect into thread-like bodies called chromosomes. (There is some evidence that this process itself is controlled by a large protein.) During this collection process, the DNA's intercoiled helical strands are pulled apart or unwound, and each acts as the template for the condensation of another helical partner, formed from nucleic acid residues in the fluid of the cytoplasm. The process is completed as the resulting pairs of chromosomes are lined up (by contractile protein?) midway between the asters of the mitotic apparatus, and perpendicular to the spindles which join the asters, just before the actual division takes place.

Replication of DNA and of the whole chromosome requires the action ol subtle physical forces: the DNA helices must be pulled apart for individual replication, before they are polymerized to form the chromosomes, which in turn are lined up in a predetermined fashion in the mitotic apparatus; and this is then forced to split in two. The nature of the forces which do these jobs, and of the guiding principle which controls the order and speed with which they are done, are essentially unknown. However, contractile forces of molecular origin are now well known in myosin, and m.i\ be important

152

BIG MOLECULES

here; chemical condensations and osmotic pressures, changed as the nuclear membrane disappears and the fluid of the cytoplasm enters, are other candidates. The forces seem to be too long-range to be electrical in nature.

The essential feature of the replication of the "code" or specification for the animal seems to be the reproduction of the DNA itself. It is now siir- mised that this is a cooperative action of four molecular parts: (a) one of the uncoiled DNA helices, (b) an enzyme, on which has been absorbed (c) the energy carrier, ATP, and (d) the basic polyacid which is to be "stamped" onto (or better: is to condense with) the DNA at the proper spot on the chain. This "enzyme" may be nothing more than one of the proteins syn- thesized already through RNA; it may have a series of "active sites" when uncoiled, one for each of the polyacids which is to be stamped onto the DNA helix.

Thus, at least in principle, the replication process and protein synthesis have many features in common:

Replication: DNA + enzyme + ATP -f basic polyacids

Protein Synthesis: RNA + enzyme + ATP + aminoacids

The key or code for both is carried by DNA, and thence RNA; and some- times by RNA alone.

•;*-% '.::- .'' \.$»

#*

...

~± ■

Figure 6-12. (a) Electron Micrograph of Ribosomes (containing RNA plus small protein molecules called histones) of Escherichia coli: extracted from the pulverized bacteria by ultracentrifugation from a solution 0.01 m in magnesium ions; fixed in formalin; and mounted on carbon-filmed grid negatively stained with phosphotungstic acid to give a dark background. Most particles consist of four segments about 125 A wide. Magnification 1 60,000 x , scale: 0.1 micron.

REPLICATION AND CODE-SCRIPTS

153

A. In 0.002 M-Mg++:mA 305070100

I I I I I

B

■ ' D

. . ^>vJ

>

++

I I I

B.mo.oiM-Mg -.mB 305070 i oo

(b)

Figure 6-12. (b) Two Sedimentation Patterns (A and B) of the Ribosomes shown in (a). Note how the binding of these little particles is so dependent upon the medium. The numbers are the sedimentation rates (in svedberg units) of the different particles in the ultracentrifuge: the larger particles fall faster. (Photographs (a) and (b), courtesy of S. T. Bayley, National Research Council's Biophysics Section, Ottawa.)

"Cogs" and "Cams"

It is generally assumed that the code is contained in the arrangement of the four basic (2 pyridine and 2 pyrimidine) groups in the nucleic acid chain. There are at least 20 amino acids which must be distinguished. The smallest number of 4 basic groups which could be arranged in enough differ- ent ways to distinguish 20 amino acids is 3; and 3 in principle could dis- tinguish as many as 64 amino acids (41).

Two suggestions have been made in which it is shown that, of the 64 pos- sible ways or arrangements, only about 20 are unique in a chain. One sug- gestion was made by Gamov, Rich, and Yeas in 1953, who postulated that the cyclic, helical structure of DNA would give rise to arrangements in which the 4 pyridine and pyrimidine bases jut out from the helix to form the 4 corners of a diamond on the external surface of the helix. Only 20 unique arrangements of the 4 bases could exist. Let us call this the cam theory

154 BIG MOLECULES

partly because one thinks of a cylindrical cam with coding on its walls (Fig- ure 6-13), and partly because it is a degeneration of Gamovl

The other suggestion, made by Crick, Orgel, and Griffiths in 1957, was that in a linear arrangement of only 4 characters, only about 20 unique groups of 3 could be written, provided that no character be counted as be- longing to more than one group of three — that is, if there is no overlap. We think here of a helical molecule with 20 arrangements of 3 bases which de- fine the code information along the chain. Partly because the process re- sembles the meshing of carefully fitted gears, and partly because of the initials of the inventors of the theory, let us call it the cog theory. Figure 6-13 is a schematic representation of the cam and the cog.

triplet base code

sugar ridge

cam cog

Figure 6-13. Cogs and Cams for Coding on DNA. Each spot represents a

pyridine or pyrimidine base.

Both theories have serious drawbacks, not yet resolved. In the Crick model, the amino acids in solution must "know" that they are forbidden to indulge in overlap; while in the, Gamov model a severe geometric restriction exists, viz., the DNA molecule (and hence the RNA whose shape is deter- mined by DNA) must always hold a very specific and rigid helical structure if the diamond arrays are to persist on the surface.

However, successes in a flurry of investigation, genetic and biochemical, have engendered the belief that the basic facts of the amino-acid code car- ped by DNA may be completely known by 1963! There have been three recent remarkable disclosures. First, Nirenburg startled the International Biochemical Congress in Moscow in the Summer of 1961 by announcing that polyphenylalanine (a polypeptide) could be produced by adding poly- uridylic acid (i.e., an RNA, the pyrimidine bases of which are all uracil) to a cell-free solution of phenylalanine. This showed that a sequence of uracils (probably three of them) codes phenylalanine. Secondly, from elegant genetic studies, Crick et al. argued that:

REPLICATION AND CODE-SCRIPTS

155

(a) A group of three bases (or, less likely, a multiple ol three l>ases) along the DNA helix codes one amino acid.

(b) The sequence of bases is read from a fixed starting point along the helix. This determines what groups of three in sequence code an amino acid.

(c) The triplets do not overlap each other.

(d) Probably more than one triplet of bases will be found to code a single amino acid (that is, the code is "degenerate"!.

Lastly, Ochoa et al., in March 1962, disclosed a three-base coding for each of the 20 amino acids, a code based on the increased rate of amino-acid uptake by E. coli protein to which had been added the polymerized bases of known composition. Other laboratories have been publishing partial codes also. Although they may be revised even before this book is printed. Table 6-4 lists tentative codings published by four different laboratories. Underlined are the codes in which the authors have expressed greatest confidence.

TABLE 6-4. Triplet or Three-Base Codes for Each of the 20 Amino Acids of Proteins

	Symbol	Tentative Codes ( 1 962)
Amino Acid	Ochoa	Zubay	Gamov	Woese23
		e/a/.20	et a/.22	eta/."
alanine	ala	UCG*	UCG	AAC	UAG
arginine	arg	UCG	UGC	AGG	AGG
asparagine	asp N	UAA -i UAG J	UCA	AGU	GAU
aspartic acid	asp
cysteine	cys	UUG	?CG
glutamic acid	gluN	UAG -i UC( . '	UUA	AUU	UAU
glutamine	gluN
glycine	giy	UGG	UUG	CUU	GAG
histidine	his	UAC	UGU
isoleucine	ileu	UUA	UAC		CAU
leucine	leu	UUC	UCU	\GC	UCG
lysine	lvs	UAA	UGA	ccc	CCG
methionine	met	UAG	UAU		cuu
proline	pro	ICC	UCC	ecu	ccc
serine	ser	UUC	UGG	< < ;u	\\(,
threonine	thr	UAC	UAG	ACU	CAC
tryptophane	try	UGG	UAA
tyrosine	t vi-	UUA	'AU		UUU
valine	va 1	UUG	UUG	\.\u	( \<;
phenylalanine	pha	UUU	UUU	GI I	UUG

I ' lll'.ic ll

*l tnderlined < odes are

C i \ tosine those thought l>\ the respe< live

\ adenine authors to be vei

( , guanine ible I '

156 BIG MOLECULES

There are extensions and modifications of the cog and cam theories, and even other theories of the physical arrangements on DNA and RNA. The experimental problem is not made simpler by the fact that there are 20 x 19 x 18- •• = 2.3 x 1017 different ways in which 20 different amino acids can be hooked together! Some "selection rules" must therefore follow from a code, for, as Gamov says "if one could spend only one second to check each assignment, one would have to work continuously for about five billion years, which is [estimated to be] the present age of our Universe! "

Other experimental work has brightened the picture still further. For in- stance, only with a specific enzyme does an amino acid form a complex with ATP; polymerization and depolymerization occur in DNA and RNA; com- plex formation occurs between the low-molecular-weight, soluble (or "trans- fer") RNA and the DNA molecule; the helical shape of DNA is well estab- lished in moist air; and chemical analyses have been made of certain mole- cules. All these are experimental facts. There are many, many variables, better knowledge of which will clarify the theory.

MUTATIONS AND MOLECULAR DISEASES

The idea of "sick people from bad molecules" is not really new, although it certainly has been experimentally demonstrated in very convincing fashion and exploited heavily since 1948. While Washington was busy on the Delaware, Scheele in Germany showed that there is a good and bad form of adrenalin. By 1913, F. G. Hopkins was able to state with some bio- chemical authority: "Metabolic processes on which life depends consist in toto of a vast number of well-organized and interlocking enzymic reactions, interference with any one of which can product deleterious effects . . . ." The quotation from Pauling, with which this Chapter began, concerning the need for better understanding of macromolecules and catalysts, is the mod- ern approach to this question.

We have seen that, because of structural and/or compositional changes in macromolecules, the following results may accrue:

( 1 ) Change in rate of chemical processes

(2) Change in rate of physical processes

(3) Introduction of new side reactions

A simple example of (3), introduced before recorded history and persisting faithfully to our day, is offered in the different blood types in man: O, A, B, AB. These differ from each other only in that the colloidal-stabilizing mechanism of the macromolecules of the blood plasma is different: for if two of the types are mixed, they agglutinate or gel; the mixture becomes thick and refuses to flow. The physical nature of this subtle difference which makes them incompatible still escapes us. The production, by each indi-

MUTATIONS AND MOLECULAR DISEASES 157

vidual, of antibodies (big molecules?) which are specific to that individual, and incompatible with those built by any other individual for the same pur- pose, is a well known phenomenon. Thus each individual has a specific bio- chemistry and a biophysics of his own, which becomes manifested in many ways. It is not surprising, then, that even small changes in structure or composition of certain large molecules can sometimes have disastrous results.

A few examples will illustrate the point. No attempt is made to be ex- haustive. Lathe's thesis1 reviews several other molecular diseases.

Molecular Diseases

There is both a broad, generic connotation and a rather restricted, spe- cialized one associated with the term "molecular diseases. " In the sense that all diseases involve molecules which are incompatible with the chem- istry or the physics of the system, all diseases are "molecular. " However, in the more restricted sense, the term has evolved to mean diseases caused by apparently small modifications of the chemical composition or the physi- cal structure of a particular molecule. The hemoglobin diseases, recognized only within the last decade, are now the classic example.

Hemoglobins : There are at least ten known modifications of the hemo- globin molecule, each of which is associated with a pathologic condition. The normal molecule is characterized by certain values for sedimentation and diffusion constant (thence molecular wt.), electrophoretic mobility, elec- tric charge as a function of pH (determined by titration), solubility, ultra- violet absorption spectrum, etc. The most celebrated variant, S, which is found in erythrocytes from people with sickle-cell anemia, differs from the normal, A, principally in the manner in which it moves under the influence of an electric field: it moves faster, and at pH = 7, toward the cathode, whereas .4 is negatively charged at pH = 7 and moves toward the anode.

Some of the pertinent characteristics of ten different forms of the hemo- globin molecule have been collected in Table 6-5. Although the differences were first observed clinically, and then correlated with differences in physi- cal properties, recent work has established that the differences arise because of different composition or arrangement in the amino-acid sequences of the protein. There are about 600 amino acids in the molecule. X-ray diffraction studies have shown that type A (normal adult human hemoglobin) mole- cules consist of four intertwined polypeptide chains. Two of these have a valine, then a leucine residue just prior to attachment to the nitrogen of the porphyrin (heme) group; two others have a valine, histidine, leucine sequence before attachment to the (iron-containing) porphyrin group. It is now known that modifications occur right at that point: a different sequence, or even different amino acids in the sequence, can occur.

158

55

c

E

_re

c

o

O .^r ■£

en

CU 3

en

a

3

T3

O

(L)

bo

1

*— — ' en

D tj D

D

(J

o

s-. bfi

X

CO

o bo

X

CO

"o

en

15

_3

£

o

en

re

"5 en

CO

C re

XI

CJ

be re

CU

be

C

re

X

CJ

£

3 t-

+-j

CJ

cu

,re re _q ^ o re

E *" ~ P

1/5 £ u 5

~~- re ^ t- ^" -H .S" ^

o

cu i_ X

4-J

o

en

c

CU

O en

re

CU >

'5

" r ri

2 ^ 3 S"

(__

0

r-

en

-a

3

_C

_c

3

*

c

£

03

e

£

re

CJ

en

en IS

en

rs

en

IS

in

c

'o

o

CU

3

CU

C

re o

en

'o re

o

'o re

o

CO

re

o

_3

o

3

en

c

(i

3

c

e^-.

03

c

n

5c

en

_4J

en

-a

'o re

'E

re

o c

'E re

>-

c

'E

re

c

"re

£

re ^T

<-. 3

CD

t/a

<3

X)

'<3

c

re

s

o

c

o

i— i

o c

c o

a.

<b

CT3

CU

QJ

3

CU

en

CU

en

CU

en

Si j»

o

1

E

en

E

"bo

1

'<s

*s

<s

*s

«

3

& &

re en

re

en

-3

-6

^

t2

'•$

„, -o

u CL)

■z O) 00

en

O

o

^->,

ii D II

»-■

*— '

oo

1 — 1

oo

-22 -c T

1

|

1

I

w u *

, u O

a

C3

2 "-s >-od

a

«N

Q

CM

a

Elect

phor

Mobili

PH =

-

1

+

CN

■

p

c <=

"O _

,_

^_^

en

J .0

« 'c

"C

re

C

.2 "5 o <J-

£ 1

Co

CJ 1

CU

cj

Q

^

T3

12

Q.

o

■~~

<u o

O XI

^CJ

C re

C

re

X

x 3>

c

en

O

en

CO

"S

re

u-~

re

t/1

CJ

O

E o

bD

'£

E

'£

-♦—

C

CU

Q.

E

c

CO

E

2

CJ en

C re

2

C

re IS

CU

c

CJ

c

3 _re

cu C

CJ 3

o c

c re

1

'£

1

O

c

o c

O 3

17

-

re

c-

'E

CJ

IT

>>

<u

!_

'—

o>

c

t~*

re

CU

^-^

*/i

■>>

i_

>

o

re

O

re

<u

l/>

zz?

E

re

T3

-a

CU

b

CU

cu

eu

O

en

ft

CJ

■

CU

X

£

E

cs

C

V

CU

IS

CU

C

re

CU

jS

CU

c

2

c

a.

c

3

o

CJ

i

re

c

o

0

O

z

CO

p

D

z

I

Z

z

PROBLEMS 159

There may be other modifications out farther in the protein, but this is not yet known. Likewise there may be many more modifications of hemo- globin than those listed. The work is really quite new. Unfortunately, prac- tically nothing is known of the shapes of these molecules — and won't be until more is known of their structure. Sufficient familiarity with the physio- logical reactions has been estimated to be about ten years away.

The sickling of erythrocytes occurs when the hemoglobin-.^ is in an at- mosphere low in oxygen, and is a remarkable example of what "bad" mole- cules can do. It is now fairly well established that these bad molecules are so shaped that they can fit into each other and be piled up like a stack of saucers. In so piling, their strength is sufficient to push out the sides of the erythrocyte and cause it to buckle in the middle, i.e., to become sickle- shaped. On oxygenation, the stack collapses, presumably because the mo- lecular shapes are no longer so nicely complementary. Apparently the process resembles the growth of a crystal. The reader is asked to meditate on the known structure of myoglobin (Figure 6-3), and to study the pictures of Perutz et al.24 on hemoglobin, before pressing further into this subject via Reference 25.

Others. There are well over 20 diseases for which a "bad" molecule has been postulated as the cause. One other which is receiving considerable at- tention now is phenylketonuria. This is associated with mental deficiencies, and has been traced to the fact that one of the enzymes which catalyze the oxidation of phenylalanine through various steps toward pyruvic acid is not doing its job fast enough. Whether the offending enzyme molecule is not being synthesized, or has some physical deformity which renders it only partially active; or whether it or the substrate is not being transported fast enough to the place of catalysis, is not yet known. However, the result is ac- cumulation of phenylalanine in the blood stream, and interference with syn- thesis of nerve tissue.

PROBLEMS

6-1: Erythrocyte DNA has a molecular weight of above five million. Calculate the diameter of the smallest sphere into which one molecule could be compressed. (Assume an average atomic weight of 12: it has Cs, N's, O's, H's, and a few P's and S's. Assume also that each atom occupies a cube 1 .2 A on each side.)

If it were stretched out, the atoms end to end, what would he the total length of the chain?

6-2: Have you figured out how the two helical strands of DNA can unwind: for repli- cation, or for coding transfer- 1<\ A.'

6-3: Describe the four possibilities open to a big molecule in an electronically ex< ited state.

160 BIG MOLECULES

REFERENCES

1 . Lathe, G. H., "Defective Molecules as a Cause of Diseases," Thesis, Leeds Univ.

Press, Leeds, England, 1960.

2. Dixon, M. and Webb, E. C, "Enzymes," Academic Press, New York, N. Y.,

1958.

3. Pauling, L., in "Enzymes: Units of Biological Structure and Function," edited

by Gaebler, O. H., Academic Press, 1956.

4. Putman, F. W., Ed., "The Plasma Proteins, I: Isolation, Characterization and

Function," Academic Press, 1960.

5. Oncley, J. L., et al., Eds., "Biophysical Science — A Study Program," John

Wiley & Sons, Inc., New York, N. Y., 1959; papers by Kendrew, Doty, Rich, and many others.

6. Schroedinger, E., "What is Life?", Doubleday Anchor printing, 1956, of Cam-

bridge Univ. Press book, 1944.

7. Butler, J. A. V., "Inside the Living Cell," Basic Books, Inc., New York, N. Y.,

1959; Butler, J. A. V., etal., Proc. Royal Soc, A, 250, 1 (1960).

8. Solomon, A. K., Scientific American, 203, 146 (1960), and references.

9. Hoagland, M. B., Scientific American, 201, 55 (1959).

10. Reid, G, "Excited States in Chemistry and Biology," Butterworths Sci. Publ.,

1957.

11. Gamov, G., Rich, A., and Yeas, M., Adv. Biol. Med. Pkys., 4,23 (1956).

12. Davson, H. and Danielli, J. F., "The Permeability of Natural Membranes," 2nd

ed., Cambridge Univ. Press, 1952.

13. Shooter, K. V., "The Physical Chemistry of Desoxyribosenucleic Acid," Prog, in

Biophysics and Biophysical Chem., 8,309 (1957).

14. Scientific Amer., Issue on "Giant Molecules," 197, No. 3, 1957; articles by Doty,

Crick, Schmitt, Debye, and others.

15. St. Whitelock, O., Ed., "Cellular Biology, Nucleic Acids and Viruses," N. Y.

Acad. Sci., 1957.

16. Tanford, C, "Physical Chemistry of Macromolecules," John Wiley & Sons,

Inc., New York, N. Y., 1961.

17. "The Merck Index," 7th ed„ Merck & Co., Inc., Rahway, N. J., I960.

18. Bonnar, R. V., Dimbat, M., and Stross, F. FL, "Number Average Molecular

Weights," Interscience Publishers Inc., New York, N. Y., 1958.

19. Crick, F. H. C, Barnett, L., Brenner, S., and Watts-Tobin, R. J., Nature, 192,

1227(1961).

20. Speyer, J. F., Lengyel, P., Basilio, C, and Ochoa, S., Proc. Nat. Acad. Sci., 48,

441 (1962).

21. Nirenberg, M. W., and Matthei, J. B., ibid., 47, 1588 (1961).

22. Zubay, G., and Quastler, H., ibid., 48,461 (1962).

23. Woese, C. G., Biophys. and Bwchem. Res. Com., 5,88 (1961).

24. Perutz, M. F., Rossman, M. G., Cullis, A. F., Muirhead, H., Will, G., and

North, A. C. T, Nature, 185, 416 (1960).

25. Itano, H. A., Singer, S. J. and Robinson, E., in "Biochemistry of Human Genetics," G. E. W. Wolstenholme and C. M. O'Connor, Eds., Churchill Ltd., London, 1959; p. 96 ff.

CHAPTER 7

A Conceptual Introduction to Bioenergetics

Thermodynamics is a queer science. It is a system of logic based on three postulates which have never been proved or disproved. By clever juggling with symbols and ideas, it establishes relations between different forms of energy .... These are most interesting relations which allow us to peep behind the scenes of Nature's workshop .... Thermodynamics may yet tell us how Nature molds such complex phenomena as muscular contraction out of simpler reactions . (A. Szent-Gyorgyi.7)

INTRODUCTION

Scope

The manipulation of the energy available from many natural sources has been a problem of deep concern to man since the realization of the facts of motion. Then came the mastery of fire; the kinematic machine; the use of chemicals for ballistic purposes; and the water wheel for milling, and later for producing the most versatile energy form of them all: electricity. Our age is witnessing the development of the peaceful uses of atomic energy, the energy of nuclear reactions; and a slower but perhaps more far-reaching de- velopment of methods of trapping and storing the sun's radiation as heat, and chemical and electrical energy.

Thermodynamics is the study of general principles which relate to trans- fer of energy from one form to another (Figure 7-1). By contrast with some of the more clearly understood systems, bioenergetics is still in its infancy, although biochemists have done much toward describing the energetics of

161

162

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

(a)

heat 100 % conversion

(b)

Figure 7-1. Energy Interconversion, (a); (b) Degradation of Different Forms of Energy into Heat Energy (the "Heat Death").

some pertinent chemical transformations, and physiologists have done some- thing toward relating chemical energy and work. The many relationships which must exist in living systems among mechanical, electrochemical, chemical, and heat energies are as yet poorly known. This chapter attempts to summarize the conclusions which arise from a generalized approach to energy transfer, and to indicate how far they can be carried into a descrip- tion of the living system.

In this account, use will be made of three different types of symbols, small-case letters, capital letters, and script capital letters, which usually refer to 1 gram, to 1 mole, and to the whole system, respectively. The capi- tals and script capitals have the further property of being "variables of state" — being variables the value of which help to define the state or condi- tion of the system or subject, irrespective of past history. This will become more clearly understood as the subject is developed.

Some Useful Definitions

Energy (from the Greek word meaning "active in work") — usually defined as the potency for doing work. Remember the difficulties with definition raised in Chapter 2?

kinetic Energy (KE) — energy of motion; energy contained within a bound- ary by virute of the motion of the parts contained therein.

Potential Energy (PE) — literally "energy of position'1; more generally energy stored in any metastable but convertible form.

Heat Energy (HE or q) — in terms of the kinetic theory, identically equal to the kinetic energy of motion (rotations, vibrations, translations) of the com- ponent molecules.

LAWS OF THERMODYNAMICS 163

Specify Heat (c) — the heat energy required to raise 1 g of a substance one degree in temperature. A particularly important specific heat is that of water, by which the unit of heat energy is defined: One calorie is the amount of heat energy required to raise 1 g of pure water 1°C, from 3.5 to 4.5°C (where it is the most dense) at 1 atm pressure.

Heat Capacity {(.') — the heat energy required to raise 1 molecular vvt of substance 1 deg in temperature. The units of specific heat, c, are cal/deg Cent, g; and of heat capacity, C, are cal/deg Cent. mole.

Other forms of energy to be discussed are mechanical, electrical, gravita- tional, chemical, nuclear, etc. Energetics or thermodynamics is the study of interconversion of these. In biological systems the subject is usefully- called bioenergetics. That part of the subject dealing with electromagnetic and matter waves was considered in Chapters 3 and 4, and is expanded in Chapter 9.

LAWS OF THERMODYNAMICS

Statements of the Three Laws

There are three general principles which summarize human experience with energy interconversion. They are negative laws in the sense that they cannot be proved always to hold, but nevertheless never have been known to be violated.

The First Law: The first law states simply that energy can be transformed from one form to another but cannot be created or destroyed. After the equivalence of matter and energy were recognized (and proved in nuclear reactions), the law was generalized still further to read: "mass-energy" in- stead of "energy."

The Law stands as written, needing no extension, for all cases in which any form of energy is converted into heat: 100 per cent conversion can al- ways be realized. In Figure 7-1 (b) each of the arrows originates in a form of energy other than heat.

The Second Law: For any machine which converts heat into mechanical work, chemical into electrical energy, or the like, it is a universal experience that only a fraction can be converted; the rest remains unavailable and un- converted. There is thus an amount of unavailable energy as well as available energy from the conversion. The unavailable, it would be logical to assume, is the heat energy which must remain in the molecules of which the final state (i.e., the product) is composed.

The Third Law: At 0°K (-273.16°C), the absolute zero of temperature, at which all molecular motion has ceased, matter should be in a state of perfect order, the molecules being perfectly aligned or oriented, and per- fectly quiet. This law is concerned with the absolute heat energy contained in molecules at any temperature. Although our present interest is in changes

164

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

from one state to another, rather than absolute quantities in any state, the absolute quantities disclosed via the Third Law permit easy evaluation of the changes.

More Detailed Consideration of the First Law. Enthalpy or Heat Content

The internal energy of a body is defined as the sum total of all the kinetic and potential energy contained within the body. When expressed per gram molecular weight it is given the symbol U cal/mole, and is a "state vari- able," that is, one whose value depends only upon the temperature, pres- sure, and composition, irrespective of how it arrived at this condition. Heat energy, (that contained in the motion of the molecules), potential energy of the electron cloud of the atom, and the binding energy of the nucleus all contribute to the internal energy.

If a transformation takes place in one molecular weight of a substance, two things in general can occur: energy can be taken in by the substance, and work can be done. If an amount of energy, q, is taken in, and an amount of work, w, is done, the difference, q — w, must be the increase in energy of the substance during the process; this difference must be stored as internal energy, and hence the change in internal energy is:

AU = q - w

where

AU

U2 - Ux or

^final ' ' ^initial

Now AU = q — w is the concise, algebraic statement of the First Law. The concepts are illustrated in Figure 7-2.

>>

a UJ

(a)

environment

final

AU

(b)

initial

State

Figure 7-2. The First Law of Thermodynamics: (a) a state diagram showing internal energy change, A il, during a process; (b) the process: heat taken in, q, and work done, w.

LAWS OF THERMODYNAMICS 165

One could generalize to complex, nonmolar quantities of varied composi- tion; the law would still be conceptually the same:

AU = q - w

More will be said about this generalization later.

The first law can be extended into a more useful form for processes taking place at constant pressure. Since any substance, this book, for example, has an individual and independent existence in space, and since it occupies a certain volume and has an area upon which the air pressure (i.e., weight of the column of air above it) is 15 lb/sq in., the book does not have as much internal energy as it would have if it were in a vacuum, because it already has done a considerable amount of work against atmospheric pressure. That is, it has already expended enough energy (or "work of expansion"), W, to roll back the atmosphere and create a hole or vacuum in which it can exist. Hence the internal energy

U = KE + PE - W

The work of expansion, W, can be easily evaluated. Consider the cylinder with frictionless piston of area, A, enclosing a volume of gas, V. From the definition of work:

Work = force x distance

= PA x AV/A

= PA V = P( V2 - V, )

Since we are considering an initial state, Vv of zero volume, in general W = PV. Substituting,

U = KE + PE - PV

= H - PV

where H is the internal energy contained per mole in a vacuum (when P = 0). The quantity, H, is called heat content, or preferably enthalpy because really potential energy as well as heat kinetic energy is included.

A little thought about the definition will lead one to the conclusion that H should be a very useful quantity for comparison purposes because its value is independent of any volume change which may accompany a transforma- tion or process. Further, for the case of chemical reactions, AH = H2 - //, (note the parallel with A U) must be identical with q, the heat taken in dur- ing the process for the case in which the only work done is that of expansion; i.e., q = AH. Many biological processes occur in solution, with no appreci- able change in volume, and in these cases AU = AH.

166 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

Now AH = q may be positive or negative depending upon which is larger, the enthalpy of the final or of the initial state. The former characterizes an endothermic reaction; the later an exothermic reaction. As a general rule anabolic reactions are endothermic; catabolic reactions are exothermic. More specifically, the synthesis of proteins in the metabolism of the living svstem is endothermic; the combustion of glycogen and other food stores is exothermic.

For chemical reactions the value of q or AH, the "heat of reaction," can be measured calorimetrically. and quite accurate values obtained. For in- stance, for the simplest reaction

H2 + 1/2 O, = H20

the heat of reaction

&H = #final - ^initial

= H( 1 mole FTO) - H( 1 mole H2 + 1/2 mole 02)

and although the absolute value of the enthalpy (or internal energy) for neither reactants nor product is known (Who knows how to determine the sum of all the potential energies in the nucleus, for example?), the difference, AH, can be obtained with great precision: —57,798 cal/mole at 25°C, the minus sign indicating that the reaction is exothermic.

An especially useful heat reaction is the heat of formation, AH., the enthalpy change which occurs during the reaction by which the molecule of interest is formed from its elements. Actually the example above was a formation reaction. Another now follows:

6CW + 6H2(£) + 3 02(£) = C6H,,06 (glucose)

AHf = -279,800 cal/mole

From a table of heats of formation, heats of reaction can be computed as

AH = (A//,)producls - (AHf)reactants

The heat of combustion or burning of glucose could be computed, from heats of formation, from the following reaction:

C6H1206 + 6<J2(g) = 6H20(1) + 6C02(g) AH = -669.580 cal/mole

The fuel value of foods is usually expressed in units of thousands of calories: i.e., kilocalories (kcal). kilogram calories (kg cal), or Calories (Cal). Hence the fuel value of glucose is 669.58 kcal/mole. Other examples are given in Table 7-1 (A), from which is readily apparent the origin of the very useful "4-9-4 rule": the fuel values of carbohydrate, fat, and protein, are respec- tively, about 4, 9, and 4 Cal/g.

LAWS OF THERMODYNAMICS

167

TABLE 7-1. A. Heats of Combustion, or Fuel Values in Large Calories (kcal or Cal).

"Fuel"	Heat Given Out	Heat Given Out
per Mole (- AH)	per Gram
Acetic acid: CH^COOH (liq)		207.9	3.45
Carbon; graphite; coal: C (solid)		94.5	7.83
Hydrogen: H2 (gas)		68.4	34.2
Propane: C^H8 (gas)		530.6	12.1
Glucose, a sugar: C6H1206 (solid)		669.6	3.72
Sucrose, a sugar: CpH9,Ou (solid)		1349.6	3.95
Alcohol: C2HsOH (liq)		326.7	7.10
Salicylic acid: HOC6H4COOH		723.1	5.96
Carbohydrates (sugars, starches, etc.).	generally*	—	3.7 to 4.3
Fats (and oils), generally*		—	9.5
Proteins, generally*		—	4.3

3. Heat Given Out During Neutralization of Acid with Base at 25° C.

Acid	Base	- AH Cal/mole
HC1	NaOH	13.7
HC1	NH4OH	12.4
HAc	NaOH	13.3
HAc	NH4OH	12.0

C. Heats of Transition from One State to Another— "Latent Heats."

-AH Cal/mole

Ice at 0°C to water at 0°C — melting

Liquid water at 37°C to vapor at 37°C — vaporization

'Mixtures, and therefore of no constant molei ular weight. Note use of both small and large calories in thi table The large "fuel" calorie 1000 small calories de-

fined with reference to ) « H_( ).

Within the general framework of the First Law one can make some ob- servations on the whole animal. The goal of the sum of all the metabolic processes in the living system is to maintain the internal energy, TL, and the enthalpy, JC , at constant values; that is, to maintain A °d = 0 = A JC de- spite the input of energy and the output of work. The attempt is alw.i\v made by the full-grown living thing to maintain a daily balance between the net energy taken in as food (q), and the work done (w). This work may be external physical work, or it may be internal work such as transport through the circulatory system, internal muscle movements of the heart and stomach, chemical transformations, etc. . . .

168 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

The quantity of heat given off by living animals can be measured either calorimetrically or by the C02 produced, (The two measurements agree!), and when measured under conditions of a carefully defined rest, give a value related to the internal work required to keep the living system alive. This basal metabolic rate is about 70 kcal/hr, (about 1400 kcal/day) for a normal man. In other units, the basal metabolic rate amounts to about 0.1 horse- power (hp) continuously.

It is readily apparent that if an animal is ill, certain processes are running at too high a rate; heat energy accumulates, and the temperature rises. The rate of energy loss is increased. By contrast with the normal animal in which A 11 = 0, and q = w, in the ill animal w is much larger than q, the quantity (q — w) is negative, and A lU is negative. Thus the animal lives at the ex- pense of its internal energy, with resulting loss of weight — about 2 lb/day for a human, assuming complete breakdown of assimilative processes and food stored as glycogen and ignoring water loss. The quantities Tl and JC decrease with time before the "turn" or "crisis, " then increase more or less slowly back to normal because the animal begins to assimilate again during the recovery period.

The ideas outlined in the preceding paragraphs show the versatility and the usefulness of the First Law, that energy must be conserved, but of course do not illustrate all its facets. Note parts B and C of Table 7-1 for other examples.

More Detailed Consideration of the Second Law. Free Energy and Entropy

The Second Law of Thermo, does not violate the first, but rather extends it. It says: Whenever energy is transformed from one kind into another, only a fraction of the internal energy (enthalpy, if pressure is constant) change is available for doing useful work; the rest remains as heat energy of the mole- cules left at the completion of the reaction. Corollaries, although seemingly unrelated, are the following: heat energy always passes from the hot to the cold body; water always runs downhill; if energy available for doing work can decrease during the course of a process, the process will proceed spon- taneously, although not necessarily at a fast rate. (That last phrase is a very important one!)

In algebraic terms, the Second Law can be expressed as:

AH = AF + Q

Here AF is the maximum available work, the "free" energy, which can be extracted from AH, and Q is the unavailable energy. Note that both AF and Q as does AH, have units kcal/mole (i.e., Cal/mole).

The word "maximum" needs amplification. It is a fact of common ex- perience that any mechanical job can be done in several ways, some ways

LAWS OF THERMODYNAMICS 169

more efficient than others. If the job is done by the hypothetical frictionless machine, with minimum loss of energy, it is then done the most efficiently. By analogy, work can be extracted from a process in many ways, some more efficient than others. The hypothetical conditions of no waste are given the special name, reversible conditions; AF is therefore the maximum work avail- able under reversible conditions. One practical system from which nearly maximum work can be extracted is the electrochemical one, a battery for example; or, more pertinent here, the concentration cells which exist and deliver energy at living membranes.

Very common are the processes which occur under nonreversible condi- tions. The expression then becomes

A// = AF' + q' + Q_

for the reaction of 1 mole, or

A3"C = A3' + q' +Q

for the living system as a whole. Here AF' (or AJF') and q' refer to the ex- ternally available work and "frictional" loss, respectively. The latter of course shows up as heat energy, which must be dissipated to the environ- ment by any of the well-recognized methods of perspiration, excretion, respiration, etc., which will be discussed later. A useful efficiency can be defined as:

8= AF'/AF, or £= AJF/Afr

This ratio is the fraction of the reversible Tree energy change which is re- alized as useful work in the process. The value can easily be demonstrated with a flashlight dry-cell; it ranges from 0 per cent if the dry-cell is short- circuited by a screwdriver across the terminals; through any value up to about 70 per cent when operating in a flashlight; to close to 100 per cent when used only as a source of voltage with almost no current being drawn. Corresponding values for man cannot be given numerically, but must range from nearly zero for a football team which expends an unimaginable amount of energy to move a 2-lb football a few feet, to very high values for the nerve transmission and mental activity which occur during computation. Other examples will be given later.

The thermodynamic ratio AF/A/7, defined as T, is fixed by the value of the unavailable energy, Q_. It is a more fundamental quantity than 8, in the sense that it does not depend upon the frictional losses in the engine, or upon the inefficiencies of the living machine. All processes of energy conversion are producers or consumers of heat energy, and the conversion can take place only as long as heat can be transferred from one part of the system to another. When finally no further transfer is possible, the process ceases. It

170

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

is evident that the heat capacities of reactants and products help to deter- mine the position of equilibrium. Thus if a product is formed which has more degrees of freedom (i.e., modes of vibrations, translations, rotations) than the reactant, the product can store more energy as kinetic energy (as energy unavailable for work); then AFis less than H, and 7 is less than 1. In other words the products, once formed, have to be heated up to the same temperature as the environment, and are heated by an energy which could have performed useful work were this not necessary. On the other hand if the products can store less heat energy at 37° than the reactants, then A b is greater than A// and Y is greater than 1. The unavailable energy in a process depends upon the temperature and upon the heat capacities of reac- tants and products. This special heat capacity, S cal/deg C. mole, is called entropy. A list of different types of energy and their factors is given in Table 7-2. Note that heat energy is the only one listed for which the intensive factor does not have the dimensions of a force. Perhaps it should be listed as d(TS)/d.x.

TABLE 7-2. Factors of Several Kinds of Energy.

Type of Energy

Intensive (Force) Factor

Extensive (Capacity) Factor (s)

Electrical (joules) dvjdx (volts/cm)

Mechanical (ergs) F' (dynes)

P (dynes/cm2) Chemical (cal) dF/d£ (cal/mole • cm)

Thermal (cal) T(deg)

q coulombs x .v(cm)

<7(cm)

!'(cm3)

£(cm) x rz(moles)

■S'(cal/deg. mole) x n

Explanation:

£ = reaction path length. F is free energy, Mechanical force, above, is given the symbol !■' (in this Table

< »i 1 1 s ).

For the reaction or process under consideration,

a = ts2

TS,

where 2 and 1 refer to final and initial states. Then

d = TAS

Substitution in A// = AF+ Q., gives

AH = AF + TAS

which is the algebraic statement of the Second Law.

Table 7-3 lists values obtained experimentally for AH, AF and AS. An example of particular biochemical and physiological importance is the hy- drolysis of adenosine triphosphate, ATP. At pH = 7 and 37°C:

LAWS OF THERMODYNAMICS 171

AF = -7.73 kcal/mole; AH = -4.8 kcal/mole. and AS = 0.45 cal/deg mole. If the reaction occurs in a test tube, no energy is converted into useful work, and the heat produced is 4.8 kcal/mole. If, however, it is carried out in the presence of an activated actomyosin filament (the contractile unit in muscle), mechanical work (lifting a weight, for example) can be made to occur, and the amount of work done can be anything up to 7.73 kcal/mole, depending upon how it is done. If done reversibly (infinitely slowly), 7.73 kcal/mole is done, and S = 100 per cent; if done more and more rapidly, 8 becomes less and less.

The Production of Entropic Heat

Note that S is a state variable, like F, H, and U, and note that AS may be positive or negative depending on whether the heat capacity of the prod- ucts is greater or less than that of the reactants. Note further that if AS is negative, and it often is, AF will be greater than AH. This is really not surprising if one remembers that the extra energy for work was bound up as extra heat energy of the reactants. Note also that the greater the number of rotations, vibrations, and translations of which a system is capable, the greater the heat capacity and hence the greater the entropy. Therefore entropy (a heat capacity) is often used as a measure of disorder: the greater the entropy, the greater the disorder.

For the living system, we write

A3C = AJ + TAS

under reversible conditions, and

AJC = A37' + q' + TAS

for practical conditions, in which not the maximum work, A{F, but rather a lesser amount, Aj', is realized. An amount of energy, q', shows up as heat energy and adds to the reversible, unavailable heat energy, TA S kcal. Of course q' itself will factor into 7~A&', since it is a heat energy. Then if A S is the reversible entropy increase, AS' is the extra entropy increase because of the irreversibility of the process. Although q' is, strictly speaking, a waste, it is the heat energy which maintains the temperature of a man some 10 or more degrees C above his environment in spite of a steady heat energy loss to the environment. Now, the work done may be internal work, A$'inV or external work, A57'- The internal work, however, is degraded into heat internally, and forms part of q'. (Consider the pumping work of the heart, for example: blood is forced along the circulatory system against a frictional resistance, and the energy is finally expended as heat in the vessel walls.) II we exclude growth and mental work for the moment (these hopelessly complicate the argument), the contribution made by internal work to the

172

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

TABLE 7-3. Heats of Reaction, Free Energy, and Entropy Changes for Some Biologically- Important Processes.

	AH (kcal/mole)	AF (kcal/mole)	AS (cal/deg mole)
A. Illustrative Reactions (very accurately measured)
(1) Combustion of hydrogen in a fuel cell, 25°C: H2(l atm) + \|02(1 atm) = H20 (gas, 1 atm)	-57.798	-54.638	-10.5
(2) Clark Standard Cell, 25° C: Zn + Hg2S04 = ZnS04 + 2 Hg	-81.92	-66.10	-54.9
(3) Combusion of glucose, a pure sugar, 25°C: C6H1206+ 6 0, = 6C02 + 6H20(liq)	-669.58	-823.86	+ 514.
B . Free Energy-producing Biological Reactions
(1) Combustion of glycogen, per C6H10O5unit,37°C: glyc(l%soln) + 6 0, = 6 C02 + 5 H20 (under 0.003 atm CO, and 0.2 atm Gs, as in tissue)	-682.4	-703.0	+ 66.5
(2) Glycolysis, per C6H]0O5 unit, 37°C: glyc(l%soln) = 2 lactates (0.18% soln)	-32.4	-60.4	+ 90.3
(3) Binding of copper ion by albumin, a protein (P): Cu++ + P = PCu+ +	+ 1.05	-7.06	+ 27.2
(4) Dephosphorylation oi adenosine triphosphate (ATP) in muscle, 37°C: ATP"4 + H.O = ADP-2 + HP04"2	-4.80	-7.73	+ 9.4
(5) Hydrolysis of acetylcholine (ACh) in nerve: ACh + H20 = acetic acid + choline	-1.09	-0.82	+ 6.4
(6) Reversible denaturation (D) of a normal (.V) globulin (a trypsin- inhibitor in soybean) : A' — D	-57.3	-111.3	+ 174.

LAWS OF THERMODYNAMICS

173

TABLE 7-3. (Con/in.)

(7) Perfect osmotic system, osmotic pressure difference due to dif- ference of 1 mole of solute be- tween the two solutions. Water flow to equilibrium

(8) Relaxation of stretched, elastic tissue, per kcal of work done

C. Free Energy-consuming Biological Reactions

{ 1 ) Peptide bond formation in protein synthesis: R - COOH + NH, - /?'

= R - CONH -- R' + H20

(2) Pyruvate or acetoacetate synthesis: R - COOH + tf'COOH

= R -COR' - COOH + H20

(3) Blood flow, per complete cycle

(4) Man walking at 2 miles per hr

AH

(kcol/mole)

ca -1000

Af (kcdl/mole)

1.38

1.0

+ 3.0

+ 16.0 ca +0.002 ca +0.010

AS (col/deg mole)

+ 4.6

ca +400

(negative)

(positive)

Note: The values given under B and C are difficult to measure, depending as they do on pH, buffer. et< and are subject to revision. For example in B (4), the hydrolysis of ATP in muscle, values of -9.2 and - 10.5 for A /-'have also been measured, and O. Meyerhof's (1927) experimental value of ±11 = - 12.0 is quoted ex- tensively. The values change markedly with dielectric constant of the medium. (Some values have been taken from the review by Wilkie, 1960.)

metabolic heat loss, q', is numerically equal to the internal work done, A.JF'in, . The rest of the metabolic heat loss, q'irr, is a result of irreversibility in the chemical and physical processes (i.e., less than 100 per cent. The efficiency is not 100%, as is often implied in disucssions of this sort). There- fore

and both q'irr and A9"'inl make appreciable contributions to q' . An estimate of 8 for one specific case is given later. The value, 37 per cent, is probably an upper limit to 8 , because it refers to a very efficient part of the human being — the respiratory enzyme system.

For purposes of cataloguing further, the metabolic heat loss, q', can be considered to be the sum of two parts: (a) the basal metabolic heat, q'bm, and (b) the extra heat, q'rx; in excess of the basal metabolic heat. The former is a minimum value, measured under carefully defined conditions of rest. Thus (q'cx + q'hm) is the heat loss (measurable) from the body during exertion; and q'hm is the value measured when q'ex is zero.

174 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

Although the principles are straightforward enough, measurement of the quantities in these expressions is difficult. Let us make some guesses for illustrative purposes. For a normal man in North America the food intake, AJC, is about 3000 Cal/day, and the basal heat loss, q'bm, about 1400 Cal/day. These are measured values. Since the Second Law says:

A JC= A£F + TA§>

= A5' + q'hm + q'a + 7-AS then

-3000 = AS' - 1400 + q\.x + 7~AS

If the food taken in and burned was glucose, for example, XAS can be evaluated as follows. A A JC of -3000 Cal arises from 4.5 moles of glucose (Table 7-3), and therefore

TA$ = 310degK x 4.5 moles x 514 cal/deg mole = 700 Cal

Our problem then reduces to q 'cx -f AS' = -2300 Cal.

The value of total rate of heat loss has been measured for man in many aspects (look ahead to Table 8-1 1), and in an average day q'ex can be at least as large as the basal metabolic heat loss, and usually runs in excess of 2000 Cal. Therefore -AS' will be less than 300 Cal. The external work AS' can be roughly estimated, especially for an unskilled laborer. Suppose he is required to dig a hole 8 ft square and 4 ft deep; the work of lifting alone is about 30 Cal, and this represents at most a third of the total work expended in loosening, picking, and lifting operations associated with the job. Loco- motion, eating, and the other daily external expenditures probably account for the rest of the 300 Cal of external work.

An estimate of the internal work done per day can also be obtained. In our example above, the total free energy available was 3700 Cal (3000 + 700). If the efficiency, S , was 37 per cent, then

AS' + AS'int = 1370

Of this, about 300 Cal was external work, A^', as we saw above; and there- fore the internal work, ALJ'int, which kept the metabolic process running, was about 1170 Cal, 34 per cent of the metabolic heat loss, q' .

The reader is invited to consider other aspects of man's life and work from this point of view: to put other estimated values into the Second Law and juggle them about, hence to become familiar with both the clarity of concept and the difficulty of successful detailed application at the present state of knowledge.

THE DRIVE TOWARD EQUILIBRIUM

175

THE DRIVE TOWARD EQUILIBRIUM

The Driving Force

It is a familiar fact that if two mechanical forces of difFerent magnitude oppose each other at a point, the resulting movement will be in the direction of the larger force. Similarly, it seems almost axiomatic that if two systems of different free energy. F, are made to oppose each other, provided they are able to interact, the interaction will proceed in the direction of the larger. For chemical reactions, if the free energies of formation for reactants and products are known, then the free energy of reaction. AF, is simply the dif- ference between the two. This value, AF, represents the maximum amount of work available from the reaction of 1 mole of reactant into product. Since AF = Ffinaj - /'„„,,,,, a negative value of AF means that the reaction will proceed spontaneously from reactants to products. Such a reaction is said to be exergonic. If (see Figure 7-3) AF is positive, free energy must be supplied from the outside — another reaction perhaps — before reactants will go into products; the reaction is said to be endergonic. The analogy with exothermic (negative AH) and endothermic (positive AH), introduced earlier, is obvious.

State

Figure 7-3. Free Energy of Initial and Final States. For exergonic (free energy-producing) processes, AF (= Ffin — Fin) is negative; for endergonic (free energy-consuming) processes, AF is positive.

The energy-producing reactions in the living system are numerous. Nearly all the primary sources are the combustion of food products. By suitable carriers the free energy required by the endergonic syntheses of anabolism is trapped and carried through the blood stream to the locations at which the synthetic processes take place.

Naturally, free energy is not a driving force, although it is often considered as such. Nor is the partial molal free energy, (dF/dn)T<P , often called

176 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

chemical potential. These are both energies. Force is energy change per unit distance, £, along some reaction path; eg., dF/di~. Since this quantity can- not be determined for chemical reactions, it is usually tucked away (and for- gotten) in a proportionality constant. In diffusion, heat conduction, and other physical processes, however, it can be evaluated, as will be seen in the next chapter.

The Free Energy Released During the Drive Toward Equilibrium

Internal energy, U, enthalpy, H, entropy, S, and free energy, F, all refer to 1 mole of the substance or system under consideration. In any real system the value depends upon the amount of substance present. During the drive toward equilibrium, as a reactant, A, begins to decompose to product B, the concentration (1 — x) of A at any time, t, becomes less than the original con- centration, while the concentration, x, of B builds up. Hence the free energy difference decreases toward zero as equilibrium is approached, and the posi- tion of equilibrium will be determined by the concentrations, x and (1 - x)eq, at which AF = 0. Thus,

K = —^3

" (1 - *)eq The relation between K and AF per mole can be derived from funda- mental principles, and is simply stated here:

-AF = RT\nKeq

Strictly speaking this "thermodynamic equilibrium constant," K is a ratio of activities, which are defined as effective concentrations, it being remem- bered that the hydration of a molecule, the splitting of salt into ions, etc., makes the effective concentration somewhat different from that determined from the composition. In terms of activities, a, then, at equilibrium:

-AF = RT\n(aB/aA)

which separates out to

-AF = -AF° + RT In (aB/aA) if AF° refers to the standard state in which the activities are 1 mole/1, and the second term corrects for deviations from an activity ratio of unity.

More generally, aB is replaced by the product of the activities of the prod- ucts, and aA is replaced by the product of the activities of the reactants. Fig- ure 7-4 indicates how the position of equilibrium can be quite different for different processes.

ATP: The Mobile Power Supply

An ubiquitous wanderer and a molecule of unrivalled versatility is adeno- sine triphosphate (ATP), a condensation product of adenine with a pentose

THE DRIVE TOWARD EQUILIBRIUM

177

100% reac tants

Positions of Equilibrium

© ©

(D acid + alcohol

(3) HAc + NH4OH

@ HCI + NaOH

(5) salt in high cone, salt

1 0 0 % produc ts

water in low cone, salt ester + water

NH4CI + water

NaCI + water

salt in low cone, salt

Figure 7-4. Positions of Equilibrium for Several Processes.

and 3 phosphate ions. The molecule has the following structure:

Triphosphate part Pentose part Adenine part

A A . A.

r

o

■> r

^ r

0— p--o-p-o-P'-o--ch.

o

n- :h

/Nw

O"

o

c

H

(L)

H H C

J .'/I

C--C H

I I

OH OH

HC

I NH0

It enters many chemical reactions in the living cell, coupling, in some un- known manner, in such a way that the free energy of hydrolysis (splitting off the terminal phosphate group at L), or dephosphorylation as it is often called, —7.7 kcal/mole, is passed to the reaction to which it is coupled. For example, adsorbed on the enzyme myosin in muscle, the molecule hy- drolyzes, and the free energy appears as the mechanical work of contraction of the muscle; coupled with RNA it supplies energy for protein synthesis. Its hydrolysis products are adenosine diphosphate (ADP) and phosphate ion(P).

To become rephosphorylated, as it must, it is carried to the "energy fac- tory" of the cell, the mitochondrion (there are 50 to 5000 of these little double-membraned, 2- to 5-micron bodies per cell), and there the ADP and P are coupled with some step of the respiratory enzyme's oxidation of glucose by 02, receiving the 7.7 kcal of free energy needed to force the ex- pulsion of water and the regeneration of ATP. In plants, the recoupling can occur photochemically through chlorophyll and its enzyme system. The re- action can be represented as:

"discharging"

ATP + H20 , ADP + P

"charging"

178 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

and it is reversible. Left to right, it couples in wherever free energy is needed throughout the living system. Right to left it becomes "charged back up," ready to supply energy at another site.

Now the living system is not wasteful of free energy without a good pur- pose, such as to keep the system warm in a cold environment. Thus most endergonic processes occur in steps of about 8 kcal/mole, or slightly less, making full use of the free energy of the hydrolysis reaction. Likewise the oxidation of foods also goes in steps of slightly more than 8 kcal/mole each, so that the charging reaction is also not wasteful. Indeed, the very complex sets of steps in the oxidation of carbohydrates, fats, and proteins seem de- signed so that at several stages of each the ADP + P can couple in and be condensed into ATP. This is the principle of the Krebs (citric acid) cycle, for instance, in which it is estimated that 38 ATPs are reformed per mole- cule of glucose oxidized to C02 and H20. This number permits an estimate of the efficiency of the recharge process to be made:

8 kcal/mole of ATP x 38 ATP's inn „

'- x 100 = 37 per cent

824 kcal/mole of glucose

This efficiency is very respectable, especially since the reactions are going very fast. By contrast, a steam or diesel engine could probably do 20 to 30 per cent on glucose (for a short while!), and up to about 35 per cent on gasoline or oil; solar batteries can convert only about 10 per cent; and thermoelectric converters about 5 per cent from the fuel (including nuclear, or radioactive fuels). Other (like ATP/ADP) electrochemical devices — eg. batteries and fuel cells — are able to give very high efficiences (>80 per cent) if operated slowly, much less if required to operate very fast.

A simple calculation (note the approximations) will emphasize the im- portant point of how efficient the human machine really is. Man's basal metabolic rate is about 70 kcal/hr. If this is all expended through ATP, the turnover (charge-recharge) rate is 70/8 ~ 9 moles ATP/hr. If we assume that a 150-lb man of density about 1 g/cc contains on the average 10~4 moles ATP per liter, the turnover time for ATP is:

150 1b x454g/lb x 1 1/1000 g x 10~4 moles/1 „-

— 2 — x 3600 sec/hr ~ 30 sec

9 moles/hr

That is, each ATP molecule in the body is hydrolyzed and reformed about once every 30 sec! At this speed of discharge and charge, a man-made bat- tery would have an efficiency well below 1 per cent. Indeed, it would burn up in the attempt! Hence 37 per cent in the living system is truly remark-

^ , , , , • , / c 70 kcal/hr

able. To supply the basal energy, it burns the equivalent ot ~ 1 / g

~4 kcal/g

glucose each hr, 24 hr a day.

REDOX SYSTEMS; ELECTRON TRANSFER PROCESSES 179

The ATP-ADP system is one of a class of oxidation-reduction (redox) or electron-transfer systems operating in the living being. There are many others.

REDOX SYSTEMS; ELECTRON TRANSFER PROCESSES

Equivalence of Electrical and Chemical Energy

Oxidation-reduction reactions have very wide exemplification in living systems: They bring about energy-producing oxidations of food; electro- chemical reactions in the brain and nerve; hydrogenation of oils and dehy- drogenation of fats and sugars, etc. Some are simple electron-transfer re- actions, the reaction

Fe+2 __» pe+3 + g-

for example. The free energy of this /W/-reaction (There must be a place for the electron to go!) can be trapped as un-neutralized electrons — i.e., as electrical energy. In fact if a metallic or molecular electron-acceptor is present at the site, such as

H+ + e~ — 1/2 H2

the chemical free energy of the total reaction

1/2 FT + Fe+3 — H+ + Fe+2

can be drained off as electrical energy. This transformation is almost re- versible (and therefore highly efficient), even at fairly high speed. The free energy of oxidation of foodstuffs is guided by a series of redox enzymes through a particular reaction scheme, in which each step of the process is a fairly efficient redox process. Most of the free energy of each step is trapped as an electron per molecule, and then passed on at the site where it can be used.

Equivalence of electrical and chemical energy is a requirement of the First Law. Thus AF calories/ mole of reaction must be equal to the electrical energy derived per mole of reaction. Now Faraday showed about 1830 that 96,500 coulombs (amperes x seconds) are required to oxidize or reduce one equivalent weight of redox substance; and one equivalent weight is defined as the weight which will transfer one electron per molecule. Hence if the number of electrons transferred per mole, or the number of equivalents per mole, is n, and if 96,500 cou/equiv is abbreviated to F, then the product nF is the number of coulombs required to oxidize or reduce 1 mole. But elec- trical energy in joules is volts x coulombs. Therefore

-AF = nF E

What voltage is E? It is the voltage measured between the hydrogen end

180 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

and the ferrous-ferric end of the reaction cell. To make this measurement, and thereby to measure AF, one might simply bubble hydrogen over a piece of platinum (the metallic contact) in \N-ac\d soution; and attach the plati- num through a voltmeter to another platinum piece sitting in equimolar fer- rous and ferric salt solution. The two solutions must be connected if the circuit is to be complete. The value measured in this case is 0.77 v, con- sistent with a free energy of reaction of about 40 kcal per mole of hydrogen consumed. The ferric end is positive to the voltmeter, the hydrogen negative.

The concentrations may not be as stated, however, and we would expect, and indeed find, that the voltage measured would then differ from 0.77. The conditions specified in our example are arbitrarily chosen "standard state conditions": unit (1) activities of reactants and products, 1 atm pressure, 25° C; and reversibility. We have already seen what a deviation from unit activity ratio will do to AF.

Purely as a matter of convenience and of convention, since the absolute value of no redox system is known, the normal hydrogen electrode (NHE) (1 atm pressure, normal acid, and H2 on platinum) has been chosen as the standard reference, and defined as zero volts. All other redox systems are referred to this standard. In fact a table has been drawn up of known standard redox potentials, F°'s, and is called the electromotive series. However, a special table has been drawn up for biological redox systems. It differs from the standard F°'s, referred to the NHE, in two ways: all the redox reactions are measured against hydrogen at pH = 7, not zero; and since the effective concentrations or activities are not usually known for bio- logical molecules, measured concentrations are used instead; and the tabu- lated values, Eml, refer to equal concentrations (midpoint, m) of oxidized and reduced form (i.e., material 50 per cent oxidized). Table 7-4 lists some of these. A very complete discussion of biological redox systems is given in the remarkable book of W. Mansfield Clark,2 who has spent a lifetime making a systematic study of, and attempting to organize our knowledge of this subject.

Free Energy and Concentration. The Nernst Equation

The free energy of reaction, and hence the emf, F, of reaction, varies with the concentrations, as is evident from the relation between AF and K given above. Insertion of nFE° for -AF°, and nFE for -AF, and rearrange- ment gives the famous expression of the emf as a function of concentrations, introduced just before the turn of the century by Walther Nernst:

DT

E = F°- —\n(am/aTJ

nb

REDOX SYSTEMS; ELECTRON TRANSFER PROCESSES

181

TABLE 7-4. Redox Potentials fm7 of Some Important Biochemical Reactions.

Steady-state Redox Process	Ki	Redox Catalyst
Hydroxide ions - oxygen	+ 0.80 + 0.35
Ferrous - ferric	+ 0.29	cytochrome A
	+ 0.25	cytochrome C
	+ 0.14	hemoglobin
Succinate - fumarate	0.00
	-0.04	cytochrome B
Alanine - ammon. pyruvate	-0.05
	-0.06	flavoprotein
Malate - oxalo acetate	-0.10
Lactate - pyruvate	-0.18	riboflavin
Ethyl alcohol - acetaldehyde	-0.20
Hydroxy butyrate - acetoacetate	-0.28
	-0.32	DPN (diphosphopyridine nucleotide)
	-0.35	glutathione (estimated)
Cystine- cysteine	-0.39
Hydrogen - hydrogen ions	-0.42
Pyruvate - carbonate + acetyl pH	-0.48
Acetaldehyde - acetate	-0.60

Note: At pH 7, and at 50 percent oxidation, measured against the normal hydrogen electrode. Values given are approximate. Complete data on these and many other biological redox systems are given by Clark.2

E° is the value when the ratio of activities of oxidized and reduced species is unity (In 1 = 0), and the second term is the correction for any ratio not equal to unity.

Usually T is 37° C (310°K); R is always 8.3 jou/deg mole, F is always 96,500 cou/equiv; and In x = 2.303 log x. Insertion of these numbers gives the common form of the Nernst Equation

„ „0 (1060 ,

E = £° log (aox/ared)

For the simplest case,

H2 = 2H+ + 2e

the ared = 1, being an element; n = 2; and since pH = -log (aH.), and E° = 0 by definition, the emf of the hydrogen electrode, referred to the NHE, as a function of pH is:

E = -0.06 x pH volts

182

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

Plots of E vs aH+ and of E vs pH are shown in Figure 7-5. It can be seen that at the physiological pH of 7, Eml on the \HE scale is —0.42 v.

0.0

0,4 2

-0.82

-m 7

(all reduced)

100% (all oxidized)

% oxidized (b)

Figure 7-5. Reversible Potential of an Oxidation-Reduction Reaction: (a) as a function of pH,onthe normal hydrogen electrode (NHE) scale; (b) as a function of per cent oxidation. Definition of Em7: potential (on the NHE scale) when pH = 7 and when the redox system is 50 per cent oxidized.

As a further clarification and as a summary, Figure 7-6 shows schema- tically the relation between the NHE scale of £"°'s (pH = 0), to which AE values have been traditionally related through —AE = nEE, and the physio- logical scale, Em7 (pH = 7). The latter is now commonly used as a relative measure of free energy changes in biological reactions. The values in Table 7-5 have been measured simply by putting a platinum wire into a mixture of equal concentrations of sodium succinate and sodium fumarate at pH 7, containing an enzyme and a mediator (discussed later), and measuring its voltage against a hydrogen electrode in the same solution. Such measured values can be used to predict the direction of reaction, or as a basis for com- parison, but not for the determination of AE, because the effective con- centrations (activities) are not known. It is well to be clear on this limitation of the £" -, listing;.

Difficulty often arises in this subject because of notation. Different authors use different subscripts and superscripts. In this book we have de- fined, and use, only E, E°, and Em7. One should be aware of the variations which one may find. Further, one should understand clearly that the values given in the table for intermediary processes of oxidation are midpoint values; that although these redox systems are generally poised at their most stable point (Figure 7-5), a tight control must be kept by the living system at all times on the concentration of oxidized and reduced states of each system;

REDOX SYSTEMS; ELECTRON TRANSFER PROCESSES

183

that too much variation could cause a normally proceeding reaction actually to go backwards !

A special application of the Nernst Equation is discussed under concen- tration cells.

+ 1.22

+ 0.80

-0.42

pH = 0

pH=7

Figure 7-6. £m7's (center vertical line), and Their Relation to the Corresponding

P's. (See text and Table 7-4.)

Balky Redox Reactions

There are three tricks provided by nature to promote electron exchange in oxidation-reduction reactions. The first is catalysis : providing a surface or a site on which the exchange can rapidly take place. For example, electrons exchange immeasurably slowly between H2 and H+ in solution, but if a sur- face such as finely divided platinum metal is added, electron exchange is rapid, and the potential readily manifested.

The second trick is the use of an indicator redox system. If one wishes to know the redox potential of a solution in which the electron transfer is slow or sluggish, one can add a very small amount of an entirely foreign redox system, which exchanges electrons rapidly with the system of interest, and which is either itself highly colored or exchanges rapidly at a metal elec- trode. In the first case the depth of color of the resulting solution can be related to the redox potential; and in the second case the potential can be read directly against a reference electrode. Methylene blue, a colored redox dye, is one of a class of dyes commonly used for this purpose, while the addi- tion of a small amount of potassium iodide often will permit direct measure- ment of the redox potential of the solution against some suitable reference

184 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

electrode. If the redox indicator (KI, for example) is present to an amount much less than the redox systems in the solution to which it is added, it can exchange electrons (KI — * I2) until its potential (determined by ax/aKX) is the same as that of the solution.

The third trick is really a combination of the first two. If a solution con- tains two reactants, such as glucose and oxygen, which can react together spontaneously (negative AF), the reaction will be extremely slow unless the solution contains mediators. Consider one step in the over-all process, for example succinate added to pyruvate in a test tube. Although these two ions can exchange electrons (and hydrogen atoms), with the liberation of free energy, they don V unless a redox system such as cytochrome-C is present as a mediator. Its job is to couple with succinate and reduce it to fumarate, then (itself now oxidized) to oxidize pyruvate. In other words it provides a path by which the over-all reaction can go in two steps, via the mediator, whereas it could not go at all in one. The whole respiratory enzyme sys- tem is a system of mediators, permitting the complete, controlled oxidation of glucose by oxygen to go in discrete- steps, the free energy of each step being thus made readily available to recharge ATP, for example, and there- fore to be usable elsewhere in the system.

There seem to be no generic differences among electrochemical catalysts, redox indicators, and mediators. The name used depends upon one's point of view. Indeed, in his classical work on the succinate-fumarate system, Lehman (1930) called succinic dehydrogenase the catalyst and methylene blue the mediator.

MEASUREMENT OF AH, AF, AND TAS

The simplest way to measure all three energies is in an electrochemical redox cell, described in the previous section, if indeed the reaction is an oxidation-reduction reaction. Thus AF is directly related to the voltage on the NHE scale by -AF = nFE, and A S is directly related to the rate of change of AF with temperature through the relationships'

^1=-A<>; and AS = nFd-^- dT dT

Since AFand AS can be so determined, AH can be obtained from the Sec- ond Law:

AH = AF + TAS

However, AH, the heat of reaction, is itself hard not to measure! If no work at all is extracted in a calorimeter experiment, as a process is allowed to go spontaneously to equilibrium, all the free energy is wasted away into heat, and A His the quantity of heat measured in the experiment.

CONCENTRATION CELLS; MEMBRANE POTENTIALS 185

Measurement of the equilibrium constant, in the usual manner, gives a measure of AF, since

-AF = RT\n K

eq

Further,

d In Keq AH

dT " ~RT~2

and therefore measurement of the equilibrium constant at several tempera- tures allows evaluation of A //by an alternative method.

The Third Law, stated early in this chapter, provides another avenue for the determination of the thermodynamic energies. The law says that the entropy of all elements in their stable states (viz., S0°) is zero at absolute zero temperature (where all molecular motion ceases). Thus the entropy of all pure substances at 0°K is also zero. Further, the entropy at the normal body temperature of 37°C is the sum of all the little ways heat energy can be stored by the material; and it can be evaluated from the heat capacity, C. , of the substance measured at different temperatures from 37° C down to abso- lute zero. Within the past 25 years, literally thousands of "third-law en- tropies" have been so evaluated. Table 7-5 lists some of these values for biologically important molecules. Then, as Szent-Gyorgyi,13 the energetic contemporary physiologist, so aptly stated in the quotation which opened

TABLE 7-5. Some Free Energies of Formation and Third Law Entropies.

-Aff° (Cal/mole) SQ (cal/deg mole)

H20(1) 56.7 16.75

H20(g) 54.7 45.13

NaCl(s) 91.7

C2H5OH 40.2 38.4

C12H22On (sucrose) 371.6

C02(g) 51.08

HAc 94.5 38.0

this chapter, a large, formal system of very useful numbers has been calcu- lated and tabulated from known experimental results. The National Bureau of Standards, Washington, D. C, has published handbooks of useful data. Tables 7-1 and 7-3, as well as 7-5, present very carefully selected samples, of biological and medical interest.

CONCENTRATION CELLS; MEMBRANE POTENTIALS

If two vessels containing different concentrations (two glass vessels con- taining 02 at different pressures joined by a closed stopcock; or two salt

186

A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

solutions of different concentrations separated by a suitable membrane. Fig- ure 7-7) are allowed to interact, the difference in free enegery, AF, can be manifested by transport or movement of molecules or ions. By a rather neat argument involving the dependence of electrical potential upon concentra- tion of ions, it can be shown that the A/7 can also be manifested as a poten- tial difference in such a system. With suitable electrodes the value can be measured. A form of the Nernst equation relates the emf of this concentra- tion cell to the ratio of the salt activities. Thus

0.060

log (a, /a,;

This equation shows the relationship between the potential and the activity ratio for condition of no transport across the interface. For example, for a cell composed of IN - NaCl:0.1Ar - NaCl, in which the activity ratio is about 10, the value of £conc = 0.060 v ( = 60 mv).

I I

salt in J water)

membrane

dif f use interface

a i greater than o 2

Figure 7-7. Concentration Cell (left); with Transport (right).

If flow or transport of ions or water occurs, and it usually does to some extent across living membranes, the value observed, E, differs from E by a "diffusion potential," Em, which can be approximated by either the Hen- derson (1911) or Planck (1915) equations, and measured, approximately, under certain rigorous experimental conditions. Thus,

E = £

'diff

Values 50 to 100 mv are found routinely in living systems, across the mem- branes of nerve cells and red blood cells, for example (see Table 7-6). These values are due principally to potassium chloride concentration differences across the membranes. It is interesting to note that in the electric eel, simi- lar cells are arranged in series, and potential differences of 200 to 1000 v are usually observed! In nerve, the stationary values of about 80 mv are modi- fied rapidly with passage of a stimulus, due to a change in permeability.

NEGATIVE ENTROPY CHANGE IN LIVING SYSTEMS

187

TABLE 7-6. Membrane Potentials, E, Observed, and Calculated from Measured Concentration Ratios Across Cell Walls.

			E (millivolts)
System	KCI cone / KCI cone inside / outside	Observed	Calc by Nernst Eq.
Loligo (squid) nerve axon	19	1	50 to 60	74
Sepia (cuttlefish) axon	21	1	62	77
Carcinus nerve cell	34	1	82	89
Frog muscle cell	48	1	88	98
Human muscle cell	50	1	85 to 100	99

Actually, any activity difference between two solutions separated by a mem- brane is a sufficient condition for a membrane potential to exist. Three cases will give rise to a potential difference:

( 1 ) Two concentrations of the same salt (restricted flow).

(2) The same (or different) concentrations of two different salts. Even though the concentrations are the same, the effective concentrations or activities differ because of different interactions with the solvent and with each other.

(3) Free flow through the membrane, except for one macromolecular ion. This is a rather famous equilibrium, exemplified across living cell walls, and described quantitatively by Donnan.

To sort out these possibilities on living membranes is one of the hardest tasks in biophysics today. The subject will be considered one step further: the time-variation of the potential across nerve-cell membrane (Chapter 10).

NEGATIVE ENTROPY CHANGE IN LIVING SYSTEMS

The concept and the quantity entropy has been very carefully introduced in a simple manner, as a specific heat — a very special specific heat, to be sure — and this idea of entropy is sufficient for many considerations. But the implications are more far-reaching than at first suspected. Thus, an increase in entropy during the course of a reaction was described as meaning that the modes of rotation, etc., of the products were more numerous than those of the reactants. This interpretation means that the amount of complexity in the system has increased with reaction, and could be rather loosely ex- tended to mean that the amount of disorder in the system has increased. Thus the extra heat, q', lost during a process done in a nonreversible manner con- tributes quantitatively to the disorder of the system and its environment.

The idea of entropy being associated with disorder or randomness can be introduced systematically and logically through statistics. Briefly, the

188 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

method takes the following form: The properties of a quantity, In 12, are considered in some detail, and it is shown that In 12 has the two fundamental characteristics of thermodynamic entropy: (1) that In 12 for two or more in- dependent systems is the sum of the In 12's for all the individual systems — that is, that In 12 is an extensive property dependent upon quantity; and (2) that In 12 increases for all spontaneous changes occurring in a system for which the quantity of material and the energy are held constant. Both these properties have been introduced earlier, although not in just this form. The proportionality constant, R (cal/deg mole), then is introduced to relate S and In 12:

S = R In 12

In this development 12 is a pure number, the number of ways in which the particles or parts of the system can be arranged (organized or disorganized). For one of a pair of playing dice the number is 6 (six sides). For a mole, which contains 6 x 1023 molecules, this number, 12, could be counted out, if we were clever and patient enough! However, approximations can be made through the methods of statistics which give closely enough the num- ber of ways the particles can be arranged. Hence the expression above means that the entropy, S, of a system increases as the number of ways in which the system can be arranged increases. The greater the chaos or dis- order, the greater the number of ways; and the greater the entropy of the system.

It has already been shown that all naturally occurring processes, which occur irreversibly, make a positive contribution to the entropy and hence the heat energy of the universe. If there are no violations of the Second Law elsewhere in the universe, the available energy is decreasing all the time, and the universe is approaching the ominous "heat death" or "entropic death," in which the free energy will have reached zero and the entropy a maximum or upper limit. We have then the two interesting possiblities: a one-step creation during which the whole was wound up, from which condi- tion it has been slowly running down ever since; or the continuous violation of the Second Law is occurring somewhere in the universe. An interesting question, then, is: Is continuous creation occurring within the living thing?

Hence, one of the more important aspects of this study of entropy changes centers on the fact that, although the net result of any physical process must be (Second Law) a positive entropy contribution to the universe, there are some processes in which the entropy definitely decreases within a limited space; and it is not very obvious where the overriding increase, if any, occurs to the universe. The process referred to is the creation of the living thing (Figure 7-8), which, although very complex, is certainly not disordered. In fact it is much more highly ordered than the components from which it is

NEGATIVE ENTROPY CHANGE IN LIVING SYSTEMS

189

made. Growth of the living system, controlled from the outset by a molecule such as DNA (desoxyribonucleic acid), must be one of the great "consumers

of entropy" or "producers of negative entropy" Is it in the growth of an

ever-increasing number of living individuals that we find our continuous creation? .... Although during death and decay the order of life is gradually replaced by disorder, the quantity of physical order existing at any one time seems to be increasing each generation, and higher social and economic order runs parallel with the higher physical order of a larger population.

Expanding Universe (entropy increasing)

r ii i i
\ i '
	—	—
~z	LJ
1 1

Protein Molecule (very complicated but highly ordered)

Figure 7-8. Entropy Changes.

Growing Li ving Thing (entropy decreasing)

Some attempts have been made go give quantitative expression to these ideas. Most of these attempts since 1930 involve the concept of the "steady- state," which is treated in the next chapter; but even these attempts do not permit the use of numerical examples, and although inherently very interest- ing, cannot be treated quantitatively in this book. On the other hand, per- haps Teilhard de Chardin was right when he suggested that, taken as a whole, the universe is evolving toward a single, highly organized arrange- ment in which all the ("living") elementary particles of matter have achieved their ultimate state of development; that as living systems organize them- selves more and more, over many more thousands of years, the statistical expression of behavior in terms of the average of random motion of many subparticles, will gradually give way to expressive dominance by the grand ensemble of organized living things. Unfortunately we simply have no way at all of evaluating the sociological and economic interaction energies, nor indeed the psychological, spiritual and moral energies of our own minds.

Armed with the background presented in Chapters 4 to 7, the reader will now want to push on more deeply into certain aspects of energy transfer in

190 A CONCEPTUAL INTRODUCTION TO BIOENERGETICS

living systems. It is recommended that he take the appetizers, References 13 and 14, before he starts the full courses offered by References 2, 6, 10, or 15.

PROBLEMS

7-1 : If a man submits to a diet of 2500 Cal/day, and expends energy in all forms to a total of 3000 Cal/day, what is the change in internal energy per day?

If the energy lost was stored as sucrose (390 Cal/100 g), how many days should it take to lose 1 lb? (Ignore water loss for this problem.) 7-2: (a) From the following heats of formation at 25° C, compute the heat of com- bustion (i.e., the "fuel value") of d-glucose. Give the answer in Cal/mole and Cal/gram.

\Hf

All elements (Na,0,, etc.) 0

CO, -94.4 Cal/mole

HX> -64.4

C6H1206 (d-glucose) -279.8

(b) Given the heat of combustion of sucrose to CO, and H20 to be 1349 Cal/mole, compute the heat of formation from the elements. 7-3: (a) From the values given for AH and AFfor any two reactants tabulated in the text, calculate the entropy change per mole, (b) For each of these two cases, calculate the standard emf of the reaction. Are these values for pH = 7? 7-4: Given the fact that the standard emf 's for the redox systems methylene blue and maleate-succinate are respectively 0.05v and 0. 1 v, at the physiological pH of 7, calculate the standard free energy of reaction (at pH = 0). {Note how important it is to define the pH, or alternatively that the living system keep its pH con- stant.) 7-5: (a) Using the Nernst equation, plot E as afn of pH for:

(i) 1/2 H2 — H+ + e" -0.42 v

(ii) succinate — * fumarate 4- 2H+2e~ -0.00 v

(iii) 4 OH" — O, + 4e" + 2H20 +0.80 v

(iv) Cu — Cu++ + 2e"atpH = 7. +0.36 v

(b) If EQ = 0.50 v and n = 2, plot E as fn of per cent oxidation from 0 to

100 per cent.

REFERENCES

1. Clark, VV. M., "Topics in Physical Chemistry," 2nd ed., The Williams and

WilkinsCo., Baltimore, Md., 1952.

2. Clark, W. M., "Oxidation-Reduction Potentials of Organic Systems," The

Williams and Wilkins Co., Baltimore, Md., 1960.

3. Fruton,J. S., and Simmonds, S., "General Biochemistry," John Wiley & Sons,

Inc., New York, N. Y., 1953.

4. Glasstone, S., "Thermodynamics for Chemists," D. Van Nostrand Co., Inc.,

New York, N.Y., 1947.

REFERENCES 191

5. Kaplan, N. O., in "The Enzymes — Chemistry and Mechanism of Action.''

J. A. B. Sumner and K. Myrback, Eds., Vol. II. Pan 1, Acad. Press Inc.. New York, N. Y., 1951.

6. Sodeman, VV. A., Ed., "Pathologic Physiology: Mechanisms of Disease," 2nd

ed., W. B. Saunders Co., Philadelphia, Pa., 1956.

7. Szent-Gyorgyi, A., "Thermodynamics and Muscle," in "Modern Trends in

Physiology and Biochemistry," E. S. G. Barron, Ed.. Acad. Press Inc., New York, N.Y., 1952, p. 377.

8. Teilhand de Chardin, P., "The Phenomenon of Man." Harper & Bros. London,

1955.

9. Wilkie, D. R., "Thermodynamics and the Interpretation of Biological Heat

Measurements," Prog, in Biophys., 10, 259 (1960).

10. Augenstine, L. C, Ed., "Bioenergetics," Acad. Press, New York, N. Y., 1960:

dealing mainly with energy absorbed from radiations.

11. West, E. S., "Textbook of Biophysical Chemistry," The Macmillan Co.. New

York, N. Y., 1960: good discussion on energy of metabolism, with worked examples, p. 386, eg.

12. George, P. and Rutman, R. J., "The 'High Energy Phosphate Bond' Concept."

Prog, in Biophys., 10, 1, 1960.

13. Szent-Gybrgyi, A., "Bioenergetics," Academic Press, New York, N. Y., 1958.

14. Lehninger, A., "How Cells* Transform Energy," Scientific American. 205, 62

(1961).

15. Oncley,J. L.,eial., Eds., "Biophysical Science — A Study Program," John Wiley

& Sons, Inc., New York, N. Y., 1959: papers by Lehninger, Calvin, and others.

16. Lewis, G. N., and Randall, M., "Thermodynamics," revised by K. S. Pitzer and

L. Brewer, McGraw-Hill Book Co., Inc., New York, N. Y., 1961.

CHAPTER 8

Speeds of Some Processes in Biological Systems

The ultimate goal of biophysical kinetics is the understanding of that remarkable integration of heat, mass, and work transfer by chemicals which maintains so reliably the steady-state condition in every spot in the living system.

INTRODUCTION

Biophysical kinetics is the study of the rate or speed at which chemical reactions or physical processes take place. Factors which influence the speed are elucidated in detail, when possible, by experimental methods, and are then analyzed in terms of the actions of the molecules which give the over- all result. It is the study of mechanism of reaction, and of molecular mech- anism in particular.

Kinetics is formally defined as "that branch of dynamics which treats changes in motion produced by forces." It is the purpose of the subject to define and interpret these forces, which may be functions of temperature, pressure, molecular interactions, concentration gradients, electrical poten- tial, etc.

Within the broad field of kinetics there are two main subjects which are of interest in biology:

( 1 ) Kinetics of chemical reactions in solution.

(2) Kinetics of physical process such as diffusion, fluid flow, transport of electrical charge, and heat conduction.

The basic principles of the main subject are sketched, and then each of the subjects of particular interest is considered. Since chemical re-

192

GENERAL PRINCIPLES 193

actions are covered more or less comprehensively in textbooks in biochemis- try, and since physical processes are very numerous in the living animal but usually receive very little attention from the kinetic point of view, most of the effort is put on the kinetics of physical processes. The presentation em- phasizes the formal similarity of all these processes, and the fact that there are many common factors upon which the rates depend. Unfortunately we do not know enough at this time to achieve very much of the ultimate goal mentioned in the Foreword.

GENERAL PRINCIPLES

Rate-Controlling Step

If any physical or chemical process goes from initial state to final state through a series of intermediate steps, usually one of those steps is inherently slower than the others and controls the rate of the over-all process. For example, a bucket brigade passing pails of water hand to hand from the river to the burning house can transport water no faster than the little old lady who forms the slowest link. The principle is true for chemical and physical processes as well. In most processes in which we are interested, the over-all process involves physical transport as well as chemical reaction. One of the physical steps or one of the chemical steps may be rate-determining.

A measurement of the over-all rate or speed is always a measure of the speed of the slowest step. Consider the chain of events:

If the reaction B — * C is the slowest, then the over-all rate is the rate of B — C. (As an exercise, apply this principle to the over-all event of free air becoming dissolved in the blood stream. What would you expect to be the slowest step?).

Equilibrium

If a process can proceed forward or backward, starting as either reactants or products and produce products or reactants, respectively, the process will move spontaneously (although perhaps slowly) in a direction toward mini- mum free energy for the over-all reaction materials: The reaction will "stop" when the concentrations are such that the work the reactants can do equals the work the products can do, and then apparently the reactions in both directions cease. The materials have then reached thermodynamic equi- librium.

The rate of the forward reaction will depend upon the inherent attraction the reactants have for each other, and upon the concentrations of the reac-

194 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

tants. The same is true of the reverse reaction. Thus, if

aA + bB^ cC + dD

where k] is the measure of inherent attraction A and B have for each other, the over-all rate of reaction in the forward direction of a moles of A with b moles of B (i.e., i\ = -d[A]/dt, or -d[B]/dt, where [ ] denotes concen- tration), is:

,, = k,[A][A] ••• x [B][B] ••• = k,[A]"[Bf

Similarly

v2 = k2[C]'[DY

This first principle, that of mass action in reaction kinetics, was demon- strated quantitatively by Wilhelmy in 1850.

At equilibrium the over-all reaction ceases. Therefore i1, = v2 at equi- librium:

k.imBY = k2[C\[DY

[CYiDY = kL = K

[A]"[BY " k2 ' eq

where K is the equilibrium constant. This form of the Law of Mass Action was stated thus by Guldberg and Waage in 1863. For any reaction -AF° = RT\n Keq, which states that the free energy change per mole (eg., refer to sucrose oxidation) is a measure of the position of equilibrium.

Steady State

Consider again the consecutive process discussed above and consider specifically the case in which the supply of A is unlimited, so that the con- centration of A, [A], never changes. If£, > k2, A will be converted into B faster than B will be removed into C, and B will accumulate. Since the rate of the reaction B — ► C is

v2 = k2[B]

as we saw above, as B accumulates, v2 increases until it reaches the value of v{. At this point B will have reached its steady-state concentration be- cause the concentration B neither increases nor decreases further. The same is true of the other steps. In the steady-state then

»1 = V2 = Vi = V4

or

kt[A] = k2[B) = k,[C] = k4[D]

ON CHEMICAL REACTION RATES; ENZYMES

195

Since the specific rates are all different, the steady-state concentrations are different; but if the process is in the steady-state condition, the concentra- tions are constant.

If the back reactions proceed at a measurable rate, the situation is more complicated, but the principles are the same.

When you hear the word "equilibrium" used, then think: Which is meant, true equilibrium or steady-state? In the latter case, continuous processing occurs; in the former no net reaction occurs. Figure 8-1 illustrates this difference.

source (lake)

tumbling stream

Equilibrium Steady State

Figure 8-1. Equilibrium and Steady State.

ON CHEMICAL REACTION RATES; ENZYMES

Concentration and Temperature

The law of mass action has already been outlined under the discussion of the approach of a system toward true equilibrium. The rate is always pro- portional to some power of the concentration of reactants, and this index is called the "order" of a reaction.

There are really two orders obtainable from experiments, one with respect to time, and the other with respect to concentration. These will have the same value if the reaction is a simple one in which the slowest step is the first step, the one which involves reactant concentrations explicitly. If some other step than the primary one is rate-determining, or if products interfere with or inhibit the reaction, the power, a, of the concentration, [A], which describes best the over-all rate may be different from that which describes the initial rate.

Complicated cases are not considered here. Some of the simpler cases are collected in Table 8-1, which shows the rate equation and the expression and dimensions of the proportionality constant, k, called the specific rate con- stant, when a = 0, 1/2, 1, and 2. In Table 8-2 are collected values of the specific rate constant for some first and second-order reactions.

196

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

TABLE 8- 1 . Summary of Rate Equations for Some Chemical Reactions.

Order*	Rate** Equation	Expression of Specific Rate Constant	Units of Specific Rate Constant
0	v = k	k	c t	moles/ liter sec
i/2	v = k(c0 - c)*	k	2	moles'/liter' sec
i	v = k(c0 — c)	k	1 In °°	_,
t c0 - c
2	v = k(c0 - c)2	k	1 c	liters/ mole sec
1 %(cq - c)

Reactions are of the general form:

Products

(fo - c)

wherec0 is initial concentration of A, andf is the amount of some product formed at any time, t.

*The index of the concentration in the rate or velocity equation. **Velocityi> = dcjdl.

TABLE 8-2. Table of Specific Rate Constants, k

Process	Order	Specific Rate Constant (25° C)
Mutorotation of glucose	1	1.03 x 10-4sec-'
Myosin-catalyzed hydrolysis of ATP	1	3.0 x 10-4sec-'
Decomposition of N2Os	1	3.4 x 10-5sec-'
Pepsin-catalyzed hydrolysis of a di-
aminoacid substrate	1	2.0 x 10-7sec-'
Decay of Sr90	1	8.9 x I0~l0sec-1
Pyridine + ethyl iodate — ► N(C2H5)4I	2	1.25 x 10"4 liters mole"1 sec-1
Thermal decomposition of HI (gas)	2	5 x 10~4 liters mole-1 sec-1

The rate of every individual chemical reaction or physical process in- creases with increasing temperature, i.e., with increasing kinetic energy in the molecules. This is true without exception. However, in some physio- logical processes an increase in the temperature permits certain side reac- tions to occur, which so interfere with the chain of events that the rate of the over-all process decreases with increasing temperature.

For a great many chemical reactions it is found experimentally that the rate of reaction just about' doubles for every 10 Centigrade degrees of rise in temperature. For most physical processes involving mass transfer, the rate goes up from 1.1 to 1.4 times in a 10-degree rise. There are many exceptions

ON CHEMICAL REACTION RATES; ENZYMES

197

to these rules of thumb, of course: for example, certain free radical recom- binations have no temperature coefficient of rate; and by contrast the rate of inactivation of enzymes by heat, and of the denaturation of proteins, can in- crease by 1000 times over a 10-degree rise! The last column of Table 8-3 illustrates this point quantitatively.

TABLE 8-3. Dependence of Rates or Speeds of Various Processes	Dn Temperat	jre*
Process	Activation Energy, E*	Rate at 37°/Rate at 27° C
Free radical combination	0		1.0
Free radical + molecule — ► products	0 to 0.3		1.0 to 1.01
Transport in water solutions (diffusion,
viscous flow, ion mobility)	1.0 to 5.0		1.06	to 1.28
Transport in fat and lipid (diffusion,
osmosis)	8 to 15		1.5	to 2.2
Molecule + molecule — ► products
(hydrolyses, neutralizations, rear-
rangements and condensations)	10 to 30		1.8	to 5.0
(a) uncatalyzed	15 to 30		2.2	to 5.0
(b) catalyzed	10 to 20		1.8	to 3.0
Denaturation of proteins and inactivation
of enzymes	30 to 150		3.0	to 3000

'Different processes of the same general type may have different activation energies Therefore both A* and the ratio of rates are given as a range of values. Units of E* : kcal/mole.

In general this dependence upon temperature is understandable in terms of the postulates of the kinetic theory of matter. Molecules are presumed to be in a state of continuous motion and have a heat content (H) which de- pends upon the number of (degrees of freedom of) rotations, vibrations, etc. It is axiomatic that in such a case of random motion not all molecules will contain exactly the same kinetic energy at any one instant. In fact, it is in- herent in the kinetic postulates that the energy distribution must be of the form shown in Figure 8-2.

The average heat energy, Q^v, per mole of material is 1/2 RT (300 cal) for each translational degree of freedom, RT (600 cal) for each vibrational degree of freedom, and 1/2 RT [or each rotational degree of freedom. For a diatomic gas at 27°, then, with one degree of vibrational freedom, two of ro- tational, and three of translational, the average heat energy, Q^v, is 2100 cal per mole of gas.

In any collision of reactant molecules which is to result in reaction, a mini- mum or threshold energy must be involved in the collision, or else the mole- cules will simply bounce off each other. Let this threshold energy be E*. A few molecules will have the excess energy sufficient to react; not every col-

198

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

threshold energy E

Energy E

Figure 8-2. Maxwellian Distribution of Energies in Molecules.

lision need be a fruitful one. At a higher temperature, T2, more molecules have the necessary threshold energy to react, and therefore the rate is faster. Experimentally, Svante Arrhenius, about 1889, observed that the rate in- creased exponentially with the temperature. Since in solutions, the con- centrations do not vary appreciably with the temperature, the temperature- dependence is practically all in the rate constant, k. Thus

k = Ae-E*'RT

where A is a constant in moles per liter per second, E* is the threshold energy in calories per mole, R the gas constant (1.987 cal per degree per mole), T the temperature in degrees K, and "e" is 2.71828, the base of natural logarithms. Taking logarithms of both sides

In A = In A - E*/RT

or, changing to the base 10, the more familiar system:

log k = log A - E*/2.303RT

Hence a graphical plot of experimental results of rate measurements at dif- ferent temperatures plotted as log v vs \/T has a slope of -E*/2303 R; and, since R is known, the value of the threshold energy, E*, can be determined (see Figure 8-3).

Table 8-3 gives values of E* for different kinds of processes. E* is often called energy of activation as well as threshold energy, and the measured value can often aid in the characterization of the rate-determining step of a process.

ON CHEMICAL REACTION RATES, ENZYMES

199

slope

A log v A l/T

2.303 R

( T in degrees Kelvin )

Figure 8-3. Arrhenius Plot of Log Rate vs l/T; Determination of Activation Energy.

Referring back to Figure 7-3 which describes a process proceeding from an initial state to a final state, we know now from the preceding discussion that it must be modified with the insertion of an activation "hump" or bar- rier (see Figure 8-4). Thus E* is related to the extra heat content, A//}, the heat content change between initial state and "activated" state.

activated complex

c UJ

State (a)

| uncatalyzed

State (b)

Figure 8-4. Enthalpy (a) and Free Energy (b) of Components as They Pass from Initial to Final State Over the Activation Energy Barrier. Note the position of the activated complex, and the energetically easier path of the catalyzed reaction.

200 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

More Factors of the Specific Rate Constant

Various interpretations have been given to the pre-exponential term, A. The most successful has come from the theory of absolute reaction rates, which was pioneered by H. Eyring mainly in 1935, and expounded in detail in 1941 in the famous book by Glasstone, Laidler, and Eyring6, and since then in most books on physical biochemistry.

Essentially the reacting molecules are pictured (refer to Figure 8-4) as proceeding through a state in which they are in a metastable state called the "activated complex," which is more or less in equilibrium with reactants in the initial state, 1. While in this complex, the molecules can either proceed to form product, the final state, or return to reactants, the initial state.

If equilibrium can exist between reactants and complex, the thermody- namic functions can apply to this part of the reaction: thus Hi - //, = A//*; Sx - Sx = AS*; and F* - F, = AF*.

From statistical mechanical arguments the pre-exponential term by this theory reduces to"

k T

h

where t is a "transmission coefficient," which expresses the fraction of com- plexes which proceed to products (often assumed to be 1.0); kg is the ideal gas constant per molecule (R/6 x 1023 = 1.38 x 10"16 erg per deg C per molecule), and h is Planck's constant (6.63 x 10~27 erg sec).

The over-all rate, then, for a reaction such as that considered on p. 194, is:

v = [A)a[B]bT^— g*sv* e-W/xr

h

It can be seen that a measured value of rate, v, at known concentrations of A and B, plus a measured value of the activation energy, AH*, permits the value of ASX to be obtained.

Especially in biological processes has the evaluation of the entropy of ac- tivation been important. Remember, the entropy change tells us whether the heat capacity of the system has increased or decreased during the reac- tion, and since the heat energy contained within molecules increases with the complexity of the molecule, it is often possible to infer certain physical properties of the activated state, and hence of the molecular movements dur- ing reaction. This technique has proved useful in learning about the mech- anism of muscle contraction, for example, certain details of which are con- sidered in Chapter 10.

In short, the rate of a process depends upon the concentrations and the temperature, and on the free energy change accompanying the formation of the activated complex from reactants.

ON CHEMICAL REACTION RATES; ENZYMES 201

The role of a catalyst is to provide an alternate path which is energetically easier. Thus the catalyst, because of the energetic advantages it offers, acts as a guide-post to direct the reaction through preferred channels or path- ways (see Figure 8-4 (b)). This subject is now explored further.

Catalyzed Reactions; Enzymes

There are many chemical reactions and physical processes whose rate or pathway is controlled by one or more catalysts. Far surpassing all the rest in importance as biological catalysts are the enzymes. These are large pro- tein molecules, which are often bound with metallic ions and are always heavily hydrated. They have the special property that at some site(s) on the surface both the kinds of atoms and their arrangement are such that more or less specific adsorption of a "substrate" molecule can occur. The substrate molecule is the one which is to undergo hydrolysis, hydrogenation, trans- ammination, or some other reaction.

In addition to the kind of atoms and their arrangement, a third essential requirement of the enzyme seems to be the presence, in the vicinity, of a large electric charge, usually in the form of a metallic ion such as Mg++, or a charged chemical group, such as -PCV2. The role of the charged group is to distort the electronic structure of the substrate molecule as it adsorbs on the enzyme, thus to make it energetically easier for the desired reaction to occur. The most easily measured manifestation of a catalyzed process is a lowered activation energy, E*. Some values are collected in Table 8-4. Note especially the numbers for the decomposition of H202.

TABLE 8-4. Activation Enerc	gies for Some Catalyzed Biological Rei	actions.
Reaction		Catalyst	£* (Cal/mole)
Inversion of sucrose		acid(H30+) trypsin-kinase0 malt invertase	20.6 14.4 13.0
		yeast invertase	11.5
Hydrolysis of ethyl but	yrate	acid(H30+) pancreatic lipase	13.2 4.2
Decomposition of hydrogen peroxide (H202)	no catalyst platinum Fe+ +	17to 18 11.5 10.1,8.5
		liver catalase	5.5
Hydrolysis of urea		acid(H30+) urease	24.5 12.5 to 6.5

"The suffix "ase" denotes enzyme.

202

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

A typical process can be illustrated as in Figure 8-5, and described as fol- lows, a hydrolysis serving as the example: First the molecule to be hy- drolyzed (the substrate molecule, S) bumps into the hydrated enzyme mole- cule, E; and if the collision occurs at the active site and is energetic enough, a slight bond will be made between the two, forming the enzyme-substrate complex, ES. The complex can then do one of two things: it can fall apart again (in which case we lose interest); or it can be "activated" — i.e., given excess energy by favorable collisions with its neighbors — and associate with a water molecule close by, to form the activated complex, ESK This in turn can either fall apart the way it was formed, or it can proceed on to split up in a new way — as reaction products — with the substrate molecule hydrolyzed and the enzyme ready to go again.

The process is sketched at the top of Figure 8-5, the energy of the reac- tion path at the bottom, and the formal equation in the middle. For the purpose of formulation of the rate equations, the reaction can be written:

E + S^ ES (formation of the M jchaelis complex, ES) 1

*-i

ES ~^> products (activation and reaction to products) 2

where kt, k_x, and k2 are the specific rate constants for the respective steps.

prod. 2 *• E + products

Reoctonts Complex Activated complex

State —

Products

Figure 8-5. Schematic Representation of Catalyzed Hydrolysis Reaction, Showing Formation and Activation of the Intermediate Complex, ES.

ON CHEMICAL REACTION RATES; ENZYMES 203

Now this reaction can be very complicated, but for our purpose it will suf- fice to consider one (the simplest) set of conditions, and examine how the rate varies with changes in either enzyme or substrate concentration. First we assume that v_} is much faster than v2, and therefore that reaction 1 is essentially at equilibrium, or that K = kjk , .

The rate is then given by

v2 = k2[ES]

where the square bracket again denotes concentration. Now the only prob- lem remaining is to compute [ES] from the equilibrium constant. If the initial concentrations of enzyme and substrate, respectively, are [£"]n and [S]0, the concentrations of free E and S are given by

[E] = [E]0 - [ES] and

[S] = [S]0 - [ES]

and therefore the equilibrium constant is given by

K = \m

Cq ([£]„ - [ES]) ([S]0 - [ES])

This becomes simpler if only the usual case is considered, namely that in which the substrate concentration is much higher than the enzyme concen- tration; for under this condition only a small fraction of the substrate mole- cules will ever be tied up as complexes ES because there are so few enzyme molecules with which the substrate can form a complex. Hence

[S]0 - [ES] - [S}0

Rearrangement gives

[ES] =

Keq[E]0[S]() [E]Q[S]0

i + /ysio Km + [s]0

if Km is defined as 1/A~,f] . This holds for any value of [S] at any time.

Therefore the rate, v2, of the enzyme-catalyzed reaction (proportional to the concentration of complexes) is:

k2[E]0[S]

v2 = -d[S]/dt =

Km + [S]

This is the rather celebrated Michaelis-Menten Equation, and describes the rate as a function of initial substrate concentration under the particular con- ditions we assumed. A plot of v2 vs [5"]0 is shown in Figure 8-6 for both high and low enzyme concentrations. The expression says that: (1) the rate is

204

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

		high [E]0
li
>	/a	low [E]0	b
c o (J c <u cc
O
a or

Initial Substrate Concentration [S]0

Figure 8-6. Rate of a Catalyzed Reaction as a Function of Substrate Concentration for Two Different Concentrations of Catalyst.

always proportional to the enzyme concentration if the substrate is much in excess; (2) the order, or the index of the substrate concentration, declines from unity down to zero as substrate concentration is increased. In other words, (note Figure 8-6, region a) if substrate is in great excess, [S]0 > > Km, and Km + [S]Q ~ [S]0, and the rate expression reduces to

v2 = k2[E]0

with rate independent of substrate concentration; but (note region b) if the substrate is in excess of enzyme, yet [S]0 << Kr rate expression reduces to

and Km + [S]0 « Km, the

v2 =

[S]0[E]t

with rate increasing linearly with substrate concentration.

It is clear then that the nature and the extent of the binding of the enzyme- substrate complex, ES (i.e., the value of Km) is all-important: the bigger the Michaelis constant the smaller the extent of binding; and the weaker the binding, the slower the rate of hydrolysis.

It is by good chance* that these E-S complexes generally absorb electro- magnetic radiation in the visible and near ultraviolet regions of the spec- trum. Hence their existence, as well as their Km , can be determined spectro- photometrically (by light absorption), and the value of Km compared with

*This work was pioneered and developed to a highly specialized art by Britton Chance, of Yale University.

ON CHEMICAL REACTION RATES; ENZYMES

205

that obtained by measuring rates at various concentrations of substrate and enzyme.

The "catalyst law" (for enzymes, the Michaelis-Menten expression) rear- ranges to

[S\

W£]„ - K

eq

from which it is seen that the slope of a plot ofv/[S]0 vs v gives K (= 1/A"m) directly as the negative of the slope. Figure 8-7 is such a plot for the hy- drolysis of a particular dipeptide for which the stomach enzyme, pepsin, is a specific catalyst. The value of Km obtained is 0.0014 moles liter-1. This result is typical. The inverse, the value of K at 25°, will usually be found to be between 100 and 600 liters/mole, which means that the substrate must be in excess 100- to 600-fold over the enzyme if the catalyst is to be more than 90 per cent complexed (i.e., "worked hard") at all times.

There are cases (certain chymotrypsin-catalyzed reactions, for example) in which the binding of the complex is much stronger. By contrast, the myosin-adenosine triphosphate complex, formed during muscle contraction is relatively a very weak complex .... The value of Km is numerically equal to that value of the substrate concentration at which one-half the enzyme molecules are tied up as complexes. Electrical attractions and repulsions as well as the geometry of the molecules E and S determine the extent of

Keq = 700

Figure 8-7. Determination of the Binding Constant of the Intermediate Complex in a Catalyzed Reaction (pepsin-catalyzed hydrolysis of carbobenzoxy-glutamyl-tyrosine ethyl ester, a dipeptide). Values plotted are those of initial rates found experimentally for six different initial concentrations of substrate.

206 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

binding and hence the specificity of a particular catalyst for a particular reaction.

Not all of the assumptions made nor the conditions assumed in the fore- going analysis are always met. Because equilibrium does not always exist in reaction 1, Km can better be expressed as (£_, + k2)/k] , which of course reduces to l/K = k_]/k] if k_x >> k2, the case we have studied already. There are further complications, such as competition by two or more reac- tants for the one active site, which introduce more terms in the expression for v. Although these are of pragmatic interest in biological chemistry, further discussion here is beyond our scope — our purpose is simply to illus- trate complex formation and saturation of a catalyst.

It should be remembered that the rate constant, k2, can be factored into

k T

h

Because the change in entropy AS1 accompanying activation gives an indi- cation of the change in the freedom of motion within the complex ES1, deter- minations of AS1 and A//1 have become very powerful tools for understand- ing the mechanism on a molecular scale. Some values are given in Table 8-5. A very interesting success story of this kind centers on myosin, the con- tractile substance in muscle and the catalyst for ATP hydrolysis. The "state of the art1' is reviewed briefly in Chapter 10.

TABLE 8-5. Kinetic Parameters for Some Enzyme-Catalyzed Reactions.*

Enzyme Substrate (deg C) pH (moles ') (sec ]) E2* ±S2*

Pepsin carbobenzoxy-1-glu-

tamyl-1-tyrosine 32 4.0 560 0.0014 20.2 4.6

a-Chymo- benzoyl-1-tyrosine

trypsin ethyl ester 25 7.8 250 78 9.2 -21.4

Urease urea [CO(NH2)2] 21 7.1 250 20,000 9.7 - 7.2

Myosin adenosine triphos-

phate (ATP) 25 7.0 79,000 104 13.0 - 8.0

\/Km. equilibrium constant for formation of ES complex (see Figure 8-5). k2 : specific rate constant for unimolecular breakdown of the ES complex. £,* : energy of activation of ES complex. AS2*: entropy of activation of ES complex. Negative values are usually interpreted as evidence for the freeing of charged groups resulting in orientation of water molecules during activation.

Values in the last three columns were taken at high substrate concentration and therefore refer to the activation of ES complex into product.

*See the book bv Laidler15 for collections of data.

ON DIFFUSION; OSMOSIS 207

Generalization of Method

Enzymes are not the only catalysts in the living system, of course. Sur- faces, acid (H + ), base (OH ), and metallic ions are all important catalysts. The general principles outlined above apply to these equally as well as to enzymes. The factoring method of analyzing rates — that of extracting from the proportionality constant one after another the variables and universal constants upon which the rate of a process depends — in some ways has reached its highest state of development in chemical kinetics; and it is scor- ing rather remarkable successes with some very complicated biochemical re- actions. Whether this method of analysis, which ultimately reduces to analysis of the intermolecular forces and molecular movements of a biologi- cal process, is properly termed "biophysical chemistry'1 or "chemical bio- physics," is often uselessly debated. It is a matter of definition; and no definition has yet been generally accepted. We use this illustration of the factoring method not only to discuss the velocity of biochemical reactions in terms of molecular interactions, but also by analogy to discuss in the follow- ing sections the velocities of the physical processes of transport, namely dif- fusion, osmosis (a special case of diffusion), viscous flow, electrical con- ductivity of solutions and tissue, and heat conduction.

ON DIFFUSION; OSMOSIS

Diffusion may be defined as the movement, in a preferred direction, of one component relative to the other components, of a mixture or solution. The preferred direction is from the place of higher concentration to the place of lower concentration of diffusing substance. No flow of the whole fluid need occur — no turbulence, nor even convection; no gravitation, no electrical field is of importance to transport by pure diffusion.

The fact that diffusion occurs is not surprising when one remembers that all molecules are in a state of continuous motion. The more molecules of type P there are present in a particular volume of solution, the greater the likelihood that some of these will gain enough excess energy to find their way out of this volume. Consider two unit volumes with a common face, one with concentration P in Q higher than the other (Figure 8-8). Because all molecules are in continuous motion (i.e., have kinetic or thermal energy), on the average more P molecules from volume 1 pass into volume 2 than the reverse. In fact, the greater the concentration difference (actually the gradi- ent dc/dx), the greater the speed at which they diffuse, other things being equal. Figure 7-7 was an earlier impression of this same idea.

If, however, some sort of barrier to diffusion is placed between volumes 1 and 2, the rate at which P diffuses is slowed down; and the greater the thick- ness of this barrier the lower the rate becomes. To a first approximation,

208

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

high	1 o w
P	"- P

P in 0

Figure 8-8. Illustration of Direction of Diffusion of P in a Mixture of P in Q.

therefore, it is the rate of change of concentration, c, with distance, x, which determines the rate of diffusion.

These intuitions were first set down and experimentally proven by the in- genious German anatomist, Adolf Fick, in 1855:

j = DA

dc_ dx

(Fick's first law)

where dcjdx is the instantaneous rate of change of concentration with dis- tance, called the concentration gradient, in moles per liter per cm; "j" is the flux (i.e., the flow rate, v) — the number of moles passing through a particu- lar area, A cm2, in 1 sec; and D is the proportionality constant, which con- tains all the other factors — some of them still unknown — upon which the rate of diffusion depends. Self-diffusion of water across an erthythrocyte membrane is an example. Absorption of gaseous 02 by the blood capillaries in the lung is another example: both the partial pressure of 02 and the con- centration in the circulating blood plasma are constant in time. Fick's first law is limited to the case in which concentrations do not change — the steady-state condition — and the source and the sink are infinite.

However, there are many specific cases, particularly in the gastrointestinal tract and associated with assimilation of the degraded products of foods, in which the concentration gradient is not constant, the state is not steady. Any periodic or sporadic phenomenon which makes a sudden change in the rate of supply of reactants to a certain part of the living thing, will cause a deviation from the steady state. Thus in the volume in which the change occurs, the rate of change of concentration, dc/dt, is given by

dc/dt = D d2c/dx

(Fick's second law)

Since d2c/dx2 can be written — ( — , and since dcjdx is the concentration

dx \dx)

gradient, we see that the second law states that the rate at which the concen-

ON DIFFUSION; OSMOSIS

209

tration changes within a volume is proportional to the rate of change of the concentration gradient at the boundaries of the volume.

One simple example will be used to illustrate the problem described by Fick's second law. This will be done only qualitatively, for the detailed de- scription is too complicated to be practical here. Consider the red blood cell, with various components contained within, and separated from the medium by a membrane, the cell wall. There are fluids on both sides of the wall in osmotic equilibrium (see Chapter 2). This is a condition of no net change: potassium ion, at higher concentration inside the cell is being transported in both directions across the cell at equal rates; sodium ion, at higher concen- tration outside the cell, is being transported in by diffusion, out by "active transport," but both at the same rate so that there is no net change. Water moves across the membrane freely in both directions. (Recent radioactive tracer experiments using tritium have shown that complete exchange of water can occur in a few milliseconds.) If for some reason the "sodium pump," which provides the active transport, fails, then both K+ and Na+ will diffuse passively, each in the direction towards lower concentration (Figure 8-9). The rate of diffusion, expressed by the rate of change of con- centration, dc/dt, is given by the second law as D d2c/dx2. Solution of the equation for c, gives c as a function of t; or c = /(/). The form, /, can be worked out explicitly, provided certain other conditions are known. The result is approximately rK+ = c{ + c2/y/T+t0 for the decay of the internal K+ concentration and rNa+ = c[ — c'2/y/t + t0 for the buildup of internal Na+ concentration to the concentrations of K+ and Na+ in the plasma in

Time after failure (sec)

Figure 8-9. Readjustment of Concentration of Na+ and K+ Inside the Erythrocyte Following Failure of the Sodium Pump — A Diffusion-Controlled Process. Final values, 1 38 and 1 6, are those of the plasma.

210 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

which the cells are bathed. The inverse square root relationship occurs over and over again in diffusion-controlled processes.

In Figure 8-9 are shown the initial concentrations (milliequivalents per liter) of Na+ and K+ inside the cell (at / = 0), and their change toward the concentrations in the plasma (dotted lines) following failure of the sodium pump.

Diffusion Coefficient D, and Permeability Constant P.

Table 8-6 gives some representative values for the diffusion coefficient at 25°C in cm2 sec-1. The activation energy and the temperature coefficient of rate of diffusion in water solutions and in fat and lipid, were given in Table 8-3.

TABLE 8-6. Some Diffusion Coefficients (D) (cm2 sec ]).

Substance into Water (at 12° C) D x 105

Glycerine 0.42

MgS04 0.35

KC1 1.59

NaCl 1.09

Sugar 0.29

Urea 1.12

Just as the specific rate constant of a chemical reaction can be broken down into the factors upon which it depends, so also can the diffusion coef- ficient be factored. Diffusion is a "jump process," in which the movement of a species occurs by its being pushed from one position of rest to another as the result of favorable collisions with neighbors. The distance between successive positions of rest is called the jump distance, A. The activated complex in this case is pictured as being an intermediate position in which the jumping species is half way between rest sites and can go either way. Detailed analysis shows that

D = t\2 JiL e-*Ft/RT

h

where A is the jump distance in cm, AF* is the free energy of activation (Fig- ure 8-4) for the "jumper," 7" is the absolute temperature (degrees Kelvin), k is the Boltzmann constant, and h is Planck's constant. The units of D are therefore cm2 sec "'. Table 8-6 gives some values of D for different spe- cies diffusing into water.

As in the case of chemical reactions, the term kgT/h is a constant at any temperature. The low diffusion constants (in molasses, in lipids, or in fats) and high values (in water or alcohol) are determined by the values of X, and

ON DIFFUSION; OSMOSIS 211

by AF\ the energy of binding within the shroud of neighboring molecules through which the jumping species must penetrate if it is to move success- fully to the next position of rest.

Two innovations have been introduced into discussions of diffusion in recent years, one for theoretical reasons and the other for practical reasons. Firstly, it is more proper to consider activities (effective concentrations) than measured concentrations, and more proper still to consider as the "force," the gradient of the chemical potential which drives the diffusion process; and therefore dc/dx is replaced by dn/dx, in the more esoteric discussions, if not in practice.

Secondly, the thickness of the interface, at a cell wall for instance, is really a matter of definition rather than of position of chemicals. Who can say where the water phase stops and the heavily hydrated protein of the wall begins? Therefore dc/dx is hard to measure for living membranes, and re- course is made to a phenomenological trick: dx is taken into the diffusion constant, and the rate of flow is expressed as the difference between the flows in the two directions through the membrane. Thus

j =(P,ACl-(P2Ac2

where 1 and 2 represent diffusions in the forward and back reactions, and c, and c2 represent concentrations on the two sides; the (P's then have units cm sec-1 (velocity) and are called permeability constants. A few of these are collected in Table 8-7 for monovalent cations penetrating through living membranes. These permeability constants can be compared with values de- termined for synthetic interfaces also given in the table.

TABLE 8-7. Some Permeability Constants ( § ) for Synthetic and Biological Membranes.*

, _._ . Permeability Constant x 10

Intertace Diffusion ' _i.

(cm sec )

K+ into erythrocyte of: man 5.0

dog 1 .0

rat 10 KC1, KBr, KI into nitrobenzene 0.007, 0.075, 1 .4

Na+ into erythrocyte of: rabbit 3.0

dog 0.5

Na+ through frog skin 5.0

Na+ (as iodide) into nitrobenzene 0.2

Alcohols into erythrocyte 10,000 to 100,000

Water into erythrocyte ~ 1 0,000

♦Collected by J. T. Davies, J. Rhys. Coll. Chem., 54,185(1950). See also Ref. 17.

For ionic flow the values in the table can be transformed very easily into electrical resistance units. Thus if the concentration of the salt at the mem-

212 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

brane is 1 mole per liter, the values come out to 1000 to 50,000 ohms/cm2, in general agreement with values found by direct measurement for living membranes. The values determined depend on the permeability, discussed later.

Osmosis

Following the foregoing discussion, very little needs to be said about osmosis. It is simply the diffusion of water from the place of higher water concentration to the place of lower water concentration. More properly, it is the diffusion of water down an activity (effective concentration) gradient. The speed of the process is described by Fick's laws — the first for the steady state of constant concentrations, and the second for the unsteady state of changing concentrations.

Osmotic pressure and water balance, both properties of the equilibrium state, were discussed in Chapter 2.

As an anatomist, Fick naturally had an interest in these important proc- esses; but this interest must have been accompanied by a remarkable insight.

ON FLUID FLOW; BLOOD

Poiseuille's Law

Holding a special place among the kinetic processes of importance in biology is the transport of fluids, both gases and liquids, along tubes and in and out of storage chambers. One need mention only the circulation of blood and the respiration of air as examples.

The first striking fact is the flow itself: it takes place (almost) no matter how small the applied mechanical force; and the rate of flow increases line- arly with increasing driving force. Flow is opposed by frictional forces or "internal barriers" which the moving fluid must surmount — the smaller the internal barriers the faster the flow resulting from a given applied force.

Ideally at least, as was first stated by the French physicist, J. L. Poiseuille, in 1884, a liquid moves in a tube by the sliding of one imaginary layer of liquid over another. The surface layer moves very slowly, if at all, relative to the speed of layers far removed from the surface. The presumed velocity distribution is indicated by the lengths of the arrows in Figure 8-10.

Figure 8-10. The Gliding Layers in Nonturbulent Fluid Flow. Length of the arrow is pro- portional to speed.

ON FLUID FLOW; BLOOD 213

If P, and P2 are the pressures measured at the points 1 and 2 in the tube, and R is the distance from the center bore of the tube, the driving force is given by

ttR2(Px - P2)

The frictional force on the layer at distance R from the center is propor- tional to the area of the layer (2ttRI), and to the velocity difference between the layer we are considering and its nearest neighbors; in the limit this is dv/dR.

After the two forces have been equated, integration (or summing all veloc- ities from that at the center of the tube to zero at the wall) gives

P — P

v = 0£j £2(r2 _ R2)

4/

where r is the radius of the tube. This expression gives the linear speed of the layer which is R cm from the center. 0 is the proportionality constant, and is called the fluidity (the higher its value the higher the velocity).

The total volume of fluid flowing per second through the tube is calculated by summing all the elemental volumes, 2irRdR, for which v is expressed. The result is the celebrated Poiseuille equation which' expresses rate of flow (cc/sec) of liquid through a tube of radius r and length / under an applied pressure difference of AP = P] — P2:

irr4 dVldt = 0 AP cc/sec

8/

If A P is given in dynes per cm2, r and / in cm, and the speed of flow in cc per sec, the fluidity, 0, must be cm per sec for a force gradient of 1 dyne per cm;

i.e., 0 has the dimensions: — /— — . It is the velocity of flow of a fluid

sec/ cm

under a unit force gradient.

The case for gases is slightly more complicated because of the added fact

that the volume depends strongly upon the pressure and the temperature.

With the proper modifications the expression for rate of flow of gases

approximates:

Trr4 P.2 - P2

dV/dt = 0 !

16/ - Pn

if P0 is the pressure at which the volume is measured.

Fluidity, 0, and Viscosity, rj

Table 8-8 gives values of the fluidities of various substances at different temperatures. Of the liquids, ether is the most fluid one listed; glycerine at 0°C is the least fluid — indeed at 0°C it is almost a glass! The fluidity of

214

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

TABLE 8-8. Fluidities (0) poise1, or —

cm /dyne

sec/ cm

Temp (°Q	Hydrogen	Air	Ether	Benzene	Water	Butyric Acid	Castor Oil	Glycerine
-30	13040	6490
0	11980	5850	352	110	56	44	0.00041	0.000083
10	11760	5680	392	132	78	50	0.0013	0.0011
25	11300	5410	450	164	112	71	0.0036	0.005
37	10990	5290	500	196	144	85	0.01	0.02
50		5150	552	227	182	105
100		4440			352

gases decreases as the temperature is raised (see Chapter 2); but that of all liquids increases with increasing temperature. In liquids the higher the tem- perature the greater the number of particles which have the energy to over- come the internal barriers to flow; or in other words, the higher the tempera- ture the smaller the sticky frictional forces which must be overcome by the gliding laminae, and the faster the flow. The temperature coefficient of fluidity, factored as a specific rate constant, is given in the theory of rates as

<t>

V

In

-SFt/RT

V

h.X

eASt/Re-AHt/RT

where K is the volume of 1 mole of fluid, h is Planck's constant, N is number of molecules per mole, Avogadro's number, and AFX, AS\ and AHX refer to formation of 1 mole of activated complex in the glide plane as it slips from. one position of rest to the next .... The physical analogy between diffusion and flow thus is extended to the algebraic statement of the factors upon which they depend. The two processes can be directly compared in Tables 8-7 and 8-8. The experimental values of E* (related to AH1) are usually the same for diffusion and flow (Table 8-3). This indicates the inherent similar- ity of the two processes. Indeed in diffusion the particles move individually at ran- dom from one position of rest to the next. In flow a plane of particles moves as a unit, and no relative motion occurs between members of a plane; adjacent planes glide past each other. The intermolecular forces which oppose dif- fusion are the same as those which oppose laminar flow. That is, the bar- riers to flow are the same, and hence £*'s are the same. The catalysts in this case are called surface-active agents. Washing detergents are good examples.

The inverse of the fluidity, i.e., 1/0, is called the viscosity, usually ex- pressed by the symbol rj. Hence a high viscosity (cold molasses) means low

ON FLUID FLOW; BLOOD 215

fluidity. Viscosity can be considered as the frictional force opposing the

a x j- • dynes /cm . . , . . . . „ , ,

How. Its dimensions are — / , or dyne sec/cm , this unit is called the

cm / sec poise, after Poiseuille.

A very simple way to measure fluidity or viscosity is in the Ostwald vis- cometer. The capillary pipette is filled to a mark with fluid, and measure- ment made of the time it takes the fluid to run out of the pipette. This time is divided into the time taken by water, or some other fluid, to drain at the same temperature. The quotient is called the relative viscosity. A density cor- rection is necessary if the driving force (gravitational) is to be equal in the two cases.

Solutions or suspensions (of molecules or particles respectively) in water usually increase the viscosity (decrease the fluidity). The fractional increase is (r;, — ri0)/rj0, where the subscripts s and 0 refer to solution and pure water, respectively. But this value, often called 77', varies with the concentra- tion. It is convenient, then, to measure the 77' at several concentrations, and express each measurement in terms of unit concentration by dividing by the concentration at which the measurement was made. This number is called the specific viscosity. It is also concentration-dependent, because intermolec- ular interactions are higher at higher concentrations. It is useful, then, to extrapolate measurements of specific viscosity to infinite dilution (zero con- centration), for this value is the value of that part of the viscosity due to the suspension only, and unaffected by interactions which solute particles could have on each other. This value is called intrinsic viscosity, usually symbolized [77]. Values range from .02 for small- molecular- weight solutes to 20 for macromolecules, and to much higher values for suspensions of living cells.

Turbulent Flow

Laminar flow will exist in most fluids at low rates of flow. When the flow rate becomes high, the glide planes get off-track, and turbulence sets in. Small whirlpools and eddy currents are initiated, and the fluidity drops abruptly; therefore, if the rate of flow is to be maintained, higher driving force must be applied and more energy must be expended. Unless some result of particular value is derived from the turbulence (more rapid mixing of chemical reactants at a reaction site, for example), it is obviously waste- ful of energy. The circulatory system in man has certain features, such as flexible walls lined with hydrated protein "hairs," which help direct the fluid flow and damp out trends toward turbulence.

The Reynolds number, Re, a dimensionless parameter of fluid flow, is defined as

Re = 20 p vr

216

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

where p is the density of the flowing fluid, 0 the fluidity, v the velocity of flow, and r the tube radius. For homogeneous liquids flowing at constant velocity, it is general experience that the flow is laminar and turbulence can- not be maintained if Re < 2000. For blood, Re has been found to be 970 ± 80 over the pertinent range of flow rates and tube sizes. Therefore, laminar flow probably occurs in the blood vessels at all times, although turbulence may set in momentarily at the valves during the pumping action of the heart.

Properties of Blood Plasma and Blood

Previous discussion has implied that the fluidity (velocity per unit force gradient) is independent of speed of flow, v. Liquids for which this is true are called Newtonian liquids. Pure water is a good example.

However, most real liquids are at least slightly "non-Newtonian" — that is, 0 = f(v). One of the most complex examples of this behavior is blood — a suspension of cells in plasma, which itself is a water solution of salts and heavily hydrated macromolecules.

Figure 8-11 is taken from results which show that the ease of pushing the fluid through a tube — in this case a glass one — decreases rapidly with intro- duction of macromolecules and cells into water. Thus the 0 for plasma is

about half that for water [144 — /— — -); and increasing amounts of red

\ sec/ cm /

blood cells reduce the fluidity still further. Yet, to a first approximation,

> blood

AP

Figure 8-11. Rate of Flow of a Fluid Through a Tube as a Function of Driving Pressure. The slope is proportional to the fluidity, given in parentheses. The usual range of per- centage of total fluid volume filled with cells is shaded in.

ON FLUID FLOW; BLOOD

217

'synthetic plasmo"

o

synthetic plasmo plus red blood cells

AP (mmHgO/cm length)

Figure 8-12. Fluidity (slope) of Synthetic Plasma to Which Different Volume Percent- ages of Cells Have Been Added.

within the physiological range of operation both plasma and whole blood are essentially Newtonian; that is, their curves are linear; Poiseuille's law of laminar flow is obeyed.

However, closer inspection of not only very low rates of flow but also very high rates reveals that the fluidities in these ranges are lower than in the intermediate range in Fig. 8-11: the fluidity is dependent upon flow rate in these regions. Thus at low flow rates an elasticity due to the formation of liquid crystals by hydrogen bonds makes flow more difficult and has to be broken down; at high flow rates turbulence sets in and makes flow more difficult.

Figure 8-12 illustrates the first point. Notice how the fluidity (slope) changes with flow rate, when flow is slow. On the other hand, turbulence can actually be heard (or its effects can be heard) over the heart where very high flow rates accompany the high pressure part of the beat .... The de- pendence of viscosity (1/0) on tube radius (Figure 8-13), at first surprising, resolves to a question of the interruption of laminar flow when the diameter of the suspended particles (red blood cells) approaches the diameter of the tubes through which the suspension is flowing. This is the condition which exists in the blood capillaries — the process is more like an extrusion than a laminar flow. The velocity gradient across the tube is the cause of Bernoulli forces which not only make the cell spin, but also force it toward the center (the bore) of the tube. Further, the blood vessels are somewhat elastic and can increase their diameter under pressure. Thus the flow rate doubles for a 16 per cent increase in radius! This fact, plus the probably great differ- ence between the surface of glass tubes and the molecular-hair-lined** blood

**These "molecular hairs" arc hydrated protein molecules, partly detached from the wall, and jutting out into the tube.

218

SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

0 0.5 1.0 1.5

Tube radius (mm) ■»"

Figure 8-13. Fluidity of Whole Blood vs Glass Tube Radius.

vessels, makes the whole study very complicated, easily subject to gross mis- interpretation, and certainly needing more careful experimental definition.

Circulation of Blood

Description of the circulatory system is not our objective here. This was done in 1628 by, at the time, the radical physician, Sir William Harvey, whose description of experiments proving the continuous circulation of the blood — from the heart through the systemic arterial and venous systems, back to the heart, thence through the pulmonary arterial and venous sys- tems, and again back to the heart — is still one of the classics of clarity in medical literature.

The pressure difference between aorta and vena cava across the pump, the heart, is about 100 mm Hg, or 0.13 atm. Along the large arteries and veins and in the main arterial and venous branches, the pressure gradient is small; but because these vessels are of large radius, the flow rate is rapid. The pressure gradient is at its peak along the capillaries and the arterioles; be- cause they have very small radii, the flow there is slowest — just where it should be the slowest— so that plenty of time exists for exchange to occur by diffusion through the walls of arterioles and capillaries. Figure 8-14 illus-

° O

vena aorta cava capillaries

aorta 1 vena

R cava

, 1 »

capillaries

Figure 8-14. Relative Areas and Pressure Drops in Different Parts of the Human

Circulatory System.

ON ELECTRICAL CONDUCTANCE; EEG AND EKG 219

trates this point, showing the pressure changes and the relative total cross- sectional areas.

Two quantities can be measured, the flow rate (cc/sec), and the speed of flow (cm/sec). Measurements in the aorta show that enough blood flows past a flow-meter detector per second for one complete cycle to require 45 min. Insertion into the aorta of a bit of radioactive argon as an inert tracer, and measurement of how long it takes for the tracer to complete the ciruit, confirms this.

Speed is less easily measured. One method is by tracer. The ultrasonic method (see Chapter 3) introduces no pathological changes, but needs calibration.

ON ELECTRICAL CONDUCTANCE; EEG AND EKG

The next rate process to be considered in this chapter is the movement of ions under the influence of an electrical field — in other words, the con- ductance of solutions of salts in water. This subject is basic to an under- standing of the gross current paths through the human body upon which are based the techniques of electrocardiography (EKG) and electroencepalog- raphy (EEG), and also basic to some of the transport processes driven by membrane potentials which are of importance in nerve conduction and elec- trical shock treatment.

Towards the latter part of the last century the big-three "solution" pio- neers, Kohlrausch, Arrhenius, and Van't Hoff, showed that salts dissolve in water as ions. These are electrically charged and free to move about at random because of thermal energy, but subject to movement in a preferred direction under the force of an electrical voltage gradient. Positive ions are forced to the negative electrode, and negative ions to the positive electrode by the electrical field. The speed of movement, or mobility (centimeters per second under a voltage gradient of 1 v per cm) was understood quantitatively by 1923 (the work of Debye and Hiickel, Onsager, and later others) as being determined by the ease with which a charged ion, complete with "hangers- on" such as electrically charged ions and water molecules, can slip from hole to hole in the liquid. The process is very similar to diffusion, which was described earlier. The difference is that ions are charged and move under a voltage gradient, whereas the diffusing particle may or may not be charged and moves under a concentration gradient . If a potential difference exists for any reason be- tween two parts of an electrolyte, or is applied from the outside, ions move and current flows — in other words, charge is transferred. Hence this is just another transport process.

Ohm's Law Concerning Current

\{ n is the number of charge carriers per cc, w their average velocity under the impressed voltage, and q the electrical charge carried by each, then the

220 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

amount of electrical charge passing per second through a plane of 1 cm2 area, called the current 'density , I, is

/ = nwq

If A' is the number of molecules per mole: n/N is the concentration, c, in moles/cc; and qN is the charge per mole. The charge required to oxidize or reduce 1 mole of anything is zF, where F is the charge (96,500 coulombs per equivalent weight) required to oxidize or reduce 1 g equivalent weight, and Z is the number of equivalent weights per mole (i.e., the number of electrons transferred in the redox reaction). This is Faraday's law. Summed (2) for all different ions, s, then

I = FZcs

WsZs

Since cs is moles/cc and ws is cm/sec, the current density has the dimensions: coulombs per cm2 per sec, or amperes per cm2.

Note that the current increases linearly with the concentration of charged particles, with their speed, and with the charge they carry.

Specific Conductivity of a Solution, k

This is defined as the current which passes for an impressed voltage gradi- ent,13 , of 1 v/cm. That is, k = //I). This is a form of Ohm's law. Now although the dissociation of ions of a salt is usually complete, sometimes there is association and always there is hydration, and hence often the ef- fective "degree of dissociation," a, is less than 1. Introducing this concept gives

FjLcsWlzs ampS

k = a or ohm ' cm

TJ volt/cm

One more concept completes the picture. If the mobility, i±s, which is the speed under an impressed voltage gradient of 1 v/cm, is defined as ws/\), then

* = Fj^csnszsa

Note that this expression describes the rate of the electrical transport

process. Thus k is the rate in amperes at which charge is transferred across 1-cm2

area of electrolyte if the voltage gradient along the path is I v per cm. The value is

proportional to the concentration. The proportionality constant factors into

three constants (a, z, F) and the mobility, fi; and n is really the specific rate

constant for the process. Therefore n plays the same role for conductance as

does k for chemical reactions, D for diffusion, and 4> for fluid flow, respec-

cm / v tively. The units of /x are / . Values of the mobilities of small ions

sec/ cm

ON ELECTRICAL CONDUCTANCE; EEG AND EKG

221

average about 0.001 (see Table 8-9) for the ions of tissue fluids. The con- ductance, k, then is easily computed from the above expression, since a « 1 for salts in tissue fluids.

TABLE 8-9. Mobilities* (n) of Selected Ions in Aqueous Solutions at 27° C.

IT	362	OH-	207
Na'+	52	ci-	79
K+	77	I-	80
NH4+	76	N03"	74
\|Mg++	55	HCCV	46
		2S04 =	83
		Benzoate-	33

Blood Plasma Components: Albumins a-globulins /3-globulins Fibrinogen 7-globulins Erythrocytes

5.7 to 6.2 3.6 to 5.1 2.5 to 3.2 1.7to2.3 0.8tol.3 13

(buffered at pH 8.6)

*Dimensions:

cm / v sec/ cm

x 10s. For the small ions, the values refer to infinite dilution. From Ref. 20.

However, just as diffusion and fluid flow are concentration-dependent, so is electrical conductivity; and it is useful to express conductance per equiv- alent weight. It is called equivalent conductance, A, and is given by

pV ohm-1 cm-1

A = t / . m, <x

equiv//

This is the most useful way to tabulate conductivity information; and values of A of importance in determining body currents are given in Table 8-10.

TABLE 8-10. Equivalent Conductances (A) for Selected Salts in Water.

Salt	Con	centration, c (moles/1]
	0.001	0.01	0.1
NaCl	124	119	107
KC1	147	141	129
KNO,	142	133	120
MgCl2	124	115	97
Na2S04	124	112	90
KHCO3	115	110
Nal	124	119	109

222 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

The conductivity of a solution increases with increasing area and decreas- ing length of path. That is, it is given by

A

K —

L

This, of course, is the inverse of resistance, which equals

(\/k)(L/A) =(R(L/A)

where (R is the specific resistance, or the resistivity.

Example: Calculate the electrical conductivity of a finger. A typical body

solution contains about 100 meq of KC1 per liter. The finger is about 10 cm

long and 4 cm2 in cross-sectional area.

A 4

Conductance = k — = 129 x 0.1 x — = 5.2 ohms '

L 10

Resistance (= 1 /conductance) = 1/5.2 = 0.2 ohms

Current driven through this column of solution by 1 10 v applied across the ends would be:

i = 110/0.2 = 550 amp

Hence body fluids are relatively good electrical conductors. By contrast, skin is relatively a very good insulating material, and provides a measure of protection against electrical shocks. It is estimated that 1 ma of total body current does irreparable internal damage. However, the calloused fingers of some electricians are legendary in this respect: some will span the contacts of a 1 10 v circuit with two fingers and allow the ''tickle" to tell them whether or not the circuit is complete!

Difference in electrical mobility is the basis of electrophoretic separation of macromolecules, such as the globulins in solution. In Table 8-9 are some values which illustrate this. Characterization of the hemoglobins by this property was illustrated in Table 6-5. There it was called "/." Both / and \i are commonly used symbols for mobility.

The "Volume Conductor"

In a volume of electrolyte, the paths taken by the current depend upon the geometry (see Figure 8-15). Consider the two cases illustrated: (1) in a cylinder full of electrolyte, with glass walls and metal ends, the paths will be parallel; but (2) if the potential source is small relative to the electrolyte volume, the current paths diverge from the positive and converge back to the negative. Only two dimensions are represented in the figure, but the argu- ment would be the same for three.

Analogy with metal electrical circuits is usefully drawn, for in metals the carrier is the electron cloud. Ohm's law is obeyed by electrolytic conductors

ON ELECTRICAL CONDUCTANCE; EEG AND EKG

223

EKG

equipotential surface

Figure 8-15. "Volume Conductors." Top left: Metallic. Center and Bottom Left: Electrolytic, with parallel (1) and diverging and converging (2) current paths. (2b) shows current density and resistance per unit area along current paths as a function of radial distance, x, from the straight line joining the sites (A and B) of potential difference. Top right: Positions of electrodes for electrocardiogram and electroencephalogram.

(V = z7?), and the voltage drop (z'/?,) over any fraction of the resistor is pro- portional to the resistance, /?,, of the fraction in question. Thus (Figure 8-15) the total voltage drop across the resistor is iR, but is only z7?, for the fraction A-b. The same arguments are true for the electrolytic case (1) above. However, if the current paths diverge (case (2)), certain paths are longer than others, and the resistance, per unit area, along the path is there- fore higher. For a fixed voltage at the source, higher resistance means that smaller current will flow through the longer paths; in fact the current density (i.e., current per unit area along a path) will be high in the center, directly between the plates, lower as the radial distance, x, increases. The distribu- tions of current density and of resistance, per unit area, along a path are shown in Figure 8-15, (2b). In the higher resistance paths on the outside of the volume conductor the total potential drop, V, between A and B has to be the same as in paths directly between the electrodes. In the outside paths, R is higher and the current density, i/A, is lower. Nevertheless, as in the metallic case, the voltage between two points, A and b, in the outside path, can be measured with a good voltmeter, and that value is numerically equal to the voltage between A and b' deep within the conductor.

224 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

The electrodes of the electrocardiograph (EKG) and electroencephalo- graph (EEG) are placed on the outside of such a volume conductor, the body, and measure potential differences between points in outside paths. If the concentrations of salts remain constant throughout the body, as they should in the steady-state, then any variations in the voltage measured should reflect variations in the internal currents resulting from variations in source voltage, E.

In biological systems the source of the potential difference between differ- ent places or spots is invariably a concentration difference, whether uni- ionic or bi-ionic. Concentration differences occur for two reasons: (1) ion selectivity of membranes, and (2) continuous exchange with the medium through which the distribution systems (blood and lymph systems) pass. Membrane potentials cancel out over the whole system, because the im- portant ion selectors are cell walls, which completely enclose and isolate a volume. In the absence of disturbances then, concentration difference is the source of the bioelectric potentials.

However, two major disturbances exist, both of which "irritate" the mem- branes of the cell wall, cause them to become permeable, and thereby reduce the selectivity and permit mixing of otherwise separated salts. One is the mechanical pressure variations transmitted through the blood stream by the heart; the other is the electrical polarizing action of nerve. The former causes a concentration change by the application of a mechanical force, the latter by electrical interference with the membrane potentials of cells. Potential variations with time, between electrodes on the skull, above different lobes of the brain, give a precise record of the electrical action within the meas- ured region; and electrodes placed on the torso and leg at spots where a major artery runs close to the surface, give a reliable record of the pumping action of the heart. Since any mechanical stimulus will cause momentary irritation (and therefore potential variations), the measurements are always made under controlled conditions when the electrical "noise" generated by the involuntary muscles of the organs (and always present) is at a minimum.

ON HEAT CONDUCTION; 98.6° F: A CONSTANT?

Heat Production

The human body has a heat capacity, as does any other, measured as the heat in calories required to raise 1 g 1°C. Also, the ambient (surrounding temperature may vary widely — for example, from 95° F (35° C) down to — 20° F ( — 30° C). This lower value is 67 Centigrade degrees, or 1 19 Fahren- heit degrees, below body temperature, and yet the body is able to maintain within a small fraction of a degree the normal value of 37° C. Admittedly, insulation-aids such as skin, clothing, and hair play a large part; and the

ON HEAT CONDUCTION; 98.6° F: A CONSTANT? 225

temperature in different parts of the body may vary. Especially on the outer part of the skin and in the extremities (fingers, toes), the temperature is lower than 37° C — i.e., at points farthest from the glycogen storehouse, the liver, and where the area to volume quotient is high.

As we saw in Chapter 7, heat is produced by oxidation of glycogens and by hydrolysis of fats and proteins. Under the reversible conditions of a perfect energy-converting machine, no heat energy would be given off as heat because AF is used for work and TAS is needed to establish the state conditions of the products of reaction. However, the body "machine" is not perfect, and in it conversions take place at efficiencies somewhat less than the maximum thermodynamic efficiency. Thus,

AH = AF' + q' + Q

where AF' is the work extracted, Q. is the reversible, unavailable heat used to bring the products to the reaction temperature, and q' is that part of AF which could have been used to do work but which appears as heat be- cause the "engine" could not extract the work reversibly. The degradation reactions of fats and proteins are especially inefficient from this point of view, and are thus good producers of "wasted" heat energy, q', which in fact is not wasted but serves to maintain body heat-content or temperature during cold weather. (Eskimos, for example, by design eat unprocessed animal fat for its heat-producing effects.)

Heat Loss; Fourier's Law

Heat energy is lost from the body by several mechanisms, all of which are simple physical transport processes or change-of-state processes. The basic method is by conduction, for which the rate of loss, i\, is given by

K 4 dT

vx = KTA — ax

where A is the area exposed, T is temperature, and x is thickhess of the in- sulation. If T is in degrees Fahrenheit, A in square feet, and thickness in inches, the rate of heat loss is given in BTU per hour; and the proportional- ity constant, KT, is given in BTU per hr per sq ft of area per ° F per in. of thickness. Common values of KT for good insulating materials are: cork, 0.28; wood, 0.35; wool, 0.30; plaster, 0.48; fat, 0.33; skin, 0.30. Since

BTU Cal

hr ft2 °F/in. hr m2 °C/cm

the conversion, if useful, is easy. Approximately 4 BTU = 1 Cal (or kcal). Usually engineers use the units on the left side of the conversion equality, and physiologists thpse on the right side.

226 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

The important effective-thickness term which determines dT/d.v, depends upon the nature of the contact, whether skin-air, skin-water, skin-metal, etc., and also depends critically on the heat capacity and heat conductivity of the materials of the contact. Thus the rate of heat loss into cold water is greater than into cold air at the same temperature because of the higher heat capac- ity of the water; while the rate of heat loss to steel at the same temperature is greater because of the rate at which steel can conduct heat away.

Clothing increases the effective thickness and hence decreases the- tem- perature gradient: so do hair, thickness of skin, and subcutaneous fat. One of the best insulators in the body is the dermis-epidermis combination, whose effective thickness changes with the ambient temperature by virtue of involuntary, lateral muscle movements which govern the depth of blood capillaries carrying the heat energy to be thrown away: in the cold these capillaries retract, thus increasing the effective thickness of the insulation.

Aides to Conduction

Conduction is aided — often exceeded — by convection, radiation and vaporization. A very brief account of these allied processes is now given, and then a comparison drawn among the relative methods of heat loss for man in different aspects.

For convection the rate is given by:

v2 = K2 dT/dx /(») Cal/hr

where f(v) is related to "wind chill" and increases with the velocity, v, of the air flowing over the surface. Convection losses are those of air circula- tion, and act primarily by removing the layers of semiwarmed air from above the surface of the skin, thus reducing the effective thickness of insulation.

The form of/ is beyond the scope of this book, for it involves complex principles of eddy currents in the subject of aerodynamics. We shall con- tent ourselves with the general observation that the stronger the breeze pass- ing over the body, the greater the rate of cooling. In extreme cases this could be several hundred Cal/hr.

For radiation the rate, v3, is given by

v

3

aA'(Tb4- T4) (the Stefan-Boltzmann law)

where Th is skin temperature, Ta is ambient temperature, A' is the body's effective radiating surface area (70 to 85 per cent of real area (~20 ft2), de- pending upon posture and position, and correspondingly less if the area is clothed), and a is the Stefan-Boltzmann constant. For the so-called black- body, which the human body approximates in the sense that it absorbs and emits all wave lengths in the infrared (that is, those important at 37°C), the value of a is about 0.045 Cal ft"2 deg~4 hr"1. Thus if the surroundings are

ON HEAT CONDUCTION; 98.6° F: A CONSTANT?

227

at 27° C {Ta = 300°K) and if the body is uncovered, up to 100 Cal/hr could be lost to the surroundings as infrared electromagnetic radiation alone. For vaporization, the rate, vA, is given by

v< = KAAJ(v/d)SP

where Aw is the wetted area of exposed skin; v is the velocity of the air; d is the effective thickness of the heated layer of air on the surface of the skin;/(z>/rf) describes the convection which carries the moisture away; and AP is the driving "force/" i.e., the difference in vapor pressure, P, of the liquid on the surface at skin temperature and that of water at the ambient temperature - the latter reduced by the relative humidity, RH. The important factor is the last one. Thus the liquid on the surface strives to set up an equilibrium pres- sure of vapor with the atmosphere which surrounds it, but never quite suc- ceeds, since the atmosphere is nearly always undersaturated (RH < 100 per cent). For example, if the skin temperature is 34°C (91°F) and the RH = 60 percent for an ambient of 20° C (68° F), quite common conditions,

IP = P(34°) - 0.6P(20°) = 0.04 atm

At very high temperatures {T a > 80°F) this method is the body's escape valve for excess heat. Each gram of water lost by vaporization removes 0.58 Cal from the skin. In the lungs, inhaled air becomes saturated and then is

TABLE 8-11. Estimated Per Cent of Heat Loss, by Each of Four Principal Methods.

	Body's Heat Loss (Cal/hr)	Per Cent of Skin Covered	Per Cent Heat Loss by
Activity	Conduction and Convection	Radiation	Water Loss from Skin	Respi- ration*
Studying, fully clothed, 70° F	150	85	68	20	10	2
Studying, lightly clothed, 70° F	200	15	20	58	20	2
Resting for BMR test, 70° F	70	15	20	70	8	2
Running mile race, 60°F	1500	25	20	20	50	10
Sunbathing on beach, 90° F	350	15	10	8	80	2
Walking, heavily clothed, 0°F	350	95	50	8	2	40

*Assume 50 percent relative humidity. See Refs. 2 to 4, and 21

228

CD

O- x CD

	~o
	cd
	>
	o
	e
	CD
	u
	c
0)	CD
<Si	a;
CD	-Q
u	<u
0	>
i_	n
U_	_c
u
%_	i.
cd	O
c
^	O


c	0)
o	n
t:	n
o
Q. F	D

CD >	X cd
U_	>-
O)	o
c
o E	c a) £
<
to	a>
a>	o
4-	X
i_	cd
D	i_
._	a)
t-	-C

to	o
—
o	<1)
£
*_	n
o
■ I
	(j>
	>
	o
CN

	cd
00
LU	■•-
CD	o
< t—	c o

u t£j 'u

0)

Q.

l/l

■D

c o cd

c

0)

a

c o

o

_0

CD

>

CJ

C£: CD 'u o

8."

CO

a> o O °

D

K

oc

Ik.

ST

-<3

CJ

CU

t3

cj

CU

o

a.

cj cu

en

O U

~«3

CJ

cu

3 O

cj

c n	£
	03

o	en
cu	>.
<*	e
	<L>	C
C J	J3	o

E cu	£	en
u		2

5

03

5

03

3 CU

en

'5

C £

O 03

D. —

en W)

c "c

03 C

^ c

C — -

o

bD

<u

03

	tc		>-
en C o	CD o u		*-> 13	con- itv
CJ	c		o	, >
CJ	o	>>	E	03 "42
03 u	00 ,3		E 3
	03.	3	c
IT.	"3	o	_c

kK

■^ 03

CJ

03

CJ

5 ?

\j3 03

cj — '

3 en

-a

c o

U

03 CU

X

.Id

3 O

03

u

en

bf i_

cj c C

X

00

c o

o

03 *_

c

cj o C —

o ^

CJ 's_

CJ

11 ^

^ E

T3 • ~ CU

?■§

^^ 00

en ,«

3 CU

C

o

E

-o c

03 V

bn (_

03 x;

CJ

C

o

c

cu

CJ

C O o

.- ^, T3

CU >

C

o

cj

z

<

EI x

" E

o

c o

cj

K3

C "O

CU W

cj C O

CJ

cj

3

-a

o

o E

03

Oh

"2

C50

c

'5

O

<E

bo

C _o "03

C cj

03

a. c

0

3

■a

c

o

cj

o

-C CL,

o c 00 .2

I

H3

bD •

^ E 03 ii

,h "3 bD «J

c -Q

<U 3

w

229

CU

X

.2 °u

CO

>

-4— •

CO

X

£

C O O-

3

C 03

T3 CJ en

Q_

X

CJ

'0 _o

cu >

cu x

x

cj X

C

C 3 CJ

C O

cx

D

c

cj

-a c

cj

a.

CU

■a

c co

c o o

<u

C co

3 .

CO

o ^

■g^ 5 £ I ^

e u a. -o o

3 -^ C u

33 en fc .5

o £

o E

(U

x

-° -5 — " .£

D- 'to

"S c

C .2 CO

"O "5

cj U -n 'C

O cj

D. C

E 12

CO

cu cO ^ TJ C U

z

cu

c

u

o cu

X

~ X 3 <«0 CO X - cj en >^

cu cu

O * ~ .2 «J •

3 C C ^S

« « s o

I £ 5

CO "O

t: co

E X

3 3

£ o

CJ

cu

3 c

X « 3 .3 co -3

m 2 <* -E ^ —

cu

4— »

CO

E

co —

s-g

en -Id

a o

c _o

CO

3

O"

cu

'G

o

"cu > cu

1- CO cj CJ

3 °

_Q CU —

•r -c c

CJ

en en

cu

2 o

en i-i . -*-1

w —

CU U5 TJ

CJ cu cu

O en cu

a. b c

cu O

> u "O —

cu cu ^ cu

cu t- ~

CO CU

CJ CJ

c/) C

O

•a c

cO

6l0

s

> X

cj CO

C u

C t«

a. u

O CO

N

t: ex: «j —

•=. c 3

Cj en

h

>, a_c

cu

—

CJ

e« «J

.« ° "i CJ

w w s *^

Z C ^ ">

-* O •- tT

-. o- - x; tt:

>- ej •

S cj 3

rr» CO O

e0 .2 > CJ y

cj > i~ C

CU CJ 3

CJ

en

C en CJ

CJ

3 X

cj o

O

(-

a.

cu

>

us

CU

z

er.

S o

3 "C

"S X ^

CJ

jr.

CJ

CO

E 5

a

X

CJ

-c c

CO

3

o -a

CJ

o £

a cj

u

o

CJ

as

0-

£ 2

3 ^

3 «J

c C T3

c •- c

£ C 3

^— ■ O Ti

C/3 C^

° o !o £

Q. .X

CJ

3 u O <- bfl^

>■ cj

c o

— t/1 c/i

c

CO

cj —

CJ

CO l_

(0

CO I

'-3

J3

:^K s « o

^d to

o

JS c

cj

CJ

X>

CJ

> CO j3

O

an

^ 3

X -O CO

;r ■ — *-

- 3 en

< - " - -C -O "O , 5 O OC 3 3

? 'Z: ^ In CO CO 3

C ■«- ■ — U

Z q_ CJ en

O e > *J

en

u

x

cj

X cj

X

en

cj

cu

a. o

u

230 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

exhaled, with the same loss of heat per gram of water. Respiration then be- comes important, especially when the air is dry and/or cold. Urine and feces contribute a small fraction to daily heat loss.

Heat Loss from the Body Under Various Conditions

Table 8-1 1 illustrates that the escape valve for excess heat may be any one of the several methods of heat loss and will vary for different activities. The very important role of the skin as a heat insulator and as a water supplier to the surface, and the role of cover and clothing now become clear.

To sum up: the maintenance of constant body temperature is a very re- markable example of the "steady state." In Chapter 7 we illustrated heat- producing reactions — chemical, physical, mechanical, etc. In this chapter we have discussed the rates of heat-producing reactions and the rate of heat loss. In the steady state there is continuous flow — and the rate of "waste" heat production is exactly balanced by the rate of heat loss, no matter what the ambient conditions. So it is with literally hundreds of processes in the living thing.

FORMAL SIMILARITY AND INTEGRATION OF THE FIVE PROCESSES

The method of presentation used in this chapter permits us to summarize in a table the factors upon which the rates of the five processes depend, and to note their similarities and differences. Since each of the processes was dis- cussed individually, no comment on Table 8-r12 and its extension, Table 8-13, will be made now. other than to ask the reader to note that the classi- cal driving force and the role of the activated complex are both stated ex- plicity. The reader should consider these tables to be a memory aide, which, if understood, will give him a powerful grasp of the nature of each of these important processes occurring within the living system.

In the living thing, these processes are not separate and distinct, isolated from one another. On the contrary, at every spot in the body probably three or more are simultaneously operative. For instance at some point each moment, a chemical reaction, requiring the transport in of reactants and the transport out of products, produces heat which must be removed if the steady state is to be maintained. As is the trend now in engineering kinetics'9, the future of biophysical kinetics lies in the study of the integration and con- trol of rates of all the relevant processes proceeding in so orderly a manner within the framework of the steady state. Motivation for the ultimate mas- tery of biophysical kinetics is clear enough: deviations from the steady state are diseases, the most vicious of which today has the popular generic name "cancer." Some aspects of the all-important subject of control are discussed in Chapters 10 and 1 1, following (next) an important chapter on the biologi- cal effects of the ever-increasing ionizing radiation of our environment.

WEIGHTLESSNESS

231

TABLE 8- 1 3. Components or Factors of the Specific Rate Constants for Chemical Reactions, Diffusion, Viscous Flow, and Electrical Conductivity.

kj

h

I) = t\2

kj

0 = T

V

■SI-t/RT

-AFt/RT

E h

r = transmission coefficient (tau) k = Boltzmann's constant h = Planck's constant

free energy of activation "jump distance" (the distance be- tween points of rest of the moving species) volume of one mole of fluid ,V;i = no. of molecules per mole (6 x 1023 E = applied voltage

A/-'* A

I

Note Heat conduction has not yet been studied from this point of view. If volume, voltage and jump distance terms are factored out of the above expressions, they all become the same: the pre-exponential term with dimensions sec-1 ; and hence the specific rate would be dependent only upon the activation free energy for the process.

WEIGHTLESSNESS

In this era, on the threshold of space travel, it would be neglectful not to introduce into a chapter on speeds of processes occurring in the living sys- tem, the effects of gravitational force. Man must withstand a gravitational range from high-g conditions on through to the condition of weightlessness, or zero-g. So little has been published to date about those who have orbited the earth for any appreciable time that little can be written here. However, the general principle can be stated that the change in gravitational force on the human body from earth-bound to weightlessness is small relative to other forces. As a general rule, if the parts are fixed in position, they func- tion normally. Solids and contained liquids, then, show no discernible changes in speeds of chemical or physical — and therefore, presumably, bio- logical— processes.

With the gravitational restriction removed, blood circulation requires less expenditure of energy. Conversely the same expenditure of energy by the constant-pumping heart is able to accelerate the blood flow through the tissues, and provide exhilaration, just as would a slightly higher O, content in the respired air. The first astronaut, Juri Gagarin, reported that he "observed the earth and sang" dur.ing a li-hr orbital flight. John Glenn had similar experiences during a busy 4^-hr flight. Telemetered physiological data demonstrated normal biological functioning while he was weightless. However, after the 25-hr orbital trip of Gherman Titov, he reported that he felt depressed and nauseated during the flight. His successors, Nikolayev and Papov, flew weightless for several days without mishap or reported discomfort.

232 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS

Perhaps the psychological effects of isolation, uncertainty, and frustration will prove to be far more important than the effects of weightlessness on the biophysics of the space traveler. The effects of ionizing radiation in free space, unfiltered by the atmosphere, are discussed in the next chapter.

PROBLEMS

8- 1 : The rate of denaturation of a protein or of inactivation of an enzyme by heat is dependent upon the concentration of the enzyme in a rather peculiar way, which can be represented as v cc [E]n, where [E] is enzyme concentration and n is the order of the reaction, interpreted as the number of molecules of enzyme which come together to form a cluster in the inactivation process.

The temperature dependence is normal in that v cc e~E*l , where E* is the energy of activation, R is the gas constant (2 cal per degree per mole), and T is the temperature in degrees Kelvin. For one case at low concentration, n was found to be independent of temperature, and E* equal to 150,000 cal/mole.

(a) Calculate the ratio of velocity at 104°F to that at 98.6°F.

(b) Calculate the ratio for a 10°C rise in temperature.

(c) Calculate the ratio for a 10°C rise in temperature for a hydrolysis reac- tion for which E* is 20,000 cal/mole.

(d) Calculate the ratio for a 10°C rise in temperature for a transport process for which E* is 4000 cal/mole.

8-2: The basal metabolic rate of the "normal" man is about 0.1 hp. Express this in Cal/hr; in watts; in cal/sec.

8-3: Using Poiseuille's Equation, calculate the pressure which would have to be ap- plied to a No. 17 hypodermic needle (2 cm long, 0.05 cm radius), if a water solu- tion of viscosity 0.01 poises (dyne/cm. sec2) is to be forced, at a rate of 1 cc/sec, into an artery which is already 100 mm Hg average pressure above atmospheric.

8-4: Under low rates of flow, blood has a viscosity (~0.02 poise) about twice that of water; but under high rates, such as in the capillaries, it flows more easily (~0. 012 poise). Calculate the flow rate through two parallel tubes 1 mm long, of radii 0.001 and 0.005 cm, if the pressure drop is 100 cm Hg.

8-5: One milliampere of total body current may be fatal. Estimate the path length and average cross-section from hand to hand; and given the fact that the specific conductivity (i.e., of a volume of soln. 1 cm2 in area and 1 cm long) of a solu- tion of 100 milliequivalents of KC1 per liter (approx concentration of body fluids) is 0.015 ohm"1 cm"1 at 98°F, calculate the applied potential sufficient to force 1 ma of current from hand to hand.

REFERENCES

1. Newburg, L. H., "Physiology of Heat Regulation (and the Science of Clothing),"

W. B. Saunders Co., Philadelphia, Pa., 1.949.

2. Kuno, Y., "Human Perspiration," Charles C. Thomas Publ., Springfield, 111.,

1956.

REFERENCES 233

3. Burton, A. C. and Edholm, O. G., "Man in a Cold Environment," Edw. Arnold

Publ. Ltd., London, 1955.

4. Ruch, T. C. and Fulton, J. F., "Medical Physiology and Biophysics," 18th ed.,

W. B. Saunders Co., Philadelphia, Pa., I960. (See the chapter by A. C. Burton on Hematolysis.)

5. Greisheimer, E. M., "Physiology and Anatomy," J. B. Lippincott Co., Phila-

delphia, Pa., 1955.

6. Glasstone, S., Laidler, K. F., and Eyring, H., "The Theory of Rate Processes,"

McGraw-Hill Book Co., New York, N. Y., 1941.

7. Gaebler, O. FL, "Enzymes: Units of Biological Structure and Function," Aca-

demic Press, Inc., New York, N. Y., 1 956.

8. Tyrrell, H.J. V., "Diffusion and Heat Flow in Liquids," Butterworths, London,

1961.

9. Baldwin, E., "Dynamic Aspects of Biochemistry," Cambridge Univ. Press,

Cambridge, England, 1953.

10. West, E. S., "Textbook of Biophysical Chemistry," The Macmillan Co., New

York, N. Y., 1956.

1 1 . Szent-Gybrgyi, A., "Introduction to a Submolecular Biology," Academic Press,

Inc., New York, N. Y., 1960.

12. Clarke, H. T., Ed., "Ion Transport Across Membranes," Academic Press, Inc.,

New York, N. Y., 1954.

13. Wintrobe, M. M., "Clinical Hematology," 4th ed., Lea and Febiger, Philadel-

phia, Pa., 1956.

14. Nikolaev, L. A., "Problems in Modelling of Biocatalysts," Vestnik Akademn nauk

SSSR, 13 (1960) ;LLU Translations Bulletin, London, 1960.

15. Laidler, K. J., "The Chemistry of Enzyme Action," McGraw-Hill Book Co.,

New York, N. Y., 1958.

16. Dixon, M. and Webb, E. C, "Enzymes," Academic Press, New York, N. Y.,

1958.

17. Davson, H. and Danielli, J. F., "The Permeability of Natural Membranes,"

Cambridge Univ. Press, Cambridge, England. 1952.

18. Hober, R., etal, "Physical Chemistry of Cells and Tissues," The Blakiston Co.,

Philadelphia, Pa., 1945.

19. Bird, R. B., Stewart, W. E., and Lightfoot, E. N., "Transport Phenomena,"

John Wiley & Sons, Inc., New York, N. Y., 1960.

20. Conway, B. E., "Electrochemical Data," Elsevier Publ. Co., Amsterdam, Hol-

land, 1952; Parsons, R., "Handbook of Electrochemical Constants." Butter- worths Scientific Pubis., London, 1959.

21. Kleiber, \1., "The Fire of Life," John Wiley & Sons, Inc., New York, X. V..

1961.

CHAPTER 9

Biological Effects of Ionizing Radiations

The damage to living tissues caused by ionizing radiations was not al- ways as well recognized as it is today, and many of the early investigators suffered painfully as a result. On a memorial unveiled in Hamburg, Germany, in 1936, in honor of the first 1 10 investigators and physicians who died directly as a result of X-irradiatwn, following W. K. Roentgen 's discovery in 7895, we read the dedication :

"To the Roentgenologists and Radiologists of all Nations who have given their lives in the struggle against the diseases of mankind. "

INTRODUCTION

This chapter could have been the longest in the book. Indeed, it could have been expanded to be the whole book, for such is the importance of bio- logical effects of ionizing radiations, both for diagnosis and for therapy. However, we restrict ourselves here to the principles which are necessary to an understanding of the effects. Although some examples are given to illustrate the effects on humans, we carefully skirt the very complex and largely em- pirical subject of radiology, as compelling and as intrinsically interesting as the subject matter may be.

Within a few years after 1895, many effects of X rays on adult humans had been observed, and others imagined and foreseen. The early workers, and their patients, suffered from skin burns, some radiation sickness, warts, deformed fingers, loss of hair; and finally the onset of various forms of cancer (Figure 9-1).

234

INTRODUCTION 235

' * N

^

Figure 9-1. Abnormal Bone Growths in the Hand — Similar to those Suffered by the Early Radiologists. (Courtesy of A. F. Crook, Ottawa General Hospital.)

Recognition of these effects led to controls which by this time have com- pletely removed, in medical use, the gross dangers described above, although there are still subtle possibilities, as we shall see, which may yet require that even further restrictions be instituted. Some dangers are not so subtle: this is the era of the megaton bomb.

Nonmedical applications of ionizing radiation are increasing rapidly, and render it important that safety measures and medical checks be more and more indicative of absorbed dose. For instance, the development of atomic power stations, irradiation-sterilization of food (potatoes, for example, to keep them from sprouting during long shipment) and of surgical and medi- cal supplies, the production of new chemical polymers by irradiation, the detection of faults and flaws in metal castings and welds by X-ray fluoros- copy: all involve skilled and unskilled human labor. Furthermore, the in- creasing radioactivity "background" of the environment — even to the in- creasing tritium (two neutrons + one proton; a beta-emitter) content of our water supplies (blood is about 90 per cent water!) — makes it obvious, al- though perhaps distasteful, that man is being more and more heavily ir- radiated every day (Figure 9-2). Therefore the effects, especially the subtle ones, which may show up only after a few generations, must be understood

236

BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

and appreciated, especially by medical people. The three most important facts are: (1) Living tissue is killed. (2) Mutations, which may lead to cancer or to progeny which cannot live in the environment, can occur. (3) The central nervous system can become hypersensitized; and this could lead to a whole host of nervous and "somatopsychic" disorders. Radiolo- gists understand much about (1); something, but really far too little, about (2); and at this date have only an inkling about (3).

Figure 9-2. Man's Environment of Radiations. Normal background of ionizing radia- tions varies widely in the range 0.7 to 0.4 roentgens/yr, depending upon his location, natural shielding in his home, etc. Anything above 0.3 r/week is currently considered "dangerous."

DOSIMETRY

Dose Units

From the point of view of effect, the most important quantity is the rather empirical one — the rem (roentgen equivalent man). One rem is defined as that amount of damage to tissue caused by radiation of any type which pro- duces the same biological effect as does 100 ergs absorbed per gram of tissue from incident X or gamma radiation. Since one rad (radiation absorbed dose) is defined as that amount of X or gamma radiation which, when ab- sorbed, adds 100 ergs per gram (i.e., 6.24 x 1013 ev/g) to the energy of the tissue, one rem of damage is produced by 1 rad of absorbed X or gamma radiation.

DOSIMETRY

237

Two other units are of importance. The roentgen (r), the earliest unit of dose, refers to absorption by dry air, and specifically is that amount of X or gamma radiation which, when absorbed, increases the energy of dry air at STP (0°C, 1 atm pressure) by 83 ergs/g. The rep (roentgen equivalent physical) was originally defined as the tissue-equivalent of the roentgen, but with conversion difficulties being as they are, it is best defined here as that amount of X or gamma radiation which, when absorbed, increases the energy of soft tissue by 83 to 93 ergs/g.

In Chapter 5 the density of ions produced along the paths of alpha, beta, gamma or X, and neutrons was described (refer to Figure 5-1). It is logical that the biological effectiveness of a unit of absorbed radiation should in- crease with increasing density of ionization. Density of ionization is ex- pressed quantitatively as the linear energy transfer (LET). Therefore, the relative biological effectiveness of one unit (i.e., 1 rad) of absorbed radiation (of different kinds) should be proportional to the LET. For instance, slow alphas (42He++) do twenty times the damage of X rays of equivalent dose absorbed. Table 9-1 lists some average LET values for various energies of

TABLE 9-1. Linear Energy Transfer (LET) in Thousands (Kev) or Millions (Mev) of Electron- Volts Absorbed per Micron (10~4 cm) of Track for Some Atomic "Bullets." Accepted Values of Relative Biological Effectiveness (rbe).*

Type	Energy	Initial LET (Kev/micron)	rbe**
Co60 gammas	1.1 Mev	0.2	1
X rays	250 Kev	1.0	1
	10 Kev	2.0	1
	8 Kev	2.8	J
	250 kvp, usual	3.5 average	1.0 (defined)
	distribution
S35 betas	46 Kev max	0.7	1 to 2
Electrons	1 to 2 Mev	0.2	1 to 2
Protons	0.9 Mev	30	8 to 10
	8.4 Mev	5.5
Fast neutrons	0.1 to 10 Mev		10
Slow neutrons	less than 100 ev		2 to 5
Alphas	5.3 Mev	90	1
	12 Mev	50	> 20 to 10
	38 Mev	20	J
Fission recoil	65 Mev	~7000	(200?)

*From Report of the International Commission on Radiological Units and Measurements (ICRU), Handbook 78, National Bureau of Standards, Washington, D.C., 1 959, p. 50; and Ref. 19, p 1 74.

** rems //rems\ ■/ \ dose/-,

dose>

250 kvp X rays

238

BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

different radiations. One should bear in mind that the LET is not constant while the radiation energy is being absorbed by tissue because with every bit of energy lost there remains less to lose.

For several types of irradiation, approximate values of relative biological effectiveness (rbe) — i.e., damage per unit dose, relative to 250 kvp X rays — can be written down, and can be used if the reservation be kept in mind that they are rules-of-thumb, only approximate. Column 4 in Table 9-1 lists such values. In general, the higher the energy of the impinging radiation, the less energy it loses per unit length in tissue, and hence the longer it will take a source to deliver a unit of absorbed radiation. In summary, the bio- logical damage is given as:

rads x rbe = rems ^ reps x rbe

Several ways of receiving 1 rem of damage are depicted in Figure 9-3. For workers, such as radiologists, who must necessarily be exposed, it is recom- mended (by international agreement) that the whole-body dose be kept to less than 0.3 rem per week in the blood-forming organs, the gonads, and the eyes; less than 0.6 rem per week for surface irradiation. Relaxation to 1.5 rem per week is permitted if the radiation is of low penetrating power or if only limited parts of the body are irradiated. Table 9-2 gives the number of rems received under different conditions.

100 ergs of I Mev beta I rad)

5 ergs of I Mev alpha (0.05 rad)

10 ergs of I Mev neutron (0.1 rad)

I rem of damage

100 ergs of X or gamma (I rad)

10 ergs of 0.1 Mev protons (0.1 rad)

Figure 9-3. Some Ways of Receiving 1 rem of Damage.

Dose Measurement

In air the dose received is measured accurately by the ionization chamber and scintillation counters described in Chapter 5. However, in aqueous solutions or in tissue, the situation is quite different. Here the primary tar- get is water, and it breaks up not into ions but into free radicals (H + OH); these react and produce new chemicals.

DOSIMETRY

239

TABLE 9-2. Sources of Irradiation of Human Beings.

Source

Approx Dose or Dose Rate

Natural external background, including cosmic rays

Increase in background due to nuclear testing 1945-1962 peak soon after test

Average increase

Internal exposure to Ra226 and K40 from foods

K40 alone

One chest X ray: best average fluoroscopic examination

Local dose during irradiation of tumors

Median lethal dose, whole body

Maximum permissable* dose rate, whole body

0.073 rem/year (widely variable)

0 to many thousand times natural background, depending upon loca- tion

0.1% of natural

0.15 to 0.5 rem/yr 0.03 rem/yr

0.006 rem 0.2 rem ~ 1 0 rem

3000 to 7000 rem ~400 rem

15 rem/yr (0.3/wk)

*Recommended by the International Commission on Radiological Protection. 1 958.

The celebrated Fricke dosimeter is based on this principle. It is an aque- ous solution of 0.1 .\/-H2S04 containing 10 ~3 A/-FeS04 and a tracce of chlo- ride. Upon irradiation, ferrous ( + 2) is oxidized to ferric ( + 3) iron, and the amount of ferric produced is easily estimated, as FeCl, from the extent of absorption of light of wave length 3040 A. Thus 1 rad of hard X or gamma radiation has the chemical effect of converting 1.5 x 10~8 moles of Fe+2 to Fe+3 per liter of solution. The system is widely used, because it is simple, reproducible, accurate, and independent of dose rate (e.g., rads/hr). Its use- ful range is from about 500 to several thousands of rads. This dosimeter system — standard methodology, advantages and disadvantages — has been described in detail elsewhere.18

Since biological damage can occur at much lower doses than this, recent developments have been toward more sensitive aqueous dosimeters. In sealed vials, chlorinated hydrocarbons liberate chlorine and change color in crude field dosimeters — sensitive, but results are not too reproducible. Two other recent developments will now be described very briefly.

In the first, advantage is taken of the fact that certain molecules, such as hydroxybenzoic acid, in water will fluoresce. That is, if ultraviolet light

240 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

impinges on them, they absorb it, turn some of the energy into heat energy, and re-emit the rest as light in the visible region. A sensitive photocell de- tects this re-emitted light, and the photoelectric current is amplified and recorded. The reduced form of the fluorescent material, benzoic acid, does not fluoresce. Irradiation causes oxidation. The intensity of the fluorescence is a function of dose. Of the order of 1 rad can be accurately measured.

In the second, advantage is taken of the fact that the electrochemical po- tential of an electrode, measured against some suitable reference electrode, is dependent upon the ratio of the concentrations of oxidized to reduced form present in the solution. For instance, Ag/Ag+ in H2S04 is one redox system which has been shown to be practical. Irradiation produces Ag+ and the voltage of the cell (Ag in H2S04 solution vs a mercury-mercurous sulfate reference electrode) decreases as the concentration of Ag+ is increased by the radiation. Measurement of voltage vs time or irradiation thus gives a continuous measurement of absorbed dose. When done carefully, a fraction of a rad can be measured. This is the only continuous-recording and re- useable dose-measuring instrument known.

However, biological damage is not subject to such reliable, quantitative measurement. Measurement of biological damage, by its very nature, has so far had to be a quantity such as the LD50 (lethal dose50). The LD50 is that dose in rads which will kill 50 per cent of the cells or organisms irradiated (see Fig. 9-4). Further, since irradiation damage is often not immediate, but may set in only after days or even years, in the case of mammals an arbitrary limit of 50 per cent killed within 30 days after exposure has been accepted by workers in this field as a further specification of the LD50.

3 alive 3 dead

Figure 9-4. LD50: 50 per cent Lethality, Measured at Some Constant but Arbitrarily Chosen Time After Exposure (30 days for man).

As a general rule, the LD50 (30 days) for mammals is 200 to 1000 rads; for man (whole-body irradiation), it is about 400 rads (equivalent to 400 rems if the radiation is X or gamma) (of course there are no good statistical data to support this number!). For lower animals it is higher: frog, 700; bacteria, 10,000; insects, 60,000; paramecia 300,000 rads.

The LD50 is a useful measure also of the effectiveness of partial-body ir- radiation. In some cases one simply makes a suspension and estimates the number of cells left living in the tissue irradiated.

PRIMARY EFFECTS (ON CHEMICAL COMPOSITION) 241

As more is learned about effects of ionizing radiation on metabolic proc- esses, physiological measurements of effects on rates of specific processes within cells and tissues will probably add much-needed refinements to the useful LD50 number.

Incidentally, one should realize that only a small amount of energy need be absorbed to cause damage. It is the form in which this energy enters the tis- sue that is critical. Thus the LD50 for man, 400 rads, is only 400 x 100 ergs/g. This is 0.001 cal/g, roughly enough energy, if in the form of heat, to raise the body temperature only 0.001 deg! Because the energy is concen- trated in packets, so that when it is absorbed it tears apart the molecules of important biological structures, localized damage occurs at sensitive sites, enabling a small quantity of energy to promote death. Table 9-3 gives some useful irradiation data and conversion factors.

TABLE 9-3. Some Useful Numbers.

1 rad = 100 ergs/ gram = 6.24 x 1013 electron volts/gram.

1 roentgen of hard X or 7 delivers 0.98 rad to water.

1 curie of radioactive substance delivers 3.7 x 10'° disintegrations/second.

1 curie of Co60 gives a dose rate of 1 .35 roentgen/hour at 1 meter from the source.

1 curie of radium gives a dose rate of 0.83 roentgen/hour at 1 meter.

1 curie of cesium137 gives a dose rate of 0.33 roentgen/hour at 1 meter.

PRIMARY EFFECTS (on Chemical Composition)

Direct and Indirect Action

Two schools of thought have arisen on the question of how the primary effects occur. However, there are so many variables involved that it is un- likely that either will ever be proved to be unequivocally wrong.

The fact is that the solution after irradiation contains molecules (chemi- cals) which were not there before irradiation. One school maintains that this is because the solute dissolved in the water acted as a target, was blown apart by the incoming "bullets," and the fragments rearranged into a new molecule. The other school remembers that the whole target (tissue, for example) can be at least 80 per cent water, that eight out of ten potential targets are water molecules, and maintains that the primary act is the ex- citation of water, followed by its decomposition into the active chemicals hydrogen atom and hydroxyl radical. Enough energy is left over so that these are thrown violently apart. Hydrogen is a reducing agent, which can donate an electron to become H+ in solution; OH is an oxidizing agent which can accept an electron to become OH in solution. From this view, then, these molecular fragments, H and OH, cause the formation of new

242 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

molecules by their attack on dissolved solute. Figure 9-5 illustrates these two mechanisms.

unshared electron

protein protein

Indirect action Direct action

Figure 9-5. Indirect versus Target Action of Ionizing Radiations.

Effects on Some Biological Molecules

In his recent book, Swallow" has collected the known effects of X irradia- tion of hundreds of compounds of biological interest. For instance, the im- portant generalization exists that reactive peroxides are formed from all the biologically active amino acids in solution. In addition, the molecular prod- ucts of irradiated water solutions are H2, H202 and 02, each of which, and especially H202, can exert its chemistry on the solutes present.

The results are easy to state in general, difficult to state in detail, in all but the simplest cases. In general, new molecules can be produced from the old ones (plus water), and these new ones may exert catalytic, toxic, or no effect on the metabolic processes in the vicinity in which they are produced or to which they are carried by blood and lymph. In particular, the ab- sorbed radiation is known to reduce the catalytic activity of many enzymes, and to alter their molecular weights and other physical properties. Large molecules (Figure 9-6) can be broken into many parts, or can be cross-linked through new hydrogen bonds or through the oxidation of two — SH groups by H202, for example, to form an — S — S — bond, with distortion of the molecule.

One of the most intensely studied molecules from this point of view is the nucleic acid, desoxyribonucleic acid (DNA). It is thought (the reasons were given in Chapter 6) to be the main carrier of hereditary information in the living system, and hence one that should not be tampered with in human

PRIMARY EFFECTS (ON CHEMICAL COMPOSITION)

243

beings without prior knowledge of the genetic result. Butler et al (1 959) have partially clarified a rather confused picture, made not the least bit simple by the fact that the molecule is huge: as obtained from leucocytes it has a molecular weight of about five million. Two standard methods of determin- ing molecular weight (also outlined in Chapter 6) were used. One, by meas- urement of the viscosity of DNA solutions and measurement of the speed with which the molecules settle out in a high-speed centrifuge, showed that the molecular weight falls during irradiation, as though the big molecule were being split into pieces. The other, however, by light-scattering tech- niques, gave a constant molecular weight during irradiation. The implica- tion is that the molecule is broken all right, but the pieces do not completely uncoil. With such a loosened structure, easier degradation by heat should result, and that is just what has been found, not only for DNA but also for several enzymes as well.

loss of NH3 and loss of H2 rupture of hydrogen bonds

rupture of sugar-base linkage and oxidation of the sugar iberation of purine bases breakdown of pyrimidine* bases rupture of nucleotide chain liberation of organic phosphate

Nucleic acid

Figure 9-6. Things That Can Happen if a Macromolecule Such as DNA is Irradiated by

Ionizing Radiation. * Order of radioresistance: adenine > guanine » cytosine > uracil > thymine (on iso- lated components).

Enzymes are known to have various sensitivities to radiations, at least in dilute solutions. The data on these are somewhat suspect because of the marked effect of impurities. However, one of the most sensitive enzymes seems to be carboxypeptidase; ribonuclease is ten times more resistant, and catalase ten times more resistant yet. Some enzymes are inactivated even when in the dry, crystalline state (this supports the target theorists). All enzymes studied are inactivated in aqueous solutions by ionizing radia- tions— this can mean direct target action or attack by radiation-produced free radicals, probably both.

Of the small molecules present in tissues, the most interesting from the medical point of view are cysteine and certain other molecules containing the sulfhydryl ( — SH) group. These molecules are particularly sensitive to oxi- dation by radiation, and therefore are among the most effective protectors

244 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

known. By one view they scavenge free radicals H, OH, H02, etc., pro- duced in the radiolysis. By another view they attach themselves to enzymes or nucleic acids at just the spots most sensitive to radical attack ( — SH groups) and thereby reduce the effects of irradiation on the big molecules. For example, even impure acetylcholinesterase, in a solution with much other protein, is only half as sensitive to irradiation damage in the presence of 10"3 M-cysteine as in its absence. In living cells the enzymes are well protected, and seem to be resistant to much larger doses of radiation than the same molecule in vitro.

The "Oxygen Effect"

The radiation sensitivity of most molecules is greater the higher the oxy- gen content of the solution. Thus, the rate of oxidation of Fe+2 to Fe+3 by X rays is twice as high in the presence, than in the absence, of oxygen. For small molecules like phenol and the amino acids the rate is often even more enhanced by 02. This increased radiation sensitivity in the presence of oxy- gen is observed right on up the hierarchy of structures — viruses, bacteria, cells, tissues, to whole animals.

A striking practical demonstration of this effect has been shown with carcinoma tissue. Due to necrosis, many parts of a tumor can become anoxic. By increasing the pressure of the respired air this anoxia can be re- duced, with a consequent increase in the radiosensitivity of the carcinoma cells.

Now, oxygen itself is known to accelerate many metabolic reactions, and the effect of oxygen in increasing radiation damage is thought by some to result from this fact. However, in other quarters the effect is thought to occur through the radical, H02 . This radical is produced from the reaction

H + 02 — H02

after the radiolysis reaction has produced the hydrogen atoms as follows:

H20 -^ H20* — H + OH

The radical HO, is a strong oxidizing agent, since it readily accepts an elec- tron from any source to become the peroxide ion, H02~. Hence, one can consider that the H atom simply puts 02 into a form in which it can react faster. Since 02 is used up in the reaction, it must be supplied continuously if advantage is to be continuously taken of enhanced rate of destruction. Conversely, of course, oxygen scavenger molecules increase the protection of macromolecules against ionizing radiations.

The mode of action of oxygen is one of the most intriguing practical prob- lems of radiology. Once it is understood, it can be controlled and utilized

BIOPHYSICAL EFFECTS 245

more fully. Other species, such as NO and Co++ also enhance radiation effects.

BIOPHYSICAL EFFECTS

These can be considered as effects on molecular structure and type, with the resulting effects on the physical properties of agglutination and trans- port, and on the speeds of vital chemical processes.

Agglutination or Coagulation

Colloids — small particles, large molecules — are stabilized by electric charges on their surface. At any particular pH, the acidic and basic chemi- cal groups on the surface are in equilibrium with the electrolyte, and the sur- face carries a net positive or negative charge. Repulsion between like charges stabilizes the colloid. Further stabilization comes from water mole- cules adsorbed on the polar groups of the surface, so that, from the outside, the big colloid particle looks, to a particle in solution, just like a wall of ordinary water molecules.

Irradiation causes, first of all, chemical polymerization or cross-linking to occur between particles. It causes changes in the polar groups, and hence in the "water front" which the colloid presents to the solution. Finally it causes rearrangement in acidic and basic groups such that the net surface charge changes. The colloid then precipitates, or agglutinates, and becomes semisolid.

On the other hand, the colloid may be split within by radiant energy, and the structure then rearranged to a form which is unstable, and it precipitates.

Modification of Transport Properties

Thermal Conductivity. This property is difficult to measure even under the most advantageous of circumstances, and nothing is known yet about how it is affected by radiation. Structural changes induced by radiation may turn out to be of importance to the structural lipoproteins and collagen of the skin, for example.

Diffusion. As it was shown in Chapter 8, the diffusion coefficient depends critically upon the molecular structure of the medium, with particular refer- ence to the "jump distance" between rest sites in the medium and to the size and shape of the diffusing species. Naturally, if the diffusing molecule is broken up into small and free parts by the action of ionizing radiation, it will diffuse faster. Conversely, if it or the medium becomes cross-polymer- ized, diffusion will occur more slowly.

It is expected that, as more is learned about the diffusion of water, ions, and molecules through living membranes, the effects of irradiation on dif- fusion will become more evident. In the absence of definitive work on this

246 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

subject, one can only say that the possibilities exist, and should be remem- bered during discussions of the physiological effects, which are currently receiving more attention.

Fluidity (Inverse of Viscosity). Most of the useful information on the ef- fects of ionized radiations on fluidity (ease of flow in response to a physical force) has been done either on plastics or on aqueous solutions of big molecules.

From the former it has been learned that cross-linking of polythene by ir- radiation increases markedly its melting point and increases its elasticity. By contrast, irradiation of teflon (a fluorinated and inert organic) leads to hardening and embrittlement, and loss of elasticity. This might lead one to anticipate similar effects in elastomeric tissue in the walls of blood vessels, were it not for the fact that the effects are exhibited only after the absorption of a few million rads!

On the other hand, the fluidity of aqueous solutions of biologically active molecules has been intensively studied, especially as a technique of measur- ing the change in molecular weight effected by radiations. Like diffusion, many examples are known in which cross-polymerization is important, and many in which molecular rupture is to be inferred.

Electrical Conductivity. In body fluids the conductivity is high. Irradiation makes no detectable change.

It is in the inner, fatty-acid or lipid part of the living membrane (Figure 6-7) that we expect a change in conductivity. The lipid, an oil, has very low conductivity. Analogy with polythene or lucite may be useful as a guide. These materials break down internally under irradiation, such that electrons are knocked off one part of the molecule and caught or trapped elsewhere, leaving a positive site behind. The conductivity increases, because the charges are somewhat mobile, and a steady-state concentration, higher the higher the dose rate, is set up and maintained. Upon cessation of the radia- tion, the charges recombine slowly, and the conductivity drops to its original value. Although the k for these substances is very, very small (~10~21 ohm-1 cm '), it is raised as much as fifty thousand times by an X-ray dose of only 8 roentgens (r) per min. By comparison, the conductivity of a resting nerve membrane is of the order of 10~12 ohm "' cm ', due almost entirely to the lipid inner layer.

The "activation" of nerves by radiations, and some effects on the central nervous system, to be discussed in the next section, indicate that enhanced electrical conductivity may be one of the most important biophysical effects of ionizing radiations.

Chemical Reactivity

The effects of ionizing radiations on the rate of chemical reactions could be inferred from knowledge of the factors upon which rate depends. In gen-

PHYSIOLOGICAL EFFECTS 247

eral terms there are two methods by which the rate can be increased: through increase in local temperature (thermal energy of vibrations, etc.) in the vicinity of the ionized track, and through excited electronic states of re- actant molecules (photochemical processes). The mechanisms have been discussed in Chapters 4 to 8. The synthesis of new isomers and of entirely new molecules was considered also in Chapter 6, as well as the nature of toxins, catalysts, and useful and destructive mutants.

PHYSIOLOGICAL EFFECTS

Outlined in this section are the effects of ionizing radiation on cells, organs and tissues.

Sensitivity of Cells

The sensitivity, a (sigma), is the rate at which cells die because of irre- versible damage suffered during irradiation. Since the unit of absorbed dose, D, is the rad, the fraction of cells lost per rad is the sensitivity. Thus

dNIdD a =

N

cells killed per unit dose per unit number of cells irradiated. If the dose rate, dD/dt rads/sec, is a constant, p, then the sensitivity can be expressed

dN/dt

a =

p-N

cells killed per sec per unit number of cells irradiated. Based on what is now known about factors affecting the radiosensitivity of cells, the early (1905) "law" of Bergonie and Tribondeau can be extended and rewritten:

l[dN/dt]geW,a,dD/dt\

where / denotes a functional relationship between a and the quantities in parentheses; [dN/dt]g, the rate at which the cells reproduce themselves (i.e., the growth rate, or number produced per unit time); 'W , the metabolic rate — energy used up per unit time; a, a number less than 1 which varies with the state of cell division — unity at the prophase of mitosis, much less at any other time; m, the degree of maturity — unity for old, well-developed, spe- cialized cells, less for those newly formed; and dD/dt, the dose rate. In sum- mary, the sensitivity increases with increasing rate of cell division, metabolic rate, and dose rate; increases sharply at prophase; and decreases as the cell becomes more mature. The exact functional relationships are not known.

248

BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

The rule is generally obeyed, but there are exceptions. For instance, leucocytes (white blood cells) are quite mature, don't divide in vitro, divide only slowly in the body, and they have a low basal metabolic rate; but in spite of these facts, they are among the most radiation-sensitive cells known.

The relation between the number of surviving cells and the dose, Z), ab- sorbed, has had far better quantitative demonstration (Figure 9-7), es- pecially for cells. If N is the number at any time, and N0 is the number be- fore irradiation started, then

N

N0e

-aD

or log JV/jV0 = -0.434 a D

This is simply the integrated form of the natural law (see Chapter 1) which says that the rate at which cells die from irradiation is proportional to the number of living or nondamaged cells which are being irradiated. This expression describes the case in which o is constant during the whole irradiation.

Dose (rods)

Figure 9-7. Radiation-Sensitivity, a-. The Slope of the Straight Line in the Logarithmic Plot (b) for Haploid Cells. Low slope means low a. Broken curve is for multiploid cells: sensi- tivity increases as irradiation proceeds.

The radiation sensitivity constant, a, is small for radio-resistant cells (e.g., nerve cells in adults), and large for radiosensitive cells (e.g., lymphocytes). It increases with increasing oxygen concentration ("the oxygen effect"), or increasing nitric oxide concentration. This is true also for whole animals. If the dose rate is raised, the value of a increases, for the same reason it in- creases as the relative biological effectiveness of the impinging radiation is increased. It decreases with increasing concentration of certain protector chemicals, P, as we would infer from the discussion on protection of mole- cules earlier in this Chapter. Therefore we can incorporate all these effects

PHYSIOLOGICAL EFFECTS

249

into a modern version of the Law of Bergonie and Tribondeau, and write, as a memory aid:

\dN/dt]e,<W > oc, dD/dt, [02], [NO], rbe'

/

m, [P]

Survival studies have been pursued vigorously in the past few years. The exponential decay law N = N0e~aD is followed rigorously by irradiated haploid (simple-chromosome) yeast cells — linear portions on Figure 9-7. In this case a has a value (Table 9-4) of 17.2 x 10-5 rads-1 at a dose rate of 425 rads/min, with the oxygen concentration equilibrated with air. The value of a drops rapidly as the water of the medium (and hence in the cell) is partially replaced by such materials as glycerol. Furthermore, the sen- sitivity does not change down to -10°C, but drops to 4.9 x 10~5 when the solution freezes. By way of contrast, bacterial cells are about 100 times less sensitive than human cells to irradiation (Table 9-4), but eventually show the membrane rupture and internal reorganizations of all others (Figure 9-8).

TABLE 9-4. Some Measured Fractions Killed per and the Corresponding LD50's.

Rad (i.e., the Radiation Sensitivity, a)

System	105<r (per rod)	LD50 (rads)
Human beings, whole body irradiation	about 170	about 400
Diploid human cells, generally	170 to 220	320 to 400
Aneuploid cells, from human cancer of cervix	220	320
Slowly multiplying cancer cells, estimated	170 to 200	340 to 400
Rapidly multiplying cancer cells, estimated	200 to 250	300 to 340
Haploid yeast cells
normal suspension	17.2	4,000
frozen	4.9	14,000
in 1 molar glycerol	9.8	7,000
in 7 molar glycerol	4.9	14,000
E. coli bacteria
parent	2.6 to 4.5	15,300 to 26,500
18th irradiated generation (less sensitive)	1.2	58,000
Spores	0.2 and down	350,000 and up

Note: a ■ LD,n = 0.693; a = -2.303

'50

dD

In contrast to this simple, first-order law, it has been found that if chromo- somal material is present in quantities which are multiples of some basic unit (diploids, tetraploids, etc.), the rate of destruction of cells by irradia- tion is proportional to some power (of the number of cells, N) different from

250

BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

Figure 9-8. Electron Micrographs of Normal and Gamma-irradiated E. coli Bacteria. Left: Parent, shadowed at an angle of 30° with evaporated chromium metal. Note the long flagellae still intact (10,000 x). Center-. A heavily irradiated (2 million rads), radia- tion-resistant strain, remarkably elongated, and with terminal budding (7,000 x). Right: A stained, ultrathin section of a freeze-dried sample of the heavily irradiated strain, showing side budding (25,000 x). (Courtesy of I. E. Erdman and B. Kronmueller, Na- tional Health and Welfare Laboratories, Ottawa.)

unity; the plot of log (survivors) vs dose is curved, not straight, a varies, and the survival expression becomes more complicated.* Thus, the results of ir- radiation of multiploid yeast cells indicate very complicated kinetics — in- teresting enough, and of considerable significance because of what they will some day tell us about human multiploid cells under irradiation; but never- theless not truly clear now, and therefore beyond our scope to discuss here. The general rule-of-thumb is that for multiploids the sensitivity, a, becomes higher the longer the cells are irradiated. The numbers given in Table 9-4 for E. coli, for example, refer to linear portions of the log (survivors) vs dose curve, and therefore are only approximate. Higher up the animal heirarchy the deviations from this simply law are greater, and it is best then to rely on the LD50, not the a.

Arranged in decreasing order of sensitivity (<x) the following cells provide a broad spectrum of the general damage caused by whole-cell irradiation:

Lymphocytes > granulocytes > basal cells** > alveolar cells of lung > bile duct cells > cells of tubules of kidneys > endothelial cells > connective tissue cells > muscle cells > bone cells > nerve cells.

"One form, based on a multiple-hit theory, introduces a correction term:

yvyA

-oD

0

(1 - c/D)

where c is a constant.

**Producers of specialized cells of bone marrow, gonads, intestines, sometimes called stem cells.

PHYSIOLOGICAL EFFECTS 251

Microirradiation of Cells

So far, the discussion has been on whole-cell irradiation. However, by microirradiation techniques, in which just a small volume within a single cell receives radiation, it has been found that not all parts of the cell are equally sensitive. In fact, a is much higher if the nucleus (in particular the cnromo- somes within the nucleus), rather than any other part of the cytoplasm or cell membrane, is irradiated.

Microirradiation is not easy experimentally, but it has now been done with proton and alpha particles, and with X and far ultraviolet electro- magnetic rays. Production of the micro beam is done by a colinear series of apertures in a number of absorbents (e.g., lead bricks). Sometimes it is done by passing the radiation through a glass or platinum capillary mounted in a lead shield. Thus any X rays falling on the wall of a Pt capillary at an angle of 0.6 deg or less to the axis of the capillary are completely reflected, and are propagated unchanged to the exit and thence to the target. The position of the target cells can be set by means of apparatus which is not essentially different from the traveling stage of a microscope: by means of a micro- manipulator with worm gears the target can be moved into any desired posi- tion within a limited space.

Results with protons, alphas, X, and ultraviolet have all shown that the nucleus, and specifically the nucleolus which begins to become more prom- inent as mitosis begins, is far more radiation-sensitive than the rest of the cell. For example, in a specific case, irradiation through an area 2.5/i in diameter on a chromosome (~5ju x 30yu) with 36,000 rads of proton energy (60 protons, ~1.5 Mev) caused the chromosome to become sticky (to cross- link?) and the cell to die in the attempt to divide, while irradiation else- where in the cell with up to 1.7 million rads caused no change in speed or reliability of division, nor did it have any effect on the several observed suc- ceeding generations.

However, indirect effects on the chromosomes by irradiation elsewhere in the cell have been demonstrated. Nor should one infer that irradiation else- where does no permanent damage to the cell or its progeny. For such spec- tacular things as blistering of the cell wall, and coagulation of cytoplasm and of the mitochondria, as well as death to all the progeny of cells irradiated generally elsewhere than the chromosomes, have been observed. Considera- tion of the cell as "a bag of enzymes," each subject to irradiation isomeriza- tion, gives one an idea of how complex this question can be.

Unfortunately the important microirradiation studies have not, yet yielded any case in which irradiation of a certain part of the cell has caused an in- creased rate of reproduction of modified or cancerous cells. Hence, just how absorbed radiation induces cancer at the cell level remains unanswered. It is now generally assumed to be irradiation of the DNA of the chromosomes,

252 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

but it could just as well be modification of one of the catalysts of the syn- thesis of DNA, or the membrane which contains them.

There is some direct information on DNA in solution, however. By vis- cosity and titration methods it has been found that the molecule is shattered by X and a rays, to an amount of about 1.5 x 1011 chain-breaks per gram of DNA per rad absorbed. The analogy with the effect of ultrasound on viruses is usefully drawn at this point, for ultrasound quite literally shakes the molecule to pieces.

There is also some semidirect information on DNA in vivo. Thus, T. T. Puck4 and others have allowed irradiated human cells to culture, and have measured, not the LD50, but the "reproductive death" — the irradiation dose which is just sufficient to cause the cells not to reproduce. These cells are not killed by the radiation, but often show abnormalities, such as growing to a huge size or showing a change in metabolic rates. Reproductive "death" is relatively very sensitive, its L"D"50 being 25 to 40 rads in human cells. The corresponding sensitivity, a, is about 2000 (compare with the values in Table 9-4).

Irradiation of Organs and Tissues

The histologic and pathologic changes in tissues resulting from irradiation are properly part of the subject matter of radiology, and will not be dis- cussed here. However, as illustration, some of the results of whole- and partial-body irradiation are listed below, with no explanation, as simple statements.

Just as some parts of the cell are more radiation-sensitive than others, also some tissues and organs are more sensitive than others. The analogy goes further. Some parts of the human body can be irradiated relatively heavily without severe general damage; others are very radiation-sensitive. The fol- lowing list includes the most sensitive.

(1) Red blood cell manufacture slows down in the bone marrow.

(2) Manufacture of lymphocytes in the spleen is drastically reduced and cannot replace fast enough those killed by irradiation of the general lym- phatic circulation system.

(3) The skin shows reddening or blistering, after only 140 rem; larger doses can precipitate skin cancer.

(4) Impairment of secretion or of assimilation occurs in the alimentary canal, mostly as a result of membrane destruction. Sloughing off of the mucous lining of the canal is an early symptom of damage and often results in death due to infection.

(5) The critically important steady-states in the adrenal glands are upset. Because these are the source of certain rate-controlling molecules, the hor-

PHYSIOLOGICAL EFFECTS 253

mones, greater body susceptibility to heat, cold, injury, and infection results from the damage.

(6) Decreased activity of the thyroid can result, causing lower basal metabolic rate.

(7) In the lungs, the membranes across which 02 and C02 exchange be- tween blood capillaries and air takes place are broken, and persistent oxy- gen deficiency and excess carbon dioxide in the blood result.

(8) Enough radiation can ruin the very selective membranes in the kidney.

(9) Similar damage in the liver results in hemorraging.

(10) Cataracts develop in the lens of the eye from coagulation of liquid crystals. The effects may be delayed, however.

(11) Large local doses (~400 rem) to the gonads can cause sterility by killing off the sensitive spermatogenic cells. The sperm themselves are rela- tively resistant. Much lower doses could cause mutations in the DNA-gene- chromosome structure of the germ cells, while large doses could simply break the chromosomes into pieces. Gonadal doses from various sources are collected in Table 9-5.

(12) Even low doses to some tissues can produce enough variation in the cell reproduction system so that the tissue becomes carcinogenic. (This is probably the most important, and still the least understood, physiological effect of irradiation. Unfortunately, the susceptibility may not become manifested for several generations of cells.)

(13) The rate of production of antibodies is lowered markedly, and the tissue is more subject to infection and disease. This effect is related to the rapid destruction of the lymphatic tissues.

TABLE 9-5. Gonadal Doses from Various Sources*

Source Dose or Dose Rate

Background radiation 0.095-0.180 rem/yr

Maximum dose permitted to X ray workers 1 5 rem/yr (0.3 rem/wk)

Pelvic examinations, fluoroscopic ^1 rem

Salpingogram ~1.7 rem

Photographic X ray of kidney and ureters 0.9 rem

Photographic X ray of pelvis 0.7 rem

Photographic X ray of hip 0.5 rem

♦Collected by C Don."

The following general principles are important to remember:

(1) The physiological effects are direct results of changes in the rates of chemical or transport processes.

254 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

(2) The long-term damage may prove to be greatest in the chromosomes, at mitosis, but such genetic effects may not appear for several gen- erations.

(3) Damage to the fine network of molecular membranes and canals in the cell's substructure, where the enzyme-controlled protein and nu- cleic acid syntheses take place, can result in immediate physiological changes. Damage to cell walls and structural tissue is important at high dose or after some time at low dose.

EFFECTS OF WHOLE-BODY IRRADIATION

The Facts and the Complexity of the Problem

Three events, each horrible in its own way, provide the foundation of our knowledge about whole-body irradiation of normal humans. The first was the bombs at Hiroshima and Nagasaki; the second was an accident at Oak Ridge, and others, less publicized, later; and the third, unpredicted winds over Bikini and the Marshall Islands during H-bomb trials.

Three months after the publication by Roentgen of his experiments with X rays, puzzling radiation burns on the skin were observed. Within a few years, premature loss of hair and early ageing befell the early workers. From ten to forty years after intense exposure, some gruesome cancers appeared, and case histories showed they could be attributed to the exposures long before.

Careful analyses, now sixteen years in progress, of the results of the atom bombs over Japan, have yielded much modern clinical experience with radiation-induced epilation, premature ageing, and cancer. The effects re- sulted principally from gamma rays and neutrons given off by fission prod- ucts. In the Marshalls it was principally betas from heavy hydrogen (tri- tium). At Oak Ridge two scientists died slowly from a 600-rad accidental exposure during a demonstration of thermonuclear fusion, and half a dozen more received severe, but sublethal, doses. All these cases were very care- fully documented.

Studies on animals have mushroomed in the past decade. The guinea- pig, pig, mouse, dog, goat, monkey, rat, hamster, and rabbit: all have con- tributed their bit to the phenomenology. Various interesting things have been learned. For example, if any tissue is selectively protected by shield- ing, usually a substantial increase in the animal's LD50 occurs. In mice, pro- tection of a hind leg, or the intestine, or the head, or the liver, but particu- larly the spleen, causes significant increase in the LD50. In the larger ani- mals, the results of protection (shielding) of the long bones, the site of red blood cell synthesis, have been spectacular. As a corollary, irradiation of specific tissues and organs in the larger animals has shown (1) the great

EFFECTS OF WHOLE-BODY IRRADIATION 255

sensitivity of erythrocyte synthesis (perhaps aided by reflection and strong absorptions of X rays within the long bones; and (2) the rather subtle, and perhaps more serious, sensitivity of the central nervous system itself. In the first case, changes in blood count have been measured. In the second, the appearance of new and changed peaks in the electroencephalogram have been observed. The meanings of these peaks in terms of effects on memory, judgement, irritability, etc., are only vaguely understood so far.

Accumulation of all this information — effects on both human beings and animals — has provided rough rules-of-thumb which are very useful. One can be sure, however, that they are by no means final. For instance, it is known from studies of persons connected with radiation therapy in hospi- tals that doses of less than 1 rem/wk produce definite symptoms of irradia- tion damage over several years. Yet a complete diagnostic X-ray examina- tion of thorax and intestines, even when done under the responsibility of a very competent radiologist, delivers about 1 rem to the tissues being studied. Since long-term genetic effects are indicated by what information is avail- able, and since the genetic results really are not yet known for humans, maximum permissable dose and dose rate have been arbitrarily chosen for radiologists, patients, and workers with ionizing radiations in industry and government. For X and gamma radiation, the current value is 0.3 rem/wk (or 0.3 rem individually to the blood-forming organs, to the gonads, to the lens of the eye, to other organs and tissues), and it may soon be revised downward. If the rate is 0.02 rem/hr the work is considered very hazardous. However, these tolerances, as well as the minimum shielding requirements, are now very carefully controlled by the governments of most countries, and the symptoms and necessary precautions are continuously being revised and published as new information bearing on these questions accumulates. However, background irradiation from rocks, cosmic rays, tritium in the water, etc., amounts to 0.15 to 0.4 r/yr, and because of long-term genetic effects which may result from even small doses to humans, physicians, es- pecially, should be aware of the potential harm of needless and incompetent clinical exposure to diagnostic X rays, and aware of the possible effects which may result from an ever-increasing background. In these terms the probable effects of all-out or even limited nuclear war are distasteful to dis- cuss. One could mention especially those effects from radioactive gases which could enter the lungs; and those from dust-carried "fallout" contain- ing such isotopes as Sr90 which can enter the bones and teeth, and, having a low turnover rate there and being a hard beta-emitter (0.54 and 2.26 Mevs) with a long half-life (25 yrs), could irradiate the human body continuously from within — and nothing could be done about it, except to try to chelate it out by some chemical process .... However, one can provide for himself some protection (see Fig. 9-9).

256

BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

X

r>

ft

lead bricks" / four inches thick

(a)

y-rays

(_sourceS

concrete or sand bags, two feet thick

(b)

Figure 9-9. Protection against ionizing radiations is offered by relatively thin layers of heavy-atom absorbers (a), or by relatively thick layers of lighter-atom absorbers (b). Absorption follows approximately the Beer-Lambert Law (Chap- ter 4): intensity decays exponentially with thickness. Note protective chemicals in pill form!

The clinical symptoms of radiation sickness caused by the LD50 are fairly well known: diarrhoea, nausea and vomiting, followed by inflammation of the throat; loss of hair; loss of appetite; fever and pallor; rapid emaciation, and death — completed within 3 to 4 weeks of exposure. For less exposure, recovery begins after a period of time which is longer the greater the ex- posure. Repeated exposures with small doses precipitate the onset of leuke- mia or carcinogenesis, often years after the first exposure. Certain chemi- cals, mentioned earlier in the chapter, offer some protection against the chemical and physical effects which multiply into the biological effects. Further, experiments on the removal of Sr90 and other radioactive isotopes from the body after ingestion by complexing them away with the so-called chelating (complexing) agents, are showing limited promise.

Radiation Therapy

Because they are undergoing more rapid cell division and have certain instabilities which normal cells do not have, cancer cells are, as a general rule, more radiation-sensitive than normal cells. Further, by a continuous rotation of either target or radiation beam, it is a rather simple matter in principle for a radiologist to deliver a high accumulated or total dose to the cancerous volume and at the same time deliver only part of that dose to the noncancerous tissue which surrounds it. Radiation therapy is based on these two principles.

In many cases 2000 to 7000 rem of local irradiation will kill or sterilize a tumor so that it cannot grow. Machine-produced X rays, gamma rays such as those from the Co60 "bomb" (Figure 9-10), or radium needles inserted directly into the center of the tumor can be used to give local irradiation.

EFFECTS OF WHOLE-BODY IRRADIATION

257

Figure 9-10. The "Theratron Junior," Typical of Co60 "Bombs" Used in Cancer Clinics in Many Countries. Source is contained in the lead head (above), and radiation is collimated by a tubular hole. Lead absorber and counterweight is below. Both source and patient can be moved so that the patient can be irradiated from several directions. Typical charge is 1000 curies of Co60, which gives about 15 roentgens per minute at a spot 1 meter from the source (15 rmm). (Photograph courtesy of Atomic Energy of Canada Ltd.)

On the other hand, some atoms such as I131 will fit nicely into the biochem- istry of the body, localize in the thyroid, and irradiate it with betas and gammas (refer to Table 5-7).

However, there is a basic difference between the two methods of applica- tion of irradiation. Machine-made X rays, or the gamma rays from a cobalt-60 bomb provide either a constant dose rate or one which can be varied at will by the radiologist. By contrast, radioactive isotopic therapy depends upon the biochemistry of the system to transport the injected iso- tope to the locale to be irradiated, and then to excrete it. If the application of the isotope is direct (see Figure 5-9), or if the induction time is short, the isotope has a biologically effective half-life, /cff, which is the half-time of ir- radiation. In any case, the dose rate, dD/dt rads per sec, is proportional to

258 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

the average energy*** of the emission and to the strength of the source, c microcuries. Thus

dD/dt = 5.92 x lO-4^

where the constant arises from the definitions of the curie (3.7 x 1010 disin- tegrations per sec) and the rad (100 ergs absorbed per gram), and the fact that 1 Mev = 1.6 x 10~6 ergs. In the case in which /eff is shorter than the physical half-life of the isotope, the dose received integrates to

DB{t) = 74 V0;eff(l - r»«W) for any time t; or

D&{*) = 74 E0cotefr

for the total dose administered (by an initial concentration, c0 microcuries, of a beta emitter with an average energy Eg Mevs and a biological half-life oHeff days) up to the time the isotope has been practically completely ex- creted. Table 9-6 gives pertinent data for different isotopes and organs. In some cases ^eff is limited by rapid chemical turnover, in others by the decay half-life. Note that only a fraction of an isotope accumulates at a particular locale in the system. Therapy depends upon preferential uptake by an organ. The rest of the system gets irradiated too, but less.

P32 has been used successfully for the irradiation of excess white (leuke- mia) and red (polycythaemia) blood cells. Other isotopes are being used in ever-increasing numbers and amounts as new techniques (e.g., the insertion of radioactive colloidal material (Au198, for example) into the tumor: it "floats," but it cannot get into the blood stream and be washed away), and as new methods of preparation and purification become known.

The technique of bone-marrow therapy is now in an advanced state, al- though its application is limited. The principle is the complete replacement of irradiation-damaged marrow with that from a donor. Transplants are normally limited to inbred strains or to isologous animals. However, if the natural immunity reactions of human beings are completely destroyed by large radiation doses first, then complete blood transplant can be successful. Even so, further complications often arise later, in terms of a secondary disease. Rare cases of transplant from one identical twin to another have been more successful.

An advanced technique, which may keep radiologists in business even

***Genera!ly the average energy for gammas is about the same as the listed values, for gam- mas are monoenergetic; but for betas the average energy, Eg, is approximately 1/3 the maxi- mum (nominal) energy usually listed. For X rays the average energy is always well below the peak value listed — about 0.3 of the nominal kvp if the soft end has not been filtered out (by, say, 0.5 mm Al), and about 0.6 of the nominal kvp if it has.

EFFECTS OF WHOLE-BODY IRRADIATION

259

TABLE 9-6.		Data on Turnover of Some Isotopes in Humans.
			Half-life
			(days, unless otherwise
Isotope	Organ Where Chiefly Con-	Organ Weight	stated)	Per Cent of In-
	Effective	gested Activity
	centrated	(kg)	Physical	in Tissue	Reaching
			Decay	Ceff)	Organ*
H3	total body	70	12.3 yrs	19	100
c,14 \|	fat bone	10 7		• 5600 yrs]	35 180	50 5
Na24	total body	70	0.60	0.60	95
p32	bone	7	14.2	14	20
s35	skin	2	87	18	8
K42	muscle	30	0.5	0.5	70
Ca45	bone	7	164	151	25
Fe59	blood	5.4	46	27	80
Co60 -		liver spleen	1.7 0.15	I 5.2 yrs j	8.4 9	0.4 0.005
Rb86	muscle	30	18	7.8	42
Sr89	bone	7	53	52	25
I131	thyroid	0.02	8.0	7.5	20

*Rough and incomplete, but the best available information based on Recommendations of the Interna- tional Commission on Radiological Protection, 1955.

though pressed hard by the radiomimetic (radiation-mocking) chemicals, involves the use of sensitizers. As we already have seen, certain chemicals protect molecules and cells against radiation damage; certain other chemi- cals can sensitize, or increase the damage which a dose of radiation will impart to molecules and cells. For example, excess O? and certain organic mole- cules such as synkavite have been used in selected tumor treatments.

The competition from radiomimetic chemicals is not just casual! The chemical action of the sulfur- and nitrogen-mustard gases is surprisingly like that of X rays on tissue: membrane destruction, some molecules broken, others polymerized, and the cell unable to reproduce. These agents can even cause genetic changes. The technique used is to stop the natural blood flow- in the region to be treated, pump the dissolved mustard gas through the tissue for some minutes, and then to flush it out with a fresh blood trans- fusion before opening the stops again to full natural circulation.

260 BIOLOGICAL EFFECTS OF IONIZING RADIATIONS

This is the period of enthusiasm for the use of mustards in this new role (they originally saw service as war gases). As their limitations for therapy become better known, and if history repeats, both the new chemical therapy and ionizing radiation therapy will oscillate through periods of enthusiasm and reappraisal before ultimately finding their proper place in the medical arsenal.

The reader may now wish to pursue the subject matter of this chapter in more detail. The author suggests perusal of References 28 and 23, then of References 10, 1, and 2.

PROBLEMS

9- 1 : (a) From tabulated values of the sensitivity constant, a, estimate the dose which would be expected to kill 20, 50 and 80 per cent of a tumor.

(b) Suppose this tumor were just under the skin. Discuss three different ways — ultrasonic, machine-made X-rays, and cobalt-60 gamma rays — in which you could apply the irradiation.

(c) How would you monitor the air dose? The tissue dose?

9-2: How do you rationalize the facts that X rays induce cancer, and that X rays are used in the treatment of cancer?

REFERENCES

1. Alexander, P., "Atomic Radiation and Life," Penguin Books, Inc., Baltimore,

1959: a "popular" introduction to the text, Ref. 2.

2. Bacq, Z. M. and Alexander, P., "Fundamentals of Radiobiology," Butter-

worths, London, 1955; 2nd ed., 1961.

3. Hollaender, A., Ed., "Radiation Biology," McGraw-Hill Book Co., Inc., New

York, N. Y., 1954.

4. Oncley, J. L., et al., "Biophysical Science — A Study Program," John Wiley &

Sons, Inc., New York, N. Y., 1959; especially the contributions by R. E. Zirkle, W. Bloom, E. Pollard, T. H. Wood, C. A. Tobias and T. T. Puck on radiation effects.

5. Livshits, N. N., "Physiological Effects of Nuclear Radiations on the Central

Nervous System," in Adv. in Biol, and Med. Pkys., 7, 174-241 (1960): a review of the extensive Russian work, and that of others, on this important question.

6. Law, L. W., "Radiation Carcinogenesis," ibid., 7,295-337 (1960): a penetrating

survey of recent work, and a lucid account of the present position of knowledge on radiation-induced neoplasms.

7. Howard-Flanders, P., "Physical and Chemical Mechanisms in the Injury of

Cells by Ionizing Radiations," ibid., 6, 554-596 (1958).

8. Kinsman, S., Ed., "Radiological Health Handbook," U. S. Dept. of Health,

Education and Welfare, 1954.

REFERENCES 261

9. International Conference, Geneva: "Peaceful Uses of Atomic Energy. II. Bio- logical Effects of Radiation, "United Nations, New York, N. Y., 1955.

10. Butrer, J. A. V., "Inside the Living Cell," Methuen, London, 1960.

11. Swallow, A. J., "Radiation Chemistry of Organic Compounds," Pergamon

Press, London, 1960.

12. Appleton, G.J. and Krishnamoorthy, P. N., "Safe Handling of Radioisotopes:

Health Physics Addendum," Internat. Atomic Energy Agency, Vienna, 1960.

13. Hercik, F. and Jammet, H., "Safe Handling of Radioisotopes: Medical Adden-

dum," Internat. Atomic Energy Agency, Vienna, 1960.

14. Glasser, O., "Medical Physics," Vol. Ill, Year Book Publ. Inc., Chicago, 111.,

1960: many contributed articles on radiation effects on living tissue.

15. Cronkite, E. P., Bond, V. P., and Dunham, C. L., "Some Effects of Ionizing

Radiation on Human Beings," a Report by the U. S. Atomic Energy Com- mission, July, 1956.

16. Buchanan, A. R., Heim, H. C, Stilson, D. W., "Biomedical Effects of Exposure

to Electromagnetic Radiation," a Report to Life Support Systems Lab., Wright Air Development Div., USAF, 1960.

17. Shchepot'yeva, E. S., et al., "Effect of Oxygen in Ionizing Radiation." publ. by

State Publ. House for Medical Literature, Moscow, 1959 (U.S. A.E.C. Trans- lation 4265, 1960).

18. "Report of the International Commission on Radiological Units and Measure-

ments," U. S. National Bureau of Standards Handbook 78, 1959.

19. Burton, M., Kirby-Smith, J. S., and Magee, J. L., "Comparative Effects of

Radiation," John Wiley & Sons, Inc., New York, N. Y., 1960.

20. Kuzin, A. M., Shapiro, N. I., Livshits, N. N., and Breslavets, L. P., "Reviews

on Radiobiology," Inst. Biol. Physics, Publ. House Acad. Sci., SSSR, Mos- cow, 1956 (U. S. Atomic Energy Commission Translation 3353).

21. Peacocke, A. R., "The Structure and Physical Chemistry of Nucleic Acids and

Nucleoproteins," Prog, in Biophys., 10, 55 (1960).

22. Don, C, "Radiation Hazards of Mass Miniature Radiography," Can. Med. Assn.

Jour., 84, 5-7 (1961).

23. Lea, D. E., "Actions of Radiations on Living Cells," 2nd ed., Cambridge Univ.

Press, 1955.

24. Henderson, I. H. S., "Electrochemical Radiation Dosimetry," Defence Research

Chemical Laboratories, Canada, Report No. 352, 1961.

25. Hine, G.J. and Brownell, G. L., "Radiation Dosimetry," Academic Press, Inc.,

New York, N. Y., 1956.

26. Smith, D. E., Ed., "Proc. Internat. Cong, of Radiation Research," Radiation

Research, Suppl. 1, Academic Press, Inc., New York, N. Y., 1959.

27. Augenstine, L. G., Ed., "Bioenergetics," Radiation Research, Suppl. 2, Academic

Press, Inc., New York, N. Y., 1960.

28. Allen, A. O., "The Radiation Chemistry of Water and Aqueous Solutions,"

D. Van Nostrand Co., Inc., Princeton, N. J., 1961.

29. Haissinsky, M., Ed., "The Chemical and Biological Actions of Radiations,"

Vols. 1 to 5, Academic Press, Inc., New York, N. Y.; Vol. 5, 1961.

CHAPTER 10

Biophysical Studies on Nerve and Muscle

I had dissected a frog . . . and had placed it upon a table on which there was an electric machine . . . . I took up the scalpel and moved its point close to one or the other of the crural nerves of the frog, while at the same time one of my assistants elicited sparks from the electric machine .... Strong contractions took place in every muscle of the limb, and at the very moment when sparks appeared the animal was seized as it were with tetanus .... (Luigi Galvani, anatomist, surgeon, and obstetrician; 1781.)

This chapter presents an outline of some recent studies on nerve, and shows how these are related to motion effected beyond the nerve endings by excitable tissue in muscle. In the next chapter these facts are interpreted as part of the enveloping concept of the human physical system. Then some generalizations about this system are made which develop the framework in- troduced in Chapter 1 and upon which the various parts of this book are strung.

First, however: What is the nature of the physical apparatus — nerve and muscle?

TRANSIENT BIOELECTRICS IN NERVE

In Chapter 7 the rest-condition of tissue was shown to exhibit voltage dif- ferences in living membranes between the points at which solute activities differ — and even in normal bulk tissue (Chapter 8) if bioelectric currents are driven through it. Transient, or sudden, changes in voltages or currents are

262

TRANSIENT BIOELECTRICS IN NERVE 263

common, however, throughout living tissue, and play a uniquely important role in nerve conduction. Here an electrical transient — the change in voltage across the nerve cell membrane — is propagated with great speed along the surface of the cell and along the nerve fiber formed by many axons in paral- lel. The voltage change is the unit of information. First we describe how this transmission takes place.

From Volta* to Hodgkin

It was in the late 1770's in Bologna that the Italian physician, Luigi Galvani, and his wife Lucia observed quite by accident that the leg of the frog with which they were experimenting could be made to twitch if certain parts of the animal were touched simultaneously with the ends of two differ- ent pieces of metal (iron and zinc, for example) joined together. Actually they had discovered two things: the electrical voltage of a Zn-Fe couple, and the electrochemical exictation of living tissue. In the succeeding two hun- dred years a great body of facts has accumulated; these have demonstrated quite conclusively the electrochemical nature of nerve conduction and the resulting stimulation of excitable tissue. The afferent and efferent nerve systems have been well tracked and catalogued — the job of the former being to conduct commands, despatched by the brain, out to muscles and other effector tissues. The so-called "all-or-none law," which says simply that the excitable tissue will not fire (act) unless the stimulus has some minimum power, and that the impulse moves down the nerve with constant amplitude and velocity,** is now an accepted working principle for the physiologist. Various chemical and physical methods have been developed to modify the sensitivity of the nerve to stimulating agents — chemical catalysts in the form of drugs; electrical pacemakers, etc.

However, even with all this great accumulation of useful knowledge on how to modify the operation of the nervous system, it has only been since the early 1930's that definitive examination could be made of several of the many theories of operation of the nerve fiber. About that time it was realized that the main nerve axon of the squid — in this respect unique among all others — is a tube large enough (~1 mm od and several centimeters long (see Figure 10-1)) to be examined both electrically and chemically, inside and out. The fact that its physical structure could be examined by both

*In Phil. Trans., 1800, Alcssandro Volta, Professor Natural Philosophy, University of Pavia, published a paper in which he not only described his new "artificial electric organ" (i.e., the first storage battery), but also discussed the effects which electric current from this invention "exercises on the different parts of our body," effects "which will open a very wide field for reflection, . . . particularly interesting to Medicine."

**In certain unnatural media (sodium-deficient, for example) decremental propagation occurs: both amplitude and velocity decrease as the impulse moves along the nerve.

264

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

string

Figure 10-1. Nerve Cell and Axons. The length of the axon is sometimes as much as 1 00,000 times the length of the cell. Insertion of Micropipets and Micro- electrodes. Stimulating (or detecting) electrodes touching myelin sheath.

optical and electron-microscopic methods made it all the more attractive as a subject for study.

In the next section some of the pertinent information which has been ob- tained from the lowly squid is summarized. This information has formed the basis of a better understanding of the biophysics of nerve conduction. Nerve is similar enough from one species to another that some generalities can be assumed on the basis of information gained from the squid axon.

The Era of the Squid

Curtis and Cole by 1936 had placed metal electrodes inside and out- side the squid's tube-shaped axon; and with a conventional Wheatstone bridge, had made measurements of the electrical resistance (20,000 ohms/cm2) and electrical capacitance (1 microfarad (^f) per cm2) of the membrane. Further, they showed that the resistance is much lower when the nerve is actively transmitting impulses.

With the development of electronic dc amplifiers and oscilloscopes, it became possible to display the passage of the nerve impulse as detected by thin platinum-wire contacts (electrodes) touching the nerve (see bottom of Figure 10-1, for example). The impulse turned out to be a band of negative charge passing down the outside surface of the axon, from the point of stimulation to the far end. The insert in Figure 10-2 shows the electrical

TRANSIENT BIOELECTRICS IN NERVE

265

shape of the impulse. Further, the use of two pickup electrodes placed a few centimeters apart, each feeding an oscilloscope, permitted measurement of the time it takes the impulse to cover the distance between them. The speed of transmission was thus shown to be about 100 m/sec (about 200 miles/hr), less if the nerve were bathed in media of low electrical conductivity. Since an excised squid axon bathed in seawater would live and reliably transmit for about 1 hr, one can well imagine the exciting days for Hodgkin and Hux- ley of Cambridge University, working at Plymouth, England; and for Curtis and Cole at the famed Marine Biological Institute at Wood's Hole, Massa- chusetts— but hard times for the squid population in the waters close by.

direction of propagation f

(impulse)

*g£

♦^

^

wave of negativity'

leading edge

trailing edge

Figure 10-2. Potential Changes as the Impulse Passes Detector Electrodes, One Inside and One Outside the Axon. Normally the axon is negative to the outside electrolyte, but as the impulse passes, the potential is momentarily reversed.

By 1939 researchers had micropipets inside the axons (see Figure 10-1, bottom) to sample the fluids during stimulation (Table 10-1); and micro- electrodes, too, to record the change in voltage across the membrane. J. Bernstein's hypothesis (1902), that the potential difference across the rest- ing membrane is due to a difference in salt concentration, was fully con- firmed.

However, as the impulse passed any point on the nerve, the nerve mem- brane's voltage-difference from inside to outside at that point was found not only to drop to zero, but actually to reverse — the inside to become positive some 40 mv (the so-called "spike"), before it started its recovery to the normal state! There the puzzle had to stand during World War II. Fig- ure 10-2 shows how the potential difference between inside and outside the axon at a point on the surface changes as the wave of negativity passes.

266 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

TABLE 10-1. Natural Content of the Solution Within the Giant Axon of the Squid"

Substance

Concentration (millimoles/lOOOg H20)

K 400

Na 50

CI 40

Ca 0.4

Mg 10

isothionate 270

aspartate 75

glutamate 12

succinate-fumarate 17

orthophosphate 2.5 to 9

ATP 0.7 to 1.7

phosphagen 1 .8 to 5.7

*Data collected by Hodgkin.14 Compare with ionic content of erythrocytes (Table 2-1)'.

Since 1947 experiments of essentially three kinds have added valuable clues toward the explanation of just how the nerve carries information. They have been: (l)radioactive tracer experiments on sodium and potassium ions; (2) studies of the effects of changes in concentration of natural and foreign ions and molecules; and (3) electrical studies such as fixing the po- tential difference and following the current changes which result — the so- called "voltage clamp'1 technique.

In short, these three techniques have established the facts that the im- pulse is associated with: (a) a rapid increase in the membrane's permeabil- ity to Na+, an increase which lasts only about one msec; and concurrently, (b), a smaller and later increase in the K+ permeability, which has a slower recovery lasting over several msec.

(1) Tracers: Hodgkin, Huxley, and Katz were the first to use effectively the radioactive beta and gamma emitters, Na24 and K40, to follow sodium- and potassium-ion permeabilities across the axon wall. If the active Na+ salt is placed in the external solution, samples of the internal fluid can be with- drawn via the micropipet and checked periodically for radioactivity. Al- ternatively, small amounts of radioactive K+ salt can be inserted into the axon, and samples of the external fluid measured periodically for radio- activity. The rate of permeation of these ions through the axon wall when it is passive is much smaller than the rate of permeation when the axon is repeatedly stimulated and is carrying impulses. This difference in rate of penetration is greater the greater the number of pulses being passed along the axon per second.

TRANSIENT BIOELECTRICS IN NERVE 267

(2) Concentration Ratio: Table 7-12 gave data which show that the resting potential measured across living membranes is in substantial agreement with the value calculated from the ratio of the two concentrations of salt, outside and inside the membrane. Calculation is done via the Nernst equa- tion, suitably modified to express the voltage of a concentration cell:

E = 60/n log (a,/<32) mv

where n is the number of charges carried on the ions of the salt, and a, and a-, are the effective concentrations (activities) on opposite sides of the membrane.

However, such a relationship as that shown above between the potential of a concentration cell and the ratio of the activities of the salt on the two sides of the membrane is actually a special simplified case, used here for introductory purposes. More generally, when two such salt solutions with activities (effective concentrations) a, and a2 abut each other, and if diffusion is restricted so that salt cannot flow,

E = 2 —=- In ax/a2 nF

or

E = 2 x 60 log a} /a2

The 2 comes from the fact that work is potentially available from the con- centration ratios of both the positive and negative ions.

If salt can diffuse, a new factor, /_ , the transference number of the anions, enters (for reasons which will not be developed here) so that

£ = 2 L x 60 log a, /a2

Here /_ = /u_/(/*+ + M- ), where the yu's are the mobilities, or speeds, of the ions in centimeters per second when the voltage gradient is 1 v/cm. Intro- duction of the expression for <_ , and rearrangement, gives

E = 60 log a, /a2 - 60 M+ ~ M~ log aja2

M+ + M-

This expression gives the potential if cations and anions are not restricted in their motion. When both move with the same speed (KC1 in water, for ex- ample) n+ = M- (or t_ = 1/2), and the second term drops out. If the mo- tion of one is completely restricted, there can be no motion of the other if micro-neutrality is to be maintained, and the potential is given by the first term only. In such a case — charged protein ions plus salt in water, the Donnan case, for example — the values of a, and a2 are the activities of the unrestricted ion.

268 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

When the membrane is like that of nerve (Figure 10-3) — partially perme- able to several ions — the potential across it can be related to the permeabil- ity constants, (P (Chapter 8). The deduction gives

RT

E = -= ln (Z ®r cr/H (?r c J

where the summations are of the products of permeability ((P) and concen- tration (c) for all the ions (z), and the superscripts refer to outside (out) and inside (in) the cell. In other words the permeability constants express as a number the contributions which the different ions make to the potential dif- ference across the membrane. Thus a membrane which is selective can pass one ion more quickly than another, so that the (P's are not equal. In the case of resting nerve, (?K+ » (PNa+ or (PCI_ . The rapid potential changes which occur while the impulse is passing by are now generally believed to result from rapid changes in the permeabilities. The reader is invited to follow the fascinating efforts of our contemporaries, Ussing, Teorell, Sollner, Schldgl, and other membrane researchers.

outside position! outside

! of

ACE _ ACE impulse ^

r\r^^S^r^'\r^^-iy-\ /v. carbohydrate 8 ^*-^rPh$\

protein layers.

ZZZ^ZZ^^DV^aTZZCZy^f \^d layer ZL^ZT^-T^f^

I

1

© t

inside inside

0 I©* 0

loJ^r^

Na+|-

l

I

■+■

RESTING (pNQ+ low) ACTION (/JNa+high)

Figure 10-3. Illustration of Construction and Ionic Penetration (;u's) of the Nerve Mem- brane. During rest the mobilities of Na+ and K+ are low, but during action they be- come momentarily very high. (Refer back to Fig. 6-8.)

Sodium deficiency in the external electrolyte slows down the speed of con- duction. Further, it leads to a spike height which decreases as the impulse passes down the nerve — "decremental conduction," it is called. Sodium is pumped out of the axon through the membrane by a yet unknown mecha- nism, and this requires energy. It has been found that, during treatment with metabolic inhibitors, adenosine triphosphate (ATP), the mobile power supply, disappears at about the same rate at which the sodium pump slows down and stops. It is therefore inferred that reactions involving the hy-

TRANSIENT BIOELECTRICS IN NERVE

269

drolysis of ATP are probably the source of energy for this process, as they are for many other biological processes.

(3) Voltage Clamp: This is a technique, rather simple in principle, in com- mon use in solid-state research and in electrochemical research. In short, electric current is passed between two electrodes maintained at some con- stant potential difference, or voltage. A steady current is a measure of the rate of the steady-state which is operating within the system. Suddenly the voltage is changed to another value, and "clamped" there; and the current is followed closely as it changes toward a new steady-state value. The shape of the current versus time curve (Figure 10-4; top right) is diagnostic. Il- lustrated in the figure is evidence that the first part of the action spike is due to rapid sodium ion transport through the membrane: the inward current disappears if the electrolyte in which the axon is bathed contains no sodium. Of course, propagation of the impulse disappears under the same conditions also.

Theories: Quantitative descriptions of the electrical phenomena have been attempted, it being variously assumed that deviations from the Nernst equa- tion (see Table 7-12) are due to (a) poor knowledge of the activity at the

6

^y

-®-

no current

( switches open)

<h

\-®~

e

axon

current inwordl current outwardf

■(cell shorted (voltage clamped) out )

(a)

(b)

(c)

start

Figure 10-4. Voltage Clamp Technique. Two reversible electrodes, one inside and one out- side the axon are used, (a) Natural voltage (50-100 millivolts) measured across axon. Current (top, right) is zero; voltage (bottom, right) is steady, (b) Membrane voltage is short-circuited through external resistive load. Positive current (due to Na ' ) flows inward. Voltage and current both decay toward zero as energy is dissipated as heat in external load, (c) Voltage is "clamped" at unnatural value by connection to a potentiostat, a source of constant voltage. After the first millisecond, positive current (due to K+) flows outward. Within the first millisecond, inward current (due to Na + ) flows because, the membrane's per- meability to K+ is still small. The inward current is completely absent if external fluid has no sodium in it (top, right; broken curve).

270 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

given concentrations; (b) leaky membranes, through which the Na+ and K+ permeate, or diffuse down their respective gradients; (c) electrical charges permanently fixed within the hundred angstroms or so of effective thickness of membrane; or (d) changes in shape of acetylcholinesterase (ACE), an enzyme located on the surface of nerve (Figure 10-3 illustrates) and thought by some to be the cover whose shape determines whether or not Na+, or K h, or both, can enter the slip through the pores in the membrane.

Two quantitative theories permeate the literature on nerve transmission: the use of the electrical cable theory to describe the spread of a localized electrical disturbance; and the description of ionic currents through the membrane as a function of permeability.

Early in the century electrical engineers had worked out the effect of a break, or a series of breaks, in the insulation of an electric cable having a metallic conductor inside and salt water outside. By 1938 Curtis and Cole had used this application of Ohm's law to describe how a localized dis- turbance in a nerve membrane can spread on down the nerve. The key expression is:

d V

d2 V = rx + r2 dx2 r

E- V - rCm

dt

where /: is the concentration-cell voltage across the membrane in the ab- sence of a disturbance, i.e., when the membrane is resting; V is the "action" voltage at any time, /, at a distance, x, along the surface from the site of the disturbance, 0; r, and r2 are the electrolytic resistances (ohms), between 0 and x, in the outside conductor and the inside conductor, respectively; r is the resistivity of the membrane (fixed, unknown thickness) in ohm cm2; and Cm is the capacitance of the membrane, which is being depolarized (dis- charged) at a rate dV / dt. The expression teaches that the depolarization oc- curs at a rate which increases as the divergence (spread) of voltage along the surface increases, and decreases as the resistances to ion flow (r„ r2, and r) increase.

By 1952 Hodgkin and Huxley had described measured changes in mem- brane conductance of the giant axon of the squid in terms of change in the permeabilities of the simple ions of the external and internal media. The principle ideas of this theory will now be given.

Currents through the membrane are considered to charge (or discharge) the membrane capacitance and to leak Na+, K+, and other ions as well.

Thus:

/ = Cm dV/dt + /Na+ + /K+ + /

where /is total current, and the 7,'s are the currents due to the different ions. Then each /, is expressed as being the product of the membrane conduct- ance (gt ) and the driving voltage for that ion. Thus: It = gt A V

TRANSIENT BIOELECTRICS IN NERVE 271

Each gt was then related by a phenomenological trick to time and voltage in such a way as to fit the experimental results. Thus, for potassium ion,

n . fj max„4.

6K+ ~ &K + "

and

dn

= a„n{\ — n) — B„n at

where n is a dimensionless parameter which has a value between 0 and 1; it is time-dependent and is related to voltage-dependent penetration con- stants, anand /?n. The first, an, expresses the rate of K+ movement into the cell, and /?n expresses its rate out. Similar expressions have been devised for Na+ and the other ions of the system. From these expressions the total cur- rent (/) can be expressed in terms of time-dependent and voltage-dependent parameters related to permeability. With proper choice of the values of the different parameters, the experimental values of conductance as a function of time and voltage can be completely described.

These two theories have been bright lights in the quantitative descrip- tion of nerve propagation. The interested reader is referred to the analyti- cal and summary papers21,22 for the detailed arguments. The papers are difficult, but rewarding.

The charged-pore theory of membrane potential differences has been suc- cessful with synthetic membranes of collodion, ion-exchanger resins, and other synthetic polymers. It will not be developed here, although it has been put into elegant quantitative form by Meyer and Siever and, more recently, by Teorell.

This is a very active and important part of biophysics today, and, as was stated in Chapter 6, probably there is no part of the research in the subject which will be more rewarding. Hodgkin's Croonian Lecture14 is an excellent statement of the state of the art, and Nachmansohn's recent, short review,18 more from the biochemical viewpoint, will nicely balance the further devel- opment of the reader's concepts.

Is Semiconductivity Important?

It may be. We saw in Chapter 4 that the tt electrons of many organic compounds have a certain freedom and can move under the influence of an electric field. Most vertebrate nerve is sheathed in myelin, the protein-and- fat wrapping formed by the doubled membrane of the Schwann cells. This is illustrated schematically in Figure 10-1, top right, and shown very dra- matically by the electron micrograph, Figure 10-5. The myelin sheath offers physical protection to the fine nerve fibers of vertebrates. But it has further roles. For instance, since it completely covers the nerve fiber except at certain interruptions about 1 mm apart, called the nodes of Ranvier (Fig-

272

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

Figure 10-5. Electron Micrograph of an Ultrathin Section of Nerve Axon which is Myelin- ated by the Spiral Wrap of the Double-Membraned Schwann Cell. Magnification 90,000 x . (Courtesy of J. D. Robertson, Harvard Medical School, and of Scientific American.)

ure 10-1) the impulse is forced to skip from node to node, perhaps via semi- conductivity, although it may be by proton transfer ("protochemical" cells have been demonstrated in the laboratory) through the myelin. In any case the skipping mechanism is very fast, and therefore a sheathed nerve nor- mally conducts an impulse somewhat faster than an unsheathed one.

The Trigger

To fire the nerve and incite the transmission of an impulse, a stimulus is required. Stimuli are essentially of five kinds:

(1) Electrical: voltage changes applied directly to the cells of the nerve — in the brain for example.

(2) Mechanical: pressure changes causing distortion at nerve endings — ear, and mechanoreceptors associated with the sense of touch.

(3) Electromagnetic: incident radiation absorbed by pigment molecules in cells sensitive to visible light, and by other transducer molecules sensitive to warming (infrared) radiations — eye, and a multitide of closely spaced detectors all over the body's surface.

TRANSIENT BIOELECTRICS IN NERVE 273

(4) Chemical: foreign chemicals applied, or changes in concentration of natural chemicals — taste buds, dehydrated tissue cells, etc.

(5) Gravitational: continuous attraction to earth, occasionally varied by superposition of various accelerations — balance-detectors in middle ear, for example. (These are essentially of type (2).)

Deserving special mention as a trigger is trie "pacemaker" of the heart, which in man repetitively stimulates the pump to compress and relax once about every 1.3 sec 24 hr a day for life. Recordings from microelectrodes inserted into pacemaker cells show that they are self-contained oscillators. Very recently D. Noble has shown19 that if certain limiting conditions are imposed on the cable-and-changing-permeability theory described above, the theory can describe the condition of oscillating permeability and oscil- lating potential of the membrane of the pacemaker cell.

When and if the pacemaker fails, it has been shown to be possible to stimulate the heart artificially. With small transistor circuitry and small zinc-mercuric oxide batteries, it has been demonstrated recently that an artificial pacemaker can be buried, by surgery, in the abdominal cavity under the skin and stimulate a weak heart regularly for at least a year be- fore the battery has to be changed (again by surgery). This device has brought a normal life to many people.

Recent advances in microelectrode preparation have permitted glass tubes to be drawn down to an outer diameter of 0.0005 cm, filled with electrolyte, and the ends inserted carefully right into the individual muscle cells in the animal's beating heart. Thus the electrical measurements on cells working in situ are now being made. Great care has to be taken that the electrical meas- urements are not affected by the huge electrical resistance of these micrelec- trodes (try Problem 10-5). For steady potentials an electrometer with a high impedance is usually used; but for rapidly-varying potentials, such an in- strument is too slow to follow the potential changes without inducing dis- tortion. There this problem of measurement presently rests. Once it is solved, although the cross-correlation of electrical and chemical information may still not be possible in these small cells because of the size of the object under study, pharmacological problems should receive much attention with this technique. Indeed the neuromuscular junction is already being so ex- plored.

Studies on the Central Nervous System

By contrast with the normally resting peripheral nerve tissue, which is activated upon demand, the brain is a mass of spontaneously pulsating neu- ral networks, seemingly continuously energized and active. It is usually as- sumed that the basic processes are electrochemical, like those just outlined as being proper to nerve conduction. However, biophysical knowledge of

274

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

this organ is meager. Thus, while neuroanatomy, which deals with the geography of the brain and the relation of various parts of the brain to certain functions of the whole system, is well advanced, and its daughter, neurosurgery, is in a rapid state of development, physiological studies are necessarily phenomenological because of the complexity of the system under study; and biophysical studies, mainly electrical because of the fast elec- trical responses of the system, tend to be either empirical or theoretical — and hence do not assure a correct understanding of the phenomena under study. As a result of this complexity, the most important advances of the past decade have not been biophysical at all. Three different kinds of study will now be briefly noted: (a) the recording and analysis of gross electrical sig- nals of the brain; (b) the transmission across synapses in the spinal cord; and (c) the electrical behavior of single neurons in the cortex. The method of electroencephalography (EEG) is as follows: Small pellets of solder, or other metal-contact electrodes, preferably non- polarizable,*** are placed on symmetrical points of the scalp and fastened

delta

v I

theta

alpha

Hsed

beta

4h4H|rWpvHM^

Figure 10-6. Components of an Electro- encephalogram.

there with a binder such as collodion. Twelve to twenty-six leads cover the scalp in localization experiments, overlying each important lobe of the brain, and even different portions of each lobe. Voltages between these and some reference position, such as a lead to the ear lobe, are" fed into standard high- gain amplifiers, and traced by pen recorders. Five or six seconds of record- ing gives patterns (Figure 10-6) which, quite empirically, have been cata-

***A nonpolarizable electrode is one in which the voltage with respect to some reference remains unchanged when current is passed through the electrode. A silver disk coated with a thin layer of AgCl, which makes contact with the chloride-containing body salts, is non- polarizable in EEG work where the currents are very small (< 10 amp).

TRANSIENT BIOELECTRICS IN NERVE 275

logued as coming from normal or diseased tissue. Patterns taken on an indi- vidual vary with the emotional state. A creative man is said to have pat- terns quite different from one who lacks new ideas. However, the fine struc- ture of these waves is not well understood. Recorded spikes are only about 150 nv high. Characteristic spikes of different shapes and frequencies have been named alpha, theta, delta, etc. These are depicted in Figure 10-6.

Location of tumors, via predominance of the delta waves (see Table 10-2), has been particularly successful, with 73 to 90 per cent accuracy claimed. Bagchi has reported 84 per cent in 333 tries. Other abnormalities, such as epilepsy, have been studied by this technique.

TABLE 10-2. Classification of Electroencephalograph Waves.

Names of Waves

Frequency (cps) Association

delta 0.5 to 3.5 "disease, degeneration,

death; defence"* theta 6 to 7

alpha 8 to 13 a scanning mechanism?

beta 14 to 30 alertness; active response

♦Walter, W. Gray, "The Living Brain," Penguin Books, Baltimore, 1960, p. 81.

While the all-encompassing phenomenological techniques of EEG have been making useful contributions to life, studies of individual neurons, via microelectrodes in the cortex, and studies of the properties of synapses and ganglia in the spinal cord have demonstrated interesting phenomena such as: inhibition of transmission across nerve endings (strong signals passed through one nerve ending reduce the effectiveness of one close by); post- tetanic potentiation (faster and more energetic transmission through a par- ticular nerve path following a rapid succession of pulses through that path); and the promotion of epileptic-like seizures and peculiar mental images in man by electrical stimulation of particular spots in the cortex via micro- electrodes.

Transfer of an impulse across a synapse (Figure 10-7) is currently thought to be by means of "chemical" transfer rather than by "electrical," for two reasons: the observed salt concentration changes associated with a single im- pulse are very small; and there is fairly good evidence that acetylcholine (ACh) accumulates in the gap during transmission across the gap. A theory is that ACh is contained in the many little vesicles in the pre-synaptic end- ing: that, during "activity," ACh is expelled through the membrane and diffuses to the post-synaptic membrane and locally depolarizes it. The de- tails of this mechanism are still unknown.

276

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

vesicles containing ACh

e

impulse "3

i mpulse*!

/ACE

/\l8l

©

C i-K

e

impulse #2 crossing the junction

|^?^-^?r^^

No* I fl I

©

0

;7v5^1 ^wy &>?^ io^^^sv^y

500A-

©

Figure 10-7. The Synapse or Junction Between Two Nerve Endings (con- ceptual and schematic). As the impulse reaches the end of the nerve, acetyl- choline (ACh) is released in quantity from the little (~300 A) vesicles contained in the presynaptic nerve ending. This ACh depolarizes the membrane, and free flow of K+ out and Na+ in, on the presynaptic ending, and of ACh across the gap, occurs.

The neuromuscular junction, shown and described later, is similar to the neuron-neuron junction in many ways.

Synapses are apparently very sensitive to ionizing radiations, for Livshits and others in the Russian school have observed changes in the EEG pattern during even very weak (1 r/hr) X- or 7-irradiation, although peripheral nerve is relatively quite insensitive. The subtle psychological effects which result from such interference with, or modification of, the normal pulsating activity of the brain can therefore be considered as due to electrochemical noise generating by radiations from outside. Noise in our reckoning system, produced by such stresses from without, is considered a bit more fully in the next chapter. Noise from within — disordered inputs from crossed neural circuits, from the physical apparatus of memory, and from the metaphysical parts of mind, intelligence, and will — is the basis for further psychological stresses and disorders. Memory-stimulation by electric shocks applied to the interpretive cortex of the brain seems to be another experimental avenue by which man can apply biophysical methods to the study of this wonderful organ. The uninitiated but interested reader is referred to the well-illus- trated review by Penfield.8

Entering the brain are several trunk lines, each main line being many- stranded, and every strand insulated electrically from every other so that many signals may pass simultaneously down the trunk line. In the case of

THE MOLECULAR BASIS OF MUSCLE CONTRACTION 277

the two optic nerve trunks, a nerve-ending from each fiber carries an im- pulse from a rod or cone to a bipolar cell, thence to the brain. There is evi- dence now that insulation among these strands is not complete, and that parallel signals from two may trigger a third, and so on. This is a mecha- nism which seems to be operative in color vision, as was inferred in the dis- cussion on that subject in Chapter 4. Cross-stimulation seems to be very generally operable, for there is a great deal of psychological evidence that saturation of one sensing organ will have a marked effect on the sensitivity of another. Mentioned earlier was the dentist's new trick of flooding the ear with noise of a suitable frequency so that the pain of drilling cannot be felt! The physical network which accommodates, sorts, and retains certain im- pulses and rejects others is a topic for future study. Furthermore, memory is still a very mysterious phenomenon. One recent proposal about the phy- sical mechanism of memory deserves mention: the "training" of the neural network to store information is done by means of the synthesis of certain ("different") protein molecules. These result from a change in shape of the ribonucleic acid (RNA) effected by a passing stimulus — i.e., the RNA within nerve and neighboring glial (Schwann) cells. Although this does not sound very convincing at first glance, it seems to be the best model yet put forward in the baffling question of what is the physical apparatus of memory; and it certainly is consistent with the known fact that the rate of protein synthesis is very high in active nerve cells. One cannot help thinking that these "dif- ferent" proteins may be imbedded right in the membrane, and exert their effect as "permanent" changes in its permeability. In conclusion, one could say that, from the biophysical point of view, the study of the central nervous system is becoming more and more a study in applied electrochemistry, a study of membrane biophysics.

THE MOLECULAR BASIS OF MUSCLE CONTRACTION

By means of nerve, the brain exercises control over both chemical and physical processes in the body. There are good examples of each: for the former, the endocrine gland system; and for the latter, muscle. Of the two, the latter is in many ways inherently less complicated, and only it will be discussed in this attempt to illustrate how control is achieved in a particular case of a physical action. For this we need to know some relevant physical properties of muscle tissue; and, more important still from the biophysical point of view, we need to know the molecular behavior which is at the root of this physical behavior. Fortunately, both electron microscopic examina- tion of muscle-tissue slices, and kinetic methods of analysis of rate data seem to be succeeding with this problem of providing an understanding of mus- cular contraction. On the other hand, a review of muscular contraction from the molecular viewpoint has the added advantage of illustrating the powerful

278

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

methods of kinetics in displaying the physical movements of molecules. First, however, comes a discussion of the fact that activated muscle tissue often behaves like a critically damped helical spring. The model is illus- trated in Figure 10-8.

The Helical-Spring Analogy

The activated muscle has several physical properties in common with a stretched spring. The latter obeys certain well-known physical laws, for ex- ample that of Hooke: viz, the restoring force, F, is proportional to the dis- placement, As, during stretching, or

F

k,As

= kt(s - sf)

where s is length at any time, t, and Sj is the final (fully contracted) length (see Figure 10-8).

nerve endings

muscle

Figure 10-8. Stretched-Spring Model of Muscle. Defined are: s, the length at any time during shortening; s0, the initial (resting) length before contraction starts; and s,, the length at complete contraction.

THE MOLECULAR BASIS OF MUSCLE CONTRACTION

279

Now if speed, v, of shortening is always proportional to restoring force (this is equivalent to assuming the spring is embedded in a plastic or highly viscous mass, and that the spring is critically damped) then:

Integration gives

k(s - sf)

s, + (s() - sf)e-

•7 1 vJ0 7.

where s0 is the initial, or starting, length. From this the shortening speed can be expressed as a function of time by finding the derivative. It is

v = k(s0 — s,)e~kt

The fraction shortened,/, defined as (sQ — ^)/(.r0 — Sj), at any time reduces to

/= 1 -

-*/

and k becomes known as the shortening constant. This expression is illustrated in Figure 10-9, in which the fraction shortened during shortening is plotted for both the case discussed and for muscle. Elasticity in the muscle, which lowers the initial rate of shortening (df/dt), and recovery following full con- traction are the chief differences. Note that the ^-shaped curve in the case of muscle can appear to be linear, especially if sensitivity of measurement is not high enough; and hence the shortening rate ( — ds/dt) is often considered to be constant.

T ime

0,5 sec

Figure 10-9. Fraction Shortened as Function of Time During Shortening.

The larger the load, m, the smaller is the shortening constant, k. This is to say that the muscle can contract quickly if the load is light, and only slowly if the load is heavy. It is found that k varies with m in such a way

280 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

that momentum, mv, is conserved (remains constant):

£) I — 1 = constant

\ max / \ max /

where vmax is the maximum speed of shortening (no load), and ramax is the largest weight which can be lifted. Here v0 and m0 are constants. This result is often written as a product of velocity and force, when the acceleration is that due to gravity — a constant; it then becomes the "force- velocity rela- tionship." Thus for two masses, m, and m2, momentum conservation is expressed

<mx — m0\ lv~, — vAfm2 — m^

max / \ max / \ max / \ max

The denominators cancel out. Then if mass 2 is chosen to be just big enough that the muscle can sustain it but not lift it, v2 = 0, and m2 = mmax. Mul- tiplication through by g, the acceleration due to gravity, converts masses to forces (F = mg), and then rearrangement gives

(F+a)(v + b) = (F. + aji,

the force-velocity relationship, first stated in 1938 by A. V. Hill (a and b are his constants, equal to -gm0 and -v0 respectively). Figure 10-10 illustrates this equation, and says simply that the greater the force to be overcome by the contracting muscle the less the speed at which it can contract. Rear- ranged in the form

v = (Fmax-nb/(F+a)

it says that the velocity of shortening depends upon the difference between the maximum force it can develop and the actual force on the muscle. This hyperbolic relationship is obeyed by a wide variety of muscle and muscle systems, including the human arm.16

On Energetics of Muscle

The work done by the muscle in lifting a weight is given by the product mgh, where g is the acceleration due to gravity (and therefore mg is force, since F = ma) and h is height to which the weight is lifted. We saw in Chapter 7 that part (ALT') of hydrolysis of ATP — a reaction catalyzed by the con- tractile enzyme, myosin — could appear as work of contraction. Thus:

A5' = mgh

and the rest of the total free energy of reaction (A?F) is wasted because of ir- reversibility or inefficiency in the process, and thrown away as heat, TAS '.

THE MOLECULAR BASIS OF MUSCLE CONTRACTION

281

r max (or rnmax)

Velocity of Shortening , v ""

Figure 10-10. Force-Velocity Relationship (see text).

In review of the discussion in Chapter 7, we recall that the physical proc- ess derives its energy from chemical reactions, and that the heat of reaction, A3C, can appear in several forms:

A3C = AS' + q' + TAS

= a^' + a^ + ^ + taS

where A31' is the external work; AO1^, is the internal work, degraded into heat and given off by the system as heat; TA S is the reversible entropic heat, unavailable for work; and q'm is the extra heat produced because of the nonreversibility (inefficiency) of the process. It was also shown that q' can be expressed as q'bm + <7ex> so tnat

A3C = AJF' + ^ + ^ + TAS

where q'hm is the basal metabolic heat given off, and q'(.x is the excess heat given off during exertion. (These r/'s are irreversible heats, can be factored into T A S "s, and are sometimes called entropic heats.)

Now although A JC and TA S depend only upon the amount of material reacting, and q'bm is substantially constant since it refers to a particular physiological state, values of A^ ' and q[.x generally depend markedly upon

282 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

the rate at which the physical process occurs. Thus the faster the process the less efficient it is: i.e., the greater the fraction q'cx/(A^' + q'ex) which is lost as heat, and the less is the fraction A$7'/(A;F' + q'ex ) which is realized as external work. However, whether the work is done fast or slowly, nu- merically the same amount of work is done; and therefore, because Ao' is independent of speed, so must q'tx be, provided the same amount of fuel is consumed. It is a well-established experimental finding that the total heat, £•) ', given out during a shortening (the "contraction heat,,)

is constant, independent of speed of shortening. However, ~/ ', is propor- tional to the distance (a) shortened; i.e., °c ax; and the constant a has the same dimensions (energy/distance, or force) and numerical value (~400 g wt/cm2 area of cross section) as the a in the force-velocity relationship. The significance of this coincidence is not yet clear.

Careful measurements, with small thermocouples imbedded in the muscle and fast galvanometers to record small electrical currents, have shown that the contraction heat is composed of two parts: a rapid initial surge follow- ing stimulation, and completed before contraction starts; and then the con- traction heat proper. The first has been called the heat of activation, .4, by analogy with the terminology of the threshold in chemical kinetics. There- fore q'ex can be written as

q'ex = A + ax

in Hill's terminology, the first term being the activation heat and the second the contraction heat proper. +

Discussion of the production of enthalpy, JC , by biochemical reactions in muscle is beyond our scope in this book. A few notes suffice. Muscle glyco- gen is the primary fuel, being oxidized to lactic acid with — A// = 16.2 Cal/mole of lactic acid produced. This energy is used in the synthesis of creatine phosphate (CP) which acts as a secondary fuel. Both glycogen and creatine phosphate supply free energy for the synthesis of adenosine tri- phosphate (ATP), the hydrolysis of which is the immediate source of free energy for the physical work of contraction. Regeneration of the hydrolysis product, the diphosphate (ADP) is effected by reaction of ADP with CP — the famous Lohmann reaction. The enzyme myosin, which has the con- tractile property, adsorbs ATP and catalyses its hydrolysis.

+ In Hill's terms (Ref. 23, for example) the extra metabolic energy involved in contraction is composed of three parts: the work done (AJP), the activation heat (.-J), and the heat of short- ening (ax). The total energy will include q'bm and T A S ■

THE MOLECULAR BASIS OF MUSCLE CONTRACTION

283

Power of Contraction

The power — the rate of energy release, or "energy flux," as some people call it — is given by

P = d(A$')/dt + dSll/dt

= PW+ tin

the first term being the rate at which work is done, and the second the rate at which heat is liberated during shortening. Resting muscle in the steady- state condition at 20°C has a basal metabolic rate (bmr) of heat loss, dq'bm/dt, of about 2 cal per kg of muscle per minute. The rate is 2.5 times higher at 30°, 2.5 times lower at 10°C. Extrapolated to man (the example is Hill's16) — 30 kg of muscle at 37°C — the value of that part of the bmr due to muscle alone is about 18 Cal/hr, about 25 per cent of man's total bmr. During action, i.e., during a single twitch, the muscle gives out a contraction heat of about 3 cal/kg of muscle. For a fast muscle which twitches in 0.1 to 1.0 sec, therefore, the rate of heat loss, P%.n would be 180 to 1800 cal per kg per min — up to many times the bmr (~14 cal per kg per min).

Because the contraction heat is independent of rate of shortening, the rate of heat loss, P^n increases linearly with increasing speed of shortening. But the power expended to do work, (i.e., Pw ) is zero if no load is lifted (v = v ): it is also zero if the load is so heavy that the muscle can just sustain

max / * ' *■*

but not lift it {v = 0); and it goes through a maximum value for intermediate loads. Figure 10-11 illustrates this behavior of Pw and P^r The top curve gives the total power expended by the muscle.

The key to all this activity in muscle is the molecule myosin. But before discussing myosin itself, we must first understand the structure of muscle

v/v mox ►

Relative Speed of Shortening

Figure 10-1 1. Power as a Function of Fraction Shortened (after Podolsky, 1961).

284

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

tissue, as revealed by the light and electron microscopes, and a bit about the chemistry of muscle proteins, to see where myosin fits in.

Structure of Muscle Tissue

Figure 10-12 illustrates what is seen by means of higher- and higher- resolution microscopic examination of muscle. A muscle is made up of fibers, which appear striated under the light microscope. Phase contrast and interference attachments reveal that a fiber is composed of myofibrils, along the side of which lie mitochondria and nuclei (not shown). The electron microscope reveals that a myofibril appears segmented because of a repeat- ing pattern of light and dark bands throughout. Repeating patterns, bounded by the end- or "Z"-lines contain a faint "M"-line in the middle, bounded first by narrow H-zones and then the wider "A"- (for anisotropic) bands which span the middle. Isotropic 'T'-bands span the "Z"-lines (see Figure 10-12).

fibres

Tendon

Uh

i i r

(a)

Whole Muscle (■vl cm.)

Muscle Fibre

i 50-100/j)

mmm )

z z z z

1 <..,.*> '

sarcomeres

Myofibril (1-2 u)

— I —

(actin)

Figure 10-12. Schematic Drawings of Muscle Under Higher and Higher Reso- lution Microscopy, (a) Light microscope; (b) Electron microscope. During shortening the horizontal thick and thin filaments slide farther into each other, so that only the H and / bands shorten.

Under great magnification (~ 300,000 x ) a rather comical contraption is disclosed: an array of overlapping thick and thin filaments, which run paral- lel to the myofibril, and which apparently slide back and forth over each other as the muscle contracts and relaxes. Partial overlap of the thick and

THE MOLECULAR BASIS OF MUSCLE CONTRACTION

285

thin filaments gives rise to density gradients which appear to us through the light microscope as the bands (Figure 10-12 (b) and Figure 10-13).

The motive power is provided by the inherently contractile molecular actomyosin complex, a complicated protein condensation product of two complex units, actin and myosin — the former apparently primarily a struc- tural support and the latter an enzyme which catalyzes the hydrolysis of ATP. There is evidence that myosin is contained principally in the thick

*:%V

(a)

Figure 10-13. Huxley's Famous Electron Micrographs of Intermeshing Arrays of Thick and Thin Filaments of Striated Muscle Fibers, (a) Side view (longitudinal section). Note how the light H-band is formed by a discontinuity in the thin filaments. Note also the direct evidence for cross-bonds between thick and thin filaments (300,000 x). (b) End view (cross-section) (170,000x). (Courtesy of H. E. Huxley, Laboratory of Molecular Biology, Cambridge University.)

286 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

filaments, actin in the thin ones. The Z-lines are the outer edges of areas which bisect the myofibril, and have been shown to be the medium through which the stimulus, or order to contract, is carried from the surface mem- brane of the fiber (the sarcolemma) into the myofibril. The sarcolemma car- ries it electrochemically (like nerve) along the fiber.

Muscle consists of 18 to 20 per cent protein, by weight. About 60 per cent of this protein is a condensation product of several "myosins" with actin, a very complex molecule whose complete physical structure is very sensitive to the ionic content and pH of the medium. It interchanges between a globu- lar, almost spherical, hard G-actin, to a fibrous, stiff F-actin. Only myosin has the ATPase activity and can accept the free energy of hydrolysis of ATP. But the myosin of muscle is itself made up of smaller parts:

Rapidly extractable from minced muscle in salt solutions is myosin-A (called "myosin" or "/-myosin" in some books). Electrophoresis causes separation of myosin-/! into three fractions: one heavy (//) meromyosin, and two light (L) meromyosins. Only the //-meromyosin retains the ATP- ase activity, Extractable only slowly, or in other media, are myosin-/? ("natural actomyosin" or "^-myosin") and tropomyosin, which differ in physical properties from myosin-^4. Rejected by the extraction procedures is the globular G-actin, which, in the presence of ATP and dilute salts, slowly converts to the much more viscous, fibrous F-actin. The chemical composition is not simple. Thus there is some evidence that tropomyosin + G-actin + another protein constitute myosin- A. Some physical characteris- tics of myosin and actin are gathered in Table 10-3.

The muscle proteins are rich in polar residues such as — P03"3, — OH, — CONH — , and — COOH. These polar residues seem to be intimately connected with the process of contraction. Myosin's partner in the con- tractile reaction is ATP. To ATP, the fact that the catalytic enzyme, myo- sin, contracts during the hydrolysis, or splitting of ATP into ADP + P, is quite incidental. To the living system, however, the fact is vital! Dephos- phorylation occurs during or immediately after the contraction process.

Hydrolysis of ATP as a free energy-producing reaction is not confined to myosin as a catalyst, as we saw in Chapter 7. It provides the energy which drives many living processes. The following scheme represents the splitting reaction and its auxiliary reactions:

H20 + ATP4 ^ ADP2 + HP04"2

+ K2}[ +

//+ //+ //+

K, 11 + K3 11

ATP-3 ADP3 H2P04

i #i

I

THE MOLECULAR BASIS OF MUSCLE CONTRACTION 287

The L-step is the splitting reaction proper. In the vicinity of pH = 7, the values of the equilibrium constants, K\, K2 and AT3, are such that most of the adenosine is in the form of either ATP"4 or ADP 2; and hence the meas- ured values of AH and AF refer mainly to the hydrolysis itself — the hori- zontal reaction. The reaction is both exothermic and exergonic, a source of heat and a source of free energy for work. Respectable values (see com- ments in Table 7-3) are:

AF = -10.5kcal/mole

AH = -9.2kcal/mole

However, as is obvious from the reaction scheme, a shift in pH can shift the position of equilibrium of reactions 1, 2, and 3, and therefore shift the free energy of the splitting reaction. In a similar manner to the effect of hydro- gen ions, metallic cations — principally Mg++ and Ca+ + — can and do form complexes with the highly charged phosphate groups; each complex with its own equilibrium to affect the reaction scheme, and thereby to affect the values of A F and A H.

TABLE 10-3. Sedimentation Constant (s), Diffusion Coefficient (D), Molecular Weight (M), Intrinsic Viscosity ([r/0]), Length (/) and Thickness (d) of the Muscle Proteins.

Protein	s x 1013	D x 107	M	tool	1(A)	d(A)
Tropomyosin	2.6	2.4	53,000	0.523	400	15
7/-meromyosin	6.96	2.91	232,000	0.32	435	15
Z.-meromyosin	2.86	2.87	96,000	1.0	550	25
Myosin	5 to 8.2	1.0	420,000*	2.0	1700+	~25
G-actin	3.2	2.5	70,000*	0.21	290	25
*Dimers can be formed.
•f-Unfolded.
(From data collect!	:d by K. Bailey.1")

The source of the free energy in the hydrolysis reaction is the breaking of the intrinsically unstable, mutually repelling polyphosphates (as typified by ATP) and the formation of products with strong electronic resonance. When one remembers that during the splitting reaction both ATP and ADP are bound more or less tightly to the protein, one can understand why with dif- ferent proteins the energy available for doing useful work, AF, can vary.

Although the free energy of the hydrolysis of ATP catalyzed by the en- zyme myosin is certainly associated with the work done by the enzyme as it shortens, there is evidence that this relationship is somewhat indirect. This can be seen in the important facts which follow.

To a fairly good first approximation, the Michaelis-Menten Law, which relates the rate, v, of hydrolysis to catalyst (myosin) and substrate (ATP)

288 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

concentrations,

v k2[E]n[S]a [S]0 + Km

(see Chapter 8 for symbols), is well obeyed. Measurement of rate as a func- tion of temperature and substrate concentration permits evaluation of AHt, AFl and AS1, the thermodynamic quantities associated with formation of the activated state. Since AS* is usually (for various conditions) found to be positive, it is inferred that a change in configuration of the enzyme (and/or the release of adsorbed water molecules) occurs during the binding step in which an ATP molecule sits down on the myosin molecule. This step is then followed by the splitting reaction proper. In the terminology discussed in Chapter 8 and illustrated in Figure 8-5:

E + S y^ ESl — ^ product

in which process 1 is adsorption and shortening; and process 2 is the hy- drolysis step.

When experimental conditions are such that the kinetic results are amen- able to analysis without ambiguity of mechanism, analysis shows that the binding of the (enzyme) myosin molecule to the (substrate) ATP molecule occurs spontaneously with release of 6.6 kcal/mole. That is,

A/7bind,ng = -6.6 kcal/mole and

A//binding = -8.0 kcal/mole

Thus the free energy released in the binding process is a sizable fraction of that for the whole process (— 10.5). This indicates that the structural change (shortening) of the myosin molecule may occur at the time of binding of ATP, before ATP is split by hydrolysis. The inference is, then, that the resting muscle is very much like a stretched molecular spring, ready to contract when released from the forces which hold it extended. Indeed X-ray diffrac- tion patterns suggest that the famous alpha helix, discussed in Chapter 6, is the basic structure in myosin, as well as in so many other proteins.

Studies of effects of pressure and of dielectric constant on the rate have given values of the entropy of complex formation (i.e., of enzyme-substrate binding) to be A.S'bindj ~ 48 cal/deg. mole, with half of this value purely electrostatic, due to the charged groups on ATP and myosin.

Under certain experimental conditions the rate of desorption of the hy- drolytic fragments is slow, causing inhibition by the products. Activators and inhibitors can complicate the picture much further. However, enough has been shown to illustrate the fact that the kinetic methods, although very

THE MOLECULAR BASIS OF MUSCLE CONTRACTION 289

specialized in detail, provide a general mechanistic description of the physi- cal actions of the key molecules which play the vital roles.

A Theory of Contraction

One simplified working hypothesis about the physical activity of the con- tractile molecule will now be outlined. It is as though the myosin were a coiled molecule (like other proteins whose structures are known from X-ray diffraction) which, at rest, is held in a stretched condition by virtue of a se- ries of mutually repelling, charged ionic groups along its length, — COOMg+ or — NH3+, for example. Adsorption of ATP-4 to form the Michaelis- Menten complex, discharges the myosin network, permitting the interatomic restoring forces, which exist because of bent bonds, to relax the molecule to its neutralized (contracted) length. After hydrolysis, ADP"2 and P"2 desorb, because they are bound less tightly than ATP-4 and are perhaps aided by other molecular species in the vicinity. After the products have desorbed, the positive charges along the molecule lengthen the coil again, and the molecule is ready to repeat the cycle.

What is the nature of the trigger which starts ATP-4 adsorbing? The answer is not known, but the hypothesis, based on indirect (but nevertheless substantial) evidence, is that a covering molecule, the "blanket," weakly ad- sorbs on and protects the charged network of the stretched myosin. Its shape is thought to be determined partly by Mg++ ions, without which the contractile power of myosin ceases. Distortion of the shape of the blanket by the more strongly chelating (complexing) Ca++ is supposed to bare the myosin to attack by ATP-4: thus injection of Ca++ causes contraction. Nerve endings, which run almost to the membranous sheath (sarcolemma) which covers the muscle fibers, are thought by some to be capable of releasing Ca+ at the myosin sites via electrochemical stimuli propagated down nerve axons to the nerve ending, and thence down the sheath and in the Z-bands to the myosin sites.

The connectors between filaments, shown so beautifully in the electron microscope pictures of sliced muscle tissue (Figure 10-13), in this theory take on a very positive character, composition, and role: viz., the ends and par- ticular side groups of stretched myosin molecules, attached at one end to a thin actin filament, but lying within and forming part of an adjacent thick one so that shortening of the myosin molecule itself causes filaments to slide over each other, and the whole tissue to contract. The concept is illustrated in Figure 10-14. Approximate obedience of the whole muscle to Hooke's Law would qualitatively result from behavior on the molecular level. Both the chemistry of the contraction process and the physical sliding of the fibers complement the model.

290

BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

110 A

A- band "(~I000A)

Figure 10-14. Stretched and Contracting Muscle — Molecular Model. Myosin mole- cules in the thick filaments contract and expand depending upon the ionic character of the medium. Ends stick out and join to actin molecules contained in thin filament.

It is a bit ironic that, after carrying about 60 lb of these little machines, and using them himself, day and night, for many thousands of years, homo sapiens still does not know exactly how they work.

EFFECTS OF ENVIRONMENT ON CONTROL

Both nerve and muscle are pretty complicated molecular machines. The statement is also very true for the neuromuscular junction or synapse. The neuron-neuron synapse was depicted schematically in Figure 10-7. Fig- ure 10-15 is a beautiful display of the substructure of a neuromuscular junc- tion in which the nerve ending, the synaptic gap, the continuous, infolded sarcolemma, and substantial portions of two myofibrils with their thick and thin filaments and the black Z-line perpendicular to them, are all clearly visible. Repeated study of this and of Figures 10-5 and 10-13 discloses the fine, detailed design.

Although the neuromuscular system is inherently subject to disturbances of even molecular dimensions, it is remarkably well protected, and can adapt to many environmental conditions. Both the nerve fiber and the contractile molecule are buried deep within tough tissue, well fed by capillaries of the blood and lymphatic systems. Response to environmental changes is directive, and remedial action usually is swift and accurate.

However, response to the environment of radiations — both matter waves and electromagnetic — is a matter of increasing concern as our environ-

EFFECTS OF ENVIRONMENT ON CONTROL

291

^v

I

-

a4

S' J

■

m

Figure 10-15. The Neuro-Muscular Synapse (Motor End Plate). Lower right: muscle myofibrils (mf) bounded at their top edge by a continuous folded membrane. Across the gap (~500A) is the nerve-cell membrane, touched in places by fingers (sf) from the Schwann cell (Sc). Note the many little (~100A diameter) vesicles (v). The theory is that these contain acetylcholine which is released during the passage of an impulse; and that in their thermal motion they bounce against the membrane and locally depolarize it, thus to give rise to the micro end-plate potentials which occur even when the nerve is at rest. Also marked: nerve ending (n.e.), mitochon- drion (mit.), and connective tissue fibers (c.t.f.). Scale af top left: 1 micron. (Cour- tesy of B. Katz, Department of Biophysics, University College, London, and of J. Physiol.)

292 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

ment becomes "noisier." In Chapter 2, the effects of shock, blast, sound, and ultrasound were reviewed; and in Chapter 4 the effects of the warming, visible, ultraviolet, and ionizing regions of the electromagnetic spectrum were discussed. In Chapter 7 heat production, and in Chapter 8 heat loss were discussed, as also were changes in our chemical environment (poisons and catalysts — competitors) as they affect the metabolism of the system and its control. Although the details of the complicated processes of control are beyond our means in this book, enough has been introduced to illustrate the mechanisms and the A-B-C's of environmental effects — atomic, biological, and chemical, at least in general terms.

One further point will be made on the effects of ionizing radiations on the physical apparatus of control — of increasing importance, especially to medical people, in this atomic age. Nerve itself is relatively insensitive to X rays (Chapter 9). Muscle shows good resistance too: it takes thousands of rads to cause detectable damage. The neuromuscular junction, however, is much more sensitive. For instance, consider a nerve-muscle system such as the sciatic nerve-gastrocnemius muscle freshly dissected from a frog, mounted in such a fashion that the nerve can be stimulated electrically by short, square pulses of voltage applied by the platinum wire contacts refer to (Figure 10-8). If the stimulus repetition rate is chosen at about 1 pulse per sec, the muscle will respond faithfully. If now the whole is irradiated, the muscle soon stops, although the nerve continues to transmit, and the muscle will respond to a stimulus given directly to it.

Further, the neural network in the brain is now known to be affected by only a few rads; and although this radiation does not affect the motor ability of a man, there is reason to believe that short-circuiting in the network and psychological effects accrue. Since it is not likely to be the nerve cells them- selves, it is probably the synapse, or "junction box" which is implicated as radiation-sensitive.

The parallelism is clear. The neuromuscular junction and the synapse are the most sensitive parts of man's physical control system. Both of these junctions involve production of a chemical or chemicals at one spot in the junction, transport across the junction, and utilization of the chemical(s) at the other end of the junction. With the background of knowledge of the pertinent chemical and physical effects of ionizing radiations discussed in the previous Chapter, and that of the physical apparatus of control given in this Chapter, what do you think is likely to be the first molecular process to fail during irradiation of the control apparatus?

PROBLEMS

10-1: If one side of a concentration cell has KC1 at 0.002 equivalents per liter, what must be the opposing concentration so that the "membrane'' potential reaches 90 millivolts? Assume restricted diffusion.

REFERENCES 293

10-2: Two platinum electrodes placed 3.0 cm apart on a nerve fiber detect the "wave of negativity "of a transmitted impulse 0.37 milliseconds apart. Calculate the speed of transmission in meters/sec, yards/sec, and miles per hour. Compare this with the speed of sound in air (1090 feet/sec); of light through a vacuum (186,000 miles/sec); of a signal along a telephone cable (1000 miles/ sec); of the fastest thrown baseball (88 miles/hr); of the fastest sprinter (100 yds/ 10 sec).

10-3: During the testing of a reflex at the sole of the foot, the signal must travel up the leg to the spinal column and an order be transmitted back before the re- sponse can occur. If the distance is 3 ft each way, how long should the interval between stimulus and response be?

10-4: Good rules-of-thumb to remember are: (a) the speed of shortening of a striated muscle can reach a maximum value ymax of about ten times its length per sec- ond; and (b) it can exert a force which can reach a maximum Fmax of about 42 lb per sq in. of cross-sectional area of the muscle.

Assuming the model of Figure 10-5, the force-velocity curve of Figure 10-10, and the above data, calculate values of velocity with which three different weight forces can be lifted, at v/vmax equal to 0.1, 0.5, and 0.9.

REFERENCES

1. Keynes, R. D., "The Nerve Impulse and the Squid," Scientific American, 199,

No. 6, p. 83(1958).

2. Podolsky. R. D., "The Mechanism of Muscular Contraction," Amer. J. Medicine,

30,708(1961).

3. Huxley, H. E., "The Contraction of Muscle," Scientific Amer., 199, No. 5. p. 66

(1958).

4. Szent-Gyorgyi, A., "Mechanochemical Contraction in Muscle," in "Enzymes:

Units of Biological Structure and Function," O. H. Gaebler, Ed., Academic Press, New York, N. Y., 1956.

5. Morales, M. F., et ai, "The Mechanism of Muscle Contraction," Physiol. Rev.,

35,475(1955).

6. Hodgkin, A. L. and Keynes, R. D., "Active Transport of Cations in Giant Axons

from Sepia and Loligo," J. Physiol., 128,28 (1955).

7. Nachmansohn, D., "Chemical Factors Controlling Movements during Nerve Ac-

tivity, from The Method of Isotopic Tracers Applied to the Study of Active Ion Transport," Pergamon Press, New York, N. Y., 1959.

8. Penfield, W., "The Interpretive Cortex," Science, 129, 1719 (1959).

9. Walter, W. G., "The Living Brain," Penguin Books, Harmondsworth, England,

1961.

10. Shedlovsky, T., Ed., "Electrochemistry in Biology and Medicine,"John Wiley &

Sons, Inc., New York, N, Y., 1955: review papers by B. K. Bagchi, H. H. Jasper, K. S. Cole, and others.

11. Hodgkin, A. L., "Ionic Movements and Electrical Activity in Giant Nerve

Fibers," Proc. Roy. Soc, B., 148, 1 (1958); a fine review lecture.

12. Szent-Gyorgyi, A., "Chemistry of Muscular Contraction," 3rd ed., Academic

Press, Inc„ New York, N. Y., 1960.

294 BIOPHYSICAL STUDIES ON NERVE AND MUSCLE

13. Wilkie, D. R., "Facts and Theories about Muscle," Prog, in Biophysics and Bio-

physical Chem., 4,288 (1954).

14. Hodgkin, A. L., "Ionic Movements and Electrical Activity in Giant Nerve

Fibers," Proc. Roy. Soc, B., 148, 1 (1958).

15. Hill, A. V., "Chemical Change and Mechanical Response in Stimulated Mus-

cle," Proc. Roy. Soc, B, 314 (1953).

16. Paton, W. D. M., Ed. of special issue: "Physiology of Voluntary Muscle,"

British Med. Bull., 12, 161-236 (1956); see especially the papers by A. V. Hill, A. F. Huxley, D. R. Wilkie, and R. G. Bannister.

17. Bourne, G. H., Ed., "Structure and Function of Muscle," Vol. I, Academic Press

Inc., New York, N. Y., 1960; contributions by H. E. Huxley, J. Hanson, and A. Csapo.

18. Nachmansohn, D., "Basic Aspects of Nerve Activity Explained by Biochemical

Analysis," J. Amer. Med. Assoc, 179, 145 (1962).

19. Hodgkin, A. L., and Huxley, A. F., "A Quantitative Description of Membrane

Current and its Application to Conduction and Excitation in Nerves," J. Physiol., 117, 500 (1952).

20. Cole, K. S., and Curtis, H. J., "Electric Impedance of the Squid Giant Axon

during Activity, "J. Gen. Physiol., 22,649 (1939).

21. Suckling, E. E., "Bioelectricity," McGraw-Hill Book Company, Inc., New York,

N. Y., 1961.

22. Noble, D., "A Modification of the Hodgkin-Huxley Equations Applicable to

Purkinje Fibre Action and Pace-Maker Potentials," J. Physiol., 160, 317 (1962).

23. Three short papers on contraction of muscle, Nature, 167 (1-951): by A. V. Hill,

p. 377; by A. Szent-Gydrgyi, p. 380; and by H. H. Weber, p. 381.

24. Stacy, R. W., Williams, D. T, Worden, R. E., and McMorris, R. O., "Essen-

tials of Biological and Medical Physics," McGraw-Hill Book Company, Inc., New York, N. Y., 1955: Chapters 32 to 34.

25. Brazier, M. A. B., "The Analysis of Brain Waves," Scientific American, 206, 142

(1962).

CHAPTER 11

The Language and Concepts

of Control

The natural systems are of enormous complexity, and it is clearly neces- sary to subdivide the problem ....

The first part of the problem [is] the structure and functioning of such elementary units individually. The second part of the problem consists of understanding how these elements are organized into a whole, and how the functioning of the whole is expressed in terms of these elements ....

The number of cells in the human body is somewhere in the general order of W15 or 10m. The number of neurons in the central nervous system is somewhere in the order of 10w . . . . All artificial automata ["thinking machines''''] made by man have numbers of parts which, by any comparably schematic count, are of the order of W3 to W6 . . . . The prototypes for these [living] systems are the modern computing machines ....

[However], whereas I can conceive of a machine which could reproduce itself, I cannot imagine a machine which could create itself/ (John von Neumann, Vanuxem Lectures, Princeton, 1952.)

INTRODUCTION

In the very first chapter of this book we introduced rather superficially the concept of man as an integrated system operating in continuous ex- change with his environment. During the next few chapters we dwelt on the forces, momenta, and energy which comprise this exchange, and showed what these are, their properties, and their effects on the living system. Through the middle of the book we dwelt on the workings of individual parts

295

296 THE LANGUAGE AND CONCEPTS OF CONTROL

of the human being, discussions proceeding from first principles of physics and physical chemistry. Then, to introduce control biophysics, in Chap- ter 10 we considered some of the physical aspects of control of the system. All this was in mechanistic terms, based on the movements of atoms and molecules.

In Chapter 8 we saw what happens if the speeds of biological processes are not regulated and intermeshed. To illustrate the molecular mechanics of control, we chose nerve and muscle, and discussed how commands are passed down the nerve, across synapses, and then across the neuromuscular junction to cause contraction. Probably the stimulation of the endocrine gland system to chemical activity would have served equally well, although to use that example would have required a rather bold and risky step into biochemistry, which probably has the most prolific scientific literature of our time, whereas there are plenty of problems yet in biophysics which warrant attention.

The principles and the language of the engineering concepts of control are universal, however. They refer equally well to the monitoring of a chemical processing plant, to the guidance of an intercontinental ballistic missile, to the control of a large telephone exchange, or to a human being. There are persons working in the computer technology who now believe that there is a critical complexity to control systems above which they will have enough versatility to be completely self-determining, like man, in many situations: "ultrastability," Ashby calls it. The clever English logician, A. M. Turing, was one of those persons; he predicted, slightly before his death in 1954, that by the year 2000 a computer will be built which will confound its interroga- tor with its ability at intellectual repartee! Most others are much more con- servative. In any case, as von Neumann indicated in the introductory quota- tion, the Turing computer would need a prodigious 109 (one thousand mil- lion) parts and cost one or two orders of magnitude more in dollars! With these possibilities, however, it should not be necessary, in view of the lessons of history, to recall that careful definitions of general terms such as "intel- ligence," "learning," etc., should precede philosophical and scientific dis- cussions of these questions. Here we confine ourselves to subject matter which is experimentally testable (at least in principle), and therefore we are able to leave the philosophical discussion of these terms to others.

THE SYSTEMS CONCEPT REDEFINED

Man In His Environment

Life is a continuum of events, with no isolation. A system is a collection of things or events contained within some specified boundary. Man is such a

THE SYSTEMS CONCEPT REDEFINED

297

system, or more properly a subsystem operating within a larger system — the environment. To man there are inputs, and from man there are outputs. Inputs are information, or noise, and energy. Outputs are information, work, or losses. (One would hope that only some of his output is noise.)

Figure 11-1 illustrates this concept. Note the directions indicated by the arrows. For example, information enters through the sensory organs which are responsive to chemical, electrical, gravitational, electromagnetic, and mechanical stimuli. It enters raw, essentially unsorted, except for the fact that only part of the information available from the environment is able to enter through the five senses. For example only those electromagnetic radia- tions of wave length 4000 to 7000 A are recorded through the eyes, and some in the infrared region is detected by mechanoreceptors just below the sur- face of the skin. Otherwise the whole spectrum of electromagnetic radia- tions in the environment so far as we known goes undetected.*

MAN

ENVIRONMENT

				ene rgy
	i nforma t ion

^.sensory
			organs work 8 losses
		in formation te»

Figure 11-1. The Human Being as a "Black Box" in His Environment.

Some of the inputs are ordered, sorted, and organized (lectures to students presumably are). This is true information. Some inputs are not ordered, nor are they even useful; this is noninformation, or noise.

Work and losses, as well as thermodynamic and practical efficiencies, were discussed in Chapter 7, and the reader should recall again the prin- ciples of available and unavailable energy, and of efficient and nonefficient operation of machines.

*This raises the irrelevant but interesting question of how the still-controversial extra- sensory perception (ESP) might occur, with its manifestations of telepathy, clairvoyance, etc. Supposing we accept the psychological evidence in favor of ESP, the job in biophysics is to try to understand how ESP could occur. Speculations can take three directions. Thus informa- tion reaches our central nervous system directly (i.e.. not via the senses) as: (a) electromag- netic radiations of wave lengths out of the range of the senses; (b) matter waves of wave lengths out of the range of the senses; or (c) some new, yet undiscovered radiation

298 THE LANGUAGE AND CONCEPTS OF CONTROL

Information and Entropy

The broad use of the term "entropy" as a quantitative measure of the amount of disorder in a system, or subsystem, was introduced in Chapter 7. Now we carry the concept one step further. For communication, which re- quires a description of a system in words or codings, the simpler the system the simpler the information needed to describe it. Four sticks standing fixed in a row (||||) is a very simple system, A, easily described; but the same four sticks comprise an infinitely complex system, B, if the four sticks are thrown off a roof-top and each stick allowed to assume any position and degree of rotation during fall. The information required to describe A unambiguously is small; likewise its entropy or disorder is low. By contrast the information required to describe B unambiguously is relatively very large; its entropy or disorder is high.

Therefore, a measure of the quantity of information needed to describe some- thing is the entropy of the system being described.

It follows that if the information, S, put into a computational system such as man becomes distorted for one reason or another, the changed informa- tion is now 5" + AS, where AS is the distortion. It is always positive, in- creasing the entropy.

However, if two inputs, Sl and S2, are faithfully recorded and analyzed, and if from the two informations a third piece of information, a synthesis of the two, occurs, then the total information needed to describe S} and S2 is less than the sum 5\ + S2, and the total entropy has thereby been decreased .... One's information is now better organized. One remembers now a simple principle which describes both systems 1 and 2.

Measurement

Measurement implies a reference. What is measured is a difference be- tween two quantities, one of which is taken as the reference, against which many similar quantities are measured. The fact that no two physical beings are in all respects identical implies variation. Variation in turn introduces uncertainty.

There is an inherent uncertainty in all measurement, a principle first propounded by Heisenberg. The formal statement of this is known as his "uncertainty principle." It takes various forms, a simple statement of which is the following: To make a physical measurement, energy must be trans- ferred between the object and the measuring device; otherwise there is noth- ing to detect; this transfer introduces uncertainty, because the object is not now the same as it was before the energy was transferred: the smaller the object the more difficult it is to measure its properties.

However, in the macroscopic physical world, objects are big enough so that this uncertainty is far smaller than are gross errors in measurement,

THE SYSTEMS CONCEPT REDEFINED 299

be they random or constant errors. No measurement is likely to be perfect. We are always faced with this probability of error, and of (biological) varia- tion in the thing being measured.

The human machine is subject to error in measurement, just as is any other machine. It is no accident that athletic competitions, especially by professional athletes, are described as "games of inches," the differentiating factor being the ability to estimate distance under great psychological stress.

In summary, it is a measurement which is fed back into a computer to guide it in making corrections to its actions. This measurement is ot the dif- ference, A, between where one is and where one wants to be — that is, of the error. The error is increased by noise.

Noise

The subject of the detection of a signal of information (energy) over back- ground was discussed in Chapter 3 in the discussion of sensitivity of a detec- tor and the VVeber-Fechner Law. The principles introduced there apply also to the detection of information to be fed to a computer. If the source provides a strong signal over background, the detector will feed a correspondingly strong signal to the computer. If the background noise is high (i.e., the signal-to-noise ratio is low) the signal sent to the computer may not be in- telligible (discernible from the background). Strength of the signal, back- ground noise, and degradation of the information by noise introduced in the detector determine what the computer receives as input.

Unfortunately there usually are many strong signals entering a detector, only some of which are useful. Those which are not useful are also noise, like the background. The machine must be able to classify signals: to accept the information and by-pass the rest. One of the most useful systems yet built to separate information from noise is the EEG analyzer, a machine which scans the information and sorts the rather complex total waves into their three or four main components.

Continuously confusing the control circuits of a human being is an un- remitting input of noise — disordered, and perhaps not even useful informa- tion. Noise can take several forms. First of all it may be of either external or internal origin. External noise comes in from the environment through the senses. It is probably better to call it incomplete rather than disordered, for there is order and regularity reaching our senses from everywhere about us in nature. The trouble arises because we have only a limited eapa< it\ or interest — subject to, or determined by our freely-chosen goals in life. In other words, what is useful, interesting information to one man is noise to another; and for one man, what is noise at () P. M. may not be so at 9 A. M. (traffic information, for example). This is unfortunate, but nevertheless true. It is unfortunate because it means that two men with a common interest in

300

THE LANGUAGE AND CONCEPTS OF CONTROL

some narrow field may each have rejected as noise some information border- ing on the subject which would be more pertinent to their discussions than either realizes. This is one of the reasons for disputes, sometimes very heated ones, between logicians who are specialized in different fields. Then of course there are man's errors in logic — and they are a fact too. Over even an hour's test, the adding machine will demonstrate man's errors in logic very vividly.

We have seen that there is variation in nature. There is also order. There is variation in the physical structure of man's sensory organs. Therefore the nonverbal impressions which two men have of the same object may be quite different. The verbal impression each would give — thanks to training, experience, and definition — would, however, be about the same. It is gen- erally accepted that the essentials can be abstracted by one and com- municated to another by words. The variations can be described also, if they can be observed. Further, McCulloch and Pitts showed in a famous deduction that if anything can be described fully in words, the description can be programmed accurately into a man-made computer, provided the computer is comprehensive enough. Therefore our own "built-in" com- puter, as well as the man-made one, should have the physical capability to receive (as well as give) a complete description. Yet language has a drift in meaning over a course of time. Does the concept also drift?

Feedback

Control of a system by its computer is accomplished by feeding back into the controller the result of the measurement of difference or error (Figure 11-2). The computer can then dispatch the corrective order, the order which when carried out will reduce or eliminate the error. This is accomplished in mechanical and electrical machines through what is called a control am- plifier, a device which takes the determined error, amplifies it, and inverts it as the corrective "order" to the process. In the living thing this is ac- complished either by the conditioned reflex of the autonomic nervous sys- tem, or the voluntary control by the central nervous system.

(a)

(b)

Figure 11-2. The System Diagram, I. (a) General feedback only; (b) General plus

particular feedbacks.

THE SYSTEMS CONCEPT REDEFINED

301

Since the corrective order must operate in a direction opposite to the measurement of error, the principle is one of negative feedback. For instance, if a factory's production occurs at a rate larger than the rate of sale, product soon piles up: the amount of product, measured against some economically sound inventory, increases. The difference, A, increases. Fed back into the production line, this information (A) is used to cause a decrease in the rate of production, so that the excess inventory will decrease toward zero. Again, in cholesterol synthesis, the rate is controlled by enzyme-catalyzed proc- esses in which there exists inhibition by a reaction product. Thus, as the cholesterol concentration gets larger, more of it absorbs on the enzyme, and the over-all rate of synthesis slows down because of the inhibition. Hence there can be general feedback to control the over-all process, or there can be particular feedbacks to control small parts of it (Figure 11-2 (b) ) .

As a whole, the human body obtains feedback from the five sensory organs plus a number of other internal detectors such as the organ of balance in the inner ear and the temperature controller at the base of the brain. Man's thermostat, in the hypothalamus at the base of the brain, was recently appreciated for the first time. The trimmer, or fine controller, is the cerebellum.

The human body has the physical properties of a zero-seeking servo- mechanism — a device which sets for itself a goal, attempts to achieve that goal, then measures the error in the achievement before it feeds this informa- tion back negatively through a control amplifier so that the error is can- celled. The system diagram in its barest essentials of general feedback is given in (a) of Figure 11-2, while (b) illustrates the case oi particular feed- backs.

The feedback and the amplification of the error by the control ampli- fier, are both critical if satisfactory control is to be achieved — as we can see from Figure 11-3. The broken line denotes the task and the solid lines the

the task

overshoot

	error A
_ -1 feedback	J\ — servo
^ ■ — •'C y^.	'-'». — ">.
	negative feedback

TIME

(a)

(b)

Figure 11-3. The System Diagram, II. (a) Hunting, overshoot, and "dead-beat" approach to the task; (b) Operating process and negative feedback.

302 THE LANGUAGE AND CONCEPTS OF CONTROL

achievement for an elementary process such as heating a house. More sensi- tive detectors provide more accurate feedback and reduce the oscillation about the task. The loss of fine control in a man's attempt to walk along a straight line under the effects of drugs, disease, or alcohol is well known.

A recent innovation into the heating systems which the human body has had for thousands of years is the facility for anticipation. This takes two phy- sical forms in the human being, only one form in the heating system. The one which is common to both, is the early-warning system: the external thermostat in the heating system, which predicts a change inside as soon as the weather changes; the kinematic (or kinesthetic) sense, for example, in the human which tells him where his hands are even when his eyes are closed. In addition, the human has a memory, which helps his anticipation by extrapolating from the present situation into the future along a path sug- gested by previous experience. Modern computers have the memory circuits and the extrapolation circuits too.** Whether man will eventually be able to make computers which can abstract and then extrapolate with abstrac- tions, as man can do, remains for the future to answer.

The sensory detectors are so sensitive in the human, and the cerebellum such an effective trimmer on the control apparatus, that man is the ideal ex- ample of a "dead-beat servo," with no cycling at all about the task .... This is true only as a first approximation, however. Thus the physical trim of a trained athlete or of a practiced surgeon is far more precise than that of his neighbor. Similarly, those who are afflicted with Parkinsonism or al- coholism are less precise in their physical and chemical process control. Precise control of the biological chemistry and physics is at the very root of the prevention and cure of disease, and of life itself.

Memory, Concept and Implementation

The mind stores information. Physical machines can be made to do this by (a) magnetic tapes or magnetic cores, (b) on-or-off relays, (c) slow pene- tration processes in which electric or sonic signals bounce around inside crystals for a time before escaping, and (d) electrochemical devices such as capacitors. In fact the machine can be programmed to collect information while it is operating and use it thereafter, thus closely simulating man's memory. A recent postulate about the physical nature of neural memory apparatus is that the repeated, passing electrical signal distorts the RNA

** Perhaps the earliest popularly recognized and amusing example of machine out-anticipat- ing man came during the counting of the U. S. Presidential election returns in 1 948. The com- puter, UNIVAC, on the job seriously for the first time, started predicting a Truman victory at about 8:15 P.M., much to the derision of the human political pundits. By 11 P.M. the pun- dits were beginning to waver, remarking that the pollsters could possibly be wrong. Mean- while UNIVAC was pounding out a 99 per cent certainty for Truman. Dewey finally con- ceded to Truman at 2 A.M !

THE SYSTEMS CONCEPT REDEFINED 303

molecule for a time sufficiently long to give the oddly-shaped protein mole- cules an opportunity to synthesize. These then slip into the chemistry of the cell and perhaps later affect the rate of a reaction which guides the neural switching pattern which is characteristic of the fact so "memorized." The machine can be taught a rudimentary classification, and can thereafter classify appropriate inputs. That a machine could be made which can take random information and develop a classification, as Farley says,17 "is not impossible; it is just excruciatingly difficult/'

However, the question of whether a machine can be made which will be able to develop a concept or abstract idea is destined to remain unanswered for the foreseeable future, for it is subject to only one experimental test: a machine must be built capable of developing a concept, and then it must be able to tell us about it! As a first step a machine must be developed which can do abstract mathematics. Already the groundwork is being laid. In the meantime, concepts as such are probably better analyzed from within the framework of epistemology, in which, like mathematics, logical self-consis- tency is the final criterion of certainty.

Physically very real, however, is the implementation of a concept through the action of physical things. An artisan produces with his hands, in real ma- terials, a structure in conformity with the concept in his mind. Having made one, he can make others. Having been told of an object in great enough de- tail (i.e., having been given a concept), he can make the object. Thus the surgeon fashions a heart valve in conformity with a concept in his mind; but he modifies in detail as he goes along if he finds odd shapes or formations which need correction.

Control Biophysics

The discussion in the proceeding sections has defined terms for com- parison of the modern computer with man's brain as units of control. Both can accept, store, and redeliver information, and in this sense can learn. Both can do logical arguments, (i.e., decide on the basis of premises), do arithmetic and solve equations. Both can issue commands which result from logical arguments, and can receive feedback which tells whether or not the commands are being successfully carried out.

There are major differences. The brain is usually able to find another route to accomplish a task if the direct route is physically damaged. Gen- erally, malfunction of one component of a machine will stop its operation, al- though Ashby's machine was said to have sufficient parallel circuitry that he could rip out a wire at random and the machine still function. Machines are generally much more accurate and much faster than humans at computa- tion. Machines have not yet been made which can do abstract mathe- matics, or do pattern recognition other than rudimentary classification, al-

304 THE LANGUAGE AND CONCEPTS OF CONTROL

though the best informed opinion today is that it will be possible, but diffi- cult, to construct a machine to do such work. On the interesting subject of self-control or self-determination, which implies judgment of what is good and bad, and free choice to do either, nothing can be said about what a machine' of the future will be able to do. Today's machines are completely deterministic — as are many of man's acts.

The question of whether creativity and the emotional, psychic, and reli- gious experience of man can be contained within the physical structure of the human brain is unanswerable from the framework of science, because the extrapolation from experimental test is simply too far to be reliable. This will be especially evident to those doing experimental work even in heavily experimented subject matter: the results are, even there, always full of sur- prises! To assume an answer to this question, then, would be unscientific, since experimental verification is not yet possible.

A more useful question for control biophysics is: "How far can physical equipment be made to go toward reproducing the functions and behavior of man's brain and mind? How does the brain actually do the job of con- trolling so finely the human body? The answer seems to he in models or representations.

This is the interest of biophysics in Samuel's checker-playing machine; Shannon's chess-playing proposal; the U. S. Naval Research Laboratory's self-replicating machine; psychologist Ashby's homeostat, which adapts it- self into compatibility with a new environment; Walter's Machina Speculative and MIT's mechanical hand— robots which have component parts which give them many of the response characteristics of animals; and other ma- chines, some much more complex.

Within the past few years there has been considerable effort expended in making models of the nervous system. The work falls roughly into two forms In one, man attempts to represent or reproduce the biological phe- nomena as closely as possible. In the other he explores the behavior of simu- lators-electronic elements, for example, whose electrical behavior is similar to that of the nervous system. For example, M. L. Babcock, F. Rosenblatt, B. G. Farley and L. D. Harmon have all done intriguing pioneer work. Farley et al. have simulated the firing pattern of a two-dimensional array of neurons (Figure 11-4) by programming their TX-2 computer with cor- relative information on 256 circuits, each of which can do several of the tricks that a single nerve cell can do. An input (stimulus) at some point causes a firing pattern to occur throughout the network; and, if properly displayed on a television screen, this firing pattern can be watched as it progresses. With such an apparatus a study can be made of the characteris- tics which lead to different firing patterns. There and elsewhere the follow- ing have been simulated: the all-or-none firing pattern of the axon, the slow

ANALOGIES 305

axon

nucleus

neuron Figure 11-4. A Neural Network.

chemical step of the crossing of the synapse, and the smaller, graded, at- tenuating potential induced at the far side of the synapse. Because other properties such as a slow wave of electrical activity on the neuron itself, vari- able spike amplitude, varying wave form and overshoot of the spike, and shifting baseline potentials are ignored, the simulations are still approxi- mate. Replicated by such simulation have been: (a) intensity of electrical activity as a function of time; (b) burst firing; (c) repetitive firing; (d) ac- commodation, and change in excitability. Further, the simulated circuits have disclosed certain conditions under which the firing frequency of the net- work will shift. This is a clue from the machine about a phenomenon which has not yet been observed experimentally by neurophysiologists. Thus workers in the field hopefully look forward to advances in man's understand- ing of his brain through its simulation by machines. The reader is en- couraged to study the papers by Bullock,18 and of Harmon,19 and to treat himself to the optimism of Reiss,17 and the careful analysis of Farley,17 thereby to prepare for himself a proper perspective of this exciting new aspect of biophysics.

We turn now to an outline of the principles upon which are based the two great classes of computers, digital and analog.

ANALOGIES

The Digital Nature of Nervous Propagation

The electrochemical burst arising at the point of stimulation and moving rapidly along the nerve, and called the impulse, was discussed in Chap- ter 10. To a first approximation, the nerve is either stimulated into action or it is not. This is the "all-or-none" property. The stimulation must be

306 THE LANGUAGE AND CONCEPTS OF CONTROL

above some critical minimum strength,*** otherwise the nerve will not fire. That the threshold is not really as critical as is often claimed, and that the spike, or "wave of negativity," modifies its shape under certain circum- stances, are useful facts to know and are thought by some physiologists to be more important that the spike itself. The main point for the moment, however, is that the passage of a stimulus is a binary process, to a first ap- proximation always the same. Only the pulse-repetition frequency (pulses per second) can change; this is frequency modulation.

For example, in the case of transmission of a signal from the pressure- sensing device which reports blood pressure, the nerve encodes the informa- tion as a frequency: the higher the pressure the greater the number of pulses per second (e.g., 125 pulses per sec for high pressure, 70 for low). There is an inherent accuracy in the counting, or digital, method of transmitting in- formation— more so than in the decimal-expansion method. The accuracy comes from repetition, or redundancy.

The Digital Computer

Information can be fed into a machine in either of two ways: intermit- tently or continuously. If done intermittently, it takes the form of pulses of energy. The number of pulses then becomes the important thing, for in the number is contained the information in question. Thus five pulses means one thing, three another, and so on. (The Morse code was an early example of this idea.) Since number is important, counting and recording of number are necessary. Therefore, the performing of operations on the information becomes simply a matter of arithmetic, nothing more. Since it is numbers, or digits with which the arithmetic is done, a machine which processes in- formation in the form of numbers is known as a digital computer. An adding machine is a primitive example; IBM's "650" has intermediate complexity; and IBM's 7090 (see Figure 11-5) is a 20,000-component, complicated ex- ample. It has 32,000 words of high-speed memory and can add two 10-digit decimal numbers in 4.5 microseconds — facts to be compared with 2000 words for the 650 and an addition time of 800 microseconds.

In computation with digits we normally use the decimal system, with units often. This system was chosen quite arbitrarily by our ancestors dur- ing a process of arithmetical evolution in which they counted in twos (hands), tens (fingers), twenties (fingers and toes), etc. Other systems could have been chosen equally well. For instance the binary system (units of two), it is now realized, more closely represents many naturally occurring phenomena than does the decimal system. Thus only two digits are needed

***That is, a minimum energy must pass through the nerve membrane — most simply stated: a current, at some voltage, for some length of time (amps x volts x sec = joules).

ANALOGIES

307

to describe the switch on your reading lamp because there are only two positions, "off" and "on." The former is recorded by the digit zero (0) and the latter by the digit one (1).

Figure 11-5. IBM's 7090 Digital Computer — A typical installation. A big, fast, transis- torized machine, it can be used to simulate neural networks. To the right of the operator's console are the card reader and printer; to the far left are the magnetic tape units. (Cour- tesy of International Business Machines, Inc.).

At the same time, the binary system of two digits can nicely represent in- formation which is transmitted as pulses, because the information-carrying equipment either is or is not delivering a pulse of energy at any particular instant. If it is, it is described by the digit 1; if it is not, by 0. Remember now that information is carried along the nerve in the form of electrochemi- cal explosions. The nerve is either firing (1) or it isn't (0). Therefore, the all-or-none law is basically a physical manifestation of the binary number system.

In summary, digital computers built of mechanical or electric binary ele- ments (e.g., relays) not only compute, but also provide a prototype or model for the study of nerve transmission and neural switching.

The Analog Computer

This second general class of computational machines is built around the fact that useful electrical or mechanical analogies can often be made of phys-

308 THE LANGUAGE AND CONCEPTS OF CONTROL

ical phenomena, analogies which can be used to enable a continuously varying measurement to be recorded, amplified, analyzed or operated upon, and the results used as an immediate control on the process. Analogies can be very simple. A small-scale drawing can be used in the solution of a geo- metrical problem of finding the height of a tree from the length of its shadow. The sliderule is an analogue of logarithm tables. The addition of two con- tinuously varying numbers can be done by superposing two electrical cur- rents, each in a separate circuit and proportional to one of the numbers, and measuring the total current through a common part of the circuit.

This principle has been built into analog computers. Much of the analog computer is electrical, but mechanical wheels, gears, cams, and levers, and magnetic and electromagnetic devices are used wherever they can provide a closer analogue to the real process being represented. Such computers are ideal instruments for solving simultaneous and differential equations, as will be shown in an example in a later section.

Many continuously varying systems are suited to analogies of this sort. Generally speaking there are continuous processes in the living thing, the most easily recognizable ones being at the molecular level, continuous ex- pression of which was detailed in Chapter 8. The general control of the sys- tem is a result of control of each process at the molecular level. Thus the speeds of the parts control the general health of the whole, and the general health of the whole in turn adds the fine adjustment to the speeds of the parts.

However, on a larger scale analog control is not so easy to recognize, partly because the physiological basis for digital control by the pulsating nervous system is easier to study experimentally than the continuous varia- tion which are superimposed on the pulses; and partly because this language of control has not yet been successfully used to describe chemical regulatory systems such as the endocrine glands. * One can find many examples of analogies used disparts of a controlling system in the living thing, but one .is hard put to it to describe clearly at this time a full analog computer which is in complete control of part of the living system. Many neurophysiologists now feel that the digital computation may be only a small part of the complete story of control, even in the central nervous system.

New Dimensions

In summary, then, the human being, and indeed every living organism, has control operations which might be described in the same terms used to describe digital and analog computers. How fruitful this description will

+ See Schueler's recent book for examples of pharmacological control.

THE COMPUTER IN BIOLOGICAL RESEARCH 309

be in man's understanding of his control biophysics is hard to predict; but today it is an exciting avenue by which people are approaching the subject.

Quantitative description of these ideas is developing rapidly, as an inte- gral part of missile and space technology, in which man has control of the characteristics of the components, through design. The neuronal circuit, with switches (synapses) (Figure 1 1-4), is about a billion times smaller than the vacuum tube circuit, and perhaps about a million times smaller than the transistor circuit, and a thousand times smaller than thin-film, solid-state circuits now in the research stage. The neuron operates on the movements of ions rather than electrons, and much has yet to be learned about its opera- tion. Further, the number of "components" in the brain is about a million times the number in the largest of today's computers. Therefore it is certain that quantitative description of the control circuitry of the central nervous system is a long way off !

Inherent in all these systems is an error, or noise, or background, above which the information, the signal, must be distinguished. It is easy to build an analog computer with a precision of about 1/1000; harder to build one with 1/10,000: and impossible to build one with 1/100,000 or less because machining of parts and electrical measurements cannot be made with greater precision. By contrast, simply increasing the number of components can increase the precision of the digital machine to 1/10,000,000,000, if it is desirable and practicable.

Since the central nervous system operates with about 10,000,000,000 com- ponents, or neurons, and since it has both digital and analog facility, the problem of understanding this system is obviously not an easy one. Al- though the normal operation of this system is wondrous enough, errors in "switching" can give rise to a whole host of disorders — problems not only for the neurologist but also some that are likely to keep the psychologist and psychiatrist in business for a long time to come.

THE COMPUTER IN BIOLOGICAL RESEARCH

As a tool in medical research, the computer can do many useful things. The day may not be too far off, for instance, when medical clinics will be equipped with general diagnostic machines which, when properly fed with factual information on symptoms, will not only punch out a statement of what the possible diseases are but also arrange them in order (with the most probable one at the top) and state what further examinations can most profitably be done to save the time of the physician and the money of the patient. The machine-processing of records and accounts in clinics and hos- pitals is closer still. With us now is the use of computational machinery to help the researcher in studies of those biophysical problems in which rea- sonably precise quantitative measurement is possible. Rapidly maturing as

310 THE LANGUAGE AND CONCEPTS OF CONTROL

an aid in diagnoses is the determination of rates of specific steps within an over-all process from measurements of those variables which are susceptible to measurement. It will be recalled that in Chapter 8, in the discussion on the steady-state, we emphasized how necessary it is that all the small steps of a process should proceed at some well-defined rate if the over-all steady- state is to be maintained. Further, we discussed at length the factors upon which rates depend. The use of radioactive tracers to examine the steady- state was described in Chapter 5.

The topical and interesting, if not classical, study of the biochemical kinetics of iron metabolism in the red blood cells, work which was reported by Huff and Judd1 in 1956, ties many of these ends together. It is a very instructive work because (a) measurements were made of iron turnover rate by a radioactive tracer technique, using the hard gamma emitter, Fe59; (b) they were analyzed by means of an analog computer programmed to a model based on known and suspected biochemical kinetics of iron; (c) the comparison was made between normal human beings at atmospheric and at reduced pressure; and those with polycythemia vera, aplastic anemia, and other blood diseases; (d) both the factual information and the results of the analyses have unquestioned clinical importance; and (e) the report is written clearly and concisely, and is an excellent source of the detail which cannot be given here.

Kinetics of Iron Metabolism

The study by Huff and Judd was on the kinetics (rates and mechanism) of iron in human blood plasma, as followed by measuring turnover rates of Fe59. The iron exchanges with various "pools" (Figure 1 1-6), which are not precisely specified because they are not precisely known. Two possibilities are shown in the figure; but many other pools of iron-containing pigments, such as peroxidase, catalase, cytochrome, and myoglobin are ignored. Also the iron may exchange with that from the intestine as well as that recircu- lated from the bile. Therefore this work must not be considered complete.

A microcurie dose of tagged iron was administered intravenously in the chemical form in which it naturally occurs in the blood. From time to time after injection, blood samples were taken and the plasma's radioactivity measured. At the same time the body was surveyed outside with a highly collimated Geiger counter which would pick up the flow pattern by detecting Fe59's hard gamma rays.

For the first few hours the loss follows the "natural" law that the rate is proportional to the amount present, or

da , = ka

dt

THE COMPUTER IN BIOLOGICAL RESEARCH

311

where a is activity in per cent of initial value, and k the specific rate of loss or iron, in hours-1. Values of A; for different subjects are given in Table 11-1.

u	ki	V	k3	w
iron exchanging with plasma but not going directly into red blood cells	iron in red blood cell precursor system
k2	all of the iron in the plasma	-k<	k5

(a)

iron exchanging with plasma but not with iron of spent red blood cells, (storage phase)

iron exchanging with plasma and aiding the break- down of spent red blood cells (reticulo endo- thelial phase)

m

all of the iron n the pla sma

(b)

iron i n red blood cell precursor system (bone marrow)

Figure 11-6. Schematic Flow Sheet for Production of Red Blood Cells, Showing Two Models or Theories, (a) and (b), of the Metabolism of Iron. The k's are specific rate con- stants, assumed to be for first-order reactions.

If this law were obeyed rigorously, the story would now be complete. However, this law is seen to be badly broken if measurements are continued for a few days instead of a few hours: the rate constant diminishes as the

TABLE 11-1. Values of the Turnover Rate Constant* for Iron in Blood Plasma.

Subjects

k(hr-')

Normal subjects Polycythemia vera Aplastic anemia Normal subjects taken to

1 5,000 ft above sea level Normal subjects living at

15,000 ft above sea level

0.18to0.21

0.9 to 1 . 1 (very fast turnover) ~0.05 (very slow turnover)

0.3 to 0.4

0.25 to 0.30

*For the first few hours onlv.

312 THE LANGUAGE AND CONCEPTS OF CONTROL

fraction of injected Fe59 diminishes in the plasma. The analysis was in- tended to suggest why.

Recollection of the content of Chapter 8 will permit verification that the rates of the various steps in these two schemes (Figure 11-6) are given as follows:

du/dt = — k\u + k2v

dv/dt = +k-[u — (kn + k3)v + kAw

dw/dt = +k3v - (kA + k5)w for model, or scheme (a), and

dx/dt = -kxx + k2y

dy/dt = +A,.v - (k2 + £3 + k5)y + k4z

dz/di = + k-iy - k4z

dm/dt = + k5y — kbm

for model, or scheme (b) in Figure 1 1-6.

The problem for the REAC C-302 analog computer, then, was to find a set of solutions to these equations so that the concentrations u, v, w, and x, y, z, and m (all in per cent remainder of radioactive iron added) could be ex- pressed as a function of time, from time zero, when the tracer was added, out to about ten days, the last of the measurements. More specifically stated, the problem was: For what values of the rate constants, k, would the concen- trations v and y, for example, have values which corresponded most closely with the concentrations measured by sampling? If the k's could be so found, then some knowledge would exist about the relative rates of the various metabolic processes into which this added iron enters from the plasma.

We shall not discuss how the computer was programmed, for this is in- volved and would serve no useful purpose here. Suffice it to say that the values of A could be adjusted as voltages on control potentiometers, much like the volume control on a radio. They could be adjusted and readjusted until the best fit of the experimental data was obtained. Some final, best-fit values are given in Table 11-2, from which it can be seen that the rates of the processes defined by Figure 11-6 do indeed change markedly from nor- mal to diseased patients. Note, for instance that the slow step in the aplastic anemia case is the synthesis of bone marrow (A5 ), while this is just the proc- ess that runs amok in polycythemia vera.

This is only a first approach to this problem, and is described here pri- marily to illustrate the method, and the power, of machine-aided analysis. As the authors state, in future runs certain other experimentally measurable

REFERENCES

313

TABLE 1 1-2. Table of Rate Constants and Steady-State Concentrations Evaluated by Ana- log Computer and Giving Best Fit to Experimental Results.

	Normal	Polycythemia	Aplastic
	Humans	Vera	Anemia
*1	12	34	1.2
k2	80	495	150
*3	200	960	120
*4	62	280	108
h	395	2000	50
K	40	44	40
X	29.5	27.5	1480
y	4.42	1.89	11.1
z	14.3	6.5	12.4
m	43.7	85.9	13.8

quantities will be fed into the analysis: red cell turnover rate, iron turnover in the percursor step, the side reactions in the reticuloendothelial phase and in the iron pigments, for example, plus better pre-experimental clinical data.

REFERENCES

1. Huff. R. L. andjudd, O. J., "Kinetics of Iron Metabolism," Ada. in Biol, and

Med.Phys., 4,223 (1956).

2. von Neumann, J., "The General and Logical Theory of Automata," in "The

World of Mathematics," J. R. Newman, Ed., Simon & Schuster, Inc., New York, N. Y., 1956, p. 2070.

3. Hutley, A. M., "The Engineering Approach to the Problem of Neural Organiza-

tion," Prog, in Biophysics and Biophysical Chem., 11, 26 (1961).

4. Walter, W. G., "The Living Brain," Penguin Books, Ltd., Harmondsworth,

England, 1961.

5. Ashby, R., "Design for a Brain," Chapman and Hall, Ltd., London, 1952.

6. Rothstein, J., "Communication, Organization and Science," The Falcon's Wing

Press, Indian Hills, Colorado, 1958.

7. Stacy, R. W., "Biological and Medical Electronics," McGraw-Hill Book Co.,

Inc., New York, N. Y., 1960.

8. Abrams, Sir Adolphe, "The Human Machine," Penguin Books Inc., Baltimore,

Md., 1958.

9. "The Language and Symbology of Digital Computer Systems," R.C.A. Insti-

tutes, Princeton, N.J. , 1961.

10. Wiener, N., "Cybernetics," John Wiley & Sons, Inc., New York, N. Y., rev. edn..

1961.

1 1 . Cherry, C, "On Human Communication," John Wiley & Sons, Inc., New York,

N. Y., 1957.

314 THE LANGUAGE AND CONCEPTS OF CONTROL

12. von Neumann, J., "The Computer and the Brain," Yale University Press, New

Haven, Conn., 1958.

13. Adrian, E. D., Bremer, F., and Jasper, H. H., Eds., "Brain Mechanisms and

Consciousness," Blackwell Scientific Publications, Oxford, 1954.

14. Shannon, C. E., "Mathematical Theory of Communication," University of Illi-

nois Press, Urbana, 111., 1949.

15. Thomson, Sir C, "The Two Aspects of Science," Science, 132, 996 (1960).

16. Teilhard de Chardin, P., "The Phenomenon of Man," Harper & Bros., London,

1955.

17. Barnard, G. A., Chairman, "Proc. 1962 Spring Joint Computer Conference,"

The National Press, Palo Alto, California, 1962: see papers by Ernst, Reiss, Farley, Harmon and Tiffany.

18. Bullock, T. H., "Neuron Doctrine and Electrophysiology," Science, 129, 997

(1959).

19. Harmon, L. D., " Artificial Neuron, "Science, 129,962 (1959); see ref. 17 for sum-

mary of more recent work.

20. Rosenblatt, F., "Perceptron Simulation Elements," Proc. Institute of Radio Engi-

neers, 48,301 (1960).

21. Minsky, M, "Steps toward Artificial Intelligence," Proc. IRE, 49, 8 (1961); see

also his bibliography on artificial intelligence, IRE Trans, on Human Factors in Electronics, March 1961.

21. Davis, M., "Computability and Unsolvability," McGraw-Hill Book Co., Inc.,

New York, N. Y., 1958 (interpreting Godel's incompleteness theorem as ap- plied to computers).

22. Scheuler, F. W., "Chemobiodynamics and Drug Design," McGraw-Hill Book

Co., Inc., New York, N. Y., 1961 .

23. Donaldson, P. E. K., "Electronic Apparatus for Biological Research," Butter-

worth's Scientific Publications, Ltd., London, 1958.

24. Proceedings of the Institute of Radio Engineers, 50, Issue No. 5, May, 1962: a review

of the progress of the last 50 years, and prognostications for the next — with special emphasis on informational science and control. Many contributors.

Epilogue — A Perspective

It is useful to have a perspective of a subject such as biophysics. In the Introduction we located the subject nestled in among other pure and bio sciences. However, the questions raised about information and control in the last chapter — about man's brain and the computers which he is fashion- ing— make us wonder where biophysics fits in among those disciplines which are not physical sciences. In other words, Where does the biophysics of man fit into the framework of all knowledge about man?

F. O. Schmitt has introduced the thought very nicely:*

"Biophysics, like biochemistry, has to reckon with hierarchies of organiza- tion and with the properties that are characteristic of systems no less com- plex than those provided by living organisms at each particular level of organizational complexity: viz., molecular, macromolecular, subcellular, cellular, supercellular, organismic, and superorganismic . . . theoretical biology must deal not only with the properties of cellular constituents but also with the properties of the organism as a whole."

Interpreting man as an organism, complete with his esthetic, emotional, and religious experiences, and as part of a superorganism complete with social, cultural, and religious activities, we can view man's knowledge of him- self, his history, and his destiny, in a very broad and intriguing perspective. However, within the framework of the logical disciplines as they now exist, we know: that logic and experiment are the tools of the scientist; that logical ^//-consistency is the final test for philosophers and mathematicians; and that the theologion has logic, the results of natural science, and revelation in his workshop.

Man's intellectual destiny is to know the truth — about the Creator, about Man, and about Nature — even though "man's body is but a fleeting thing."** He has the right to know, the ability to find out, and the responsi- bility to try. Ultimately there is no substitute for the truth in any intellectual disciplines.

Classification of inputs into "information" and "noise" (in the sense in which these terms are used in the last chapter) is man's greatest obstacle to knowing all about man, for such classification is highly subjective.

'Biophysical Science — A Study Program," J. L. Oncley, el ai, Eds., John Wiley & Sons, Inc., New York, N.Y., 1959, pp. 5 and 6.

**Ecclesiasticus, 41, 11.

315

316 EPILOGUE— A PERSPECTIVE

Man's problem is to find the truth, in spite of the noise which plagues him from without and within. There are many pitfalls. Will he find truth by rejecting a prion, or subjectively, part of the input? Or by rejecting logic's prime tenet of the excluded middle, as some now suggest? .... I think not.

Tables of Common Logarithms and Exponential Functions

Abbreviated Table of Common Logarithms*

N.	log N	N	log N	N	log N	N	log N
10	000	34	532	58	763	82	914
12	079	36	556	60	778	84	924
14	146	38	580	62	792	86	935
16	204	40	602	64	806	88	945
18	255	42	623	66	820	90	954
20	301	44	644	68	832	92	964
22	342	46	663	70	845	94	973
24	380	48	681	72	857	96	982
26	415	50	699	74	869	98	991
28	447	52	716	76	881	100	1000
30	477	54	732	78	892
32	505	56	748	80	903

* Examples: log 1.6 = 0.204; log 72 = 1.857; log 0.5 = 1.699, or = 9.699-10.

Abbreviated Table of Exponential Functions

e"x	X	X e	— X e	X	X e	e-x	X	e*
1.000	0	1.000	0.549	0.6	1.822	0.050	3.0	20.1
0.951	0.05	1.051	0.497	0.7	2.014	0.030	3.5	33.1
0.905	0.10	1.105	0.449	0.8	2.226	0.018	4.0	55
0.861	0.15	1.162	0.407	0.9	2.460	0.011	4.5	90
0.819	0.20	1.221	0.368	1.0	2.718	0.0067	5.0	148
0.779	0.25	1.284	0.287	1.25	3.490	0.00055	7.5	1808
0.741	0.30	1.350	0.223	1.50	4.482	0.000045	10	22,026
0.705	0.35	1.419	0.174	1.75	5.755
0.670	0.40	1.492	0.135	2.00	7.389
0.638	0.45	1.568	0.106	2.25	9.488
0.607	0.50	1.649	0.082	2.50	12.182

317

List of Symbols

GREEK LETTERS USED AS SYMBOLS

a — alpha — a radiated particle (Ch. 4, 5, 9); degree of ionization (Ch. 8);

state of cell division (Ch. 9); membrane penetration rate in (Ch. 10). /?— beta — a radiated particle (Ch. 4, 5, and 9); membrane penetration

rate out (Ch. 10). 7 — gamma — ratio of specific heats measured under constant pressure and

constant volume (Ch. 3); radiated electromagnetic radiation (Ch. 4, 5,

and 9). <5 — small delta — a small, measureable length (Ch. 1). A— capital delta— 'a little bit of" (Ax, Ay, AS, AH, AF, etc.). e — epsilon — dielectric constant (Ch. 2); incremental energy (Ch. 4). 7] — eta — viscosity (Ch. 8); the neutrino (Ch. 5). r]Q — eta subscript zero — viscosity of solvent (Ch. 8). [77] — eta in square brackets — intrinsic viscosity (Ch. 8). 6 — small theta — scattering angle (Ch. 4). K — capital kappa — specific conductivity of a solution (Ch. 8). A — small lambda — usually a decay constant (Ch. 5); a wavelength (Ch.

3); jump distance (Ch. 8). A — capital lambda — equivalent conductance (Ch. 8). A0- — equivalent conductance at infinite dilution (Ch. 8); a nuclear particle

(Ch.4). p. — small mu — mesons (Ch. 4); free energy per mole ("chemical po- tential") (Ch. 7). v — small nu — frequency (Ch. 4). 7r — small pi — the constant circumference/diameter of a circle; osmotic

pressure (Ch. 2 and Ch. 6); pion (Ch. 4). p — small rho — density (Ch. 2).

p — small rho overscored — ratio of densities of solvent to solute (Ch. 6). a — small sigma — standard deviation (Ch. 1); Stefan's constant (Ch. 8);

specific radiation sensitivity (Ch. 9). 2 — capital sigma — a fermion (Ch. 4); a type of bond (Ch. 4); see also

below, r — small tau — transmission coefficient. 0 — small phi — fluidity (Ch. 8); a dependent variable.

319

320 LIST OF SYMBOLS

\p — small psi — an independent variable; pressure or amplitude (Ch. 3). ^ — capital psi — potential. co — small omega — unit of resistance, ohms; angular velocity of centrifuge

(Ch. 6). £ — small xi — reaction path length (Ch. 7). Q — capital omega — the number of ways a system can be arranged (Ch. 7).

MATHEMATICAL SYMBOLS

/ — elongated S to represent elongated sum — the sum of an infinite num- ber of infinitely small parts : the integral sign. a — the ''infinity1' sign. <x — the proportionality sign.

V^the root sign; if no number appears in the hook, a square root sign. y^ — capital sigma — to denote the summation of a finite number of small but finite parts. d — rounded "dee11 — the partial differential symbol. = — identically equal to. X — as superscript — refers to activated complex.

Index

a — a number or constant; acceleration; mo- lecular extinction coefficient; activity or effective concentration .-1 — a reactant; area; activation heal of

muscle A — angstrom unit (10~ cm) Absorption, of electromagnetic radiation, 80-82

of matter (acoustic) waves, 53 Acceleration, definition, 27

due to gravity, 30

in a centrifuge, 30, 137 Acetylcholine, ACh, as substrate for acetyl- cholinesterase, ACE, 276

in nerve, 275 ff

thermodynamics of hydrolysis of, 172 Acetylsalicylic acid, formula, 84

infrared absorption spectrum of, 84 Acoustic transducers, 51 Acoustic waves, nature of, 48-49

absorption of, 52, 54

cavitation by, 61

clinical applications of, 62-65

decibel scale for, 55

detection by ear, 56 ff

penetration of, 54

physiological effects of, 60-62

reflection of, 53

therapy by, 62-65

velocity, 50 Actin, 286

Action potential (See Nerve propagation) Activity, specific, 1 13

of strontium and radium, 113

thermodynamic (effective concentration), 176 Activation energy, and rates of physical and chemical processes, 198-200

table of values for catalyzed and un- catalyzed reactions, 201

enthalpy, defined, 200

entropy, defined, 200 Acuity, visual, 87-90

and scanning by the eyeball, 90

Adaptation, dark-, 88 Adenine, 149

Adenosine triphosphate, 29, 177 as mobile power supply, 177, 178 in Krebs cycle, 178 in muscle, 282 in nerve, 268

in protein and DNA synthesis, 151, 156 hydrolysis by myosin, 177, 286, 288 thermodynamics of binding to myosin, 288 Adrenalin, isomers of, 144, 156 All-or-none law, 263, 305

and binary number system, 307 Alpha amino acids, 127

polymerization of, into helices, 130 Alpha helix of proteins, 131

in myoglobin, 132 Alpha keratin, 130 Alpha radiograph, principle, 107 of demineralized bone, 108 of filiform papillae of tongue, 108 Alpha rays or particles, 102 absorption of, 105

energy distribution of, from a source, 1 13 ionization by, 104, 105 penetration of, 116-118 physical properties of, 103, 104-105 Alpha waves (in EEC), 274 Amplitude of matter (acoustic) waves, 55 Anemias, hemolytic and unnamed, 158

sickle cell, 157-159 Anticipation, by brain and computers, 302 Aperture, numerical, of microscope, 98 Arrhenius' equation, 198 Arterial pressure, 218

Assimilation, impaired by ionizing radia- tions, 252 Astigmatism, 90 Ashby's computer, 296, 304 Astronauts, acceleration of, 30

weightlessness of, 45, 231 Atom, structure of, 71 Atomic nucleus, structure of, 73, 103 Atomic orbitals, or electron shells, 71

321

322

INDEX

ATP (See Adenosine triphosphate) Autoradiography, principle, 107-108

on blood flow in brain, 120 Avogadro's number, 71 Axon of squid, ion content of, 266

b — number of bels b — a number or constant bmr — basal metabolic rate B — a reactant

Background of ionizing radiations, 235, 239 Bacteria, genetic recombination of, and cod- ing, 148 effects of ionizing radiations on, 249, 250 ultrasonic radiations on, 63 ultraviolet light on, 93 Bacteriophage, and DNA synthesis, 148 Bagchi, on EEG, 275 Balance, kinematic, 99

water, 40 Basal metabolic rate, defined, 168 Bases, purine and pyrimidine, in DNA and

RNA, 149 Basilar membrane, 58 Becquerel, and radioactivity, 69 Beer-Lambert law, 81, 136 Bel, definition, 55 Bends, the, 33

Bergonie and Tribondeau, law of, 247, 249 Bernstein, hypothesis of, 265 Beta rays, absorption of, 105-106

energy of emission, and neutrino, 1 15 integrated dose by, 258 ionization by, 105

physical properties of, 103, 105-106 range in air and soft tissue, 1 18 Binding, interatomic, 74 intermolecular, 41-43 Bioenergetics, 161 ff

chemical sources of energy, 166, 167, 173-174 acetylcholine, 172, 275 adenosine triphosphate, 170, 172, 176,

178, 282 caloric value of foods, 166 creatine phosphate, 282 fats, carbohydrates, and proteins, 166 glycogen, 172 table of values, 172 electrical energy transfer and, 179 ff n — it transition, 147 via redox systems, 179 ff via mobile 7r-electrons, 146, 147 via electronically excited states, 145 of interaction of tissues with: infrared radiations, 82-83 ionizing radiations, 93-95, 234 ff

matter (acoustic) waves, 52, 54 ultraviolet radiations. 91-93 visible light, 83-91, 95-99 of mechanical systems:

by matter (acoustic) waves, 52-53, 56-59 by molecular vibrations, etc., 145 by muscle contraction, 280-284 of metabolic processes (See Heat loss,

170, 174) specific references to, 189-190 Birefringence, flow, 139 Black body radiation and the sun, 79 Blood, circulation of, 218 effects of gravity on, 34-35 fluidity and composition of, 216, 219 laminar and turbulent flow in, 212, 215,

217 pressure drops in circulation of, 218 Blood flow in brain, tracers, experiments, 119

Boltzmann's constant, 200 Boltzmann distribution of energies, 197 Bonds, covalent, ionic and dative, 74-75

cross-, induced by X rays, 94

hydrogen, 41, 43, 131-133

interatomic, 74

intermolecular, 42 Bone, impact resistance of, 34

effects of ionizing radiations on, 252

iron turnover rate constants, normal and diseased, 31 1

marrow therapy, 258 Bosons, 73

Bragg's law for scattering of X rays, 127 Brain, as computer, 295-296

as controller of human system, 303-305, 309

electroencephalograms of, 273-277

(See also Central nervous system and Computers) Bremstrahlung, 106

Burns, on central nervous system, 273-275 Butler, on irradiation of DNA, 243

reviews on biophysics, 66, 160, 294

c — a constant; concentration; specific heat

C — a reaction product

Cable theory, introduction to, 270-271

cal, — small calorie, 28

Cal, or kcal — large calorie (= 1000 cal)

Calculus, definitions of terms of the, 15-17

Cancer, chemical therapy, 259 localization, 62, 94, 97 radiation therapy, 62-65, 256-258 of skin, induced by irradiation, 252

Candle, a photometric unit, 87

INDEX

323

Capacitance, electrical, of double-layer of

membranes, 264 Carbohydrates, 125 ff

structure and properties of, 129 polysaccharides, 133 with lipids, 134 in living membranes, 140 fuel value of, 166 Cataracts, nature of, 91

induced by ionizing radiations, 253 Cavitation, 61 Catalysts, principle, 199 enzymes as, 201 ff for balky redox reactions, 183 Cells, division of, effect of ionizing radia- tions on, 247 ff distortion of, by bad molecules, 157-159 leucocytes, DNA content of, 243 membrane of:

electron micrograph and schematic dia- grams of, 141, 272 structure and properties of, 140, 264 water flow through, 37, 142 nucleus of, illustration, 264 radiation sensitivity of, 247 fT, 250, 251 Central nervous system, studies on, 273-277 behavior of neurons, 274 effect of ionizing radiations on, 276 electroencephalography and the, 274 transmission across synapses in spinal cord, 274, 275 Charge, electrical, definition of, 38 and Coulomb's law, 39 on colloids, 40 Chemical potential, n< 176 Chemical reactions, factors of rate expres- sions, 228 Chemiluminescence, 146 Chromosomes, effects of irradiation during

mitosis, 251, 252 Clark, book on redox systems, 180 Classification of inputs of information, 299, 315 of subject matter of biophysics, 3 problems of, by a computer, 303 subjective character of, in man, 299, 315 Cochlea, 58 Codes, molecular, 125, 148 ff

biochemical information on, 154, 156 cogs and cams in, 154 in bases of nucleic acids, 1 53-1 56 genetic information on, 154-155 table of three-base, 155 Cole, on nerve propagation, 264 Collagen, molecular weight and dimensions, 139 of skin, 134

on tongue, 108 properties of, 129, 137 tensile strength of, in tendon, 133 Colloids, agglutination of, by ionizing radia- tions, 245 blood groups and, 40, 156 electrostatic forces and, 40 stability of, 40, 156 Color, complementary pairs, 89

sources of, 83 Color blindness, 90 Color vision, theories of, 89-90, 27^ Compton absorption and scattering of X and

7 rays, 80, 105-106 Complex, activated, 200, 202

enzyme — substrate (Michaelis). 202 Computers, analog, 305, 307-308 problem for, 312

and the brain, 295, 296, 303-305, 309 and representation of nerve phenomena,

304-305 calculations by, on iron metabolism, 309-

313 data processing, storage and retrieval by,

302 determinism in, 296, 304 digital, 306-307 number of components in, vs brain, 295,

296, 309 Turing's, 296

with animal-like behavior, 296, 304 Concentration cells, potentials of, 267

(See also Electrical potentials, and Mem- branes) Concepts in the mind, 302, 303, 315 Conductivity, Electrical, 219 ff (See Electrical conductivity) heat, 244 ff (See also Heat conductivity) Conductor, "volume" — principle of, 223

and EKG and EEG, 224 Cones, distribution and properties of, 85-86 Convection in heat transfer, 226 Cooling, Fourier's law of, 225

Newton's law of, in terms of vapor pres- sure, 227 Control, concepts and language of, 295 ff, 315 effects of environment on, 290 ff endocrine, over biochemistry of body, 277,

308 nervous, over muscle, 277 Control biophysics, 296, 303-305

brain vs computer, 303 ff Corey, on alpha helix. 12"

Cornea, 85

inflammation of due to ultraviolet, 93

Coulomb's law, 74 cps — cycles per second

324

INDEX

Crick, on coding theory, 154 Cross-stimulation of neural networks, 277 Curie, as unit of radioactivity, 1 13

Mme. Marie and Pierre, 102 Current, electronic, in certain organics, 74, 147

factors of, 219-222

in active membranes, 270-271

ionic, in salt solutions and tissues, 219 Curtis, on nerve propagation, 264 Cybernetics, 295 ff Cytosine, 149

d — infinitesimal amount of, or full differen- tial symbol; distance; lattice spacing; deuteron D — depth (ft) in water; diffusion coefficient;

radiation dose; reaction product Do — integrated beta dose to tissue db — number of decibels (10 db = 1 b);

definition, 55 de Broglie's pilot waves, 72 Debye-Hiickel theory of electrolytes, 219 Decay {See Radioactive decay) Delta, a symbol: A, meaning "a change in" Delta waves in EEG, 275 Depth perception, 91 Derivative, full and partial, 16 Desoxyribosenucleic acid (DNA)

chemical composition of, 133, 148, 149

coding in {See-Codes)

helical structure of, 133, 148, 150

molecular weight of, 139, 150

physical properties of, 129, 148

pyrimidine and purine bases in, 149 Detection of ionizing radiations, 107 ff

by fluorescence, 109

by induced chemical reactions, 1 1 1

by ionization of a gas, 107

by photography, 107, 108 Deuteron, ionization by, 104

penetration of, 116-118

physical properties of, 103, 104-105 Deviations, standard, and others, 19-20 Diastolic pressure, 35 Diathermy by infrared, 82-83 Diffusion, 6, 207 ff

as a rate process, 210

driving force for, 211, 228-229

effect of ionizing radiations on, 245

Fick's laws of, 208-209, 228

of water: osmosis, 142, 212

w fluid flow, 214 Diffusion coefficient, definition of, 208

factors of, 210, 231

table of values, 210

Diffusion potential, 186

Dipoles, induced and permanent, 41

in chemical bonds, 41-42

interaction of, 42-43 Disc, intervertebral, strain on, 34 Disintegration, radioactive (See Radioactive

decay) Donnan, on membrane selectivity, 187, 267 Dosimetry, radiation, 107-1 11, 238-241

electrochemical, 240

fluorescence, 240

Fricke ferrous sulfate, 239

in gases, 107-1 1 1 Doty, on macromolecules, 135, 136, 139 Dunn-Fry law, 64

e — base of natural logarithms, 2.71828 e+, e~ — positive and negative electrons E — enzyme ([E] = concentration of enzyme);

reversible electromotive force Eq — emf of standard state E* — energy of activation ^difl — diffusion potential Econc — concentration potential Em7 — midpoint potential £— efficiency, AF'/AF Ear, bones in, 57

detection by inner, 56-58

external, 57

membranes of cochlea, 58

middle, amplifying action of, 57

sensitivity, absolute of, 50, 51, 56

theory of hearing, and, 57 Edema and water balance, 37-38 Efficiency, £ = AF'/A/-', 169

in muscular contraction, 171

of metabolic processes, 171-173 Elastic modulus, definition, 34

of bone, 34 Elastic reactance, and sound absorption, 53 Elasticity of bone, 34

of capillary walls, 35

of cell membranes, 37-38

of muscle tissue, 278-279 Electric potential, definition of, 38

and free energy of reaction, 180

electrodes for the measurement of, 264

electromotive series of, for biological systems, 180

measured against the normal hydrogen electrode (NHE), 180

membrane, values of, 187

midpoint, Em7, 180, 181, 183

of concentration cells, 186, 187,267-268

theory, 180-182,270-271 Electric shock, damage from, 222

INDEX

325

Electric field strength, definition, (voltage gradient), 38, 40

across living membranes, 40, 143

in ionization chambers, 107 Electrical conductivity, 219 ff

and dimensions of the conductor, 222

effect of ionizing radiations on, 246

Ohm's law of; an analysis, 219-222

of electrolytes, in body, 219

of organic materials, 74, 147

specific, defined, 220 Electrocardiography (EKG), recording,

223 Electrochemical nature of nerve propaga- tion. 266 Electroencephalography (EEG), analysis, 275, 299 effect of ionizing radiations on, 276 Electrolytes, ionic transport in, 219 ff, 228 conductivity of, 219, 222 in giant axon of squid, 266 in red blood cells, 38 Electrolytic cells (See Redox systems) Electromagnetic spectrum, 77 ff detailed table of properties, 78-79 (See Infrared radiations, Ionizing radia- tions, Ultraviolet radiations, and Visible radiations) Electromagnetic waves, 76 absorption of, 80-82 interaction with matter, 77-80, 82-95 Electromotive force (See Electrical potentials) Electron, charge and mass, 68 properties of, 68, 103 and current flow, 219 ff

Electron microscope, principles and limita- tions of, 100

Electron microscopy, illustrations: of bacteria, 250 of collagen fibers, 134 of muscle, 284, 285 of neuromuscular junction, 291 of ribosomes of cell, 152 of Schwann cell and nerve axon, 272

Electron volt (ev), unit, 77

Electroretinogram, 90

Elementary particles, 73, 82 Endergonic (synthetic, anabolic) processes, 175

Endothermic processes, 166

Energy, kinetic and potential, 28, 161 ff

chemical, 166, 167

electrical, 45

factors of, 29,45, 175

heat, 45, 162

interconversion of various kinds, 162, 163- 171

internal, definition, 164

in thermodynamic systems, 161 ff

in visual processes, 87-90

mechanical, 45

of matter waves, sound and ultrasound, 49

of muscle contraction, 280

transfer processes, 179 ff

references, 189-190

(See also Bioenergetics) Enthalpy of reaction (heat content change) definition, 165

fuel value of foods, 166

of combustion, mixing, and of transition, 166, 167

table of values, 172 Entropy, as a specific heat, 29, 170

as a factor of heat energy, 29, 170

and information, in communications the- ory, 298

and order vs disorder, 171, 187,298

and probability, 188

negative change in, in living systems, 187

of activation in enzyme catalysis, 200, 206

of reaction in chemical and physical proc- esses, 171

table of values, 172 Enzymes, as biological catalysts, 201-204, 286, 289

table of rate parameters of reactions cata- lyzed by, 206 Equilibrium, as a dynamic process, 193

as a thermodynamic process, 176, 185, 194

the drive toward, 175 Equivalent conductance, defined, and ex- emplified, 221 Errors, kinds, analysis of, and means of expressing, 17-20

in measurement, and effects on biophysi- cal control, 298 Erythema, energy of ultraviolet to produce, 92

Erythrocytes (See Red Blood Cells) ev — electron volt

Excitation, all-or-none property of nerve, 262-263, 305 and electrical conductivity, 74, 147 and photosynthesis, 91 and stimulation of eye, 87 of molecules, electronic, 145 thermal, of rotations and vibrations, 145

Excited states of molecules, 143-146

Extinction coefficients, molar and molecular, 81

326

INDEX

Exergonic (degradation, catabolic) proc- esses, 175 Exothermic processes, 166 Exponential relationship, defined, 10, 23 Exponents (See Indices)

Extrasensory perception (ESP), 297 (foot- note) Eye, architecture and parts of the, 83-85

cataracts on the, 91

color vision of the, 89-90, 277

depth perception, 91

optic nerve endings in, 89, 277 electroretinogram ol, 90

rod and cone cells; pigments in, 88

sensitivity, 89

twilight vision, 87

/ — a function (form unspecified): /(*), f(v), f(v/d), etc.; focal length of lens; frequency

f — free energy per mole (Gibbs' free energy); force

F — Faraday's constant, 96,500 cou/equiv.

AF — reversible change in free energy per mole of reaction; maximum work

AF' — external work per mole of reaction

5J — free energy of whole system

Air — reversible change in free energy of whole system; maximum work

AC? ' — external work done

A3'

-internal work done

Falling body, description of, 15 Faraday, on electrolysis, 68, 220 Farley, on neural simulation by com- puters, 303, 304 Fats, fuel value of, 166

lipids and, properties of some, 129 Feedback in biological systems, 300

general and particular, 301

negative, 301 Fermions. 73

Fick, laws of diffusion of, 208-209, 228 Field strength, defined, 38, 40

across living membranes, 143

in ionization chambers, 107 Fletcher, on speech, 47, 59 Fluid flow, 212 ff

as a molecular process, 214

factors of rate expression for, 228

laminar and turbulent, 212, 215

Newtonian and non-Newtonian, 213

Poiseuille's law of, 213

Reynolds number, 215 Fluidity or specific rate of viscous flow

and molecular weight of dissolved macro- molecules, 138

definition of fluidity constant, 213

effect of ionizing radiations on, 246

effect of tube length and radius, for blood, 217

inverse of viscosity, 138, 215

of plasma and blood, 216

table of values, 214

temperature coefficient of, 214 Fluorescence, definition of, 146

and discovery of radioactivity, 102

and discovery of X rays, 68

in amino acids, nitrogen compounds, and proteins, 147

in solids and liquid detectors of ionizing radiations, 110, 239-240 Force, basic definition, and dimensions, 26, 28

and energy, 45, 175, 228-229

driving, in chemical processes, 175

electrical, electromagnetic and magnetic, 42, 44

generalized, 26-27, 44, 45, 228, 229

intermolecular, 41-43

osmotic, 35-38 Force-velocity relationship for muscle, 280 Fourier, law of heat conduction, 225

analysis of EEG, method of,

analysis of diffracted X-ray spectrum Free energy, defined, 168

and equilibrium, 175-177

as maximum work, 168-169

of formation, 185

of reaction; table of values, 172 Functions, definition and illustrations, 9-16

g — grams

g — acceleration due to gravity, 30 gt — ionic conductances through nerve mem- branes, 270-271 o-forces, and atmospheric pressure, 31

on man in several aspects, and upon im- pact, 30 Galileo, on falling bodies, 14 Galvani, on electrochemistry and nerve, 263 Gamma rays, absorption, mechanisms of, 106

effect of, as ionizing radiations, 105

energy distribution of, 113

integrated dose of, 258

penetration of, 116-118

physical properties of, 103, 106 Gamov, on the atomic nucleus, 74

on coding theory, 154 Gases, effects of pressure on, 31

solubility (Henry's law), 33 Geiger counter, 109 Genetic effects of ionizing radiations, 253

INDEX

327

Gibbs, throus5ho1.1t thermodynamics, 161 ff Glasser, source books on biophysics, 261 Gonads, radiation dose on, from various

sources, 253 Gray, on mechanoreceptors, 56 Ground state, definition of, 76, 145 Guanine, in DNA, 149 Guldberg and Waage, on mass action, 194

in alpha helix of proteins, 130-131 Hydrogen peroxide, formed by electromag- netic radiations, 111, 241 by intense ultrasound, 61 Hydrostatics, 34-35 Hypermetropia, 91

Hypothalamus, as man's temperature con- troller, 301

h — Planck's constant

// — enthalpy, or heat content, per mole;

Henry's constant A// — change in enthalpy, per mole; heat of

reaction per mole JC — enthalpy of whole system A JC — heat of reaction Haldane, on scientific terminology, 6 Half-life, biological, 121; table of values, 259

physical, 1 12; table of values, 115 Halley, first on statistics, 17 Hearing (See Ear) Heart, pacemaker of, 273

pumping action of, 35 Heat, activation, in muscle, 282

basal metabolic, q'bm, 30, 174

extra metabolic, q'ex, 174

total metabolic, q\ 174

energy from absorbed radiations, 241

of shortening of muscle, 282

production and loss in body, 167, 224 ff Heat capacity, definition, 163 Heat conduction, Fourier's law, 225, 228 Heat content, or enthalpy, 164 Heat death. 188 Heat loss, 173-174,224-227

irreversible, q'irr, 173 Heat of combustion, neutralization, reaction,

and transition, 167 Heisenberg, on wave mechanics, 72

on uncertainty principle, 298 Helmholtz and Young, three-pigment theory

of color vision of, 89-90 Hemoglobin, structure and properties of,

126, 129 Hemostatics, 34-35 Herrick, on ultrasonics in medicine, 65 Hill, about biophysics. 1. 2

on muscle, 280 Hodgkin. on nerve, 263, 266, 270-271 Hodgkin-Huxlev theory of nerve propaga- tion, 270-271 Hooke's law of elasticity, 34, 278 Hopkins, on bad molecules, 156 hp — horsepower, 28 Huxley, on muscle, 285 Hydrogen bond, nature and strength, 43, 47

1 — current

/ — current density; intensity; power; one of a

number. / — ion currents, 270 / or /0 — intensity or power at a chosen ref-

erence point / — threshold intensity

A/,

/,

/

0

w * 1 Ichthyoccl, molecular weight of, 135, 139

Illumination, 87

Impact resistance, 34

Impulse, and injury, 34

of nerve (See Nerve impulse) Index of refraction, and microscopy, 96-98 Indicator redox systems, 183 Indices, laws of, and logarithms, 20-21 Information, theory, and control, bio- physics, 303

and entropy, 298

definitions and terminology, 295 ff

storage and retrieval, 302 Inertia, definition of, 27

and reflection of acoustic waves, 53 Infinitesimals, 12

Infrared radiations, absorption and effects of, 77, 82-83

spectra, assignments, 84 Insulation, thermal; skin, hair, and clothing

as, 227 Insulin, structure of, 126, 128

tracer studies with, 121 Integration, nature of mathematical, 16 Intellectual destiny of man, 31 5 Intensity or power, of matter waves. 55 Intermolecular forces, kinds, 41-42 Internal energy, 164 Inverse Square law. illustration, 52-53 Ionic mobility, ^ or /, 220 Ionic transport in electrolytes. 2 1 9 ff , 228 Ionization chambers, 69, 108-110 Ionization, degree of, in electrolytes, 220 Ionizing radiations, 77, 93-95

absorption of, 81, 105-106, 242

action, direct and indirect, 241-242

Compton scattering of, 105

detection. 1(14 111

328

INDEX

Ionizing radiations (contin.) dose measurement of, 236-237 effects of, biological, 93, 234 ff biophysical, 245-247 on molecules, 243, 252 on neuromuscular junctions, 292 whole body, 254-256 energy loss of (LET), 104 excitation by, 93 pair production by, 105-106 production of foreign molecules by,

242-244 therapy by, 93, 256 Iron metabolism, kinetics of, 310 Irradiation, natural sources of, 239 Isomers, definition, 143 Isotopes: decay schemes, 114, 116 stable and unstable, 73, 104 tables of biologically useful, 114, 115,259

j — flow rate; flux during diffusion; current Joule, unit, 28 Junction potential, 186

k — constant, usually a specific rate constant, such as k,, k7, etc.

kw — kilowatt

KE — kinetic energy, 28

k — Boltzmanns constant (ideal gas constant per molecule)

K — constant in light scattering equation

A" — equilibrium constant

A" — Michaelis constant

A t — thermal conductivity

Kamen, on tracer isotopes, 118

Katz, on neuromuscular junction, 291

K-shell electrons, 71

Kelvin, on measurement, 8

Kendrew, on structure of myoglobin, 126, 132

Kinetics, definitions, 12, 92 biophysical, 192 ff

in analysis of iron metabolism, 310-313 in analysis of muscle contraction, 287-289

Kinetic processes, five: similarities and in- tegration of, 228-229, 230

Kuzin, on tracers, 122

kvp — kilovolt potential

/ — distance; mobility

L — length of an electrical conductor; sym- bol of a splitting reaction Lambert, unit of illumination, 87 Lambert's law, 80-81 Land, on color vision, 89 LD50 lethal dose for 50 per cent of sample, values, 240, 241

Lehmann, on mediators, 184 Leibnitz, on limits, 1 1 Lenses, 85

aberrations and astigmatism, 90-91

aperture of, 98

in microscope, 96-100 LET— linear energy transfer (-dE/dx), 104,

237 (Table) Levers, bones in ear as, 58

classes and illustration of, 31

mechanical advantage of, 30 Life, 75 Light, nature and absorption of, 76, 80, 83 ff

energy quanta of, 76, 80

extinction coefficient of, 81

sources, 79

wave and particle nature, 177 Limits, 11-12 Linear energy transfer (LET), 104, 237

(Table) Lipocellulose, 134 Lipoproteins, binding forces in, 42

encephalitis, and binding in, 42

structure of, 129, 134 Liquid crystals, 124 In — natural logarithm Load-velocity relationship for muscle, 280 Logarithms, definition and laws of, 21

table of, 317 Lohmann reaction, 282 London-van der Waals' forces described, 42 Loudness of sound, 55

relation of, to sensitivity of detector, 56

m — meter

m — constant; mass; degree of maturity

M — momentum; molecular weight

Mev — million electron volts

cJTl — Young's modulus

Machines, computing {See Computers)

Macintosh, an anesthesia, 33, 56

Macromolecules, crystalline, 127-134

dissolved, 135-140

excited states of, 145

in living membranes, 140-143

molecular weights, methods and table, 135-140

mutations in DNA and RNA, 154-156

physical properties of typical, 128-129 Magnetic field, effect on cell division, 44 Mainland, on medical statistics, 19, 25 Martin and Johnson, on microscopy, 95 Mass and inertia, 27 Mass action, law of, 194 Mathematics, in biophysics, 8

review, 9-25

INDEX

329

Matter (acoustic) waves, 47-48 absorption coefficient of. 52-54 and noise, 59 divergence of, 52 frequencv of different sounds, 50 penetration. 54

physiological effects of intense. 60 power of certain sources (Table). 51, 60 speech, 59

ultrasound and ultrasonics, 47 ff velocity of, in air, water and solids, 50 Maximum permissible doses of ionizing

radiations. 252, 255 Maxwell, on distribution of thermal energies, 198 on electromagnetic theory, 76 Measurement, and control, 298

errors in, 17-20 Mechanical advantage of a system, 30 Mechanoreceptors, 58 Mediators, 84 Membranes, living:

chemical composition and defects of, 140 effects of ionizing radiations on, 253 in the inner ear, 58 permeability of, 37, 142, 268, 270 phenomenological studies on, 142, 268 physical properties of, 140, 264 selectivity, 271, 268 synthetic, 268-271

thickness, by electron microscopy, 141 Memory, of computers, 302

suggested physicochemical nature of, 27" Michaelis constant, Km, 203

and binding of enzyme to substrate, 204, 205 Michaelis-Menten equation, 203

in muscle, 288 Microelectrodes, 186, 264 ff (See also Elec- trical Potentials) Microendplate potentials, 291 Microirradiation, principle and techniques, 251 of cells and chromosomes, 251 Microradiography, 107-108 Microscopes, electron, 100 fluorescence, 100 optical 95, 96-98

interference, phase, polarizing, 98-100 resolving power of, 98 X-ray, 100 Miner, Shackelton, and Watson, on sensory

data, 102 Mitochondria, as energy factories of cell, 177 structure of membrane of, 141

Mobility, ionic, defined, 220 and conductivity, 220 of ions in nerve membranes, and potential,

267 table of values, 221 Molecular absorption of matter waves, 53 Molecular diseases, definition, 157

anemias, etc., 157-159 Molecular weight, determination of, for

macromolecules, 136-139 Momentum, definition of, 29

conservation of, in shortening of muscle,

280 transfer of, in fluid flow, 214 Moroney, on statistics, 17, 25 Morphine, infrared spectrum of, 84 Motor end plate, micropotentials at, and ir- radiation of, 291-292 ms — millisecond Muscle, bands in, 284 biophysics of, 161, 277 ff chemical composition and structure of, 284,

286, 287 electron microscopy of, 285 energetics of contraction of. 161, 280-282 fibers of, 284, 285

force-velocity relationship, 280, 281 helical spring analogy, 278 molecular mechanism of contraction

(theory) of, 286-290 speed of shortening, and load, 280, 281 strength of (in problem), 293 work done by, 280 Musical sounds, composition of. 50 Mustard gases, as radiomimetic chemicals,

259 Mutations:

and molecular diseases, 156 ff

induced by chance, through excited states,

146 induced by radiations, 253 induced by radiomimetic chemicals, 259 Myelin, electrical conduction in, 271

formation by Schwann cells, 272 Myoglobin, physical properties of, 129

structure of, by X-ray diffraction, 126, 132 Myopia, 90 Myosin, as ATPase, 282 ff, 287

as contractile molecule in muscle, 286 molecular weight of, by several methods. 287

n — usually a constant; order of a reaction; time-dependent phenomenological pa- rameter in nerve transmission theory; valence change, or number of equivalents

330

INDEX

per mole; nonbonding orbital; neutron; order of diffracted radiation; number of moles

_/V — a number, used generally as a depend- ent variable; number of radioactive atoms; number of impinging particles

yV0 — a reference state for .\

Nachmansohn, on biochemistry of nerve conduction, 271 on ACE, 276 n — 7r transition, electronic transition from nonbonding orbital to a 7r-orbital, il- lustration and energy of, 147 molecules which can undergo the, 147 mutations resulting from the, 146 Nernst equation, 180

and hydrogen electrode, 181-182 in concentration cells, 267 method of derivation from thermody- namic principles, 180

Neutrino, 73, 106 Nerve, action potentials of, 262 ff axons, 264 ff change in structure in phenylketonuria,

159 electrolytic conduction of, 265, 306 propagation velocity of, 265 Nerve impulse, as a transient bioelectric, 262, 265 digital nature of, 263 shape of spike, 265, 306 Nerve propagation, concentration changes during, 267 experiments on, 266 ff permeability changes during, 271 theory of, 269 ff tracers in the study of, 266 Neural networks, simulation of properties

by computers, 304-305 Neuron, illustrations of, 264, 291 in central nervous system, 274 propagation along axon of, 262-265, 269- 271 Neurosonic surgery and therapy, 72-73

Dunn-Fry law, time to paralysis vs intens- ity, 64 Neutron activation, for analysis, 1 19

Neutrons:

in nucleus, 82

ionization by, 105

nature and physical properties, 103, 106-107

penetration by, 1 18 Newton, law of cooling, 227

laws of motion, 27

Nirenburg, Ochoa, et al., on coding in

nucleic acids, 154 ff Noise, and absolute threshold of hearing, 55

and control, 296

from several sources in man's environ- ment, 60

in the computer, and control, 309

influence on information, 315

subjective character of, in man, 299, 31 5 Nonpolarizable reversible electrodes, 274 Nucleic acids (See DNA and RNA)

structure of, 149, 150 Nucleus of an atom, 73-74, 103-104

properties and stability, 103 Nucleus of a cell, 264

0 — zero

" — degree sign (° C, ° F and ° K: degrees Centigrade, Fahrenheit, and Kelvin, respectively) Ohm's law, 40, 219

Optics (See Eye, Color vision. Light, etc.) Orbitals, atomic and molecular, 74-75

electron migration and energy transfer along 7T-, 74, 145-147,271 Order, of differential equation, 16

of reaction, 195-196, 311 Organization, and definition of life, 75

from subatomic to superorganismic, 315 Osmosis, as a special case of diffusion, 36, 212 driving force for, 36 in living systems; water balance, 37 through red blood cell wall, 142 Osmotic pressure, as a thermodynamic property, 36 and water balance, 37 and restoring pressure in cell walls, 37-38 and molecular weight of macromolecules,

136 cell plasma composition and, 38 Otoconiae, 99 Otology, 57 Oxidation-reduction reactions (See Redox

systems) Oxygen effect in radiation sensitivity and radiology, 244

p — distance from image to lens; proton

P — pressure; number of points, or even a

single point; power or energy flux, 283 /'M — power expended as work, 283 I\yt — power expended as heat, 283 (P — permeability constant Pacemaker of heart, 273

INDEX

331

Parkinson's disease, ultrasonic therapy and.

61, 63 Paralysis, acoustic irradiation to, 64-65 Partic Irs. elementary, 73

Pauli, exclusion principle, 72

Pauling, on molecular diseases, 125, 157

on alpha helix in proteins, 127, 131 Penetration of radiations into tissue, 1 1"

I Set also the specific radiation) Penfield, on stimulation of cerebral cortex,

276 Permeability constant, of synthetic and natural membranes, 21 1, 267 of potassium and sodium, 268 changes, in nerve, during action, 270-271 Perspective in biophysics: among biological sciences, 2 within all knowledge of man, 315 Perutz, on hemoglobin, 159

on isomorphous replacement in X-ray dif- fraction, 126 Phlebostatic axis, 35 Phosphorescence, and 7r-bonding, 146

in amino acids and proteins, 146 Pholot atalyzed synthesis of vitamin D2, 92 Photoelectric absorption of electromagnetic

radiations, 105, 106 Photon, 76

Photophthalamis, induced by ultraviolet. 93 Photopic vision, 86

Photosensitive cells, 85 (See also Color vi- sion; Pigments) Photosensitized reactions, 91-92 Phototherapy, 92-93 Physii s, state of, about 1890, 67 Pi(7T) bonds. ^4. 75

and phosphores< en( e in amino acids, 146 in photosynthesis, 92

Piezoelectric i rystals, 51

analogy with transdui er cells in ear, 57

Pigments, visual, 86 90

absorption spectrum of rhodopsin, 88

chlorolabe and erythrolabe, 90

Helmholtz theory ol three, in color vision, 89

Land theory of two, 89 Pitch of sound. r^ I Planck's constant, "1 . 80

Plasma, blood, ion content of and osmotic pressure, 38

fluidity of, 216. 217

proteins in, 22 1 Pliicker. on electrical discharges in Podolskv. on muscle power, 283

Poiseuille's law. 212 213

and measurement of fluidity, 213, 214

obedience of blood to, 216 Polarized light (See Mn roscopy) Pores in living membranes, 140

effective diameter of, in red blood cells, 142 Potential, defined as an energy, 38

bioelectric, differences of, 38, 39

chemical, n, 176

(See also Electric potentials)

Power, units of, 28

of matter (acoustic) waves, 49 of muscle contraction, as heat, l'^, and work, Pw, 283 Pressure, basic definitions, 32-33 as a stress, 33 on a skin-diver, 37 osmotic, 35-38 Prisms, 78-79, 82

Propagation of excitation along nerve, 265, 306 frequency of, 306

redundancy, and reliability of informa- tion, 306 velocity of, 265 ( See also Nerve impulse) Proportional counter, 109 Protanope (color-blind), 90 Protectors against ionizing radiations, 243 Proteins, 125 ff

alpha-helical structure of crystalline, 131,

132 binding to cellulose and lipid, 134 chemical composition and structure, 128-

129 cross-bonding induced by X rays, 94, 242 hydrogen bonding in, 1 $0 mechanism of synthesis of, guided by

DNA, 151-152 tables of molecular weights, 128-129, 287 Protons, exc hange in hydrogen bond, 43 ionization by, 106 penetration of. 116 118 physical properties of, 10.3 psi — pounds per square in< h

q — quantity ol electrii charge; distance of object from lens, flux, or amount ol ma- in i.il being transpoi ted a. ross an area in unit tune, energ) taken in 1>\ a swcm q . (Set Rates, temperature coefficient of) q'. — basal metabolic heat given ofl by a nonreversible process in living system, 281

332

INDEX

q'. — total heat given off by an irreversible

process q'ex — heat, over and above q'bm, given off

during work

q' = ?'bm + ?'ex = A $' + ?'irr

Q, — number of cells which die in a given time; reversible heat per mole

Q0 — whole population of cells

Q10— sameas(?]0

Q — reversible, unavailable heat of whole process

Q' t — contraction heat of muscle

Quantum, 76, 145

Quantum theory of Planck and Bohr, 76

r — radius of a tube; radius of a sphere; roent- gen R — universal gas constant per mole; electri- cal resistance; distance /?90 — light scattered by 90° by macromole- cules of a layer from the center of a tube r«, r2 — resistances

(R — electrical resistivity, or specific re- sistance rad, radiation absorbed dose, 236

and rem, 236 Radiation of electromagnetic waves: infrared (See Infrared radiation) ionizing (See Ionizing radiations) ultraviolet (See Ultraviolet radiation) visible (See Visible radiation) Radiation of matter (acoustic) waves (See

Matter waves) Radiation of heat energy, 226 (See also

Infrared radiation) Radioactive decay, law of, 24, 112 and biological half-life, 121 and physical half-life, 112 schemes for certain isotopes, 1 14 Radioactive mapping, 122 Radioactivity, 69, 102

energy distribution, 113, 115 natural background of, 235, 239 separation of emanations, 69 source strength, 1 1 3 Radioactive isotopes as tracers, 115, 118 ff autoradiography, 107-108, 120 biological half-life, 121,259 distribution and localization, 120-122 in absorption and secretion studies, 120 in radioactive mapping for medical diag

nosis, 122, 130 in studies of fluid flow, 119, 122 in studies on nerve, 266 penetration of, 102, 116-118, 118 (Table)

Radiomimetic chemicals, 259 Radiosensitivity of cells, 250

under microirradiation, 251 Randall, textbook in biophysics, 46 Rate or speed, defined, 13 of chemical reactions, 195 ff

catalyzed by enzymes, 199, 201-206 temperature coefficient of (?10), 197 Rate constant, specific, 195

in kinetics of iron metabolism, normal

and diseased, 31 1 factors of, 198-200 table of values, 196 rbe (See Relative biological effectiveness) Red blood cells, axial accumulation and spin of, 217 cell wall structure of, 141 effect on blood fluidity of, 217 effect of ionizing radiations on, 252 ion content of, 38

kinetics of iron metabolism and, 31 1 sickling of, 158-159 size of pores in wall, 142 water balance in, 37 water penetration of, 142 Redox systems, as electron transfer proc- esses, 179 ff equivalence of electrical and chemical en- ergy in, 179 hydrogen, and pH, 181-182 indicators for, 183 iron in heme as, 132 mediators for, 184

midpoint reference potential, Em7, 182 Nernst equation for, 180 normal hydrogen electrode (NHE) as ref- erence, 181-182 potentials of, 180, 181, 186, 187,267-268 Redundancy, and precision, 305, 306 rem (See Roentgen equivalent man) Replication processes, theory of, 151 Reproductive death, induced by ionizing

radiations, 252 rep (See Roentgen equivalent physical) Resistivity of body fluids, 221, 222 Resolving power of microscope, 98 Relative biological effectiveness (rbe) of

ionizing radiations, 237-238 Relative humidity and heat loss, 227 Reversible conditions, defined, 169 Reynolds number of blood, 215, 216 Rhodopsin, a pigment, 86-88 Ribosomes, 151-152 Ribosenucleic acid (RNA), 129, 148, 151 Robertson, on membrane structure, 272 Roentgen, on X rays, 67, 234

INDEX

333

Roentgen, unit, 237

Roentgen equivalent man (rem), 236

and LET, 237

and rbe, 238, 239 Roentgen equivalent physical, 237 Rushton, on color vision, 88 Rutherford, on atomic structure, 69-72

s — elongation; length or distance; sedimenta- tion coefficient

S — space or distance between points; sensi- tivity of a detector; entropy per mole; substrate for enzyme-catalyzed reactions; [S], concentration of substrate; state; sickle cell variant of hemoglobin. A.Y — change in entropy per mole of reaction £ — entropy of whole system A§ — change in entropy in a process; dis- tortion. Saltatory conduction (See Electrolytes) Samuel, on computers, 304 Sanger, on insulin, 126 Scalae: media, tympani, and vestibuli, 58 Scattering experiments, 70 Schmitt, on collagen, 133

on theoretical biology, 315 Schroedinger, on wave mechanics, 71

on mutations, 145 Schwann cells, and myelin sheath, 272, 27" Scintillation counters, 110, 111 Scintography and radioactive mapping, 111,

122 Scope of biophysics, 1-2 Scotopic (twilight) vision, 88 Second law of thermodynamics, 168, 188 Sedimentation, 137, 138, 153 Self-consistency, logical, in mathematics

and philosophy, 315-316 Semiconductivity, of organic materials, 74, 145-147 in nerve propagation, 271 Sensation of loudness, 55 Sensitivity, and background noise, 55-56 of ear, 51, 56 of eye, 89 to ionizing radiations, 247

Sensitivity constant, ff, for ionizing radia- tions, 247-249 Sensory data, about, 47, 102 Series, infinite, in biophysics, 22-24 Servomechanism, man as a, 301

properties of a, 300 Shannon, on computers, 304 Shock, 30

Shortening, rate and rate constant for, in

muscle, 279 Sickle-cell anemia, physical basis of, 159 Signal-to-noise ratio, 299 Sommerfeld's atom, 71

Sonic and ultrasonic therapy, methods and effects, 62-65

in dentistry, 63

physicochemical basis for, 61, 64

paralysis induced by, 64-65

sterilization by, 63 Sound (See Matter waves) Specific heat, 28, 163

Speech, range of frequency, and power in, 59 Spike, in nervous propagation, 265, 306 Spring, muscle as a, 278 Statistical methods of expressing deviations,

19 Stacy, textbook on biophysics, 56, etc. Steady-state, and equilibrium, 195

effects of ionizing radiations on, 253

kinetic processes and, 229 Stereoisomers, 143

Sterilization, by beta and gamma rays, 250, 252

by ultrasound, 63, 252

by ultraviolet light, 93 Stimuli, kinds of, for nerve, 272 Strain and stress on bone; elasticity, 34 Sugars, (See Polysaccharides) Substrate of enzyme-catalyzed reaction, 201 Sun, as earth's primary source of energy, 79 Swallow, on irradiation effects on mole- cules, 242 Symbols, list of, 319

Synapse, and central nervous system. 276, 304-305

effect of ionizing radiations on, 292

neuromuscular, 291

neuron-neuron, simulation of, 304

transmission across, 276 Systems, concept, 6 ff, 296-297

diagram illustrating feedbacks, 300, 301

pans, 7, 8, 297

properties and theory, 296-301, 315 Systolic pressure, 35

Szent Gyorgyi, on energetics, 161, 185, 191, 293

t — time; time to paralysis

T — temperature (in deg. Kelvin unless other- wise stated) Tanford, on macromolecules, 126 Target theory of radiation damage, 241, 242 Teilhard de Chardin, on life, 75, 1 89

334

INDEX

Temperature, and rates of processes of body,

control and regulation of, 225 ff Tensile strength, denned, of collagen, e.g.,

133 Therapy, 93, 256 {See also Ionizing radia- tions, Sonic and ultrasonic therapy, etc.) Thermal conductivity, 225

effect of radiation on, 245 Thermodynamics {See Energy, Bioenergetics) Threshold energy and reaction rates, 197- 199, 201 (Table) of nerve propagation, 306 Thymine, 149

Thyroid, radioactive mapping of, 122 Tissues {See properties of interest) Touch, 58 Transducers, 51, 58 Tracers {See Radioactive isotopes) Transmission {See Nerve) Transmission coefficient, 200, 231 Transport processes {See individual listings) Troland, unit of retinal illumination, 87 Tumors, irradiation of, 62-65, 239, 256-258 Turbulent flow, in blood, 215, 216 Turnover of radioactive isotopes in humans,

259 Turning, idealized computer, 296 Twilight vision, 87

u— mobility of an ion in an electric field;

;/+ for cation; u~ for anion V — internal energy per mole A U— change in internal energy per mole of

reaction lU — internal energy of system A 'U — change in internal energy in a process Ultracentrifuge, 137 Ultrasound, ultrasonics. 47 ff medical applications of, 62, 63 physiological effects of, 60-62 {See Matter waves; Sonic and ultrasonic therapy) Ultrastability, in a computer, 296 Ultraviolet light, absorption of, 81 microscopy, 100 photosynthesis by, 91-92 sterilization by, 93 wavelengths and sources of, 79 Uncertainty in measurement and control,

72, 298 Uracil, in DNA, 149 Urey, and amino acid tracing, 1 1 8

-rate or speed; voltage -volts

V — volume; voltage or electrical potential Y— specific volume (volume per mole or per

gram) U — voltage gradient

van der Waals, forces between molecules, 41 van't Hoff, electrolyte theory of, 219-220

reaction isotherm (formula) of, 185 Variables and variation, definitions, 9 Viscosity (inverse of fluidity; See Fluidity) and measurement of molecular weight of

macromolecules, 215 as a rate process, 214

intrinsic, relative, and specific, defined, 215 Visible light {See Light) Vision, color, 89-90, 277

twilight, 87 Visual purple {See Rhodopsin) Volta, on artificial electric organs, 263 Voltage clamp technique, on nerve, 266, 269 von Bekesy, on hearing. 57 von Neumann, on computers and the brain, 295

w speed of an ion under an impressed

voltage; weight; energy transferred by electromagnetic radiation; angular ve- locity of a centrifuge; physical work done U' — work of expansion

.ruy energy used per unit time in metabolic

processes Walking, heat lost while, 227 Walter, on EEG, 275, 304 Water balance, 36, 37-38 Waves, brain (EEG), 275, 304 in arteries, 35 induced in tissue by intense ultrasound,

53, 60 matter (acoustic), 48 Maxwell's electromagnetic, 76 "of negativity," in nerve, 265, 306 pilot, de Broglie's, for orbital electrons, 72 Weber-Fechner law, in ear, 55 in eye, 89 in general, 299 Weightlessness, effect on rates of biological

processes, 231 Wilhelmy, on mass action, 194 Work, chemical, of synthesis, 167 done by muscle. 167. 280-283 expansion, in a process, 165 external, A 5', 169, 171 internal, A iT'lnt, of body, 167, 169, 171 physical, 167, 281 {See also Energy, Bioenergetics)

INDEX

335

v — usually an independent variable; distance X — electromagnetic radiation (X rays) X rays, 77, 78-79, 93-96, 243, 252

absorption of, 94

characteristic (Moseley; atomic number), 77

discovery of, 234

effects of, 243, 252

in medical diagnosis, 94-97

nonmedical applications of, 235

penetration by, 68

properties of, 78-79

therapy by, 93, 234 ff

wavelength, 77 X-ray diffraction, principle, 127

method of isomorphous replacement in, 132

X-ray burns, 234

V — usually a dependent variable y0 — a constant; initial value of y Y — a thermodynamic fraction, A/*'/A//, or

A3/A.TC Young-Helmholtz theory of color vision, 89 Young's modulus of elasticity, 34

Z — usually an independent variable; number

of changes carried by an ion Z-line, in muscle, 290 Zero-seeking servomechanisms, 301, 302

'CO /•«

^

LIBRARY

.'•'

' . ■:

		■Vv
		.
		i "# f ■:-.■: % ■
		. -
		f ' t ^ ■: ';:.

f

*i

% ;■! "I

•'

?rri •.•;■'

i

■

o

m

i i §

.n'M ...» w

V

■

P. 1 ■ ; ■'

•■.. .

'" .. ''

i

1 I 41

I

"• • I

i *i



	■_.





1
■. 3 "^•'■•vS'jsI'Hb^*'? j^'ir







1 H
.

		■

•	■ \|	II

	III	■
? ■■■"
	II
	_

■	1 1

,

'

.

,: '

'■&% ;;':,:r

\

C,t

-

•

■

	1	^^^^^^^ ^^^^M^M

	■





	1	■
	■


	1	1

	■
1

	1
1	1
^^^
^^^^^^^^M	■ ■
^^^^M
c		gl

'

-

■

I''-

■

.

'

v

								• t
«

':£