SYMPOSIUM ON
INFORMATION THEORY IN BIOLOGY

y r, o

SYMPOSIUM ON

INFORMATION THEORY
IN BIOLOGY

Gatlinbiirg, Tennessee, October 29-31 , 1956

Edited by

HUBERT P. YOCKEY

Oak Ridge National Laboratory

With the assistance of

ROBERT L. PLATZMAN HENRY QUASTLER

Purdue University Brookhaven National

Laboratory

SYMPOSIUM PUBLICATIONS DIVISION
PERGAMON PRESS

NEW YORK LONDON • PARIS • LOS ANGELES

PERGAMON PRESS INC.

722 East 55th Street, New York 22, N. Y.
P.O. Box 47715, Los Angeles, California

PERGAMON PRESS LTD.

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First published J 958

Library of Congress Card No. 58-9687

Printed in Northern Ireland at The Universities Press, Belfast

CONTENTS

PAGE

Foreword ix

A. M. Weinberg

Preface xi

PART I. INTRODUCTION

A Primer on Information Theory 3

Henry Quastler

Some Introductory Ideas Concerning the Application of Information Theory in
Biology . 50

Hubert P. Yockey

PART II. STORAGE AND TRANSFER OF INFORMATION

Editorial Introduction 61

The Cryptographic Approach to the Problem of Protein Synthesis 63

George Gamow and Martynas Ycas

The Protein Text ^ 70

Martynas Ycas

Discussion 101

Protein Structure and Information Content 103

L. G. Augenstine
Discussion 1 23

Specific Mechanisms of Protein Synthesis and Information Transfer in the
Developing Chick Embryo 124

H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann
Discussion 135

The Mechanism of Action of Methyl Xanthines in Mutagenesis 136

Arthur L. Koch

Evidence for a Negative Feedback System Controlling Liver Regeneration 148

Andre D. Glinos

Fluctuations in Neural Thresholds 153

Lawrence S, Frishkopf and Walter A. Rosenblith

PART III. DETERMINATION OF INFORMATION MEASURES

Editorial Introduction 169

Chemistry and Biochemistry at Low Temperatures and Discrimination of States
and Reactivities 171

Simon Freed

Discussion 1 80

75193

vi Contents

Information Content of Tracer Data With Respect to Steady-state Systems 181
MoNES Berman and Robert L. Schoenfeld

The Domain of Information Theory in Biology 187

Henry Quastler

Discussion 196

Some Membrane Phenomena from the Point of View of Information Theory 197
Herman Branson

Efficiency of Information Transmission by Biochemical Co-factors 204

Peter D. Klein

Discussion 209

Antigenic Specificity 211

Bernard N. Jaroslovv and Henry Quastler

Information Content and Biotopology of the Cell in Terms of Cell Organelles 218
Charles F. Ehret

Quantification of Performance in a Logical Task With Uncertainty 230

A. Rapoport

PART IV. DESTRUCTION OF INFORMATION
BY IONIZING RADIATION

Editorial Introduction 239

Electron Spin Resonance in the Study of Radiation Damage 241

Walter Gordy

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 262
Robert Platzman and James Franck

Information and Inactivation of Biological Material 276

Harold J. Morowitz

Discussion 28 1

The Absence of Radiation-Induced Disulfide Interchanges 283

Arthur L, Koch

A Proposed Mechanism of Protein Inactivation 287

L. G. Augenstine
Discussion 29 1

PART V. AGING AND RADIATION DAMAGE

Editorial Introduction 293

A Study of Aging, Thermal Killing, and Radiation Damage by Information
Theory 297

Hubert P. Yockey

Entropic Contributions to Mortality and Aging 317

George A. Sacher

Contents vii

A Quantitative Description of Latent Injury from Ionizing Radiation 331

H. A. Blair

Some Notes on Aging 341

Hardin B. Jones

Cancer as a Special Case of a General Degenerative Process 347

Harry Auerbach

Discussion 351

Free Radicals as a Possible Cause of Mutations and Cancer 353

Walter Gordy

PART VI. INFORMATION NETWORKS

A Probabilistic Model for Morphogenesis 359

Murray Eden

Functional Geometry and the Determination of Pattern in Mosaic Receptors 371
John R. Platt

PART VII. THE STATUS OF INFORMATION THEORY IN BIOLOGY

The Status of Information Theory in Biology: A Round Table Discussion 399

Edited by Henry Quastler

Author Index 403

Subject Index 41 1

FOREWORD

Alvin M. Weinberg

Director, Oak Ridge National Laboratory

The reader of this book may wonder why it is that an institution such as the
Oak Ridge National Laboratory, which is primarily interested in the control
and release of nuclear energy, should also be interested in sponsoring a meeting
on Information Theory in Health Physics and Radiobiology.

The answer rests in the fact that among the activities that are pursued at
this Laboratory there are two which bear very directly on general problems
of growth and of the impairment of growth by radiation and allied agents.
Broad programs in fundamental research in the basic physical mechanisms
and in the basic biological manifestations of radiation damage have been
established in the Health Physics Division and in the Biology Division. In
the Biology Division there is a great deal of experimental work being done on
protein synthesis, on the mechanism of action of the nucleic acids, and on
problems of the characterization of the nucleic acids. In the Health Physics
Division there is a lively interest in the problems of dosimetry and the basic
mechanisms of the interaction of radiation and matter. It is in establishing
a tie-up between the physical and biological aspects of radiation damage that
information theory may play an important role. We hope that this conference
will help to assess the value of information theory to phenomena involved
in the interaction of radiation and living matter.

<r?

IX

PREFACE

Biology has made extensive use of many instruments and methods developed
in the physical sciences. In recent years certain biological fields have been able
to make increasing use of and have developed mathematical methods for their
special purposes. Perhaps the reason this has not occurred earlier is that
sufficiently simple and important systems or situations do not present themselves
in biology. The life sciences, therefore, have developed most of their theoretical
structure without mathematics playing a leading role. Nevertheless, the need
for mathematical methods in biology has long been felt, as the pioneering work
of Fisher, Haldane, Wright, and others, has emphasized.

The possibility that the life sciences could develop mathematical systems
suitably their own, so that this form of research could be added to the already
powerful research tools available, was the common denominator in this sym-
posium. In order to address ourselves to a single task, the principal emphasis
was on information theory. The reader will note that in several papers there
is, willy-nilly, a reference or two to the ideas of cybernetics. Perhaps this
presages a greater influence in biology of this mathematical sibling of information
theory.

Our symposium and this book owe a debt to the pioneering effort oi
Henry Quastler and the book he edited in 1952 entitled Information Theory
in Biology. Among the newcomers to the fields of biology in which information
theory has found an application since 1952 is radiobiology. Since radiation
is an excellent way of introducing noise, the force of information theoretic
ideas may well be effective in achieving a better understanding of radiobiologic
problems in the future. By the same token, health physics will benefit by an
appreciation of the relation between radiation damage and aging.

Our book is about a mathematical theory but it is also a book about
experimental biology. This is properly so, for the development of clear ideas
about nature is as much a part of science as any activity carried on in the
laboratory. Experiment and theory do their best work in double harness.
It should be understood that, although something has been done here to bring
earlier work up to date and to-present new material, much remains to be done.
The information theory point of view suggests many problems of both a
theoretical and an experimental character. We hope that good advantage
will be taken of this fact.

The conference was entitled A Symposium on Information Theory in Health
Physics and Radiobiology and was held in Gatlinburg, Tennessee, 29-31 October
1956. The articles composing this volume were written in the ensuing months
and so represent the authors' results and opinions after the contact with his
confreres. As a result of this collocution some of the authors contributed
additional papers not given at the symposium.

The symposium could not have been carried through without the labor
and good judgment of the other editors. Professor Robert L. Platzman and
Dr Henry Quastler. It is a pleasure to acknowledge the encouragement of

xi

xii Preface

Dr Alvin M. Weinberg and Dr Robert A. Charpie, Director and Assistant
Director of the Oak Ridge National Laboratory. Appreciation is due Dr Karl
Z. Morgan, Director, Health Physics Division and to Dr Alexander Hollacnder,
Director, Biology Division. Any success that has been achieved is due to the
contributors and to those named above. Responsibility for errors or omissions
is that of the undersigned.

H. P. Y.
Health Physics Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee

PART I

INTRODUCTION

A PRIMER ON INFORMATION THEORY*

Henry Quastler

Biology Department, Brookhaven National Laboratory, Upton, New York

SYNOPSIS

I. Introduction: Historic development of information theory; reason for its present
popularity. System theories in general; specific role of information theory.

II. The representation of information: Paul Revere's code; essential features of representa-
tion of intelligence. Possibilities of representing information; variety of means; data and
operations; conscious and non-conscious acts of representation; generalized meaning of
'information'. 'Real' and 'symbolic' events; abstraction preceding representation. Symbol,
alphabet, 'words': units of representation. Binary representation, or standard method of
symbolization ; (a) simplest case: number of 'real' categories an integral power of two,
words of equal length; (b) any number of categories: words of unequal length, Fano's
'confusion-proof code, minimum-bulk code; (c) groups of events represented by single
words; (d) unequal probabilities: general rule to obtain a minimum-bulk code; (e) any
probabilities: general formula of minimum bulk in standard representation; (f) representation
theorem. Exercises.

III. The measure of information or uncertainty : Information acquired and uncertainty
abolished. The amount of uncertainty a function of probabilities of events, not their nature,
causes and consequences; amount of information and representability; the //-function; the
'bit'. Some properties of the Shannon-Wiener information function: independence, con-
tinuity, additivity, naturalness of scale; values for probabilities zero and one; effects of
averaging and of pooling. Exercises.

IV. Information measurements pertaining to two related variables: Generalized meaning
of 'communication'. An example of two related variables: heights of father and daughters;
joint uncertainty, internal constraints: the T-function; effects of scale on H and T. Two-
part systems in general: the six information functions for two variables. Communication
systems: nomenclature. Noise: the height correlation as example of a noisy channel;
channel capacity; manipulation of information does not increase its amount. Error detection
and correction: redundant information; theorem of the noisy channel ; economics of error
checking. Actual communication systems: signals and channels as physical entities. Exercises.

V. Organization (systems, structures, pattern): Organization, communication, redundancy.
Systems analysis: informational analysis, informational challenge and performance; general
limitations on information-processing. Multi-part systems. Unitization. Conclusion.

Appendix I: The evaluation of information content: Typical difficulties. The relativity of
information measures; arbitrariness of selections which determine actual values. Approxima-
tion methods. Examples: rate of information transmission in conversation; information
content per printed letter.

Appendix II." Answers to exercises.

* This paper is based on a report of the same name issued as Office of Ordnance Research
Technical Memorandum 56-1, in January 1956. The memorandum was written at the sugges-
tion of Dr Sherwood Githens, Jr, Director of the Physical Sciences Division of the Office of
Ordnance Research; he and his staff were very helpful at all stages of the execution of this
project, and it is a pleasure to extend them thanks. The present revised version was prepared at
Brookhaven National Laboratory, under the auspices of the Atomic Energy Commission.

3

Henry Quastler

I. INTRODUCTION

There appears to be a gap in the literature on information tiieory. One can
find several articles explaining what information theory is; several of those
are understandable to a reader with little knowledge of mathematics ; in fact,
some are at the general magazine level. One can also find a number of books
and articles explaining how information theory is to be used, but all of these
are on a highly technical level. I am not aware of any presentation which is
not highly technical and rigorous yet sufficiently explicit and pragmatic to
enable a reader to make some practical use of information theory. This paper
is intended to serve as a stopgap to fill a temporary current need. It is designed
to have some of the aspects of an elementary textbook, including a few exercises.
The examples are largely drawn from communication engineering and engineer-
ing psychology, these being the most convenient ways of interpreting information
theory; however, the whole theory could be expounded without any reference
to conscious communication.

Information theory is based on the concept that information is measurable.
This idea is not new. In physics, the notion of a measurable relation between
information and degree of orderliness (entropy) dates back to Boltzmann's
work in 1872 and its development in 1929 by Szilard (1). In 1918, the statis-
tician R. A. Fisher (2) needed a criterion to assess the degree to which the
information contained in experimental data is utilized by a given statistical
procedure; he worked out a measure of information which has been used in
statistics ever since. Later, the need arose for a measure of information-
carrying potential as a consequence of the tremendous development of tele-
communication, and in 1928, R. V. L. Hartley (3) published such a measure.
In 1948, Wiener (4) observed that a measure of infomiation content is a basic
ingredient to the study of communication, which itself is a basic ingredient
to the study of control in its broadest sense. In the same year, the communi-
cation engineer C. E. Shannon (5) published an article on the mathematical
theory of communication which in several respects went beyond previous
studies. This article is highly technical; it is very difficult reading; it appeared
in a specialized journal {The Bell Systems Technical Journal) and it pertained
to no other field than telecommunication. It certainly did not look like an article
destined to reach wide popularity among psychologists, linguists, mathema-
ticians, biologists, economists, estheticists, historians, physicists . . . yet this
is what happened. In 1949, the University of Illinois Press issued a book (6)
which consisted of a reprint of Shannon's earlier article and a paper by Warren
Weaver; in this paper, the generality of the concept of 'amount of information'
was forcefully expounded. The literature on 'information' has been increasing
ever since at an almost explosive rate.

What are the reasons for these startling consequences of such a highly
specialized article? One reason is, of course, that it is a very good article.
The other is that the concept of a measure of information fulfills a general
and deep need of our time. The sheer bulk of the information now available
increases at a rapid rate. Accordingly, the representation of information becomes
a more and more critical problem, and information theory offers general
principles concerning representation. Also, we are developing organizations

A Primer on Information Theory 5

which are more and more complex; they depend for their functioning on
successful and efficient communication, and information theory offers general
principles about communication.

Information theory is related to a group of specialties which are either
new or have recently increased tremendously in popularity, as has information
theory itself. To name but a few: operations analysis; the theory of experi-
mental design; decision theory; theory of linear programming; cybernetics;
game theory; theories of administration; group dynamics; and others.

A little pondering over this list suggests a few generalizations:

(i) all of these sciences are mathematical, the fields of probability and
statistics being referred to most frequently;

(ii) each employs a system of evaluation* of something;

(iii) each deals with complex situations; in every one, there is a multi-
plicity of possible choices as arrangements of some sort, and in
most of them, a large number of interrelated factors affect the
choices. Thus, they all can properly be called system theories;

(iv) none of these sciences is primarily concerned either with the physical
nature of the system considered or with the mechanisms by which
its parts are interrelated.

These are the common features. However, each of the endeavors named
is a special science since each deals with a different aspect of systems. It is an
open question whether because of their similarities these different sciences
can be gathered under one common discipline that could be called General
Systems Theory (and is the basis of a society formed in 1954).

Information theory, thus, is only one of several system theories. The parti-
cular concern which characterizes it in contrast to the related specialities is
measurement of the degree to which a thing (or a condition, or an event) is
specified; that is, of the degree to which it differs from other possible things
(conditions, events). Communication and organization are treated in terms
of a mutual specification. One way to illustrate the essence of information
theory is to compare it with statistics. Statistics and information theory both
deal with the diversity among the elements of a set, but in different ways.
Statistics treats diversity as a nuisance, and tries to establish what can be
stated or done in spite of it. Information theory treats diversity as an asset
without which operations such as selection, communication, representation,
specification, would not be possible; it tries to establish what can be achieved
because of a certain degree of diversity. The 'information' evaluated in Infor-
mation Theory is thus not the every-day information. The 'information' in
a message, for example, as a type of event, is the measure of the amount of
knowledge (intelligence) which a message of this sort ideally can convey through
the medium of symbolic representation.

To many people, information theory looks highly promising on first contact;
to some people, it still looks promising after serious study. Information theory
has become well established among engineers. In psychology, it has achieved

* In some cases values are frankly imposed, in others they are inferred from observed
behavior. This does not necessarily mean that the values must be consciously imposed;
goal-directed behavior can occur without any conscious act of fixing values.

6 Henry Quastler

a certain status. In biology, economics, political science, esthetics, linguistics,
information theory has interested many people, but the active users are only
a handful.

II. THE REPRESENTATION OF INFORMATION

'One if by land, two if by sea.' Paul Revere and his fellow citizens did
not know information theory, but they knew and utilized what is at the basis
of information theory, namely, the principle of the representation of intelligence.
The Paul Revere code is not quite up to modern standards, but it has the
essential properties:

(i) The news concerning the road of approach of the enemy was translated
into another kind of intelligence, nam.ely, lights hoisted on a steeple; this
translation is useful because it transforms a hard-to-broadcast piece of intelli-
gence into one which is easily broadcast;

(ii) the range of all possible events was subdivided into categories of
interest. The code could have been reduced to one which indicated only the
enemy's arrival. It could have been expanded into one conveying more
accurately the direction of approach, or signalling the enemy's strength and
other details of possible interest. In this case, a more complicated code would
have been necessary, and this would have increased the possibility of misunder-
standings. Proper economy of categorization is an important feature in
representing information ;

(iii) the representation employed a code previously agreed upon. No
light meant no enemy approaching, one indicated land, two indicated sea. It
seems that no agreement was made concerning simultaneous approach by land
and by sea, but the message 'three lights' would have been correctly interpreted
by all concerned.

Possibilities of Representing Information

There is no limit to the number of possibilities of representing one kind of
information by another. (It may be observed that the term 'information' covers
more ground than the word 'intelligence'. Generally, the word intelligence is
restricted to conscious informiation.) The only condition for representation is
that a complete system of translation, a code, be agreed upon. The limitations
are set only by the ability to discriminate information to be represented, by the
ability to produce accurately a desired representation, and by the range of
the code.

Representation is not restricted to discrete categories of intelligence. A
continuum of information or state of affairs can be represented by a physical
continuum such as a range of voltages or the rotation of a shaft. Any kind of
information, discrete or continuum, can be represented by the charges in an
electron tube, by the magnetization of a spot on a metallic surface, by the
deflection of the beam of a cathode ray tube, by a hght falling upon a photo-
graphic emulsion, and so forth (7).

It is possible to represent not only data, but also operations on data. On a
slide rule, numbers, a kind of intelligence, are represented on scales by marks,
which is a form of encoding. The operation of multiplication is encoded by
positioning the slide and the indicator, and decoded by the act of reading from

A Primer on Information Theory 7

a scale. The slide rule, thus, is an early and modest example of an information-
handling device. At present, machines exist which accept and store considerable
symbolic information concerning data and operations, and which will execute
a wide range of manipulation with this information. There is good reason to
believe that machines will actually be built which can compute any number
that can be computed, and which, even more generally, can arrive at the results
of any thinking which can be described by explicitly-defined operations.

In the situations so far mentioned the relation between the original and the
translated (coded) intelligence was based on a mutual agreement. Translation
of information is not restricted to such a situation; it may be based on a
one-sided choice of code, one not explained to the receiver. This occurs in the
case of conditioned reflexes: each time a dog is fed, a bell rings; after some
time, the information 'the bell is ringing' comes to represent the infonnation
that 'food is about to be served', and leads to preparations for eating. The
code is established by the experimenter; the dog is not consulted. In fact, the
representation of information does not have to be at the level of conscious
awareness in any way. For instance : the system which regulates one's breathing
and thereby his oxygen intake has come to depend for its regulation not on the
oxygen content of the blood itself, but on the concentration of carbon dioxide.
Ordinarily, the COg level in the blood is a reliable representation of the O2
level; under certain conditions the representation ceases to be correct, and
then difficulties can occur. In all of these cases, just as in those with arbitrarily-
fixed codes, information theory is concerned with the general laws which
govern the possibility of translating one kind of information into another; it
will be obvious by now to the reader that the term 'information' in the technical
sense covers a good deal more than in everyday language.

^ReaV and 'Symbolic' Events

We now turn to a more formal and general discussion of the principles of
representation of information. We will deal here only with information that
occurs in discrete units; however, the transition to treatment of the continuous-
function type of information would not be difficult.

In our discussions, the terms real and symbolic will replace the cumbersome
expressions 'something to be represented' and 'something representing'. It will
be remembered that 'real' and 'symbolic' refer not to properties of things, but
to their functions in a given situation, and that the term 'symbolic' may but
does not necessarily imply that a conscious act of symbolization has occurred.
The 'symbolization' of the need for oxygen by the carbon dioxide level illustrates
that 'symbolic' is here used in a wider sense than is customary.

'Infonnation' is not a disembodied something; it is always related to some
actual carrier — a thing or an event. We will use whichever word is appropriate
in a given situation; the word event is most frequently used as a generic term.
However, it must always be remembered that other terms could be substituted ;
information theory applies equally to all kinds of carriers of information. In
formal language, one refers to the information carriers as elements of discourse,
or points in sample space, or configurations of properties.

A concrete event, in all its richness of detail, is not amenable to complete
representation. The only complete representation of a particular man, at a

8 Henry Quastler

particular moment, is that man, at tliat moment. Amenable to symbolic
representation are only certain aspects of the concrete event, for instance, the
fact that this man, at that time, belonged to a category labelled 'male' student
junior year, college of engineering, grade average 4.32, etc. This kind of
information lends itself to representation, e.g., by the position of certain slots
on a Hollerith card. In general, when we speak of representing events, we mean
not concrete events in their whole individuality, but only their abstractions as
instances of a category of events. In formal language, the aspect of informational
interest of an event is its 'class membership', or the name of the 'set of points'
to which it belongs.

The first steps, then, in representing information, are (1) the decision of
what to consider as elementary carriers of information, or elementary events,
(2) the decision as to what features of these events are to be considered as
relevant, and (3) a comprehensive listing of all classes of events corresponding
to the various features or combinations of features. Ideally, this analysis of
the real situation should be completed before the task of symbolic representation
is started; in practice, it will often be convenient to base a temporary system
of representation on an incomplete analysis, and introduce subsequent refine-
ments and adaptations as needed. A library catalogue, arranged by subject
matter, is a good example of a system of representation which must remain
flexible and capable of growing.

Symbol, Alphabet, 'Word'

The basic unit of symbolization is called a symbol. The set of all available
symbols constitutes an alphabet. In the simplest form of representation, each
individual event is translated into a single symbol that represents that kind of
event. This can be done if the alphabet is large enough to have a separate
symbol for each of the categories required to classify real events. The Paul
Revere code is an example.

The one-by-one method of representation lacks flexibility and is cumbersome.
Often a smaU alphabet is used to express a wide range of possibilities. In this
case, single events must be represented by combinations of symbols; these are
called code groups, or 'words'. For instance, an alphabet of twenty-six letters
is used to represent several hundred thousands of English words, and is flexible
enough to accommodate any number of new words; this is achieved with an
average of 4.5 letters per word (where the letters are not used with greatest
economy!). In turn, an alphabet consisting of only two symbols, the dots and
dashes of the Morse code, is sufficient to account for all the twenty-six letters,
plus the ten digits, plus punctuation marks and a few standard concepts, without
ever employing more than six symbols in a single code group, or 'word' (as
defined above, not in the ordinary sense!). According to Gamow and Ycas
(this volume), each of twenty amino acids in a protein can be represented in
the RNA molecule by a 'word' of three nucleotides; in this case, the sequence
of letters in the word is considered irrelevant.

Binary Representation

Simplest Case — For developing a general theory of the representation of
information, it will be convenient to reduce all representations to some standard

A Primer on Information Theory 9

form. Any standard form would be acceptable; it has become customary to
employ the simplest of all possible alphabets, the binary alphabet. The two
symbols commonly used are T and '0'; it must be emphasized that '0' does
not necessarily imply the absence of some physical action; e.g., T and '0' might
stand for right-left, positive-negative, dash-dot, etc. The standard symbolization
of any event will be a binary number, such as 1001 101 ... , where the symbolic
meaning of each digit and combination of digits is fixed by some law of associa-
tion.

It must be pointed out that the Morse code is not a strictly binary representa-
tion if one thinks of whole messages. The Morse code is really a quaternary
code. This is so because, in addition to the 'blacknesses', the dots and dashes,
it uses two 'whitenesses' of different length, namely, an inter-letter space and
an inter-word space. Both of these are integral parts of the code system, because
otherwise we could not know whether this:

means 'hen', 'sue', 'sin' or 'site'.

How many events can be represented by words made up of a certain number
of binary symbols? There are two different 'words' (T and '0') consisting of a
single symbol; they can represent a partition of a set of real events into two
classes. There are four different two-symbol 'words' (11, 10, 01, 00), and, in
general, 2" code groups consisting of /z binary symbols. Accordingly:

A sequence of « binary tests will discriminate between 2" possibilities;

A sequence of « binary choices will select any one of 2" alternatives;

A sequence of n binary statements will identify any one of a set of 2" items,

etc.

Conversely, if a code book with r distinct representations is to be made up
in standard binary code, then each word will have to be a binary number with
about log2 r digits*. For instance, eight categories of events can be represented
by code groups consisting of three binary symbols (3 = log2 8):

Category A 1 1 1

Category B 1 1 0

Category C 10 1

Category D 1 00

Category E 0 1 1

Category F 0 10

Category G 0 0 1

Category H 0 0 0

Observe that the meaning of each binary symbol depends on its position and
on the nature of the other symbols in the word. For example, a 1 in the second
position means 'A or B or E or F' ; if preceded by a 0, then it can mean only
'E or F'; if also followed by a 1, then it designates 'E', unequivocally. This

* Logarithms to the base 2 can be found in pubHshed tables, or read on a slide rule with a
log-log scale, or obtained by multiplying the base- 10 logarithms by 3.322.

10 Henry Quastler

implies that any digit of the symbolic word, considered by itself, does not
necessarily represent a given operation. For instance, a set of recognition
operations, such as a naturalist's key, could well be arranged as a sequence of
binary tests. In such a case one will not always apply the same sequence of
tests; in general, the choice of the second test will depend on the outcome of
the first, the choice of the third on the outcome of the previous two, etc.
Accordingly, the code book will have to specify what operations and what
outcomes a particular symbol designates.

Sequences of code words will represent series of 'events'. Suppose our
message were to represent the sequence of events 'G C A'. Using the code given
above, we get:

001101111.

Observe that the 'words' in the message are not separated by spaces; a space
with a defined symbolic meaning (such as a 'whiteness' in the Morse code)
would make the alphabet ternary rather than -binary. The receiver will not miss
the spaces ; he is expected to know the code and, accordingly, to read the message
in groups of three digits, beginning with the first one at the left.

Any Number of Categories — In general, the number of categories to be
encoded is not an integral power of two (such as 2,4,8,16,32 . . .). We could
always use the nearest higher power of two as the basis of the coding scheme.
For instance, if we had five categories to represent, then we could simply use a
portion of our three-digit code for eight categories:

Category A 1 1 1

Category B 1 1 0

Category C 1 0 1

Category D 100

Category E Oil

In this example, the symbolization possibilities of the three digits are not
fully utilized. This is not economical; one will suspect that it is possible to
achieve greater economy in number of digits. This can mean only that some
of the five categories will be represented by two digits only. Some words will
have two, and some three digits; the decoder will not have the benefit of being
able to cut up the message into pieces of equal length. Therefore, it becomes
imperative that the words themselves indicate unequivocally the correct partition.
This will be the case if no combination of code groups is identical with any
other combination of code groups; otherwise, confusion may arise. For
instance, the following:

Category A 1 1

Category B 10

Category C 0 1

Category D 0 0

Category E 1 1 1

A Primer on Information Theory

11

is useless because the message '1 1 1 IT could be read as 'A E' (11 1 1 1) or 'E A'
(111 11).

R. M. Fano (8) has devised a simple method for establishing a confusion-
proof code. It goes as follows: all the categories to be encoded are divided up
into two groups; the symbols T and '0' are assigned to these. Each of the
two groups is, in turn, subdivided into subgroups; these are designated '1' and
'0' in the second digit. The procedure of subdividing is continued until no
subgroup contains more than a single category. At any stage of partitioning,
the subgroups may contain unequal numbers of categories; accordingly, the
number of steps to complete the coding does not have to be the same for all
categories. This results in words of unequal length. In spite of this, messages
composed of code groups formed according to this rule will be perfectly un-
equivocal.

Fano's method will be illustrated by three ways of making up a code for
five categories :

(a): separate category 'A' from the others in the first step; use two more
steps to subdivide the remaining four categories.

Category

1st step

2nd step

3rd step

Final code

A
B
C
D
E

I

0
0
0
0

0 1
0 1
0 0
0 0

0 1 1

0 1 0

0 0 1

0 0 0

1

0 1 I

0 1 0

0 0 I

0 0 0

{b) : Use the first step to separate 'A or B' from 'C or D or E' :
Category 1st step 2nd step 3rd step Final code

A

1

1 1

1 1

B

1

I 0

1 0

C

0

0 I

0 1

D

0

0 0

0 0 1

0 0 1

E

0

0 0

0 0 0

0 0 0

(c): First step as in {a); the second step is used to separate 'B' from 'C or
D or E'; the third separates 'C from 'D or E'; and the fourth separates 'D'
from'E':

Category

1st step

2nd step

3rd step

4th step

Final code

A

1

1

B

0

1

1

0 1

C

■ 0

0

1

0 0 1

D

0

0

0

1

0 0 0 1

E

0

0

0

0

0 0 0 0

r

12 Henry Quastler

These are the three Fano codes with five words; all other codes can be
reduced to one of these three by rearranging the names of the events. All three
codes are confusion-proof. In decoding, one retraces the steps of encoding; the
code book shows, unequivocally, whether any symbol in a given sequence is a
terminal one, or whether it does not yet identify a single category. For instance,
suppose code (c) has been used, and the message received was:

000000101.

The first zero indicates 'B or C or D or E'; the second, 'C or D or E'; the
third, 'D or E'; the fourth designates 'E', unequivocally, and is a terminal
symbol. We mark off the four zeros and proceed. The first symbol of the second
code group is a zero, as is the second; this indicated 'C or D or E'; the next
symbol is a one, which is a terminal symbol and designates 'C. The remaining
code group, '01', means 'B', and the whole message is decoded unequivocally:
'E C B'.

Code (b) has the minimum bulk, or lowest average number of digits per
word (2.4 digits, against 2.6 digits for code (a) and 2.8 for code (c)). The rule to
obtain the minimum bulk code with any number of categories is as follows:
all divisions and subdivisions must be between groups of categories of as nearly
as possible equal sizes. To find the word length in this code, detemiine the
largest integer k compatible with the condition that

2^ ^r< 2*^+1

{k ^n <k + \).

Then, using equipartition as nearly as possible, each word will be of length k
ov k -\- 1, and the average number of binary symbols per category encoded will
be somewhat larger than logg r. In the example just given:

r = 5, loga r = 2.33

k = 2, k -{- I = 3, average length of word = 2.4.

The worst discrepancy between log2 r and average word length occurs for r — 3.
We have:

Category A 1

Category B 0 1 ;

Category C 0 0

logs 3 = 1.58

A' = 1, A' + 1 = 2, average length of word = 1.67 symbol

excess digits per word = 1.67 — 1.58 = 0.09 or 5.7 per cent

of 1.58

Groups of Events — The excess of average word length over logo r is due to
some partition (especially an early one) dividing the set of categories into

A Primer on Information Theory 13

portions of unequal size. In the case of three categories the first partition
separates category 'A' or 33 per cent of all categories, from 'B or C\ representing
67 per cent. This situation can be improved when it is allowed to represent
pairs of events, instead of single events. There are nine pairs of the events A, B,
and C, designated AA, AB, AC, BA, etc. We use the first symbol to subdivide
them into two groups of four and five, respectively; each of these groups is
subdivided by the second symbol, etc. We obtain:

Pairs of real events Symbolic representation

AA ' 111

AB 110

AC 10 1

BA 10 0

BB Oil

BC 0 10

CA 0 0 1

CB 0 0 0 1

CC 0 0 0 0

29
Average: — = 3.22 symbols per pair of events, or 1.61 per single event.

Excess digits = .03 < 2 per cent

By going from pairs to triplets, the limiting value can be approached still
closer. In general, if the group of events to be represented can be made as large
as desired, then the limiting value can be approached as closely as desired.

Unequal Probabilities — In general, categories occur with unequal probabili-
ties. In this case, subdividing the categories into sub-sets containing equal
numbers of categories will not result in a minimum-bulk code. Consider, for
instance, the three Fano codes for a set of five categories. Suppose category
A accounts for 80 per cent of all occurrences, and the other four for 5 per cent
each. In this case, code (a) will yield minimum bulk with an average of 1.4
digits per word, followed by code (c) with 1.45 and code (b) with 2.1 digits.
The general rule to obtain a minimum bulk code, with any number of categories
and equal or unequal probabilities, is as follows : all divisions and subdivisions
should be between groups of categories of as nearly as possible equal aggregate
probabilities.

The average number of digits in a minimum bulk code is found by the
following consideration: let p{i) be the probability of an event falling into
/'th category, where / may stand for A, B, C, . . . , if the categories are designated
by letters, or for 1, 2, 3, ... , if the categories are numbered. For the time being,
we consider only probabilities which are integral powers of 1/2, i.e., 1/2, (1/2)^ =
1/4, (1/2)3 ^ 1/8^ (1/2)4 _ 1/16^ etc.; i.e. we set p{i) = {Xjiyi where z^ is a
positive integer. In such a case, each step in the coding procedure can be a
partition into groups of equal aggregate probabihty; then, the code word for

14 Henry Quastler

each category will have exactly r^- binary digits. This is illustrated in the following
example:

Category

Probabihty, p(i)

Zi

representation

A

1/2

1

1

B

1/8

3

0 1 1

C

1/8

3

0 1 0

D

1/8

3

0 0 1

E

1/16

4

0 0 0 1

F

1/32

5

0 0 0 0 1

G

1/32

5

0 0 0 0 0

32/32 = 1

The first step separates 'A' (p = 1/2) from all other categories (aggregate
probability = 1/2); the second separates 'B or C (aggregate p = 1/4) from
'D or E or F or G' (aggregate /? = 1/8 + 1/16 + 1/32 + 1/32 = 1/4); the
third separates 'B' from 'C (p, 1/8 each) and 'D' (/j = 1/8) from 'E or F or G'
(aggregate /7 = 1/8), etc.

The average number of digits per code word is the sum of the z/s, weighted
by the probabilities />(/) ; in our example:

2p{i) • z, = 1/2 + 3/8 + 3/8 + 3/8 + 4/16 + 5/32 + 5/32 = 70/32 = 2.19

i

From p{i) = (1/2)^

we get : logg p(/) = z, • logg ( 1 /2)

and, because: logg (1/2) = —1

we have: z^ = —loga /?(/)•

We get (for/?(/)'s which are integral powers of 1/2!) the following result:
Average number of binary symbols per event = —^p(i) logg /)(/).

i

We will check this result for the case of equiprobable categories. For
r categories, the probabihty of every one will be 1/r; so:

-lp(i) log2/'(0 = -r--- log2 - = log2 r

i r r

This is the expression previously obtained for equiprobable categories.

Any Probabilities — What if probabihties are not limited to the values 1/2,
1/4, 1/8, etc. ? In this case, it will — in general — not be possible to make divisions
into exactly equiprobable groups. We would suspect that in this case the
coding will be less than optimally efficient; accordingly, the average length
of a code word will be somewhat higher than —^p(i) logg /?(/). The approxi-

mation is usually not bad. This is illustrated in the following example which
shows the construction of a binary code for the letters of the English alphabet,
taking into account their relative frequencies. As expected, it turns out that

A Primer on Information Theory

15

each category, /, is represented by a code word of approximately —\og2pO)
digits; accordingly, its contribution to the weighted average is not far from
the ideal value of —p{i) log, /?(/), and the mean code length is only very slightly
greater than the limiting value of —]£/?(/) logg /?(/)•

Table I.

Fano Code for English Letters

1

2

3

4

5 6

7

No. of

digits in

code word

Contribution

/

pU)

Code

-10g2/'(/)

to weighted

-/>(/) X logipO)

average
2x4

2x5

E

.132

HI

3

2.92

.393

.384139

T

.105

110

3

3.25

.315

.341411

A

.086

101

3

3.54

.258

.304398

0

.080

1001

4

3.64 1 .320

.291508

N

.071

1000

4

3.82

.284

.270938

R

.068

0111

4

3.88

.272

.263725

I

.063

0110

4

3.99

.252

.251275

S

.061

0101

4

4.04

.244

.246137

H

.053

0100

4

4.24

.212

.224606

D

.038

00111

5

4.72 .190

.179278

L

.034

00110

5

4.88

.170

.165862

F

.029

00101

5

5.11

.145

.148126

C

.028

00100

5

5.16 .140

.144436

M

.025

0001 1 1

6

5.32 1 .150

.133048

U

.020

000110

6

5.64

.120

.112877

G

.020

000101

6

5.64

.120

.112877

Y

.020

000100

6

5.64

.120

.112877

P

.020

000011

6

5.64

.120

.112877

W

.015

000010

6

6.06

.090

.090883

B

.014

000001

6

6.16

.084

.086218

V

.009

0000001

7

6.80

.063

.061162

K

.004

00000001

8

7.97

.032

.031863

X

.002

0000000011

10

8.97

.020

.017931

J

.001

0000000010

10

9.97

.010

.009965

Q

.001

0000000001

10

9.97

.010

.009965

z

.001
1.000

0000000000

10

9.97

.010

.009965

4.144

4.118347

We have already met a situation where a binary code was less than optimally
efficient (in the sense of minimum length of code words); that was the case
of r equiprobable categories, when r was not an integral power of 2. In this

16 Henry Quastler

instance, it was possible to approximate optimal efficiency by symbolizing
groups of events instead of single events. The same principle works in the case
of probabilities which are not integral powers of (1/2). We will illustrate
the method in the case of a situation with two alternatives.

Example: Let there be two categories of events, 'A' and 'B', with associated
probabilities, p{K) and /?(B) :

/'(A) = .7

/KB) = .3

The limiting value of symbols per event is:

-IKO log2 AO = -(0.7 logo 0.7 + 0.3 log2 0.3) = 0.881291 . . .

i

If this situation is to be represented on the basis of single events, then one
needs one binary digit per event.

Event Probability Representation

A 0.7 1

B 0.3 0

Average number: 1.0 symbol per event; excess 12 per cent.

The following two-event clusters are possible: AA, AB, BA, BB. If the two
events are independent, then the probability that both occur is the product
of their individual probabilities :

p(AA) =7;(A) -piA), p(BA) =/7(B) - p{A\ etc.

Setting up a Fano code, we get:

Event Probability Representation

AA .49

AB .21

BA .21

BB .09

1

0 1

0 0 1

0 0 0

Average 1.81, or 0.905 symbols per event; excess 3 per cent.

If we can encode groups of three real events, then we get still closer to optimum
economy :

Event Probability Representation

AAA .343

AAB .147

ABA .147

BAA .147

ABB .063

BAB .063

BBA .063

BBB .027

1 1

1 0

0 1 1

0 1 0

0 0 10

0 0 11

0 0 0 0

0 0 0 1

Average: 2.686, or 0.895 digit per event; excess 1^ per cent.

A Primer on Information Theory 17

Even with more pronounced unbalance of frequencies, tiie minimum value
of binary digits per word is soon approximated. For/)(A) —■ .89 and /;(B) = .11,
the limiting value is .50. In single-event-code, one needs one digit per event;
for two-event-sequences, .66 digits; for three-event-sequences, .55; and for
four-event-sequences, .52.

We have begun our discussion of binary representation with the case of
2, 4, 8, 16, ... , equiprobable categories. We then generalized to cases with
any number of categories, and proceeded from the representation of single events
to clusters of events. Next, we introduced unequal probabilities, of value
1/2, 1/4, 1/8, ... . Finally, we dropped all restrictions. We can now state,
with full generality:

If a real situation is categorized into r categories, with associated proba-
bilities p(i), (where / = 1, 2, . . . , r), then it is possible to represent each

r

event with an average of no more than — 2 p(i) log2 pii) binary symbols.

i = l

Representation Theorem — In general, the closer we v/ant to approximate
the minimum bulk of representation, the larger the groups of sequences which
must be encoded. This entails the following penalties :

1. There will be a delay in waiting for a whole group of events to occur
or to be registered, and

2. The encoding and decoding procedures, and the code book itself, will
become the more elaborate the larger the groups coded.

It is obvious that the code which is most economical in terms of bulk of
representation is not necessarily optimum in over-all performance. There
will be cases where it might be worthwhile to sacrifice economy in word length
for ease in decoding. If the reader will work through exercise 4, then he surely
will appreciate this possibility. Whether or not minimum bulk of coding is
favorable, in a given case, cannot be derived from informational analysis.
What information theory does is to establish a limiting value of the number
of symbols, of a given kind, which are needed to represent the information in
a given factual situation; in some cases, like those here discussed, information
theory will also show how such coding economy can be achieved; but it can
never prescribe that this is what should be done.

It would be quite legitimate to inquire, at this point, why we have gone to
so much trouble to find out how to achieve binary representation with minimum
bulk ? Is not the result of doubtful value, in view of the fact that a tolerable
approximation to minimum bulk can usually be achieved with the simplest
means, and that a close approximation often entails prohibitive costs in encoding
and decoding? The answer is this: by establishing the minimum length of
code words in standard binary representation, we have implicitly established
a general condition of representability :

If an event can be represented by (on the average) n binary digits, then it
can symbolically represent, or be represented by, any other event that can
also be coded into n binary digits.

This can be immediately generalized to groups of events: Let 5"^. and Sy be
the number of real and symbolic events in a group, and n^. and «„ the average

18 Henry Quastler

binary representation per event and per symbol. Then, the general condition
of representability can be stated as follows :

^y ' f^u ^ ^X ' ^X

EXERCISES

1. A weakness of the Paul Revere code is that there is no positive signal for "peace and
quiet". Hence, the colonists could not be sure whether the absence of a warning signal meant
"peace and quiet" or a disturbance in the communication system. Show how two lights
could be used to indicate the four situations by positive signals.

2. Any integer can be written as a sum of powers of 2(1,2,4,8,16, • • •)• For instance:

27 = 16 + 8 + 2 + 1
= 2* + 2=' + 21 + 2»

In binary notation, one indicates the power by position, and writes a '1' in appropriate position
if this power does enter the sum, a '0' if it does not. Thus, '27' becomes 11011.

(a) Write the following numbers in binary notation: 0,1,2,3,4,5,6,7,8,9,10,12,16,1955.

(b) Write the following binary numbers in decimal notation: 1001, 1011, 10010011, 100000.
Any proper fraction can be written as a sum of powers of 1/2, (1/2, (1/2)^ = 1/4, (1/2)^ = 1/8,
etc.). For instance: .75 = 1/2 + 1/4, or, in binary notation, .11.

(c) Translate into decimal notation: .001, .1001001

3. (a) encode the message 'ABCDE' in code (a) of the five-word codes described earlier,
(b) decode the message: '000001011011' in code (b).

4. This assignment is coded in the Fano code for English letters given earlier.
001001001 10000101 1 1001 1 10001 10001001 10101001001001 1000001010001 1001010
1 101001 10000010101 1111111 1001001001001 1 1 1 1 10001 10010101 101000000101001
0101 100000001 1 1 100000101 10100010101 1 1000100001 1 101 1000010101 101 1001010
0101 100101 1 1 1 1 1 101001000100001 101111 101 101 110111 101 1000001 1 10010010010
001 1 100001 110101111111 1001001 1 100001 1111011 100101 100101 1 10001 1 1 101 1000
001001 1 1 100100101 1 10010001 100101001001001001 1 1 1 1 100001001 101 1001001 100
100101 1 10100100101 1 1001001 1 1 10 100000 1 10010000001 1 1 10000010001001 1 1 1000
001001001001 1 101 101000000101 101 1000001 1 1001 1 1 1 1 1001001001001 1 101 101000
000 101 1010001 1 1 1 1 101010101 101000101 1 1 1001 1001 1000000001 1 1 1 1 10010001 10
010110011000 111

(This assignment is very tedious but it is good practice.)

5. Given a real situation with three categories and probabilities p(A) = .8, p{B) = .15,
p(C) = .05. Construct a binary code which comes within 10 per cent of the minimum bulk.

6. A protein is thought to be a linear arrangement of amino acids of which there are
(about) twenty kinds in each cell. The specificity of a protein depends mostly on the sequence
of amino acids, i.e. a protein can be considered as a 'message' written in a twenty-letter
alphabet. It is known that, in the living cell, protein specificity is determined by nucleic
acids. These are linear arrangements of nucleotides, of which there are four different kinds.

Question: what is the minimum number of nucleotides needed, on average, to specify
each amino acid? Assume all amino acids to be equiprobable.

III. THE MEASURE OF INFORMATION OR UNCERTAINTY

It seems reasonable to equate the amount of information acquired, as a
result of an event, to the amount of uncertainty which its occurrence has

A Primer on Information Theory 19

abolished*. The prior uncertainty does not depend on the event that has
actually happened, but, rather, on the whole set of events which could have
happened at this particular occasion. For instance, if one wishes to compute
how much information is acquired, on the average, by a glance at the speedo-
meter, one proceeds to estimate how uncertain a motorist is before he glances.
The amount of this uncertainty must depend on the number of needle positions
which the motorist thinks he can distinguish. Suppose his speedometer scale
reaches from zero to one hundred and he can read the position to the nearest
mile per hour; then, he will be able to distinguish 101 positions, and the amount
of his uncertainty will be somehow related to this number. However, it wouldn't
be realistic to relate his uncertainty only to this number, 101. Because, suppose
his speedometer scale ranges up to 150 instead of 100 miles per hour; yet,
when he is driving along the highway at a moderate speed, this extra portion
of scale does not contribute in any way to his uncertainty; he will be quite
sure that his needle will not be in this interval. In fact, he will expect to find
his needle somewhere within a range of about 10 m.p.h., and he will be almost
certain to find it within a somewhat larger range of, say, 20 m.p.h. Thus, to
describe his uncertainty realistically, we must not only state every possible
result of his reading, but will have to qualify each by a statement of expectation
or probability.

The Amount oj Uncertainty

As before, we turn to a binary situation to obtain a simple perspective of
the problem. Suppose somebody has made a record of 100 tosses of a coin;
he has registered only whether the coin fell 'head up' or 'tail up', but neglected
all other features such as on what spot the coin came down, which direction
the head faced, etc. What is the average amount of information in the record
of any one toss? In other words, what is the amount of uncertainty before
the record is seen ?

The uncertainty must be a function of 'two', the number of alternatives;
it must be modified by their relative frequencies. If it is known that the record
is that of a coin so thoroughly biassed that 'head' always turns up, then there
will be no uncertainty at all; if the coin is moderately biassed, then the outcome
of a toss will be uncertain but not qui.te as much as with an unbiassed coin.
If we don't know the bias of a particular coin, then we do not know exactly
how uncertain we should feel about the outcome of a toss. If we know that
the record contains 60 'heads' and 40 'tails', then a record of 'head' will show
up with a probability of .60, a record of 'tail' with a probability .40. The
uncertainty can be described by a statement of these probabilities:

Probability of head up 0.60

Probability of tail up 0.40

In the same way we can describe any number of binary uncertainties with
a 60-40 choice between any class 'A' and its complement 'non-A' — where
'A' and 'non-A' may be males and females, hits and misses, friends and foes.

* At some time there was some discussion whether uncertainty and information should be
given opposite signs. Present usage prescribes the same sign for both.

20 Henry Quastler

These uncertainties differ in any number of respects from each other. They
win be of interest in very different situations; the kind of infomiation needed
to produce certainty is not the same; neither is the usefulness of this information,
and so on. However, there is something in common between all uncertainties
which can be characterized by the probabihties:

Probabihty of 'A' 60

Probabihty of 'non-A' ... 1 — .60

One aspect of this 'something-in-common' is that an arrangement of any 60
A's and 40 non-A's can be coded to represent any other 60 A's and 40 non-A's
—heads or tails, males or females, hits or misses, friends or foes. Once such
representation has been established, then the uncertainty concerning one
event will be abolished by information concerning the other. We have previously
equated the amount of information with the amount of uncertainty it removes.
Accordingly, it can be said that the amounts of uncertainty and information
must be equal in all situations characterized by a binary alternative with
probabilities .60 and .40.

The foregoing consideration exposes the fundamental features of the
measure of information :

(1) Information is a measurable abstract quantity; its value does not
depend on what the information is about, just as length, or weight, or tempera-
ture have values which do not depend on the nature of the thing which is long,
heavy, or hot ;

(2) Information is related to the ensemble of possible outcomes of an
event; its value depends on the probabihties associated with these outcomes,
but not on their causes, and not on their consequences.

What remains is the development of a measure which comphes with this
concept of 'amount of information'; this is merely a technical problem. An
obvious generalization states that whenever two events have the same number
of possible outcomes, and identical sets of probabihties are associated with
the two ensembles of possible outcomes, then these two events have identical
information contents. However, we wish to be able to compare events with
quite different probability sets; for instance, we wish to be able to say which
uncertainty is greater, that associated with a situation with three equiprobable
alternatives, or that where there are four possibilities with probabilities .8,
.1, .05 and .05. To answer such questions, we have to derive a measure which
is a single number, whatever the number of possible categories and their
associated probabihties.

Such a measure is readily derived from the equivalence of uncertainty
with the information which removes it. We may represent the information
content of an uncertainty-removing piece of intelligence in any manner we
wish. We stipulate that this information should be represented in a standard
fashion, namely, by using a binary alphabet. In addition we stipulate that
the binary representation be coded in such a manner that the expected number
of symbols is minimized. We thus obtain a unique number; namely, the
minimum average number of binary symbols needed to abolish the uncertainty
associated with a given situation. This number will be called the amount of
uncertainty or information of this situation.

A Primer on Information Theory 21

The function here needed has already been derived as the condition of
representabiHty. If two situations can be made to represent each other, then
information on one can aboHsh uncertainty concerning the other. Thus,
mutual representabiHty implies equal information content, and representation
in the standard binary system yields a general measure of information content.
This measure is the 'amount of selective information' as defined by Shannon
and Wiener (4, 5). It is expressed as follows:

Let X be a classification with categories i and associated probabilities
p{i); then the information content oj x is designated H(x) and given by*:

H(x)^ -2 p(i) logo p(i)

i

The units of this function are the binary digits needed for representation
of a given event, and are called bits. It must be remembered that the 'bit' is
a technical unit of amount of information and not a small piece of information.
A single chunk of information may contain many bits or a fraction of a bit.

Some Properties of the Shannon- Wiener Information Function

The Shannon-Wiener information function has been derived (admittedly, in
a loose fashion) from a consideration of standard representation of information.
We will now consider a number of its properties and see that they correspond
losely to the behavior which one would intuitively expect from a good
measure of information.

(1) Independence — Let / be one of the possible categories of an event x,
p{i) the associated probability, and F{i) the contribution of the /th category
to the uncertainty. It is desirable that F{i) be a function of and only of p{i).
The function / ^

F{i)^ -pii)\og^p(i)

fulfills this requirement. /

(2) Continuity — A small change of /;(/) should result in a small change in
F(i); in other words, F(i) should be a continuous function of p(i). The function
p{i) log2 p(i) is continuous.

/(3) Additivity — It is desirable that the total information derived from two
dependent sources should be the sum of the individual information; in other

* The information function looks (except for a scale factor) like Boltzmann's entropy-
function; this is not a mere coincidence. The physical entropy is the amount of uncertainty
associated with a state of a system, provided all states which are physically distinguishable are
considered as different, that is, if the categorization is taken with the finest grain possible.
In most situations dealt with in information theory, large numbers of states which are physically
distinguishable are lumped into equivalent classes. The category "one light on the steeple" is
a good example; an enormous number of physically distinct states are compatible with this
definition, but they are all lumped into one class. The distinctions upon which categorizations
are based are usually a very small percentage of the distinctions one could make. Thus,
physical entropy is an upper bound of the information functions which can be associated with a
given situation, but it is a very high upper bound, usually very far from the actual value. For
this reason, I prefer not to use the word 'entropy' as synonymous with 'information'.

A very thorough discussion of the relation between information and entropy has been given
by Brillouin (9).

22 Henry Quastler

words, the uncertainty concerning independent events should be the sum of
the individual uncertainties.

Let y be an event with categories j and associated probabilities p{j). Let
p{i,j) be the probability of the event pair that x falls into category / and v
into category y. Then, the function

Hix,}') = -lp{i,j)\og2p(i,j)

will measure the uncertainty associated with the event pair.
If X and y are independent events, then

p{Uj)^p{i)-p{])

As a matter of fact, this relation is often used to define independence. In this
case, we have

H{x, j) = - 2 p{i.j) logo p{i) ■ pij)

i.j

= -lp(hj)^og^pii) - lp('J)\oz.2p(j)

It is known that

J.piUj)=p{i)

j

IpiUj)=p(j)

Substituting these expressions, we obtain

Hix, >0 = - 2 Pii) log2 /XO - 2 p(j) loga p(j)

i .

= H(x) + H(y). ^ H^^^) ^ H^'^^^'i^f^^

Thus, the Shannon-Wiener function fulfills the postulate of additivity.

(4) Natural Scale— X\yQ prototype of uncertainty is that associated with a
50-50 choice. So, the unit of uncertainty should be the uncertainty associated
with this situation. In this case, both/s have the value 1/2, and

Hix) = -(1/2 log2 1/2 + 1/2 log2 1/2) - 1

Thus, the Shannon-Wiener function is seen to have an appropriate scale factor.

We have derived the infonnation function from the postulate of eflScient
binary representation, and have found that the function so defined has the
desirable properties of independence, continuity, additivity, and natural scale.
We could have started differently, setting up these four properties 2i^ postulates.
It can be shown that these four postulates (or other sets of four similar postu-
lates) define uniquely the Shannon-Wiener function. Working it this way,
we would have derived the fact that the function so defined has the desirable
property of efficient binary representation.

The function F{p) is plotted against/; in Fig. 1. The graph shows a curve
which originates and terminates at F = 0, and has a flat top with a maximum

A Primer on Information Theory

23

of F= 0.53 for/) = 0.37. Inspection of the graph reveals some more important
properties of the function F{p) :

(5) nO) = 0:

When a particular class of events is certain not to occur {p = 0), then it does
not contribute to the measure of uncertainty.

(6) F(1) = 0:

F(p) = - p logp p

F(p) 0.3

Fig. 1. Graph of F{p) as a function of/?

When a particular class of events is certain to occur {p = 1), i.e. excludes
all other classes, then there is no uncertainty about the outcome.

(7) Effect of Averaging:

F

> i[F(p,) + F(p^)]

The function of the average is greater than or at least as large as the average
of the function. When the probabilities associated with two disjoint categories
are averaged, then the uncertainty becomes larger. Figure 2 is a graphical
demonstration of this effect.

The extreme case of averaging occurs if all r categories in a classification
are considered equiprobable. Then,

Pi') = 7
I, 1 1 11

max. of H(.x) = — ^ - log., - = — /• • - lo?., -
,-1 /• ^- r r - r

max. of H(.x) = log, r

24

Henry Quastler

In particular in a binary classification,

r = 2

max. of H{x) = 1

Thus, the maximum uncertainty associated with two alternatives is one bit; it
occurs if both alternatives are equally probable (this is the case of the unbiassed
coin!).

(8) Ejfect of Pooling:

F(pi + P2X F(Pi) + np2)
The function of the sum is smaller than the sum of the functions. That is,
pooling of two classes in one equivalence class reduces uncertainty (exactly

P|+ Po

F(P|1 + F(P2J

Fig. 2. Graphical demonstration of the effect of averaging

by that uncertainty which is associated with the distinction between the two

pooled classes). Extreme pooling results in a single category with probability 1 ;

this means uncertainty 0. Figure 3 demonstrates the effect of poohng.

The function F(p) = —p logg p has been tabulated. The reader is advised

to use Fig. 1 to obtain approximate values for use in working the exercises

below. For more precise values, one of the existing tables may be consulted

(10, 11).

EXERCISES

7. Compute the uncertainty associated with:

p(A) = .60
/•(non-A) = .40

8. Compute H(x) for two alternatives, and plot the value against /7(A).

9. Answer the question posed previously: which uncertainty is greater, that associated
with a situation (x) with three equiprobable alternatives, or that (y) where there are 4 possibili-
ties with probabilities .8, .1, .05 and .05.

A Primer on Information Theory

25

10. Estimate the uncertainty of a motorist like the one described at the beginning of this
section.

11. Certain languages have considerably fewer letters than English (that is, about 18 to
20), yet the information content per letter is nearly the same. How is this possible?

12. A situation has an unlimited number of alternatives, with probabilities of 1/2, 1/4,
1/8, 1/16, etc. in geometric progression. What is the measure of uncertainty?

F(P|)+ Flp^)

FlPl + Pg)

fj P,+ Pg P2 p,+ P2
2

Fig. 3. Graphical demonstration of the effect of pooling
The function of the sum is on the intersection between the curve and the
ordinate over the sum; the sum of the functions is on the intersection of the same
ordinate with a straight line through the origin and the midpoint of the straight
line which connects the intersections of the curve with the ordinates over pi and
P2, hence:

F(p, + P2) < F(p,) + F(p,)

IV. INFORMATION MEASUREMENTS PERTAINING TO
TWO RELATED VARIABLES

In the two preceding sections we have discussed how to represent information,
and how to measure amounts of information. Both procedures become impor-
tant if information is to be manipulated. The manipulation most commonly
used is communication.

26

Henry Quastler

In infonnation theory, we use the word 'communication' in a wider sense
than usual — just as the word 'information' is used in a wider sense than usual.
We understand by 'communication' any relation between variables, accomplished
by any means whatsoever, conscious or otherwise, provided that it results in a
mutual reduction of uncertainty. For instance: if one watches one of two
tennis players, without looking at the other, he derives a considerable amount
of information about the unseen player's action. Thus, the seen player transmits
information about the unseen player — although in this case, the transmission
of information is incidental and not normally utilized, as one ordinarily looks
at both players.

An Example of Two Related Variables

The following example is purposely selected to represent an instance of
unintentional communication. The table below is based on Pearson and Lee's
measurements of heights on 1376 father-daughter pairs. To simplify the analysis,
we have grouped the data in coarse intervals of 3 in. each, and converted all
frequencies into percentages.

Table II. Heights of Fathers and Daughters; Probabilities and

Information Measures

Joint probabilities of heights, pii,))
(Pearson and Lee's data, 1376 father-daughter pairs)

jt 59.5

62.5

65.5

68.5

71.5

74.5

pU)

-p\og2P

1% = 53.5

.001

— .

—

—

—

.001

.01

56.5

.001

.007

.006

.001

—

—

.015

.09

59.5

.005

.022

.060

.027

.005

—

.119

.37

A-t 62.5

.004

.042

.156

.152

.039

.001

.394

.53

65.5

—

.009

.075

.175

.095

.010

.364

.53

68.5

—

.001

.011

.035

.039

.010

.096

.32

71.5

—

— •

—

.003

.006

.002

.011

.07

Pij)

.010

.082

.308

.393

.184

.023

1.000

1.92

-plog^p

.07

.30

.52

.53

.45

.13

* height of fathers, in 3 in. intervals
t height of daughters, in 3 in. intervals
+ center of intervals

2.00

Information Functions:

H{x) = -S/'(/)log2/j(/) = 1.92 bits

i
my) = -i:p(j)\og,p(j) = 2.00 bits

H(x) + H(y) = 3.92 bits

H{x,y) = -i:piij) log, p(i,j) = 3.70 bits

ij

Tix.y) = H(x) + H(y) - H{x,y) = 0.22

bits

A Primer on Information Theory 27

From the marginal sums, the uncertainties concerning the height of daughters,
H{x), and of fathers, H(y), are computed as described in the preceding section.
The uncertainty concerning both heights in a father-daughter pair is computed
in similar fashion from the joint probabilities, p(i,j). This function is properly
called the Joint uncertainty, or uncertainty of the two-part system ; its symbol
is H(x,y). It is compared to the sum of the two individual uncertainties. If
the two heights were completely independent of each other, then the joint
uncertainty should be equal to the sum of the individual uncertainties. In our
case, it is smaller by 0.22 bits. The deficit is a measure of the internal constraints
in the system, which lead to an association between heights of fathers and
daughters. The function is designated by the symbol T(x;y). Its defining
equation is : j,^^ .^^ _ ^^^^ _^ ^^^^ _ j^^^.^^

This information function is germane to other statistics which measure the
relatedness of two variables, such as the coefficients of correlation and of
contingency. The T-measure is of very general applicability; the values of the
variables do not have to be quantitative, not even ordered — they must only
be distinguishable. For instance, one can compute a T-measure for a relation
between color and shape.

The two functions, H and T, differ in the way in which they are affected by
change of scale. Let us consider what would have happened if he had chosen
one-inch intervals instead of three-inch intervals. It could be the case that only
one one-inch interval out of any group of three is occupied at all. Then, the
information that a certain height falls into a given three-inch interval would
automatically locate it in some one-inch interval; hence, the uncertainty is
not increased by the subdivision of intervals. However, this is an extremely
unlikely situation. It is much more likely that the three one-inch intervals are
populated with approximately equal frequencies. In this case, additional
information of logg 3 = 1.58 bits is needed to specify the proper one-inch
interval. Then, the uncertainty concerning the height of fathers with regard to
a one-inch scale will be 2.00 + 1.58 = 3.58 bits, and the uncertainty concerning
the height of daughters 1.92 + 1.58 = 3.50 bits. The joint uncertainty will be
increased by a factor of logg 9 = 3.17, because each cell in the table will be
replaced by nine cells as one goes from three-inch intervals to one-inch intervals.
If one uses a still finer grain, going from inches to millimetres, then the individual
uncertainties can be increased by another 4.7 bits, the joint uncertainty by 9.3
bits. This is quite the expected behavior. The more categories are recognized,
the greater the uncertainty of classification. The uncertainty can become infinite
for a continuous function. However, it will always remain finite for any set of
real observations.

T, on the other hand, depends very little on the scale interval used. With
very coarse grouping, T tends to be less. In the extreme cases, where all heights
are pooled into one single class, all individual and joint uncertainties vanish,
and with them their differences. In the other extreme case, where measurements
are taken and registered to so many digits that no two results are alike, we must
get //(x) = //(;,') = //(x,v) = r(x;v) = loga 1376. But, between these un-
reasonable extremes, the measure of constraints is characteristic of the system
and not of the scale which is used in measuring it.

28 Henry Quastler

Two-part Systems in General

We proceed to a general treatment of a two-part system x, y. Let / and 7 be
the categories of x and v, respectively, and p{i) and p{j) the associated
probabilities. Further, let p{i,j) be the probability of the joint occurrence
[{x = i) and (y =;)].
Then:

H(x)^ -2 p{i) 10^2 p{i)

i

H(y) = -Ipij)^og,p(j)

H(x, y) = - 2 p(i, j) logs p{i, j)

ij

We introduce the conditional probabilities,

Piij) Prob { V = y if X = /}

/>,.(O....Prob{x = /ifj=y}

When X = i then y must have some value j with certainty (or probability
1.0), that is

IPiiJ) = 1
j

Equally,

Ip^iO = 1

i

Furthermore, the probability of the joint occurrence [x ~ i and y = j] can be
factored into the product of the probability that x equals /, times the conditional
probability that y = j ii x — i; equally, it can be factored into the product of
pij) times Pj{i). So :

P(i,j)=pii)-Pi{j)

^Pij)-Pj(0

The conditional probabilities yield naturally conditional uncertainties. For
instance, the uncertainty of j, if it is known that x = i, will be

Hiiy) = -IPiij) loga/^XO
3

The average uncertainty of j, under the condition that x is known, is designated

by H/y). It is obtained as the weighted average of the //Xv)'s-

i

Substituting the value of H^{y), we get

tJxiy) = -Ipii) 1 Piij) ^og2Pi(j)
I j

and remembering that

Pii}) - -jay

we get

A Primer on Information Theory

29

Expanding the logarithm gives

HAy) = -IpUj') iog2/X^y) + Ip(ij') Iog2/X0-

ij io

Noting that

lpiJJ)=p(i)

3

we get

H/y) = -IpiiJ) loga /?(/,;■) + lp(i) loga /?('■).

ij i

We have seen that the first term on the right side is H(x, y) and the second
-H{x). So:

H,(y) = H(x, y) - H{x) and H(x, y) = H(x) + H^y)
A parallel development shows that

H(x, y) = H(y) + H,{x)

This relation is quite obvious if put into words: the joint uncertainty con-
cerning two variables is equal to the sum of the uncertainty concerning either
one variable plus the conditional uncertainty concerning the second variable if
the first one is given.

H(

K)

W/////////////////^^^^^

- > ' f II ^ ^

"• lly (X) *■

1

"(x;y)

— U f V ^ K

- H^(y)

y//////////////^^^^^^

.^

H

(>

1

y)

V

» \

^

Fig. 4. The relation between information functions shown graphically

The difference in uncertainty concerning )', depending on whether or not x
is known,

H{y) - Hly\

is the gfl/rt in certainty about y derived from observing x. Substituting for
^^rCj')' weget:

H{y) - Ely) = H{y) + H{x) - H{x, y)

The expression on the right side is the defining equation for T{x\y):

H(y) + H{x) - H{x, y) - T{x; y).
It follows from this derivation that Tis a symmetrical function:

r(x; jO = rO-; x) = H{x) - H,{x) - H{y) - HJy)
and it becomes clear why Tis a measure of the mutual reduction of uncertainty.
The relations between the six information functions, H(x), H{v), H(x, v), H^(y),
Hy(x) and T(x;y), can be demonstrated graphically as in Fig. 4.

30 Henry Quastler

In normal code representation, i.e. reduced to efficient binary operations,
the information functions have the following meaning:

H(x) . . . .number of operations which specify x

Hy{x) . . . .no. of operations which specify x if v is given

T{x; v) . . . .no. of operations which apply to the specification of both x and v

H(x, y)- ■ ■ .no. of operations which specify the whole system.

Inspection of the graph shows that:

H(x) > H,ix)

H(y) ^ H,(y),

that is, the conditional uncertainty cannot be greater than the unconditional
uncertainty.*

Communication Systems

When a system not only transmits information but exists primarily for that
purpose, then it is called a communication system. No class of two-oart systems
has received as much attention as that of the communication system. In a
simple communication system, tlie two parts are called the source and the
destination of information. The distinction between source and destination must
be based on external grounds; the informational relations between the two are
perfectly symmetrical. The relevant states of the source are called the inputs,
or signals sent, and the relevant states of the destination are the outputs, or
signals received. A single state is called a symbol, and a higher unit composed
of several symbols, a message. The conditional probabilities for each pair of
signals sent and received form a matrix called the channel. Note that the word
'channel' is again used in a sense wider than customary. A 'channel' may but
does not have to be a means of physically conveying information. For instance,
if two variables x and y do not affect each other but are both affected by a third
variable r, then knowledge of the state of x is likely to reduce the uncertainty
concerning the state of y, and vice versa; hence, information is transmitted
between the two variables, and they are connected by a 'channel' in the sense of
information theory — although they do not communicate with each other directly.

* However, this is true only for an average conditional uncertainty, and does not apply to
every particular condition. The following example will help to fix the ideas: Consider a
diagnostic test for a certain disease; suppose the nature of the test and the occurrence of the
disease are such that in 98 per cent of the patients the test is negative ; that of the positive tests,
50 per cent are spurious ; and that virtually every case of the disease will give a positive test.
Then, if the test is not performed at all, the diagnostician's uncertainty as to the presence of the
disease in any given patient, is

-(.99 log2 0.99 + .01 log2 0.01) = .081 bits/patient.

If the test was negative then the uncertainty is zero. But, if the test is positive, the chances
are equal that it is or is not spurious; hence, the uncertainty is I.O bit, and the diagnostician is
more in doubt than he was before. However, the average uncertainty, conditional upon his
performing the test, is reduced to

.98 X 0 + .02 X 1.0 = 0.020 bits/patient.

A Primer on Information Theory

31

The information functions in a communication system are designated as
follows:

H(x)
H{y)

Tix;y)

.uncertainty of source

.uncertainty of destination

. ambiguity

.equivocation

.information transmitted, or communicated

Amounts of information transmitted must be referred to some unit of action.
In particular, it is customary to compute transmissions per symbol or per unit
time.

A channel which associates one and only one output with each input, and
no output with more than one input, is called a noise-free channel or transducer;
in this case,

H{x) = H(y) = H(x,y) = T(x;y);
HJ,y) = H,{x) = 0.

We can think of a noise-free channel as a means by which information at
the source is represented at the destination. Physically, this involves two acts
of representation: first, states of the channel are selected so as to represent the
inputs, according to some agreed-upon code; this is called encoding. Next, the
states of the channel are translated into meaningful states at the destination ;
this is called decoding. All we have stated about representation, representability
and amounts of information could now be restated in terms of encoding and
decoding operations. In this sense, the relation which we introduced as the
'condition of representability' is also known as the Theorem of the Noise-free
Channel; and all the examples and exercises of representing information could
be re-interpreted as coding operations.

Noise — Few real channels are noise-free; in general, more than one output
can follow a particular input. For instance, the 'channel' which links a daughter's
height to her father's is far from noise-free; the following table gives the
conditional probabilities:

Table III. Data of Table II in Form of a Communication Channel

Conditional

probabi

ities, p

(0

/ = 53.5

56.5

59.5

62.5

65.5

68.5

71.5

HAx)

j = 59.5

.10

.50

.40

_

1.36

62.5

.01

.09

.27

.51

.11

.01

—

1.80

65.5

—

.02

.19

.51

.24

.04

—

1.74

68.5

—

—

.07

.39

.45

.09

.01

1.70

71.5

— .

.03

.21

.52

.21

.03

1.74

74.5

—

—

—

.04

.45

.43

.09

1.55

32 Henry Quastler

The last column, Hj{x), is the uncertainty concerning the height of the daughter
if the height of the father is known ; it is not too surprising to find this uncertainty
smallest in the extreme cases, and always smaller than the unconditional
uncertainty of 1.92 bits.

The father's height 'communicates' some information about the daughter's
height; the amount communicated is 0.22 bits. It is not more than that for a
number of reasons. Some of the deficit in information about the daughter's
height is undoubtedly due to ignorance, and could be reduced by taking proper
account of various concomitant factors. Some of the uncertainty may be
irreducible, due to a truly random process — possibly the selection of the particu-
lar chromosomes which go into determining the daughter's height. In the strict
sense, the term 'noise' is reserved for the effects of random disturbances, and
not to the eff"ects of ignorance. However, the problem of the final distinction
between uncertainty due to randomness and uncertainty due to ignorance is
an extremely delicate one; the practical information analyst will usually be
satisfied to treat any uncertainty as due to noise, which results in the greatest
reduction of certainty. This interpretation will be subject to revision in the
light of additional knowledge.

The two-part system 'father's height-daughter's height' is not a communica-
tion system, and this is one reason why so little information is transmitted.
Suppose the numbers which define the 'father's heights' categories were not
observed in a given population but could be chosen arbitrarily; for instance,
they might be input voltages applied to a system. Accordingly, the 'daughters'
heights' might be output voltages, and the table of conditional probabilities
becomes a statement of the transfer function of the system. It is obvious that
this system can be made to transmit more than 0.22 bits per symbol. For instance,
using onlyy = 59.5 andy = 74.5, with equal frequencies, one would transmit
about .90 bits per signal. In general: for each channel, Piij), there exists a set
of input probabilities, p(i), which maximizes the transmission rate. The rate so
obtained is called the channel capacity.

Even with best utihzation of the possibilities of a channel, it can do no more
than transmit all the input information, and in general it will not transmit quite
all of it. This leads to an important generalization : Manipulation of information
cannot increase its amount; it can at best preserve it, and it is likely to reduce it.

This important statement will be clarified by the discussion of an apparent
exception. Suppose A wishes to send a message to B over the channel C;
conditions being very good, B picks up not only almost perfectly the message
sent by A but acquires, in the course of doing so, considerable amount of
information about conditions in the channel. His total information received
might be more than that contained in A's message; still, he has lost some of the
information contained in the message. In general: as a result of manipulating
information, there can be more output information than there was input
information — but the contribution of the input information to the total cannot
be more than the amount of input information.

Error Detection and Correction

A codebook states which output should be associated with any given input.
A noise-free channel fulfills these requirements perfectly. In a noisy channel

A Primer on Information Theory 33

Other outputs than the required ones appear; in other words, a noisy channel
produces errors. Errors lead to loss of information, and a reduction in the
rate of transmission; in a noisy channel,

Tix;y)<H(x)

Hy(x) > 0.

This loss is unavoidable. However, it is at least possible to spot and correct
the errors which have occurred. It is one of the main endeavours of information
theory to devise methods to do this efficiently.

An error in a message can never be found unless the message contains some
extra information which can be used for this purpose. For instance, if the
message consists of a string of four digits chosen without any constraint:

5 3 8 7,

one has absolutely no possibility of knowing whether or not it contains any
errors. If it has been agreed upon that the message will be repeated, then one
can detect errors :

5 4 8 7

5 3 7 7,

and if the message is repeated several times, these errors can be detected and
corrected, with arbitrary certainty if the number of replications can be made
sufficiently large:

5 3 8 7

5 3 7 7

5 3 8 7

5 4 8 7

5 3 8 1.

In the second case, the possibility of error detection was bought at the price
of making two digits do the work of one; the message is said to be 50 per cent
redundant. In the last case, the price of error correction is the use of five digits
to transmit a single one, or a redundancy of 80 per cent.

Introducing redundant information in the fonn of a simple replication is
straight-forward and eiTective, but not very economical. Error detection could be
achieved more efficiently by simply adding the sum of the digits to the message:
be achieved more efficiently by simply adding the sum of the digits to the message :

5 3 8 7 2 3.

Here, the redundant information is only one-third of the total. In fact, giving
only the last digit of the sum as 'signature' is almost as effective, and requires
only 1 digit in 5, or 20 per cent redundant infonnation. The signature check
illustrates a general principle: a given amount of redundant infonnation in a

34 Henry Quastler

message can be used for error checking the more effectively the more evenly it
is related to all parts of the message.

It is always possible to achieve reliability, in the presence of noise, by the
use of redundant information; in fact, one can approach perfect reliability
arbitrarily closely if one is willing to provide enough redundant information.
The amount of redundant information needed, for a given noise level and a
given desired reliability, will depend on the efficiency of coding. The ideal
relation between noise level and redundant information needed is formulated
in Shannon's fundamental Theorem of the Noisy Channel. This theorem can be
stated as follows: if a certain amount of information is to be transmitted with
perfect reliability in the presence of noise, then it is necessary to provide at
least as much redundant information as the amount of equivocation introduced
by the noise ; furthermore, this amount will be sufficient if the coding is maximally
efficient.

There exist several proofs of this theorem; none of them is easy to follow,
and all are existence proofs — that is, they prove that an error-checking code
exists which will fulfill the requirements, but they do not say how to construct
it. In fact, perfectly efficient error-checking codes seem to be realizable only in
a few special cases; however, close approximations to ideal efficiency are easily
obtained if it is permissible to use message blocks of great length (12).

The economics of error-checking are dominated by three factors:

(I) the frequency and costliness of errors

(II) the cost of adding redundant information

(III) the availability and costliness of checking procedure (encoding and
decoding).

The work of Shannon and his followers has dealt with one particular situation :
encoding and decoding procedures are supposed to be reliable and gratis, the
error frequency is to be reduced to almost zero, and redundant information is
supposed to be used as sparingly as possible. As long as the theory is not
completed even for this case, one cannot expect to develop a more general theory.
Some qualitative notions of what it will entail can be gathered from a considera-
tion of a much-used, and presumably well developed communication system,
namely, printed language. Symbols are gathered into various checking units
(words, sentences, paragraphs, chapters) ; on each level, there operate constraints
which will help to locate and correct errors. For instance, this sentence will be
read corretly even though one letter has been onitted and one word misspelled.
It 3eems that the redundancy per letter, in a coherent English text, is about 60
per cent. Paragraphs are constructed in such a way that the sense can be
grasped even if whole words or even sentences are missing or perturbed, and
the essence of a whole chapter is, in general, understandable even if a whole
paragraph should be left out.

Actual Communications System

So far we have dealt with two-part systems in a purely abstract way. 'Sources'
and 'destinations' are defined simply by the states which they can assume.
'Channels' are tables of conditional probabilities; in the simplest case, the
channel is a kind of telephone book which associates every input to some

A Primer on Information Theory

35

particular output. If the association is not unequivocal, then the channel is
said to be noisy. 'Noise' is defined as a random perturbation of the input-
output link. Those are nice, clean concepts, not to be confused with realities.
The 'channel' exists on paper only, and is not the same as the mechanism which
links two parts of a system. The infonnational relation between heights of
fathers and daughters does not reveal the nature of the mechanisms involved;
whether fathers affect their daughters' heights by means of their genes, or of
the food they provide, or of the mother they select for them, cannot be decided
on grounds of informational relations. Indeed, I believe that Buddhist tradition
would explain the correlation on the grounds that daughters select their fathers;
as far as information theory is concerned, this is perfectly acceptable.

The scheme shown in Fig. 5 is a somewhat closer approximation to reality:

NOISE

SOURCE

MESSAGE.

• ENCODER

TRANSMITTER

SIGNALS

CHANNEL

SIGNALS

DESTINATION [J^^SSAGE ^ qe-qqqer l.^ RECEIVER (— '

Fig. 5. A diagrammatic representation of a communication system

It is customary to treat all links but the channel as noise-free. If need be, one
can introduce noise into the other links of the model by some straight-forward
adaptations.

If signals and channels are physical entities, then it is relevant to investigate
their physical capacity of carrying information. Suppose the nature of a unit
of action and the physical constraints are such that the channel can assume any
one of m states during one unit of action; then, these states can be made to
represent log., m bits of information. It is the function of the encoder-trans-
mitter system to match the diversity of messages generated by the source to
the diversity of states which can be assumed by the channel; those, in turn, are
matched to the diversity of messages intelligible at the destination by the
receiver-decoder system.

As long as the demands on the channel are light, the matching process is
not much of a problem. However, it may become very difficult if the channel
is to be driven at capacity, and if the various states of the channel are not of
equal value; some may be more subject to noise effects than others, some may
need more time than others, some may necessitate more effort than others.
In general, one will tend to favor the safest, shortest, and easiest states. However,
this must not go too far; if one goes to the extreme of using the very 'best'
state, then the channel does not transmit any information at all. To find
optimum compromises between informational needs of source and destination
and physical capacities of the channel, between amount of information used to
carry messages and amount of information needed for noise reduction, is one
of the fundamental problems of the theory of information and communication.

36 Henry Quastler

EXERCISES

13. The following table gives the number of times the four possible combinations of two
flower colors with two pollen shapes were found :

Pollen shape

Flower color :
Purple Red

Long 296 27

Round I 19 85

Is there information transmission between these two characters ?
14. Define the following functions, and derive their values (in terms of //-functions)

J{x,y; z)

T(x; y, z)

T(x; y; z)

15.

Ad

agnostic test

gives

the following results:

true negatives . .
false negatives . .
true positives
false positives . .

85%
5%
3%
7%

What is the informational value of the test?

What is the maximum informational value that any test could give in this situation?

16. A teletype machine sends 2.3 groups of five binary symbols per second. What is the
maximum possible rate of information transmission ?

17. Same machine as in Exercise (16). All code groups are equiprobable. Error probabili-
ties are as follows: symbols nos. 1 and 4 are always received correctly, nos. 2 and 3 are wrong
1 1 per cent of the time, no. 5 is wrong 1 per cent of the time. All errors are equiprobable.
Compute equivocation and amount of information transmitted.

18. You are to send 2-bit messages through a channel which has the property that one in
five binary symbols is bound to be in error. Construct four sequences of five binary messages
which will allow the reconstruction of the original message. What is the efficiency of the code?

V. ORGANIZATION

Systems, Structures, Pattern

A system is an organized whole made up of interrelated parts. Organization
is based upon the interrelations between parts. The parts may be strongly or
weakly coupled; their effect on each other may be quantitative or qualitative.

(Z> Kr)

Fig. 6. A simple communication network

If two parts are coupled in any fashion, then knowledge of the state of one must
imply some information about the state of the other. Accordingly, any interrela-
tion can be technically represented as a channel. So, two components of a
system can be symbolically represented by a simple communication network of
two parts, referred to as two nodes and one channel:

A Primer on Information Theory 37

Let H(x) be the amount of infonnation needed to know what state x is in.
If y is known, some of this information becomes unnecessary, or redundant.
This amount, T{x;y), is an index of the degree of coherence, constraint, integra-
tion, or organization which prevails in the system.

Consider the pair of words 'green valley'. These two words form a small
system — a whole made up of interrelated parts. The whole has a meaning
which neither part alone has. The price for this feature is elimination of many
other possible connotations of 'green' and 'valley'. As a result, the information
content of the word combination is smaller than the combined information
contents of the two words. The difference must show up as redundant informa-
tion. The presence of redundancy implies that each word contains some
information about the other. This is best demonstrated by successful error
checking. The errors 'preen 'for 'green', and 'volley' for 'valley' would not be
found in isolated words, but can be spotted in the pair.

System Analysis — There seem to be three general viewpoints under which
relations within a system are assessed: (a) the amount of information trans-
mitted— on the technical, semantic and pragmatic level ; (b) the degree of control
or cause-effect relations, dominance; and (c) the utility, or value, of the relation
to one or both of the related parts. Information theory deals only with the
first viewpoint. It does not concern cause-effect relations, or what causes the
information to flow, and it is not concerned either with the utility of the flow of
information.

Informational analysis of a system will be of interest if and only if the
informational challenge is serious, that is, when a system has to process informa-
tion at a rate which crowds its capabilities. The informational challenge is
the result of:

(1) The diversity which is characteristic of the tasks; this can be expressed
as ///task. A system which is faced with the same task all the time or most of
the time may be working very hard but the difficulty is not an informational
one.

(2) The precision which is required ; this can be expressed as the ratio TIN.
That is, the diversity of tasks is informationally challenging only insofar as
it is expressed in a diversity of responses. A system with a small response
repertoire may be working very hard, but not in the informational domain.

(3) The time which is allotted for the fulfillment of each task. A system
with very modest informational equipment can solve many tasks if given ample
time. For instance, the extremely simple logical machine devised by Turing (13)
will solve any solvable problem if given very much time.

The time rate of informational challenge of the system is the product

H T tasks _, . .

X 7> X — TT — = Tlumt time.

task H unit time

The infoiTnational output of the system will be measured in //-measures
but the effective output, or informational performance, in terms of T-measures,
as T per task or T per unit time. The limits of the informational performance
of a system can be found by systematically varying the informational challenge
and observing the resulting performance. In such studies it is important to

38 Henry Quastler

make sure that the system's performance is hmited informationally, and not
by difficulties of sensing inputs or generating outputs.

It is possible to vary the informational challenge in a number of modes;
e.g. one can vary the number of sources of information, or the amount of
information per source. Challenging in various modes reveals whether or not
there exist several modes of limitation. It seems that the informational perfor-
mance wliich a system can produce in single tasks may be limited by the follow-
ing factors, singly or in conjunction :

(1) the amount of information which can be processed effectively in a
single task,

(2) the number of independent information-carrying components which
can be involved in a single act of infomiation-processing,

(3) the informational contribution from each independent component,

(4) all information-carrying components must be assembled within a
certain length of time ;

(5) in addition, there seem to be two general limitations on time rates:
there is a minimum time for each act of information processing, and

(6) the over-all rate of information-processing is limited (only this last
limitation has the character of a channel capacity).

This list of limitations is based on psychological experiments (14) but is believed
to apply to all types of systems.

Multi-part Systems — The informational system analysis is not restricted
to two-part systems. A system of three components can be represented as a
three-node network with a connecting channel:

Fig. 7. A simple three-node network

Again, it is merely a matter of convenience which node, or set of nodes, one
treats as the input, or independent variate.

The treatment can be extended to any number of components. Thus, a
nine-node network is equivalent to one man receiving infomiation from eight
sources, or feeding information into eight sinks; or, to four men watching
two sources, communicating with each other, and feeding information into
three sinks; to a sentence of nine words; to a decision based upon eight factors.

The more parts there are to a system, the more difficult becomes the infor-
mational analysis (15, 16). This is territory that has been but recently opened,
and we are still largely concerned with the formulation and highly tentative
application of concepts. It will be helpful to consider a parallel effort, namely,
the study of organization by game theory (17). One result of this study is that
each time a new player is added, the organization (the 'game') acquires a new
qualitative feature. One-person games deal with problems of maximum;
the addition of a second person introduces competition; of a third person,
coalition; of a fourth person, an asymmetric role of one player in relation to
the group of the other three, von Neumann (17) points out that it is at this
junction that the most remarkable problems begin to appear; also at this junction,

A Primer on Information Theory 39

there occurs a change from a rigorous and complete exposition to a heuristic
and incomplete one.

The situation is similar in the study of organization by information theory.
Each time a new part is added to a system, a qualitatively new information
function appears. As long as one deals with a single variable, the problem
is one of efficient use of existing variations. A two-part system introduces
relations between parts; a three-part system, relations between relations; a
four-part system, relations between a part and a complex of relations.

Unitization — It is an empirical fact that when a system is complex enough
to require very many components, the phenomenon of unitization occurs.
That is, some components get organized in such a way that they interact strongly
among each other, and act as a unit with respect to the remainder of the system
and the external world. Unitization seems to be a necessary evil; it might be
an important key for the study of complex organization and complex mental
activities. The phenomenon has never been really explained; it is possible
that a quantitative treatment will be made possible through the use of infor-
mation theory (18).

Unitization is always coupled with the phenomenon of limited span. Any
real part has a limited information content. In any single act of communication,
the capacity for non-redundant transmission of a part is limited by its own
infomiation content. This amount must somehow be partitioned into inter-
action with the external world, and interaction with the other members of the
unit. If each of these interactions is to be of significant size, then only a limited
number is possible. The interaction of a unit with the outside may be only
a fraction of the information traffic within the unit. Hence, several units can
be organized into a secondary structure of greater versatility, and this process
can be repeated on successive levels of organization.

There appears, thus, a possibility that information theory can be helpful
in formulating both the causes and the effects of unitization, and in establishing
rational interpretations of the size of the units. This would be a very important
contribution to any theory of organization.

Conclusion — We have proceeded from simple processes of representation
to discussions of communication and, finally, organization. It was attempted
to treat in a heuristic and perspicuous manner the basic principles of Information
Theory: there exists a generalized concept of 'information' which includes
communication and organization and is so general that every real event or
structure has its informational aspects; this general concept is related to a
measurable quantity; the operation of taking a measurement of this quantity
is done by means of symbolization in a standard language. The functions
as defined obey two fundamental theorems: the Representation Theorem,
and the Theorem of the Noisy Channel. Both theorems impose a limit on
the amount of information which can be effectively processed in a given
situation; both also state that it is possible to reach this limit.

APPENDIX I
THE EVALUATION OF INFORMATION CONTENT

The examples and exercises should have familiarized the reader with the
techniques of taking information measurements. However, the investigator

40 Henry Quastler

who wishes to use this knowledge in his field is bound to run into some diffi-
culties. A typical difficulty is that a natural situation does not present itself
neatly classified with a complete set of categories and probability measures.
It often takes considerable ingenuity to supplement the missing components
of the picture. Wherever ingenuity must be used, the result will not be unequi-
vocal. Hence it becomes important to estimate not individual information
measures but rather whole ranges compatible with reasonable assumptions.

The Relativity of Information Measures

'Information content' is a measurable quantity, just as length; and, just
as length, it is a function and not a property of a particular set of events. The
theory of relativity asserts that the measured length of an object depends on
certain relations between the object and the measuring system. However,
under everyday conditions these relations will not produce any significant
effect and, most of the time, lengths behave as if they were properties of objects.
The infomiation content of an event depends on the manner in which this
event is related to the frame of reference of the evaluating system. Unlike
with length, these relations are not fixed under everyday conditions. Therefore,
information content behaves only rarely as if it were a property of an event.

The amount of information, H{x), associated with an event, x, is defined
as the expectation of the logarithm of the probability that x will fall into some
category, /. Thus, the measure of information depends on three decisions:

(1) the choice of a unit event,

(2) the establishment of categories,

(3) the selection of a set of probabihty measures.

In general, each of these decisions involves a degree of arbitrariness. Accor-
dingly, a considerable range of information measures will be compatible with
a given real situation.

The question of an appropriate selection of a unit event cannot be solved
by mechanical application of hard and fast rules. There is a lower limit to
the size of elements, imposed by limits of observability. In general, selection
of these lower limits will force one to take cognizance of a tremendous amount
of detail, most of which is bound to be irrelevant. Thus, one will try to select
a unit event broad enough that all irrelevant details are submerged in its internal
structure, yet narrow enough so that no relevant relations get lost within the
unit event. In practice, one has to make a guess, subject to revision by later
experience. This difficulty occurs with all kinds of analyses, and is not specific
to informational analysis.

The situation is quite similar with respect to categories. There, too, exists
a bound, imposed by the capabiHties of discrimination. In general a large
number of discriminations can be made which are irrelevant to the problem
at hand. For instance, if one deals with the semantic content of a printed
message, it will be quite irrelevant to categorize by shapes of letters, quality
of paper, type of printing ink, etc. The decision is not always so easy. For
instance, in categorizing the atoms found in living matter it will, by and large,
not be necessary to distinguish between isotopes; in the overwhelming majority
of occasions, differences between isotopes will have no effect. Occasionally, of

A Primer on Information Theory 41

course, a particular isotope located in a sensitive spot and decaying at a critical
moment can have very large effects. In a case like this, the selection of a set of
categories becomes a matter of compromise.

The probabilities, finally, are never actually known. We have to estimate
them, on more or less sound bases. In many situations where generalized
information theory is used, the bases for estimating probabilities are rather
uncertain. Therefore, it becomes important to assess the dependence of
information functions on fluctuations of probabilities.

The contingent nature of information measures has not always been obvious.
All early applications of infomiation theory dealt with telecommunication
systems. In all of these, all informational characteristics are perfectly well
defined. In Morse code, all we have to know is whether a particular information-
carrying element is a blackness or a whiteness, and whether it is long or short.
In pulse code modulation, the only thing that counts is presence or absence
of a pulse within a stated interval of time. In pulse amplitude modulation,
all information is vested into the amplitude of pulses. In all these cases, there
is no question about the infomiational characteristics of the process under
consideration.

The situation is radically different in the larger domain of applied infor-
mation theory. For instance, take the case of two people transmitting information
to each other by talking. The information-carrying element is a clause; to
simplify our analysis, let us consider just words (remembering that the infor-
mation content of a clause cannot be greater than that of its constituent words).
Now, each person culls his words from a reservoir which is known to be large,
but its actual size is not exactly known. The information content of a single
word depends on the probability of its use, and these probabilities are not
exactly known either. Furthermore, they will hardly be the same for both
persons involved in a conversation. Also, each word can have several meanings,
one of which may be more or less determined by the context. The relations
between words, meanings, and context, again, are not the same for any two
people. This is not all. Information is conveyed not only by the choice of
words but also by inflection of voice, loudness, timing, and accompanying
gestures. In such a situation we have obviously no hope ever to obtain a
precise, unequivocal, and incontestable measure of information content.
We are, thus, confronted with two alternatives. These are: not to use infor-
mation theory, or to try to devise ways of producing usable approximate
estimates. Obviously, our choice is the latter alternative (19).

Approximation MetJiods

It appears that the approximation methods to estimate infonnation functions
are based on the following rules:

1. Averaging increases uncertainty;

2. Pooling decreases uncertainty;

3. Disregarding constraints increases uncertainty;

4. Rare events have small effects on uncertainty measures;

5. Smafl variations in probability have small effects on uncertainty measures;

6. In systems, information functions can be estimated in different ways,
and care should be taken to select the most appropriate one;

42 * Henry Quastler

7. If it is not possible to measure the actual infonnation functions desired,

then one can try to substitute closely related measurable quantities.
In the following paragraphs, these rules will be amplified and illustrated.

1. Averaging Increases Uncertainty — The fact was demonstrated in Section
III. It suggests a simple bracketing procedure: obtain a lower and upper
bound of uncertainty by using probabilities which are certainly more and
less unbalanced than they actually are. In particular, if the number of categories
is known but their respective probabilities are not, then one can follow Laplace's
procedure and set all probabilities equal which maximizes uncertainty.

2. Pooling Decreases Uncertainty — This, too, has been proven in the third
section. It is equally of value in bracketing procedures: using only categories
actually discriminated puts a lower bound on uncertainty; assuming more
categories than could be of interest establishes an upper bound.

3. Disregarding Constraints Increases Uncertainty — Let x and y be different
events, where y may differ from x only in time or place of occurrence or in
any other respects. If H(x) is the uncertainty of x, and Hy(x) the uncertainty
of .Y if y is known, then:

H^x) < H(x).

That is, knowing some other event, y, cannot increase the average uncertainty
concerning x; it will leave it unchanged if there is no association between x
and y; it will reduce it if constraints exist which are manifested in a statistical
association between x and y.

Rule 3 can be used for a bracketing procedure. Disregarding constraints
yields an overestimate of H(x) ; introducing constraints known to be too strong,
an underestimate.

Constraints have to be very marked to cause large changes in H(x). For
instance, the large inequalities of letter frequency in English texts reduce H
from a possible maximum of 4.7 bits per letter to 4.1 bits; the strong constraints
between successive letters and words result in an additional reduction to
1.5-2.0 bits per letter.

Formally, rule 3 is a special case of rule 1.

4. Small Effects of Rare Events — The information functional is a sum of
terms of the form (—p log/»). This function rises steeply between zero and .10,
hence, small probabilities contribute little to the total sum. For instance,
ten equiprobable alternatives correspond to an H of 3.32. If one of these
alternatives is replaced by ten separate sub-categories, each of probabihty
.01, then the resulting H is 3.65. If instead of ten, one introduces 100 equi-
probable sub categories, each with probability .001, the resulting H is 3.99,
or equivalent to sixteen equiprobable categories.

A good example turned up in a study by A. A. Blank. He calculated the
information content of single Enghsh words. For particular reasons, the sample
was restricted to four letter words. Thorndyke's list contains 1550 such words.
H, based on the observed frequency of these words, is 8.13 bits per word.
Of these words, 119 occur with the greatest frequencies. Computing H on
the basis of these words alone gives a value of 6.34 bits per word. Thus, taking
into consideration only about one tenth of all categories already yields about
four-fifths of the final information function.

A Primer on Information Theory " 43

This means that information functions can be estimated successfully as
soon as the more common occurrences are categorized. The remaining
infrequent occurrences will not contribute very much, and that contribution
can be easily bracketed between values based on numbers of categories which
are certainly too small and too large.

5. Small Effects of Small Variations in Probability — The curve of the
function F(p) =^ —p log p has a flat top. Small changes in probability in
this region have small effects.

Consider the simplest case, of two categories. If their probabilities are
equal, then //= 1. If the ratio of the probabilities is 1:2, then 7/= .92. If
the ratio is 1 :3, a very considerable deviation from equality, H is still .81.

For a larger number of categories, the insensitivity of H against probability
distortion is still mOre pronounced. If one replaces equiprobable alternatives
by probabilities staggered arithmetically or geometrically, stipulating only
that the span between the extreme value should be not more than one order
of magnitude, then the resulting changes in //are quite small.

This implies that the assumption of equiprobability, which gives an upper
bound as stated in rule 1, will not go very far from the true value unless proba-
bilities are radically unbalanced. The stretch bracketed between an upper bound
based on equiprobability, and a lower bound based on a distortion undoubtedly
stronger than the real one, will not be very large.

6. Alternative Ways of Estimating Information Functions — In systems
with several nodes, the compound infonnation functions can always be esti-
mated in several ways. For instance, in a two-node communication system,
the quantity which is the function of greatest interest, the amount of information
transmitted, T(x;y), can be computed in three alternative ways: as differences
between input uncertainty and equivocation, as difference between output
uncertainty and ambiguity, or as difference between the sum of uncertainties
of input and output and the uncertainty of their union. It usually is worthwhile
to inspect the data very carefully to estabhsh which of the set of functions can
be most easily and most accurately computed. In many cases, the quantities
most readily computed are not those which result directly from the plan of obser-
vation or experimentation. For instance, in most experiments it would be
natural to measure output uncertainty and ambiguity, but it is easier to measure
input uncertainty and equivocation.

7. Substitution of Related Quantities — In many cases where it is not practical
to compute the proper information measures, one can compute information
measures associated with related quantities. Take the case of estimating the
amount of information v/liich an individual can transmit after a single glance
at a display. This quantity is very difficult to determine; but, it is fairly easy
to determine the amount of information which can be elicited from an individual
by a short interrogation procedure after he has had a glance at the display.
This function is not quite the one we want, but presumably closely related to
it. Another example: in the case of mental arithmetic, we have no way of
estimating the actual amount of information processed, but we can readily
estimate the amount of information which must be processed if computations
are done in the way in which the subject claims he computes. In cases of this
kind one will use the measurable quantity instead of the desired one. Of

44 Henry Quastler

course, results so obtained have to be used with a certain amount of restraint.

Example: Rate of Information Transmission in Conversation — ^The working
of the approximation methods can be shown by two examples. The first
example is that which we used to illustrate the need for approximation methods;
namely, that of estimating the amount of information in conversation.

We consider first the infomiation carried in words. To establish an upper
bound, we ask how much information must be transmitted so that the receiver
can recognize every single word spoken.

This upper bound, in bits per second, is the product of the rate of words
per second times bits per word. A rate of 2.1 words per second is typical for
lively discussions. The number of bits per word in English context has been
estimated as 6.5 bits (±25 per cent). This yields 11 to 17 bits per second.

Words are not the only method of communication between two persons
conversing face to face. It can be shown, however, that all other means of
communication add little to the total transmission rate.

We will now try to establish a lower bound. Of course, no general lower
bound exists; it is easy to find examples where infomiation is transmitted at
the rate of 1 millibit per second, or less. What we want is an 'upper lower
bound' a lower bound of the amount of information transmitted between
people who try to communicate at some speed, and under reasonably favorable
conditions. Such a bound is obtained by analysis of pragmatic communication.
We look at situations where the verbal messages elicit or control actions.
We make an informational analysis of the relations between actions and verbal
messages. This will yield an amount of information demonstrably transmitted,
and it certainly represents a lower bound to the amount of information com-
municated.

At this time, we have a single case where pragmatic communication has
been evaluated accurately in informational terms. Felton, Fritz and Grier (20)
measured the amount of pragmatic communication between an airplane pilot
coming in for a landing and the control tower operator. They found an average
rate of 2 bits per second, computed in terms of actual effects of the messages.
Both pilot and control tower operator have all interest to communicate as
fast as they can. On the other hand, they do so in the presence of a very high
level of noise which reduces verbal communication to probably about one
third of its optimum rate.

We conclude, thus, that information transmitted through verbal communi-
cation is certainly not less than 2 bits per second nor more than 17 bits per
second, and very likely within the range between 6 and 12 bits per second.
This estimate is rough but not at all unrealistic.

Example: Information Content per Printed Letter— A very elegant way
of computing an information measure under unfavorable conditions was
used by Shannon in his analysis of the 'entropy' of printed English (21). The
information content of a single letter is easily determined as a function of
relative letter frequencies. However, constraints between neighboring letters
lead to a reduction of information content, and in order to estimate this
reduction exactly one would have to investigate the probability distributions
for long sequences of letters. This is manifestly impossible. Shannon, therefore,
proceeded to estimate a related quantity; namely, the amount of information

A Primer on Information Theory 45

concerning language constraints which can be ehcited from a person familiar
with printed English by a carefully planned interrogation. The subject is given
a text which is truncated at some point; he is asked to guess the next letter.
If he is successful, then he is told to go on; if not, he is told to try again. Records
are taken of the number of times a letter is correctly identified at the first,
second, third, . . . statement. In this setup, the experimenter acts as source
of auxiliary infoimation, emitting sequences of the type 'wrong . . . wrong
right', with an 'alphabet' of twenty-six different sequences (if repetitions are
excluded, the letter must be identified after no more than twenty-five wrong
guesses). The informational output of the auxiliary source depends on the
relative probabilities of the various sequences. These probabilities are very
unequally distributed. In a large percentage of the cases, the first statement
is correct; the most frequent message from the auxiliary source is 'right'.
The next highest probability is for the sequence 'wrong-right'. Messages
with up to three 'wrongs' make up the vast majority of cases; the remaining
categories, with from 4 to 25 'wrongs', have low probabilities. As was pointed
out before, they contribute little to the estimated value of H. This means that
we arrive at an estimate of the information furnished by the auxiliary source
essentially as a function of two to four probabilities.

The amount of information per single letter is known to be about 4.1 bits
(on the basis of relative frequency of letters in English texts). This is the amount
of information per letter which the subject needs to reconstruct the whole
text. Of this amount of information, a certain measurable fraction is furnished
by the auxiliary source. The remainder must come out of the subject's head,
and is based on his knowledge of language constraints. The amount of infor-
mation so elicited will not be quite as high as the information content of
language constraints, but it is a closely related quantity. By the ingenious
trick of effectively reducing the size of the alphabet, this quantity has been
made easily measurable.

APPENDIX II
ANSWERS TO EXERCISES

1 . One light — peace and quiet

two lights, vertically — enemy approaches by land
two lights, horizontally — enemy approaches by sea
two lights, diagonally — enemy approaches by land and sea
(This is not the only possible solution)

2. (a) 0, 1, 10,11,100,101,110,111, 10000, 1001,1010,1100,10000, 11110100011

(b) 9, 11, 147,32

(c) .125, .6703125

3. (a) 10110100010000
(b) EDCBA

4. 'Construct a confusion-free code using five binary digits for each letter and compare
the performance of this code with that of the above by encoding and decoding a message like
this one'.

Use part of the 32 code words made up of 5 binary digits, such as: 1 1 1 1 1 , 1 1 1 10, 1 1 101 ,
11100, etc. The message will be, on average, 21 per cent longer than with the most efficient
code (5 is 121 per cent of 4.14), but it is much easier to decode. Some of the unused code
words can be used for punctuation, etc. The teletype works on this principle.

46 Henry Quastler

5. Limiting value :

-(.8 logo .8 + .15 log, .15 + .05 logo .05) = .883
Single event code:
A 1 .8
B 0 1 .3
C 0 0 .1

1.20 -0.883

1.20, excess is — = 36 per cent.

0.883

Two-event code:

Event pair Prob. Code

AA

.64

1

.64

AB

.12

0 1 1

.72

BA

.12

0 1 0

AC

.04

0 0 11

.32

CA

.04

0 0 10

BB

.0225

0 0 0 1

.09

BC

.0075

0 0 0 0 1

.0375

CB

.0075

0 0 0 0 0 1

.06

CC

.0025

0 0 0 0 0 0

1.0000

1.8675
.934 digits

per event

excess =

= 5J%<10%

6. Let X designate amino acids

;, and y nucleotides.

nx = log;

J 20 = 4.322

Sx=l

tty = log

;, 4 = 2.0

1 >

' ^-^^^ - 2 161

Sy

2.0 ^-^^^

7.

P

-p\og,p

.60 .44

.40 ^

H(x) = .97

8. The curve looks similar to F(p), but has a flatter top and is symmetrical, with a
maximum of 1.0 at p{l) = .50.

9. H(x) = log2 3 = 1.58

-p log, p

y:.S
.1

.26

.33

.05

.22

.05

.22

i/(j) =

mx)

1.03

my)

A Primer on Information Theory 47

10. A realistic description of his uncertainty might be:

prob (55-64) = .95

prob (55-54) -- .02

prob (65-70) = .02

prob (any other speed) = .01

Within each range, all speeds are considered equiprobable.
We will derive the answer in two steps, obtaining first the uncertainty as to the speed range:

Range p —p log., p

55-64

.95

.07

50-54

.02

.11

65-70

.02

.11

any other speed

.01

.07

.36 bits

Next, we observe that the range from 55 to 64 miles per hour contains ten speeds (deter-
mined to the nearest mile) which are equiprobable. The uncertainty measure for ten equi-
probable categories has been found to be log., 10 = 3.32. This uncertainty will arise 95 times
out of 100; its expected contribution to the total uncertainty is 3.32 ■ 0.95 = 3.15. The other
ranges are treated equally :

Range

No.

of sub-classes

ir)

log^r

P • logo r

55-64

10

3.32

3.15

50-54

5

2.32

.05

65-70

5

2.32

.06

all other

81

6.35

.06

3.31 bits

We thus need (on average) .36 bits to determine the range of speeds, and an additional 3.31
bits (on average) to identify the speed to the nearest mile, within the range. The total uncer-
tainty is 0.36 + 3.31 = 3.67 bits.

Of course, different expectations would yield different uncertainties.

1 1 . The letters occur with more nearly equal frequencies.

12. Two bits.

„, . , /323 323 104 104\ ^^ ^.

13. i/(shape) = - — log, h — lo", — -- .80 bits

\427 ^-427 427 "■427/

rrr , ^ /315, 315 112, 112\ ^. ,.
//(color) = - — loga h — log., — = .83 bits

\427 ^427 427 ^-427/

17/1 K ^ ^96 , 296 27 , 27 19 , 19
//(color, shape) = - — log, 1 log., 1 log., —

\ 427 ^- 427 427 ^' 427 427 ^" 427

+ ^log„^) =1.26 bits

427 ^- 427/

r(color; shape) = .80 -I .83 - 1.26 = .39 bits

48

Henry Quastler

14. T{x, y; z) = mutual reduction of uncertainty between x and y on one hand,
z on the other
= H(x, y) + Hiz) - H(x, y, z)
nx;y, z) = H(x) + H(y, z) = H(,x,y, z)
T(x;y; z) = total constraint in a tri-variate system
= H{x) + H(y) + H{z) - H{x,y, z)

15.

Test

Actual

pos

neg

pos

3

7

10

neg

5

85

90

8

92

H{y) = .40

H(x) = .47

H(x,y)
nx;y)

.84
.03

The informational value of the test is .03 bits.

Its maximum possible infonnational value equals the amount of uncertainty before the
test, viz. .40 bits.

16.

2.3 X 5 X 60 = 690 bits/minute

17. Begin by computing the output uncertainty. The probabilities of receiving each signal
are obtained as the sum of receiving it correctly (0.2 for Nos. 1 and 4, .178 for 2 and 3, .198
for 5) plus the addition due to errors (1/4 of the errors, for each erroneous transmission).
This procedure yields //(out) = 2.32 bits. Next, compute the ambiguities. These are zero for
symbols no. 1 and 4. For 2 and 3, the ambiguity can be computed as the sum of the information
needed to ascertain that an error has occurred (—0.11 loga 0.11 — 0.89 loga 0.89) plus the
information needed to find out which of the possible and equiprobable four errors has occurred,
which is 0.11 x 2.0 bits/symbol. Symbol no. 5 is treated similarly. The average of the ambi-
guities is 0.31 bits, hence T equals 2.32 — 0.31 or 2.01 bits — a loss of about one-sixth of the
input information.

18. One solution is the following:

11000
10101
OHIO
00011

A single error will result in the reception of a word which is not in the code book. If one
follows the rule of substituting that message in the code book which differs from the received
one by one digit only, then every error (provided there is only one!) will be corrected.

A five-digit binary message can carry five bits of information. If it is known that one error
has occurred somewhere in a group of five symbols, then the information needed to locate
the error is loga 5 = 2.33 bits. With maximum efficiency, one should use only 2.33/5 or 46.5
per cent of redundant information (which could be achieved by coding large sequences of
five-digit words!). In our case, the redundant information is 3/5 or 60 per cent, and we trans-
mit with an efficiency of 40/53.5 = 75 per cent. (Observe that there is less uncertainty if it is
known that there is one error in every five-symbol word, than when it is only known that the
error rate is 20 per cent !)

A Primer on Information Theory 49

REFERENCES

1. L. Szilard: tJber die Entropieverminderiing einem thermodynamischen System bei
Eingriffen intelligenter Wesen. Z. Phys. 53, 840-856 (1929).

2. R.A.Fisher: On the mathematical foundations of theoretical statistics. Phil. Tram. {A)
222, 309-368 (1922).

3. R. V. L. Hartley: Transmission of information. Bell Syst. Tech. J. 7, 535-563 (1928).

4. N. Wiener: Cybernetics, J. Wiley and Sons, New York (1948).

5. C. E. Shannon: A mathematical theory of communication. Bell Syst. Tech. J. 27,
379-423, 623-656 (1948).

6. C. E. Shannon and W. Weaver : The Mathematical Theory of Communication, University
of Illinois Press, Urbana (1949).

7. L. N. Ridenour: Computer memories. Sci. Amer. 192, 92-100 (1955).

8. R. M. Fang: The transmission of information. Tech. Rep. Mass. Inst. Tech. Res. Lab.
Electron., no. 65 (1949)

9. L. Brillouin: Science and Information Theory, Academic Press, New York (1956).

10. L. DoLANSKY and M. Dolansky: Tables of log-, Ijp, etc.. Tech. Rep. Mass. Inst. Tech.
Res. Lab. Electron., no. 227 (1952).

11. E. Klemmer: Tables for computing informational measures. Tech. Rep. A. F. Cam-
bridge Research Center, ARDC.

12. Articles by J. E. Golay, P. Elias, I. S. Reed, R. A. Silverman, and M. Balser in: Trans-
actions of the I.R.E. Professional Group on Information Theory (1954).

13. A.M.Turing: On computable numbers, with an application to the Entscheidungs-
problem. Proc. Lond. Math. Soc. 42, 230-265 (1937).

14. H. Quastler: Studies of human channel capacity. In: Information Theory, ed. by
C. Cherry, Academic Press, New York (1956).

15. Wm. McGill and H. Quastler: Standardized nomenclature : an attempt. In: Infor-
mation Theory in Psychology, ed. by H. Quastler, Free Press, Glencoe, 111. (1955).

16. H. Quastler: Information theory terms and their psychological correlates, ibid.

17. J. von Neumann and O. Morgenstern: Theory of Games and Economic Behavior,
Princeton University Press, Princeton (1947).

18. H. Quastler, H. H. Chase, W. Montagna, M. V. Edds, Jr., P. F. Fenton, and P. B.
Weisz: Essays on biological unitization. Rep. Control Systems Laboratory, Univ. 111.,
No. R-52(1953).

19. A. A. Blank and H. Quastler: Notes on the estimation of information measures.
Rep. Control Systems Laboratoiy, Univ. 111., no. R-56 (1954).

20. F. Fritz and G. W. Grier, Jr.: Pragmatic communication. In: Information Theory
in Psychology, ed. by H. Quastler, 232-243, Free Press, Glencoe, 111. (1955).

21. C.E.Shannon: Prediction and entropy of printed English. Bell Syst. Tech. J. 30, 50-64
(1951).

SOME INTRODUCTORY IDEAS CONCERNING THE
APPLICATION OF INFORMATION THEORY

IN BIOLOGY

Hubert P. Yockey

Oak Ridge National Laboratory, Oak Ridge, Tennessee

Abstract — The model of protein synthesis in the cell which has been built up as the result of
the work of many researchers has been used as a basis for applying the principles of infor-
mation theory in biology. The main Une of the argument has been the role of noise in the
genome. The discussion has been kept as independent as possible of special models.

It was shown that in a real organism noise must exist in the genome and that an ensemble
of organisms may be represented by a probability distribution in H, p{H, A). Individuality is
thus incorporated in a very natural way. Dancoff 's principle requires that there be a lower
limit for viability for this distribution. Ha.

The action of a deleterious agent which induces errors in the genome by acting on nucleo-
tide pairs is assumed to be represented by an equation of the first order:

^ = -j(X)p,(j) + ija)

where /(A) measures the effectiveness of the deleterious agent, of which A is a measure,
in producing defects. A differential equation for H(X) is derived and it is shown that
{dHldX)E^ as a function of A behaves like J{,X).

I. INTRODUCTION

Information theory finds its place in biological thought through its ability
to deal quantitatively with organization and specificity. The importance of
these concepts has long been recognized in biology, but this realization is
rather sterile unless a quantitative form of expression can be found. One is
reminded of a quotation from Lord Kelvin, '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 meagre and unsatisfactory kind.'

The need for expressing biological quantities in numbers is clear but solving
the problem of how to do it is very much like belling the cat. Biology doesn't
seem to have any problems both really simple and terribly important such as
some which occur in the physical sciences. The application of first principles
has come much more slowly in biology for perhaps this reason. That ideas
of great general application do exist in biology is exemplified by Mendel's
laws and by the theory of evolution.

One of the purposes of this article, and indeed one of the purposes of this
book, is to explore the practical and theoretical consequences that may be
found in the discovery that biochemical specificity of proteins is carried, largely
at least, by the exact order of twenty amino-acid residues. The suggestion of

50

Some Introductory Ideas Concerning the Application of Information Theory in Biology 51

Watson and Crick (1) that genetical infomiation is carried by the exact
order of four kinds of nucleotide pairs provides a molecular vehicle for the
genetic control of protein specificity. Gamow (2) was the first to see that
this control implied the existence of a four-letter to twenty-letter code.
Thus by following the logical consequences of purely biological, or perhaps
biochemical, problems one is lead directly to a problem purely mathematical
in character.

This notion of the role of order, which is basic to information theory, is
worth pursuing in biology since it provides a way of measuring what we are
speaking about and expressing it in numbers. Furthermore, from the results
of applying the theory to specific problems, we may obtain an experimental
check on the validity of these ideas as first principles. In this article we shall
apply these considerations to the storage and transfer of biochemical specificity.
We shall explore, in particular, the role of noise in the genetical message. In
my article in Part V the theory is applied to the practical problem of calculating
and understanding survivorship curves.

The present status of the means of storage and transfer of specificity is
given by Gamow, by Ycas and by Augenstine in their respective articles in
this volume. The question of the exact way in which information is destroyed
by read-off error, radiation damage, aging, thermal fluctuations, biochemical
side reactions, and so forth, is of equal importance. This problem is also
discussed in this volume but no final and detailed account can be given at
this writing. Nevertheless, since there is virtue in attempt, we shall attempt
the development of a mathematical formahsm which is information theoretic
in character.

Most animals and plants exist at one time, at least, in the form of a single
cell; we can consider that cell to contain a substantial part of the directions
for the development of the organism. Since infonnation is conserved unless
lost due to noise, it shall be assumed that the mature organism is characterized
by substantially the same information content as the fertilized egg or seed.
In order to fix the idea we shall develop the formalism on the basis of Watson
and Crick's suggestion concerning the role of DNA. It should be remembered
that the central ideas of this paper are independent of much of the detail
embodied in Watson and Crick's papers and are dependent only on the possi-
bility of genetical endowment being conveyed by a series of structures composing
an information bearing molecule.

Suppose we imagine the symbols A, B, C, D (Gamow's predilection is to
the less prosaic spades, clubs, hearts, diamonds!) arranged in one-to-one
correspondence with the nucleotide pairs of the DNA found in a particular
given cell. The cell will have been selected from a number of similar but not
identical cells in a colony under study. This colony may be thought of as
being indefinitely large, so that in principle we may consider the ensemble
of all possible organisms identifiable as being members of the colony. Since
the number of nucleotides in DNA is finite, the number of elements in this
ensemble is also finite. Because of this one-to-one correspondence it will be
seen that the set of symbol sequences, which is the mathematical model of the
ensemble of organisms, will contain the informational or specificity properties
of the ensemble of organisms.

52 Hubert P. Yockey

The importance or value of a theory lies, among other things, in its capability
of treating a wide variety of phenomena from a single point of view. It is
well to think, at the start, of the field of validity this theory may have and,
if it should fail, the significance of its failure. If it should be discovered that
Watson and Crick's suggestion has very little bearing or applicability then
this development, while negative, is still a valuable result. One would then
perforce search for another explanation for the great detail and specificity
characteristic of any biological phenomenon. At present it is the most detailed
proposal based specifically on molecular chemistry. The theory here developed
is essentially statistical and may be expected to express its results in the form
of expectation values, probabihty distributions, and their functions. The
statistical character of the theory is directly in the line of thinking of both
modern biology and modern physics. It should be kept clearly in mind that
information theory deals with organizational problems and so some aspects
of organisms will be outside its scope. In this sense it may be that the role
information theory will play in biology will parallel that played by thermo-
dynamics in physics and chemistry.

II. NOISE IN THE GENETICAL INFORMATION

The Instability of a Perfect System

Let us consider an ensemble of organisms and discuss the communication
of information from the DNA to protein. There is evidence discussed by
Gamow and by Ycas in this volume that the code which translates information
from the four-symbol DNA code via RNA to the twenty-symbol protein
code is based on triads of nucleotide pairs. Indeed it can be seen that it must
be at least the triads since a twenty-symbol alphabet carries 4.32 bits per symbol
whereas the pairs in a four-symbol alphabet carry exactly four bits per symbol,
assuming no intersymbol constraints. The triads carry six bits per symbol
and so this represents some inherent redundance. It would be desirable to
express this formalism in terms of the DNA triads of nucleotide pairs ; however,
this requires a knowledge of the DNA to protein code. These data are missing.
Our objective is to develop the mathematical fomialism in as simple a way
as possible so it appears more appropriate to consider the communication of
specificity from DNA to RNA. Here we are dealing with a coding between
two four-symbol alphabets.

Suppose we are considering an ensemble of organisms which is isogenic, and
further that this means that each organism is characterized by exactly the
same order of nucleotides in the DNA of its nucleus. We shall now show that
this situation is unstable and that therefore a real ensemble of organisms will
be represented by an ensemble of messages recorded in its DNA. From this
it will follow that there is a distribution in the message entropy, characteristic
of any ensemble of organisms, even one which is isogenic.

The message entropy is

H=H,-H, (1)

where H^ is the message entropy of the genetical information and H„ is the
loss of information due to noise. That is, //„ is the loss of information from

Some Introductory Ideas Concerning the Application of Information Theory in Biology 53

some fault cither in the duplication process in the germ line or the somatic
line or from incorrect rcad-o(T of any kind. //„ may be expressed in terms of
the read-off or transition probabilities (3) of a letter of kind / to a letter of
kindy, Piij). The probability of letter / is p{i).

H=H,-\-y p{i) p^ij) log2 p,{j) (2)

Consider the case where these probabilities are a function of some variable 1.
In the application of these considerations A is the measure of some deleterious
influence such as dose of ionizing radiation. Form the derivative dHjd?.:

ciHldX = log2 e 2 (MO ic¥>^) P.ij) + Pii) loge pSi) {dIdX) p,{j)

+ P.(j)ioi,p,{J){dldX)p{i)] (3)

The absolute value of dHfdX will become indefinitely large because of the
second term in equation (3) as any p^{j) approaches zero if p{i) ^ 0 and
(dldX) pi{j) 7^ 0. This may happen, in particular, if any p/ij) approaches one
for then SL\lpi{k), (j ^ k) approach zero. This situation {p,{j) = 1) corresponds
to the assumption that there is always a correct reproduction in the DNA
duplication or in the RNA read-off. Under these circumstances the first term
is finite and the third term is zero.

Watson and Crick regard a mutation as being reflected by a change in
order of the nucleotide bases in DNA. This is apparently always possible;
they have suggested a biochemical scheme by which this can be affected. This
means that in a real biological system p{i) ^ 0 and {djdX) p/ij) 7^ 0. A real
ensemble of organisms will be represented by an ensemble of genetic messages.
This will be true even if the ensemble is isogenic. Some noise must exist in the
genetical information; if the noise is less than equilibrium it is quickly intro-
duced.

There is some experimental evidence in support of this conclusion. Burdette
(4) prepared populations of isogenic Drosophila. One strain had the same low
incidence of tumors in both sexes (about 4 per cent) and the other had a high
incidence (about 60 to 80 per cent) even greater in males than in females. The
tumor incidence of the isogenic strains was initially much lower in each case
than the stock from which it originated. But in each case, by the twelfth genera-
tion, the tumor incidence of the isogenic strain had returned to about the same
rate as that of the original stock. Tumor incidence is a morphological mal-
function and, as shown in this and other experiments, is under genetic control.

The fact that all flies were not tumor bearing and the gradual return of the
isogenic strains to the tumor incidence of the strains from which they were
selected, reflects the accumulation of errors in the genome. The results of the
experiment are in accord with the proposition proved above.

Representation of the Ensemble 0/ Organisms by a Probability Distribution in H:
piH, A)

If we grant that perfect systems do not exist, the other side of the coin is,
how imperfect may they be? This question was first discussed by Dancoff and
QuASTLER (5) and their conclusion, which is known as Dancoff's principle,
states that the amount of redundance is just that required to reduce the error

54 Hubert P. Yockey

rate to a tolerable level. According to this principle, we may expect that errors
will continue to accumulate in the genome of a given organism until at some
point serious difficulty including death will occur. This will be reflected by
some value of H, which we call //^, limited by viabihty. An argument for a
lower limit H^^ has been given previously (6).

Errors will accumulate in the genome but at the same time there is a favorable
selection for those members of the ensemble which have low equivocation.
This represents a certain reserve capacity to withstand the insults of existence.
It may therefore be expected in general that the message entropy of the ensemble
of organisms will be described by a probability distribution. This distribution
can, perhaps, be calculated from first principles, at least for simple cases, when
more is known about the storage and transfer of genetical information.

Death of an organism is defined in different ways in various fields of biology.
Permanent loss of reproductive power is the definition of death usually expressed
or implied in bacteriology (7). This is the definition chosen in spite of the fact
that there are many inteiTnediate stages between the active living cell and the
dead cell. It is known that yeast cells which have lost the power to multiply
may still be able to fennent (8). Zelle and Hollaender (7) have recently
pointed out that attempts to explain the bactericidal effects of irradiation on
the basis of one mechanism are unrealistic. In the case of animals the cessation
of metabolism, not the loss of fertility, is the criterion of death. These criteria
of death are not really different or antagonistic. Since loss of function is implied
by loss of information content any experimentally convenient definition of
lethality may be used to suit the problem at hand. The lower end of the distribu-
tion in message entropy will therefore be determined by the specificity required
by the environment.

A communications analogy may clarify the notion further. Suppose we
have a message, with redundance, which is sent through a communication
channel with a small but finite noise level. The message contains instructions
to perform some necessary task. A recording is made and the message is sent
through again, and so forth. Eventually, depending on the noise level of the
channel and the redundance in the message, it will be just barely intelligible. No
further recordings can be made without loss of part of the required information
content. The ensemble of recordings is analogous to the ensemble of organisms.
It will be seen in either case that there is a distribution of information content
among the elements of the ensemble.

Individuality finds a place in the theory developed here in a very natural
way. This feature corresponds more to reality (9) than theories which must
explain non-uniform response as fluctuations. Besides the experiments of
Burdette mentioned above it will suffice to note one other example of biological
individuality.

Consider the experiments of Schott (10, 11), Hetzer (12), Lambert (13),
GowEN (14), discussed by Gowen (15), on Salmonella tvphimurium in mice and
Salmonella gallinarum in fowl. The host population is exposed to the pathogen
and the survivors are chosen for further breeding. The case for mice is typical.
The survival ratio improved from 18 per cent to 93 per cent in six generations,
but remained nearly constant after that. One hundred per cent survival was
not achieved. The survival ratio is characteristic of the ensemble not of the

Some Introductory Ideas Concerning the Application of Information Theory in Biology 55

individual. Gowen (15) also prepared six strains of mice by sibling malings
for twenty or more generations. When survival was tested the survival ratios
were 1, 14, 34, 63, 64, 83 and 88 per cent. These results again stress the
importance of individuality as Gowen pointed out.*

Point Mutations and Chromosome Aberrations

We have now arrived, via our discussion, at territory familiar to the radiation
biologist. This is the controversy over the role played by point mutations and
chromosomal aberrations induced by deleterious agents such as x-rays. This
subject has been ably discussed recently by Muller, Kaufmann, Giles, Carlson,
SwANSON and Stadler, and by Kimball (16). The point of view of these
authors varies. Kimball takes the stand with Lea (17) that the death of cells is
due to chromosome aberrations which become effective at cell division. Swanson
and Stadler point out that the two effects occur together and that a clear cut
separation has not yet been accomplished. Muller points out some difficulties
with the mutation by breakage interpretation. Russell (18) states that gross
chromosomal aberrations, although they cause early death of embryos, are
probably not an important radiation hazard to man.

From the point of view of this article each of these effects is a way of intro-
ducing disorganization in the genome. The point mutation mechanism is the
biological analogue of the 'white noise' of the communications engineer. The
other extreme is not found in communication engineering but involves a strong
correlation between errors and is reflected as a loss of whole paragraphs or
other gross mutilation of the message. Each of these extreme cases will be
important in applications of information theory in biology. Unfortunately, the
second case has not been studied mathematically and so it is not known how
to calculate the equivocation it introduces.

It is therefore necessary to proceed with the calculation of only the part of
the equivocation which corresponds to point mutations. Since one of our
objectives is to develop a fundamental theoretical treatment of radiation hazard
to man, Russell's comment encourages one to think that this procedure is
v/orthwhile. It should be remembered that equivocation from these two extreme
conditions may have the same dependence on the deleterious influence. This is a
point which requires further mathematical study.

The Interaction of the Deleterious Agent nith DMA and the Decay of H

According to the Watson and Crick model of DNA there seems to be no
biochemical reason why there should be an interaction between nucleotide
pairs. The biological requirements for protein specificity do not seem to demand
an intersymbol influence (19). The matter is not closed, but the evidence favors
regarding the interaction of a deleterious agent with a nucleotide pair to be of
the first order.

We have previously suggested that the action of ionizing radiation or other
deleterious agent may be such that the nucleotide pair is altered in such a way
that it mimes another symbol as far as protein synthesis is concerned (6). It

* Individuality as an integral feature in biology has been emphasized recently by Rcxier J.
Williams: in Biochemical IncUvidiiality, J. Wiley and Sons, New York, Chapman & Hall,
London (1956).

56 Hubert P. Yockey

may be thrown into an excited tautomeric form from which it recovers by
relaxation. Possibly one can account for biological recovery by such a
mechanism. The consideration of recovery is omitted from this paper for
simplicity and we shall need only the notion expressed in the first sentence of
this paragraph.

In view of the above remarks we may write the following equation for the
rate of change of /?,()) with A:

idldX) p,ij) = -y,,(A) p,{j) + c,,(A) (4)

The first terni represents the loss in nucleotides responsible for the {i,j)
transition. The second term is due to the gain in nucleotides engaging in the
(i,j) transition coming from other nucleotides altered by the deleterious agent.
This can be brought into sharper focus by thinking of the binary case. Suppose
q is the correct and p is the incorrect read-off probability. We are calculating the
equivocation, or damage to the message, resulting from point errors. This means
that, accordingly, a letter is not deleted but is read off either correctly or
incorrectly. This letter switching process may continue until half the letters are
correct and half are incorrect; at that point p = Ijl and q = 1/2. The infor-
mation content vanishes. In the case of a four letter alphabet a letter which is
acted upon and which may therefore change or may retain its original read-off
character has an a priori probabiUty of 1/4 to remain or to become a correct
letter. Thus the second term is required by the normalization condition.

Equation (4) describes the effect of the interaction of the deleterious agent,
say the x-ray dose, with the information bearing molecules in the cell. It
corresponds to current views of reaction kinetics. Should it be discovered that
some effect, for example, inter-symbol influence, should be taken into account
then equation (4) may be altered suitably. The following argument would then
still be cogent except that the new form of equation (4) would be used. Present
experimental evidence substantiates equation (4) and we have no present
justification for greater complication. In fact the /./A) and c-j{X) represent more
detail than is available. Sum equation (4) over ally:

2 (d/dX) pij) = - 2 JM plj) + 1 cM (5)

Since J J

IPi(j)=l; I(dldX)p,(j) = 0 (6)

j j

o = -2^a)AO')+2c.>a) (7)

3 3

If the /,/A) and the c^/A) may be replaced by an average value J(X) and c(l),
equation (7) becomes, for a four-letter alphabet:

0 = -J{X) + 4 cU) (8)

c(X) = +yiX) (9)

Equation (4) may be written as follows:

(dldX) p,(j) - -7(A) p,{j) + i/(A) ( 1 0)

Some Introductory Ideas Concerning the Application of Information Theory in Biology 57

Given (dldX) p^d) as some function of A, equation (3) may be regarded as a
differential equation for //(A). This equation has a simple form if the y,v,(A)
and the c,,(/l) may be replaced by their averages y(/l) and iJ{?>.).

{dHldX) = log2 e 2 {p{i)J{X)[ p^ij) + I] -{-p{i)m [-^p,{j) + I] loge/;,(;)

-\-p,{j)\og,pij){dicrA)p{i)] (11)

{dHldXy= -J{X) log2 e lp{i)p,{j) loge/^(7)
+i J(A) log2 e 2 p{i) loge PiCj)
+log2 e 2 Piij) HePiij) {dldX) pii) (12)

Substituting equation (2) in equation (12) and rearranging we have
{dHldX) + J{X)H = J{X)H, + ya) 2 pii) \o^z Piij)

i.j

+ lPi(j)iog,p,(j)(dld?i)p{i) (13)

i.j

The third term on the right of equation (13) is negligible for biological
systems. To show this we must discuss first the method of calculating the
{dldX) pU). By definition (3) the following relation holds:

p{i)=lpii)p^ii)- (14)

i

Form the derivative with respect to A and substitute equation (4) :

{dldX) p{i) = llpij) {dldX) p,{i) + pAi) (dIdX) p(j)] ( 1 5)

j

{djdX) pii) = - 2 y,, /.,(/•) pij) + 2 q. pij) + 2 pM) i^m p(j) ( 1 6)

j i J

The equations (16) are a set of differential equations for the p{i). They may
be rearranged in the usual form:

{dldX) pii) - 2 PjO) idldX) pij) = - 2 Jji PiU) pij) + 1 c,i pij) i 1 7)
j j J

We are interested in the conditions when the id/dX) pii) vanish. The condition
is of course that the terms on the right of the equations (17) are all equal and
that the detenninant of the coefficients of the idjdX) pii) be different from zero.
Among the circumstances in which this will occur are those where all p^ii) =
q and all Pi{k) = p ii j^ k). That is, all letters are equally probable and one kind
of error is as likely as the other. In my paper in Part V the behavior of dH/dX
under the much stronger conditions that the J^j and c^j vanish at A = 0 will be
needed. Then, of course, providing that the determinant of the coefficients of
the idldX) pii) be different from zero, all id I dX) pii) = 0. It may therefore be
expected that except under most exceptional and special conditions the idfdX) pii)
will be very small or will vanish.

It can be further shown that for a nearly perfect system the coefficients of
the idldX)pii) in equation (13) are small compared to one. Dancoff and

58 Hubert P. Yockey

QuASTLER (5) have estimated the error rate per cell per generation to be some
10-1 tQ jo-2 times the spontaneous mutation rate per cell generation (10^* to
10~i^). Taking this to mean that

Piii) = q^{\-p) and p^ij) = p ^ \Q~^ (i ^j)
we see that

/'^(01og2/7,(0 = +log2(l -p) ^-p = -10-6

p,(j) log^Piij) = -6 X 10-« log2 10 ^ -10-5 (18)

Because of the discussion given above this term in equation (13) may be neglected.
Equation (13) gives the value of {dHjdX) at the values of /?/;) corresponding
to Hg^. Let these values be plij).

dH

= J{X)[H, -H, + 12 P{i) log2 p'm ( ' 9)

dH

The coefficient of /(A) will be a constant so that —

dl

will behave as a function

Ha

of X like J{X). This result will be needed in my article in Part V.

REFERENCES

1 . J. D. Watson and F. H. C. Crick : Genetical implications of the structure of deoxyribose
nucleic acid. Nature, Lo/tcl. Ill, 964-967 (1953).

/. D. Watson and F. H. C. Crick: The structure of DNA. Cold Spr. Harb. Symp. Quant.
Biol. 18, 123-131 (1953).

J. D. Watson and F. H. C. Crick: Molecular structure of nucleic acids. A structure for
deoxyribose nucleic acid. Nature, Lond. 171, 737-738 (1953).

2. G. Gamow: Possible mathematical relation between deoxyribonucleic acids and proteins.
Biol. Mcdd., Kbh. 22, (3), 1-13 (1954).

3. C. Shannon and W. Weaver: The Mathematical Theory of Communication, University
of Illinois Press, Urbana (1949).

4. W. J. Burdette: Incidence of tumors in isogenic strains. /. Nat. Cancer Inst. 12,
709-714(1952).

5. S. M. Dancoff and H. Quastler: The information content and error rate of living
things. In: Information Theory in Biology, ed. by Henry Quastler, 263-373, University
of Illinois Press, Urbana (1953).

6. H. P. Yockey: An application of information theory to the physics of tissue damage.
Radiat. Res. 5, 146-155 (1956).

7. M. R. Zelle and A. Hollaender: Effects of radiation on bacteria. In: Radiation Biology,
ed. by A. Hollaender, Vol. 2, chap. 10, McGraw-Hill, New York (1955).

8. O. Rahn: The order of death of organisms larger than bacteria. J. Gen. Physiol. 14,
315-337 (1930).

9. R. Pearl: On the distribution of differences in vitality among individuals. Amer.
Nat. 61, 113-131 (1927).

10. R. G. Schott: The inheritance of resistance to Salmonella aertrycke in various strains
of mice. Thesis, Iowa State College Library, 1-59 (1931).

11. R. G. Schott: The inheritance of resistance to Salmonella aertrycke in various strains
of mice. Genetics 17, 203-229 (1932).

12. H. O. Hetzer: The genetic basis for resistance and susceptibility to Salmonella aertrycke
in mice. Genetics 22, 264-283 (1937).

Some Introductory Ideas Concerning the Application of Information Theory in Biology 59

13. W. V. Lambert: Genetic investigations of resistance and susceptibility to disease in
laboratory animals. Rep. Agric. Res., Iowa Agric. Exp. Sla., 89-90 (1931); 91-92 (1932);
115(1933); 142-143(1934); 158-159(1935); 147-148(1936).

14. J. W. Gowen: Genetic investigations of resistance and susceptibility to disease in
laboratory animals. Rep. Agric. Res., Iowa St. Coll. Agric. Exp. Sta., 158-159 (1937);
151-153 (1938); 156-160 (1939); 192-194 (1940); 171-172 (1941); 189-190 (1942);
178-182 (1943); 204-210 (1944); 278-283 (1945); 257-260 (1946); 230-232 (1947).

15. J. W. Gowen: Significance and utilization of animal individuality in disease research.
/. Nat. Cancer Inst. 15, 555-570 (1954).

16. A. HoLLAENDER (cd.): Radiation Biology, McGraw-Hill, New York (1955).

17. D. E. Lea: Actions of Radiations on Living Cells, Cambridge University Press,
Cambridge, England (1955).

18. W. L. Russell: Genetic effects in mammals. In: Radiation Biology, ed. by A. Hollaender,
Chap. 12, McGraw-Hill, New York (1955).

19. M. Ycas: The protein text. This volume.

PART II
STORAGE AND TRANSFER OF INFORMATION

A CENTRAL issue in modern biology, which touches in some degree all branches
of that science, is the problem of species specificity and its relation to protein-
specificity and synthesis. The subject can be approached from many points of
view but the one adopted by the authors of the papers in Part II is to seek the
solution in terms of the properties of a communication system

The justification for considering, from this point of view, a phenomenon
which looks, at first sight, to be purely biochemical lies in the recent discovery
that protein specificity is expressed as an exact order of amino acid residues.
If this is even substantially the case then it is germane to discuss such problems
in these terms. In fact, a number of current papers on protein synthesis and
specificity have recourse, at one point or another, to the language of information
theory. Since the specificity of proteins is thought to be coded in the exact order
of pairs of nucleotide bases in DNA, the relationship of DNA, RNA, and proteins
can be considered from aspects which are mathematical rather than purely bio-
chemical.

Gamow was the first to notice these mathematical aspects. He and Ycas
pursue in this part some of the issues which they reveal. The influence one hopes
these considerations will have on the experimentalist is clear. Additional data
on the amino-acid residue sequences and other structural data for a large number
of proteins can be put to immediate practical use in solving for the protein code,
and therefore in understanding more about protein synthesis. Unfortunately,
mainly due to the lack of sufficient protein text, few definite answers can be given.
But it is possible to eliminate some past errors and to phrase the question in a
sharper fashion than before.

The notion that an abstract quantity such as information is stored in the
genetic material and is transferred to proteins during their synthesis raises
immediate questions as to how this is done, how much is transferred, and how
this quantity is aff'ected by changing experimental conditions. These questions
are attacked from diff"erent analytical and experimental points of view by the
papers by Augenstine, by Mahler, Walter, Bulbenko and Allmann, and by
Koch and by Glinos.

The information theoretic properties of communication systems of particular
concern to the papers in this part are the coding problem, the representation
theorem, and redundance. Each paper deals with issues of its own but in terms
of these ideas to a greater or lesser degree. It is in this way, among others, that
information theory may grow to be as useful to the biologist as thermodynamics
is to the chemist, whether his subject is clearly one in communication as is that
of Frishkopf and Rosenblith or somewhat less clearly that of protein specificity.

H. P. Y.

61

THE CRYPTOGRAPHIC APPROACH TO THE
PROBLEM OF PROTEIN SYNTHESIS

George Gamow and Martynas Ycas

University of Colorado and University of New York

Abstract — The Watson and Crick suggestion concerning the role of DNA in replication,
mutation, and protein synthesis requires a coding between the four-letter DNA alphabet and
the twenty-letter protein alphabet. An attempt has been made to discover this code by crypto-
graphic methods. Various schemes have been worked out but no success obtained at this
writing. There is hope that as the number of protein sequences increases this problem will
be solved.

Speaking about information storage and transfer in a living cell, one always likes
to compare the cell with a large factory. The cell nucleus is the manager's office,
directing the work of the factory, and the chromosomes are the file cabinets in
which all blue prints and production plans are stored. The cytoplasm is the
plant itself with the workers and machinery carrying out the actual production ;
those are, of course, the enzymes catalyzing various biochemical reactions. If
something goes wrong with the information stored in the chromosome, the
corresponding enzyme will also do a wrong thing. Consider, for example, an
enzyme which produces the pigment necessary for color vision. If the particular
section of chromosome carrying the directions for producing that pigment is
defective, the enzyme will not get the correct instructions, and will not produce
the right type of pigment. As a result, the individual will be color blind.

The materials of chromosomes and of enzymes are chemically different,
except that in both cases we deal with long molecular chains formed by the
repetition of a comparatively small number of different units. DNA (deoxyribo-
nucleic acid), forming the chromosomes, is a sequence o^ four different units
or 'bases': namely, adenine, thymine, guanine, and cytosine. For sake of
picturesque presentation, we may associate them with four suits of cards:
spades, clubs, diamonds and hearts. Each DNA molecule is equivalent to a
sequence of cards many thousand units long, and the way in which different
suits follow each other contains, in code form, the instructions to the original
cell (fertilized ovum) and its descendants to develop into a rosebush, a skunk,
or a man.

The first question is this. How is information which is carried by DNA
molecules of the chromosomes duplicated when the cell goes through the process
of division? An answer can be given on the basis of the model of DNA proposed
about three years ago by J. Watson and F. Crick (1). They started with the
fact, first noticed by E. Chargaff (2), that the number of adenines in any
given DNA molecule is always equal to the number of thymines, while the
number of guanines is always equal to the number of cytosines (3). In the
playing card analogy there are as many spades as there are clubs, and as many
diamonds as hearts. This suggests that we deal here with a double-stranded

63

64

George Gamow and Martynas YCas

^\.

/

/ /

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I

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u -J.

/

-u

c

*c

<

♦

o

X-U-X -^
u=u.

I

I
K

r/

~o

0=u

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\-/ \

/^" \

-u — ^

■<J.

\\

\

4
I

O

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-U X

./

-o

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^-\ /■

O"^ /
X — u

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/

X

I /

/r

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U

The Cryptographic Approach to the Problem of Protein Synthesis 65

sequence in which red and the black cards are paired together. A heart is
always paired with a diainond (and vice versa), while a spade is always paired
with a club (and vice versa). The fact that DNA molecules also contain one
sugar (ribose) and one phosphate for each 'base' suggests a molecular model
similar to a rope ladder. The vertical ropes on both sides are formed by 'sugar-
phosphate- sugar-phosphate-' sequences, while the paired bases form rigid
horizontal steps attached to sugars on both sides. The reason why the above-
mentioned pairing of bases takes place is two-fold. Cytosine and thymine
(hearts and clubs) are 'pyrimidines', being formed by a single C — N — ring with
different atomic groups attached to them. Adenine and guanine (spades and
diamonds) are 'purines', and contain in their structure two connected rings, one
with six atoms, and the other with five.

The chain shown in Fig. 1 is a sequence of sugars and phosphates. To
each sugar is attached a 'base', and in tliis section of the molecule you see four
different bases. Two of them (hearts and clubs) are short, and two others
(spades and diamonds) are long. Now, in order to run the second strand beside
it in the parallel way, we should attach short bases to long ones, and long
bases to short ones. Of course, in the playing card analogy again, one could
also join a heart to a spade and a club to a diamond. But this is excluded because
in these cases hydrogen atoms will be in the wrong places to form proper
hydrogen bonds between these two bases.

The evidence supplied by an x-ray diffraction pattern indicates in addition
that the DNA molecule has a helical shape, being twisted around its central
axis by 36° each step. Thus, it makes a complete turn each 10 steps.

The Watson and Crick (4) theory of dupHcation of DNA molecules proceeds
as follows. When the cell is ready to divide, there appears a large number of
free nucleotides in the nucleoplasm surrounding the chromosomes. A nucleotide
is defined as one of the four bases with a sugar and a phosphate attached to it.
At that time the double stranded DNA molecule splits into two single strands
along its main axis, and each strand is regenerated by catching the corresponding
free nucleotides from the surrounding medium. Thus, each heart separated by
splitting from its diamond gets another diamond from the solution, and each
diamond gets another heart. As the results, we get two new double stranded
DNA molecules, each identical with the original one. Once in a while a mistake
may be made in this duplication process, and we call it a mutation. So much
for the structure and functioning of DNA molecules.

Now we come to the problem of information transfer from the chromosomes
to the enzymes. How does the sequence of bases (card suits) in DNA determine
the structure of the enzyme? Enzymes are proteins, and are formed by long
sequences of twenty different chemical groups known as amino acids. It is well
known that there are as many as twenty-four or twenty-five amino acids, but,
as Dr Yeas tells us in more detail in the next paper, one can show that the
extra ones in the original protein synthesis are modifications of the original
twenty which take place after the protein molecule is synthesized. Thus, for
example, 'proline' is an original amino acid used in protein synthesis, whereas
'hydroxyproline' is its postsynthetic modification. Since we symbolized four
bases of nucleic acid molecule by four playing card suits, it is reasonable to
symbolize the twenty basic amino acids, which have complicated chemical

66 George Gamow and Martynas Ycas

names, by twenty letters of a (reduced) English alphabet. Thus, one protein
molecule may look like:

. . .arreducesugarreducesug. . .
and another like:

. . . akeacoloruisionpigmentma . . .

Just to give an example of how the sequence of amino acids in protein
molecules may affect their biochemical activity, we will give the example of two
closely related hormones: oxytocine and vasopressin. Both are formed by a
sequence of only nine amino acids:

Oxytocine — Cys-Tyr-Z/ew-GIun-Aspn-Cys-Pro-Lew-Gly
Vasopressin — Cys-Tyr-PAe-Glun-Aspn-Cys-Pro-vlr^-Gly

The two sequences are identical except for the substitutions in the third and
eighth place. However, their functions are rather different. Oxytocine has the
property of causing the contraction of the uterus in the process of childbirth.
If you inject it into the blood of a cow, even if the cow is not pregnant it will
go through all motions it would go through if a calf were to be born. Vaso-
pressin, on the other hand, has rather different properties: it contracts the
blood vessels and causes increased blood pressure. Thus, simply by changing
two amino acids out of nine, the action of the hormone is completely changed.

Whereas replacement of some amino acids in a protein may completely
change its biological function, there also exist replacements which distinguish
the same protein taken from different species of animals. Thus, for example,
insulin A, which is formed by a sequence of amino acids with twenty-one
members, differs for cattle and swine in the eighth and tenth place. Human
insulin, which has not yet been analyzed, possibly differs slightly from that
extracted from cattle and swine. Nevertheless, the latter are successfully used
on human patients.

Since there must exist a definite relation between the sequence of bases in
nucleic acid and the sequence of amino acids in proteins, we can ask ourselves
what this relation is. Here we have to return to our analogy of a factory. The
v/orkers from the factory do not walk into the manager's of^ce to find out what
to do, and the manager also does not go to the plant to instruct workers per-
sonally. There are people, called foremen, who get the information from the
manager's ofiice and tell the workers. In the cell the role of foreman is carried
out by RNA molecules (ribonucleic acid) which are, presumably, very similar to
the molecules of DNA. They are different only in that one oxygen atom is
missing in each sugar of DNA, and there is a slight change in one of the four
bases, which in RNA is called urosil instead of thymine. RNA is presumably
synthesized by DNA inside the nucleus and receives the set of instructions
carried by DNA. Then it passes out into the cytoplasm, and is incorporated into
the so-called microsomes, i.e. foremen's offices, where the synthesis of proteins
takes place.

We do not yet have a model of the RNA molecule. It seems, however,
that in this case the pairing rules of adenine to thymine (urosil), and guanine
to cytosine do not hold, which suggests that RNA molecules are single-stranded.

The Cryptographic Approach to the Problem of Protein Synthesis

67

Since RNA serves as an intermediary between DNA and proteins, we have here
two problems. First, how is RNA formed by DNA ? Second, how are proteins
synthesized by RNA? The first problem may turn out not to be very difficult
because of the close similarity between the two molecules. For example,
RNA may be a non-regenerated half of DNA with small changes in sugars
and in one of the bases. It may be that the absence of the oxygen atom in RNA's
sugar is responsible for the failure to form a double-stranded configuration.
However, we still do not know the answer to this question.

The second problem concerning the synthesis of proteins by RNA mole-
cules presents more challenge to the imagination. How can a sequence formed
by four different units (four bases) be translated in a unique way into a sequence
formed by twenty units (twenty amino acids)? Here is a possibility which
seems to us to be very likely. Suppose one plays a game of poker in which
only three cards are dealt, and pays attention only to the suit of the card. How
many different hands will one have? Well, one can have a 'flush', i.e. three
cards of the same suit. There are four different flushes: three hearts, three
spades, etc. Then one can have a 'pair', i.e. two cards of the same kind, and
one different. How many of those are there? One has four choices for the
suit of the pair, and three choices for the third card. Thus, there are altogether
twelve possibilities. The poorest hand will be a 'bust', i.e. three different suits.
There are four different busts: no hearts, no diamonds, etc. We have altogether
twenty different possibilities. This 'magic number' 20 is just the number of
amino acids participating in the primary process of protein synthesis. We
may imagine that each amino acid in the synthesized protein is determined
by a triplet of bases in the RNA template.

Since the distances between neighboring amino acids in the extended
polypeptide chain are equal to the distances of neighboring bases in the poly-
nucleotide chain (both being equal to 37 A), it was at first natural to suppose
that the correlation between the two chains looks in a way shown in Fig. 2,

RNA-Template

where individual bases are shown by circles and the amino acids by triangles.
This represents the so-called over-lapping code in which the neighboring amino
acids have in common two bases in the RNA template. If the transfer of
information from nucleic acid to protein is carried out according to such an
overlapping code, there must exist a definite inter-symbol correlation between
the amino acids constituting protein molecules. Thus, for example, if a certain
amino acid is determined by two adenines and some other base, its neighbors
will be preferably amino acids which also contain adenine in their template
transcript. In order to see whether or not such a correlation between the

68

George Gamow and Martynas Ycas

neighbors really exists in the known protein sequences, it is necessary to test
all possible assignments between the twenty amino acids and the twenty possible
base triplets. The number of all possible assignments of that type is 20! =
3.10^^, Since 3.10^^ represents the age of our universe (5 bilhon years) expressed
in seconds, the straightforward test of that kind would require quite a consider-
able time even if we could test one assignment each second ! However, as it
often happens in cryptographic problems, one can sometimes find parts of the
message which reduce quite considerably the amount of necessary work. Thus
the code messages sent by German spies during the war were likely to contain
the combinations of letters corresponding to various possible ports of embark-
ation of American expeditionary troops. The same happens in protein sequence.
For example, the adrenocorticotropin molecule contains the sequence:

— Lys — Lys — Arg — Arg— Pro — Val — Lys — Val —

In this sequence there are two identical amino acids in succession followed
by another pair of identical ones. In the English language there are not many
words having such a property. (Tennessee is one of the rare examples!) Then
lys repeats again three steps later, and has identical neighbors (val) on both
sides. These facts simplify the problem to such an extent that, instead of
spending five billion years, it was possible to find a single assignment between
the amino acids in the above sequence, and the base triplets in the course of an
afternoon. At first it was thought the problem had been solved, but, when one
tried to extend these assignments to the other parts of the ACTH molecule
and to the other known protein sequences, one was led to direct contra-
dictions. In the course of subsequent decoding work, other examples leading
to similar contradictions were found, and it became clear that the thing just
will not work. In fact, as Dr Yeas discusses in the following article, it seems
that there is no correlation between the neighboring amino acids whatsoever.
This negative result can only mean that the original hypothesis represented
in Fig. 2 was incorrect, and that in the process of protein synthesis the nucleic
acid molecule is not present in its extended form. If, as seems to be true, we
deal here with a "non-overlapping code" in which each amino acid is determined
by an individual base triplet of its own (Fig. 3), we are forced to assume that

RNA-Template

Fig. 3.

the RNA molecule is shrunk by a factor of three. We can imagine, for example,
that during the process of protein synthesis the RNA molecule has the shape
of a spiral as shown in Fig. 4.

Closely connected with the problem of a non-overlapping code is the problem

The Cryptographic Approach to the Problem of Protein Synthesis

69

of "punctuation". Indeed, a sequence of bases can be broken into a set of
non-oveiiapping triplets in three different ways depending upon the base with
which we start. The three dilTerent readings of tiie same template can be des-
cribed mathematically as 3n, 3n/l, and 3n/2 (3n/3 being the same as 3n).

A|

3.6 A

As was suggested by Dr Barbara Law, three possible readings of the same
RNA template may explain an interesting regularity first noticed by Dr
Martynas Yeas. He observed about two years ago that, in a case of seven
proteins for which the sequences of amino acids were known, the total number
of amino acids in the protein molecule was a multiple of three : nine amino
acids in oxytocine and vasopressin, twenty-one in insulin A, thirty in insulin B,
thirty-nine in ACTH, 126 in ribonuclease, etc. This could be explained if one
assumes that each RNA template synthesizes the proteins in all three possible
vv'ays, and that these three different readings are afterwards united in one
linear sequence. If this were true, there must exist a cryptographic correlation
between the first, second, and third "thirds" of each protein molecule. One
thinks of how such a correlation could be checked, but it seems to be very
difficult indeed. Recently, though, the existence of such a correlation became
rather doubtful, since two protein sequences published recently contain 29 and
124 amino acids.

In summing up, we should say that the problem of finding the nature of the
correlation between polynucleotide chains of nucleic acids, and the polypeptide
chains of the proteins is still unsolved, although various methods for establishing
such a correlation have been worked out. We may hope, however, that with
the increased number of known protein sequences, this problem will be solved
in one way or another.

REFERENCES

1. J. D. Watson and F. H. C. Crick: Molecular structure of nucleic acids. Nature, Lond.

171, 737-738 (1953).

2. E. Chargaff: for reference see S. Zamenhof, G. Brawerman, and E. Chargaff: On the

deoxypentose nucleic acids from several micro-organisms. Biochim. Biophys. Acta. 9,
402-405 (1952).

3. G. R. Wyatt: Nucleic acids of some insect viruses. /. C^'//. P/(V.v/o/. 36, 201-205 (1952).

4. J. D. Watson and F. H. C. Crick: Genetical implications of the structure of deoxyri-
bose nucleic acid. Nature, Lond. 171, 964-967 (1953).

6

THE PROTEIN TEXT

Martynas Ycas

Department of Microbiology, State University of New York
Upstate Medical Center, Syracuse, New York

And strange to tell, among that Earthen Lot
Some could articulate, while others not:

And suddenly one more impatient cried —
'Who is the Potter, pray, and who the Pot ?'

The Book of Pots

Abstract — The sequence of residues in proteins, regarded as a text written in a twenty symbol
alphabet, is examined. The following tentative conclusions are drawn:

1. Twenty amino acids are distinguished by the protein-forming mechanism. Super-
numerary amino acids arise from the regular twenty by secondary modification of protein-
bound residues.

2. Each residue in the protein has a separate genetic representation.

3. There is no intersymbol correlation between adjacent residues.

4. Natural selection is not the only factor determining the frequency of occurrence of the
various kinds of residues. It is suggested that the method of encoding protein sequence
information in nucleic acid imposes differences in frequency of occurrence on the different
kinds of residues.

5. Peptide chains are not multiples of some fixed number of residues.

The encoding and transfer of genetic (DNA) information to RNA and protein is discussed,
as well as the problem of the independent reproduction of RNA viruses. While the data set
certain limits on the possible ways of encoding and transferring information, they are not
sufficient for a unique solution of these problems.

Ribonucleic acid of Tobacco Mosaic Virus (TMV) has been shown to deter-
mine the sequence of amino acid residues in the protein of the virus (1, 2, 3).
It seems logical therefore to believe that the sequence of other proteins is also
determined by RNA.*

Since RNA is essentially a linear sequence of four kinds of nucleotides,
while proteins are linear sequences of about twenty kinds of amino acid residues,
the RNA molecule can be regarded as a text, written in a four-symbol alphabet,
which encodes another text, the protein, written with about twenty symbols.

* The following abbreviations will be employed. RNA — ribonucleic acid; DNA — deoxy-
ribonucleic acid; Ad — adenylic acid; Gu — guanylic acid; Cy — cytidylic acid; Ur — uridylic
acid; ala — alanine; arg — arginine; asp — aspartic acid ; aspn — asparagine; asx — asparticacid
or asparagine; cys — cysteine; glu — glutamic acid; glun — glutamine; glx — glutamic acid or
glutamine; gly — glycine; his — histidine; ileu — isoleucine; leu — leucine; lys — lysine; met —
methionine; phe — phenylalanine; pro — proline; ser — serine; thr — threonine; try — trypto-
phan; tyr — tyrosine; val — valine; Hlys — hydroxylysine ; Hpro — hydroxyproline; serP —
phosphoserine. Peptides are written with the amino group to the left, the symbols being
connected by a dash ( — ). The sign (*) signifies a terminal residue. Sequences considered
uncertain are in parentheses ( ). Symbols in parentheses, with commas between (ala, gly)
mean that the sequence is not known.

70

The Protein Text 71

Several attempts, none completely convincing, have been made to determine
the coding system employed (4, 5, 6, 7). Cryptography must be based on a
study of texts, and 1 shall therefore attempt an examination of protein molecules
from this point of view. The following aspects of protein structure will be
examined :

1. The number of kinds of amino acids which occur in proteins.

2. The effect of mutations on amino acid sequence.

3. Whether intersymbol correlations exist between adjacent residues.

4. The frequency of occurrence of the various amino acid residues.

5. Whether any restrictions exist on the length of peptide chains.

After considering the empirical evidence, I shall indicate its bearing on the
problem of encoding protein sequence information into the RNA molecule.

I. THE NUMBER OF AMINO ACIDS OCCURRING IN PROTEINS

In previous studies (6, 7) it has been assumed that proteins are composed of
exactly twenty different kinds of residues. Since in fact more than twenty
kinds of residues occur in proteins, the assumption requires some justification.

All organisms, from viruses to mammals, use the same building blocks
for their proteins. With minor qualifications this is also true of the nucleic
acids, but not true of the third major class of biologically-occurring high
polymers, the polysaccharides. The amino acids which invariably occur in
all organisms and virtually all proteins are the following: ala, arg, asp, aspn,
cys, glu, glun, gly, his, ileu, leu, lys, met, phe, pro, ser, thr, try, tyr, val. The
number in this list is exactly twenty.

It will be noted that I omit cystine from this list. Because of its structure,
cystine corresponds to two residues. The structure of insulin (8) shows that
one cystinyl residue can occupy non-adjacent positions in a peptide chain
or even participate in two different chains. Cystine is best regarded as an
oxidation product of cysteine, formed after incorporation of the cysteinyl
residue into the peptide chain. This view is supported by the recent discovery
of an enzyme which reversibly catalyzes the reaction

2 cysteinyl :^ cystinyl

when these residues are protein bound (9). Another example of such a reaction
may be the cyclic oxidation and reduction of protein SH groups during the
various stages of cell division (10).

In addition to the above twenty, other alpha amino acids occur in nature.
Some of these, such as homocysteine, citruline and ornithine are well known
biochemical intermediates but do not occur in proteins. It is clear that the
number of amino acids which occur in proteins is limited by an inability to
incorporate, rather than make, amino acids. Hydroxyglutamic acid and
norleucine, previously believed to be protein constituents, have been shown
not to exist as natural products (11). Alpha amino-adipic acid has been isolated
from an impure protein hydrolyzate, but it has not been demonstrated that
it is a protein constituent in the same way as other amino acids (12). Diamino
pimelic acid, commonly occurring in bacteria, appears to be associated with
the polysaccharide material of the cell wall (13, 14).

Nevertheless, there are amino acids, other than the twenty enumerated,

72 Martynas Ycas

which certainly occur in proteins. These include hydroxylysine and hydro-
xyprohne (in collagen), phosphoserine (in a number of different proteins (15)),
thyroxine (in thyroglobulin) and tyrosine — O — sulphate (in fibrinogen) (16).
The distribution of these amino acids is different from the regular twenty.
Whereas the twenty amino acids occur in virtually all proteins, the super-
numerary ones have an erratic distribution, being confined to one or to a few.
The suggestion was first made by Crick, that the supernumerary amino acids
are the result of modifications of some of the regularly occurring amino acids
after these have been incorporated into a peptide chain. The biochemical
evidence for this is as follows.

When one of the twenty regularly occurring amino acids is presented labeled
to an organism, it is rapidly incorporated into protein and most of the label
is found in the corresponding residue. It should be noted that glutamine and
glutamic acid are separately incorporated and do not arise one from another
by addition or subtraction of amide groups after incorporation (17). (A
similar demonstration for the analogous case of asparagine and aspartic acid
is still lacking.) Clearly, therefore, these amino acids are the precursors of
the corresponding protein-bound residues.

The supernumerary amino acids behave differently. Thus lysine is the
precursor of hydroxylysine (18), but C^* or tritium-labeled hydroxylysine
is not incorporated into collagen (19). Similarly, proline is the precursor of
hydroxyprohne, but proline is a much better precursor of the hydroxyprolyl
of collagen than is hydroxyprohne itself (20, 21). These amino acids, then,
are not incorporated as such, but presumably are formed by oxidation of
protein-bound proline and lysine. Phosphoserine likewise is formed by phos-
phorylation of protein-bound serine (22). Thyroxine is apparently formed from
the tyrosine residues of thyroglobuhn (23). There is no information at present
on the metabolism of tyrosine — O — sulfate.

Since not all appropriate residues are secondarily modified, this inter-
pretation imphes that the enzymes catalyzing such conversions show specificity
for sequence in the protein. At least one enzyme is known which shows such
specificity. Prostatic phosphatase dephosphorylates phosphoserine in the
sequence asx-serP-glx-ileu-ala, but not in glx-serP-ala (24). It is therefore
suggestive of some enzyme specificity that hydroxyprohne in collagen occurs
mainly, if not exclusively, before glycine (25) (Table IV). Other amino acids,
as shown later, shovv' no such neighbor preferences. The region determining
whether proline is to be oxidized or not probably includes more than three
residues, as indicated by the isolation from collagen of the tripeptides ala-
pro-gly; ala-Hpro-gly and ser-pro-gly; ser-Hpro-gly (Table IV).

The biochemical evidence thus appears to indicate that the protein-forming
mechanism selects exactly twenty different kinds of amino acids, and that the
supernumerary ones arise by secondary modification of protein-bound residues.
A possible cause for error in this conclusion should be noted. It is virtually
certain that amino acids are not incorporated as such, but in the form of some
sort of activated derivative. If the same amino acid were to form more than
one derivative, the number of items to be selected would of course exceed
twenty. There is no evidence for this at present, and only further advances
in biochemistry can decide whether this is the case.

Tlie Protein Text 73

II. GENETIC EFFECTS ON PROTEINS

There is an increasing body of evidence indicating that tiie details of protein
structure are genetically determined. A study of the effect of mutations on
proteins should therefore tell us something both about the nature of mutations
and the protein forming mechanism. Known cases of genetic effects on proteins
are listed below.

1. In man hemoglobin occurs in several electrophoretically distinguishable
forms, the presence of each being apparently controlled by alleles of a single
gene (26). Hemoglobin C differs significantly in amino acid composition
from hemoglobin A (27). Hemoglobin A and S have been degraded in a
controlled fashion with trypsin and the resulting peptides separated. The
difference between these hemoglobins is apparently confined to a short section
of the molecule (28).

2. Two electrophoretically different hemoglobins occur in sheep. Their
presence is determined by alleles of a single gene (29).

3. Two forms of lactoglobulin occur in cow's milk, and like the hemo-
globins are determined by different alleles of one gene. Crystallographic
investigations indicate unit cells of the same size, but there are very slight
differences in the diffraction pattern, which the investigators attribute, possibly,
to the substitution of a few amino acid residues by others (30).

4. Mutants of Neurospora and Escherichia co/i produce abnormally heat-
labile forms of tyrosinase (31) and a panthothenic acid synthesizing enzyme (32),
respectively. It is clear that a change in the proteins has occurred, but unfor-
tunately there is no further information on its physico-chemical nature.

The genetic evidence indicates that there is no interaction between alleles
controlling the synthesis of different variants of one protein. If both alleles
are present, both types of protein are formed. A possible exception should
be noted. The N-terminal groups of wheat gliadin are reported to be phe,
of rye gliadin phe and glx, but unexpectedly the ghadin of wheat x rye hybrids
was found to have no amino or carboxyl terminal ends, indicating, possibly,
a cyclic protein (33). This case obviously needs further study*.

The evidence cited above shov/s that the properties of proteins are gene-
determined, but it does not indicate clearly what these properties are. More
detailed information is available on this point from a comparison of homo-
logous proteins of related species, if it is assumed, as is usually done, that
species differences are the result of gene mutations.

Available evidence on amino acid sequence of homologous proteins is

* There is considerable confusion as to the N-terminal residues of wheat gliadin. Fraenkel-
CoNRAT (51) misquotes Deich and Soreni (33) as stating that the N-terminal residues are
phenylalanine and histidine, apparently because of a misunderstanding in Chemical Abstracts
(138). KoROS, whose paper I was able to consult only in abstract (139), reports histidine as
N-terminal. Ramachandran and McConnell (140), working with wheat gliadin but failing to
specify the species, also find histidine. Deutsch (the same as Deich quoted above, the differ-
ence in spelling being due to transliteration from the Cyrillic) reports that gliadin from Triticiim
durum and Triticum milgare has N-terminal phenylalanine (141). This is misquoted as tyrosine,
and tyrosine and glutamic acid, respectively, by Ramachandran and McConnell (140).
The original paper of Deutsch (141) was also unavailable to me.

74

Martynas Ycas

collected in Table I. Mutations (as inferred from differences between homo-
logous proteins) do not produce a general scrambling of protein sequence,
but a replacement of one or more residues, leaving the rest of the sequence
unchanged. Since homologous proteins can differ by a one residue replacement,
it is clear that individual residues, rather than groups of residues, are represented
in the genetic material.

Table I. Sequences in Homologous Proteins from Different Species
Protein Species

Insulin (34)

. cys-thr-ser-ileu-cys .
. cys-ala-ser-val-cys . .
. cys-ala-gly-val-cys . .
. cys-thr-gly-ileu-cys .
. cys-thr-ser-ileu-cys .

Pig

Cattle
Sheep
Horse
Whale

Myoglobin (35)

*val . . .
*val . . .

*giy . . .

*gly . . .

Finback whale

Sperm whale

Horse

Seal {Phoca vitulina)

Protamine (36)
(Composition, not sequence)

glyasefaalaovaliileui
glyaseraalagvalaileuo

Salmo irhleus
Salnio trutta

Serum albumin (37, 38)

*asp-ala .... leu*
*asp-thr .... ala*

Man
Cattle

•

Cytochrome c (39)

. . . cys-ala-glun . . .
. . . cys-ser-glun . . .

Horse, Cattle, Pig, Salmon
Chicken

Vasopressin (40)

. . . pro-arg-gly-NHo*
. . . pro-lys-gly-NHa*

Cattle
Pig

Protein

The Protein Text

Species

75

Hemoglobin (41)

*val-leu .
*val-gly .
*val-glun

*val-leii .
*val-gly .
*val-asx .

*val-leu .
*mct-gly .

*val-Ieu .
*val-ser . ,
*val-asx .

*val-leu .
*val-gly .

*val-leu .

Horse, Pig

Dog

Cattle, Goat, Sheep
Guinea pig

Rabbit, Snake
Chicken

Gliadin (33)

*phe . . .
*phe . . .

Wheat

*phe . . .
*glx . . .

Rye

Fibrinogen (42)

*tyr . . .
*ala . . .

Man

*tyr . . .
*glx . . .

Cattle

ACTH (43, 44, 45)

. . . pro-ala-gly-glu . . .
. . . pro-gly-ala-glu . . .

Sheep
Pig

. . . glu-ala-ser-glu . . .
. . . glu-leu-ala-glu . . .

Sheep
Pig

Hypertensive p-ptide (46, 47)

. . . val . . . Cattle

. . . ileu . . . Horse

76 Martynas Ycas

Protein Species

Virus (48)

. . . thr-ser-gly-pro-ala-thr* TMV (M, YA strains)

. . . thr(thr,ala)pro-ala-thr* TMV (HR strains)

It is possible that a mutation may suppress an amino acid determining site
altogether. This is indicated by the tentative finding of Akabori (quoted in
(41)), that the 'B' chain offish insuHn has the sequence . . . pro-lys*, as compared
with the sequence . , . pro-lys-ala* in cattle.

In some cases (ACTH, TMV), two adjacent replacements differentiate
one homologous protein from another. It is not probable that this is due to
two independent but adjacent mutations, but rather that a single mutational
event has affected two residue-determining sites. Such a view is made plausible
by the work of Benzer (49). He has shown that mutations in bacteriophage
involve small sections of DNA, of molecular dimensions, but that these sections
can be of diflferent lengths. Presumably the length of the mutated section deter-
mines the number of residues changed in the protein. It is perhaps not too
sanguine to hope that eventually it may become possible to measure crossover
values in terms of distance in residues along a protein chain, and thus obtain
an estimate of the number of bases in DNA determining a single residue
selecting site. The present difficulties of such an approach are of course obvious
(50).

It would be of interest to determine if there are any restrictions on the
replacement process. Restrictions might be expected on the following grounds.
More than one nucleotide must determine an amino acid site. If the process
of mutation were predominantly to change some, but not all nucleotides
determining a site, then obviously not all sites would be interconvertible in
one step. A study of any such restrictions would be of great value, since their
nature would depend on the coding principle and could be used to infer the
latter.

Table II. Replacements Inferred from Table I and their
Frequency of Occurrence

Occurrence

3
2
2
2
2
2

Replacement

val

<->ileu

ala

<->thr

ala

■<—> ser

ala

<->gly

ala

<-> leu

ser

<-^gly

ala

<-^gIx

val

4^gly

val

<->met

phe

<-^glx

slur

i<-^ asx

arg

<->lys

The Protein Text

77

Known replacements in homologous proteins are collected in Table II.
In the small sample we have (nineteen replacements), half recur twice or more,
suggesting strongly that the process, as observed, is not a random one. Unfor-
tunately, the sample is not unbiased. Certain replacements arc lethal or semi-
lethal (hemoglobin S, for example), and are, without doubt, selected against.
What we actually observe has therefore passed through the sieve of selection.
The direct genetic approach to this problem is tedious, because of the difficulty
of determining the phenotype (the amino acid sequence), and rapid progress
is scarcely to be expected. A much larger body of data on homologous proteins
may, however, enable us to reach a decision on whether the replacement
process is intrinsically restricted or not.

An additional point emerges from a consideration of such protein mole-
cules as consist of more than one chain (Table III). It will be noted that there

Table III. Terminal Residues of Proteins having more

than one Peptide Chain

(The exact number of chains is not indicated.)

Protein

N-terminal

C-terminal

Reference

Cytochrome c

fhis
jhis

(51)

Growth hormone

[ala

phel
phej

(51)

Triosephosphate-
dehydrogenase

fval
Ival

met \
met

(51)

Collagen

giy

ala J

(51)

Gliadin (wheat)

phe

(33)

Glladin (rye)

fphe
Iglx

(33)

^ lactoglobulin

peu
|leu

ileu \
ileu

(51)

Fibrinogen (man)

ftyr
lala

(51)

Fibrinogen (cattle)

ftyr
glx

(51)

Hemoglobin (horse)

fval

jval

(41)

Hemoglobin (cattle)

fval
\met

(41)

78

Martynas Ycas

is a strong tendency for the terminal residues of such proteins to be identical.
This is certainly not due to the chains being identical in all cases, since the
hemoglobins, for example, do differ in the penultimate positions (Table I).
Rather it appears to indicate that multi-chain proteins arise by reduplication
of genetic material, so that the several chains start out by being identical,
but gradually diverge in the course of evolution in the same way as homo-
logous proteins of different species. This hypothesis, as applied to the hemo-
globins and insulin, has been previously discussed (6). Determinations of the
residue sequence along different chains of one protein may therefore throw
additional light on the replacement process.

Table I shows that the process by which replacements become established
is very slow. Elucidation of the sequence of homologous proteins may therefore
make it possible to determine phylogenetic relations between large groups
such as phyla, which cannot now be certainly determined from morphological
and embryological evidence.

III. CORRELATIONS BETWEEN ADJACENT RESIDUES

Are there any forbidden combinations of adjacent residues? An examination
of the sequence of residues in proteins (Table IV) could provide an answer
to this question.

<0 Q.Q. too 3>- CO

_iq: men >-_» _i_i —
<< < < oo oo X

3(oHuJOttQ:>-a:_i
ui>-iiJXD:uxir>4

ALA
ARG
ASP

ASPN
CYS
GLU

GLUN
GLY
H IS

ILEU
LEU
LYS
MET
PHE
PRO
SER
THR
TRY
TYR
VAL

••
••

•

•

•
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• 9

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Fig. I. Dipeptlde sequences now known to occur in proteins, compiled from
Table IV. The N-terminal amino acids are plotted in the rows, the C-terminal

in the columns.

There are of course 400 possible pairs of the twenty amino acids. The
known protein sequences in Table IV have been broken down in the following
way. A sequence, say, of ala-arg-gly is broken down into the dipeptides ala-arg,
arg-gly, and the appropriate cells in Fig. 1 are then filled, the N-terminal
residues being represented by the rows, the C-terminal by the columns. Using
all the data available in Table IV, Fig. 1 shows that somewhat more than half
of all possible dipeptide combinations are known to occur. The question

The Protein Text 79

Table IV. List of Known Sequences in Proteins

Actin (52)

. . . his-ileu-phe*

Adrenocorticotropin (45)

*ser-tyr-ser-met-glu-his-phe-arg-try-gly-lys-pro-val-gly-lys-lys-arg-arg-pro-val-lys-val-tyr-pro-

ala-gly-glu-asp-asp-glu-ala-ser-glu-ala-phe-pro-leu-glu-phe*

Carboxypeptidase (53)
*aspn-ser; ser-thr

a Casein (54, 55)

serP-glx ; *lys-ieu-val-ala-glx-asx

Chymotrypsinogen (56, 57)
leu-ser-arg-ileu-val ; aspn-ser-gly-(glun-ala)

Clupein (58, 59)

*pro-ser-arg; ser-ala-arg-arg* ; arg-arg-arg-arg;

Collagen (60, 61)

ala-Hpio-gly; ala-pro-gly; glx-arg; glx-Hpro-gly; gly-asx-gly; gly-glx; gly-pro-ala;
gly-pro-glx; gly-pro-gly; gly-pro-Hpro ; ser-Hpro-gly ; ser-pro-gly; ala-gly-ala; gly-gly;
ser-gly; thr-gly; ala-asx; asx-asx; asx-glx; asx-gly; glx-ala; glx-glx; glx-gly;
glx-gly-gly; glx-met; glx-phe; ser-asx; val-glx; ala-arg; arg-gly-gly; arg-val-gly;
ser-arg; val-arg; ala-lys; asx-arg; lys-gly; pro-ser; pro-thr; ser-ala; thr-ala;
lys-pro-gly ; leu-ala ; ala-ala-gly ;

Cytochrome c (39)

. . . val-glun-lys-cys-ala-glun-cys-his-thr-val-glu

r Globulin (rabbit) (62)
*ala-leu-val-as\ . . .

Glucagon (63)

*his-ser-glun-gly-thr-phe-thr-ser-asp-tyr-ser-lys-tyr-leu-asp-ser-arg-arg-ala-glun-asp-phe-val-

glun-try-leu-mct-aspn-thr*

Hemoglobin (41)

*val-glun-leu; *val-leu; (horse). *val-gly; *met-gly; *val-ser; *val-glx; *val-asx;

(various species, see Table 1 .)

80 Martynas Ycas

Hypertensive peptide (46)
*asp-arg-val-tyr-val-his-pro-phe-his-leu*

Insulin (cattle) (8)

'A' chain: *gly-ileu-val-glu-glun-cys-cys-ala-ser-val-cys-ser-leu-tyr-glun-leu-glu-aspn-tyr-cys-

aspn*

'B' chain: *phe-val-aspn-glun-his-leu-cys-gly-ser-his-leu-val-glu-ala-leu-tyr-leu-val-cys-gly-

glu-arg-gly-phe-phe-tyr-thr-pro-lys-ala*

/5 Lactoglobulin (64)
his-ileu*

Lysozyme (65, 66, 67, 68)

thr-asx-val-glx-ala ; ileu-glx-leu-ala-leu; asx-glx-ala; leu-thr-ala; glx-asx-ileu ;
thr-glx-ala-gly ; ser-asx-gly-met-asx; asx-ala-met-lys-cys-arg; val-thr-pro-gly-ala ;
ser-asx-arg; lys-phe-glx-gly ; arg-cys-glx-ala ; ser-phe-asx-glx ; thr-asx-arg-arg ;
thr-gly-asx-val ; ser-val-cys-ala-lys-gly ; gly-cys-asx ; leu-gly-ala-val ; asx-ileu-pro-cys ;
arg-cys-lys-gly ; ser-val-asx-cys-ala ; asx-leu-cys-asx ; arg-asx-cys-ileu; ser-arg-leu;
ser-asx-cys-arg-Ieu ; arg-asx; arg-gly; asx-asx; gly-leu; ileu-arg; ileu-asx; ileu-val; leu-leu;
ser-ala; ser-leu; val-ala; *lys-val-phe-gly-arg; arg-his-lys; asx-gly-ala-asx-leu* ;
glx-ser-phe-asx ; ala-lys-phe-glx; asx-tyr-arg-gly ; arg-gly-tyr-ileu-leu ;
asx-ala-tyr-gly-ser-leu-asx; leu-pro; ala-ala-met ;

Melanophore expanding hormone (69, 70)
*asp-glu-gly-pro-tyr-lys-met-glu-his-phe-arg-try-gly-ser-pro-pro-lys-asp*

Myoglobin (71)
* gly-leu

Ovalbumin (72, 15, 73, 74, 64)

val-ser-pro* ; asx-serP-glx-ileu-ala ; glx-serP-ala; ala-gly-val-asx-ala-ala ; cys-ala; cys-val;

cys-gly; cys-phe; thr-cys; ser-cys; cys-glx; glx-cys; phe-cys; asx-cys; val-cys;

Oxytocin (75)
*cys-tyr-ileu-glun-aspn-cys-pro-Ieu-gly-NH2°'

Papain (76)
*ileu-pro-glu

Pepsin (77, 15)
*leu-gly-asx-asx-his-glx ; thr-serP-glx ;

Prolactin (78)
*thr-pro-val

The Protein Text 81

Ribonuclease (79)

*lys-glu-thr-ala-ala-ala-lys-phc-glun-aig ; lys-ser-arg-aspn-leu-lhr-lys-asp-aig ; lys-aspn ;

tyr-glun-ser-tyr ; tyr-Iys; lys-his; asp-ala-ser-val*

Salmine(80, 81)

*pro-arg-arg; arg-pro-val-arg-arg; pro-ileu-arg; val-gly; arg-val-ser-arg ; arg-ileu-arg;

arg-ala-ser-arg ; arg-gly-gly-arg; arg-ser-ser-arg ; val-gly;

Serum albumin (37)

*asp-ala (man); *asp-thr (cattle);

Silk fibroin (Bombyx) (82, 83, 84)

gly-ala-gly-ala-gly-[ser-gly-(ala-gly)„]8-ser-gly-ala-ala-gly-tyr

n usually 2, mean value always 2.

gly-val-gly; tyr-gly; phe-gly; gly-ser-pro-tyr-pro ; tyr-pro-ser-tyr

Tobacco mosaic virus (48)
thr-ser-gly-pro-ala-thr*

Tropomyosin (52)
ala-ileu-met-thr-ser-ileu"''

Trypsinogen (85)
*val-asp-asp-asp-asp-lys-ileu

Vasopressin (40)
*cys-tyr-phe-glun-aspn-cys-pro-arg-gly-NH2*

Wool (86)

ser-cys; gly-cys; thr-cys; ala-cys; leu-cys; cys-gly; cys-thr; cys-ala; cys-val; cys-leu;

cys-phe ;

remains whether any of the blank cells represent forbidden combinations,
or whether they are merely the result of accidents of sampling.

To answer this question statistically, the frequencies of occurrence of various
combinations have been plotted in Fig. 2. There are more blank cells here than
in Fig. 1, as a portion of the data has been discarded to avoid obvious sources
of bias. Thus the sequences of silk, collagen, wool and protamine have been
omitted, since these proteins have an obviously aberrant structure. Likewise,
sequences of less than three residues have not been used, since the ease of

82

Martynas Ycas

isolation of various dipeptides varies, making it possible that the frequencies
of some peptides have been systematically over- or underestimated.

Figure 2 can now be treated as a contingency table with 761 degrees of

<
<

O

a:
<

CL

tn

<

Z
Q-

<

>-
o

_i
o

Z
Z)

-I
o

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-I
O

X

13
U.'

LJ

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CO

>-
-I

1-
UJ

2

I

a.

O
(E
Ol

UJ
CO

1-

V
CC

>-
H

-1
<

>

0

ALA

4

1

2

3

1

3

3

2

1

3

1

1

1

26

ARG

1

3

2

2

4

1

2

1

1

1

18

ASP

1

2

4

2

1

1

1

1

13

ASPN

2

2

4

3

2

2

3

1

1

2

2

24

CYS

4

2

3

1

1

2

1

1

1

1

1

1

19

GLU

4

1

1

2

1

1

1

1

1

1

16

GLUN

4

1

1

1

1

2

1

3

1

2

1

18

GLY

3

1

1

1

2

1

1

2

1

1

2

2

1

1

1

21

H IS

1

3

1

1

1

1

8

ILEU

1

2

1

1

1

2

2

10

LEU

1

1

1

2

2

3

1

1

2

2

4

20

LYS

1

1

2

2

1

2

1

1

1

3

1

1

1

2

20

MET

2

1

1

1

5

PHE

1

1

4

1

1

1

1

1

1

2

14

PRO

2

1

1

1

1

2

2

1

1

1

3

16

SER

1

4

1

3

1

1

2

1

1

2

1

1

1

2

2

4

28

THR

2

2

1

1

1

1

3

4

1

16

TRY

1

1

2

TYR

1

1

2

1

2

2

1

1

1

2

1

1

16

VAL

1

1

2

3

3

4

1

1

1

1

1

1

2

22

b
c

S2
58

20
38

II

24

21
45

19
3B

13
27

22

40

27

48

6

14

11

21

23
43

16
36

6

II

15
29

16
32

20
48

II

27

2
4

15
31

24
46

330

Fig. 2. Frequencies of occurrence of dipeptide sequences in proteins, plotted as
in Fig. 1. The sequences of clupein, collagen, salmine, silk fibroin and wool have
not been used. Sequences of less than three residues, as well as those where the
acid and amide forms of glx and asx are not differentiated, were also not used. On
the basis of the study of Ohno (68), glx and asx in lysozyme are assigned to glun
and aspn, respectively. The seven-residue sequence common to ACTH and MEH
was counted only once, a — marginal totals of rows ; b — marginal totals of columns
c — marginal totals of rows and columns.

freedom, and the null hypothesis, that there is no correlation between adjacent
residues, tested. The deviation X from the expected distribution in Fig. 2 is
calculated as:

{a^_ -f- a,^{Oj, + ^.;)1^

(1)

{a,^ -I a.i){aj. + a.j)
An

where n is the sum of the marginal totals (330), a^j the value of a cell in column /
and row j, Oj and a,, the marginal totals in column and row respectively of
the residue defining the column, <7._, and a_,. the analogous values for the residue
defining the row. For computational purposes (1) reduces to:

^="(2'K+«i. +«.)"')

From Fig. 2, A = 392. The value of /, which is calculated from
is 0.414, which is less than 1.645, the 5 per cent confidence limit.

(2)

(3)

The Protein Text

83

It may therefore be concluded that there is no evidence for any intersymbol
correlation between nearest neighbors. Inspection of sequences reveals like-
wise no obvious correlations of residues more than one removed from each
other, but to decide this question definitely will require more knowledge of
longer sequences than is now available.

Gamow, Rich and Ycas (6) have previously studied this question of
intersymbol correlation. They examined a grid diagram, similar to Fig. 2
but embodying fewer data, to see whether the frequencies of entries follow
the PoissoN distribution. This method is invalid, since it does not take into
account the fact that different amino acids occur with very different frequencies.
I am glad to avail myself of this opportunity to correct these authors.

IV. FREQUENCY OF OCCURRENCE OF DIFFERENT AMINO ACIDS

Amino acids occur with different frequencies in proteins. Some, like leucine,
are consistently abundant, others, like methionine, consistently rare. The
frequency of occurrence of the various amino acids in the bulk protein of a
whole organism, Escherichia coli, is shown in Fig. 3.

aiatt

, , E.COLI PROTEIN

10

+H

\ • AMINO ACID
L^„ + TRIPLET

j;

\ \

ucA S6f

_i 6

_

o

+i°"

2

2

1

1 1

10
RANK

20

Fig. 3. Composition of bulk protein of Escherichia coli (87), amino acids arran-
ged in order of abundance. The vakies for glu, glun and asp, aspn arbitrarily
taken as half of glx and asx, respectively. The value of cysteine taken from
Roberts and Cowie (88). 'Triplets' refers to the frequencies of triplets of
nucleotides, calculated according to the hypothesis of Gamow and Ycas (7) from
the composition of E. coli RNA (89).

Data on the composition of twenty-three proteins are summarized in Table V.
This table shows that the composition of individual proteins is not too different
from that of bulk protein. The most abundant amino acid usually has a
frequency of about 0.10 to 0.12, the least 0.005 to 0.01.

Table V suggests the possibility that the differences in composition of
various proteins may be merely the result of chance fluctuations from a mean,
and not importantly related to biological function. This notion may not be
as far-fetched as might appear at first sight. The most important function of
proteins is catalysis, and the enzymatically active site probably involves only
a few amino acids. In addition, proteins of a given organism appear to have

84 Martynas Ycas

an important mutually complementary relation to each other which enables
them to be retained by the cells. This is shown by experiments with injected
catalase. Homologous catalase injected into guinea pigs is absorbed by the
tissues, but heterologous catalase is rejected (108). Similarly, homologous
antibodies readily pass the fetal barriers in rabbits, heterologous pass much
less readily (109). This phenomenon is probably connected with the anti-
genicity of proteins. The antigenically active sites of proteins are probably
also small, and therefore the exact sequence and composition of the major
part of the protein m.ay be irrelevant to function. It might be expected, then,
that the exact structure of small parts of a protein molecule would be rigidly
determined, and any mutation affecting this portion would be eliminated by
selection. Mutations affecting the 'irrelevant' portions may not affect the
viabihty of the organism, and the same protein in different species may therefore
diverge by a process of 'evolutionary drift.' That this process is real is strongly
suggested by the facts known about cytochrome c. This enzyme serves the
same function and has the same prosthetic group in both yeast and mammalian
tissues, but the two cytochromes have very different elution volumes from
ion exchange resin columns (110), almost certainly indicating a large difference
in amino acid composition.

If for each kind of residue there is a characteristic rate of replacement by
mutation, the proteins should approach a definite equilibrium composition,
if selection is a minor factor. More definitely, each protein will constitute
a 'random grab' from a universe of amino acids, the frequencies of the amino
acids in this universe being determined by the equilibrium condition.

Qualitative considerations suggest that there is something other than selection
which tends to make a given amino acid occur with a certain frequency. Certain
amino acids, alanine, leucine, isoleucine and valine have aliphatic side chains
lacking any obvious reactive functional group. The data on replacements
(Table II) indicate, apparently, that one is as good as another, as far as their
function in a protein is concerned. Yet leucine is systematically more abundant
than isoleucine. These two amino acids are so similar that it is difficult to
separate them by paper chromatography. Each of the other aliphatic amino
acids has its own characteristic frequency, likewise.

Quantitatively, if a sample of « items is drawn at random from a population
where an item of type A occurs with frequency p, the distribution of A in a
large series of samples is given by the binomial (p + q)", where q = \ — p.
In particular, the variance cr^ of the distribution of A is given by

o- == npq (4)

If the hypothesis of a 'random grab' is correct, then in a collection of proteins
the variances of amino acids should be related to the mean value of their
frequencies and to the size of the proteins, expressed as the number of residues
per molecule.

An immediate difficulty is that the sizes of the proteins listed in Table V
are not known, and these certainly differ one from another. It should be
particularly noted that the relevant size is not necessarily that obtained from
physical measurements of diffusion, osmotic pressure and sedimentation. This
is because there is ample evidence that physical molecules can be the result of

The Protein Text

85

aggregation of smaller, chemically identical units. Furthermore, from the
evidence presented in Table III, the several peptide chains constituting some
proteins may not be identical, but are nevertheless quite similar. The statistically
relevant size of hemoglobin would then be somewhere between 600, the approxi-
mate number of residues in the whole molecule, and 150, the average size of
the four subunits.

Disregarding this difficulty, 1 have plotted the variance of each amino acid,
calculated from Table V, against pq (Fig. 4). All points (except glx) fall within

O.IO

0.05

• GLX

• PRO

gly^^'leu

CYS» /ARG,

0.05

0.10

pq

Fig. 4. Plot of variances of amino acids against/?^, where/? = mean frequency
of occurrence of amino acid, ^ = 1 — /?. Line n = 100 calculated variance for
sample size (protein) of 100 residues, (glx) is plot with the values from tropo-

mysin and y casein omitted.

(or very close to) one standard error of the line for n — 100. The fact that the
sizes of the proteins are not identical tends to scatter the points, making agree-
ment with the hypothesis somewhat more significant. The large deviation of glx
is due to its abundance in two proteins, y casein and tropomyosin. If these are
omitted the agreement is good.

The evidence therefore permits (but of course does not prove) the hypothesis
that the composition of proteins is mainly determined not by selection, but
rather approximates to a 'random grab' from a single universe of amino acids.

There is of course no question that selection can produce proteins of very

86

Martynas Ycas

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The Protein Text

87

unusual composition. This occurs mainly in cases where the mechanical pro-
perties of protein fibers are important, as in keratin, collagen and silk. These
have been omitted from Tabic V. The most extreme case known to me is the
silk of the Congolese moth Anaphe nialoneyi, where glycine and alanine together
constitute 94 per cent of the entire protein (1 1 1).

Fox and Homeyer (1 12) have also noted the general similarity of composition
of various proteins, but have interpreted it in a quite novel manner. Their
suggestion is that proteins are similar because the time that has elapsed since
the origin of life has been too short to allow more differences to develop between
the various proteins, all of which are presumed to be descendants of a single
molecule. I believe the composition of silk tends to indicate that there has been
ample time for any conceivable differentiation.

V. LENGTH OF PEPTIDE CHAINS

I have previously called attention to the apparent fact that the number of
residues in naturally occurring peptide chains is an exact multiple of three (113).
Since then, a more exact determination of the composition of ribonuclease (79)
and the elucidation of the structure of glucagon (63) have shown that this
statement is incorrect (Table VI). In view of the predominance of chain lengths

Table VI. Length of Protein and Peptide Chains in Number of Residues
(Note: Cystine counted as two cysteine residues.)

Protein or peptide

Number of residues

Reference

Oxytocin

Vasopressin

Melanophore expanding hormone I (hog)

Insulin 'A' chain

Glucagon

Insulin 'B' chain

Melanophore expanding hormone II (hcg)

Melanophore expanding hormone (ox)

Ribonuclease

9
9
18
21
29
30
30
48
124

(75)

(40)

(69, 70)

(8)

(63)

(8)

(114)

(114)

(79)

that are multiples of three, it might perhaps be suspected that the exceptions
are due to secondary removal of residues, as occurs, for example, in the activa-
tion of pepsinogen, trypsinogen, chymotrypsinogen and fibrinogen. The tenta-
tive finding of Akabori (quoted in (41)), that the B chain of fish insulin has
twenty-nine residues, rather than the thirty found in cattle insulin, makes it
doubtful that secondary removal of residues is the explanation. Since twenty-
nine (the number of residues in glucagon) is a prime number, and not a factor
in the chain lengths of other peptides, it seems reasonable to conclude that
peptide chains are not multiples of some fixed number of residues.

VI. THE CODING PROBLEM

Having examined the protein text, we can now discuss what conclusions we
may draw as to the storage, transfer and replication of the information contained
in the protein molecule.

88 Martynas Yc^as

The gene, and by inference DNA, is thought to contain the infoiTnation
which eventually appears as a sequence of amino acid residues in the corre-
sponding protein. As shown by a study both of the replacement process and of
the amino acid sequences, each residue has an independent genetic representa-
tion. These representations are presumably aligned in linear order on the DNA
molecule. There is in fact no evidence at present that the gene is anything other
than a linear sequence of amino acid determining sites, although the possibility
that it may also determine the structure of immunopolysaccharides in an
analogous fashion cannot yet be dismissed.

Recent biochemical evidence (which I shall not discuss here) indicates that
it is RNA, not DNA, which is directly involved in the process of protein forma-
tion. Transfer of information therefore involves at least two steps : DNA to
RNA, and RNA to protein.

The straightforward inference would thus be that DNA serves as a template
for the formation of RNA. Absence of cytoplasmic inheritance supports the
view that RNA is not a self-replicating structure. This is also supported by four
lines of biochemical evidence :

1. The initial rate of incorporation of labeled precursors into nuclear RNA
is much greater than into cytoplasmic RNA (115).

2. In Amoeba depleted of RNA, RNA only regenerates if a nucleus is
present (116).

3. A one-way flow of RNA from nucleus to cytoplasm can be demonstrated
(117).

4. The rate of RNA fomiation is minimal at the time DNA is replicating
(118).

Unfortunately, this conclusion may be an oversimplification. There is no
lack of biochemical evidence pointing in the opposite direction:

1. The composition of nuclear and cytoplasmic RNA is not identical (119).

2. The time curves of precursor incorporation into RNA do not indicate
that the nuclear fraction is the precursor of the cytoplasmic (115).

3. Radioactive precursor is incorporated into the RNA of enucleated
Acetabularia plants (120).

4. Different strains of RNA viruses are self-replicating. This is difficult to
explain if RNA is the product of a DNA template.

The problem is to reconcile these apparently discordant facts. Consider
first the determination of RNA structure by DNA. Since both DNA and RNA
are texts written in a four symbol alphabet, it is natural to suppose that the
coding problem is very simple. It is sufficient to assume that one nucleotide of
DNA determines one nucleotide of RNA (121). Recent evidence indicates,
however, that this is incorrect.

It is possible to suppress protein synthesis in susceptible bacteria with
chloramphenicol. When this is done using amino acid-requiring strains, it can
be demonstrated that amino acids are required for RNA synthesis, even though
no protein synthesis is taking place (122, 123, 124). The natural inference,
supported by several converging lines of evidence, is that it is not the nucleotides
themselves which are the precursors of RNA, but rather compounds containing
both a nucleotide and an amino acid. This leads to a unitary picture of the
synthesis of RNA and of protein. When such precursors are lined up on a

The Protein Text

89

protein-synthesizing template (RNA), the amino acids polymerize to form
protein; when lined up on DNA, the nucleotide portions polymerize to form
RNA (Fig. 5).

If this is correct, an obvious conclusion follows. Since omission of a single
amino acid stops RNA synthesis, the RNA-fonning mechanism must distinguish
not four, but a minimum of twenty different kinds of items. But since the
product contains only four, the RNA in general must contain less information
than the template that made it. Several nucleotides in DNA must be involved
in selecting a single nucleotide of RNA. Since the template must contain more
information than the product, RNA cannot be the template for itself; i.e. it
cannot be self-replicating. There is an important exception to this statement.

AMINO ACIDS

NUCLEOTIDES

TEMPLATE

Fig. 5. Schematic representation of the synthesis of RNA and protein from
common precursors (see text). The nature of the template is presumed to deter-
mine whether the aligned precursors polymerize to produce protein or RNA.

If the information in the template is reduced below a certain level, it is possible
to obtain a product identical to the template itself. The formalization is as
follows.

While in process of formation, the RNA molecule can be visualized as a
sequence of nucleotides to which amino acids are attached (Fig. 5). Before
removal of amino acids on polymerization the informational content of the
'proto-RNA,' of length n, is n loga 20. After removal of the amino acids the
information content is reduced to n logg 4. If restrictions of some kind exist
on the number of combinations allowed, the number possible for 'proto-RNA'
will be reduced to b[n loga 20]; (b < 1). Such restrictions on 'proto-RNA' will
result in less severe restrictions on the RNA itself, since in general one con-
figuration of RNA can correspond to numerous different configurations of
'proto-RNA'. Therefore, if there are 20*" possible configurations of 'proto-
RNA', RNA itself has 4*^" possible configurations available (1 > c > b).

The information content of RNA will equal that of 'proto-RNA'

bn log2 20 = en log2 4

(5

when 1 > c^ 2.166. Since the information content of 'proto-RNA' is now
the same as that of RNA, an RNA template could, fonnally, be self-replicating.
It is now possible to reconcile the genetic and biochemical facts outlined
above. Assume that the synthesis of RNA proceeds in two steps. At the first
step, a strand of RNA is synthesized using a DNA template. Information is
thus transferred from DNA to RNA. The next step is supposed to occur in
the cytoplasin. RNA material is added to the nuclear-synthesized RNA, but
in a manner which does not add to the informational content. A model for

90

Martynas Ycas

this process could be the building up of a complementary strand of DNA, as
in the Watson and Crick scheme for DNA reproduction (125).*

Normally, the process stops at this stage, since the RNA molecule has
insufficient information to act as a template for itself. In the case of viruses,
however, the cytoplasmic process of adding new material to the original RNA

Table VII. The Composition of the Protein and RNA of Viruses

Composition of protein in moles per cent, of RNA as fractions of 1. t value

assumed. It should be noted the influenza virus contains lipid, and the protein

analysed may in part be of host provenance.

Tobacco

Tomato

Turnip

Southern

Influenza

Protein

Mosaic

Bushy Stunt

Yellows

Bean Mosaic

A

(126)

(127)

(128)

(129)

(130)

ala

9.6

8.5

6.6

7.5

5.9

arg

6.4

5.3

1.6

6.4

6.0

asx

10.3

11.1

4.2

7.3

11.7

cys

0.7

0.8

2.3

0.9

—

gbc

8.7

5.7

7.1

6.8

7.0

giy

3.9

8.6

4.2

8.9

7.0

his

0.0

1.2

1.5

1.3

1.9

ileu

5.2

3.3

9.0

6.2

8.3

leu

7.1

10.9

8.6

8.3

8.5

lys

1.1

3.4

8.0

3.0

5.2

met

0.0

0.8

2.1

2.6

3.2

phe

5.7

3.6

2.5

3.5

4.7

pro

5.5

3.9

10.2

5.3

4.7

ser

10.0

8.6

8.4

8.7

4.4

thr

11.6

11.0

13.9

11.5

6.5

try

1.1

0.5

0.6

i.ot

1.1

tyr

2.4

2.8

1.5

4.1

3.6

val

10.8

10.0

7.9

6.7

6.1

amide

12.7

11.4

8.0

—

—

RNA

(131)

(127)

(132)

(131)

(133)

Ad

0.30

0.26

0.22

0.26

0.23

Gu

0.25

0.29

0.18

0.26

0.20

cy

0.19

0.21

0.38

0.23

0.24

Ur

0.27

0.26

0.22

0.25

0.33

results in the production of material identical to the template itself. From this
point of view, an RNA virus can be regarded as a specialized RNA molecule,
which because of restrictions on the sequence of 'proto-RNA' can act as its
own template, utilizing the normal RNA-synthesizing mechanism of its host.
The composition of the RNA of viruses lends some support to these ideas.

* It is obvious that until more is known about RNA structure the question of its replication
can be discussed only in general terms. If RNA is a double-stranded structure, the nucleotide
composition shows that bases in the two chains cannot be uniquely paired as in DNA, but each
base must pair with one of two others, as shown by the equality of 6-keto and 6-amino groups
(89). In attempting to elucidate the details of RNA reproduction information on the number of
strands, whether each strand contains all the information of the whole structure, and where the
complementary strand is synthesized, is of crucial importance.

The Protein Text 91

Normally the number of 6-keto (Gu + Ur) and 6-amino (Ad + Cy) groups in
RNA is equal (89). Virus RNA does not necessarily obey this rule, indicating
that it differs in this respect, at least, from all the others (Table VII).

This hypothetical scheme is presented to show that the apparent contradic-
tions of the genetic and biochemical evidence do not make it logically necessary
to abandon a unitary view of RNA reproduction.

The coding of protein information into RNA has attracted considerable
attention, but cannot as yet be considered as solved. Study of the protein text
indicates that any solution will have to meet several requirements.

Firstly, since exactly twenty amino acids are incorporated into protein,
it is clear that at least three nucleotides are needed to determine an amino acid.
Gamow (134) has proposed that 20 is a 'magic' number, which is the result of
the existence of twenty possible sites of three nucleotides each. Four kinds of
items, taken three at a time, give twenty different combinations, if order is
disregarded.

Crick, Griffith and Orgel (135) point out, however, that there is at least
one other way of deriving a 'magic' 20 number. They start by considering the
problem of what it is that delimits one amino acid-determining site from
another, the 'punctuation mark problem'. Assuming that three bases determine
a site, it is a problem why the 3n + U 3n + 2, 3« + 3 bases represent a site,
while 3« + 2, 3n + 3, 3« + 4 do not. They solve this problem by assuming that
only certain triplets of nucleotides correspond to an amino acid (sense sites),
while others do not (non-sense sites). The criterion separating these two types
of sites is the following. The set of sense sites are all triplets which, when
placed next to each other in any possible combination, give sense sites only
at positions 3/z + 1, 2?i + 2, 3n -j- 3, but not otherwise. For example, the triplet
AAA is a non-sense site, since when placed next to itself it gives the sequence
AAAAAA. The site is not unambiguously defined, as AAA occurs both at
the 1-3 position and at the 2-4 position. They find that there are exactly
twenty triplets (out of sixty-four) which satisfy the criterion of sense sites, as
follows :

ABA

BCA

ADC

BDD

ABB

BCB

ADD

CDA

ACA

BCC

BDA

CDB

ACB

ADA

BDB

CDC

ACC

ADB

BDC

CDD

Other ways of selecting twenty sense sites are also possible. The sense sites,
these authors suggest, may correspond to amino acid-selecting sites of RNA.

The 'punctuation mark problem' could, of course, also be solved if amino
acids were selected in a sequential manner starting from one end of the template.

Secondly, besides the requirement that at least three nucleotides are required
to determine an amino acid site, the study of proteins indicates that these amino
acid determining sites are independent and share no nucleotides with their
neighbors. This conclusion follows from the absence of any intersymbol
correlations in the protein text, and also from the fact that a mutation (as
inferred from a study of homologous proteins) can result in a change at one
site only, leaving the rest of the sequence unchanged. The number of nucleotides

92 Martynas Ycas

in the template must therefore exceed the number of residues in the correspond-
ing protein by a factor of at least three.

Absence of intersymbol correlation shows that the 'overlapping' codes
discussed by Gamow, Rich and Ycas (6) do not correspond to reality.

The third requirement is somewhat more hypothetical. From the evidence
presented above, it would appear that selection is not the sole factor determining
the frequency of occurrence of the various amino acids. This is strongly
suggested by the different frequencies of amino acids with aliphatic side chains,
and particularly by the characteristic preponderance of leucine over isoleucine.
It is therefore reasonable to believe that the coding principle itself imposes
certain differences in frequency on the various amino acids.

If only one configuration of nucleotides corresponds to each amino acid,
the coding per se cannot make some amino acids frequent and others rare.
This can be done, however, if some amino acids have more than one configura-
tion of nucleotides to which they correspond. For this reason I am inclined to
believe that the type of coding proposed by Crick, Griffith and Orgel (135)
does not correspond to reality.

Gamow and Ycas (7) have proposed a code that formally meets these three
requirements. An amino acid is presumed to be determined by three nucleotides,
taken without regard to order. In addition, the number of nucleotides in the
RNA is assumed to be three times the number of amino acid residues in the
corresponding protein. This has the following consequences:

1 . There are twenty such triplets, the same as the number of amino acids.

2. Neighboring triplets share no nucleotides between them. Any sequence
of amino acids is thus permitted.

3. The frequencies of various amino acids, calculated on the assumption
that the sequence in RNA is random, are unequal. This is because the expected
frequency of any triplet is given by the product of the frequencies of the com-
ponent nucleotides and the number of configurations for the given composition.
Thus there are six triplets (all presumed to determine the same amino acid) of
the type ABC, three of AAB and one of AAA.

The pattern of frequency distribution of the various triplets, calculated in
this manner, corresponds very closely to the amino acid distribution, as shown,
for example, in Fig. 3 for the case of E. coli.

I believe that this type of coding, even if not itself the one wliich actually
occurs, is similar to the one that corresponds to reality. The most striking defect
is that it provides no explanation, in fact contradicts, the requirement that
in RNA the number of 6-keto groups should equal the number of 6-amino
groups. H. A. Simon (136) has proposed a modification to take care of this
difficulty. If RNA is a paired structure, somewhat similar to DNA, and 6-keto
bases pair with 6-amino ones, then the following four pairs of nucleotides exist
(again disregarding order) :

Ad-Gu; Ad-Ur; Cy-Gu; Cy-Ur.

If one takes these pairs, rather than the individual nucleotides, as units,
one can maintain an hypothesis of determination by sextuplets, analogous to
determination by triplets. The frequency distribution of sextuplets, calculated
for a random RNA sequence, is very similar to that obtained for the triplet

The Protein Text 93

distribution. This suggests that a whole series of codes of this type may exist,
all having similar general properties.

At present the major difficulty is not to produce a coding principle that
explains the known facts, but rather to make a choice between the many that
are possible.

The correctness of a coding principle can, in general, be ascertained from a
consistency of correspondence of the RNA and protein texts. Unfortunately,
such a direct approach is not at present possible. Except perhaps in the case of
RNA viruses, it is not possible to isolate a pure RNA corresponding to a pure
protein, and were this possible, the sequence of nucleotides could not be deter-
mined by any method currently available.

If the composition only of a series of RNA's and the corresponding proteins
is known, it is theoretically possible to check some coding schemes as follows:
If the coding scheme is correct, the various configurations of nucleotides can
be assigned to the amino acids in such a manner as to give, when summed over
the protein, the experimentally determined RNA composition, and this con-
sistently for all RNA-protein pairs. No assumption need be made that the
RNA sequence is random. Actual application of this method requires a large
number of RNA protein pairs of accurately determined composition, obviously
diftering as much as possible from each other, and the facilities of an electronic
computer.

The electronic computer is much the easier of the two to provide. At
present the data are hopelessly inadequate, although analyses of the proteins
and RNA's of viruses may eventually make such an approach possible. However,
in attempting a correlation of viral RNA and protein (Table VII), it should be
remembered that some viral RNA's do not show the equality Ad + Cy =
Gu + Ur characteristic of non-viral RNA (89). This suggests that normal
RNA may be multi-stranded, while viral may not be. It is therefore not im-
possible that viral RNA may contain all the information, but not all the material
of a protein determining structure, and hence differ in composition from it.
An additional difficulty is that it is not certain that all viral RNA is concerned
in the determination of the protein which eventually appears in the virus
particle.

In lieu of anything better, I have attempted to make consistent assignments
of triplets to amino acids on the assumption that the sequence in RNA is
random. The random frequencies of triplets were calculated for liver (Fig. 5),
Tobacco Mosaic and Turnip Yellow virus. I then tried to assign each triplet
to an amino acid in such a manner that each member of the pair would have
approximately the same frequency in the three cases. No satisfactorily consistent
assignments could be obtained by this method. Assuming that the RNA's and
proteins actually correspond, failure indicates one or more of the following:

1 . The coding principle used is false.

2. The RNA is not a random sequence.

3. The proteins of viruses are so small that relatively large deviations from
expected frequencies may be found. The molecular weight of TMV protein
is about 17000 (48, 137), that of Southern Bean mosaic about 26000 (129),
Several of the amino acids occur as only a few residues per molecule, so that a

94

Martynas YCas

difference of one or two residues from the statistically expected value produces
very large relative deviations.

Since the frequency of occurrence of an individual amino acid is small,
even a larger protein such as hemoglobin may be too small to be a statistically
valid sample for the purpose of calculating frequencies on the basis of a random
RNA sequence. The following case is of interest. The RNA's of liver and of
reticulocytes are virtually identical in composition, and therefore the proteins
(bulk liver protein and hemoglobin) would be expected to have a very similar
composition. Actually, this is not the case (Fig. 6). Considerable differences

RNA

RNA

RAT LIVER

RETICULOCYTES

A D

18.4

17.5

6 U

33.1

34.7

C Y

30.5

29.9

U R

18.0

17.9

4 6 8

LIVER PROTEIN

Fig. 6. The composition of bulk liver protein (142) and hemoglobin (93). The
RNA composition of liver from (89) of reticulocytes (143). All in moles per cent.

exist, as can be seen from the deviations of the points from the line of slope 1 .
It would be better to use for this purpose the bulk RNA's and proteins of
whole organisms and organs, were it not for the fact that bulk protein and RNA
from various sources is so similar that no strong check on the coding principle
is possible.

The method of assignments from the assumption of a random RNA sequence
fails, then, either strongly to confirm or to deny any proposed coding principle.

It is possible that as more information becomes available some light may
be thrown on the coding problem from a study of replacements of residues in
homologous proteins, if replacements prove to be nonrandom.

The reader will not fail to notice that the inadequacy of the data render
most of my conclusions tentative. More information of the type considered

The Protein Text 95

here will, of course, become available in the future and will not fail to clarify
matters. 1 have attempted to organize and analyse such data as exist, in the
hope that the value of this sort of information might become clearer, and in
order to facilitate their examination as more become available.

Obviously, data on composition and sequence are not the only possible
sources of information bearing on coding. Strong hints will eventually be
obtained from a study of RNA structure and sequence, as well as from other,
more conventional, biochemical approaches. The solution of these problems
will surely not be long delayed.

Acknowledgment— \i is a pleasure to acknowledge the collaboration of
George Gamow. I have profited from discussions of various aspects of these
problems with Drs F. H. C. Crick, Beatrice S. Magdoff and Herbert A.
Simon. Dr Louis J. Cote has given valuable assistance with statistical problems.
The errors, of course, remain my own.

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87. A. Polson: Quantitative partition chromatography and the composition of E. coli.
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88. R. B. Roberts, D. B. Cowie, P. H. Abelson, E. T. Bolton, and R. J. Britten: Studies
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89. D. Elson and E. Chargaff: Evidence of common regularities in the composition of
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90. F. Friedberg: The amino acid composition of adenosine triphosphate-creatine trans-
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The Protein Text 99

91. K. Laki, D. R. Komintz, P. Symonds, L. Lorand, and W. H. Seegers: The amino
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93. A. Rossi-Fanelli, D. Cavallini, and L. De Marko: Amino acid composition of
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94. G. JoLLES and C. Fromageot: La proteine lysante II de la rate du lapin. II, Composition
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95. W. G. Gordon and J. Ziegler: Amino acid composition of crystalline a-lactalbumin.
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96. K. Lange: Aminosaurezusammensetzung kristallisierte alkohol-dehydrogenase aus
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97. J. Muus: The amino acid composition of human salivary amylase. /. Amer. Chem.
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98. W. G. Gorden, W. F. Semmett, and M. Bender: Amino acid composition of y-casein.
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99. E. L. Smith, A. Stockell, and J. R. Kimmel: Crystalline papain. III. Amino acid
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100. E. L. Smtth, M. L. McFadden, A. Stockell, and V. Buettner-Janusch : Amino acid
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101. E. L. Smith, J. R. Kimmel, D. M. Brown, and E. O. P. Thompson: Isolation and pro-
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102. E. L. Smith and A. Stockell: Amino acid composition of crystalline carboxypeptidase.
J. Biol. Chem. 207, 501-514 (1954).

103. S. F. Velick and E. Ronzoni: The amino acid composition of aldolase and d-glyceralde-
hyde phosphate dehydrogenase. /. Biol. Chem. 173, 627-639 (1948).

104. B. A. KoECHLiN and H. D. Parish: The amino acid composition of a protein isolated
from lobster nerve. /. Biol. Chem. 205, 597-604 (1953).

105. E. L. Smith, D. M. Brown, M. L. McFadden, V. Buettner-Janusch, and B. U. Jager:
Physical, chemical and immunological studies on globulin from multiple myeloma.
J. Biol. Chem. 216, 601-620 (1955).

106. W. H. Stein and S. Moore: Amino acid composition of lactoglobulin and bovine
serum albumin. /. Biol. Chem. 178, 79-91 (1949).

107. J. F. Velick and L. F. Wicks: The amino acid composition of phosphorylase. /.
Biol. Chem. 190, 741-751 (1951).

108. R. N. Feinstein, M. Hampton, and G. J. Cotter: Species specificity of catalase.
Enzymologia 16, 219-225 (1953).

109. I. Batty, F. W. R. Brambell, W. A. Hemmings, and C. L. Oakley: Selection of
antitoxins by the foetal membranes of rabbits. Proc. Roy. Soc. B 142, 452-471 (1954).

110. B. Hagihara, T. Horio, M. Nozaki, I. Sekuzu, J. Yamashita, and K. Okunuki:
Comparison of properties of crystalline cytochrome c from yeast, beef heart and pig
heart. Nature, Lond. 178, 631-632 (1956).

111. F. Lucas, J. T. B. Shaw, and S. G. Smith: The chemical constitution of some silk
fibroins and its bearing on their physical properties. Shirley Institute Memoirs 28,
77-89 (1955).

112. S. W. Fox and P. G. Homeyer: A statistical evaluation of the kinship of protein mole-
cules. Amer. Nat. 89, 163-168 (1955).

113. M. YcAS: Numerology of peptide chains. Naturwissenschaften 43, 197-198 (1956).

114. B. J. Benfrey and J. L. Purvis: Purification and amino acid analysis of melanophor-
expanding hormone from hog and ox pituitary glands. Biochem. J. 62, 588-593 (1956).

100 Martynas Y6as

115. R. M. S. Smellie: The metabolism of the nucleic acids. The Nucleic Acids, ed. by E.
Chargaff and J. N. Davison, vol. 2, pp. 393-434, Academic Press, New York (1955).

116. J. Bracket: Action of ribonuclease and ribonucleic acid on living amoebae. Nature,
Lond. 175, 851-853 (1955).

117. L. Goldstein and W. Plaut: Direct evidence for nuclear synthesis of cytoplasmic
ribose nucleic acid. Proc. Nat. Acad. Sci., Wash. 41, 874-880 (1955).

118. K. Lark and O. Maaloe: Nucleic acid synthesis and the division cycle of Salmonella
typhimurium. Biochim. Biophys. Acta 21, 448-458 (1956).

119. B. Magasanik: Isolation and composition of the pentose nucleic acids and the cor-
responding nucleo-proteins. 77/^ Nucleic Acids, ed. by E. Chargaff and J. N. Davidson,
vol. 1, pp. 373^07. Academic Press, New York (1955).

120. J. Bracket and D. Szafarz: L' incorporation d'acide orotique radioactif dans des
fragments nuclees et anuclees d'Acetabularia mediterranea. Biochim Biophys. Acta 12,
588-589 (1953).

121. L. S. LocKiNGEN and A. G. DeBusk: A model for intracellular transfer of DNA (gene)
specificity. Proc. Nat. Acad. Sci., Wash. 41, 925-934 (1955).

122. A. B. Pardee and L. S. Prestidge: The dependence of nucleic acid synthesis on the
presence of amino acids in Escherichia coli. J. Bad. 71, 677-683 (1956).

123. F. Gros and F. Gros: Role des aminoacides dans la synthese des acides nucleiques
chez Escherichia coli. Biochim. Biophys. Acta 22, 200-201 (1956).

124. M. YcAS and G. Brawerman: Interrelations between nucleic acid and protein bio-
synthesis in micro organisms. Arch. Biochem. Biophys. 68, 118-129 (1957)

125. J. D. Watson and F. H. C. Crick: Genetical implications of the structure of deoxyri-
bose nucleic acid. Nature, Loud. Ill, 964-967 (1953).

126. F. L. Black and C. A. Knight: A comparison of some mutants of tobacco mosaic
virus. /. Biol. Chem. 202, 51-57 (1953).

127. D. De Fremery and C. A. Knight: A chemical comparison of three strains of tomato
bushy stunt virus. /. Biol. Chem. 214, 559-566 (1955).

128. E. Roberts and G. B. Ramasarma: Amino acids of turnip yellow virus. Proc. Sac.
Exp. Biol. Med. 80, 101-103 (1952).

129. B. S. Magdoff R. J. Block, and D. B. Montie: Amino acid composition of southern
bean mosaic virus. Contr. Boyce Thompson Inst. 18, 371-375 (1956).

130. C. A. Knight: Amino acid composition of highly purified viral particles of influenza
A and B. /. Exp. Med. 86, 125-129 (1947).

131. R. W. Dorner and C. A. Knight: The preparation and properties of some plant
virus nucleic acids. /. Biol. Chem. 205, 959-967 (1953).

132. R. Markham and J. D. Smith: Chromatographic studies of nucleic acids. 4. The
nucleic acid of the turnip yellow mosaic virus, including a note on the nucleic acid of
the tomato bushy stunt virus. Biochem. J. 49, 401^06 (1951).

133. G. L. Ada and B. T. Perry: Specific differences in the nucleic acids from A and B
strains of influenza virus. Nature, Lond. 175, 854 (1955).

134. G. Gamow: Possible mathematical relation between deoxyribonucleic acid and protein.
Dansk. Biol. Medd. 22, No. 3 (1954).

135. F. H. C. Crick, J. S. Griffith, and L. E. Orgel: Codes without commas. Proc. Nat.
Acad. Sci., Wash. 43, 416^21 (1957).

136. H. A. Simon: personal communication.

137. I. Harris and C. A. Knight: Studies on the action of carboxypeptidase on tobacco
mosaic virus. /. Biol. Chem. 214, 215-230 (1955).

138. T. L. Deich and E. T. Szorenyi: Chem. Abstr. 49, 1882 (1955).

139. ZoTAN KoROs: Free amino groups of gliadin. Magyar Kim. Folyoirat 56, 131-136
(1950).

140. L. K. Ramachandran and W. B. McConnell: The terminal amino acids of wheat
gliadin. Canad. J. Chem. 33, 1463-1466 (1955).

The Protein Text 101

141. T. Deutsch: N-terminal amino acids of gliadins from wheal and rye. Ada Physiol.
Acad. Sci. Hiwg. 6, 209-224 (1954).

142. B. S. ScHWEiGERT, B. T. GuTHNECK, J. M. Price, J. A. MiLiER, and E. C. Milier:
Amino acid composition of morphological fractions of rat livers and induced liver
tumors. Proc. Soc. Exp. Biol. Med. 72, 495-501 (1949).

143. G. Rost: Zusammensetzung der ribonucleinsaure der reticulozyten. Naturwissenschaften
43,499(1956).

DISCUSSION

Koch: I should like to comment on the result of some recent tracer experiments that have
been conducted in Dr Swick's laboratory at the Argonne National Laboratory (1, 2, 3).
What we have tried to do is to ask ourselves something about the total balance of the turnover
of RNA, DNA, and protein in the tissue which is most often studied by the biochemist;
namely, rat liver. The interesting thing that comes out of this is that when suitable tracer
experiments are done, you can make the definite statement that in a single cell DNA is syn-
thesized when it is produced and DNA stays as a cell compound until the death of the ceil,
whereas on the other hand it is very easy to show that all of the RNA in the cell is turned over,
and it is turned over essentially with about the same half-life that all of the proteins are turned
over in the ceil ; that is, there are no special classes of proteins that are not turned over, especially
classes of RNA that are not turned over in this tissue.

The immediate conclusion from this is that, inasmuch as the amount of protein is many
times more than the amount of RNA, on a molar or other basis, there can be no one-to-one
hand-off of this kind. In other words, you cannot take the DNA and make the RNA from it
without using it over and over again in a different way than has been suggested here.

YcAS : While it may be true that there is turnover of RNA in rat liver, I believe, on the basis
of work with micro-organisms, that there is no obligatory turnover of RNA associated with
protein synthesis. The RNA, which is part of the protein forming mechanism, is a passive
template, and apparent coupling or dissociation of protein and RNA turnover is adequately
explained, I think, by the assumption that both have common precursors.

Koch: I would just like to add that in the case of micro-organisms it is fairly clear that the
protein turnover does not occur (4). It is also pretty well established that DNA and RNA
turnover do not occur in an actively growing culture. So the concept of turnover in the micro-
organism is not a relevant one. But what it does mean is that you cannot accept some of the
proposals that have been described that inherently require the obligatory breakdown of some-
thing (RNA), concomitant to the synthesis of another type of molecule (protein).

MoROWiTz: I would like to introduce some evidence for an alternative approach to the
problem of intersymbol influence. In some work recently published by Sidney Fox (5) analyses
are reported on the total protein of soybean, corn, wheat, and rye. These analyses indicate
that a very high proportion of the protein molecules have lysine in an N-terminal position and
arginine in the next position. This approach to statistical constraints involves an experimental
analysis of a population of proteins from a single source as contrasted to Dr Ycas' theoretical
analysis of a population of unrelated proteins.

We have attempted to determine if any constraints are to be found in E. coli protein. The
preliminary results indicate that methionine is found in N-terminal positions in a proportion
consistent with a chance distribution. Cystine and cysteine in N-terminal positions may show
a considerably greater constraint.

YcAs: I think that the method used by Fox and yourself introduces an obvious source of
bias, if what you are trying to do is look for intersymbol correlations. The abundances of
different species of protein in a cell are not equal, and more abundant proteins contribute more
end groups. You have to examine the proteins one by one, giving the same statistical weight
to each.

A similarity in end groups of proteins from related species indicates not an effect of inter-
symbol correlation, but rather descent from a common ancestor. As can be seen from the data
I summarized, proteins change only slowly in evolution.

Branson: There is one question which has been opened up by Dr Gamow's and Dr Ycas'
comments; namely, the whole problem of redundancy in protein molecules. The evidence is
fairly conclusive, I believe, that so far as the antigenic action of a protein is concerned, the

102 Martynas Ycas

active region is approximately 1 5 A on a side. If the same is true of other biological functions,
a great deal of surface area in a protein is passive. At least it is passive for a given specific
function. Thus it is reasonable to inquire how much of a protein molecule you can whittle away
and keep a given biological property.

There is a fairly convincing teleological explanation for this redundancy. In the early
history of living systems, the membranes containing the living material might have been rather
leaky. Thus to retain the small biologically-active components within the cell, they had to be
associated with a large but inactive structure which would not pass out through the large spaces.
In the evolutionary scheme, then, there remain many large units where really the functional
part is relatively small. So that when one amino acid is taken out and another put in, the sub-
stitution does not make much difference so long as it is not in the essential small functioning
unit of the protein molecule.

YcAS : I am also of the opinion that mere size of an enzyme may be quite important for the
totality of its biological functions, even if it seems to make no difference to the catalytic function
as measured in a test tube. Which part of a protein is significant and which is not is a matter
of what function we are measuring. I doubt that at present we know all the functions of
a protein from the point of view of the organism itself.

REFERENCES

1. R. W. SwiCK and D. T. Handa: The distribution of fixed carbon in amino acids. /.
Biol. Chem. 218, 557 (1956).

2. R. W. SwiCK, A. L. Koch, and D. T. Handa: The measurement of nucleic acid turnover
in rat liver. Arch. Biochem. Biophys. 63, 226-242 (1956).

3. R. W. SwiCK and A. L. Koch: The measurement of nucleic acid phosphorus turnover
in rat liver by the constant exposure technique. Arch. Biochem. Biophys. 67, 59-73 (1957).

4. A. L. Koch and H. R. Levy: Protein turnover in growing cultures of Escherichia coli.
J. Biol. Chem. 217, 947-951 (1955).

5. S. Fox: Evolution of protein molecules and thermal synthesis of biochemical substances.
Amer. Sclent. 44, 347-359 (1956).

PROTEIN STRUCTURE AND
INFORMATION CONTENT*

L. G. AUGENSTINE

Brookhaven National Laboratory, Upton, New York

I. INTRODUCTION

In stating that a given system has an information content of a certain number
of bits, care must be taken to specify not only the context within which this
number has been derived but also an attempt must be made to give meaning
and utility to this measure. Specifying the context is particularly important
since for most systems there are many levels at which the information content
can be derived. For example, the information content for a cell is very low, if
one is concerned only whether it is living or dead, but it is very large if one is
interested in specifying the parameters of each of its individual elementary
particles. In this article, estimates will be made of the information content of
given proteins by taking into account that they are a sequence of amino acids
which can assume only a discrete number of configurations. An attempt will
be made to study some of the factors which affect the infonnation content and
the types of constraints which must operate in the elaboration of proteins.
Some idea of the magnitude and types of the constraints pertinent to proteins
can be obtained from parallel studies on proteins and printed English (for which
the constraints are known). Finally, the information content based upon
structure will be compared with estimates of information content obtained
within the context of protein function.

Although the fact has not always been fully appreciated, information
measures are usually more effective in selecting among alternative hypotheses
than in suggesting new ones. This particular trait arises from the fact that
information estimates, which depend only upon the probabilities associated
with a class of experimental outcomes, will often describe the degree to which a
number of variables interact but indicate little or nothing about the behavior
of the individual variables. As a result no novel synthetic procedures or
selection principles are advanced here to explain the manner in which polypep-
tide sequences and/or configurations are determined. Rather, in this paper
information theory considerations have been used to evaluate alternative
explanations of some aspects of protein construction.

II. ESTIMATION OF STRUCTURAL INFORMATION CONTENT

AND CONSTRAINTS

At the structural level the total information content (/() of a protein will be
treated as the sum of two terms; one (/,) depends upon the amino acid sequence

* Research carried out at Brookhaven National Laboratory under the auspices of the U.S.
Atomic Energy Commission.

103

104

L. G. AUGENSTINE

• VALUES CALCULATED FROM PROTEINS

X VALUES CALCULATED FROM ENGLISH PARAGRAPHS

800
700

'~^

MYOSIN
• TROPOMYOSIN

600
500

I

ALBUMIN rO''^^"^"^'^^^^"^

400

—

• INSULIN (48,000)

•
SILK FIBROIN

EDESTIN

'• • OVALBUMIN

ZE1N»

« •GROWTH HORMONE
"^PEPSIN CHYMOTRYPSINOGEN

300

— ;3-LACT

OGLOBULIN^'

>

200

• GLIADIN

.BOVINE SERUM ALBUMIN
^ •lactogenic HORMONE

100

HORSE MYOGLOBIN ♦•^^TH

-RIBONUCLEASE
>(» INSULIN (12,000)

X

•SALMINE

X

N

1 1

1

1 1

lyd^jmox 0.50

0.60

0.70

0.80

0.90

1.00

Fig. 1 . Values of /s/C/Jmax as a function of the number of symbols,
A^ in proteins and paragraphs.

N/m

Fig. 2. Distribution of the normalized frequency, ^—^ of letters and

amino acids in the language and protein samples. See the text

for further discussion.

Protein Structure and Information Content 105

and the other (I^) upon the configurations of the polypeptide chain in the
native molecule. Treating sequence and configuration independently should
lead to overestimates of 1„ since the pennissible configurations will depend
upon the sequence. However, care has been taken to reduce the interaction
of the two terms as much as possible, so that for the purposes of this paper no
significant discrepancies should occur.

Sequence' There are twenty amino acids which are most commonly incor-
porated into proteins. Therefore the maximum value of /^ is 4.32 bits (logg 20)
per amino acid residue.* It would occur when the twenty amino acids occur
equiprobably. Values less than the maximum would occur due to any con-
straints upon the amino acid sequence. Branson (I) calculated /, of twenty-six
proteins for wliich the frequency of occurrence of the twenty amino acids had
been determined (disregarding possible sequential dependencies). He found
that those which formed part of a living structure of an organism had an ^
which was greater than 0.70 of the maximum value. His analysis is shown by
the dots in Fig. 1. The X's show the result of a similar analysis on language
samples. The language study was based on ten paragraphs chosen from diverse
sources such as want ads, newspaper articles, textbooks, and magazines and
differs from that usually used in analysis of language in that it is based on the
paragraph rather than on large continuous samples.! In this case, letters have
been treated like amino acids and paragraphs like proteins. Except for the
single value of 0.99 the values from proteins and paragraphs agree quite
well.

Similarities between the distribution of amino acid frequencies and letters

can be seen further in Fig. 2. There the ordinate indicates the number of

times that a particular normalized frequency occurs ; the normalized frequency

is the number of times, n^, that the /th symbol (either amino acid or letter)

occurs, divided by N/m, the expected number of times that each type of symbol

should occur if all m different kinds of symbols had equiprobable occurrence

in the sample of TV symbols. As can be seen in Fig. 2 the distribution of the

n ■
normalized frequencies -ttt- for the letters (solid fine) and the amino acids (shaded

^ A'//?;

area) are almost identical except for the higher incidence of rarely-used letters
in language. This small difference might not have occurred if some of the
rarer amino acids, for which assays are difficult, had been included in the
data.

Constraints — The fact that the distribution of amino acids in non-structural
proteins deviates from equiprobability about the same as (or possibly a little less
than) the letters in written English, indicates that the constraints producing such
unequal frequencies should be of the same order of magnitude as (or slightly
less than) those governing English texts. However, this tells nothing about the

* This value disregards any influence of residue 'complexions'. However, it is difficult to
see how factors other than the identity of the residues can be very important, when one con-
siders the freedom of rotation of the /^-groups with respect to the polypeptide chain.

t It was felt that such a small-sample statistics study was preferable to one based upon large
samples (such as a determination of confidence intervals for /, as a function of the paragraph
size), since by essentially duplicating the analyses applied to proteins, insightas to the limita-
tions of that procedure could be observed.

106 L. G. AUGENSTINE

nature of the constraints or the manner in which they arise. The obvious
question arises — is the unequal distribution due to unequal availabihty of the
amino acids or is it due to constraints imposed in the processes of synthesis, i.e.
by 'intersymbol influence' ?* Is the make-up of the pool of amino acids available
to the protein-synthesizing centers indicative of the nature of the processes
involved in amino acid synthesis or have these processes become adapted to the
peculiar demands of the proteins being synthesized? This is essentially the
same as looking at a collection of printer's type and asking the question, did
the printer select his supply of type because this particular distribution of
letters was all that was available to him or did he purposely purchase his
particular assortment because he had found that it satisfied his needs?

The possibility that the unequal availability of amino acids in the cellular
pool may produce the unequal distribution does not seem likely. The experi-
ments of Roberts, Cowie et al. (2, 3) at the Carnegie Institution indicate that it
requires a five to thirty-fold excess of exogenous amino acids, such as valine,
leucine and isoleucine, before the incorporation of these amino acids into
protein is seriously affected in E. coli. In fact, once a substance has been
incorporated into the amino acid pool of yeast, 1000 times the normal con-
centration of exogenous amino acid does not affect its incorporation into
protein (Cowie). Although these are excellent experiments they do suffer
from problems of cell membrane permeability, intracellular diffusion, etc.;
however, they, along with numerous experiments involving amino acid deficient
mutants, suggest that as long as the minimum required amount of each amino
acid is present the frequency distribution of the amino acids in the pool has a
relatively small influence on the distribution of amino acids incorporated into
protein.

Two methods have been utilized in searching for intersymbol influence

in proteins. In the first (reported previously (4)), the behavior of the normalized

n-
amino acid frequencies -rjj— were studied in individual proteins. The average

normalized frequency of the individual amino acids for the twenty-six proteins
was tabulated. Comparing the normalized frequency for the individual amino
acids in particular proteins with the corresponding average value from the
26 proteins indicated large deviations in many cases. The gross deviations
were examined for correlations between pairs of amino acids, both for positive
and negative effects. Examination of the 26 proteins indicated that although
there are some correlations between the frequencies of individual amino acids
combined in single proteins, none was strong enough to be measurable with
any degree of confidence for a sample as small as 26 proteins.

Similar examinations of the normalized letter frequencies in paragraphs
were investigated for significant deviations of pairs or groups of letters. Although
strong intersymbol influences are known to exist between letters (e.g. between

* 'Intersymbol influence' is a term commonly used to designate sequential dependencies,
i.e. influences upon the identity of a particular element by neighbouring elements, which are
not the only types of constraints which might be imposed by a synthesizing center. It is easy
to imagine the possibility of unequal 'acceptability' for diff"erent symbols at individual sites on
a template in which the factors affecting the specifications of each location are independent of
the neighbors.

Protein Structure and Information Content 107

q and u) no significant results were detected. Thus it can be concluded that
such analyses do not exclude intersymbol influences of the same type or order
of magnitude as those in language.*

Gamow, Rich, and Ycas (5) have made a more exacting study of possible
inter-symbol influences affecting amino acids. They treated the known amino
acids as a series of dipeptides which they tallied into a 20 X 20 matrix similar to
the 26 >: 26 digram matrices common in language analyses. The distribution for
nonstructural proteins in such a 20 X 20 matrix followed quite closely a
Poisson distribution. This they state is compatible with the assumption that
the occurrence of a given amino acid does not affect the identity of its nearest
neighbor. Their comparable analysis for English language gave a distribution
which deviated from a Poisson.

The Poisson distribution associated with the amino acid dipeptide analysis
is not too significant since the sample of experimentally determined sequences
is not necessarily a reliable representation of the bulk of amino acid sequences
in nature. As Gamovv', Rich, and Ycas point out, their available sample is
strongly affected by the composition of ACTH, lysozyme and insulin for which
the complete sequences have been determined and the shorter sequences from
other proteins are biased due to differential bond labilities within the protein
which give rise preferentially to certain amino acids occurring as terminal
peptides in the sequences isolated.

It was felt that a possible explanation of the difference noted between
digram analysis of letters and amino acids was that amino acids were also
grouped into word-like structures but that the average number of symbols
per 'word' was different than that found in English. Therefore, separate
digram analyses were performed on English words having two to five letters,
six to nine letters and those having ten or more. All the samples were selected
so that the average cell density in the 26 x 26 matrix was 0.44, the same as
that of Gamow, Rich, and Ycas, and these also all showed significant deviations
from a Poisson distribution.

MoROwiTZ (6) and some of the Biophysics group at Yale have been investi-
gating the possibility that a polypeptide chain is a segment selected from either
a single or a small number of repeating sequences which are invariant for a
given chromosomal complement. The particular segments chosen and the
unique fashion in which they are combined and folded would then account
for the highly specific properties of the individual proteins. The possibiHty
also exists that there was an initial long, or at least restricted, set of sequences
from which present day polypeptide sequences have evolved in a manner similar
to that by which organisms have evolved. Gamow^, Rich, and Ycas (5) have
pointed out the most striking evidence for a "phylogenetically common ancestral
sequence" in their comparison of the A and B chains of insulin, where the
same amino acids occur in equivalent positions in both chains four times.

The known sequences containing five amino acids or more (from Table I,
ref. 5) were examined for repeating or matching sequences. (This was done by
superposing the sequences in all possible permutations.) These data indicate
that for proteins from a given species any single repeating sequence must

* See the discussion by Dr Platt at the end of this paper.

108 L. G. AUGENSTINE

be at least forty amino acid residues or longer. Comparing the sequences
of different types of proteins indicated that (a) there is not a master sequence
operating among species, or (b) evolution, i.e. amino acid substitution, has
been so extensive as to make it undetectable, or (c) the master sequence is
200 residues or longer. The additional sequences (for hormones of sub-protein
size) cited by Ycas (7) show that short polypeptide sequences with only minor
amino acid differences do occur in cells of different species. Thus, the occurrence
of repeating or a restricted number of amino acid sequences may be an explana-
tion of the unequal amino acid frequencies observed.

This possible restriction provides a basis for estimating the minimum
value of Ig. A single, long, completely-detennined sequence would provide
a situation of minimum infonnation content for polypeptides selected from it.
To select A'^ residues from a sequence of S amino acids would require < log2 S
bits to find N and < logo {S — N) bits to determine the starting point; or
by another selection procedure, < logg (5" — 1) to find the starting point and
roughly logg S/l to determine the end point. Either of these methods of
selection gives an estimate of the minimum of /^ which is of the order of 2 log2
S bits. This is a very low minimum since according to the best present estimate
(which is obviously too low) S f^ 200 and thus 2 logo 5 ^ 15. Therefore,
the minimum of/,, is of the order of 0.1 bit/residue since A^ > 100 for proteins.
Even if 5" is found to be 10^ (2 logg S)IN will still only be ~ 0.4 bits/residue.
Thus, the search (6) for long master sequences of amino acids is of considerable
interest with respect to information content considerations.

Summarizing for 7^, we can say that for nonstructural proteins the potential
information due to the amino acid sequence should be of the order of 0.85-0.95
of the possible maximum value. Although the constraints necessary to produce
such an effect should be of the same order of magnitude as those in printed
English, tests comparing language and the available proteins for which amino
acid composition or sequences are known indicate that the constraints operating
in the elaboration of proteins are probably different from those associated
with language. Further, it seems unhkely that the unequal frequency of amino
acids in proteins is due to unequal availability of the amino acids in the cellular
pool. The possibility that polypeptide chains are segments selected from a
single or restricted number of repeating sequences may be an explanation of
the unequal frequencies, in which case /^residue would be close to zero.

Configuration '• With the present state of knowledge the factors affecting
/^ are much more difficult to assess. The number of states available to a poly-
peptide chain whose bonds retained all of the lability they had as uncombined
amino acids would be essentially innumerable. In fact, about the only con-
figurations ruled out would be those resulting in closure of the chain upon
itself. However the D- and L- forms do not both exist in nature and as has been
pointed out by Pauling, Corey and Branson (8), the a-C, N and O group
in the backbone of the polypeptide chain is essentially the planar, resonance

O

/
/

structure — C -N— . Other than these primary restrictions the polypeptide
chain, in the absence of intramolecular or secondary bonding structures is
essentially a random structure.

Protein Structure and Information Content 109

Kauzmann (9) has given an excellent discussion of the known types of
intramolecular bonds which are responsible for protein folding and which should
therefore affect 7^. The most common type is the H— bond, especially those
formed between the carboxyl O and the amide H. These are essentially non-
specific bonds which can form between any pair of amino acid residues in
which the C — O and N — H bonds are oriented at the proper angle. A stronger,
more specific, but less common H^ — bond can form between the phenolic
OH groups of tyrosine and the carboxyl group of glutamic or aspartic acid
(9, 10). Another common type of bond stems from the van der Waals forces,
which can exist between the atoms in different portions of the same or neigh-
boring chains. The third type discussed by Kauzmann is the so-called hydro-
phobic bond, which is distinct from the more commonly discussed van der
Waals bonds. This results from the tendency of the more hydrophobic amino
acid residues to avoid the aqueous phase and adhere together to form a sort of
intramolecular micelle. These bonds, although they possess a low order
of specificity, may contribute a good deal of stability since they arise as a
result of the fact that the more hydrophobic amino acids cannot participate
in the strong H-bonding with the solvent water molecules. Salt bridges, which
are the ionic bonds formed between the negatively charged (glutamic and
aspartic) and positively charged (lysine and argenine) residues, are another
type. However, Jacobsen and Linderstrgm-Lang (11) have presented evidence
which indicates that these bonds are of negligible importance as intramolecular
protein bonds. One of the most important types of intramolecular bond (at
least according to current theories (12)) is the highly specific S — S bond formed
between cysteine residues in different portions of the same or neighboring
chains. The formation of disulfide bonds as well as the 'strong' H-bonds greatly
reduces the number of physical states available to the molecule since they can
only be formed at a very few sites in the molecule. Since these two types of bond
are the most specific of the intramolecular bonds, they are undoubtedly the
most effective in determining variations in structure between different kinds of
proteins.

Repetitions Structures: Intramolecular bonds fonned in such a fashion
as to produce repetitious structures reduce 4 tremendously. In the helical or
pleated sheet structures proposed by Pauling, Corey and Branson (8) (and
illustrated in (13)) the number of free parameters necessary to describe the
configuration completely is extremely low and therefore the information content,
/f, is also very lov/. In the helices it is only necessary to specify the length
(that is, the total number of residues R), the pitch (3.7 or 5.1 residues per turn)
and the exact orientation of the helix with respect to a reference point in the protein.

An estimate of the lower bound of /^ can be obtained from these factors
as follows: 1) To find the exact number of residues, /?, in a helix requires about
2 log2 R bits.* 2) The pitch requires 1 bit (3.7 or 5.1 residues/turn of the helix).

* It is rather interesting that the determination of the value of any integer, either + or —
(other than zero), requires exactly In bits, where 2"~^ < i? < 2" (which is close to 2 logs R):
II bits are necessary to find that |^| is in the range indicated, // — 1 bits to find \R\ and 1 bit to
determine R, i.e. the sign. For example, let R = —48: six questions which can be answered
by yes or no will show that \R\ is 33-64; five more questions will determine that of the 32
possible values \R\ = 48 and one yes or no question determines R = —48. Thus, 2* < i? < 2«
and 111 = 12 bits.

110 L. G. AUGENSTINE

3) A reasonable value for the number associated with specifying the interhelical
bonds would seem to be 7?/2 bits. This arises by assuming RjA interhelical
bonds, i.e. one bond per turn of the helix, and the previous discussion of intra-
molecular bonding indicates that the identity of each interhelical bond requires
about 2 bits of information. Another reasonable value for this factor is i?/4; this
would occur for 1 one-bit interhelical bond or 1 two-bit bond every other turn,
which attempts to take into account that disulfide and "strong" H-bonds
are probably the most important interhelical bonds. Actually this factor could
be zero since it may not be possible to specify interhelical bonds independent
of the sequence. 4) The information necessary to specify the orientation of
each helix with respect to some reference point in the protein is the most
difficult factor to estimate. It may be almost zero, since the interhelical bonds
may unequivocally determine the orientation of the helix. On the other hand,
it should not be larger than (log2 R + 30) bits, where logg R bits is sufficient
to determine a specific residue and 30 bits to specify its orientation. The 30
bits would be assigned to the six parameters associated with the two vectors
necessary to specify orientation. An average 'grain' of 1 :32 is undoubtedly
too coarse for specifying the orientation of a. single isolated helix, but is probably
adequate for specifying a helix which is oriented in relation to others in the same
molecule.

The 7?/2 and 30 and the zero terms have been combined to give 'high'
and 'low' values for the estimation of the minimum of /,.. These are calculated
as /^residue (in bits) by

/./residue - "!' LO W (1)

and

30+3 logo R
= 0.50H n ff^GH (2)

The results as a function of R are shown in Fig. 3. Pauling, Corey and
Branson (8) cite examples of heUcal polypeptides for which Ris 11, 18 and 36.
The corresponding region of Fig. 3 has been shaded. From these considerations
it would appear that the minimum value of /<. should be about 1 to 4 bits/residue
depending upon R.

Although many proteins appear to be helical in nature, there are others,
such as ribonuclease (RNase), which from the available evidence would seem
not to be. In RNase the structural specificity appears to be determined pre-
dominantly by the S — S bonds with the other intramolecular bonds adding
stabihty to the structure. A further discussion of the relative importance of
the specific and non-specific intramolecular bonds in maintaining structure
will be presented later.

It is obvious that an upper limit cannot be assigned to /. as readily as to
7^.. However, since the structures proposed by Pauling, Corey and Branson
probably represent polypeptide configurations for which /. is near minimum,
it would appear that one bit/residue is a reasonable lower limit for 7^. From
the estimates of 7, and 7^ presented here, it appears that for the proteins of
general interest 7^ should have a value in excess of 4.5 bits/residue although

Protein Structure and Information Content

111

if il is found that polypeptides are chosen from a single, long master sequence
the value could be as low as 1 .0 bits/residue.

Estimates of 4.5 bits per residue or greater at the structural level give a
total information content, /,, for the non-structural proteins in excess of 500
bits (or in excess of 100 bits if the minimum estimate turns out to be the true
one). Such an estimate is in sharp contrast to the estimates of 10 bits or less

1000

3

o

UJ

o

z

o

UJ

m

13
Z

/RESIDUE-- 0.50 +

30+3 \oq, R

3 loq^ R

Ij./ RESIDUE (IN

Fig. 3. Limits for estimates of the minimum of 4 as a function of the number

of residues per helix. The shaded area indicates helical polypeptide sizes reported

by Pauling, Corey and Branson (8).

obtained by Quastler and his co-workers (14) as the amount of information
which must be transmitted for the proper functioning of most protein-controlled
systems (e.g. enzymes, immune bodies).

III. ESTIMATION OF STRUCTURAL INFORMATION CONTENT

NECESSARY FOR FUNCTION

A disparity of at least one order of magnitude or more in passing from
one context or level of organization to another is of considerable interest.
The ten-fold difference indicates that only a small part of the information
potential is actually utilized in information transmission.

Does this indicate that information transmission in such systems is very
noisy and therefore organisms obtain good transmission by utilizing a very
high degree of redundancy? Dancoff (15) proposed a principle of maximum

112 L. G. AUGENSTINE

error in which he postulated that an organism (or for instance a protein-
controlled system) will commit as many errors as are consistent with normal
function, but that the inherent error rate, which is probably quite high for such
reactions, is maintained at a tolerable level by the use of redundancy. Resorting
again to the language analogy — a protein corresponds to a paragraph in
complexity and its function may correspond to the thought which is conveyed
by a paragraph.

Does the difference in information content between the two contexts mean
that in the process of evolution the organisms found that particular polypeptide
configurations contained structures which could perform useful functions,
but that these polypeptide permutations contained a large amount of excess
and useless infomiation which has been perpetuated along with the small
amount of information associated with the necessary structure ?

Does it indicate that much of the protein structure is involved in secondary
features of information transmission (e.g. the acquisition, concentration,
and transport of energy) and only a small part of the total information content
of the protein is intimately engaged in the process of information transmission ?

Or does it indicate that each enzyme or p'rotein is capable of mediating
many reactions and our experimental ingenuity has not been able to determine
more than just a few of them ? (This is analogous to attempting to measure
the information transmitted by a source wliich is transmitting through many
channels, by monitoring only a single channel.)

The discussion which follows will attempt to throw some hght on these
questions. However, two important considerations must always be borne in
mind when one is deahng with proteins. They are first and foremost colloidal
in nature and therefore much of their activity falls in the realm of surface
reactions. In the globular proteins it is quite likely that much of the total
structural information content is in the interior of the molecules and therefore
is unavailable to participate in information transfer occurring at their surface
and can only participate in secondary operations similar to those mentioned
above. The second consideration involves the question, just what is required
for the transmission of one bit of information by a protein system? It seems
very likely that one bit of potential structural information will not always
transmit the same amount of information; rather, the efficiency of transmission
will depend upon the context within which the performance is measured.
For example, it is probably much simpler to attach either a hydroxyl or methyl
group to a benzene molecule (which would involve one bit of determination)
than it is to construct either a 3.7 or 5.1 helix (which also involves one bit
of determination). This is somewhat analogous to the relative difficulties of
determining whether a symbol is 0 or 1, or to determining whether one should
get married or not !

Ig necessary: It appears in some cases that a fairly large fraction of the
potential surface information due to the amino acids present is superfluous.
For instance, it has been found in insulin that a large fraction of the residues
cannot be critical for function. lodination, sulfonation and chelation, each
of which can mask surface i?-groups, have been found not to affect insulin
activity. Those residues which are species-specific can also be ruled out as
being critical for function. Unfortunately, it is difficult to determine the exact

Protein Structure and Information Content 113

degree to which a particular type of residue is masked by a given treatment,
so that it is impossible to state exactly the fraction of surface residues which
are not critical. In a similar manner, it is possible to mask the lysine and arginine
residues on the surface of trypsin without destroying its activity (16). In fact,
acetyltrypsin is available commercially (17) and has the ideal feature that with
its lysine and arginine /^-groups masked, its ability to act as a substrate for
other molecules of trypsin is decreased. Haurowitz (18) has also pointed out
that some of the antigenic properties of proteins are in many cases not affected
by iodination or sulfonation of receptive surface groups.

The work of Raacke (19) has shown that a certain amount of surface
heterogeneity (as demonstrated by electrophoretic behavior) is still compatible
with a fully active protein. Her results plus the uncertainty found in the analyses
of amino acid compositions indicate that an uncertainty of the order of 3 to
10 per cent can occur in the amino acid complement without loss in charac-
teristic function. The results of Roberts and Cowie (mentioned previously)
involving competition in the amino acid pool also indicate that about 3 to 20
per cent variabihty in amino acid incorporation can occur. However, it should
be borne in mind that each position in the polypeptide sequence may not have
a 3 to 10 per cent tolerance associated with it; rather, those residues which
participate in active sites likely have a zero tolerance.

/j necessary: Kalnitsky and Rogers (20) have reported that approximately
15 per cent of the ribonuclease molecule can be digested off with carboxy-
peptidase before activity is lost. Work reported by Anfinsen (10, 21) indicates
that this estimate may be a little high. Rather, he reports that the carboxy-
tenninal three amino acids (valine, serine, alanine) can be removed with no
loss in activity; but, that digestion with pepsin which splits off these three
plus their neighbor, aspartic acid, and also ruptures a "strong" hydrogen
bond in the vicinity produces loss in activity. Partial digestion by subtilisin
(10, 22), which apparently digests central portions of the polypeptide chain,
leaves the activity of the RNase intact as long as the digested portion is not
oxidized. It is also known that fragments obtained either by hydrolysis or
partial enzymatic degradation from myosin (23-25), trypsin (26), chymotrypsin
(27, 28), lysozyme (29), papain (30) and pepsin (31, 32) retain their activity
in certain situations. The results with pepsin and papain are particularly
striking. Hill and Smith report no loss in the molar activity of papain (toward
a synthetic substrate) after an average of 120 of its 180 residues had been removed
by leucine-aminopeptidase (an N-terminal type enzyme). Perlmann has reported
that some of the dialyzable fragments (which represent 20 per cent of the
total original protein) resulting from pepsin auto-digestion retained 1 to 5
per cent of the original activity toward hemoglobin, but about 75 per cent
of the activity of the intact pepsin when tested against the synthetic substrate
acetyl 1-phenylalanyl diiodotyrosine. These latter results indicate strongly
that pepsin, at least, has more than one active site and the site specific for pep-
tide linkages adjacent to an aromatic amino acid depends upon the integrity
of only a small portion of the molecule.

4 necessary: Of parallel interest to the above considerations is the question
of how much configurational infonnation, I„ is necessary for function? The
work of Anfinsen and others (10, 33) indicates that the configuration of RNase

114

L. G. AUGENSTINE

can be considerably disrupted without loss in activity. They found that rever-
sible denaturation in 8 M urea did not cause permanent loss in activity; in
fact the RNase was still active in 8 M urea in which its specific viscosity was
8.9 as compared with 3.3 in aqueous solution. This large increase in specific
viscosity indicates that the so-called native configuration can be opened con-
siderably without destruction of activity. However, Anfinsen reports that
oxidation with performic acid, which disrupts the disulfide bonds, causes
irreversible inactivation and an increase in specific viscosity to 11.6.

The phenomenon of complete loss in activity upon the appearance of the
full sulfhydryl titer has been observed in most proteins. It has also been known
for a number of years that different degrees of loss in characteristic activity
can occur. A number of workers (34, 35) have studied reversible inactivation
of enzymes in which it has been observed that a partial unfolding of the mole-
cule can occur with a rise in specific viscosity, change in the optical rotation
of the protein solutions, changes in solubility, etc., which upon the proper
treatment can be reversed. The thermodynamics for reversible denaturation
shown in Fig. 4 indicate that quite hkely the first step is common from protein
to protein since AF* is remarkably constant for all proteins. Reversible denat-
uration invariably shows an increase in entropy. However, AS* is not constant
from protein to protein but varies by a large amount as shown by the unhatched
areas to the right in Fig. 4.

The author has proposed (12, 36) and discussed elsewhere in this volume
(37) a hypothesis involving three steps, which attempts to explain this pheno-
menon by ascribing the constant AF* to the initial opening of a disulfide
bond. This first step is followed by the rupture of a number of neighboring
intramolecular bonds (step 2) with a resulting opening of the molecule indicated
by the increase in entropy. According to the proposal, this opening of the mole-
cule is sufficient to disrupt the spatial arrangement of critical amino acids causing
loss in activity, but enough stability and configuration is retained so that under
the proper conditions the original native structure, or at least a structure
compatible with activity, can restitute. In this hypothesis the rupture of a
second disulfide bond (step 3) allows irreversible inactivation to proceed with
essentially complete destruction of the characteristic protein structure.

A conversion (using an equivalence derived in reference (38)) has been
made in Fig. 4 from AS* to A/^. By assuming an average amino acid residue

Table I

Protein

M.W. X 10-3

M.W.

^- 120

A/, (bits)

A/./iV
(bits/residue)

Pepsin

Trypsin

Emulsin

36
20
38

300

167
317

78
30
48

0.26
0.18
0.15

Amylase
Hemoglobin

59.5
67

496

558

36
110

0.07
0.20

Egg albumin

40

333

226

0.68

Lacto peroxidase
Insulin

93
12

775
103

340
18

0.44
0.18

Protein Structure and Information Content

115

weight of 120, A/,/residue is given in Table I for those proteins in Fig. 4 for
which the molecular weights are available.

Thus A/, for the loss in specific activity is of the order of 0.25 bits/residue
(the 0.68 value for egg albumin does not correspond to a loss in specific activity).
This indicates that destruction of the right 5 to 25 per cent of /, (assuming
/p is close to our minimum estimate of I to 4 bits/residue) causes loss of function,
which may be reversible or irreversible depending upon which intramolecular
bonds are disrupted.

PEPSIN

T= 298° K

T= 323° K

PROTEINASE

TRYPSIN (KINASE)

TRYPSIN

INVERTASE

INVERTASE

VIBRIOLYSIN

TETANOLYSIN

HEMOLYSIN (GOAT)

RENNIN

T = 328°K

LEUCOSIN

INVERTASE (YEAST
I NVERTASE

T=333

EMULSIN (WET)
AMYLASE (MALT)
SOLAN IN
HEMOGLOBIN

TOSS" K
EGG ALBUMIN

T=343°K
PEROXIDASE (MILK)

T= 353° K
INSULIN

Fig. 4. The equivalence between AS* and A/^ for thermal inactivation. The

shaded areas to the left represent AF* and the clear areas to the right AS*.

(Adapted from Fig. 1, ref 12, by courtesy of University of Illinois Press.)

Summary

The above discussions indicate that redundancy considerations are not
the explanation of the large excess of structural information content; rather,
that only a small fraction of the potential information on the surface of the
molecule is actively utilized in information transfer. Haurowitz (18), for
instance, has pointed out that experiments with substituted antigens indicate
that the antigenic specificity resides in an area on the surface of the protein
which is approximately 10 to 15 A in diameter. Results cited here suggest

116 L. G. AUGENSTINE

that the four or so amino acid residues which would occupy such a surface
area (13) may occur as neighbors on the same chain (30-32). Other results
mentioned previously (20, 21, 33) suggest that the critical amino acids do not
occur in sequence in a single polypeptide chain. This follows from the con-
sideration that digestion should be able to consume an average of about 50
per cent of the protein molecule before an active site composed of four or
five adjacent amino acids would be encountered ; whereas one of four or five
amino acids making up an active site should be encountered, on the average,
after about a 20 to 25 per cent digestion of the molecule if the amino acids are
distributed roughly at random. In addition, Kennedy and Koshland (39) has
found that phospho-glucomutase when placed in 6 M urea loses its activity but
recovers it upon dilution, which also indicates separated locations for the
critical amino acids. Therefore it may not be possible to state a general rule
concerning the relationship between the loci of critical amino acids within
polypeptide chains.

It seems that the role of intramolecular bonds is to insure that the amino
acids which are critical for function are maintained in the proper spatial
relationship to each other so that function can occur. Here again it is impossible
to state a general rule as to how many of these intramolecular bonds can be
disrupted before loss of function occurs, since apparently all of the hydrogen
bonds can be broken in RNase without loss in function but not so in phospho-
glucomutase. However, the integrity of the more specific secondary bonds
(such as S — S) seems to be much more critical for the maintenance of function.
The digestion experiments with pepsin and papain indicate further that it is
important where in the molecule the bonds are destroyed.

Other than ruling out redundancy as a possible reason for the discrepancy
between the large potential information and the measured performance, it
is difficult to choose among the other possibilities mentioned. The results
with pepsin and papain, which have been mentioned, suggest strongly that much
of the information content may be unnecessary for function, but has been
perpetuated along with the critical content. However, the results with pepsin
indicating that multiple sites do exist makes it impossible to assign a certain
fraction of the information content as 'garbage'. How much of the polypeptide
chain is involved in secondary features of information transmission and the
structural complexity necessary for transmitting one bit of information are
factors which are now being actively investigated by a number of workers.

The various estimates of 7^, I^ and /<. are tallied in Table II.

Table II

I total ~ I sequence + 'configuration

Maximum
Plausible
Minimum

Necessary for performing
a single specific function

— 4.32 —

>4.5 3.5 >1.0

1.0 15/A^ 1.0

10-90% 25% 35-90%

Protein Structure and Information Content 117

IV. CONJECTURES

Some of the results considered in preparing this paper lead to rather interest-
ing speculation. The repetitious minimum entropy polypeptide structures
proposed by Pauling, Corey and Branson (8) have already been mentioned.
Such configurations may be generally applicable to macromolecules, since
helical structures have also been proposed for desoxyribonucleic acid (DNA)
polymers (40) and some viruses (41). Crane (42) states that helical configura-
tions occur in linear (uni-dimensional) crystals, i.e. structures where progression
from each sub-unit to its essentially identical neighbor is by a repeated process
of translation and rotation. Lumry and Eyring (43) predict that once hydrogen-
bonded secondary structures are formed the characteristic protein 'conformation'
is determined by tertiary folding such that the free energy is minimized. How-
ever, this does not explain why crystallization should initially occur and be
maintained in solution; and to the author's knowledge no one has advanced
arguments which provide a complete basis to account for the apparent preval-
ence of minimum entropy biostructures, although there have been discussions
of how living organisms produce 'order from disorder' or 'order as a result
of order' (44). Considering the innumerable configurations available to bio-
logical polymers, the question arises 'Are there criteria which determine that
the seemingly improbable, highly ordered structures occur spontaneously?'
or 'Are these structures imposed at some specific stage in biosynthesis?'

Studies on the reversible denaturation of proteins (34, 35) suggest that the
latter possibihty is more probable: that is, mild mistreatment can be reversed;
whereas, once a certain molecular disarray or instability occurs, an unfolded
state results from which the characteristic, native structure does not reconstitute.
Neurath et al. (35) make the interesting point, that even if denaturation is
complete enough so that physical properties such as solubility, crystallizing
ability, or diffusion constants are seriously affected, some of the molecules
may subsequently revert to a biologically active form; whereas, others will
tend to reverse the molecular disarray by forming a more condensed state
but without successfully restoring the native biological properties. This suggests
that, although polypeptide chains have an inherent tendency to form semi-
condensed configurations, the highly ordered, biologically-active structures are
probably not only imposed during biosynthesis, but represent quasi-stable
structures with built-in constraints which tend to cause small fluctuations
to revert, i.e. a limited amount of disorder can be restrained without the inex-
orable Second Law prevailing. Neurath (35) has also reported that the amount
of disarray compatible with reversibility depends upon the type of denaturation.
Further, denaturation is not reversible under all conditions but may await
a change in pH or temperature. However, it is interesting that although an
entropy increase is invariably associated with denaturation, removal of the
denaturing agents can cause a decrease, which appears to contradict the Second
Law; we will later resolve this apparent contradiction.

The quasi-stability of native configurations is suggestive of the situation
in diatomic molecules where stability conditions are readily depicted as a
local 'weir (relative to the surroundings) or null area in a two-dimensional
energy-configuration plot. However, since two dimensions would allow only

118

L. G. AUGENSTINE

a very gross specification of the myriad degrees of freedom of macromolecules,
some form of multi-dimensional space will be necessary to represent their
stability conditions. The biologically significant portion of such a macro-
molecular space will also be a 'well', but in a multi-dimensional surface rather
than a line plot and will be centered near the locus of native structures in configu-
ration space. A fraction of the well will represent conditions consistent with
an active macromolecule and the remainder, conditions characteristic of
reversible inactivation. Anything outside the well will correspond to states
inconsistent with the restitution of a native configuration.

The multi-dimensional space can be of sufficient dimensionahty so that
all configurations differing by a 'single step' are neighbors. In such a 'fine-
grain' specification each microstate and its probability density (as a function
of energy, for example) can be represented. However, such a scheme has
drawbacks: first, it has little novelty since any situation can be completely
described by a sufficient number of parameters ; second, a model dealing only
with microstates would be extremely diflftcult to test experimentally; and
third, the excessive dimensionality makes it useless as an aid in envisioning
possible mechanisms of macromolecular rearrangements.

Thus, a 'coarse-grain' specification, which requires reducing the dimension-
ality by transforming the microstates into a more useful set of macrostates,
is desirable. This general operation can be schematized by the use of the follow-
ing contingency table :

Table III

■< Molecular Energy >

^1 ^2 ^k ^n

°'lll '''lia '^llk '^lln

°'l21 (^122 <^12i- ^12n

^m °'ij2 '^lik OCljn

"'all °'212 '^21fc ^2ln

'^iil '^iji ■

"■ijk

• a,.

A plausible specification for a multi -dimensional space is given in Table III,
where a sufficient number of binary digits is used so that each microstate
can be unequivocally identified, e.g. the two atoms involved in each bond
as well as the bond length and angle could be identified. Each ol^j^. represents

Protein Structure and Information Content 119

the probability density of a given microstate for molecular energy state E,^,
where the ranges of /,y and k can be essentially infinite.

A transformation to a 'coarse-grain' scheme which seems worth consider-
ation is as follows. Each macrostate, M, (depicted by the leftmost column
of digits in Table III) designates only which bonds exist in the macromolecule,
e.g. sulfur atom no. 7 is hooked to carbon no. 179 and sulfur no. 11, C-563
to C-564 and N-201, etc. Mechanistically all microstates, w,;, contained
in a given macrostate, M,, are grouped together by ordering the digits (or
analogously ordering the axes in space). To complete the transformation
other bond properties, e.g. length and orientation (the other column of digits
in Table III), and their associated probabilities (the right hand portion of
Table III) are lumped into two gross categories to provide an intuitively manage-
able representation. This 'lumped fine structure' for each macrostate, Af,-
can be represented on an 'energy-deviation' {ED,) plane at the locus (in trans-
formed configuration space) corresponding to A/,: 'deviation' is a measure of
instabihty, i.e. the extent to which individual microstates, /77,^, deviate from
the configuration »7,^ corresponding to maximum stability for macrostate
Mj. An example of a method for constructing such values is: (a) find the set
of digits «?,s in the middle column of Table III which represents maximum
stability for macrostate M^ and (b) determine how many of the corresponding
digits of /;?,, and m^j differ. This number provides an excellent measure of
'deviation' because each microstate has a unique Z)-value and 'neighboring'
microstates have adjacent Z)-values. Assigning probabilities to pairs of 'energy'
and 'deviation' values completes the "fine" to 'coarse-grain' transformation.
This requires summing the probabilities, a,^;;,, of those microstates associated
with a particular D-value. The probability densities for E and D values can
be arranged into contours of equal probability to avoid further complications
of adding a third coordinate to the ED plane. These contours will possibly
be quite irregular in shape and may well be discontinuous, since the only
obvious restriction on their form is that they be non-intersecting.

It should be noted that 'lumping' on to 'energy-entropy' planes would
have provided a simpler transformation than that to the 'energy-deviation'
planes. The microstates corresponding to a given 'deviation' can be equated
to an entropy value by the usual — S/^jlog/), procedure, where the /7/s are
the probabilities (properly normalized) associated with the microstates. Such
a scheme was considered, but was found to be intuitively less useful than the
ED transformation.

The 'energy-deviation' scheme is of considerable interest when one con-
siders possible mechanisms of both protein inactivation and enzymatic activity.
Suppose, for instance, that the energy of a molecule in a native configuration
is slowly raised, e.g. by external heat: the point representing 'molecular state'
will be driven to new loci in multi-dimensional space. Undoubtedly a trajectory
is followed such that the locus resides, 'statistically', on the contour which
has the maximum probability permissible or consistent with its energy content
and macrostate at any instant. This means that the locus first progresses over
the EDj plane of the particular native configuration. A/,-. Eventually a locus
will be reached where the probability contour occupied is lower than the corre-
sponding contour on an adjacent ED plane. The molecular state will then

120 L. G. AUGENSTINE

jump to that adjacent macrostate by some fomi of bond rearrangement.*
Even without an immediate change in molecular energy due to external heat,
the jump will likely be followed by an instantaneous migration of the molecular
state locus on the new ED plane. This would be anticipated since the new locus
might not be the position of maximum probability for that instantaneous
molecular energy. A sufficient increase in temperature would eventually
drive the trajectory out of the fraction of the null region corresponding to an
active molecule: with sufficient mistreatment the locus would be driven com-
pletely out of the null region into the portion of configuration space representing
irreversibly inactivated molecules.

Molecular energy will decrease when external heat is removed, and the
molecular rearrangements will be reversed or not depending upon the sym-
metry of the multi-dimensional surface of the well. Where denaturation is
reversed merely by reversing the denaturing conditions, apparently the inacti-
vation trajectory is retraced or else the null region is a smooth "well" with no
intervening metastable positions in the reversal trajectory. Thus, for reactiva-
tion the two trajectories would not have to be identical but need only form a
•closed loop.

Asymmetry in the probability contours of even one of the ED plots traversed,
could cause the inactivation and reversal trajectories to diverge sufficiently
so that metastable, non-active configurations would result. Such situations
have been observed experimentally; for instance, thermal denaturation at
alkaline pH is not reversed upon cooling until the pH is adjusted to acidic
conditions (35). Since a change in pH should alter the ED contours it is easy
to envision how it could make the reversal of denaturation more likely by
changing the transition probabilities between macrostates and thus alter the
reversal trajectory. Such an alteration would resolve the apparent contra-
diction of the Second Law: a changed pH would act as a 'Maxwell Demon
guiding the footsteps of the reversal trajectory'.

Considering its likely statistical nature, it is probable that much of the
trajectory of the locus of molecular states proceeds along essentially negligible
probability gradients, not only with respect to transitions from one macrostate
to another but more particularly with respect to instantaneous displacement
from the locus of arrival on a new ED plane. Such transitions should be readily
reversible and in general of limited consequence except as they lead to regions
of larger gradients. However, a 'low-gradient' region would allow considerable
leeway in trajectories. This would permit multiple pathways which would
account for the spectrum of effects often observed following physical denatura-
tion. In those transitions involving bonds which latch large segments of the
molecule together (12) (e.g. interhelical bonds) gross molecular rearrangements
could occur so that the trajectory would pass through regions of large probability
gradients. Such transitions would not be instantaneously reversible and would
therefore be relatively important in driving the trajectory away from the "active"
portion of or even out of the 'well'.

My proposed inactivation hypothesis discussed later (37) attempts to

* Somewhat more rigorous discussions of factors aflfecting the trajectory of the locus of
molecular state in similar multi-dimensional plots have been given by Teller (45) and Lumry
and Eyring (46).

Protein Structure and Information Content 121

specify the identity and sequence of high-gradient transitions. On this basis
energy from an absorbed quantum, ionization or thermal process would
migrate through the molecule in a fashion represented mainly by a 'low
gradient' trajectory. However, once the energy or charge becomes localized
in a bond of low ionization potential involved in latching large segments
of the molecule together, a 'high-gradient' transition, not readily reversible,
would occur. The inactivation efficiency of absorbed energy will thus be
a function both of the locus of the molecular state at the time energy is
absorbed as well as its resulting trajectory; where the trajectory depends
upon the amount of energy introduced, the point of absorption and any
external factors which affect the contours on the ED planes. For instance,
the quantum efficiency of UV varies considerably with pH for a number of
enzymes (47).

The interdependence of energy, configuration and probability proposed
here provides a formalism for depicting enzyme action. It is fairly typical
of enzyme, as well as other types of catalysis, that reactions proceed which
are normally not feasible because of steric or energetic hindrances. It is entirely
possible that because of their large size, enzymes act as large energy reservoirs
whose function is to "deliver" a quantity of energy to a particular site or com-
plex in an irreversible fashion. Another possibility is that energy may not
be delivered per se but as a change in configuration of the enzyme with a
corresponding alteration in the spatial relationship between reactants complexed
to the enzyme. Within these proposals the formation of the enzyme-substrate
complex could have an important function. It could act as an external agent
affecting the ED contours so as to cause a directed alteration in trajectory,
leading finally to a completed enzyme catalysis. Effective, i.e. rapid and
essentially irreversible, enzyme catalysis will likely depend upon (1) an E — S
complex formation which involves a high-gradient transition, so as to enhance
a drastic alteration in the trajectory of molecular state, and (2) the directed
trajectory passing through a high-gradient region, preferably just before
completion of catalysis, in order to make reversibility unlikely.

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122 L. G. AUGENSTINE

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Protein Structure and Information Content 123

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H. Neurath, J. Greenstein, F. Putnam, and J. Erickson: The chemistry of protein
denaturation. Cliem. Rev. 34, 157-265 (1944).

36. L. AuGENSTiNEand R. Ray: Trypsin monolayers at the air-water interface. III. Structural
postulates on inactivation. J. Phys. Chem. 61, 1385-1388 (1957).

37. L. Augenstine: Discussion of a proposed mechanism of protein inactivation. (Part IV
of this volume.)

38. L. Augenstine: Information and thermodynamic entropy. In: Information Theory in
Biology, ed. by H. Quastler, 16-20, University of Illinois Press, Urbana (1953).

39. E. Kennedy and D. Koshland: Properties of the phosphorylated active site of phos-
phoglucomutase. J. Biol. Chem. 228, 419-433 (1957).

40. J. D. Watson and F. H. C. Crick : Molecular structure of nucleic acids. Nature, Land.
Ill, 737-738 (1953).

41. H. Fraenkel-Conrat: Rebuilding a virus. Sci. Amer. 194 (6), 42^7 (1956).

42. H. Crane: Principles and problems of biological growth. Sci. Monthly 70, 376-389
(1950).

43. R. LuMRY and H. Eyring: Conformation changes of proteins. /. Phys. Chem. 58,
110-120 (1954).

44. E. ScHRODiNGER : What is Life? Cambridge University Press, Cambridge, England (1946).

45. E. Teller: The crossing of potential surfaces. /. Phys. Chem. 41, 109-116 (1937).

46. R. Lumry and H. Eyring: Energy exchange in photoreactions. In: Radiation Biology III,
ed. by A. HoUaender, 1-70, McGraw-Hill Book Co. (1956).

47. P. Finkelstehm and A. McLaren: Photochemistry of proteins VI. pH dependence of
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48. H. Simon: On a class of skew distribution functions. Biometrika 42, 425-440 (1955).

DISCUSSION

Platt: Simon (48) has shown that skewed distributions (Yule distributions), such as those
in Fig. 2, can be obtained from models based on probabiHty assumptions much weaker than
those we were looking for. Thus our inability to determine constraints from a study of the
distribution of amino acid and letter frequencies in proteins and words is not surprising.
However (in agreement with our summarizing statement for that section), Simon points out
that the occurrence of a Yule distribution does not obviate more stringent constraints as the
underlying probability mechanism.

SPECIFIC MECHANISMS OF PROTEIN SYNTHESIS

AND INFORMATION TRANSFER IN THE

DEVELOPING CHICK EMBRYO*

H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann

Department of Chemistry, Indiana University, Bloomington, Indiana

Abstract — Some preliminary data on precursors and pathways of protein biosynthesis in
chick embryos have been presented. The tentative conclusions stated are:

1. Egg white proteins are not utilized for the synthesis of embryonic proteins up to and
including the ninth day. Soluble proteins added to the yolk are incorporated effectively, and
preferentially to some of the yolk proteins proper.

2. Proteins, peptides and amino acids injected into the yolk sac are incorporated at
approximately equal rates. Considering the relative available pool sizes of the various pre-
cursors present in the egg, added proteins have to be regarded as the preferred amino acid
source of embryonic proteins.

3. A common precursor formed efficiently from proteins and relatively slowly from added
amino acids and peptides is considered a likely intermediate in the process.

4. Homogenates of adult organs injected into embryos can be used to elicit a response
previously reported for organ transplants, i.e. the apparently specific transfer of labeled
material from donor organs to the corresponding organ in the embryonic host. The super-
natant fraction of the cytoplasm appears to be, at least in part, responsible for the results
observed.

I. INTRODUCTION

It is the purpose of this contribution to describe, in brief, some preHminary
experiments on a controlled biosynthetic activity, namely, the precursors and
pathways of protein formation. It differs from most of the papers in this
symposium in dealing with phenomena rather than with concepts and in the
absence of any attempt to establish a functional correlation between these
biological phenomena and information-theoretical abstractions. It shares
with other papers in this volume the properties of being highly tentative,
and in presenting data and comments on a subject to which it is felt information
theory should eventually make significant contributions. With the hope
that arrival of that time might be hastened and that thought and discussion
might be stimulated, our data are presented for consideration. Some of the
results are derived from single experiments only and thus lack further con-
firmation. All of the approaches and conclusions reported are still under active
investigation and thus subject to revision and modification.

Embryos were chosen for the experiments since their cells exhibit two
fundamental and related properties, both apparently controlled by the nuclear

* The investigations reported have been supported by grants-in-aid of the National
Heart Institute, National Institutes of Health, U.S. Public Health Service (Grant No. H 2177)
and of the National Science Foundation. This article is contribution No. 746 from the
Department of Chemistry, Indiana University.

124

Specific Mechanisms of Protein Synthesis in the Developing Chick Embryo 125

machinery, which set them apart from otlier cells of higher organisms. These
are: the capacity for replication, that is, rapid yet controlled growth; the
capacity for differentiation, that is, continuous yet controlled change and
evolution (1). Therefore, one might consider this the system of choice for
attempts at discovering how the information content of the hereditary material,
the genetic potentialities, are translated into progressive biochemical capabilities
and thus into physiological and morphological realities (2). The experiments
were done with chick embryos in ovo because of the ease of handling and the
essentially closed and self-contained nature of the experimental system. Further-
more, there is a relative paucity of reliable, modern information available
about their metabolism and that of embryos of higher vertebrates in general,
as contrasted to the large body of knowledge derived from experimental
embryology.

Our eventual aim is to study the initiation, the mode, and the control of
synthesis of highly specific, respiratory enzymes as an indicator of controlled
biosynthetic events; however, our initial investigations deal with the more
modest one of a definition of parameters for embryonic protein synthesis (3).
For any protein formed de novo, as has been pointed out by Spiegelman (4)
essentially three different mechanisms may be envisaged:

1. The rearrangement of pre-existing protein molecules; namely, the
urprotein hypothesis of Northrop (5), with suitable modifications.

2. The accretion of amino acids on to pre-existing proteins or peptides.

3. De novo synthesis from amino acids.

In the special case of the formation of induced enzymes in rapidly dividing
bacterial cells and cell-free systems derived therefrom, the evidence is over-
whelmingly in favor of the third alternative (4, 6). The situation is not nearly
as straightforward in the vertebrate systems studied. On the one hand, for
example, Work and collaborators investigated the synthesis of milk proteins
(7), Velick, Simpson and co-workers the synthesis of several specific enzyme
proteins for muscle (8, 9), and Loftfield and Harris the synthesis of liver
ferritin (10). All this work was in vivo and by different experimental techniques,
but all these authors presented strong evidence for the last alternative and against
the first two. On the other hand Anfinsen and his co-workers, working with
hen's oviduct in vitro, have demonstrated that in short term incubations
incorporation of amino acids into freshly formed ovalbumin is non-uniform,
which is suggestive of the second alternative, but that after longer periods
there is a redistribution towards unifonnity (11). Similar results have also
been obtained for ribonuclease and insulin synthesis by pancreas sHces.

In the case of the proteins of the chick embryo proper, Francis and Winnick
have presented data on the incorporation of labeled amino acids in free and
protein-bound form as possible precursors of cardiac muscle protein grown
in tissue culture (12). The amino acids of the proteins did not exchange with
large pools of the corresponding unlabeled acid in the medium, and from this
and from experiments with doubly-labeled proteins it was concluded that
proteins could be transferred from a nutrient embryo extract medium to
heart muscle protein without release of free amino acids. Tracer experiments
of this sort, as will be discussed later, do not, however, prove the direct transfer

126 H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann

of protein, but solely suggest that there may not be free equilibration between
the free added amino acid pool and amino acids formed and utilized metaboli-
cally during precursor protein breakdown and product protein formation
respectively.

Another potentially very fruitful line of investigation is provided by some
experiments of Ebert's, the results of which tentatively suggest the incorporation
of organ specific adult proteins into those of embryos subsequent to chorio-
allantoic grafts of the donor organs (3, 13). These researches were the out-
growth of findings by Murphy (14) and by Danchakoff (15), made some
forty years ago, that such transplants of adult chicken spleen lead to a specific
enlargement of the host organs. A systematic re-investigation of the phenomenon
by Weiss led to the conclusion that transplants of kidney and liver, as well
as injections of organ breis of six-day old chick embryos into four-day old
hosts, could lead to similar effects (2). Weiss correctly pointed out that experi-
ments of this sort did not permit a choice between a 'template' or a 'specific
precursor' type of mechanism. Ebert's investigations are designed to shed
some light on this question as well as on the more general ones of protein
synthesis and organ specific growth control in embryonic development.

In our own investigations we have made use of S^^-labeled organ homo-
genates, isolated proteins, peptides, and amino acids to gain some insight into
the pattern of embryonic protein biosynthesis. In this work we have been
interested not only in the immediate but also in the original precursors, which
in this case must consist of all or part of the egg white and yolk proteins.
Preliminary accounts of some aspects of this work have appeared (16).

II. METHODS AND RESULTS

1 . Preparation oj Labeled Precursors

In the experiments to be reported in tliis and subsequent sections S^^-
labeled proteins, peptides, and a mixture of amino acids were prepared bio-
synthetically as follows: Torulopsis utilis was grown on S^^-sulfate (obtained
from Oak Ridge National Laboratory), according to Wood and Perkinson. (17)
After extraction with organic solvents (18) the yeast protein was hydrolysed
with a 1 :1 mixture of 6N HCl and 90 per cent fomiic acid. Humin was removed
by centrifugation and a portion of the neutralized hydrolysate, which also
served as source of amino acids in the experiments to be reported, corresponding
to 50 mc of the original S^^, was injected intraperitoneally into a laying White
Leghorn hen in two doses, about five hours apart. Eight hours after the second
injection the blood was withdrawn by heart puncture, allowed to clot, and serum
albumin and serum globulin prepared (19). The oviduct was removed from
the hen, and ovalbumin prepared essentially as described by Steinberg and
Anfinsen (11). All proteins were treated with cysteine at a pH of 8.0 to 8.5
to assure removal of exchangeable S^^, and then dialysed. Peptides were
prepared by peptic hydrolysis of the proteins. Aliquots of the radioactive
amino acids, peptides, and proteins were prepared by standard methods and
counted. In the tracer experiments, 0.05 to 0.1 ml aliquots of the radioactive
precursor solutions, containing 0.3 to 1.8 mg and 6000 to 25,000 counts per
minute each, were injected into the yolk or the albuminous portion of some two

Specific Mechanisms of Protein Synthesis in the Developing Chick Embryo 127

to three dozen unincubatcd, embryonated White Rock eggs. The punctures
were sealed with paralTin wax and the eggs then incubated at 38° C under
conditions of controlled humidity. Starting with the fifth and ending with
the ninth day after the injection, embryos were harvested and a number pooled.
The mixture was homogenized for about three minutes in a Potter-Elvehjem
homogenizer in Ringer's isotonic saline solution, made up to 10 ml (fifth and
sixth days) or 20 ml (seventh through ninth days), and precipitated with tri-
chloracetic acid (final concentration, 8 per cent). Dry protein powders were
then prepared and counted (20).

2. Is There Evidence for Selective Utilization of Egg-white or Yolk Proteins'}

In the first set of experiments, chicken serum albumin injected into yolk
or egg-white was used as a protein tracer. Table I shows the results of two

Table L Injection of Chicken Serum Albumin into Embryonated Eggs

njection

Egg

white

Egg yolk

Day after i

% of injected

activity found

per embryo

Protein wt of
embryo in mg

% of injected
activity found
per embryo

Protein wt of
embryo in mg

5

.006
.008

5.5
7

0.79
1.12

5
6.5

6

.012
.100

13
16

1.34
0.31

11
19

7

.015
.029

28
29

2.84
1.58

17

27

8

.016

45

4.04
3.35

43
48

9

.088
.133

72
79

2.86

7.28

53
87

series of experiments. The spread of the data is indicative of the precision,
reliability, and reproducibility usually obtained in experiments of this sort.

Let us now make the following assumptions: (a) that the injected protein is
a true tracer for egg-white and yolk protein respectively, i.e. that no permea-
bility or other pool barriers exist for its equilibration with the corresponding
unlabeled egg proteins; and (b) that there is no selectivity in the uptake mechan-
ism of the embryo either for or against a serum albumin tracer as a typical
precursor protein. Now we can calculate data shown in Table II and compare
the observed mean of the amount of protein actually formed, with that expected
on the basis of the above assumptions. The latter value is calculated by
multiplying the weight of total yolk or egg-white protein, about 3000 mg
each, by the per cent of the injected activity incorporated per embryo (from
Table I).

There are profound discrepancies between the calculated and the observed

128

H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann

values. Those for the egg white are only a small fraction of those expected,
while those for the yolk are uniformly about two-fold greater. It is thus
apparent that at least one of the assumptions cited cannot be valid. The
simplest modification would be to postulate that assumption (b) is not true,
and that over the time-period studied egg white proteins are not precursors

Table II. Amounts of Embryonic Protein Formed Compared
to that Calculated from Tracer Data

Protein (mg/embryo)

Day after
injection

Observed

Calculatec
Egg-white

1*
Yolk

5

6

0.21

28.8

6

15

1.68

24.9

7

29

0.66

66.3

8

45

0.48

111.0

9

76

3.30

152.0

* From injected albumin tracer.

of embryonic proteins. Soluble proteins injected into the yolk can be utilized
for this purpose, and may be more efficient than some of the yolk proteins
proper.

3. Is There Evidence for Selective Utilization of Amino Acids, Peptides or Proteins ?

In the next series of experiments we compared serum albumin, albumin
peptides and amino acids all injected into the yolk, with the same precursors
injected into egg white. The design of the experiment was the same as before
and the results of one run are summarized in Table III,

Table III. Incorporation of Protein Precursors into Chick Embryos*

Day

after

Precursors injected into

YOLK

Precursors injected into
egg-white

injection

albumin

albumin

amino

albumin

albumin

amino

peptides

acids

peptides

acids

5

0.75

0.44

0.34

0.0063

0.35

1.19

6

1.30

0.90

1.53

0.013

0.56

3.03

7

2.80

1.70

3.86

0.015

1.59

3.48

8

4.05

4.72

5.15

0.016

2.32

4.94

9

2.85

8.52

9.18

0.088

5.94

5.65

* Expressed as per cent of injected activity recovered per embryo.

We see that except for albumin injected into egg-white, which has already
been discussed, all the precursors tested appear to be utilized with approxi-
mately equal efficiency regardless of whether they are injected into the yolk
or the egg white. This is not limited to serum albumin, but holds true equally
well for serum globulin and ovalbumin and their peptides as is shown in Table IV.

Specific Mechanisms of Protein Synthesis in the Developing Chick Embryo 129

Table IV. Incorporation into Embryos of Proteins and
Peptides Injected into the Yolk*

Day after
injection

S. albumin

S. globu-
lin

Ovalbu-
min

S. albumin
peptides

S. globulin
peptides

Ovalbumin
peptides

5

0.75

1.10

0.45

0.44

0.20

0.95

6

1.30

1.75

0.80

0.90

0.55

1.65

7

2.80

2.35

0.40

1.70

1.15

2.20

8

4.05

2.55

1.45

4.72

2.20

—

9

2.85

4.50

2.95

8.52

4.50

6.60

Expressed as per cent of injected activity recovered per embryo.

4. Is There Evidence for Organ-specific Transfer?

In order to test the hypothesis of organ-specific transfer advanced by
Ebert we have attempted to extend investigations of this sort to the use of
S^^-labeled aduh chicken Hver and heart homogenates. These were prepared
from deep-frozen organs of a White Leghorn hen injected with a mixture of
S^^-amino acids, and treated as described above.

After several months the tissues were thawed and homogenized in a tris-
(hydroxymethyl)-aminomethane buflfer solution at pH 7.4 containing 0.9 per
cent KCl, first in a Waring blender and then in a Potter-Elvehjem homogenizer.
The liver and heart homogenates, made up to 10 per cent (weight/volume)
with the same buffer solution, were then treated with cysteine at a pH of 8.0
to 8.5 to assure removal of all exchangeable S^^. After dialysis, some undis-
solved material was removed by low-speed centrifugation, and the relatively
clear supernatant fluid was used for intravenous injection into 9-day-old
chick embryos. Embryonated White Rock eggs were incubated at 38° C
under controlled humidity conditions for a period of 9 days. They were then
candled, and the location of the blood vessels was marked on the shell of each
egg. An area of about 1 cm^ of the shell above the vessel was carefully cut out
by means of a dental drill and burr without injuring the membrane, and the
small square was removed with a razor blade. A drop of mineral oil was placed
on the membrane to render it transparent, and 0.1 ml of the liver or heart
homogenate was intravenously injected in the direction of blood flow. The
eggs were reincubated for 24 hours and the embryos were excised. Hearts
and livers were removed, the organs were pooled, and homogenized; dry
protein powders were prepared for counting as described before. Similarly
aliquots of the homogenates used for injection were prepared and counted.

The results of these experiments are given in Table V. In all, two series
of experiments make up the Table. In the first series, twenty-four embryos
each were injected with heart and liver homogenates; of these, twenty-two and
eleven respectively survived.

In the second series, forty-four out of forty-seven embryos injected with the
heart preparation survived, while the number of survivors was twenty-two
out of twenty-eight for the liver homogenate. Thus the table summarizes
data obtained on 99 survivors out of 123 embryos that were injected: 66/71
for heart; 33/52 for liver.

130

H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann

It can be seen that the relative specific activity of hearts is higher than that
of hvers when chicken heart homogenate is injected, whereas the relative
specific activity of the livers is higher than that of hearts when chicken-liver
homogenate is injected.

Table V. Incorporation of Activity from Adult-Tissue Homogenates into Nine-
Day Embryos after Twenty-four-hour Incubation

Injection

Item

Chicken heart homogenat

Chicken liver homogenate

CoLint/min per embryo injected

398

398

2780 2780

mg injected per egg

0.1

0.1

0.1 0.1

Organs investigated

Hearts Livers

Hearts Livers

Livers Hearts Livers Hearts

No. of organs cut out

22 11

22

11

11 11 11 11

Dry protein wt of organs

obtained (mg)

38.2 72.0

38.8

70.0

84.7 20.9 77.6 22.4

Wt counted (mg)

18.3 29.8

23.4

30.0

30.1 11.6 30.2 12.6

Count/min observed*

21 24

22

19

366 173 389 214

Corrected count/min per 30 mg

28 24

25

19

365 286 386 340

Relative specific activity

1.00 0.86

1.00

0.76

1.00 0.78 1.00 0.87

Counts per minute are within 5 per cent standard deviation.

III. CONCLUSIONS

The experiments on soluble protein tracers added to yolk and egg-white
demonstrate quite clearly that proteins added to the egg-white or, probably,
egg-white proteins themselves are incorporated with such low efficiency as
to rule out any important contribution from this source to the protein of the
developing embryo, at least up to and including the ninth day. Incorporation
of protein from the yolk is rapid, and soluble proteins injected into this source
may be utilized preferentially to some of the yolk proteins themselves. This
utilization of yolk rather than egg-white proteins as a source of embryonic
protein during this period is in accord with other investigations, notably the
quantitative protein depletion studies of Rupe and Farmer (21). For the
intervals studied, amino acids, peptides and proteins, even those of relatively
'foreign' origin such as the serum proteins, all apparently provide an equally
acceptable source of S^^ for embryonic protein synthesis (within an order of
magnitude or so), provided they are injected into the yolk. Now the protein
tracer must be diluted by at least a portion of the 3.0 g or so of yolk protein —
an estimate of approxim.ately 50 per cent would appear reasonable in view of
the results reported above. On the other hand, amino acids or peptides cannot
be diluted to any appreciable extent since the pools of these substances in the
egg are vanishingly small (22). From this one might conclude that proteins
themselves or substances easily formed from them must be the preferred precur-
sors of embryonic proteins. Since the egg protein ovalbumin is used no more
efficiently than the more "foreign" serum proteins, the pathways of assimilation
for these precursors, available to the embryo, must have at least some inter-
mediates in common. The data on peptides may find a similar interpretation.

Specific Mechanisms of Protein Synthesis in the Developing Chick Embryo 131

These intermediates are not free amino acids, as evidenced by their relatively
low incorporation rates. They may be small peptides or activated forms of
amino acids, formed readily and reversibly from protein precursors, but not
identical and not in equilibrium with the pool of added low-molecular weight
precursors. This view would be in accord with the findings of Francis and
WiNNiCK (12), although not with their interpretation. The occurrence of
pools of modified amino acids, incapable of equilibrating with those in the
medium, has been demonstrated in micro-organisms. Thus Gale, working
with Staphylococcus aureus, found that added glutamic acid could be so trans-
formed, and the modified fonn used for protein synthesis (24). Similarly
CowiE and Walton (25) have presented evidence that the pools of amino
acids formed metabolically in Torulopsis utilis and utilized as effective precur-
sors in protein synthesis, are present in some modified form, possibly as com-
plexes adsorbed onto macromolecules, and do not equilibrate freely with
added amino acids in the medium. In all the cases presented, this metaboli-
cally active form of the amino acids may be formed by a variety of pathways
as indicated below.

Proteins

1

[Peptide Intermediates]

y

>'

1

Free peptides ^'Amino Acids'-^ Free amino acids

(modified)

Recent investigations, especially by Zamecnik and his collaborators, (26)
have disclosed that free amino acids are first 'activated' by enzymes in the
soluble portion of the cytoplasm (27), probably through mixed anhydride
formation with adenylic acid (27, 29, 30) prior to their incorporation into a
protein-bound form (30, 31), which takes place in RNA-rich granules associated
with the microsomal fraction of homogenates (32, 33, 34). Whether or not
the metabolically active form of amino acids alluded to above can be equated
with these aminoacyl adenylates has not yet been established.

An alternative explanation, which has been invoked to account for apparent
preferential utilization of proteins over amino acid precursors in the formation
of specific proteins, postulates proteolysis and protein synthesis sites in such
close spatial juxtaposition as to permit ready transfer of intermediates from
breakdown to synthesis site at the expense of penetration of the latter by
added amino acids. This has been suggested by Loftfield and Harris (10)
as the mechanism operative in ferritin synthesis, and by Walter et al. (20)
in the transformation of serum into organ proteins. Purely spatial factors
of this sort are probably not the determining ones in the present instance,
since it can be demonstrated that the bulk of the proteolytic activity is centred
in the yolk (23), and thus remote from the synthetic activity which is, presum-
ably, occurring in the embryo itself. It is hoped that critical experiments
now in progress will permit a choice to be made between the various alter-
natives suggested.

132 H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann

We have shown that the organ-specific locahzation phenomenon, previously
observed with chorio-allantoic transplants, can be dupHcated by the injection
of homogenates of aduh tissue. Similarly Tumanishvili et al. (35) found almost
simultaneously that host organ enlargement could also be elicited by the same
technique. This demonstration of the essential similarity of two approaches
clears the way for an investigation of the problem by means of relatively
straightforward biochemical and enzymological techniques rather than the
more demanding ones of experimental embryology. Obviously only a bare
beginning has been made. The findings will have to be confiiTned and extended
and several relatively trivial explanations excluded. Among such explanations
are, for instance, the transfer of whole cells on the one hand, and differential
composition and/or incorporation rates with respect to cystine and methionine
in the two tissues studied, on the other. Ebert claims to have eliminated both
these alternatives in his transplantation experiments; in the light of the available
information, they are not very likely in the present case. Nevertheless they
will have to be rigorously excluded. Our tentative interpretation of the prelimi-
nary results described is identical with that advanced by Ebert: that we are
dealing with a specific transfer of rather large units from the donor preparation
to the embryonic organ.

Preliminary experiments indicate that the injection of either heart or liver
(donor) homogenates leads to an increase in specific activity in the liver as
compared to the heart. The effect in this case is therefore non-specific and
possibly related to the higher mitotic and synthetic activity of liver relative
to heart, i.e. to fuller differentiation. Another line of approach which promises
to be of some interest is to determine the cell fraction or fractions, if any,
responsible for eliciting the effect both with respect to the donor and the acceptor
organ. Impetus is added to this approach by the recent experiments which
have focussed attention on the soluble and microsomal fractions as being
involved in the initial phases of protein synthesis. In preliminary experiments
with fractionated, dialysed heart homogenates the data of Table VI were

Table VI. Transfer of Label from Donor Heart
Fractions into Organs of Recipient Embryos

Fraction

Relative specific activity of

embryonic organs

(heart/liver)

Homogenate

Nuclei

Mitochondria

Microsomes

Soluble

1.17, 1.32, 1.23

0.65, 0.74

0.22 (?)

2.56

1.85, 2.50, 1.49

obtained. The number of data in each row corresponds to the number of
experiments actually performed. Thus the results for the microsomal and
mitochondrial fractions must be regarded as exceedingly tentative. With this
proviso, components of the soluble fraction of the cytoplasm might be regarded
as responsible for the phenomenon observed with whole heart homogenates.

Specific Mechanisms of Protein Synthesis in the Developing Chick Embryo 133

A similar observation has been reported by Kutsky who found the supernatant

fraction of embryo extract to be most active in stimulating the growth of heart

fibroblasts in vitro (36).

REFERENCES

1. For a very stimulating and up to date review the reader is referred to: B. Ephrussi:
Enzymes in Cellular Differentiation, in: O. H. Gaebler: Enzymes: Units of Biological
Structure and Function, Academic Press, New York City, 29-40 (1956).

2. For an intriguing hypothesis involving control of organ development by diffusible com-
ponents see the following articles: P. Weiss, in A. K. Parpart: The Chemistry and
Physiology of Growth, Princeton University Press, 135-186 (1949).

P. Weiss: Self regulation of organ growth by its own products. Science 115, 487-488

(1952).

P. Weiss: Some introductory remarks on the cellular basis of differentiation. /. Embryol.

Exp. Morph. 1, 181-211 (1953).

3. The present state of knowledge, with special emphasis on protein biosynthesis, is admirably
reviewed in the following: J. D. Ebert: Some aspects of protein biosynthesis in develop-
ment, in: D. Rudnick: Aspects of Synthesis and Order in Growth, Princeton University
Press, 69-112(1956).

4. S.Spiegelman: On the nature of the enzyme-forming system, />;; O. H. Gaebler: Enzymes:
Units of Biological Structure and Function, Academic Press, New York City, 67-89
(1956).

5. R. S. Alcock: The synthesis of proteins in vivo. Physiol. Rev. 16, 1-18 (1936).

J. H. Northrop, M. Kunitz, and R. M. Herriott: Crystalline Enzymes, 2nd ed.,
Columbia University Press, New York (1948).

S. B. KoRiK and H. Chantrenne: The relationship of ribonucleic acid to the in vitro
incorporation of radioactive glycine into the proteins of reticulocytes. Biochim. Biophys.
/^cfa 13,209-215 (1954).

6. D. S. HoGNESS, M. CoHN, and J. Monod: Studies on the induced synthesis of /3-D-
galactosidase in Escherichia coli. The kinetics and mechanism of sulfur incorporation.
Biochim. Biophys. Acta 16, 99-116 (1955).

7. P. N. CAiMPBELL and T. S. Work: The biosynthesis of protein. Uptake of glycine, serine,
valine and lysine by the mammary gland of the rabbit. Biochem. J. 52, 217-227 (1952).
B. A. AsKONAS, P. N. Campbell, and T. S. Work: The biosynthesis of proteins. Synthesis
of milk proteins by the goat. Biochem. J. 58, 326-331 (1954).

B. A. Askonas, p. N. Campbell, C. Godin, and T. S. Work: Biosynthesis of Proteins.
Precursors in the synthesis of casein and )3-lactogIobulin. Biochem. J. 61, 105-115 (1955).

C. Godin, and T. S. Work: Biosynthesis of proteins. The effect of intravenous peptides
on casein synthesis in a lactating goat. Biochem J. 63, 69-71 (1956).

8. M. V. Simpson and S. F. Velick: The synthesis of aldolase and glyceraldehyde-3-
phosphate dehydrogenase in the rabbit. /. Biol. Chem. 208, 61-71 (1954).

M. V. Simpson: Further studies on the biosynthesis of aldolase and glyceraldehyde-3-
phosphate dehydrogenase. J. Biol. Chem. 216, 179-183 (1955).

9. M. Heimberg and S. F. Velick: The synthesis of aldolase and phosphorylase in rabbits.
J. Biol. Chem. 208, 725-730 (1954).

S. F. Velick: The metabolism of myosin, the meromyosins, actin and tropomyosin in
the rabbit. Biochim. Biophys. Acta 20, 228-236 (1956).

10. R. B. Loftfield and A. Harris: Participation of free amino acids in protein synthesis.
/. Biol. Chem. 219, 151-159 (1956).

11. D. Steinberg and C. B. Anfinsen: Evidence for intermediates inovalb umin synthesis.
/. Biol. Chem. 199, 25-42 (1952).

C. B. Anfinsen and D. Steinberg: Studies on the biosynthesis of ovalbumin. /. Diol.
Chem. 189,739-744(1951).

10

134 H. R. Mahler, H. Walter, A. Bulbenko and D. W. Allmann

M. Vaughan and C. B. Anfinsen: Nonuniform labeling of insulin and ribonuclease

synthesized in vitro. J. Biol. Chem. Ill, 367-374 (1954).

M. Flavin and C. B. Anfinsen: The isolation and characterization of cysteic acid

peptides in studies of ovalbumin synthesis. J. Biol. Chem. Ill, 375-390 (1954).

D. Steinberg, M. Vaughan, and C. B. Anfinsen: Kinetic aspects of assembly and

degradation of proteins. Science 124, 389-395 (1956).

12. M. D. Francis and T. Winnick: Studies on the pathway of protein synthesis in tissue
culture. /. Biol. Chem. 202, 273-289 (1953).

13. J. D. Ebert: The effects of chorioallanteic transplants of adult chicken tissues on homo-
logous tissues of the host chick embryo. Proc. Nat. Acad. Sci., Wash. 40, 337-347 (1954).

14. J. B. Murphy: The effect of adult chicken organ grafts on the chick embryo. /. Exp.
Med. 24, 1-6 (1916).

15. V. Danchakoff: Equivalence of different hematopoietic anlagen (by method of stimula-
tion of their stem cells). II. Grafts of spleen on the allantois and response of allantoic
tissues. Amer. J. Anat. 24, 127-189 (1918).

16. H. Walter, A. Bulbenko, and H. R. Mahler: Precursors of embryonic chick proteins.
Nature, Lond. 178, 1176-1177 (1956).

H. Walter, D. W. Allmann, and H. R. Mahler: Influence of adult tissue homogenates
on formation of similar embryonic proteins. Science 124, 1251-1252 (1956).

17. J. L. Wood and J. D. Perkinson Jr. : Yeast biosynthesis of radioactive sulfur compounds.
J. Amer. Chem. Soc. 74, 2444-2445 (1952).

18. R. B. Williams and R. M. C. Dawson: The biosynthesis of L-cystin and L-methionine
labeled with radioactive sulphur S^\ Biochem. J. 52, 314-317 (1952).

19. W. Friedberg, H. Walter, and F. Haurowitz: The fate in rats of internally and exter-
nally labeled heterologous proteins. /. Immunol. 75, 315-320 (1955).

20. H. Walter, F. Haurowitz, S. Fleischer, A. Lietze, H. F. Cheng, J. E. Turner, and
W. Friedberg : Metabolic fate of injected homologous serum proteins in rabbits. /.
Biol. Chem. 224, 107-119 (1957).

21. C. O. RuPE and C. J. Farmer: Amino acid studies in the transformation of proteins
of the hen's egg to tissue proteins during incubation. /. Biol. Chem. 213, 899-906 (1955).

22. A. L. Romanoff and A. J. Romanoff: The Avian Egg. J. Wiley and Sons, New York
City. (1949).

23. A. L. Romanoff: Membrane growth and function. Ann. N.Y. Acad. Sci. 55, 288-301
(1952).

24. E. F. Gale: Assimilation of amino acids by gram-positive bacteria and some actions of
antibiotics thereon. Advances in Protein Chemistry 8, 285-391 (1953).

25. D. B. CowiE and B. P. Walton: Kinetics of formation and utilization of metabolic
pools in the biosynthesis of protein and nucleic acid. Biochim. Biophys. Acta 21, 21 1-226
(1956).

26. M. D. Hoagland, E. B. Keller, and P. C. Zamecnik: Enzymatic carboxyl activation of
amino acids. /. Biol. Chem. 218, 345-358 (1956).

27. P. SiEKEViTz: Uptake of radioactive alanine in vitro into the proteins of rat liver fractions.
/. Biol. Chem. 195, 549-565 (1952).

28. J. A. DeMoss and G. D. Novelli: An amino acid dependent exchange between inorganic
pyrophosphate and ATP in microbial extracts. Biochim. Biophys. Acta 18, 592-593
(1955).

29. P. Berg and G. Newton: Acyl adenylates : the interaction of adenosinetriphosphate and
L-methionine. /. Biol. Chem. 222, 1025-1034 (1956).

30. E. B. Keller and P. C. Zamecnik: The effect of guanosine diphosphate and triphosphate
on the incorporation of labeled amino acids into proteins. /. Biol. Chem. 221, 45-59
(1956).

31. H. Sachs and H. Waelsch: The effect of pyrophosphate on amino acid incorporation
into rat liver microsomes. Biochim. Biophys. Acta 21, 188-189 (1956).

Specific Mechanisms of Protein Synthesis in the Developing Chick Embryo 135

32. J. W. LiTTLEFiELD, E. B. Keller, J. Gross, and P. C. Zamecnik: Studies on cytoplasmic
ribonucleoprotein particles from the liver of the rat. J. Biol. Chem. 217, 111-123 (1955).

33. M. V. Simpson and J. R. McLean: The incorporation of labeled amino acids into the
cytoplasmic particles of rat muscle. Biocliim. Biophys. Acta 18, 573-575 (1955).

34. G. C. Webster and M. P. Johnson: Effect of ribonucleic acid on amino acid incorpora-
tion by a particulate preparation from pea seedlings. /. Biol. Chem. 217, 641-649 (1955).

35. S. TuMANisHviLi, K. M. Djandier, and I. K. Skanidze: Specific stimulation of the
growth of the chicken embryo by the effects of tissue extracts. C.R. Acad. Sci., U.R.S.S.
106, 1107-1109(1956).

36. R. J. Kutsky: Growth stimulating effects by nucleoprotein and cell fractions on chick
heart fibroblasts in vitro. U.S. Atom. Energ. Comm., U.C.R.L. No. 2270 (1953).

DISCUSSION

Quastler: It is useful to compare the informational requirements of various alternative
methods of protein synthesis.

If the whole protein is synthesized directly from amino acids, then each locus on the
template must carry sufficient information to specify a single amino acid, or approximately
four bits; this is well within the informational capacities of chemical reactions. If the incor-
poration occurs in two steps, as has been suggested, then each step might have to specify no
more than two bits.

If the protein is synthesized from peptide chains, then the informational requirements are
much more stringent. Consider the linking of two peptide chains of, say, five amino acids each.
If each of the ten amino acids can be any one of the whole set of amino acids, then the linking
operation must, in some way, identify ten amino acids, for a total of about forty bits — which
is a very large amount of information to be processed in a single act. The requirements are
greater — in fact, almost certainly too great — if two chains of ten amino acids are to be linked.
The following possibilities exist which allow the use of large fragments without imposing high
informational requirements : (a) the terminal amino acid in a chain identifies automatically
the other members — this would imply very strong sequential dependencies within peptide
chains, and consequently a low informational capacity of the whole amino acid sequence;
(b) linkages are formed without reference to the nature of residues remote from the locus of
linkage, and the resulting proteins are torn down again if not functional — in this case, the
probability of producing functional sequences by chance is small, and the efficiency of protein
synthesis is low; or (c) the protein studied is such that the exact sequence of residues is irrelevant.

THE MECHANISM OF ACTION OF METHYL
XANTHINES IN MUTAGENESIS

Arthur L. Koch

Department of Biochemistry, College of Medicine, J. Hillis Miller
Health Center, University of Florida, Gainesville, Florida

Abstract — The biochemical findings relating to the action of methyl xanthines on bacteria
and bacterial extracts have been reviewed. These observations, together with those of Novick
and SziLARD on the mutagenic activity of these substances, have suggested that the biological
action results from an inhibition of enzymes of nucleic acid biosynthesis. Consequences of
this hypothesis have been discussed relative to the regulation of growth of cell constituents.
Alternative hypotheses are enumerated.

I. INTRODUCTION

A NUMBER of agents, both chemical substances and radiations, cause mutations.
One particular class appears to be potentially most fruitful in an attempt
to understand the genetic replication process. This class includes purines and
related compounds. Particularly important are the plant alkaloids responsible
for the pharmacological effects of coffee, tea and cocoa. If these substances
are added to a continuously growing culture of bacteria, the mutation rate
is caused to increase markedly (1, 2).

If we compare the structures (Fig. 1) of the alkaloids caffeine, theobromine
and theophylline, with the purine bases normally present in nucleic acids of

Me N-

= C C-

,/

Me

Me N C-

CAFFEINE

H N-

Me N-

Me

>

THEOBROMINE

Me N C-= 0

I I

SI

Me-

-N C-

THEOPHYLLINE

XANTHINE

-NH,

-OH

H2N C

/

ADENINE

Fig. 1 . The structure of purine derivatives

GUANINE

all species, adenine and guanine, the similarity is readily apparent. The former
are methyl derivatives of xanthine, the latter amino and deoxy derivatives of
xanthine. It is tacitly assumed that these agents are mutagens because of this
similarity.

136

The Mechanism of Action of Methyl Xanthines in Mutagenesis

137

II. TRACER STUDIES

The first possibility to test was that these compounds, or products derived
from them, are utihzed for the synthesis of the nucleic acid of the host (3).
To do this we prepared these substances as well as some others, labeled with
carbon 14 in the 8-position of the heterocyclic nucleus. These were then added
to growing cultures o^ Escherichia co// under conditions similar to those employed
by NoviCK and Szilard (I, 2) in their studies.

In Table I the data so obtained are presented. Adenine and guanine as
well as the deaminated derivatives are very well incorporated into the nucleic

Table I. Incorporation and Mutagenicity
oj Various Purines

RSA* of DNA

purines

Mutagenicity

Adenine

0.3

+

Guanine

0.20

±

Hypoxanthine
Xanthine

0.30
0.20

—

Theobromine

0.00002

+ + +

Caffeine

0.00001

+ + +

Theophylline

0.00001

+ + +

*RSA = relative specific activity = ratio of the specific activity of the
purine isolated from the bacteria to that of the growth medium.

acids of both the RNA and DNA type, whereas all methylated substances
are incorporated only to a very small extent, if at all. On the other hand,
the correlation of mutagenesis is the reverse.

A mutation is a very rare event, and though these agents, when present
in quite high concentration, may raise the mutation rate by a factor of fifteen
or so, this still only corresponds to one event in 10'^ duplications.

The small amount of radioactivity that is found associated with the DNA
from cells grown in the presence of radioactive mutagens is probably experi-
mental contamination. However, although these experiments are technically
excellent, they cannot begin to exclude the possibility that a methylxanthine
molecule is incorporated into the DNA molecule in the process of the rare
mutational event itself, since the resultant incorporation for one locus would
be many orders of magnitude below the trace amount observed here. Considera-
tion of the structures of these substances, however, makes this possibility
rather unlikely.

In the formation of the normal 9-A^-riboside or 9-A^-deoxyriboside linkages,
the single replaceable hydrogen which may be in either the 7- or 9-position is
replaced by the glycosyl residue. In the case of caffeine or theobromine, which
are 7-methyl derivatives, this is not possible because of the prior replacement
of the hydrogen by the methyl group. Thus even though the methyl group is

138 Arthur L. Koch

attached to the 7-position it prevents bond formation at the 9-position. Con-
sequently, the methyl group must be removed if the molecule is to be incor-
porated into the nucleic acids.

The isotopic data, as well as other information, are adequate to demonstrate
that there is not a single molecule of enzyme present in these bacteria capable
of removing this methyl group (3). Therefore it would appear that certain of the
mutagenic materials are not and cannot be converted into a form in which they
can be linked covalently to cell materials, not at least by the 9-A'^-glycosyl
bond which has been universally found in biological materials.

III. PURINE METABOLISM IN ESCHERICHIA COLI

The next possibility we investigated was that the mutagens act by inter-
fering with nucleic acid biosynthesis. First, however, it is necessary to discuss
the metabolism of the organism under study. Fig. 2 summarizes, from the

Adenine
Hypoxanlhine
and derivatives

Glycine

CO, ''"'C '" ^^r

Serine _- / \ 0"

DR

Glucose
Formate
Ammonia J ) _ "GR - '- G « ' 6D

Guonine
Xanthine
and derivatives

CELL WALL

AD

♦ONA

Fig. 2. The purine metabolism of Escherichia coli

available tracer data, the pathways of purine synthesis in growing cultures
of the test organism (4, 5, 6, 7, 8). C^*-labeled COg (4), glycine (8), and serine
or formate (unpublished) lead to the formation of RNA adenine, DNA adenine,
RNA guanine, and DNA guanine, all of equal specific activity. The activity
in the purines derived from CO2 and glycine is such as to indicate that the
well-accepted scheme for purine biosynthesis is the major pathway in tliis
organism (4). C^Mabeled adenine and hypoxanthine and their derivatives
yield adenine samples of equal, but lower, specific activity in both RNA and
DNA. From these facts it is inferred that there are three pools at which purine
metabolism branches, namely, a 'purine' pool which is common to all cellular
purines, and an 'adenine' and a 'guanine' pool which are precursors of the
corresponding purine in both types of nucleic acid. So far, attempts to find
a precursor which enters purine metabolism at some point beyond the 'adenine'
or 'guanine' pool have failed. Even when the intracellular adenine-C^"* ribo-
nucleotides were specifically labelled (5), the incorporation into the purines
of the ribose nucleic acid was equal to that in the deoxyribose nucleic acids.
It should be mentioned that in organisms under conditions of rapid growth,
the soluble intermediate pool concentrations relevant to this scheme are small
(5). It was impossible to demonstrate guanosine, adenine deoxyriboside,
guanine deoxyriboside or phosphorylated derivatives.

The Mechanism of Action of Methyl Xanthines in Mutagenesis

139

Although the tracer data dehneate the pathways, they do not define the
intermediates. It is, however, possible to conclude from available enzyme data
that 'adenine' and 'guanine' pools are made up at least in part of the free
bases themselves. This follows from the fact that the known enzymes of purine
metabolism which might be involved in the conversion of the hypothetical
'purine' precursor to the two types of nucleic acids catalyze reactions involving
the free purine base. The purine nucleoside hydrolases, purine nucleoside
phosphorylases, purine #-trans-glycosidases, and purine nucleotide pyro-
phosphorylases yield the free purine base. These enzymes and the postulated
pathway of direct reduction of the riboside to the deoxyriboside constitute
the only pathways of interconversion of ribose and deoxyribose purine com-
pounds that can be imagined at present. Since the reductive pathway is known
not to occur in E. coli (9) (although the interesting work from Volkin's labora-
tory may be relevant (10)), it appears quite likely that the free purine base is
involved in the 'adenine' and 'guanine' pools.

In addition to these general considerations, the specific observation of
Lampen and Manson (11) that purine deoxyriboside phosphorylase is inhibited
by adenine led us to investigate the inhibition of phosphorylases of E. coli
by methyl xanthines.

IV. ENZYMATIC INHIBITION STUDIES

The main conclusion from these studies (12, 13) was that the organism
possesses enzymes, particularly nucleoside phosphorylases of both types
(ribose and deoxyribose), that are inhibited by purines generally but specifically
by the mutagenic substances. It was also found that even in the presence of

10 20

CAFFEINE CONC. (mM)

30

5 10 20

CAFFEINE CONC. (mM)

Fig. 3. The inhibition of purine nucleoside phosphorylase.

The effect of caffeine concentration on the arsenolysis of adenine riboside is shown

at the left, and on adenine deoxyriboside on the right. The systems contain

arsenate to prevent the complication of back reaction.

large amounts of inhibitors enzyme action was not completely repressed
(Fig. 3). In all cases this suggested the presence of more than one enzyme
catalyzing the reaction under study. Studies of the effect of pH and the separa-
tion of the bacteria into several chemical fractions supported this notion.

140

Arthur L. Koch

The activity in various fractions was differently affected by caffeine and this
effect was different in acid and at neutrahty and at alkaline reaction (see Table
II). This finding explains the relatively low toxicity and bacteriostatic power
of the plant alkaloids.

Table II. Inhibition of Inosine Arsenolysis by Caffeine

Enzyme preparation* No.

Inhibition produced by
10 [J. moles caffeine per ml

Distribution of activity
(measured at pH 7)

pH5.0

pH 7.0 pH 9.0

6-1 (soluble)

6-2 (particulate)

6-3 (phosphate extract)

per cent
29
64
78

per cent
59
97
78

per cent
35
46
6

per cent
67
17
16

TOTAL

100

* Enzyme Preparation 6-1 was most active at pH 5, preparation 6-2 at pH 9, and preparation
6-3 at pH 7.

In more recent work (13) three new enzymes have been demonstrated in
extracts of this organism: an inosine hydrolase, a purine-pyrimidine trans-
ribosidase, and a purine-purine transribosidase. All are inhibited to some
degree by various purines. The results of the enzymatic studies are summarized
in Table III.

Table III. Enzymes of Nucleic Acid Metabolism

Type

Specificity

Inhibition by
methyl purines

Adenosine deaminase

Ribose

0

Cytidine deaminase

Deoxyribose
Ribose

0
0

Purine phosphorylases
Pyrimidine phosphorylase

Deoxyribose
Ribose

Deoxyribose
Ribose

0

some
some
0

Inosine hydrolase
Purine-pyrimidine trans-

Deoxyribose
Ribose
Ribose

0

+

glycosidase
Purine-purine trans-

Ribose

-f

glycosidase

V. WORKING HYPOTHESIS

The mutagenic agents do inhibit enzymes that appear to be directly linked
to the path of nucleic acid synthesis, but how can such an interference affect the

The Mechanism of Action of Methyl Xanthines in Mutagenesis 141

mutation probability? We have proposed (12) that this may result from a
change in the steady slate concentrations of the intennediates that are to be
assembled together to form the macromolecular DNA. This must happen
without any change in the flow of intermediates, in accord with the experimental
fact that the growth rate of the bacteria is not affected significantly by the
mutagens when present at concentrations that give rise to large changes in
the mutation rate (1).

Let us first consider the consequences of lowering of the concentration of
whatever adenine deoxyriboside or guanine deoxyriboside derivative is
involved in the polymerization reaction leading to macromolecular DNA. The
Watson-Crick model for DNA assumes that the specificity lies in the forma-
tion of two or three hydrogen bonds between specific pairs of nucleotides:
adenine and thymine, and guanine and cytosine. It has been suggested by
Watson and Crick (14) that the mutational event is the entry of a heterocylic
base which is not complementary. This would yield a double helix which
is energetically less stable. Upon subsequent duplication this yields two stable
molecules, one of the parental type and one of a new mutant type.

guanine thymine

Fig. 4.

It is to be recognized that the mutational event is an improbable one, and
therefore quite improbable structures may be involved. Two options for the
unfavorable pairing are available. First, two pyrimidines or two purines may
become situated opposite each other. This gives structures that should be
capable of forming hydrogen bonds, but are either too long or too short.
Alternatively, a purine and a pyrimidine may pair, but the purine may occur
in the uncommon tautomeric form and consequently pairing will occur abnor-
mally. Watson and Crick (14) suggested adenine in the lactim form binding
with cytosine, more probable is the pairing of guanine with thymine (Fig. 4).
This pair has the proper dimensions; there are no steric difliculties. In this
structure guanine is written with the oxygen in the 6- position in an enol form.
X-ray-diffraction workers have concluded that guanine is ordinarily found in the
keto form, but the evidence is not strong that the keto form is even dominant
(15), and considerations of the resonance possibilities indicate a considerable
stabilization of the enol fonn because the latter allows aromaticity of the
heterocyclic ring.

Thus, guanine-thymine pairing might well be of likely occurrence. With
this in mind, we have attempted in our enzyme studies to find differences of
the effects of mutagens on the inhibition of reactions of the adenine compounds,
as opposed to the guanine ones, that would be implied if this structure were to

142

Arthur L. Koch

account for the mutational activity of these methylated purines. So far we have
been unable to detect any such differences. We may have been examining the
wrong systems.

For the present we shall tentatively suggest the pair thymine-cytosine (Fig. 5)
as the culprit. This pair is shorter than the conventional structures. In the
very interesting paper by Donohue (16) a large number of possible pairings
are suggested. For our purposes most of these are unsatisfactory because they
give rise to helices possessing a two-fold axis parallel to the hehcal axis, whereas

thymine cytosine

Fig. 5.

in the Watson-Crick structure this two-fold axis is perpendicular to the
helical axis, and thus consistent hehces formed by substitution between the
two types can not occur. One structure (Donohue's no. 22) would fit into the
symmetry of the Watson-Crick model and it is the pairing suggested in Fig. 5.

VI. STEADY-STATE CONSIDERATIONS

Whatever may be the critical or quantitatively most significant substitution
in this type of mutational change, the hypothesis we have proposed requires
that the concentration of terminal pools be altered. The experimental data
that we have obtained have been primarily with purine ribonucleoside phos-
phorylase which catalyzes a step which is clearly non-terminal in DNA synthesis,
and very likely the reaction catalyzed by purine deoxyriboside phosphorylase
is also not the transformation of the last small-molecular-weight intermediate
into DNA.

Although it may be that the terminal processes are inhibited, let us examine
some possible situations that might lead to an alteration of the steady-state
concentration of the penultimate substance without influencing the steady-state
flux of DNA synthesis. To do this, the question of bacterial growth itself must
be raised. Bacteria grow autocatalytically. Hinshelwood (17) as well as
others have pointed out that this results from an interaction of catalytic units.
Thus, if the amount of one component, P (protein), controls the rate of synthesis
of another component, N (nucleic acid), then

dP

dt

dN
~di

k,P

(1)

The Mechanism of Action of Methyl Xanthines in Mutagenesis 143

where k^ and k^ are characteristic constants. The steady-state solution of this
pair of equations is

P = p (,\Vki^k^l \

(2)

where P^) and A^,, depend on the initial conditions and the constants Aj and ko.
Thus both P and A^ increase exponentially at the same rate and each therefore
appears to be 'autocatalytic'.

Clearly, processes of this kind are responsible for the maintenance of constant
growth rates and constant composition of cells during the exponential growth
of bacteria. However, the control of the system by this type of interaction
cannot explain the regulation of synthesis of intermediates for the biosynthesis
of either P or A'^. Additional regulatory processes must be considered. From
equation (2) it is evident that for any constituent of the cell (intermediate or
enzymatic catalyst) the steady concentration increases autocatalytically. If
expressed as amount per unit number of bacteria or per unit bacterial mass,
any cell constituent may be considered constant. Thus, if such a transformation
is made, we can consider a system with time-invariant concentrations of inter-
mediates and catalysts and also time-invariant fluxes. Thus, the steady-state
treatment of reaction rates is immediately applicable to our problem. The most
general formulation is that of Christiansen and has been well described by
Hearon (18, 19).

In essence the rate expression for each step of a concatenated reaction
scheme, in which a substance is produced in one step and utilized in the next,
is written down. Each of the terms in these expressions is the product of the
intermediate with a rate constant and also with either unity or with the concentra-
tion(s) of the other chemical reactant(s). If the product of the two latter factors is
set equal to a quantity W, bearing suitable subscripts to identify the term, and
if the usual steady-state assumptions are made, then the solutions for both the
flux of the system or the over-all reaction rate v and the concentration of each
intermediate [A'J may be computed. If the very last reaction is irreversible,
equations (3) and (4) are obtained.

W.W^W^"- W,

[X,] = V

(3)

Wi-,1 '"W^

(4)

The assumption of the irreversibility of the last step is made necessary by
the well-known metabolic stability of DNA. Recent experiments (20) demon-
strate the extreme irreversibility in the normal adult rat. The evidence
for growing cultures of E. coU is less stringent (21, 22) but does permit this
assumption in comparison with the tremendous synthetic rate in these
organisms.

144 Arthur L. Koch

Now if in addition we assume that some step is either rapid in the direction
of synthesis or irreversible, then it may easily be seen that the reaction velocity
V, is completely independent of subsequent steps. Thus, the synthetic rate can
be made to depend on the level of a few catalysts or other reactants involved
earlier in the sequence. Consequently, increased protein synthesis would cause
increased synthesis of a very few enzymes critical for nucleic acid biosynthesis,
and this would lead smoothly to increased DNA synthesis without requiring
exact synchronization in the increase of each enzyme on the biosynthetic path-
way. The concentration of the last intermediate i'j_i can be seen from equation
(4) to be vlW^, and thus is completely independent of any step that has no effect
on the reaction velocity, v.

This case does not therefore satisfy the requirements suggested above to
explain the mutagenic effects of the plant alkaloids. The independence of
growth rate in the presence of caffeine could be explained simply by assuming
that the inhibition occurs after some fast or irreversible reaction; but the
action of the inhibitor on any but the final step has no effect on the concentration
of the immediate precursor of the macromolecule, and thus cannot affect the
probability of mutation.

The scheme considered above has two desirable features: it permits a
reciprocal control of nucleic acid by the level of protein synthesis, and it prevents
the accumulation of large amounts of intermediates. Let us now turn to a
possible mechanism that will do these two things but also will fulfill the conditions
imposed by our ideas of the mutation event. Such a mechanism occurs in
systems showing product inhibition. Here the rate of production of the final
product will depend on the level of some enzyme catalyzing a step late in the
reaction sequence, but at the same time, the inhibition prevents the unlimited
synthesis of earlier intermediates.

Product inhibition is of common occurrence. It has been suggested as having
metabolic significance in two cases (23, 24) in which the product of a reaction
sequence inhibits some earlier reaction than its own formation. In the present
case it has been shown that adenine deoxyriboside is an inhibitor of the phos-
phorylase (12) as well as purine bases. Let us assume that all of these agents
are competitive inhibitors of enzyme action, although this remains to be demon-
strated conclusively.

Under such conditions the reaction velocity is given by the well-known
expression for competitive inhibition (see, for example, (25))

K, K, + Ul) + US)

where Kis the maximal velocity obtainable, K^ is the Michaelis-Menten constant
for the substrate S, and Ki is the constant for the binding of the enzyme with
the inhibitor, 1. If Kj{I) is the dominant term in the denominator, this expression
simplifies to give:

K.V(S) ...

In the present case, adenine deoxyriboside is the inhibitor which is formed
from the substrate adenine and deoxyribose-l-POj. Now, if the net rate of

The Mechanism of Action of Methyl Xanthines in Mutagenesis 145

removal of adenine deoxyriboside is to be maintained constant and determined
solely by the process of removal, then a steady-state will quickly ensue in which
(S) oc (/), and in which the rate of formation of / is dependent only on the rate
of utilization. The concentration of / will become adjusted to estabHsh such a
condition.

In the presence of the mutagen, the total inhibitor is effectively derived from
three sources; deoxyribosides, free normal bases, and the mutagen. While
maintaining constant synthesis of DNA, the effect of the mutagen will then be
to decrease the level of the normal reaction product, adenine. Similar relations
will hold for guanine deoxyriboside.

It should be noted that in this case, although not in the case considered
above, any number of intermediates may occur between the step under considera-
tion and the polymerization step, if these reactions are rapidly reversible. Then
a change in adenine deoxyribose concentration will lead to a proportional
change in the precursor immediately used for the formation of the macro-
molecule.

This model can then utilize the enzymatic finding, and the biological facts.
There is, however, one additional fact that should be introduced, viz. certain
specific substances, the purine ribosides (26), are anti-mutagens. That is, these
substances will prevent the action of caffeine and related compounds in causing
mutations. Moreover, they will decrease the so-called 'spontaneous mutation'
rate.

This can be tentatively explained on the basis that these substances are
substrates or immediate precursors of the substrates of the key step, and that
their increase simply affects the system so as to cause an increase in the concen-
tration of purine deoxyribosides and thus a decrease in the mutation rate.

VII. ALTERNATIVE HYPOTHESES

In concluding, I should like to list various hypotheses that one should consider
in this type of chemical mutagenesis. They will be considered in order of the
intimacy of the mutagen with the duplication process.

1. The mutagen is incorporated into the nucleic acid. This is tentatively
rejected as indicated above, from the tracer evidence, and the argument that
methylation in the imidazole ring prevents A^-glycoside formation. It should
be noted that production of a self-duplicating 'methylated gene' can be rejected
because the mutants cannot metabolize methyl purines and certainly do not
require them (3).

2. The mutagens inhibit enzymes of nucleic acid biosynthesis, and this causes a
change in the concentration of intermediates. This latter effect changes the
probability of mutation. This is the hypothesis we favor, but it is clear that a
great deal of work will be required to establish it or some variant thereof. It is
also clear from what has been said above that special circumstances must occur
in order that the proposed mechanism can work.

3. The mutagen causes some change in the general metabolism of the organism
and this leads to a change in the mutation probability. It is certainly true that
the mutation probability is dependent on a great many factors. Kihlman (27,

146 Arthur L. Koch

28), working with plants, has suggested such a mechanism to explain chromo-
some breakage induced with caffeine derivatives. He proposes that ATP is
necessary for the aberrations produced by the compound 8-ethoxy caffeine.
However, there appear to be considerable differences between the two systems;
with the bacteria one thinks the process involved is one of 'point mutation', but
certain clearcut differences are evident in the two types of material with regard to
the interaction ofoxygen tension and ionizing radiations. (Compare (2) and (27),

4. The mutagen causes the organism to 'adapt' to its presence, and thus causes
widespread alterations in the amount of enzymes and intermediates. This could
lead to a change in mutation rate. This may be in fact the explanation of the
effect of adenine (12). This substance inhibits the growth of bacteria which
have previously been grown in its absence. Growth resumes when the organism
has 'adaptively' produced an 'adenine deaminase' activity which is not de-
monstrable in bacteria grown in its absence. This shift in metabolism can then
be envisioned to lead to changes in the mutation rate.

This list is probably sufficiently inclusive to include the right answer if there
is only one, but at least the necessary research, both with test tubes and with
pencil and paper, to test these possibilities is feasible.

REFERENCES

1. A. NoviCK and L. Szilard: Experiments on spontaneous and chemically induced
mutations of bacteria growing in the chemostat. Cold Spr. Harb. Symp. Quant. Biol.
16, 337-343 (1951).

2. A. Novick: Mutagens and anti-mutagens. Brookhaven Symp. Biol. No. 8, 201-214
(1956).

3. A. L. Koch: The metabolism of methyl purines by Escherichia coli. I. Tracer studies.
J. Biol. Chem. 219, 181-188 (1956).

4. A. L. Koch, F. W. Putnam, and E. A. Evans Jr.: The purine metabolism of Escherichia
coli. J. Biol. Chem. 197, 105-112 (1952).

5. A. L. Koch: Biochemical studies of virus reproduction. XI. Acid soluble purine meta-
bolism. /. Biol. Chem. 203, 227-37 (1953).

6. M. E. Balis, C. T. Lark, and D. Luzzati: Nucleotide utilization by Escherichia coli.
J. Biol. Chem. 212, 641-645 (1955).

7. E. Bolton: Biosynthesis of nucleic acid in E. coli. Proc. Nat. Acad. Sci., Wash. 40,
764^772 (1954).

8. A. L. Koch: The kinetics of glycine incorporation by Escherichia coli. J. Biol. Chem.
217, 931-945 (1955).

9. I. A. Rose and B. S. Schweigert: Incorporation of C^* totally labeled nucleosides
into nucleic acids. /. Biol. Chem. 202, 635-644 (1953).

10. E. Volkin and L. Astrachan: Phosphorus incorporation in Escherichia coli ribonucleic
acid after infection with bacteriophage T2. Virology 2, 149-161 (1956).

11. J. O. Lampen: Symposium on Piwsphorus Metabolism, vol. II, ed. by W. D. McElroy and
B. Glass, Johns Hopkins Press, Baltimore, 363-380 (1952).

12. A. L. Koch and W. A. Lamont: The metabohsm of methyl purines by Escherichia
coli. II. Enzymatic studies. /. Biol. Cliem. 219, 189-201 (1956).

13. A. L. Koch: Some enzymes of nucleoside metabolism oi Escherichia coli. J. Biol. Cfiem.
223, 535-549 (1956).

14. J. D. Watson and F. H. C. Crick: The structure of DNA. Cold Spr. Harb. Symp.
Quant. Biol. 18, 123-131 (1953).

The Mechanism of Action of Methyl Xanthines in Mutagenesis 147

15. D.O.Jordan: The physical properties of nucleic acids. In: The Nucleic Acids, Cii. hy E.
Chargaff and J. N. Davidson. Vol. I, 447-492, Academic Press, New York (1955).

16. J. Donohue: Hydrogen-bonded helical configurations of polynucleotides. Proc. Nat.
Acad. Sci., Wash., 42, 60-65 (1956).

17. C. N. HiNSHELWOOD : The Chemical Kinetics of the Bacterial Cell, Clarendon Press,
Oxford (1946).

18. J. Z. Hearon: The steady-state kinetics of some biological systems. I. Bull. Math.
Biophys. 11, 29-50 (1949).

19. J. Z. Hearon: Rate behavior of metabolic systems. Physiol. Rev. 32, 499-523 (1952).

20. R. W. SwiCK, A. L. Koch, and D. T. Handa: The measurement of nucleic acid turnover
in rat liver. Arch. Biochem. Biophys. 63, 226-242 (1956).

21. A. D. Hershey: Conservation of nucleic acids during bacterial growth. J. Gen. Physiol.
38, 145-148 (1954).

22. A. L. Koch and H. R. Levy: Protein turnover in growing cultures of Escherichia coli.
J. Biol. Chem. Ill, 947-957 (1955).

23. R. A. Yates and A. B. Pardee: Control of pyrimidine biosynthesis in Escherichia coli
by a feedback mechanism. /. Biol. Chem. Ill, 757-770 (1956).

24. H. F. Umbarger: Evidence for a negative-feedback mechanism in the biosynthesis of
isoleucine. Science 123, 848 (1956).

25. P. W. Wilson: Kinetics and mechanism of enzyme reactions, in Respiratory Enzymes,
ed. by H. A. Lardy, 22-67, Burgess Publishing Co., Minn. (1949).

26. A. NoviCK and L. Szilard: Anti-mutagens. Nature, Lond. 170, 926-927 (1952).

27. B. Kihlman: Chromosome breakage in Allium by 8-ethoxy-caffeine and X-rays. Exp.
Cell Res. 8, 345-368 (1955).

28. B. A. Kihlman: Oxygen and the production of chromosome aberrations by chemicals
and X-rays. Hereditas 41, 384-404 (1955).

EVIDENCE FOR A NEGATIVE FEEDBACK SYSTEM
CONTROLLING LIVER REGENERATION

Andre D. Glinos

Growth Physiology Laboratory,
Walter Reed Army Institute of Research, Washington, D.C.

Abstract — Cell division was induced in the resting liver of the rat by lowering the concentration
of serum constituents through plasmapheresis, and was inhibited in the regenerating liver by
increasing the concentration of the serum by fluid intake restriction.

Electrophoretic analysis of serum proteins and histochemical investigation of the organiza-
tion of cytoplasmic ribonucleoprotein of the liver cells during regeneration suggest that
plasma proteins may participate as information-carrying agents in a negative feedback system
controlling the growth of liver cells.

Liver is an excellent tissue for investigating mechanisms of growth control
because it regenerates very rapidly. In the rat, removal of up to two-thirds of
the total mass of the liver is followed by active cell division leading to complete
restoration of the organ within two weeks.

As early as 1923 Akamatsu (1) reported that tissue cultures of rabbit hver
grew better in plasma from partially hepatectomized animals than in normal
control plasma, and more recently it was shown that cell division can be induced
in the resting liver of a parabiotic rat by a partial hepatectomy performed on
its partner (2, 3, 4). These findings were considered to indicate the presence
or the increase of growth-stimulating factors in the plasma of partially hepatec-
tomized animals.

In our own studies on the possible participation of the humoral system of
communication in the control of this growth, blood serum from animals
undergoing liver regeneration was assayed in tissue culture (5). These cultures
showed a comparable outgrowth in a high concentration of serum of partially
hepatectomized rats and in a low concentration of normal serum. A high
concentration of normal serum showed inhibitory effects. Based on these
findings a hypothesis was formulated with regard to the induction of the
regenerative process in the liver which follows partial hepatectomy.

According to this hypothesis, certain constituents of normal blood serum
exert a growth-inhibitory action at their normal concentration. Partial hepatec-
tomy would be expected to result in a decrease of the serum concentration of
these constituents. Thus in turn regenerative growth is initiated. During
regeneration, as the number of liver cells increases, the concentration of these
constituents will also increase. When the original equilibrium between a given
number of liver cells and a given concentration of the serum constituents is
restored, further growth is expected to cease. The evidence for a negative
feedback system of this type should satisfy the following two conditions:

1. Induction of growth in the resting tissue by plasma dilution.

2. Inhibition of growth in the regenerating tissue by plasma concentration.

148

Evidence for a Negative Feedback System Controlling Liver Regeneration 149

Figure 1 illustrates the application of the classical method for plasma
dilution, plasmapheresis, and the results obtained. Normal adult male rats
were used. Blood was withdrawn every twelve hours corresponding to 31 to
38 per cent of the initial total blood volume of the animals in the first group

RATE

TIME IN HOURS

36-48

60

72-96

MEAN

0%

<.002
.003

.002
<.002

.004
.002

.002

31-38%

<.002
.022

.002
.048

.009
.002

.014

39-46%

.168
.002

.019
.054

.441
.197

.147

MEAN

.048

.031

.163

Fig. 1. Induction of cell division in the resting liver by plasmapheresis.
A total of eighteen adult male rats was used.
The rate of plasmapheresis is expressed as the percentage of the initial total blood
volume of the animal replaced by saline per 12 hours. In the control group 0
rate refers to the fact that blood was merely withdrawn and re-injected, with the
animals submitted to the same stressful conditions of restriction, anesthesia,
venipuncture etc. as the experimental groups. The mitotic activity was obtained
by counting 50,000 cells, and expressed as the per cent mitotic index. When no
mitosis was found, the mitotic index was recorded as <0.002.

and 39 to 46 per cent in the second. The bleedings were followed by re-injections
of the blood cells suspended in an equal volume of saline. Under such conditions
cell division was induced in the resting liver of adult rats and was intensified
with increasing dilution of the plasma. In this experiment, then, the evidence
obtained satisfies the first condition for a negative feedback system.

With respect to the second condition, the method used to achieve plasma
concentration was restriction of fluid intake as illustrated in Fig. 2. Two experi-
mental groups were used, differing with regard to the weight of the animals
and the extent of the partial hepatectomy. All animals were partially hepatec-
tomized and tube-fed an identical isocaloric fluid diet containing 3 per cent
water. The controls were given drinking water ad libitum but the experimental
animals were deprived of water for the duration of the experiment, which was
sixty-four hours, starting sixteen hours prior to the operation and continuing
for forty-eight hours postoperatively, at which time the animals were sacrificed.
A measure of total body-water loss obtained by this regimen is given by the
difference in weight change between experimental and control animals in each
group. A measure of the plasma concentration achieved is given by the difference
in total protein change. In both the experimental groups an effective inhibition
of cell division in the liver was obtained; this inhibition became greater with
increasing concentration of the serum. On the other hand mitosis in the
intestinal epithelium was not affected. The evidence obtained in this experiment,
then, satisfies the second condition for a negative feedback system.

The smaller extent of total body-water loss and plasma concentration in
the first group can be ascribed to the greater initial weight of the animals in

11

150

Andre D. Glinos

this group. It is well known that when dehydration proceeds slowly the main-
tenance of plasma volume at the expense of extravascular fluid may be quite
successful. This is significant since the extravascular fluid of the liver must parti-
cipate in the transmission of information to the liver cells. The serum albumin
fraction in this experiment was found to be low when liver cell division was
present and nonnal or slightly increased when liver cell division was absent.
In the framework of the present discussion this feature is somewhat suggestive

DEGREE

OF

HEPATECTOMY

TREATMENT

NO. OF RATS
ANO WEIGHT

WEIGHT
% CHANGE

SERUM PROTEIN
% CHANGE

SERUM ALBUMIN
% CHANGE

MITOSES
/50000 CELLS

30 %

(MEDIAN LOBE)

CONTROLS

iO

457

- 7.9

- 4.7

- 16.0

81.4

FLUID
RESTRICTION

9
458

- 12.9

+ 5.0

- 14.0

18.0

10 %
( CAUDATE
LOBE)

CONTROLS

8
331

- 9.1

+ 1.8

- 26.2

16.5

FLUID
RESTRICTION

8
313

- 17.6

+ 28.9

+ 8.1

0.1

Fig. 2. Inhibition of cell division in the regenerating liver by fluid restriction.

The experimental variables are defined in the text.

The percentage changes refer to differences in weight, total serum protein, and

serum albumin between the values obtained before treatment and those obtained

at sacrifice.

when it is considered that albumin is synthesized in the liver. In view of these
facts it was thought that an investigation of changes in protein metabolism of
the liver cells, early after partial hepatectomy, could help in elucidating the
possible role of the serum proteins and the extravascular fluid of the liver in
the transmission of information to the liver cells.

In this, we took advantage of the many observations showing histochemically
detectable changes in the organization of cytoplasmic ribonucleoprotein with
increasing demands on the protein synthetic mechanism of the cells (6, 7).
Briefly stated, these changes consist of the disappearance from the cytoplasm
of discrete basophilic bodies which are associated with ribonucleoprotein; the
cytoplasm then stains unifonnly with basic dyes. Rats were sacrificed at frequent
intervals after partial hepatectomy and their livers fixed and stained with
gallocyanin chrome alum. Within thirty minutes after partial hepatectomy the
ribonucleoprotein-associated basophilic bodies started disappearing from the
cells in the periportal area. This change proceeded gradually toward the center,
so that eight hours after the operation all cells, even those in the centrolobular
area, were affected. After this time reconstruction of the basophilic bodies
proceeded in the opposite direction from the center of the lobule towards the
periphery. At 24 hours cells in the centrolobular area had completed the cycle

Fig. 3. Regenerating liver twenty-four hours after partial hepatectomy.
Central vein at lower left corner. Adjacent centrolobular zone with cells con-
taining ribonucleoprotein-associated basophilic bodies in their cytoplasm. Middle
and periportal zones with mostly altered cells having a uniformly basophilic

cytoplasm. Two mitotic figures in the middle zone among altered cells.

to face p. 150

Evidence for a Negative Feedback System Controlling Liver Regeneration 151

showing well organized basophilic bodies, whereas cells in the middle and the
periphery of the lobules remained altered (Fig. 3).

Confirming the earlier data of Harkness (8), we found that cell division
begins between 16 and 24 hours postoperatively in the periportal area. This
is significant because cells in this area remained altered for the longest time.
The changes in cytoplasmic ribonucleoprotein organization indicate an activa-
tion of the protein synthesizing mechanism of the liver cells after partial hepa-
tectomy, proceeding in a topographical pattern related to the direction of the
intralobular blood flow. According to the Law of Mass Action these changes
would be expected to appear with decreased protein concentration in the
immediate environment of these protein-secreting cells. The cells in the periphery
of the lobules would be expected to react faster and longer since the ones more
centrally located are in an environment richer in protein produced by the more
peripheral cells. This interpretation was, in part, verified experimentally by

TREATMENT

FLUID

SERUM PROTEIN
CHANGE

LIVER
RIBONUCLEOPROTEIN
CHANGE

ADDITION

SALINE

- 11.8

0

DEXTRAN

- 31.2

+

SERUM

+ 7.9

0

REPLACEMENT

SALINE

- 19.2

+

DEXTRAN

- 37.8

+

SERUM

- 8.7

0

Fig. 4. Induction of cytoplasmic ribonucleoprotein

changes in the liver by plasma dilution.

A total of six male adult rats was used.

Addition refers to a single intravenous injection of 5.5 ml of fluid. Replacement

refers to a 5.5 ml single plasmapheresis treatment. All animals were sacrificed

two hours after treatment.
Serum protein change refers to the percentage difference between the values

obtained before treatment and those obtained at sacrifice.

Liver ribonucleoprotein change refers to the disappearance of the basophilic

bodies from the cytoplasm of the cells in the periportal area.

showing that changes in the cytoplasmic ribonucleoprotein of the cells in the
periportal area appear rapidly after a sudden decrease of the serum protein
concentration (Fig. 4). After partial hepatectomy, however, these histochemical
changes occur as we have seen within thirty minutes before any appreciable
changes in the plasma proteins.

The relationships between increased pressure in the portal system following

1 52 Andr£ D. Glinos

partial hepatectomy and regeneration have been demonstrated by Grindlay
and BoLLMAN (9). It is conceivable that, under conditions of increased pressure
immediately following partial hepatectomy, the transfer of protein and water
from the intravascular to the extravascular space is altered and results in a
rapid lowering of the protein concentration of the interstitial fluid of the liver.
This leads within a short period to increased protein production in the liver
cells and sometime later to cell division.

REFERENCES

1. N. Akamatsu: Ober Gewebskulturen von Lebergewebe. Virc/i. Arch. 240, 308-311
(1923).

2. B. G. Christensen and E. Jacobsen: Studies on liver regeneration. Acta Med. Scand.
234, Suppl, 103-108 (1949).

3. N. L. R. Bucher, J. F. Scott, and J. C. Aub: Regeneration of the liver in parabiotic
rats. Cancer Res. 11, 457-465 (1951).

4. A. S. Wenneker and N. Susman: Regeneration of liver tissue following partial hepa-
tectomy in parabiotic rats. Proc. Soc. Exp. Biol. Med. 76, 683-686 (1951).

5. A. D. Glinos and G. O. Gey: Humoral factors involved in the induction of liver regenera-
tion in the rat. Proc. Soc. Exp. Biol. Med. 80, 421^25 (1952).

6. S. Lagerstedt: Cytological studies on the protein metabolism of the liver in the rat.
Acta Anat., VII, suppl. 9, 1-116 (1949).

7. A. F. HowATSON and A. W. Ham: Electron microscope study of sections of two rat
liver tumors. Cancer Res. 15, 62-69 (1955).

8. R. D. Harkness: The spatial distribution of dividing cells in the liver of the rat after
partial hepatectomy. J. Physiol. 116, 373-379 (1952).

9. J. H. Grindlay and J. L. Bollman: Regeneration of the liver in the dog after partial
hepatectomy. Role of the venous circulation. Surg. Gynec. Obst. 94, A9\-A96 {\952).

FLUCTUATIONS IN NEURAL THRESHOLDS*

Lawrence S. Frishkopf and Walter A. Rosenblithj

Research Laboratory of Electronics,
Massachusetts Institute of Technology, Cambridge, Massachusetts

Abstract — Over the past twenty-five years several independent investigations of the responsivity
of nerve tissue have led to the conclusion that the threshold of a resting neuron fluctuates
in time. The conclusion is based on the study of sensory and motor fibers, of monosynaptic
arcs and neuromuscular junctions. A number of these studies have been reviewed and com-
pared. The degree of threshold correlation among neurons of a given 'pool' or population
has been considered for several systems. A number of possible sources of threshold fluctuation,
giving rise to correlated and uncorrected threshold variations, have been distinguished.

A mathematical model based on the concept of fluctuating thresholds has been described
and applied to the problem of ensemble response from the peripheral auditory nervous system.
The results of three experiments have been described and compared with the predictions of
the model.

I. THE CONCEPT OF A FLUCTUATING THRESHOLD

The threshold of a nerve fiber is defined as the minimum stimulus intensity
that will cause an action potential to propagate. If the threshold of a nerve
fiber were a fixed parameter — not changing in time — its value could be deter-
mined by presenting stimuli of increasing intensity. The fiber would fail to
respond to all stimuli less than some value Srp, and would respond to all stimuli
greater than Srp\ Sj, would then be the threshold of the fiber. However,
careful experiments on a number of specific neural systems — sensory and motor,
peripheral and central — have shown that such a unique value Sj, does not
exist; instead, there is a range of stimulus values, 5^ to ^'2, such that a stimulus
S lying within that range, when repeatedly presented at a rate well below that
which would involve the refractory period of the fiber, sometimes evokes and
sometimes fails to evoke a response. We find that the fiber responds in a fraction
p of all trials and that p{S) is a monotonic function that rises from zero to one
as the stimulus increases from S-^ to 5^2. Stimuli less than S^ never evoke a
response; stimuli greater than So always evoke a response. We conclude that
the threshold of a neuron which exhibits this behavior is a time-varying para-
meter. The value p approximates the fraction of the time that the threshold is
somewhere below the stimulus value S. An equivalent statement is that p
approximates (and for large sample size, approaches) the probability of finding
the threshold of a fiber below the value 5".

* This work was supported in part by the U.S. Army (Signal Corps), the U.S. Air Force
(Ofiice of Scientific Research, Air Research and Development Command) and the U.S. Navy
(Office of Naval Research).

t Also in the Department of Electrical Engineering, M.LT.

153

154 Lawrence S. Frishkopf and Walter A. Rosenblith

II. SUMMARY OF STUDIES OF OTHER WORKERS

The class of phenomena that we have been discussing was first observed by
Blair and Erlanger (1). They reported that an electric stimulus, repeatedly
presented to a single sciatic nerve fiber of the frog, will for most stimulus values
either always produce or always fail to produce a response. The transition
between these two situations, however, is not sharp. Upon raising the shock
intensity, a value is reached at which the fiber sometimes responds and some-
times fails to respond to repeated stimulation. In order to obtain a response
every time it is necessary to raise the shock intensity an additional two per
cent, far in excess of the uncontrollable variation in the stimulus. Moreover,
Blair and Erlanger were able, on occasion, to record simultaneously from
two fibers whose potentials could be distinguished by their difference in latencies.
On repeated testing with a near-threshold stimulus, sometimes both would
respond, sometimes one, sometimes the other, and sometimes neither. Such a
result cannot be accounted for on the basis of stimulus instability alone.

The most complete study of this kind that has been published to date was
made by Charles Pecher (2) in 1939. Using a technique similar to that of

A- A-
J^ .^
^ J\^

Fig. 1 . Left : ink tracings of recordings from single units of frog sciatic nerve,
showing occurrence and failure of response to repeated presentations of identical
shock stimuli. Right: same, with amplitude of pulse producing the shock raised
4 per cent. Each series shown is part of a longer sequence of 100 presentations.
Thirty-five responses were obtained with the weaker stimulus (left); 85 responses
were obtained with the stronger stimulus (right). After Pecher (2).

Blair and Erlanger, he also found a stimulus range in which a fiber sometimes
responded and sometimes failed to respond to a constant stimulus. Some of
his data appear in Fig. 1. In the column on the left we see the responses to
successive identical stimuh, of which some produce a response and some fail
to do so. In the second column the intensity was raised four per cent. In

Fluctuations in Neural Thresholds

155

Fig. 2 the percentage of responses of a fiber is plotted as a function of stimulus
intensity. Again each point is based on 100 stimulus presentations. The total
range of thre'shold variation is, on the basis of these data, about seven per cent.
The function shown in Fig. 2 approximates the threshold probability function
p(S) that was discussed earlier.

100

7b

50

25

O

'/]':

-.y^:

97 98 99 X)0 101 102 103

Fig. 2. Relation between stimulus intensity (abscissa) and the number of respon-
ses obtained in 100 presentations at a fixed intensity from a single unit of frog
sciatic nerve (see Fig. 1). The interpolated solid line approximates the threshold
probability function of a unit. From Pecher (2).

Fig. 3. Left: ink tracings of simultaneous recordings from two units of frog
sciatic nerve to repeated presentations of identical shock stimuli. Units A and B
are identified by their latencies. Right: same, but recording from two other
units, identified by their amplitudes. After Pecher (2).

In the left column of Fig. 3 the responses of two different fibers were simul-
taneously recorded from a single electrode; the responses arc distinguishable
by their latencies. At a fixed level of stimulation all possible combinations of
response occur: fiber A responds alone, fiber B responds alone, both respond,
neither responds. On the right we see the responses from two other fibers;
here the responses are distinguished by their amplitudes. Again, all possible

156

Lawrence S. Fpushkopf and Walter A. Rosenblith

combinations occur. Such a result can only be explained as a result of spon-
taneous variation in fiber threshold. If threshold were fixed and the stimulus
unstable, then only three of the four combinations could occur. That combina-
tion would be excluded in which the fiber with higher threshold fires alone.

When responses from two fibers can be distinguished, an opportunity is
offered to test the degree of correlation of threshold fluctuation among different
fibers. If fluctuations occur independently in two fibers, the probability of both
firing to a single stimulus would be the product of their probabilities of firing
separately. Any correlation in threshold variations would alter the probability
of joint firing. These probabilities can be approximated by counting the number
of times that fiber A fires, that fiber B fires, and that both fire, and dividing
each by A'^. In the table below the results of such measurements by Pecher

Table I

Calculated

Number of
stimuli

Number of
responses of
fiber A

Number of

responses of

fiber B

number of
simultaneous

responses
(independence

assumed)

Observed

number of

simultaneous

responses

100

78

25

19.5

19

188

129

26

17.8

18

285

205

33

23.7

18

222

150

79

53.4

56

370

214

93

53.8

50

194

113

34

19.8

19

155

110

62

44.0

40

218

168

87

67.0

59

236

152

24

15.5

17

are given for nine different fiber-pairs. In all of these instances the computed
and observed frequencies of joint occurrence are in good agreement. The
hypothesis of independent fluctuations is thus supported by this experiment.

Pecher tried to determine whether or not for a single fiber the 'response
no-response' pattern to a sequence of periodic stimuli can be accounted for
by the hypothesis that successive responses occur with equal and independent
probability p. He chose a criterion of independence that relates the variables
r and n^, where n^ is the number of times that a sequence of r successive responses
(bounded at each end by the absence of a response) occurs in a sample of
length A^(r<A^):

/• + ^ In nj. = K

where k and K depend on/) and A'^ (3). On the basis of samples of 1000 to 2000,
Pecher concluded that within statistical limits a linear relation exists between
r and In n^ for rates of stimulation less than one per second. At higher rates
the criterion was no longer satisfied. This is not a sufficient test for independence,
since one could construct sequences which satisfy this relation and yet contain
strong internal regularities.

Fluctuations in Neural Thresholds

157

Pecher also reported that the latencies of responses to identical shock stimuli
exhibit variability of a sort that cannot be attributed to stimulus instability.
The variability is greatest for stimuli near threshold.

RosENBLiTH (4) has obtained a threshold probability function for single
units in the auditory system of the anesthetized cat. These results are shown
in Fig. 4. Responses to repeated clicks were recorded by means of a micro-
electrode from a unit in the cochlear nucleus. The ratio of the number of
responses to the number of stimuli is plotted for various stimulus values;
the range of threshold variability is about 1 5 dB.

Lloyd and McIntyre (5) have investigated the variability in the responses
of single ventral root motoneurons [triceps surae) to identical shock stimuli

60 50 40 30 20 10 0
dB BELOW CLICK REFERENCE LEVEL

Fig. 4. Percentage of clicks eliciting a response from a single element in the

cochlear nucleus of the cat as a function of click intensity. Each point is based

on 10 to 40 click presentations. The interpolated solid line approximates the

threshold probability function of a unit.

delivered to the gastrocnemius nerve in decapitated cats. Here, the impulse
traverses a single synapse in the spinal cord. It was found that at every stimulus
level there were neurons that sometimes responded and sometimes failed to
respond. Some neurons always responded; others never responded. By raising
the stimulus level, the latter could be brought into the range of partial response
and, in some cases, of certain response. Different motoneurons receive different
amounts of transsynaptic stimulation when a shock is applied to the sensory
bundle. The strength of the effective stimulus is said, in this terminology, to
depend on the 'transmitter potential' of the synapse. The 'firing index' of a
motoneuron is defined as the percentage of trials in which it responds. Lloyd
and McIntyre measured firing indices for 110 motoneurons under a variety
of stimulus conditions. A histogram showing, for a constant stimulus, the
number of motoneurons in each firing index interval is seen in Fig. 5. For the
purpose of this histogram, units with firing indices of zero and 100 were not
counted.

An appreciable change in stimulus strength changes the firing index of a
particular motoneuron but affects the histogram very little. From this we can
conclude that the distribution of motoneurons with respect to the effective
stimulus level is approximately uniform. The situation may be visualized with
the help of Fig. 6. Each vertical line represents the effective stimulus or 'synaptic
drive' to one motoneuron; all motoneurons in this idealization are assumed
to be identical, but subject to different effective stimuli. The curve represents

158

Lawrence S. Frishkopf and Walter A. Rosenblith

the threshold probability distribution common to all of the neurons. Units
with synaptic drive to the left of the distribution have firing indices of zero ;
those to the right have firing indices of 100; and units with synaptic drive in
the range of the distribution have intermediate firing indices. As the stimulus
level is raised, the synaptic drive to every unit is shifted to the right by the

16—1

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.1 10

S 8

>
u

z

UJ

D

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hi

cc

20 40 60 80
FIRING INDICES

100

Fig. 5. Histogram showing the number of spinal motoneurons (triceps surae)
within each firing index interval ; responses were obtained by delivering repeated
shocks to the gastrocnemius nerve. The firing index of a unit is the percentage of
total stimulus presentations to which the unit responds. Units with firing indices
of zero and 100 are not included in this diagram. From Lloyd and McIntyre (5).

same amount; thus some units with a firing index of zero will be shifted into
the intermediate range ; some with intennediate firing indices will be shifted into
the range of firing index 100. But because the units are uniformly distributed
the same number will move into the intermediate range as move out of it,
and the distribution of intermediate firing indices will remain unchanged.

Fig. 6. Idealized relation between the threshold probability distribution of a
motoneuron and the levels of synaptic drive to diff"erent motoneurons of a

population (see text).

The particular choice of a bell-shaped probability distribution will lead
to the U-shaped histogram of Fig. 5. For it is clear that if we divide the abscissa
in such a way that equal areas under the distribution are subtended, those
intervals will be largest near the tails of the distribution (firing indices near
0 and 100) and smallest at the center of the distribution (firing index near 50).
Since the density of units along the abscissa is uniform, this means that many
more motoneurons will have firing indices between 0 and 10 than between
45 and 55.

Fluctuations in Neural Thresholds

159

As in the study by Pi chlr, the degree of correlation of thresJiold variation
for members of the same pool of motoneurons was investigated. The extent
of correlated and uncorrelated fluctuations is a measure of the relative impor-
tance in producing fluctuations of events extrinsic and intrinsic to the fiber.
In the spinal cord there is reason to believe that threshold fluctuation is, at
least in part, the eff'ect of background activity in other fibers. Such activity
would presumably aff'ect many fibers in a neighborhood; the threshold fluctua-
tions of these fibers would therefore show definite correlations.

To determine the extent of correlated variation Rall and Hunt (6) recorded
the response of a ventral root together with the response of a single moto-
neuron belonging to an adjacent root; an example of such a recording is
shown in Fig. 7. Fig. 8 shows the results of an experiment based on a thousand

-n

nHHi

« 1

Fig. 7. Simultaneous recording of the responses of a single motoneuron (hori-
zontal deflection) and of an adjacent ventral root (vertical deflection)
upon repeated stimulation of the gastrocnemius nerve with identical shock stimuli.

From Rall and Hunt (6).

such responses. The population response amplitudes were divided into class
intervals, and the number of responses within each class interval was plotted.
For each population response within a class interval, the occurrence or failure
of a unit response was noted and the number of unit responses plotted
(shaded area). The unit responded a total of 697 times out of 1000. If
the population response and the unit response were not correlated, the firing
index of the unit would be about the same in each class interval. This is clearly
not the case. Instead, firing occurs infrequently when the population response
is small, and more often as the population response grows. The probability
of unit firing when the population response amplitude is in a given class interval
— that is, the ratio of shaded to unshaded amplitude — is plotted in the lower
part of the figure. If unit response and population amplitudes were uncorrelated
this function would be a horizontal line at about 0.7. However, it is also clear
that correlation of unit and population response is not complete. In other
words, the thresholds of the units within the population vary with respect
to one another, in addition to their collective (that is, correlated) fluctuation.
If this were not so, a particular unit would respond only after all units of
lower threshold had responded; therefore its probability of response would
be zero if the population response were smaller than a certain value, and would
be one if the population response were larger than that value. The lower curve
would therefore be a step function.

III. POSSIBLE SOURCES OF THRESHOLD VARIATIONS

Fatt and Katz (7) have found that at motor endplates miniature end-plate
potentials occur more or less randomly even though no stimulus is present.

160

Lawrence S. Frishkopf and Walter A. Rosenblith

They regard these potentials as being the result of spontaneous firings in the
fine terminal branches of a motor nerve. The occurrence of an impulse in the
nerve causes simultaneous firing in about a hundred such teitninals, giving
rise to the normal end-plate potential. Spontaneous firing implies the existence
of a local source of varying excitation. Fatt and Katz compute that for
fibers with a diameter of 0.1 /,( thermal fluctuations in ionic concentrations

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z
u

o

UJ

cr

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1

1

ifin

140

-

r^'l

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100

-

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80

-

f —

60
40

_

^

20

r-H

-'■> 1 .t, i. -i I

n^

{/

^T

/

/

O " 2 4 6 8 10 12 14 16 18 20 22 24 26 28
POPULATION RESPONSE AMPLITUDE
1.0
0,9
0.8
0.7
0.6
0.5
0.4
0.3
0.2

0.1
O

/

Fig. 8. Top: the upper curve is a histogram of population response amplitudes
obtained as in Fig. 7 from triceps surae motoneurons by delivering repeated
identical shock stimuli to the gastrocnemius nerve. The lower curve (shaded) was
obtained from single-unit recordings like those shown in Fig. 7 ; the number of
single-unit responses associated with population responses in each amplitude
interval is plotted. Bottom : for a given population amplitude interval the number
of single unit responses is divided by the total number of trials in that interval,
and the ratio plotted as a function of population amplitude. The interpolated
solid curve is a sigmoid fit to the data points and approximates the probability of
unit response as a function of population amplitude. Note that when the popula-
tion amplitude is large, the probability of unit response is large, and when the
population response is small, the single unit probability is small, thus signifying a
high degree of correlation among the thresholds of different units of the popula-
tion. From Rall and Hunt (6).

could cause variations of resting potential of 1 mV to 2 mV. Though probably
insufficient to produce excitation, such a variation would cause threshold
fluctuations and contribute to spontaneous firing.

Both Pecher (2) and Hunt (8) have discussed possible sources of threshold
fluctuation. Pecher considers in detail the apparent threshold variation that
would result from statistical variations in the number of ions traversing the
axon membrane when a constant potential is applied across it. Assuming
that the excitatory current that he uses is uniformly distributed over a cross
section of the nerve trunk, he concludes that at threshold about a million ions
traverse a single nerve fiber. The statistical variation in this number of ions is

Fluctuations in Neural Thresholds 161

given by its square root, leading to a variation of about 0.1 per cent. This
is several orders of magnitude below the range of threshold variation that he
observed. However, he points out that the number of ions actually effecting
excitation is probably considerably less than the value mentioned above and
the resultant variability correspondingly greater. Pecher also considers as
a possible source of threshold fluctuations local statistical variations of mem-
brane potential, of the sort discussed by Fatt and Katz.

Hunt discusses two classes of possible sources of threshold fluctuation
for spinal motoneurons : (a) sources with a local origin such as we have mentioned
above, which give rise to an independent component of threshold variation
and (b) sources whose effect is felt by many fibers and which therefore produce
at least partially correlated variations in threshold. In the latter category
are included the effects of activity of spinal interneurons. By using a drug
(myanesin), in doses that block transmission through polysynaptic paths
without reducing monosynaptic reflex responses, a considerable reduction
in the range of variation of population response amplitudes was obtained.
On the basis of this result it appears likely that internuncial activity is important
in producing correlated threshold changes in spinal motoneurons.

IV. A MATHEMATICAL MODEL

Let us consider a mathematical model which is based on the concept of
fluctuating thresholds, and which attempts to derive the ensemble behavior
of large numbers of neural elements from assumed properties of neural units
in a specific area of the nervous system (9, 10, II).

This model is based on data obtained from the peripheral auditory system
of the cat. When an electrode is placed near the round window of the cochlea,
responses to clicks can be detected; such responses contain a component that
represents the summated activity of peripheral auditory neurons. Fig. 9 shows
such population responses at a number of intensities. In Fig. 10 the average
peak-to-peak amplitude of such responses has been plotted as a function of
stimulus intensity. The resultant 'intensity function' relates the number of units
firing and the intensity of the stimulus.

The present version of the model (11) postulates the existence of several
independent populations of neural units; within a population all units are
identical. The threshold of a unit is a fluctuating parameter which can be
described by a probability distribution; threshold variations in different units
occur independently. At a rate of stimulation slower than one per second the
'response no-response' sequence obtained from a single unit is assumed to
consist of a series of independent events. Thus we postulate units whose
statistical properties resemble those found by Pecher in the frog's sciatic nerve.

The experiments used to test the model fall into three classes: two-click
experiments (9, 10), measurements of variability of response amplitude (II),
and studies of masking of click responses by noise.

When two clicks are delivered at an interval of less than approximately
100 msec the population response to the second click is smaller than it would
be if the first click had not occurred. This effect is more pronounced the
stronger the first click and the smaller the interclick interval, as illustrated

162

Lawrence S. Frishkopf and Walter A. Rosenblith

in Fig. 11. Consider the ratio of the response amplitude ^R^ to a second click
and the response amphtude R^ to the same click presented alone. In Fig. 12
this ratio is plotted, for a fixed second-click intensity, as a function of the inten-
sity of the first click. The parameter is the interval between clicks, At. If

STIMULUS INTENSITY

IN DB

(RE 1.29 VOLTS)

•90

•40

-80

-30

■70

•20

-60

■10

■60

3 msec

3 msec

0 DB RELATIVE GAIN -12 DB

Fig. 9. Ink tracings of responses obtained from an anesthetized cat to clicks over
a 90-dB range. The electrode was located near the round window. Note that the
voltage gain of the recording equipment was reduced by 12 dB (factor of i) for
stimulus intensities above —40 dB. The first peak represents the summated
activity of first-order auditory neurons. With this calibration, click threshold for
humans (verbal report) is about —95 dB.

we assume a one-population model, we obtain the result that the ratio 1R2IR2
is Hnearly related to the intensity function for the first click, provided that
the second-click intensity (S^) and At are held constant. Specifically, we obtain

rR. , ^^^^\l - giS„ Ar)] (1)

R,

1 -

Rr

Determination of a single intensity function therefore permits us to predict
the dependence of this ratio on S^ for any value of 5*2 and of At. We may

Fluctuations in Neural Tiiresholds

163

u

E 3.0

AMPLITUDE (-c^) AND LATENCY
(-•-)OF N, AS A FUNCTION OF
2-5\-|NTENSITY OF CLICK STIMULUS "

150

125^

-100 -80 -60 -40 -20 0

CLICK INTENSITY (dB RE 1.29V ACROSS

PHONE)

Fig. 10. Intensity function (open circles). A''i is the first diphasic response com-
ponent seen in the traces of Fig. 9. The amplitude measurement is made between
the positive and negative peaks of N^. Each plotted point is the median of about

ten such measurements.

m
o

o

o

in
tr

50 DB

30DB

RESTING RESPONSE

tl -lODB

12.2 MSC 30MSC 6IMSC

TIME INTERVAL BETWEEN CLICKS

Fig. 11. Two-click paradigm: the responses shown are to a constant intensity
(—45 dB) second click. The vertical set shows the effect of varying the intensity
of the first click; the horizontal set shows the effect of varying the interval
between clicks. Upper right: response to a — 45 dB click presented alone.

From McGiLL (10).

in each case choose one constant, ^(5*2, At). Fig. 12 shows a number of fits
to the data points which were obtained in this way; 5*2 is constant and each
curve corresponds to a different value of At.

In a second group of experiments the standard deviation of a hundred
response ampHtudes was computed at each stimulus intensity, and the result
was plotted as a function of stimulus intensity. It is readily shown that N

164

Lawrence S. Frishkopf and Walter A. Rosenblith

independent units, each with a probability p of firing, will have a standard
deviation of total response proportional to \/Np{\ — p). As a function of
/; this quantity has minima at zero and one and has a maximum at/? = ^. The
value of p at any stimulus intensity can be obtained from the intensity function.

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g(Al

A

6.4

0.05-

B

9.1

0.15

C

12.2

0.27

D

21.5

0.46

E

30

0.54

F

61

0.70

G

102

0.83

60 40 20 0 60 40 20 0 60 40 20 0

INTENSITY OF FIRST CLICK IN dB BELOW
REFERENCE LEVEL

Fig. 12. 1R2IR2 (see text) as a function of first click intensity. In each block tiiis
ratio is plotted for a different interclick interval, as indicated at the lower right.
The intensity of the second click was —45 dB throughout. The curves are obtained
from the first click intensity function and eq. (1); the parameter ^(At), whose
values are given at the lower right, is chosen in each case to give the best
fit to the data. After McGill (10).

Fig. 13. Intensity function (upper) and the corresponding amplitude variance
function predicted by the model: (a) for one population; (b) for two disjoint
populations. Oq was chosen arbitrarily. Note that a peak of the variability
function occurs at the stimulus value at which an intensity function component
reaches half its maximum amplitude.

Fig. 13 shows the kind of variability function obtained by assuming one and two
disjoint populations; Cq is the stimulus-independent component of variability
arising from biological and non-biological sources. We have shown (II) that
instability in stimulus intensity, which would also lead to a peaked variability
function, can account for at most three per cent of the observed variability.
A detailed study of the shape of the intensity function led us to postulate

Fluctuations in Neural Thresholds

165

two populations of neural units, one consisting of 'sensitive' units and one of
'insensitive' units. In the three animals tested, variability measurements over
the sensitive range are in good agreement with the theory stated above. One
case is shown in Fig. 14. The intensity function and the probabilities obtained
from it are shown with the derived standard deviation function. Here, Oq is
determined from measurements of baseline variability in the absence of a
stimulus; TV is chosen to give the best fit to the data. Over the sensitive range

CLICK INTENSITY (DB RE I.29VACR0SS PHONE)

Fig. 14. Comparison of the theoretical variability function (with 70 per cent con-
fidence limits) and the measured values of cr, over the range of initial growth of the
intensity function. Each point represented by a solid circle is based on 100
responses; the open circles are based on the first fifty of these responses. The
corresponding intensity function, and the probabilities obtained from it, are also

shown.

(— lOOdB to — 60 dB) the data fall within the indicated confidence interval
approximately seventy per cent of the time, as they should if the model is
correct. Over the insensitive range of the intensity function (—60 dB to
0 dB), the standard deviation shows a complex behavior which cannot be simply
reconciled with the idea of a single population over that interval.

The third aspect of this study concerns the masking of the neural responses
to clicks by a background noise. Fig. 15 shows the effect of a constant noise
level on response amplitude at several stimulus values. In Fig. 16 we have
plotted these masked and unmasked intensity functions. The observation
was made that a very weak level of continuous noise was sufficient to reduce
almost to zero the N^ response to a fairly intense click. A fixed threshold model
would predict masking of only the units whose thresholds are below the noise
level. If the threshold fluctuates, however, and does so rapidly, nearly all
units of a given population will drop below the noise level and fire in a short

12

166

Lawrence S. Frishkopf and Walter A. Rosenblith

RESPONSE TO CLICK
ALONE

CLICK INTENSITY
IN DB
(RE 1.29 VOLTS)

CLICK RESPONSE IN RELATIVE

PRESENCE OF NOISE GAIN

(-82 DB RE 1.29 VOLTS)

-60

ODB

-50

-40

^x^

v/-'

-30

•12 03

-20

-10

-3 m sec -

-3 msec-

Fig. 15. Ink tracings of responses obtained from an anesthetized cat to clicks

over a 60-dB range, with and without background noise; noise level, —82 dB.

Note that the voltage gain of the recording equipment was reduced by 12 dB

(factor of i) at a click intensity of -30 dB.

Fluctuations in Neural Thresholds

167

interval preceding the click; this assumes, of course, that the noise level lies
within the range of threshold fluctuations of the unit.

By a quantitative treatment based on these qualitative notions we have
been able to show (a) that the hypothesis of a fixed threshold does not account
for the observed data and (b) that over the sensitive range of the intensity

i25r

100

75

50

I 25

^^^_ NO NOISE BACKGROUND

(COMPOSITE OF 3 FUNCTIONS)
NOISE BACKGROUN0(OB RE 1.29V ACROSS
PHONE lUNFILTEF

-92
-82

-67

-80 -70 -60 -50 -40 -30

CLICK INTENSITY (06 RE 1.29V ACROSS PHONE)

Fig. 1 6. Intensity functions for clicks, with an(d without noise backgroun(i ; noise
levels —92, —82 and —67 dB. Each point of the masked functions represents the
average A''i amplitude of ten responses to identical stimuli. The upper curve was
obtained by averaging the three unmasked functions which correspond to the
masked functions shown ; thus each point represents the average A''i amplitude of
thirty responses to identical stimuli. Typical data on which these curves are

based are shown in Fig. 15.

function a single population of units making threshold 'jumps' at a rate of
about 2000 times per second can account for the data. In addition, it is observed
that low level noise has little effect on the intensity function over the insensitive
range, except to reduce it by the constant contribution of the sensitive popu-
lation. The need for a division of units into at least two populations is thus
confinned. When the noise level is raised into the insensitive range the observed
effect is not nearly so marked, implying either that more than one population is
involved in that interval or that the rate of threshold fluctuation is considerably
slower than for the sensitive units.

It is noteworthy that population analyses based on two very diff'erent
experiments, variability and masking, have a great deal in common.

REFERENCES

1. E. A. Blair and J. Erlanger: A comparison of the characteristics of axons through
their individual electrical responses. Anier. J. Physiol. 106, 524-564 (1933).

168 Lawrence S. Frishkopf and Walter A. Rosenblith

2. C. Pecher: La fluctuation d'excitabilite de la fibre nerveuse. Arch. Int. Physiol. 49,
129-152 (1939).

3. A. Hald: Statistical Theory with Engineering Applications, p. 344 (eq. 13.3.6), J. Wiley
and Sons, New York (1952).

4. W. A. Rosenblith: Some electrical responses from the auditory nervous system. Pro-
ceedings of the Symposium on Information Networks, Polytechnic Institute of Brooklyn,
223-247 (1954).

5. D. P. C. Lloyd and A. K. McIntyre: Monosynaptic reflex responses of individual
motoneurons. J. Gen. Physiol. 38, 771-787 (1955).

6. W. Rall and C. C. Hunt: Analysis of reflex variability in terms of partially correlated
excitability fluctuation in a population of motoneurons. /. Gen. Physiol. 39, 397-422
(1956).

7. P. Fatt and B. Katz: Spontaneous subthreshold activity at motor nerve endings. /.
Physiol. 117, 109-128 (1952).

8. C. C. Hunt: Temporal fluctuation in excitability of spinal motoneurons and its influence
on monosynaptic reflex response. J. Gen. Physiol. 38, 801-811 (1955).

9. W. J. McGiLL and W. A. Rosenblith: Electrical responses to two clicks: a simple
statistical interpretation. Bull. Math. Biophys. 13, 69-77 (1951).

10. W. J. McGill: a statistical description of neural responses to clicks recorded at the
round window of the cat. Ph.D. Thesis, Harvard University (1952).

11. L. S. Frishkopf: A probability approach to certain neuroelectric phenomena. Research
Laboratory of Electronics, Massachusetts Institute of Technology, Tech. Rep. No. 307
(1956).

PART III
DETERMINATION OF INFORMATION MEASURES

It is possible (as shown by several papers in this volume) to apply information
theory to biology without introducing any actual information measures. Indeed,
if one considers that it is very difficult to estimate information measures for
living systems, and that the resulting measures are of an irreducibly relative
nature, one might wonder whether it is worth-while to take such measures at
all. However, it is difficult if not impossible to validate firmly the application of
information theory without critical tests based on quantitative measurements;
moreover, one hopes to discover lawful relations in the results of the measure-
ments themselves. So, attempts are being made to estimate information contents
associated with various biological structures and functions. All the papers in
this part are chiefly concerned with such estimations; some from a general
point of view, some with regard to particular systems, ranging in complexity
all the way from simple molecules to whole men.

H. Q.

169

CHEMISTRY AND BIOCHEMISTRY AT LOW

TEMPERATURES AND DISCRIMINATION OF

STATES AND REACTIVITIES*

Simon Freed

Chemistry Department, Brookhaven National Laboratory,
Upton, New York

Abstract — In order to apply information theory to biochemistry and biology at the molecular
level it is advantageous to reduce the number of classifications and specifications involved by
reducing the temperature of the system. In this way the number of species and states with
their reactivities is reduced. At the same time the chemical noise level falls and in consequence
a resolution may be obtained between components whose properties are practically indis-
tinguishable at ordinary temperatures. Weakly bonded systems and intermediates become
more easily detectable not only because of an increase in their concentration, that is, an increase
in their signal, but in addition because the noise level is weaker at the lower temperatuie.

Illustrations are given from chemistry where reactions in solutions proceed at the tempera-
tures approaching that of liquid nitrogen. The information content of irreversible reactions
at room temperature may be thought of as being stored in intermediates that participate in
reversible reactions at the low temperatures.

Once the properties of the more stable states have been understood, the way is clear for
investigating the system in its thermally active states since allowance can be made for the
presence of the former. In this way, an ordering of experimentation according to temperature
will bring into activity successive components of the system.

Examples have been selected mainly from work on the preservation of biological systems
at low temperatures which indicate that biochemical and biological processes may likewise
be investigated and that the finer discriminations and specificities associated with lower
temperatures may be brought to light in these fields also.

If we wish to measure a physical property, such as electrical conductivity or
viscosity, with an instrument which we have no intention of modifying, there
is little point in seeking the information content of the instrument. On the
other hand, if we wish to employ chemical substances as probes for uncovering
structures of enzymes by means of enzyme-substrate reactions, we are at once
confronted by the need of the structural and functional information of our
probes. In fact we are discussing properties at the molecular level. Pure
substances at this level are mixtures composed of molecules in various energy
states with their characteristic configurations, motions, and reactivities. The
application of information theory to biology at the molecular level requires
therefore a great expansion in the number of categories and specifications.
It is to reduce this number in a systematic manner and make these categories
more precise that I wish to draw upon the relation that has been recognized
between information and entropy which asserts that the amount of information

* Research performed under the auspices of the U.S. Atomic Energy Commission.

171

172

Simon Freed

required to specify the system will be less at lower temperatures. The system
will redistribute itself from higher to lower energy levels so that only the more
basic ones remain appreciably occupied. Fewer chemical species are now
present and also active. There has been, in a sense, a reduction in chemical
noise differing in its frequency spectrum from the continuum characteristic
of an electrical conductor. Chemical noise reflects the structural properties
of molecules and may consist of dominant discrete frequencies associated
with virtual continua of modulations. Usually these represent couphng of the
electronic system of the molecule in a given atomic configuration with its

300

■

II

B

77

II

1

1

II

4

1

Fel

III

1

l|l 1

II

1 |1

If 1

Fig. 1 . The variation of absorption spectrum of praseodymium chloride with
temperature. Line drawings of visible absorption spectra of crystals of anhydrous
praseodymium chloride (PrClg) at room temperature, at that of liquid nitrogen,
and that of liquid helium. Sharper spectra, improved resolution, and fewer hnes
are evident at lower temperatures. The fewer hnes correspond to fewer energy
states which are occupied by the praseodymium ions. At room temperature the
blocks of diffuse spectra are actually not uniform in intensity but are more
intense as a rule in those regions where the spectrum of the crystal at 77°K
possessed its most intense line spectrum. The greater diffuseness of the lines and
their increased numbers at the higher temperature may be regarded as chemical
noise associated with the spectroscopic signals from the more stable states at the

lowest temperature.

own vibrations, restricted rotations, etc. If the molecules are complex, fluctua-
tions between difl'erent atomic configurations may contribute to the noise.
In addition, coupling of the molecule in each of its states with the molecules
of its environment in different configurations leads to more and more densely
spaced energy levels which I referred to as the continua.

A reduction in temperature removes thennal energy required to activate
some motions and effect changes in configurations, and reduces the number
of perturbations of a given configuration. Not only are fewer species present
but each species is more sharply defined; thus, less infonnation is required
for specifying the system than at higher temperature. Clearly, the system is
now more specific in its reactions than at higher temperature and its specificity
can be related to more sharply defined geometric configurations. The chemical
system has become a more precise probe.

The following illustrations have been selected for the simplicity of their
phenomena rather than for their direct relevance to biology.

The sharp absorption spectrum of a crystal of a rare earth salt (Fig. 1)
shows very clearly that at the lower temperature fewer lines are present; they
are sharper and more clearly resolved and the general diffuse background
prominent at the higher temperature (not shown in the line drawing of the
figure) becomes decidedly weaker. There are then fewer kinds of absorption
centers at the lower temperature and, because the stable states are exposed to

Chemistry and Biochemistry at Low Temperatures

173

more sharply defined environmental fields, there are fewer kinds of pertur-
bations.

An especially vivid example of a solution showing somewhat similar pheno-
mena is given by the fluorescence spectrum of solutions of europium chloride
in ethanol at various temperatures (1), The spectra were taken to discover the
discrete number of lines in the three separate sets which may furnish the point

4000

4500

5000

Fig. 2. Absorption spectra of carotene (90% alpha and 10% beta). A — In hep-
tane at room temperature; B — In equal volumes of liquid propane and propene

at 77°K.

group symmetry of the electrical fields about europium ion in the solution.
It is clear that at room temperature the continuous noise is so great as to make
enumeration impossible. As the temperature is lowered a few discrete Hnes
can be resolved with such definiteness that they serve to eliminate some of the
possible point group symmetries. At the temperature of liquid nitrogen and
even at the temperature of dry ice adequate resolution is clearly achieved and
the number of possible symmetries of the environmental fields is reduced to
one only.

Figure 2 gives the absorption spectrum of a substance of some biological
interest, /9-carotene, and illustrates the increased contrast between absorption
and transmission at the lower temperature, that is, the increased signal to noise
ratio.

Figure 3 is presented to illustrate the resolution into components of what

174

Simon Freed

is apparently a single species at room temperature. The figure reproduces
the absorption spectra of chlorophyll b in ethyl ether and methanol (2). Our
first inclination is to ascribe the differences in the spectra to the perturbations
produced on the structure of the chlorophyll molecules by the two types of
solvent molecules. Figure 3b is a magnification of the Soret band in the blue

400

500 600 700

WAVELENGTH IN mjJi

Fig. 3a. Absorption spectra of chloro-
phyll b at room temperature. The thin-
lined curve with maxima at shorter wave-
lengths represents a solution of chloro-
phyll in ethyl ether; the thick-lined curve
gives the spectrum when the solvent is
methanol.

4100

5000A

Wavelength

Fig. 3b. The dependence of the absorp-
tion spectra of chlorophyll b on tem.pera-
ture. Only the Soret band in the blue is
shown. Enlarged scale of wave-lengths.
At 300"K the solvent is 20% propyl
ether, 80% hexane. At the lower tem-
perature it is 20% propyl ether, 40%
propane, and 40 % propene. The hexane
was substituted at 300°K for the hydro-
carbons propane-propene since they are
normally gases at room temperature.

region and shows that a solution of chlorophyll b in ether is really a mixture
of two species (etherates) in equilibrium with each other in roughly equal
amounts and clearly resolved at 180°K. A study of the dependence on tempera-
ture of the absorption spectrum of chlorophyll b in methanol reveals that in
this solvent, chlorophyll b also exists as a mixture of solvates which are about
equal in concentration at room temperature and together they yield the com-
posite spectrum. However the spectrum of each alcoholate differs very little
in shape from that of each etherate. Fig. 4 illustrates a form stable at a lower

Chemistry and Biochemistry at Low Temperatures

175

temperature reacting to produce reversibly a stable intermediate but at still
higher temperature ending in an irreversible reaction.

The following specific observations may prove worthwhile in illustrating
what is probably a rather common phenomenon. Chlorophyll b dissolved in

CHLOROPHYLL B'

IN 15%

MONO-i- PROPYL AMINE

AND 1:

1 PROPANE

-PROPENE

230°K

! :
: :

I93°K

• i

; 1

z

>

o

i^ '•

H

^t^^^^

1 i

cr

X^-

\ ;

o

CD

y^ 1 >

<£

tv

-^"'"^

^^V '^

1

\

1

—

1

4000 5000

WAVELENGTH %

6000

Fig. 4. Chlorophyll 6' in 15% mono-/-propyl amine in 1 : 1 propane-propene.

To show the presence of the red-brown intermediate stable at 193''K which is in

equilibrium with the original chlorophyll. At temperatures higher than about

235''K, an irreversible reaction occurs.

ether is deposited as a green powder by pumping off the ether at room tempera-
ture. When the temperature of the powder is reduced to that of dry ice (about
193°K) and propylamine is condensed upon it at this temperature, it dissolves
quickly, forming a red solution. Note in Fig. 4 the new absorption between
5000 A and 6000 A. A rise in temperature transforms the color into the green
of chlorophyll with its characteristic spectrum which reverts back reversibly
to the red substance when the temperature is reduced. However, if the tem-
perature is kept any length of time at about 235°K or higher, an irreversible
reaction sets in. For example, at room temperature the red color lasts only
a fraction of a second. This evanescent red color is produced in the well
known phase test for chlorophyll.

Figure 5 represents a chemical reaction which appears rapid even between
167°K and 75°K. Chlorophyll h dissolved in di-/.so-propylamine is undergoing

176

Simon Freed

transformation probably in an acid-base reaction. The quick readjustment
to equilibrium is shown by the interchange in relative intensities of the bands
in the red region. The band furthest towards the red grows in as the temperature
is reduced, at the expense of the band near it toward shorter wavelengths.

That these reactions occur rapidly at such temperatures is not very sur-
prising since little heat of activation is required for this type of reaction. Figure
6 depicts a type of oxidation-reduction at low temperatures. When iodine

3000

4000 5000 6000

WAVELENGTH ANGSTROMS

7000

Fig. 5. Chlorophyll b in 15% dipropylamine diluted with equal proportions of
propane and propene. A chemical readjustment toward equilibrium occurs

between 170°K and 75°K.

is finely divided it rapidly dissolves in isoprene at the temperature of dry-ice,
193°K. A brown solution forms at the solid-liquid interface but it decolorizes
very quickly, becoming colorless a little distance from the iodine surface. In
the light of other investigations it was surmised that the solution is brown
because of the presence of a 1:1 (molecular iodine-hydrocarbon molecule)
addition compound which possesses a characteristic absorption band in the
ultraviolet region. To build up any appreciable concentration of this compound
it would evidently be necessary to make solutions of iodine in isoprene below
193°K. When a solution of isoprene in propane (to which propene had been
added to increase the solubility of isoprene) at the temperature of liquid
nitrogen (77°K) is mixed with a solution of iodine in propane and propene.

Chemistry and Biochemistry at Low Temperatures

177

the new band anticipated in the ultraviolet does not appear within a day or
two. Figure 6 indicates what happens when such a solution is warmed. At
146°K the absorption band shown is due to the iodine-propene molecular
addition compound which has been identified in a previous experiment. At
150°K appears the anticipated new band arising from the compound iodine-
isoprene. At 154°K, this band quickly disappears irreversibly and at the same
time decoloration of the solution occurs. The molecular iodine has been removed,
presumably by the halogenation of the double-bond system of isoprene, just

0.

q:
o

(J)

CD

WAVELENGTH

Fig. 6. Isoprene dissolved in 1 : 1 propane-propene to which iodine dissolved in
1 : 1 propane-propene has been added. The new absorption band which appears
at 1 50°K is due to a 1 : 1 molecule addition compound of the iodine to isoprene.
Its disappearance at 154°K is due to an irreversible reaction, probably
halogenation across the double bond.

as had occurred when solid iodine reacted with isoprene at the temperature
of dry ice. This oxidation appears to require the prior formation of the inter-
mediate molecular addition compound stable at about 150°K at the concen-
trations employed.

By investigating the properties and reactions from the lowest practicable
temperature upward we would observe the appearance of new thermally
activated states and their subsequent reactions.

1 78 Simon Freed

In analogy with the phenomena illustrated we would expect that a knowledge
of biochemical and even biological processes of considerable value may be
gained by investigations at low temperature. Support for these expectations
comes mainly from recent investigations directed toward the preservation of
cells, tissues, and entire organisms. Even more cogent for our purposes are
the instances of partial preservation at low temperatures which becomes more
effective at still lower temperatures. Unless explicit references are given, the
following examples are drawn from the excellent review by Audrey U. Smith (3).
For example, H. F. Smart found that twenty-one species of bacteria, yeasts,
and molds continued to multiply in frozen media at 264. 1°K. Sizer and Joseph-
son found that lipase was active at 248. 5°K, tryptic digestion proceeded at
258°K, and that invertase continued to hydrolyze sucrose at 255°K. At 203°K,
however, they could detect no hydrolysis during several weeks. In the preser-
vation of red blood cells, about ten per cent deterioration occurs per year at
dry ice temperature, 193°K, but scarcely any loss is incurred when they are
kept at the temperature of liquid air, 80°K. Ovarian tissue failed to survive
nine days at 193°K but survived more than a year at 80°K under otherwise
similar conditions (4). Revival of rats after cooling to 273. 5°K was reported
by Andjus (5, 6).

Irreversible reactions are then clearly progressing at low temperatures,
in red blood cells and ovarian tissue at 193''K and at somewhat higher tempera-
tures in the enzymatic reactions. If the simple reactions such as those of isoprene
and iodine, chlorophyll and propylamine serve as models, the irreversible
reactions are preceded in their first and intermediate stages by reversible reactions
at still lower temperatures.*

Becquerel found that rotifers, spores of bacteria, non-sporing bacteria,
algae lichens, mosses, and seeds of higher plants, after having been dried in
a vacuum of 10^^ mm Hg over barium oxide, could be successfully kept at the
temperature of liquid helium (4°K). Parkes showed that human spermatozoa
survived exposure and storage at 80°K. Ovarian, testicular, pituitary, and
adrenal tissue have given functional grafts after storage at 80°K, especially
if glycerine was added. Luyet established that vinegar eels, spermatozoa
muscle fibres of frogs, and hearts of embryonic chicks could be revived after
sudden cooling to the temperature of liquid air (80°K). It is then not surprising
that enzymes have been cooled to such temperatures without loss of subsequent
potency. It would seem then that a number of biochemical and biological
processes are available for study at low temperatures.

I shall consider both homogeneous and heterogeneous solutions. The
first implies that solvents must maintain all the reactants in solutions fluid
at low temperatures. It would seem well worthwhile to employ conventional
solutions at as low temperatures as possible, and aqueous systems near zero
degrees or under supercooled conditions. It has been shown (8) that proteins

* Lovelock (7) ascribes the deterioration of red cells to a physical mechanism rather than to a
chemical process, namely, that the dissolution of lipoprotein and other components of the cell
membrane proceeds more rapidly than the biochemical processes can repair them at the low
temperature. Since the lipoprotein etc. is presumably bound as an integral part of molecules
composing the membrane material, the physical process may also be initiated by reversible
chemical transformations.

Chemistry and Biochemistry at Low Temperatures 179

such as enzymes are soluble in some non-aqueous solvents and that a few
enzymes can be recovered with virtually their full potency. Since some of the
solvents have melting points below that of water they can be utilized for investi-
gations of solutions of proteins at relatively low temperatures. It appears
entirely possible that had the solution process been carried out at lower tempera-
ture a larger fraction of the enzymes would have been recovered without
deterioration. Indeed it may prove fruitful to undertake studies at low tempera-
tures of the first stages of reactions which are toxic at ordinary temperatures
since the toxic substances may be removed at temperatures so low that httle
permanent injury is done to the enzyme or organism.

In analogy with the dissolution of finely divided chlorophyll and iodine
by solvents at low temperatures it is to be expected that at low temperatures
heterogeneous reactions are also possible between substances in solution and
biological materials having high specific areas. Ready-made for such reactions
with solutions seem sections of tissue with water removed by freeze-drying.
Likewise Becquerel's procedure of removing water by pumping at room
temperature would prepare material for reaction at low temperature. Some
of the reactions with the surfaces constitute a generalized staining. Many
staining processes are acid-base reactions and would be expected to be rather
rapid at low temperatures. As has been remarked, molecular steric factors are
as a rule more specific at the lower temperatures in general; hence finer dis-
criminations between structures within the surfaces are to be anticipated.

REFERENCES

1. E. V. Sayre, D. G. Miller, and S. Freed: Symmetries of electric fields about ions in
solutions. Absorption and fluorescence spectra of europic chloride in water, methanol,
and ethanol. /. Cfiem. Phys. 26, 109-113 (1957).

2. D. G. Harris and F. P. Zcheile: Effects of solvent upon absorption spectra of chloro-
phylls A and B. Bot. Gaz. 104, 515-527 (1943).

3. A.U.Smith: Eifects of low temperatures on living cells and tissues. In: Biological Applica-
tions of Freezing and Drying, tA. by R. J. Harris, 1-62, Academic Press, New York
(1954).

4. A. S. Parkes and A. U. Smith: Regeneration of rat ovarian tissue grafted after exposure
to low temperatures. Proc. Roy. Soc, (B) 140, 455-470 London (1953).

5. R. K. Andjus: Sur la possibilite de ranimer le rat adulte refroidi jusqu'a proximite du
point de congelation. C.R. Acad. Sci., Paris 232, 1591-1593 (1951).

6. R. K. Andjus and A. U. Smith: Revival of hypothermic rats after arrest of circulation
and respiration. J. Physiol. 123, 66-67 (1954).

7. J. E. Lovelock: Physical instability and thermal shock in red cells. Nature, Lond. 173,
659-666 (1954).

8. M. J. Loiseleur: Sur quelques proprietes des proteides en solutions organique. Bull.
Soc. Chim. Biol. 14, 1088-1100 (1932).

J. J. Katz: Anhydrous hydrogen fluoride as a solvent for proteins and some other bio-
logically important substances. Arch. Biochem. Biophys. 51, 293-305 (1954).
E. D. Rees and S. J. Singer: A preliminary study of the properties of proteins in some
nonaqueous solvents. Arch. Biochem. Biophys. 63, 144-159 (1956).

1 80 Simon Freed

DISCUSSION

Mahler : I can see where this might be useful in the study of the rate of formation of
enzyme-substrate complexes. This is a reaction which proceeds much too rapidly to be
measured by most ordinary techniques. It is only with very rare and very stable enzyme
complexes and by using very interesting and very sensitive experimental devices that Chance*,
for instance, has been able to study this at ordinary temperatures. But if one can find the right
kind of solvent for both substrate and enzyme — -there is no reason to assume that some of
these solvents might not work — one might be able spectroscopically to study the rate of
formation of enzyme-substrate complexes at low temperatures.

* B. Chance and G. R. Williams: The respiratory chain and oxidative phosphorylation.
In: Advances in Enzymology, ed. by F. F. Nord 17, 65-134. Interscience, New York. (1956).

INFORMATION CONTENT OF TRACER DATA
WITH RESPECT TO STEADY-STATE SYSTEMS*

MoNES Berman and Robert L. Schoenfeld

Division of Biophysics, Sloan-Kettering Institute, New York

Abstract — A method for the quantification of information in data from tracer experiments
on steady-state systems is presented. It is shown that if the system is represented by n com-
partments a point in an n^ dimensional space can serve to represent a specific model. Further-
more, uncertainty about the system due to statistical fluctuations and incomplete data can be
represented by regions in the n"^ dimensional hyperspace. A unit of information for such a
system is defined and serves as a measure of the amount of information necessary to determine
the system to within a desired accuracy.

In order to express the data in terms of the generalized n^ dimensional space, a set of
invariants is defined for the data. A concise matrix relation is shown to exist between the
invariants of the data and the parameters that characterize the compartmental system. The
matrix relation allows mappings between the data and the system.

The method presented is applicable to any compartmentalized system that shows linear
kinetics.

I. INTRODUCTION

This paper is concerned with the quantification of information contained
in data from tracer experiments performed on steady-state biological systems.
In general, the same set of data may be analysed in terms of different systems
of various degrees of complexity. To define the information content of the
data, therefore, it is necessary to specify the system in terms of which the data
are to be analysed.

It can be assumed for many tracer experiments that the system! consists
of a discrete number of compartments (or pools) each representing a locali-
zation or chemical state of the labeled material, with exchange of molecules
between compartments. The rate of exchange of the unlabeled molecules
between compartments is in general a non-linear function of the amounts of
material in the compartments. If, however, the system is in a steady state and
the amount of the tracer is sufficiently small compared to its unlabeled isotope,
the rate of exchange of the tracer may be treated as a linear function of the
amounts of labeled material in the compartments (1).

The problems that arise in treating the data of tracer experiments are:
first, to define the information content in the data, and second, to translate
the information in the data into values of the system parameters (the turn-over
rates of the compartments). In addition, it is desirable to have a measure of

* This work was supported in part by the U.S. Atomic Energy Commission Grant
AT(30-1)-910.

t For this paper, the word 'system' will be used to mean a specific number of compartments
independently of how they are interconnected. The word 'model' will refer to a specific
configuration of the system.

181

13

182 MoNES Berman and Robert L. Schoenfeld

uncertainty in the values determined for the system parameters. The uncer-
tainty in these values arises from the fact that the collected data may not be
sufficient to define the system completely and that the collected data have
associated fluctuations.

A method for the quantification of the information in data and the systematic
formulation of models consistent with it is presented here. The information
content in the data is expressed by a set of invariants, and a concise matrix
relation is shown to exist between the invariants of the data and the system
parameters. Uncertainties in the data due to incompleteness or fluctuations
are mapped into a generalized co-ordinate space which also represents the
degrees of freedom of the system parameters and their uncertainty. The
uncertainties in the data are expressed in terms of regions in the generalized
co-ordinate space in such a way as to suggest a criterion for their quantification
with respect to the system.

II. DATA INVARIANTS AND SYSTEM PARAMETERS

The response of the system to a tracer injected into any one compartment
can be expressed in terms of the amounts of tracer in the various compartments
as a function of time. If we define the probability per unit time for a transition
from any compartment / to compartment j as A^^, then the kinetics of the
tracer in the /th compartment of an n compartmental system can be represented
by the following set of differential equations :

^^ = -K^iit) +lh^qlt) (/ = 1, 2, • • •, n) (1)

where ^^(0 is the amount of tracer material in the ;th compartment at time t
and

hi ^ i hi (2)

is the probability per unit time that any molecule in compartment / will leave
that compartment.

The inequality sign expresses the possibility that a molecule may leave the
entire system from compartment / as in the case for open systems.

The solution of the set of differential equations (1) is:

n

q,{t) = I A,, e-^' (3)

i=i

In a recent paper (2) we have pointed out that data expressed in the form of
equation (3) have the following properties:

(a) There are at most n a^- in the data and these are invariants of the system
and independent of the initial conditions or site of measurements.

(b) The Ay.^ represent n^ independent variables in the data. Specification of
the initial conditions reduces the Aj.^ to {n^ — n) independent variables which
are a function of the system parameters only. The Aj^^ thus represent {n^ — n)
invariants of the system parameters.

Information Content of Tracer Data With Respect to Steady-state Systems 183

(c) The n a,- and rr" Aj.j comprise a necessary and sufficient set of data to
define uniquely the parameters of the system.

(d) A simple matrix relation (3) exists between the Aj^^ and a,- of the data and
the A,y of the system. This relation can be written:

Ml = \A l«l

or

where

I3I

— Aj2 — Aj3

/122 — "^

23

1

32

a =

h

33

ai

(-11

(4)
(5)

A,

11
1

'31

All
-^22

^32

'13
'23
^33

0
0

0 0
iy.2 0
0" a.

Equation (5) expresses the system parameters in terms of the invariants in
the data. If these invariants are known, the fractional turnover rates, Aj-;,
can all be determined. However, in most cases the experimental data are
incomplete in that certain of the A^j and a^ are not known. For these cases,
an infinity of models mathematically consistent with the data can be obtained
from equation (5) by inserting arbitrary values for the unknown Aj.j and a^,
preserving the initial conditions and other constraints in the data. Most of
these arbitrary models, however, will be physically meaningless because some of
the fractional turnover rates will be negative. Consequently, it is necessary to
investigate what range of values of the unknown A^^ and a, correspond to
physically meaningful models. This can be done by relating variations in A^^j
and a.; to variations in the X^j.

One may define (2) a matrix |P| in such a way that the product \PA\ will
preserve the known A^j. The number of variables in \P\ will be equal to the
degrees of freedom in the Aj^j. If both sides of equation (4) are premultiplied by
the matrix \P\ this equation can be rewritten:

(6)
(7)

a

\PXP-'^\ \PA\ = \PA\
which is of the form

[A'l l^'l = |/1'| |a|
where

M'l = l^^l (8)

\l'\ = \PKP-^\ (9)

Equation (9) expresses a mapping of the matrix \X\ corresponding to varia-
tions in the unknown Aj,j only. It also represents a general solution of all
models mathematically consistent with the data in terms of a minimum number
of variables. This solution is expressed in terms of an arbitrary model represented
by the matrix \X\.

Similarly, we can define a matrix \D\ so that the product |aZ)| will preserve
all the known a^. Incorporating this into equation (4), we get

|;.^Z)^-i||^| = |y4||aZ)| (10)

1 84 MoNES Herman and Robert L. Schoenfeld

which is of the fonn

mMI = MIH (11)

where

|a I = |ax^|

|A'| = \UDA-^ (12

Equation (12) represents a mapping of the matrix |A| in terms of the variations
in the unknown a^ only.

By applying the restriction that every fractional turnover rate must be

positive,

r,, ^ 0

A',,^iA',i (13)

i = \

equations (9) and (12) limit the range of values of the variables in the matrices
\P\ and \D\. Since these variables are all independent, they represent a co-ordinate
space of dimension equal to their number. Every point in this space specifies a
set of values for the variables in the matrices |P| and \D\ and, thus, defines a
model through equations (9) and (12). The restrictions on the range of values
of the variables as expressed by equation (13) correspond to a region in the
co-ordinate space in which all physically meaningful models must lie.

The choice of the starting point for the transformations indicated above is
completely arbitrary and does not affect the final result. Any mathematically
consistent model leads to a region in the mapping space corresponding to
proper physical models.

III. UNCERTAINTY MAPPINGS IN GENERALIZED SPACE

We now wish to examine the problem from a somewhat different point of
view. The system is represented by n^ X^^, generally independent of each other.
We can, therefore, consider the X^^ to represent an n^ dimensional space, and any
point in that space as a specific model of the system. It was also indicated
earlier that the data could be represented by a set of invariants composed of
n oij and {n^ — n) A^j or a total of n^ invariants. Hence, the transformation
from the data space to the X^^ space is dimensionally consistent and unique.

This means that a complete set of A^j and a^ corresponds to a point in the
\X\ space, and vice versa. By definition, however, the values of the A,,- must all
be positive. Consequently all the models must lie in a restricted region of the
\X\ hyperspace. This restriction carries over to the data space, limiting the region
in which the Aj^j and a^ may lie.

Any specified A^j or a_, implies a one dimensional constraint in the data
space. This carries over as a one dimensional constraint in the \X\ space, and
restricts all models to a surface in the hyperspace. If, however, the value of
A^j or oij is known only within a certain range, the surface has correspondingly a
certain thickness.

When several A^^ or a^ are known, the dimensions of the space in which all
models must he is reduced by a corresponding number. Statistical uncertainties

Information Content of Tracer Data With Respect to Steady-state Systems 185

for any of the known values correspond to similar uncertainties along the
appropriate co-ordinates in the hyperspace.

Thus, if all Aj,j and a^ are known exactly, a point in the hyperspace of n^
dimensions specifies the model. If all the data are known to within a certain
statistical precision, the most likely model is estimated as a point in the n~
dimensional space surrounded by a region that corresponds to the statistical
uncertainty. If some Aj^j or a_, are unknown, the corresponding dimensions in
the n^ dimensional hyperspace extend to the limits imposed by the relation that
all Xjj are positive.

IV. UNIT OF UNCERTAINTY

Based on the point of view presented, we can define a unit of uncertainty
to be a certain volume of the hyperspace. The size of the volume so defined is
arbitrary; it may correspond to a volume that is equivalent to the actual
standard deviation in the data, or to some convenient standard deviation that
may serve as a reference. The information necessary to define the system can
then be expressed as the number of binary choices, or bits of information,
necessary to reduce the total uncertainty space to the size of a defined unit.

V. CONCLUSION

The treatment presented provides a framework in which information in data
from tracer experiments on steady-state systems can be quantified in terms of a
compartmental system and its parameters. Before the information can be
quantified, however, a number of compartments has to be chosen for the system.
Unless this is known from independent sources, the method in choosing the
number of compartments is based on the minimum number of exponential terms
that 'reasonably' describe the data. This, at present, is by no means a unique
procedure.

It was shown in this treatment that a model representing the system can be
expressed as a point in a generalized co-ordinate space, and that any uncertainty
in the system can be represented by a certain region in that space. The nature
of the uncertainty (whether incomplete data or statistical fluctuations in the data)
did not matter in the treatment.

There is, however, one difference in the regions of the hyperspace corre-
sponding to these two sources of uncertainty. The difference is in the probability
that any model in the region represents the true system. In the case of incomplete
data, the probability density over the entire region is assumed constant; that is,
every model in the region is considered equally probable. In the case of statistical
fluctuations, however, a certain point or unit volume represents the most likely
model, and the rest of the points or unit volumes decrease in probability in a
manner governed by the statistics of the data.

The region in the |A| hyperspace can serve to define the information content
in the data of the system as a whole or of each parameter of the system, namely
the turn-over rates, separately. The latter can be obtained by investigating their
values over the bounded region.

One need not necessarily deal with all the dimensions of the hyperspace. One
can express the uncertainties in terms of a subspace whose dimensions are equal

] 86 MoNES Berman and Robert L. Schoenfeld

to the degrees of freedom of the system, as imphed by equations (9) and (12).
In this case, however, the statistical variations of the collected data cannot be
represented since their dimensions are omitted. Any new data to be collected,
however, can be represented in this subspace. The significance of any new data
can also be evaluated by the relative reduction in the size of the region in the
subspace. A unit of uncertainty may be defined for this subspace as was done for
the hyperspace.

In references (1) and (2) it was shown how information about the system from
steady-state measurements and thermodynamic considerations can be combined
with tracer data to form a unified methodology in reducing the uncertainty
about the system. The treatment presented here can be extended to include such
additional information.

Whereas the concepts presented here are relatively simple, the application to
specific problems involves considerable work. One can handle two or three
compartmental systems with few degrees of freedom fairly easily using a desk
calculator. The handling of more complex systems becomes quite time con-
suming. It is hoped that a programming of this on digital computers can be
worked out for routine applications.

REFERENCES

1. M. Berman: The formulation of biological models from tracer and steady-state data.
Ph.D. Thesis, Polytechnic Institute of Brooklyn (unpubUshed) (1957).

2. M. Berman and R. Schoenfeld: Invariants in experimental data on linear kinetics and
the formulation of models. /. Appl. Phys., 27, 1361-1370 (1956).

3. H. Margenau and G. M. Murphy: The Mathematics of Physics and Chemistry, chap. 10,
Van Nostrand, New York (1943).

THE DOMAIN OF INFORMATION THEORY

IN BIOLOGY*

Henry Quastler

Brookhaven National Laboratory, Upton, New York

In the proper course of events, a theory is introduced to account for a specific
body of facts ; then nobody will presume to expatiate upon the domain of the
theory. With information theory and biology, the situation is less simple. The
modern development of the theory stems largely from C. E. Shannon's concern
with certain problems of communication engineering (1). I have heard Shannon
say that he was somewhat dubious about the extension of his results to remote
fields, and that he felt that people working in other disciplines might do
better to develop their own theories. This is not what happened. Shannon's
theory has been taken up with enthusiasm by psychologists, linguists, historians,
planners, librarians, sociologists, and by biologists with a wide variety of
interests. Motives for such generalizations were supplied by Wiener, who
pointed out that all control (in the animal and in the machine) depended on
communication, and that all communication involved measurable quantities of
information (2) ; and by Weaver, who emphasized the great generality of the
information concepts in a searching study (1).

It appeared then that information theory was a tool made to order to deal
with a vast variety of problems. This variety, however, is not limitless. There-
fore, a discourse on the domain of information theory is indicated. One part
of this discourse will deal with the negative domain, or with some of the limita-
tions of the theory. The other part will be concerned with positive applications ;
it is largely an attempt to give clearer definition to the somewhat vague hopes
most people have when proposing to apply information theory.

It is curious that applied information theory produces rather violent reactions,
some of them negative. Certainly, it is entirely possible that every biologist
who works with information theory, or any other systems theory, is wasting
his time. But this, of course, applies to anybody who works with a new theory.
It is difficult to see how applying information theory should irritate people —
unless the cause should be the very pleasure of gently playing with the theory.
Every scientist is aware that there is a 'difference between the labor of thought,
and the sport of musing', and knows well the danger inherent in the latter.
To go on with Dr Johnson: 'There is nothing more fatal to a man whose
business is to think, than to have learned the art of regaling his mind with those
airy gratifications .... This is a formidable and obstinate disease of the intellect,
of which, when it has once become radicated in time, the remedy is one of the
hardest tasks of reason and of virtue. Its slightest attacks, therefore, should be

* Research carried out at Brookhaven National Laboratory under the auspices of the U.S.
Atomic Energy Commission.

187

188 Henry Quastler

watchfully opposed' (from The Rambler). Is this why so many scientists do
not mind too much having collected a lot of useless data but dread to be
found working with a useless theory ?

I. APPLICATIONS

Every kind of structure and every kind of process has its informational
aspect and can be associated with information functions. In this sense, the
domain of information theory is universal — that is, information analysis can be
applied to absolutely anything. The question is only what applications are
useful.

1 . Use of Basic Concepts

The basic concepts of information theory — measures of information, of
noise, of constraint, of redundancy — establish the possibility of associating
precise (although relative!) measures with things like form, specificity, lawful-
ness, structure, degree of organization. This alluring promise has introduced
the information concepts into the thinking of many biologists. The results of
conceptual applications range from harmless modernisms of language to very
serious reasoning. In particular, the information concepts seem to lend them-
selves readily to dealing with the problems of emergence and destruction of
order in complicated systems.

The problem of emergence of order is usually treated in terms of Darwinian
machines, large more or less random assemblies of parts which can both
function and, in some manner, register the results of their functioning. The
resulting feedback loop produces some order amazingly fast (3, 4). The theory
of random networks is a very active field, and some very competent men expect
that the main contribution of information theory to biology (and to other
fields concerned with very complicated systems) will come from this endeavour.

Closely related is the problem of destruction of orderhness. In biology,
this is the problem of aging and decay; it is the topic of a major fraction of
this conference (5, 6, 7).

2. The Representation Theorem

The use of the basic concepts of information theory becomes more powerful
if one considers that the behavior of information measures follows certain rules;
these rules are the theorems of information theory. There are two basic theorems
which I like to call the 'representation theorem' and the 'noise-and-redundancy
theorem'. The first has to do with the possibility of representing one kind of
information by another kind of information. There are absolutely no quahtative
limitations as to how information can be represented ; but, there is a quantita-
tive limitation: any physical entity can assume only a limited number of
distinguishable states, and this limits the degree to which it can represent
information. This degree is further modified by the rules of selecting successive
states. The applicability of the representation theorem depends to a high degree
on knowing the process by which states are selected.

The representation theorem applies every time information is transferred —
because the transfer does involve representation of the information existing

The Domain of Information Theory in Biology 189

in the transmitter, in the medium and, finally, in the receiver. It can thus be
stated as follows: A source cannot transmit more information than it has, a
receiver cannot register more information than it can display. This sounds
trivial, but the point is that information contents can be precisely estimated
in ways which are not trivial. The representation theorem implies that it is
possible to establish an upper bound of the flow of information simply by
investigating the terminals. It is, thus, a one-sided conservation principle; being
one-sided, it is not as strong as the two-sided conservation principles which are
so commonly used in physics. It becomes stronger in situations where one
may assume that the inequality approaches an equality.

There are two conditions which are conducive to the establishment of full
conservation of information: one, that information is a valuable and critical
commodity, and two, that noise can be minimized. The concept that informa-
tion is the most precious commodity for living things has been formulated
strikingly by Schroedinger in his assertion that 'living things feed on orderli-
ness'— that they feed because they need fresh supplies of orderliness, not of
energy or matter (8). The need for fresh supplies of orderliness presupposes
that orderliness is somewhere lost, that is, that noise is present. This, however,
does not mean that noise is present everywhere. Some processes may occur in
'clockwork fashion', without loss of information. That is the case which
Schroedinger classifies as 'generation of order from order'. He suspects that
each individual act of transmission of genetic information from parent to
offspring occurs without serious loss of information. This idea agrees with the
current (Watson-Crick) model of DNA duplication; it recurs in Gamow's and
YcAs' models of information transmission from genetic to somatic material (9).

3. The Noise-and- Redundancy Theorem

Infonnation transfer from one body of information to another is not often
with clockwork regularity. As a rule, interferences occur which will more or
less affect the process of information interaction. Interference can be of many
kinds: the worst kind of interference is one the results of which are not pre-
dictable in detail. In this case, some information will be irretrievably lost.
However, in general some but not all order is lost. It is one of the most significant
results of information theory to have shown that order and disorder can be
measured by a common yardstick. Hence, it is possible to investigate the
quantitative relations between total information, noise, and remaining order-
liness. The second basic theorem of information theory states that the amount
of information effectively transmitted is exactly the amount of information
transmitted minus the amount of information lost because of noise. This implies
that a source can transmit a certain amount of information reliably in the
presence of noise provided it transmits more than the desired amount of
information. This surplus must be distributed over the whole activity because it
is never known which portions of the total activity will be interfered with by
noise; necessarily, the surplus takes the form of redundant information. Thus,
the second fundamental theorem states precisely the relation between amount of
information to be transmitted, amount of information which will be lost through
noise, and amount of redundant information needed to make up the loss. Like
the first fundamental theorem, it is a one-sided conservation principle; it limits

190 Henry Quastler

the amount of order which can prevail in an 'order-from-disorder' situation.
Again, the one-sided conservation principle will become more powerful if it can
be assumed to approximate a two-sided conservation. However, very stringent
conditions must be fulfilled if one expects to use the second theorem. There is
some reason to believe that these conditions are at least approximated in some
biological situations; this is stated in Dancoff's principle (10).

Dancoff' s principle deals with the economics of information. In 'noisy'
situations, information is lost and errors will occur unless they are checked
by redundant information. Now, errors may be costly, but so is redundant
information; accordingly, the optimum amount of redundant information
will be not that which makes all errors vanish, but that which minimizes the
sum of the cost of errors plus the cost of redundant information, plus the cost —
in information units — of error checking. Dancoff's principle asserts that any
organism or organization which has gone through competitive evolution has
approximated such an optimum; that is, it will commit as many errors as it
can get away with, and use the minimum of redundant information needed
to hold errors to this level. It follows from Dancoff's principle that the amount
of redundant information in a system is bound to be limited, even if it is a
system of enormous information content like a living thing. This is of great
interest particularly in radiobiology, because what radiation does very effectively
is to destroy information.

4. The Estimation of Information Measures and the Search for Invariants

It may well turn out that the qualitative and semi-qualitative applications
of information concepts are going to be the most important contribution of
information theory to biology. But, even successful qualitative applications
have very little power in excluding the possibility that other sets of concepts
could have been used just as successfully; besides, all scientists like to take
measures. Thus, the problem arises of estimating information measures
associated with biological structures and functions.

One fundamental diflficulty appears immediately: information measures
are relative and not absolute ; hence, any information measure associated with
a given set of biological objects will depend on the set itself and on the scientist
who does the estimating. To be sure, one can establish objective bounds.
Thus, if a certain genetic locus is known to be capable of having thirty-two
distinct allelic states, which are transmitted to the offspring with equal prob-
ability given the proper conditions, then the information stored in this locus
cannot be less than five bits. If it is also known that the region containing
the locus under consideration comprises no more than, say, 20,000 atoms,
then the total information stored cannot be more than about 60,000 bits (10).
These brackets are safe, but they are too wide to be of interest. They can be
very much reduced if one introduces specific assumptions. For instance, if
the locus is known to contain no more than, say, 2 X 50 nucleic acid residues,
and if one assumes that the genetic information is completely coded in the
sequence of the residues on one strand of a double helix, with the information
carried by each residue corresponding to unconstrained selection from four
possibilities, then the upper bound is reduced to 100 bits — but its validity is
less absolute.

The Domain of Information Theory in Biology 191

Because of the relative nature of information measures, it will always
be up to the ingenuity of the biologist to find ensembles which result in useful
measures. In many cases, even the estimation of a limit is of interest: as in
Ehret's demonstration that a few bits could be sufficient to specify the
nature of cytoplasmic structures (11), or the result easily derived from
D'Arcy Thompson's work (12) that apparently considerable differences in
fonn could be coded in, say, a few nucleic acid residues.

The relativism of information measures is a basic difficulty in estimation ;
besides, the biologist will encounter a number of technical difficulties arising
from the fact that 'message sets' and 'selection rules' are not perfectly known.
A number of approximation methods for such situations have been worked
out (13).

The relative nature of information measures and the technical difficulties
of their estimation, cast some doubts on the usefulness of actual information
measures in biology. Only experience will show whether these doubts are
justified or not. Measures will be valuable if they lead to the discovery of
invariants. In psychology, some invariants seem to be crystaUizing out of
a number of measurements: there seem to be invariant upper limits for the
channel capacity for single activities; for the range of classes distinguishable
in a single act, etc. (14). In biology, independent estimates of information
transfer associated with three elementary biological functions (allelic, anti-
genic, enzymatic specificity) have yielded closely similar values (15). Much
more material will be needed before we can draw definite conclusions.

The analysis which underlies the estimation of information measures
presents certain novel features. Consider, for instance, the informational
analysis of a honnonal control system. The traditional approach consists
in isolating one hormonal function and one hormone after the other. In
principle, this quest never ends — although physiologists might hope that some
day they will run out of undiscovered hormones. The information theorist
attacks the problem from the opposite end. He will argue that each hormone
molecule constitutes a message from a control organ to a target organ, a
message which is diffusely broadcast through the blood stream. In general
each message must contain two parts, an address and an order. Actually,
one or the other part can be omitted. We can imagine a hormonal control
system in wliich only the addresses are specified — the 'order' may be completely
determined in the target organ, and be executed automatically upon receipt of
the only kind of hormone molecule with the proper address; or, the address
may be unspecific, but the order such that only the right target organ can
execute it. One would expect that the natural systems be somewhere between
these two extremes. For the sake of simplicity we will consider a system in
which only addresses are specified — the foiTnal results have complete generality.
Thus, each hormone will be represented only by the address of the target
organ. In the interest of detailed and accurate control, it is desirable to have
a maximum number of different addresses. Any duplication of addresses
will lead to concomitant responses in other organs. On the other hand, the
'reading' of every single address involves distinguishing it from all other
addresses; the greater the variety of addresses, the greater the labor in every
single act of recognition. A compromise is indicated between the demand

192 Henry Quastler

for a great variety of addresses and the contradictory demand to keep each
address simple. For any kind of system, there will be an optimum number of
different hormones; the actual number will depend on the relative strength
of the two competing needs. By Dancoflf's principle, we expect that the actual
number will not be too far from the optimum number.

We can add another line of considerations on the number of possible addresses.
In order to fulfill its function, the hormone molecule has to enter into some
kind of relation with the target organ ; most likely, it has to form a complex.
Now, the total surface area of any molecule that can enter into a specific
complexing process is rather limited, and so is the number of molecular con-
figurations available to living organisms; hence, a limited space accommodates
only a limited number of significantly different configurations — and this limits
the number of different hormones possible (and, incidentally, the number of
distinct antigens and antibodies, enzymes and co-enzymes).

The example illustrates the concern with the whole system which is charac-
teristic of many applications of infomiation theory. It also illustrates a rather
profound difference between the information theorist and many of his scientific
colleagues. The information theorist will remain fairly cool at the news that
another enzyme, or hormone, or vitamin has been isolated ; his basic question
is: 'How many more are there to be discovered?'

II. LIMITATIONS

Information theory could not possibly apply to a wide variety of situations
if it were sensitive to every detail in every situation. Like thermodynamics
(to which information theory is related) it has a vast domain of application,
and like in thermodynamics, the vastness of the domain is paid for by a limited
scope of every single application (16). The following four limitations deserve
emphasis : (i) information measures refer to ensembles and not to single instances,
(ii) they are relative and not absolute, (iii) informational capabilities are often
not fully utilized, (iv) information measures are related to other aspects of
systems such as utilities and mechanisms but the relations are not simple.
None of these observations is particularly profound, but each one has been
overlooked by competent investigators.

1 . Information Measures are Functions of Ensembles

Information measures are not defined for particular historical occurrences
or existing individual things; rather, they are defined for whole ensembles of
events that could happen, or things that could be. The information measures
are descriptive of the operations by which a particular item is selected from the
set of possible items, and are associated with the whole set and not with any
particular item that happened to be selected in a particular instance.

Ensembles are specified by their elements, by the classification to which
these elements are subjected, and by the probability measures associated with
the diverse classes. If these specifications are known, then the information
functions can be derived — but not vice versa. For example: if it is known
that a certain chemical system contains certain enzymes and certain substrates,
if the probabilities of the various coUisions and the probabilities of all possible

The Domain of Information Theory in Biology 193

outcomes of such collisions are known, then it is possible to derive a number
of information functions for this system; on the other hand, a given set of
information functions is compatible with any number of chemical systems.

2. Relativity of Information Measures

In the early applications of information theory to problems of communi-
cation, the ensembles to be used were virtually defined by the situation. Thus,
in dealing with Morse code, the element is clearly the single symbol, the classes
are dot, dash, letter space and word space, the probabilities are the large
sample frequencies. Similarly, in dealing with printed English as an objective
phenomenon, one natural unit (not the only one, though!) is again the single
symbol, and classes and probabilities can be determined from any large sample.
The situation is immediately more complicated if we deal with a particular
person's concepts of printed English; the 'subjective probabihties' are not the
same as the objective relative frequencies. Much confusion has come to
psychologists from disregarding the fact that the probability measures upon
which a subject bases his operations are not necessarily those known to be
correct — in one sense — to the experimenter (17).

There are situations where there is considerable leeway in defining the
elements, classifications, and probability measures of an ensemble, and accord-
ingly considerable variation in the infonnation measures which can be associated
with the situation. This is strikingly illustrated by the attempts to measure
the infonnation contents of molecules. Estimates have been based on con-
siderations of structure (10, 18, 19, 20) or function (15, 22). Recently, Rashev-
SKY and his associates (21) have shown that information measures can be
associated with the topological representation of molecules. Each of these
approaches yields some value of the information content of a molecule, and
these values do not have to be identical. Yet, every one of them is a legitimate
information measure. This may be disappointing, but hke all abstractions,
information measures are not 'right' or 'wrong' — they are only more or less
useful. In the case under discussion, we may legitimately ask how the various
ways of estimating information measures are related to the actual processes
of information storage and transmission by molecules, to reaction rates, to
the activity of antimetabolites, etc.

As a rule, the specifications of an ensemble do not result unequivocally
from the given situation. Consequently, information measures are not properties
but functions of a given situation — they are defined by the situation and the
ensemble used in dealing with it. Information measures are irreducibly relative;
they can be accurate and precise, but they cannot be absolute. The usefulness
of a particular information measure in a particular context will depend on the
way the defining ensemble is set up. Unfortunately, there exists no calculus,
no set of hard and fast rules which tells one how to select the most appropriate
elements, classifications, and probability measures. The choice must be made
by guess, and its ultimate justification is only in the results it yields.

3. Informational Capabilities and Performance

An informational capability represents an upper bound to some class of
informational performances — but a particular performance does not have to

194 Henry Quastler

approach this bound. One cannot transmit information through a channel
at a rate higher than the channel capacity, but it is very easy to transmit at a
lower rate. For instance: human capacity of transmitting information can
be limited on the input side, on the output side, or centrally; if the limitation
is central, then it can be due (a) to the limited channel capacity, but also to
limitations of (b) the rate at which discrete acts of information-processing
can be performed, of (c) the amount of information per single act, of (d) the
number of information-carrying components considered in each act, of (e)
the maximum amount of information per component, or finally, (f ) to inefficient
coding (14). Parallel situations are likely to exist in molecular biology. For
instance, Augenstine (18) discusses the fact that the amount of information
which can be coded into an amino acid sequence is considerably greater than
the amount of information needed to account for the functional specificity
of a protein. This could mean that the channel capacity is only fractionally
utilized, or that functional specificity is coded in an entirely different fashion.

4. Information Measures and Other Aspects of Systems

If the mechanism of a reaction is known, then the probabilities of all input-
output associations can be computed, and the information measures derived
from them. On the other hand, an infomiation measure does not define a
single mechanism — however, it imposes a condition with which input-output
tables and, by implication, mechanisms have to comply. For instance, in
the problem of the DNA-protein code studied by Gamow and Ycas (9),
"" • the infoiTnational analysis furnishes conditions which the code must fulfill
but does not yield the code itself. Accordingly, the informational analysis
has served, repeatedly, to reject a proposed mechanism. It can, of course,
never be used to prove a mechanism.

Amount of information is in general related to the utility of being informed
— but the relation is not necessarily one of simple proportionality; in fact,
the utility of information is not always a monotonically increasing function
of its amount. Similarly, the information content of a structure is in general
related to the difficulty of construction, but the relation is not one of simple
proportionality.

The 'amount of information' in a statement is related to its capacity of
carrying semantic information, but this capacity is rarely fully utilized (23).

III. CONCLUSION

I have tried to outline some of the applications and possible applications,
and I hope to have shown that there is much promise in this field. I have tried
to outHne some of the limitations of applying information theory— and I
hope to have shown that they are not serious, provided one is always aware
of them. To make more progress, we need much more mathematical work,
and we need very much more experimental work. In looking over the past of
information theory in biology, a very strong emphasis on theory— more or
hss rigorous— is obvious; although more theory is needed, the most pressing
need is now for a large body of good specific experiments. Also, it should be
rewarding to examine closely other related possibilities in theoretical biology.

The Domain of Information Theory in Biology 195

For some reason, our time has been (and still is) exceedingly fertile in producing
theories dealing with systems, or in reviving and greatly expanding existing
theories of systems. Information theory is one of several system theories —
a very rewarding one, I believe, but one with very specific limitations; it should
be useful to search specifically for theories with different limitations to supple-
ment information theory.

REFERENCES

1 . C. E. Shannon and W. Weaver: The Mathematical Theory of Communication, University
of Illinois Press, Urbana (1949).

2. N. Wiener: Cybernetics, J. Wiley and Sons, New York (1948).

3. R. W. Ashby: Design for a Brain, J. Wiley and Sons, New York (1952).

4. M. Eden: A probabilistic model for morphogenesis. This volume.

5. H. P. Yockey: An application of information theory to the physics of tissue damage.
Radiat. Res. 5, 146-155 (1956); and, A study of aging, thermal killing, and radiation
damage by information theory. This volume.

6. H. B. Jones: Some notes on aging. This volume.

7. H. A. Blair: A quantitative description of latent injury from ionizing radiation. This
volume.

8. E. Schroedinger : What is Life? University Press, Cambridge, England (1944).

9. G. Gamow and M. Ycas : The cryptographic approach to problems of protein synthesis.
This volume. M. Ycas: The Protein Text. This volume.

10. S. M. Dancoff and H. Quastler: The information content and error rate of living
things. In: Information Theory in Biology, ed. by H. Quastler, 263-273, University of
Illinois Press, Urbana (1953).

11. C. Ehret: Information content and biotopology of the cell in terms of cell organelles.
This volume.

G. Karreman: Topological information content and chemical reactions. Bull. Math.
Biophys. 17, 279-285 (1955).

E. Trucco: a note on the information content of graphs. Bull. Math. Biophys. 18,
129-135, (1956).

12. D'A. W. Thompson: Growth and Form, Cambridge University Press, Cambridge, England
(1952).

13. H. Quastler: Approximate estimation of information measures. \n: Information Theory
in Psychology, ed. by H. Quastler, 124-139. The Free Press, Glencoe, 111. (1955).

14. H. Quastler: Studies on human channel capacity. In: Information Theory, ed. by
C. Cherry, Academic Press, New York (1956).

15. H. Quastler: The specificity of elementary biological functions and the measure of
specificity. In: Information Theory in Biology, ed. by H. Quastler, 170-188; 41-71,
University of Illinois Press, Urbana (1953).

16. L. J. Cronbach: On the non-rational application of information measures in psychology.
In: Information Theory in Psychology, ed. by H. Quastler, 14-30. The Free Press, Glencoe,
111. (1955).

17. H. Quastler (ed.): Information Theory in Psychology, The Free Press, Glencoe, 111.
(1955).

18. L. G. Augenstine: Protein structure and information content. This volume.

19. H. J. MoROwiTz: Some disorder-order considerations in living systems. Bull. Math.
Biophys. 17, 81-87 (1955).

20. H.Branson: Information theory and the structure of proteins. In: Information Theory
in Biology, ed. by H. Quastler, 84-104, University of Illinois Press, Urbana (1953).

21. N. Rashevsky: Life, information theory and topology. Bull. Math. Biophys. 11,119-12)5
(1955).

196 Henry Quastler

22. P. D. Klein: Efficiency of information transmission by biochemical co-factors. This
volume.

23. R. Carnap and Y. Bar-Hillel: Tech. Rep. Res. Lab. Electr., Mass. Inst. Tech., no. 247
(1952).

DISCUSSION

A. Rapoport: It is admirable of biologists to look 'up to' physicists and mathematicians,
but it is somewhat embarrassing to physicists and mathematicians to be looked upon with
such confidence as a source of methodological gifts which can be immediately applied in
biological investigations. It is noteworthy that the greatest discoveries of the physicists are
stated in 'pessimistic' terms. They are statements about what cannot be done. For example
the First Law of Thermodynamics is essentially a definitive demolition of an age-old dream.
The law says in effect that the perpetual motion machine cannot be constructed. But it also
holds out a hope of a machine that will keep on working provided only that a large supply of
heat is available — the so-called perpetual motion machine of the second kind. The Second
Law of Thermodynamics puts an end to that dream. It says that such a machine cannot be
constructed either and prophesies the 'heat death' of the Universe. Maxwell introduced
his demon in the hopeful conjecture that the intervention of an intelligence might restore the
order lost by the continual increase of entropy. Szilard in his now classical paper showed
that this too is an illusion, that the demon must pay for the restored order by becoming
'disordered' (a biologist would say 'denatured') himself.

Yet it would be a mistake to consider these discoveries as admissions of defeat only.
Each has brought a broadened understanding; the First Law of Thermodynamics by revealing
heat as a source of energy ; the Second Law by revealing the role of entropy. Szilard's
investigation rests on quantum-theoretical principles and so provides an important juncture
between thermodynamics, information theory, and quantum theory. It appears, therefore,
that the grand discoveries of physics have a sobering effect. I think the principles of information
iheory are of a similar kind. Typically they are statements of hmitations. Their constructive
side is in defining the framework in which the search for new knowledge or for new means of
prediction and control must be confined.

SOME MEMBRANE PHENOMENA FROM THE
POINT OF VIEW OF INFORMATION

THEORY*

Herman Branson

Howard University, Washington 1, D.C., U.S.A.

Abstract — The methods of information theory and of irreversible thermodynamics are applied
to membranes. Equations are derived for the negentropy production of a membrane maintain-
ing a concentration difference. The results are converted to bits. When applied to typical
data for a nerve transporting Na+ against a concentration gradient, the equation gives for the
negentropy or information production,

H=7.3 X 10^^ bits/cm'' second.

Enumeration based on Na+ : Cl~ : K+ = 1 : 1 : 10 gives a value of

4.3 X 10'^ bits/cm* second.

In a classification of the significant problems of biophysics Danielli (1) listed
four. Two of these relate intimately to membranes and their role in biological
systems: cell permeability and cell electrophysiology. It is almost mandatory,
then, to inquire into the behavior of membranes from the point of view of
information theory. For if information theory is to have relevance to important
biological problems, a coherent relation should be exhibited for membrane
phenomena. This attitude was exhibited in the initial attempts to discuss
biological problems within this discipline in Quastler's pioneering book (2).
The formidable complexity of biological membranes is a recurring theme
in the immense amount of experimental data which are being accumulated.
Phenomena encountered in biological membranes may range from those
explainable by the assumption of simple pores of various sizes, to those requiring
charged pores, and on to those necessitating a picture of the surface as possessing
pores, binding sites, permeability barriers, enzymes, and transport mechanisms.
It is possible, however, to ignore the details of structure and specific mechanism
— as is usually the case in thermodynamics — and formulate a limited model
of membrane activity satisfactory to our analysis. Thus membranes may be
classified by the manner in which they react to or treat a given substance.
If we schematize the membrane as separating two media in each of which the
reference substance is soluble, calling one region the 'inside' and the other
the 'outside', we may introduce the following notation :

Indifferent: A membrane is indifferent to a substance if the concentration
of that substance is the same on both sides of the membrane
at all times. Thus Q = Q, for all /.

* This work has been supported in part by the U.S. Atomic Energy Commission,
AT(30-l)-892.

197
14

198 Herman Branson

Responsive : A membrane is responsive to a substance if tlie concentrations
of that substance differ on each side at the same time. But
neither concentration is zero. Thus, Q ^ Cq for some t.
Exclusive: A membrane is exclusive with respect to a given substance
if, for all time, the concentration on one side is finite but the
concentration on the other is zero. Thus, Q = 0 and Q 7^ 0,
or Q ^ 0 and Q = 0, for all t.
The analysis of this paper will be limited to substances to which a given
membrane is responsive. It must not be concluded, however, that indifferent
and exclusive substances are of no biological significance. There are examples
where seemingly the most important role of a membrane is its action to exclude
a given substance from the internal medium or keep a component from diffusing
out.

The preliminary work (2) on a responsive membrane attempted to derive
by the methods of irreversible thermodynamics an expression for the negen-
tropy production of a membrane maintaining a concentration difference.
The approach rested upon the concept that the entropy is an absolute maximum
at equilibrium. Hence any deviation from equilibrium would mean a decrease
in the entropy. Expanding the change in entropy, A^, in a Taylor's series about
the equilibrium point yields as the first approximation, since the first derivative
terms vanish at equilibrium,

A5=-l/2 2gj.m«i«m • 0)

Equation (1) was combined with some descriptive equations for the membrane
and the final result

^ = fta (2)

was deduced. In equation (2), H is the negentropy or the information (3), a is
the rate constant governing the rapidity with which the membrane would
approach uniform concentration on each side if it were not actively maintaining
the concentration difference and k is Boltzmann's constant (1.380 X 10"^^ ergs
per degree).

Equation (2) had to be examined to determine if it is apphcable to a mem-
brane maintaining a considerable concentration difference. Its significance
with respect to the relation

A5ir,. = A: In Q/Q (3)

had to be clarified (4). Equation (3) gives the irreversible production of entropy
for the passage of a single particle from concentration Q to the concentration
Co. If Co is greater than Q-, we have the situation postulated for the membrane,
thereupon A^'u-r. is negative and may be equated to information, H.

Derivation of the Rate of Production of Information

The methods of irreversible thermodynamics as presented by DeGroot (5)
are applicable to effect the derivation. Following DeGroot's nomenclature,
we have

^S = J^X, + J^nXm + h^, (4)

Some Membrane Phenomena from the Point of View of Information Theory 199

where A^" is the rate of entropy production. The J's are 'fluxes' and the A"s
are 'forces', u is energy, in matter, and // chemical potential. The J's are related
to the A"s through

Assuming an isothermal system, the A"s and y's are

X, = -^m^T J,-^

dt

dt

Whereupon, equation (4) becomes

AS = -J„, ^fl|T - J^ AmIT. (5)

Substituting into equation (5),

/* ^ //q + i^rin a
where a is the activity, we get

A^ = (R In ajao) ^ + 7? Am d/dt (In ajoo). (6)

dt

The a's refer to the activities in the two different regions.

Equation (6) is the basic relation replacing both equations (2) and (3). If we
assume that the activities may be replaced by the concentrations and that we
are concerned with the passage of A^ particles from a lower to a higher concen-
tration, Cq > Q, then equation (6) becomes

^^Ii=k-^ In Co/C, + Nk didt (In CJC,).

If the outside is taken to be very large with no change in concentration by the
addition of the particles from within,

H=A:^lnC./C,--^. (7)

Equation (7) gives the rate of decrease of entropy or the rate of production
of negentropy or information by a membrane which is transferring material
from a lower to a higher concentration where the particles leave at the rate
dNjdt and the concentration within changes at the rate dCjjdt. Thus one may
look upon equation (7) as the dynamic equation describing real transport. On
the other hand equation (2) describes a situation where there is no macroscopically
discernible change in concentration within or without. But inasmuch as the
membrane maintains a concentration difference, it is producing information
at the rate given to continue the imbalance.

200 Herman Branson

If the concentration within is stabihzed in such a manner that for a sUght
change the system returns to the resting value following the equation

(1/Q) dCJdt = -a (8)

where a is analogous to the rate constant appearing in equation (2), equation (7)

may be written

dN
i^ = A: — in Co/C, + kN^- (9)

Equations (8) and (9) seem harmonious with equation (2) interpreted as being
applicable to the resting case when there is no net transport or to actual trans-
port with the condition that Cq — Q.

The application of equation (9) to a fluctuation should follow this sequence.
Initially Cq = Q, and AA'^ particles jump from one solution to the other.
The rate of negentropy production or the rate of production of information
is /^ = A///A? = k^Noi. At the end of this fluctuation equation (9) becomes
for the next fluctuation kANcc

IC -1- AC\
n = A:(AA^/A/) In L I ^ J + k^N^. (10)

Suppose that the next fluctuation is the movement of A A'' particles in the direction

opposite to the first fluctuation in the same interval of time, A?. We should

expect fi to be the negative of its original value. Expressing the logarithm

1 + AC/C
in equation (10) as In -j . , and making use of the relation

In 1^ = 2(A' + A-^/S + • • •), for X'' <\,

the equation becomes

ii^lk AMI At AC/C + kAN(x
but

AN I At AC/C = ANIC AC/ A/ = -AA^a

from equation (8), and since AC is negative in the second fluctuation.

Finally: AH = —kANoL At.

Thus the system returns to the equilibrium position on the entropy surface
with an increase in entropy exactly equal to the decrease of entropy experienced
in the first fluctuation.

Analysis for Charged Particles

In the derivation of the basic equations (6) and (7), the chemical potential
was employed, which limits the applicability of the analysis to uncharged
particles. To derive the corresponding equations for an ion, the electrochemical
potential /li' replaces ju,

fx' = juq' + RT\na-^ZF(i>

where Z is the valence, F is the Faraday, and 0 is the potential. Substituting

Some Membrane Phenomena from the Point of View of Information Theory 201

and carrying through an identical analysis as followed in deriving equation (7),
H becomes

A --= k[{dNldt) In CJC, -f A^a] -]- {ZqlT)[cINldt(cf>, - - <f>,) ^ ^

where q is the numerical value of the charge on the electron, when the membrane
transports ions from the lower concentration to the higher concentration,
C, - Co.

Application to a Nerve

Data on the movement of ions across the nerve membrane may be substituted
into equation (11) to obtain numerical values for ff. The knowledge of the
transport of ions across the nerve membrane although quite extensive is still
not complete enough to permit unequivocal choice of a model. There are
two possibihties which suggest themselves for consideration. In the first,
following the transport of an impulse, the nerve returns to its resting condition
with respect to the concentration of Na+ or K+ before it can pass another
impulse. The resting potential is reached at the beginning of this period.
Calling this example model one, we have these data for a squid axon (6):

[K+] Co =10 C, = 410

[Na+] Co = 460 Q = 49
[C1-] Co = 540 Q = 40

in units of millimoles/kg. At 300°K, (f)Q — (f)^ = 50 mV with the outside positive.
If the length of the recovery period is taken as 1 millisecond, the equation (11)
becomes*

n = kidNjdt) [In Co/C, + (ZqlkT)(cf>, - cf>,)]. (12)

The first term on the right yields for the concentration gradient above

for K+, // = 5.3 bits/ion-unit time,

for Na+, H — 3.3 bits/ion-unit time,
for Cl~, li = 3.7 bits/ion-unit time.

* In applying equation (1 1) the second and fourth terms contribute negligibly. Examining
the two terms with the data that 3.7 /iju moles of Na+ enter per impulse per cm*, a cylindrical
nerve of 100 ^i radius with unit surface area would have,

Area = iTrrl = 1 cm^

Vol = 7Tr^l= 5 X 10-' cm';

and assuming that the nerve has the density of water, the section would weigh 5 x 10' gm.
So 49 m mole/kg would correspond to 2.5 x 10^ jufi mole/cm', whereupon for sodium

H = 2.25 k{dNldt) + 1.5 x 10"° kN per millisecond

= 2.25 kidNjdt),
since

AAT = N and A/ is taken as 1 millisecond.

202 Herman Branson

The term ^ (<^o -«/•.)= 1 -94

at 300°K. Using this value, the combined rates for both the concentration and
electrical terms are

K+: H = 2.5 bits/ion-unit time,

Na+: //= 6. 1 bits/ion-unit time, (13)

C1-: H = 0.9 bits/ion-unit time.

log2 e
These values have been arrived at by multiplying equation (11) by — j — to

convert from k units to entropy units.

[The conversion factor was derived in a previous paper by the author in

considering proteins (2). It is easily shown that log,, x logj, y = 1, which means

that this conversion factor is the same as that derived by Linshitz (!) and others

(8).]

On the basis of the first model the 3.7 /^/^ moles of Na+ entering during
the impulse would be extruded during the millisecond following the return
to the resting potential. This time interval requires that the nerve produce
information at the rate

7^ = 9.3 X 10^5 ergs/°K cm^ sec,
or (14)

fl=\35 X 1016 bits/cm^sec.

The alternative model is that the nerve does not extrude the Na+ in so short
a time. Rather the nerve passes it from within to the outside at a rate of
20 i^fjL mole/cm^ second (9). However, the acceptance of this view does not
alter equations (13). Inserting this value for Na+ in equation (12) results in

if = 7.3 X 1013 bits/cm2 sec. (15)

The experimental results seem to favor this model; thus equation (15) is the
more reasonable result in comparison with equation (14).*

The alternative mode of viewing the nerve according to information theory
makes use of the concept that the sodium ions are chosen from the pool of ions
within the nerve by some mechanism. Within the nerve the ratios are
Na+ : CI" : K+ = 1 : 1 : 10. The mechanism chooses the Na+ from this group,
requiring logg 12 bits of infomiation for each Na+ selected. This value,
3.57 bits/ion, leads to

i^ = 4.3 X 1013 bits/cm2 sec, (16)

for the nerve based on the second model which transports 20/^// moles cm^ sec.
of Na+ against the concentration and electrical gradient. Assuming that the

* Dr Leroy Augenstine made the astute observation with respect to equation (14) in the
discussion that it is consistent with a value of 10^ A" for the area of a protein and that on 1 cm^
of nerve there could be 10^^ proteins transporting one ion per millisecond. It may weaken the
argument to assume that the nerve surface has that many protein molecules. The lower value
1.20 X lO^ions/cm^ second is consistent with any combination of rates and numbers of
protein molecules responsible for transport such that the product equals this numerical value.
Thus 1 .20 X 10" protein molecules transporting an ion per miUisecond are suitable and require
that only 0.001 of the nerve surface consists of such proteins, each of 10* A^ area.

Some Membrane Phenomena from the Point of View of Information Theory 203

information units, the bits, appearing in equations (15) and (16) are identical with
those used in discussing the information content of the printed page, the
interpretation is that a cm^ of nerve has an enomious rate of production. The
analogy of course is to a person who is called upon to separate red balls (Na+)
from white (K+) and blue (CI ) balls in a box where he would reach in, pick
up a ball, look at it, and if it is red it is taken out, and if not it is replaced.
The nerve has some equivalent separating mechanism with the infomiation
rate of equation (15). In terms of a familiar example, taking the information
content of a single printed page as 10* bits (9), equation (15) requires that the
cm^ of nerve surface produce information equivalent to that contained in a
library of 7.3 million volumes of a thousand pages each second — this is over
half the number of books in the Library of Congress! The value given by
equation (15) is not inordinate, however, in comparison with the estimates of the
information content of biological objects (9), where for man the value is of the
order of 10^5 bits.

The result in equation (16) may be viewed as the minimum information
production necessary to effect the separation of sodium. The numerical value
may be in error, for the choice could be from among more ions than the three
employed. It is of interest to note that the nerve does not possess perfect
coding inasmuch as it uses 1 .7 times as much information to effect the separation
as is required. Alternatively the information efficiency may be expressed as
59 per cent. These comparisons may be without substance because of the
inadequacy of the data. The only relevant comparison may be that the physio-
chemical determination of information production as summarized in equation
(15) is of the same order of magnitude as the value determined by enumeration
in equation (16).

REFERENCES

1. J. F. Danielli: Cytological research and biophysics. Nature, Loud. 162, 753 (1948).

2. H. R. Branson: A definition of information from the thermodynamics of irreversible
processes. In: Information Theory in Biology, ed. by H. Quastler, 25-40. University of
Illinois Press, Urbana (1953).

3. L. Brillouin: Science and Information Theory, Academic Press, New York (1956).

4. R. C. Tolman and P. C. Fine: On the irreversible production of entropy. Rev. Mod.
Phys. 20, 51-77 (1948).

5. S. R. DeGroot: Thermodynamics of Irreversible Processes, Interscience, New York (1952).

6. R. W. Stacy, D. T. Williams, R. E. Worden, and R. O. McMorris: Essentials of Bio-
logical and Medical Physics, McGraw-Hill, New York (1955).

7. H. LrNSCHiTz: Information and physical entropy. In: Information Theory in Biology. qA.
by H. Quastler, 14-15, University of Illinois Press, Urbana (1953).

8. S. M. Dancoff and H. Quastler: The information content and error rate of living things.
In: Information Theory in Biology, ed. by H. Quastler, 263-273, University of Illinois Press,
Urbana (1953).

9. A. L. Hodgkin and R. D. Keynes: Active transport. Symp. Soc. Exp. Biol. 8, 423-437
(1954).

EFFICIENCY OF INFORMATION TRANSMISSION
BY BIOCHEMICAL CO-FACTORS*

Peter D. Klein

Division of Biological and Medical Research, Argonne National Laboratory,

Lemont, Illinois

Abstract — Amodelfor the transmission of information by biochemical co-factors is described.
Two points of information transfer are apparent : formation of the holo-enzyme and formation
of the holo-enzyme-substrate complex. The reduction in uncertainty taking place at these
points is related to the sets of compounds existing before and after these points, and the values
for artificial situations calculated.

It is concluded that the artificial situation is an estimate of the minimum selection capabili-
ties of the enzyme system.

Co-factors are compounds of molecular weight 100 to 2000 which participate
in a host of biochemical reactions. They are not metabolised per se, but serve
as catalysts. The moiety with which co-factors cooperate may in this instance
be limited to proteins. Co-factors for a particular protein may be either
exogenous (vitamins) or endogenous (hormones).

The flow diagram (Fig. 1) represents the fate of a co-factor in the organism.
A particular apo-enzyme can operate on a substrate or class of substrates if
provided with the suitable co-factor. In this case the co-factor is assumed to
be a vitamin. Therefore, preliminary to its appearance in the cell, the com-
pound must of necessity be ingested, absorbed and transported into the cell.
Inside the cell, the compound may or may not be excreted again. Each time
that it exists in a 'free' form, it has a finite possibility of leaving the site of
action, including transformations which lead to the degradation of the molecule
so that it cannot function. This possibility is represented by Probability Point 1 .
This and subsequent probability points have the following characteristics:
A molecule 'passing' through this point may undergo two or more transitions;
each state resulting from these transitions has a certain probability but there is
no control over the state into which the molecule passes.

Next, it may be imagined that a collision between the compound and the
apo-enzyme for which it may be destined takes place, leading to the formation
of a complex. The formation of this complex, however, depends upon mutual
exchange of information between the apo-enzyme and its co-enzyme and is
indicated by Decision Point 1 . For example, if the co-enzyme for cocarboxylase
collides with the apo-enzyme for riboflavin, no information exchange takes
place and there is no complex formation. If, however, sufficient information
is exchanged, there results the formation of the holo-enzyme, or in the case of
the competitive inhibitor, a pseudo-holo-enzyme. Both forms of holo-enzyme
have, of course, a dissociation constant, indicated by Probabihty Point 2.

* This work was performed under the auspices of the U.S. Atomic Energy Commission.

204

Efficiency of Information Transmission by Biochemical Co-factors

205

f ' VLf

I COMPOUND 1-7— •

INGESTED

ABSORBED

PROBABILITY POINT
DECISION POINT

TRANSPORTED I
[BOUND]

REACTION

Fig. 1. Pathway of utilization for a hypothetical co-factor.

CELLULAR CONSTITUENTS
APO-ENZYME ACCEPTORS
SUBSTRATE ACCEPTORS

Fig. 2. Topological considerations in evaluating information
transmission by a co-factor.

206 Peter D. Klein

The collision of the holo-enzyme with a potential substrate represents another
decision point (Decision Point 2). Again, a complex will be formed if sufficient
information is transferred. It is at this point that the pseudo-holo-enzyme
must present the wrong information in order to be an effective inhibitor. This
results in repeated cychng in the innermost loop diagrammed.

The enzyme-substrate complex has a finite probability, designated Probabi-
Hty Point 3, of decomposing unchanged before the reaction is catalysed to
decompose the substrate into product and regenerate the holo-enzyme.

There are, then, two points in tliis flow sheet at which information can be
exchanged; between the co-factor and the apo-enzyme and between the holo-
enzyme and the substrate. These are the two points to which attention will be
devoted.

At neither decision point is the decision unequivocal. There are several
types of co-factor-substances which may form a complex with the apo-enzyme
and several of these complexes are acceptable, though to differing degrees, to
the substrate. The situation is graphically presented in the set diagram Fig. 2.
The largest circle represents the class of all possible organic compounds. Let
B designate these substances. A subset of 5, composed of the organic substances
which normally occur in cells, is designated C. Another subset of B, designated
A, is comprised of substances acceptable to the apo-enzyme for complex forma-
tion. The set A.C'\ includes those compounds normally occurring in cells which
are able to complex with the particular apo-enzyme considered ; the set (A~A.C)
contains those substances which form a complex with the apo-enzyme but are
not normally found in the cell.

A subset of A, designated A.S, contains all compounds which complex with
A and react with the substrate. (There may be other substances in B which
would react with the substrate, if complexed with a proper apo-enzyme ; but
these are not of concern here.) These substances which are contained in the
set C.A.S are the natural co-factors for the apo-enzyme-substrate pair under
consideration; the substances in the set A.S-C.A.S are artificial co-factors;
the substances C.A-C.A.S are natural antimetabohtes ; those in the set A-A.S
are artificial antimetabolites.

The information measures associated with the two decision processes can
be derived from the diagram. Let H(X) designate the uncertainty associated
with the set X; then:

H(C) is the uncertainty of substances in a normal cell. To give this quantity
meaning, we shall consider it to be the uncertainty about the nature of an
organic molecule which normally collides with the apo-enzyme.
H{C.A) is the uncertainty concerning a substance which has formed a
complex with the apo-enzyme.

H(C.A.S) is the uncertainty concerning the complex which has reacted
with the substrate. It should be noted that in dealing with a given apo-
enzyme and a given substrate (or class of substrates) all uncertainties in
question are due to the co-factor.

t The set X. Y contains all substances which belong to both the set X and the set Y. The
set JV- 7 contains those substances which are contained in A' but not in Y; alternatively this set
is designated X-X. Y, all substances which belong to X but not to both X and Y. The latter
notation is more explicit and will be used here.

Efficiency of Information Transmission by Biochemical Co-factors 207

The informational performances at the decision point are related to the
reduction of uncertainty, AH, at these points, i.e. the difference in uncertainty
before and after:

A//i = H{C) - H{C.A)
AHii = H{C.A) - H{C.A.S)
AHiji = H{C) - HiC.A.S)

The comparable functions for artificial situations are given by:

AHi* = H{B) - H{B.A)
AHii* = H{B.A) - H{B.A.S)
AH*iji = H(B) - H{B.A.S)

There is a fundamental difference between natural and artificial functions.
The quantities H{C) as well as H{C.A) and H(C.A.S) do not depend on the
experimenter; furthermore, because of the constancy of the internal environ-
ment, they can be considered to be numbers approximating natural constants,
subject to relatively small fluctuations. The function AHjji represents the
normal informational performance achieved in the particular metabolic process
considered, whose average value has been placed at 9 bits (1). The quantity
H{B), on the other hand, is completely or partially controlled by the experi-
menter, who regulates the availability of substances in B; H(B.A) and H{B.A.S)
depend on apo-enzyme, substrate and on the experimenter. Accordingly, the
AH* functions have, in general, very little interest since it is easy to make AH*
vanish by offering only a single co-factor which can be used, or to give it a
very high value by introducing numerous compounds which are known not to
react with the apo-enzyme or substrate.

A great body of data is available, however, which lends itself to an examina-
tion of the AH* functions as well as H{B.A) and H{B.A.S) from the standpoint
of the systems' responses to a series of compounds closely resembling the natural
co-factors. The values obtained may be regarded as a sort of minimum residual
uncertainty associated with the various systems, and they form the subject of
this report.

We shall define the uncertainty functions H{B.A) and H(B.A.S) as:

H(B.A) = -i:pJog,p,

H(B.A.S)=-i:p,,log,p„,

where p^ and p^^ are the normalized biological activities of the compounds
tested in a particular system. Thus if four compounds were tested for their
ability to combine with the apo-enzyme and all were found to be equally active,
their /7^ would each be 0.25 and H{B.A) would be 2. This method of calculation
takes into account the fact that with equal concentrations, equal activity may
not be observed and that the information is of necessity related to the concentra-
tion required to produce a complex.

A word is in order as to the mechanics of calculation. The basic data were
derived in large part from Williams and co-workers' treatise on the B vitamins
(2) ; data on thyroxine are due mainly to the work of Bruice, Kharasch and

208

Peter D. Klein

WiNZLER (3). H{B) was defined as the logarithm of the total number of
compounds tested, both for ability to replace the natural co-factor and for
those having antimetabolite activity. H(B.A) was calculated from the com-
pounds active as antimetabolites plus those having substrate activity; in the
former case, the inhibition index (number of molecules of inhibitor required to
overcome the action of one molecule of the true compound) was considered as
the reciprocal of biological activity and suitably transformed to agree in dimen-
sion with the other data. H(B.A.S) was, of course, derived from the group
which showed ability to replace the natural co-factor.

RESULTS AND DISCUSSION

The H functions and AHi*, Ai/u* and ^Hju* are fisted for a variety of
compounds in Table 1. In addition, compounds for which partial data were

Table I

Compound

Organism

N H{B) H{B.A) H(B.A.S) A/Zj* AHu* AZ/fn

Biotin

MO

33

5.04

3.01

2.67

2.03

0.34

2.37

Riboflavin

MO

40

5.32

2.91

2.61

2.41

0.33

2.71

Riboflavin

R

18

4.16

2.93

2.61

1.24

0.33

1.57

Folic acid

C

11

3.46

2.74

1.97

0.72

0.77

1.49

Folic acid

MO

51

5.67

3.97

2.55

1.70

1.42

3.12

Thiamine

R

8

3.00

1.39

0.99

1.61

0.40

2.01

Thyroxine

F

34

5.09

2.55

1.47

2.54

1.08

3.62

Thyroxine

R

43

5.43

4.28

3.22

1.15

1.06

2.21

/j-Amino benzoic acid

MO

72

6.17

4.90

3.27

1.27

1.63

2.90

Biotin

R

4

2.00

—

0.13

—

—

1.87

Unsaturated fatty acids

R

10

3.32

—

1.85

—

—

1.75

Pantothenic acid

C

4

2.00

—

1.86

—

—

0.14

Vitamin D

R

10

3.32

—

2.08

—

—

1.24

Pantothenic acid

R

10

3.32

—

2.19

—

—

1.13

Nicotinamide

C

5

2.32

—

2.23

—

—

0.11

Ascorbic acid

G

10

3.32

—

2.33

—

—

0.99

Nicotinamide

D

13

3.70

—

2.66

—

—

1.04

Pyridoxine

R

11

3.34

—

2.85

—

—

0.49

Choline

R

35

5.11

—

3.12

—

—

1.99

Carotene

R

15

3.90

—

3.68

—

—

0.22

Estrogens

R

18

4.16

—

3.88

—

—

0.28

Average

3.96

2.39

1.57

Key: MO: Micro-organism
R: Rat
C: Chick

F: Frog

G: Guinea pig

D: Dog

available are included. Fig. 3 presents some values for the first group in graphic
form.

It can be seen that there is a range in H{B.A) of 1.39 to 4.90 and in H(B.A.S)
of 0.13 to 3.88. There is also a marked tendency for A/Zn* to be smaller than
A//^*, suggesting that the greater portion of the selection process is assumed by
the apo-enzyme/co-enzyme complex formation, but sight must not be lost of

Efficiency of Information Transmission by Biochemical Co-factors

209

the fact that the area H(B.A)-H(B.A.S) (representing antimetabolites) is
dependent upon the number of successful inhibitors of a co-factor which have
been devised.

Over-all, the mean reduction in uncertainty in terms of actual compounds is
such that when confronted with fifteen compounds, assumed to be equally

Fig. 3. Residual uncertainties associated with two co-factors.

effective, the system can weed out ten of these, leaving the equivalent of five,
equally active, co-factors. Comparison of this to H(C) and H{C.A.S) is of
course not plausible from these figures, but clearly indicates the relative chaos
of the universe B, from the standpoint of the enzyme system : the assembly of
letter-perfect molecules of protein or nucleic acids would be impossible under
these circumstances. Nevertheless, these figures may have some interest as
the minimum limits of discrimination ability by enzyme systems.

REFERENCES

1. P. F. Fenton, cited by H. Quastler: The specificity of biological functions. In: Information
Theory in Biology, ed. by H. Quastler, 170-188, University of Illinois Press, Urbana
(1953).

2. R. J. Williams, R. E. Eakin, E. Beerstecher Jr., and W. Shive: The Biochemistry of B
Vitamins. Reinhold Publishing Co., New York (1950).

3. T. C. Bruice, N. Kharasch, and R. J. Winzler: A correlation of thyroxine-like activity
and chemical structure. Arch. Biochem. Biophys. 62, 305-317 (1956).

DISCUSSION

Quastler: The following interpretation of the 'residual uncertainty of co-factors' may be
considered :

Given a particular apo-enzyme-substrate system, and the set B of all substances bi which are
or might be co-factors. Let c, be the reaction rate constant of the system in the presence of the
(potential) co-factor b,. Suppose that all Ci's have been determined; it seems that there are
two statistics of general interest: the average size of the c's, which characterizes the reactivity
of the system in general, and the dispersion among the c's, which characterizes its specificity.

210 Peter D. Klein

To study the specificity independently of general reactivity, we normalize the c/s by setting their
sum equal to one. We consider a function called the tolerance of the apo-enzyme-substrate
system ; the tolerance function shall have the following properties : it shall be zero if only one
Ci is not zero; it shall increase with the number of substances b with non-zero c's; for a given
number of substances the tolerance shall be called highest if all c ,'s are equal. These postulates
are satisfied by the information function :

Value of tolerance = — V ^r- log2 ^?^—

Tentatively, one might assign a physical meaning to the tolerance as follows : the reaction
rates are replaced by (suitably normalized) probabilities of a reaction following a collision ;
it is assumed that the system can exist in a number of mutually exclusive states (configurations)
and that a reaction will occur if the system is in the proper configuration; then, the c^'s are
proportional to the fractions of the time the system is in a configuration compatible with
functioning with the substances 6,. The value of the tolerance is the uncertainty concerning the
actual state of the apo-enzyme-substrate system.

XVvf

i

f / *^

/**

UJ / , ,

•3r >'*■

ANTIGENIC SPECIFICITtS^ ''^z

v:

Bernard N. Jaroslow and Henry Quastu

Division of Biological and Medical Research,

Argonne National Laboratory, Lemont, Illinois

and

Department of Biology, Brookhaven National Laboratory,

Upton, New York

Abstract — The production of a specific antibody involves a transfer of information, and so
does the specific reaction between antibody and antigen. This paper deals with the 'vocabulary'
of this communication process. An antigenic determinant is considered as a 'word' of a
certain number of 'letters', subject to certain constraints. It is shown that the number of
'words', the number of 'letters', and the degree of constraint can be estimated by methodical
random sampling. Experimental methods suitable for this purpose are discussed. Preliminary
results are given.

I. INTRODUCTION

The question, 'How many different antigens are there?' is one that has not
been explored up to now, but which arises naturally if information theory
is applied. Information theory interprets the process of antibody formation
as the transmission of information from the antigen to the antibody-forming
mechanism, with the information then utilized and again transmitted when the
antibody reacts selectively with the appropriate antigen. It is then natural
to ask how much information is transmitted from antigen to antibody and
vice versa. More explicitly, one will ask certain questions about the kind of
information traffic between antigen and antibody — the 'vocabulary' in which
this information traffic is coded, the 'alphabet' that is used to make up the
words of the vocabulary. Now, information theory is not concerned with
specific features of 'alphabet' and 'vocabulary' but with general properties
of both, such as their sizes. The problem, 'how large is the vocabulary of
information transmission between antigen and antibody,' is closely related to
the question posed above. A preliminary estimate by one of us (1) has led to
a rough estimate of some 125 to 500 different protein antigenic determinants,
and a smaller number of different carbohydrate determinants. No attempt
was made, at that time, to estimate the number of antigens of other chemical
constitutions. Although these figures appear very small in the light of the
specificity of immunity to the multitude of infectious agents, the antigen com-
plexes of the organisms represent an array of many different determinants
and their over-all specificity can be much larger than that of a single antigen.
The present investigation is an attempt to measure antigenic specificity.
The general plan of the experiment is based on information theory; the specific
methods are based on agar diffusion precipitin tests developed by Oudin (2).

* Work performed under the auspices of the U.S. Atomic Energy Commission.

211

212 Bernard N. Jaroslow and Henry Quastler

II. NOMENCLATURE AND MODEL

An antigen, GN, consists of a specific detenninant G and a carrier moiety
A'^ which is a macromolecule (MW > 10,000), i.e. protein, hpo-protein, glyco-
protein, etc. G may consist of three or four amino acid residues, a mono- or
disaccharide, an aliphatic chain, etc., with its specificity dependent upon order,
size, polarity, or optical configuration of the residues. There may be a number
of antigenic determinants, of the same or different specificities, on the surface
of N, so that one molecule of antigen may combine with several molecules
of antibody, e.g. 5 for ovalbumin to over 200 for hemocyanins (3). Combining
capacity as well as antigenicity (ability to induce antibody formation) is usually
proportional to the molecular weight of A'^.

An antibody, AB, consists of a specific combining site A and a carrier
moiety B which is always a globulin, usually y-globulin. The combining site
is believed to be a chemical and/or spatial configuration which combines with
the specific antigenic determinant through hydrogen bonds. The number of
combining sites per antibody molecule is thought to be two or one.

The A-G reaction may be manifested in a number of ways: precipitation
of a soluble antigen, agglutination of a particulate or cellular antigen, or lysis
of a cellular antigen in the presence of complement.

We consider a heterophile reaction as one in which the reaction between
C2 and y^i is indistinguishable from the homologous reaction of G^ and A-^
although G2 and G^ come from different sources. By cross reaction we mean
the phenomenon wherein G2 reacts with A^ but the strength of reaction is less
than that of the homologous one {G^ and A^.

We can describe an antigenic determinant, G, as a 'word' of k 'letters'.
By letter we mean antigenically active residues such as amino acids, mono-
saccharides, etc. Let r be the size of the alphabet, i.e. the number of available
letters; then

H (letter) = a • logg r.

a is a constant which ranges from zero to one. Its upper limit occurs if all
'letters' occur with equal probabihties, and no two letters can ever have equiva-
lent effects.

The average information content of a worfi? averaging k letters is given by:

H(G) = ^- k- H (letter).

/9 is a constant which ranges from zero to one. Its upper limit occurs when
all letter combinations are equally probable, i.e. if there is no 'intersymbol
influence'. The lower limit would obtain if there existed only one antigenically
active combination of letters.

To fix the ideas on the measuring of /-, H (letter), k and H(G), we give
the corresponding values for printed English:

r = 26 k {=ii4.5

log2 r = 4.7 ^ f^ 0.6

a ^ 0.87 H{G) ^ 10

//(letter) = 4.1

Antigenic specificity 213

III. EXPERIMENTAL TESTS

1. Occurrence of the Heterophile Reaction

The incidence of heterophile reactions will depend on the number and
relative frequencies of the various antigenic determinants. As nothing is known
so far about relative frequencies, we assume them to be equal; this will yield
a lower bound of the number of different G's. Under the assumption of equi-
probability, we use the following argument (4): Let Q and C_, be different and
(as far as known) unrelated antigen complexes; let m^ and nVj denote the number
of antigens in the complexes which can be differentiated and demonstrated,
by a given technique, by reaction with the specific antisera S^ and Sj\ let
hij be the number of heterophile reactions observed ; let A^ be the total number
of different antigenic determinants which this technique will differentiate. Then,
the maximum likelihood estimate N of N is given by:

"a

Assuming ft to be one, we have:

H(G) ^ logo N
and

This is a preliminary test of r'^'^.

2. Classification of Cross Reactions

The strength of the cross reaction presumably depends on the number of
letters in common, and on the nature of these letters. We assume as a working
hypothesis that the former factor is the leading one. Then, if we grade the
strengths of many cross reactions, we expect to find a distribution into clearly
separated groups such as strong, less strong, weak, . . . etc., cross reactions.

We suspect that the strong cross reactions are those in which the G-pair
has (^ — 1) letters in common, the next class those with (k — 2) letters, and the
weakest observable reactions those with one common letter. Then, the number
of distinguishable classes of strengths of cross reactions should be (k — 1).

This may develop into a test of k.

3. Ratio of Incidence of Heterophiles to Incidence of Strong Cross Reactions

By our hypotheses, the probability of occurrence of heterophiles is the
probability of having all letters in common; now, for k letters, assuming p to
be one, the number A^ of different words is:

TV = r'^'^.

Then, probability of a given word = {\jrY^'

and, probability of a heterophile = (1//-)

15

<xk

214 Bernard N. Jaroslow and Henry Quastler

Since we propose that in the strong cross reaction we have (^ — 1) letters
in common, the probabihty of this event is:

There are k sets of {k — 1 ) letters in a A:-letter word ; hence,

probability of a strong cross reaction --^a k{\lrY^^~''-^
and

probability (iieterophile) (l/r)"^" 1

probability (strong cross reaction) <xk{\lr)^-^^~^^ a.kr'^

This is a test of a kr'^. One can construct similar tests for the ratio of strong
to weak cross reactions, if experimental results warrant this.

Optimally we have, thus, three experimental determinations of three para-
meters which have computable theoretical values.

IV. METHODS

It is essential to this study that the test antigens be as nearly as possible
a random sample of natural antigens. Since related organisms regularly have
common antigens, we chose our sources so that no two were in the same phylum.
We used Guyer (5) as our guide to classification.

Entire organisms were placed in a Waring blender for two minutes with
phosphate buffer (pH 7.4) as the extracting agent. If the antigen source was
of microscopic proportions it was ground in a mortar and pestle containing
sterile powdered carborundum. The material was centrifuged at low speed
to remove the gross particulate material and 0.2 per cent formahn was added as
a preservative.

Rabbits were immunized with a series of four intravenous injections of
antigen over a ten-day period. They received another series of three injections
a month later and were bled three days afterwards. Serum was collected,
complement was inactivated by incubation for one-half hour at 56°C and
1 : 10,000 merthiolate was added as a preservative.

Our test system was double diffusion agar precipitin test based on the methods
of OuDiN (2) and Ouchterlony (6). Antiserum (0.5 ml) was placed at the
bottom of a test tube (4 mm i.d.). The antiserum was topped with a layer of
1.5 ml of 1 per cent agar. After the agar had gelled, the antigen (0.5 ml) was
added. Both antigen and antiserum diffused towards each other through the
agar, and where they met in the proper proportions a band of precipitate
became visible. For antigens with different rates of diffusion separate bands
appeared. Thus, the number of bands of precipitate estabhsh a lower limit
for the number of antigens in the extract.

We should be able to differentiate between heterophile and cross reactions
because the formation of a precipitate is dependent upon the relative concen-
trations of antiserum and antigen. In the region of great antibody excess no
precipitate forms, although all the antigen is combined with antibody. In
the region of large antigen excess no precipitation is seen, although all the
antibody is combined with antigen. Between these two zones is a region in

Antigenic Specificity 215

which precipitate appears. Thus, in a heterophile reaction, two antigens
diffusing towards each other through a field of antibody will form two lines
of precipitate that become confluent on meeting. Although free antigen mig-
rates past the diffusion front of the other, no precipitate will form because
all the antibody is already combined in what is a region of antigen excess.
In the case of cross reactions a different situation exists. As Landsteiner (7)
and many others have demonstrated, where the antigenic determinants differ
from one another, the heterologous antigen will precipitate only part of the
antibody, leaving enough antibody in solution to form precipitate when homo-
logous antigen is added. Thus, the peptide glycyl glycyl glycyl glycyl glycine
(heterologous antigen) fonns a precipitate with antiserum to glycyl glycyl
leucvl glycyl glycine (homologous antigen). If this precipitate is removed and
the antiserum is then mixed with the homologous antigen a precipitate will
appear. The antibody that reacts with the heterologous antigen is probably
'imperfect', i.e. its specificity is less than that of the uncombined or 'avid'
antibody. In our system one would expect, then, that the advancing homologous
antigen would find uncombined antibody behind the front of the heterologous
antigen and form a line of precipitate there. We hope that we will be able to
grade the intensity of this reaction through some aberration in the band of
precipitate and thus be able to classify the cross reactions as to relative strengths.

V. RESULTS

As of this writing, we have obtained some preliminary data which we present
here as an indication of the limits or power of our test system.

We obtained antisera to whole body extracts of the following organisms:

Grasshopper Melanoplus differentialis phylum Arthropoda

Frog Rana pipiens phylum Chordata

Bacterium Escherichia coli sub-division Bacteria

Horse mussel Modiolus modiolus phylum MoUusca

Sea pen Ptilosarcus quadrangularis phylum Coelenterata

Giant star fish Pisaster giganteus phylum Echinodermata

In addition we tested extracts for which we had no antisera. These were:

Baker's yeast Saccharomyces cerevisiae sub-division Fungi

Earthworm Lumbricoides terrestris phylum Annelida

The results of testing each of the six antisera against each of the eight
antigen extracts are shown in Table I. We observed from four to ten homo-
logous reactions per test and two heterologous reactions. Since we have no
data on the number of homologous reactions for yeast and earthworm extracts
we assigned each of them a value of 7.3, which is the mean of the homologous
reactions for the other six tests. Then, we have six tests, in each of which m^
was (on average) 7.3; w,, being the sum of antigens in all other complexes,
was 7 X 7.3 = 51 ; the average number of heterophile reactions was 2/6 = 0.33.
Then, if reciprocal tests are considered as independent, we obtain:

- 7.3x51 ,,_
^ 033 ^^^

loggTV^ 10 bits

216

Bernard N. Jaroslow and Henry Quastler
Table I. Precipitin Reactions in the Agar Diffusion Test*

Ant

igen

Antiserum

Grasshopper

Frog

E. coli

Horse
mussel

Sea
pen

Star
fish

Yeast

Earthworm

Grasshopper

4

0

0

0

0

0

0

0

Frog

0

10

0

0

0

0

0

0

E. coli

0

0

4

0

0

0

1

0

Horse mussel

0

0

1

9

0

0

0

0

Sea pen

0

0

0

0

7

0

0

0

Star fish

0

0

0

0

0

8

0

0

* Each figure signifies the number of visible precipitin reactions in each test.

VI. CONCLUSION

The estimate obtained from our preliminary test is extremely crude; how-
ever, it agrees fairly well with the earher (1953) estimate. The number of
homologous reactions we observed was surprisingly low. We expect that
with more potent antisera it would increase markedly. If the observed
reactions are found to be cross reactions, or if repetition of the test with another
set of antigens gives fewer heterologous reactions, the value for TV would go
up radically. Also heterophile reactions will have to be differentiated from
each other to prevent a common heterophile such as the Forssman antigen
or the Wasserman cardiolipid antigen from lowering the value for A'^ by multiple
appearances in the tests. On the other hand, the similarity with Quastler's
estimate suggests that the order of magnitude of TV after further experimentation
will not be much greater.

The preliminary tests were made with antigen complexes. It is known
that simultaneous immunization with many antigens does not produce sera
of optimum potency. In later tests, it might be worthwhile to try to isolate
antigens which show cross reaction or heterophilia, and use them to produce
more potent antisera.

In the final analysis, we hope to obtain an estimate of the number of factors
or signals that are needed to characterize an antigen as to its specificity.

REFERENCES

1. H. Quastler: The specificity of elementary biological functions. In: Information Theory
in Biology, ed. by H. Quastler, 177-181, University of Illinois Press, Urbana (1953).

2. J. Oudin: Methode d'analyse immunochimique par precipitation specifique en milieu
gelifie. C.R. Acad. Sci., Paris 111, 115-116 (1946).

3. W. C. Boyd: Fundamentals of Immunology, 2nd ed., p. 91. Interscience, New York
(1948).

4. W. Feller: An Introduction to Probability Theory and its Applications, vol. 1, p. 37,
J. Wiley and Sons, New York (1950).

Antigenic Specificity 217

5. M. G. Guyer: Animal Biology, 4th ed., 60-79, Harper, New York (1948).

6. O. Ouchterlony: In vitro method for testing the toxin-producing capacity of diphtheria
bacteria. Acta Path. Microbiol. Sram/. 25, 186-191 (1948).

7. K. Landsteiner: The Specificity of Serological Reactions, rev. ed.. Harvard University
Press, Cambridge, Mass. (1945).

INFORMATION CONTENT AND BIOTOPOLOGY OF
THE CELL IN TERMS OF CELL ORGANELLES*

Charles F. Ehret

Division of Biological and Medical Research,
Argonne National Laboratory, Lemont, Illinois

Abstract — The cell organelle is regarded as a characteristic structural unit of the organism
that bridges the gap between the molecular and cellular levels of organization. It may arise
from the nucleus as a primary organelle, or from other cytoplasmic organelles. A provisional
flow-diagram is presented, according to which specifically different cell structures are derived
from primary organelles by sequences of relatively simple events that involve two to five
binary decisions.

I. INTRODUCTION

A MAJOR limiting factor in estimates of information content of the organism
resides quite obviously in assumptions that are made regarding organization
of its component parts. Thus in terms of atoms, //(man) = 2 X 10^^, and
in terms of molecules //(man) = 3 X 10^^. The reduction in this second
Dancoff-Quastler estimate (1) of information content is permitted by
limitations placed upon possible positions of atoms as a result of the restricted
number of molecular configurations found in Hving systems. It follows that
if many of the molecular and macromolecular configurations that are theoreti-
cally possible actually occur in only a limited number of anatomical and micro-
anatomical (organellar) configurations, then a further reduction of this estimate
by several orders of magnitude is possible. In reductio ad absurdum the terms
might be alive or not, as Augenstine has suggested (2), and the information
content one bit or less; however, such a classification would be of more value to
exterminators than to biologists.

The existence of such organelles as chromidia, micellae, bioplasts, etc.,
that occupy in all cells a functionally meaningful position between the mole-
cular and gross anatomical levels of organization was long ago claimed by
some cytologists but denied by most (3). New evidence from electron and
phase contrast microscopy revives but considerably revises the earUer unifying
view; it allows for characterizable 'nuclear ambassadors' each equipped with
a versatile morphogenetic repertoire to roam the cytoplasm and serve the
structural and functional needs of the cell. While the evidence to date is far
from complete, its general implications are presented here.

II. ORGANELLES AND PRIMARY ORGANELLES

Firstly, we define and characterize organelles in the following manner:
1. Organelles are elements of unitization for the macromolecular species
of an organism: they occupy niches between the macromolecular and cellular
* Work performed under the auspices of the U.S. Atomic Energy Commission.

218

Information Content and Biotopology of the Cell in Terms of Cell Organelles 219

hierarchies of organization; they are sites of biosynthetic and energy yielding
cycles (4) (molecuhir 'chunking') large enough to maintain a relative degree
of themiodynamic homeostasis and biochemical independence.

2. Organelles are homologously related in two ways: (a) They are phylo-
geneticallv static. Classes of organelles present the same basic appearance
in all plants and animal cells: they show synchronic stability. Historically,
the chromosome is an excellent example; presently, cytoplasmic organelles
including mitochondria, flagella and cilia are even better described than are
those of the nucleus. Astbury has proclaimed the demonstration of the basically
similar patterns of ciHa wherever they are found as "one of the most important
microanatomical revelations of our time" (5), a statement made before De
RoBERTis' discovery of retinal rod organization (6) cited below. Basically
tubular and lamellar mitochondria are also phylogenetically ubiquitous (7-11).

(b) They are epigenetically plastic. Organelles react with or respond to
their environment and interact with other organelles to produce novel patterns
of organelle complexes and systems: they show diachronic non-fixity. The
patterns 'develop' from similar mechanics of packing, coacervation and disin-
tegration. (A relatedness akin to that described by Thompson for cells and
tissues (12).) Thus the nebenkern arises by fusion of mitochondria (13), the
acroblast by fusion of dictyosomes (14), the old nucleolus by fusion of young
nucleoli (15), the rod sacs and rod tubules of the mammalian retina by develop-
ment of the distal region of the connecting filaments, which are themselves
ciha (6), the endoplasmic reticulum by fusion of spherical vesicles, and the
'prolamellar body' and lamellated grana of the plastid by fusion of lipid vesicles
(16). Such earliest reactants we term 'primary organelles'.

3. Primary organelles arise by synthesis from molecular pools and probably
never by division of pre-existing organelles.* The specific pattern has never
been seen to divide in nature; it is only replicated. The essential contribution
to their progeny of even such classical 'dividers' as bacterial viruses (17) and
chromosomes (18) is that of a hnearly ordered code along which new code units
are synthesized, rather than that of a code which grows and 'splits'. Experi-
ments claiming genetic continuity to centrioles (19) and to blepharoplasts
(kinetosomes (20) ) do not demonstrate division of these elements, but only
continuity of topological relationships; whereas some primary organelles,
microsomal to mitochondrial in size, arise from the nucleus (15, 21) or, in
the case of the plant blepharoplast, de novo (22). Hence the organelle is not
itself an 'organism' and Altmann's 'dictum' that all granules come from
granules does not strictly apply.

4. Organelles give rise to the gross patterns and shapes of cell parts and
of whole cells by symmetrical packing, coacervation and the formation of
polarized interconnectives. They provide the periodically replicative units
of brush border (23), ciliated epithelium (24, 10) and nuclear membrane
(25, 36 — 39); the walled structures of an outer pellicle and an inner cell-mouth
(26, 48); the packed units of the cirrus (27), the polarizing units of the kinety
(28), and the vehicles of fluid transport 'by which structural lipids move in
the cell from site of synthesis to region of lamellar growth' (16).

* This is to be distinguished from the sort of mitochondrial splitting observed between the
miotic divisions during grasshopper spermatogenesis (13).

220

Charles F. Ehret

onterior

micronuc

mocronucleus

TRICHOCYST—

CILIUM

l^Gullet
System

?^^»

"^-'MITOCHONDRION- '^^ix^^Jj^'iW^^h

posterior

anterior

B.

posterior

Fig. 1 . Systems and complexes of organelles in Paramecium.
Approximate dimensions: Cilium diameter = 0.25 //

Cilium tubule diameter = 22-30 m/n
Mitochondrion tubule diameter = 34-40 m/i
Mitochondrion tubule-lumen diameter = 8-29 m/t
Cilium to cilium distance (on centers):

in gullet system = 0.5 /*
in pellicle system = 1.8 /^
length of gullet = 20 /x
A. Orientation sketch, and diagram of some hypothetical

derivatives of primary organelles.
B. Patterns of organelle packing at the free cell border.

1 . Gullet (food-intake) system consists of three organelle complexes: ciliated
peniculus (P), ciliated quadrulus (Q) and non-ciliated ribbed-wall (RW); close
packed basal 'granule'-tracts are diagrammed.

2. Surface view of hexagonal complex of pellicle system. Ciliary loci are
represented by circles, trichocyst loci by X's; kinetics are formed to the right of
the ciliary bases by overlapping kinetodesmal fibrils.

3. Schematized longitudinal section through pellicle system, along a single
kinety; the outer elements are represented as close-packed spheres bearing cilia;
the inner elements are 'coralled' out of normal packing-positions (with rare
exceptions, viz. at the intersection, on 2, left center) by kinetodesmal fibrils.
These inner elements are the trichocysts.

4. Cross-section of single corpuscular organelle of the hexagonal complex.
Four overlapping kinetodesmal fibrils are shown under the right arrow.

Information Content and Biotopology of the Cell in Terms of Cell Organelles 221

The cytological and epigenetic criteria of this definition must uUimately
be supplemented by cytogenetic criteria, since the organelles are certain to
include such elements as some plasmagenes and all kinetosomes (20, 29),
and homeostats (30). The use of the term 'organelle' in this concept has
several distinct advantages. In the first place it is particularly nebulous and
difficult to define at its limit values, an asset because "the boundaries of all
natural units are hazy" (52); and it therefore does not lack this attribute of
realism. In this way it is less mystical and arbitrary than many of the 'vital
granules' of the past, and there is much room left for the contribution of the
configurations at the 'hazy lower-boundary' to cell form and function, by
the mechanisms discussed by Wassermann (31), Gross (32) and others.

On the other hand it has sufficient traditional meaning (with or without
our four-part definition) for some cytologists to agree that all of the units
listed outside of brackets in Fig. 2 are 'organelles.' Our concept goes only
a step further in claiming epigenetic kinships.

III. ORGANELLE DECISION-TREES

Such an unorthodox but allowable interpretation of the organelle complexes
and systems of the unicellular animal Paramecium (shown in Fig. 1) leads to
the following postulates that should be useful in describing the information
content of other organisms: (a) The units of structural and functional integra-
tion in the cytoplasm are organelles ranging in size from less than 0.2 j.i to 1 //, or
are composed of such organelles as fusion structures, as complexes, and as systems
of complexes, (b) The organelles arise from primary organelles that in some
or all cases come from the nucleus as extruded nucleoli.

According to these postulates, the primary organelle or young nucleolus
starts out with a finite set of possibilities and finishes with one having been
realized. We can call the point of choice a 'decision point', and discuss the
events involved in terms of binary decisions. Decision points are encountered
at which specialization is gained and differentiation-potential (uncertainty) is
lost. The critical decision points in Paramecium are to remain intranuclear oi
become extranuclear; to remain within the fluid phase (karyoplasm or endo-
plasm) or to occupy an interface; to remain solitary or to pack; to form a
coacervate or not. A provisional decision-tree for Paramecium, as well as for
other animal and plant cells, is presented in Fig. 2. The differentiation of
organelles in Paramecium insofar as it concerns the present classification can
be accomplished in a sequence of 2 to 5 binary decisions; the informational
performance accomplished in the sequence of decisions is not more than a few
bits. Presumably, only a small number of such decisions will be needed to
account for all existing differentiations in any organism. (While it is premature
to assign probabilities to each decision point*, the practical methodology
is nearly at hand: an animal has approximately 13,000 cilia, and about
as many trichocysts; perhaps twice this number of mitochondria; a macro-
nucleus at division is capable of numerically twice generating this entire

* Pure chance, or a probability bias imposed by the micro-environment, may not be re-
garded as a sufficient cause for the choice of a particular decision in every case. We do not
suppose that each primary organelle contains all messages of the genome, and its specific
quality may therefore predetermine some choices and exclude others.

222

Charles F. Ehret

demand in the form of primary organelles (young nucleoli) < 0.5 [x in diameter.)
One interesting aspect of this scheme that is probably not artificial is that for
plant and animal cells in general, all subcategories have members, whereas for a
particular cell, such as Paramecium, numerous vacant categories exist (e.g.,
0. 101 grana-eyespot). The latter condition, not the former, is the more common

Digital
Code

f fused^

solitary

-,000

.0001

plas'

Loo

iITlIC ^. ._

packed"
interfacial

Intranuclear

(nucleo-cytoplasmic)

©001
«01

primary
organelle

extranuclear

H

A packed

plasmic

Classical Name Reference

Nucleolus (15)

Small (young)

nucleolus
Nucleolus (54, 15)

Typical (large;old)

nucleolus
[Virus] (40-46)

Nuclear membrane (25:36-39)

Mitochondrion (7-11)

Sarcosome 55)

Myogenic granule (55)

Centriole (19)
Lipochondrion
Assorted granules

Nebenkern (13)

Dictyosome (14)

Acroblast (14)

Acrosome (14)

Golgi apparatus (14,57)
Endoplasmic reticulum (16,57)
NissI substance

Plastidgrana (16)

Muscle fibers (55-58)

Eyespot (59)

Cilium (flagellum) (24)

Axial fiber (60)

Retinal rod ( 6)

Stereocilium (10)

Sensory bristle (27)

Trichocyst (61)

Cirrus complex (27)

Peniculus-quadrulus (26)
Hexagon-rhombus (47)

Ribbed wall (26)

Brush border (23)

Fig. 2. Organelle Decision Tree, representing a flow-diagram of the alternate
pathways and collisions available to a primary organelle in approacliing minimum

uncertainty in a cell.

situation in dichotomous divisions based upon a differentia and its negative (33).
The fundamentum divisionis for the first two divisions is location in the cell, and
for the next two divisions is location with reference to other organelles; it is
evident, however, that early organeller coacervation may influence the subsequent
localization of organelles, thereby upsetting the strict temporal representation
of the scheme. Whether such competitive mechanisms explain null-categories
in some cells, or whether we have simply failed to recognize the appropriate
candidates for these categories in the cells in question remains to be seen, and
of course both answers are plausible. It should be noted that the 'fusion'

interfacial
(free cell border)

solitary

packed

Information Content and Biotopology of the Cell in Terms of Cell Organelles 223

decisions are represented as branch points, which may or may not be taken ; thus
when the nebenkcrn (.1001) develops from the fusion of mitochondria (.100),
the mitochondrion loses potential on making this decision, but suffers no loss in
faihng to do so.

Admittedly several apparent and some real inconsistencies exist in this
provisional flow-diagram. For example, the development of the cilium from a
mitochondrion-hke body has already been suggested (34) in which the cilium
should appear related to, but more specified than, its supposed progenitor; the
present tree only remotely relates these. This difficulty may be resolved in a
common progenitor organelle (.1) at the plasmic-interfacial decision point.
Another inconsistency is in the separation at 0. 1 11 into cirrus-peniculus-hexagon
complexes vs. ribbed wall and brush border, the former being ciliated, and the
latter non-ciliated organelle-complexes. A more reaUstic decision in Paramecium
might be to form pellicle system unit (hexagon-rhombus complex) or to form
gullet system unit (peniculus-quadrulus-ribbed wall) dependent perhaps on loca-
tion of the primary organelle at a region of pattern homogeneity (amongst
hexagons or amongst rhomboidal elements) or at a region of pattern contrast (at
the junction of hexagons and rhomboids {kj to kj — 1 in Fig. 3, discussed in the
next section)). The latter condition is consistent with Paramecium structure, but
so far has been demonstrated only in the ciliate Stentor (35).

Several investigators (25, 36, 37, 38) have related nuclear membrane and
endoplasmic reticulum as mutual derivatives — a view not inconsistent with the
present scheme in its broadest sense; in addition to the rounds of packing and
fusion, some 'unravelling' may be involved in both cases. Viruses are pro-
visionally included in the tree because they nearly satisfy our definition, because
of their organelle-like ultrastructure, because of recent evidence for host related-
ness (40, 41, 42) and because of frequent nucleolar involvement (43, 44, 45). If
considered as particles produced by the host's gene-product synthesis that
contain a small error perpetuated by error feed-back, then the nuclear viruses
might occupy the packed (46) small-nucleolus position (.001); the cytoplasmic
viruses would be classed with 'assorted granules' (.1000) if single, and along
with 'grana' and 'fibers' (.101) if packed. It is not necessary to postulate a
'nuclear round' for the replication of either extranuclear organelles or of
cytoplasmic viruses, although this may be the usual case.

IV. PRIMORDIAL GRAPH

A material basis for nucleocytoplasmic communication is therefore realized
in the cell organelle, which in its primitive unspecified state provides the cell
with its necessary potential of structural diversity through relatively few bits
of information. A further quality related to the above (47) is that the cell's
geometry of functional relations is in some respects as similar to its cytological
structure as a wiring diagram is to its final construct. In other words, at the
level of the cell organelle (above the macromolecular and below gross cellular
dimensions), a coincidence between the functional and the structural biotopo-
logical set points of the cell exists. These relationships are represented for
organelles at an intranuclear-extranuclear decision in Fig. 3a, and for functioning
cytoplasmic organelle systems (48) in Fig. 3b. The intranuclear-extranuclear

224 Charles F. Ehret

decision occurs at binary fission, during macronuclear development, and possibly
intermittently during interphase. In most cells during mitosis the nuclear
membrane breaks down, thereby eliminating briefly the important inside-outside
relationships imposed by that membrane upon particles of large size. (While
Paramecium is an exception in that its macronuclear membrane does not
'break down', there is sufficient change to allow for the passage of particles

A. I ntra-exlranuclear

(during division)

fTOBE SYNTHESIZED) TO CONTAIN TO TRANSPORT TO ACT (defined in text)

^ ■„ N

(j'^^\ >■ % \ • » • (between divisions)

\\. /' (membrane barrier)

B. Cytoplasmic Organelle Systems

TO ACT (represents collisions of microsomes-mitochondria)

TO BEAT

TOPOLARIZEJi i • # TO SCAN

TO ANCHOR

(represents linked
TO LINK kj" ^ Y ^TOLI^Kkj-r PeHide-kineties)

TO PACK ^\ 0 TO HOLD OPEN; TO LINK kj,.,

TOLINKkj(#^ # TO SWEEP

(represents kinety) i TO FORMIC

(represents gullet system)

Fig. 3. Partial primordial graphs for organelles in Paramecium. A. Organelles

engaged in communications between nucleus and cytoplasm and in construction

of complexes and systems of organelles. B. Organelles engaged in systems for

feeding, for locomotion and for structural integration.

up to 1 // in diameter during fission (15).) The first function of the primary
organelle is to contain the message introduced presumably by the chromosomal
genes at time of nucleolar synthesis. Its next function is to move and to transport;
the function shown in the figure is to move 'out of the nucleus; this is followed
by to act (collide, fuse, develop), an accomplishment in which the message and
its vehicle are also partial power supply and building stone to make cilium,
trichocyst, mitochondrion, or whatever is dictated by uncertainty loss. The
decision tree (Fig. 2) is itself a partial primordial graph representing the
diversity of these acts.

The cytoplasmic organelle system (Fig. 3b) operates through similarly gross
functions. The function of a pellicle unit is to beat (row, propel), to pack (to fit
as a block in the pellicle wall), and to link similar units longitudinally (k^) and
latitudinally {k,)\ a column of such units (one kinety) is aligned with directional
reference to each of its ciliary bases (kinetosome) and basal fibrils (kinetodesma);
each kinetodesmal fibril lies to the right of its kinetosome; and each is over-
lapped by and in turn overlaps two or three of the fibrils antero-posteriorly

•*

- ^, . . - 4

■ vir •:, / j4 ..

.^y^,.:^;^-ar-

Plate I

The appearance of organelles in Paranicciuin under phase conlrasl and electron microscopy. (In A and B the
line represents 10 /' ; in C. D. and E it represents 1 //.)

A. Food-intake system, compression-dissected from an unfi.xed cell. From left to right, the non-ciliated 'granules'
of the ribbed wall complex followed by four columns of the ciliated quadrulus complex and eight columns of the
ciliated peniculus complex (26). Phase.

B. Macronucleus anlage in an exconjugant during extrusion of young nucleoli: net-like figure in the center is
fusion product of old nucleoli (15). Phase.

C and D. Electron micrographs of a similar stage. The smaller dark bodies are chromatic elements of the nuclear
matrix: the larger bodies at the left are young nucleoli, and at the right in the cytoplasm are mitochondria (15).

E. Electron micrograph of a single packing unit of the hexagonal complex of the pellicle system (4iS). Note the
cross-sectioned kinetodesmal fibrils in the bays of cytoplasm at each side of thecilium base; at the left, a portion of a
trichocyst with its golf-lee-like head: at the right a tubular mitochondrion (S. 9).

None of these photographs has been previously published. Each is a part of the work cited in parentheses, and
done in collaboration with Drs E. L. Powers and L. E. Roth of Argonnc National Laboratory.

to face p. 224

Information Content and Biotopology of the Cell in Terms of Cell Organelles 225

along the kinety; these units act to polarize; the array of kinetics (or entire
pelhcle system) functions to envelop the endoplasm of the whole animal. It
also functions to anchor in place other systems such as the food intake or gullet
system. The anchorage confers a new level of asymmetry, resulting in the
swimming function to scan or spiral; the function of the peniculus and quadrulus
is to sweep food particles down the intake tube; their terminal cilia act to form
food vacuoles (FV); the cilia-free ribbed wall functions to confer rigidity and
to hold open the tube, which lies within the endoplasm; the gullet system also
functions to envelop (k,',-) the endoplasm. This graph may be read in the
following way: effective beating of a kinety cilium requires polarization; both
functions require positioning upon the pellicle by latitudinal linking to adjacent
kinetics (A:/s) ; the previous functions require packing (a continuously surfaced
pellicle). Longitudinal linkage {k^) is required to prevent the dispersion of the
surface blocks from within a kinety. Each kinety organelle may perform every
function, but locally any function may be by-passed. The function to scan
requires anchorage of the gullet organelle-complexes in position on the animal;
the gullet's general function is to feed. An effective food vacuole requires that
food be swept into it by the cilia of the peniculus and quadrulus ; these functions
require that the gullet be held open by the gullet tube-wall, which requires
anchorage to the pellicle. The general function of envelopment requires the
linkage of all ^/s and A:/s. (A nearly unique quality of the ciliated protozoa,
which, however, should not be entirely ignored in the transformations to
higher forms, is the presence of what might be called 'linkage groupings'
in the cytoplasm: organelle patterns, far more complex than any known
in the metazoa, appear to be as much dependent upon the previous existence
of a related pattern in the cytoplasm as upon any nuclear genes (49); even
Stentor, with its remarkable capacity to regenerate 'kinetics' (actually pig-
mented stripes), rebuilds its mouth organelles only when a particular juncture
of maximum anisotropy in the stripe pattern is available (35).) Organelle-
functions are therefore given not in the terminology of the molecular level (whose
necessary though not strictly pertinent relations are partially represented for the
whole cell topologically in such graphs as those of the glycolytic and citric acid
cycles (50)) but in the correspondingly appropriate terms of the gross operations
performed.

According to this concept, the cell is entirely describable in minute detail
of anatomical pattern without reference to either power or fuel. It does not
matter whether the oar-like cilia are tugged by galley-slaves, gasoline engines
or a creatine-phosphate-ATP system. However, the universal usage by cells of
such engines places some restriction at the systems-coupling level, and probably
represents a nearly unique solution of the bioenergetics problem. If the model is
correct, the most complex patterns are entirely derivable by just such remarkably
simple interactions as those first explicitly delineated by D'Arcy Thompson (12).

In summary, at the organelle level fundamental topological sets are recog-
nized of two classes: those that are periodically disjoined (intranuclear from
extranuclear organelles), and those that are continuously joined at non-empty
intersections (cytoplasmic organelle-systems). Periodic coupling processes (such
as during mitosis and nuclear membrane disappearance) occur to form non-
empty intersections at all disjunctions of the first class. Below this dimensional

226 Charles F. Ehret

level and within the spheres of intracellular and extracellular molecular inter-
action, each set of the higher two classes is continuously capable of communica-
tion with every other set by means of diffusion and convection transport
phenomena.

V. CONCLUSION

In the introduction to this conference Bigelow suggested that in biological
systems with long time-constants, for a message to be useful at the receiving
point, 'all messages must be enormously complex groups of messages rather
than simple ones' (51). This expression is clearly related to the limited span
proposition (52), that is, that span of diversity is limited by difficulties of internal
control. Therefore it is not too surprising to find that epigenetic control
systems of the cell (whose internal difficulties are in the form of long time
functions and thermodynamic vulnerability) solve these difficulties by the
method of 'chunkmg' complex groups of messages into structurally and func-
tionally unitized subsystems. That the subsystems of primary organelles appear
to be phylogenetically ubiquitous might also have been predicted from the
principles of biochemical evolution. But that they are structurally so alike is
indeed a striking fact; although this is not to say that we should now expect
the cilium of whale bronchus, the axial fiber of fern sperm, the connecting
fibril of toad retina, the sweeping cilium of paramecium peniculus or the mantle
cilium of a mollusc to be exactly alike. We know that such organelles are
capable of antigenic distinctions even amongst the various stocks within a
species (53); indeed, the mechanism of such distinctions constitutes a most
crucial problem of molecular biology. That the functional and structural
diagrams of an organism in temis of its organelles are topologically homeo-
morphic is consistent with parallel relations at other levels; in its functions
between molecular and cellular levels of organization, the cell organelle fills the
last gap in a complex hierarchy of unitized subsystems that characterize the
organism from the atomic to the social level. The method of integrating these
hierarchies and of extracting quantity of infoiTnation from any organism that
employs such mechanisms remains to be accomplished.

Acknowledgment — I wish to thank my many colleagues, particularly Howard
DucofF, E. Lawrence Powers, and Robert Schweisthal of Argonne National
Laboratory for their interest and cooperation, and Henry Quastler of Brookhaven
National Laboratory for his very helpful suggestions.

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Information Content and Biotopology of the Cell in Terms of Cell Organelles 227

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18. J. H. Taylor, P. S. Woods, and W. L. Hughes: The organization and duplication of
chromosomes as revealed by autoradiographic studies using tritium-labelled thymidine.
Proc. Nat. Acad. Sci., Wash. 43, 122-128 (1957).

19. A. F. Huettner: Continuity of the centrioles in Drosophila melanogaster. Z. Zellforsch.
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20. E. Chatton and J. Seguela: La continuite genetique des formations ciliaires chez les
cilies hypotriches. Le cinetome et I'argyrome au cours de la division. Bull. Biol, 74.
349^142 (1940).

21. Akira Yuasa: Critical observations on the origin of the blepharoplast and centrosome
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22. R. Lepper: The plant centrosome and the centrosome-blepharoplast homology. Bot.
Rev. 22, 375-417 (1956).

23. H. W. Beams, T. N. Tahmisian, and R. L. Devine: Electron microscope studies on the
cells of the malpighian tubules of the grasshopper. J. Biophys. Biochem. Cytol. 1, 197-202
(1955).

24. D. W. Fawcett and K. R. Porter: A study of the fine structure of ciliated epithelia.
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25. M. L. Watson: The nuclear envelope. /. Biophys. Biochem. Cytol. 1, 257-270
(1955).

26. C. F. Ehret and E. L. Powers: The organization of gullet organelles in Paramecium
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27. L. E. Roth: Aspects of ciliary fine structure in Euplotes patella. J. Biophys. Biochem.
Cytol, Suppl. 2, 235-240 (1956).

28. C. B. Metz, D. R. Pitelka, and J. A. Westfall: The fibrillar systems of ciliates as
revealed by the electron microscope. I — Paramecium. Biol. Bull. 104, 408-425 (1953).

29. A. Lwoff: Problems of Morphogenesis in Ciliates, J. Wiley and Sons, New York
(1950).

228 Charles F. Ehret

30. J. F. Danielli: Cytoplasmic inheritance. Nature, Lond. 178, 214-215 (1956).

31. F. Wassermann: The intercellular components of connective tissue: origin, structure,
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32. J. Gross: The behavior of collagen units as a model in morphogenesis. /. Biophys.
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33. M. R. Cohen and E. Nagel: An Introduction to Logic and Scientific Method, Harcourt-
Brace, New York (1934).

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/. Franklin Inst. 261, 377-379 (1956).

45. T. H. Dunnebacke: Cytopathic changes associated with poliomyelitis infections in
human amnion cells. Virology 2, 811-819 (1956).

46. C. Morgan, H. Calderon, H. Rose, and D. Moore: Structure and development of
viruses observed in the electron microscope. IV — Viruses of the Rl-APC group. /. Biophys
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(1955).

48. C. F. Ehret and E. L. Powers: The systems and complexes of primary organelles in
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50. N. Rashevsky: Contributions to topological biology: some considerations on the
primordial graph and on some possible transformations. Bull. Math. Biophys. 18,
113-128(1956).

51. J. N. Bigelow: Unpublished.

52. H. Quastler: Unitization in biological systems. Essays on Biological Unitization,
Report No. R-52, Control Systems Laboratory, University of Illinois, Urbana (1953).

53. J. R. Preer: Gel diffusion studies on the serotypes of Paramecium. Jordan Hall Dedi-
cation Program, Indiana University (1956).

54. E. Borysko and F. B. Bang : Electron microscope observations on nucleolar structure.
J. Appl. Phys. 23, 163 (1952).

55. H. J. Weinstein: An electron microscope study of cardiac muscle. Exp. Cell. Res. 7,
130-146 (1954).

Information Content and Biotopology of the Cell in Terms of Cell Organelles 229

56. A. Moscona: Cytoplasmic granules in myogenic cells. Exp. Cell Res. 9, 377-380 (1955).

57. G. E. Palade: The endoplasmic reticulum. J. Biophys. Biochem. Cytol., Suppl.2, 85-98
(1956).

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2, 131-142(1956).

59. J. J. Wolken: A molecular morphology of Eitglena gracilis. J. Protozool. 3, 211-221
(1956).

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electron microscope. Z. Zellforsch. 42, 134-148 (1955).

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16, 464^70 (1955).

* The last eight references are not specifically discussed in the text, but are referred to as
examples in the Decision-Tree diagram, Fig. 2. Many of the cytological references cited
concur with the data rather than with the interpretations of the authors.

16

QUANTIFICATION OF PERFORMANCE IN A
LOGICAL TASK WITH UNCERTAINTY

A. Rapoport

Mental Health Research Institute, University of Michigan

Abstract — Tasks to which information theory has been apphed characteristically do not involve
'reasoning', i.e. the drawing of inferences. The present paper explores the possibility of
applying information theory to measuring performance of logical tasks. We note at once
that any task in which a necessary conclusion must be reached from given information has
formally speaking no information content. From the information-theoretical point of view,
therefore, no information is gained in the process of solving a purely mathematical or logical
problem, no matter how 'complex'.

There are problems, however, in which in addition to the making of inferences, information
must be obtained in the process of solution. Success of solution can be measured by the rate
of obtaining such information and by the degree of completeness with which it is utilized.
Assuming complete utilization at each step, the efficiency of solution depends on the efficiency
with which information is obtained. A classical example is the coin-weighing problem in
which a deviant coin and the direction of its deviation must be determined in the fewest
possible weighings. Information theory provides not only the minimum number of weighings
for such a problem but also a method for constructing the best 'strategy'.

In the present paper a particular logical task with uncertainty is discussed from the infor-
mation-theoretical point of view. It is shown that the construction of an information-getting
strategy depends very strongly on the instructions given the subjects and on the inferences
which the subjects make from the instructions. Thus the practical problem of quantifying the
performance of a logical task carries within it certain ambiguities which must be resolved if
information theory is to be of use in psychological tests based on such tasks.

Information theory is mainly concerned with a quantity called the amount of
uncertainty associated with a situation in which choices or guesses are made.
This uncertainty can be viewed as a measure of ignorance. For example, we
are the more ignorant of the value about to be assumed by a random variable
with a discrete domain, the more values it can assume and the more nearly
equi-probable these values are.

Defining every situation of ignorance is a set of postulates with a subjective
flavor. Somebody is ignorant. At least this is the case in real situations involving
subjects whose state of ignorance is to be inferred. It may be argued from certain
philosophical points of view that this intrusion of subjective concepts is unsatis-
factory, and attempts should be made to circumvent them or to eradicate them
altogether. I don't want to take sides on this question, but only to point to
some of its manifestations by way of indicating its persistence. The question
has been raised in connection with the foundations of probabihty theory.
There the attempts to circumvent the subjective element have given rise to the
so-called 'objectivist school', which sought to define probabilities of events
'objectively' in terms of the relative frequencies of the events. Opposition to

230

Quantification of Performance in a Logical Task With Uncertainty 231

'subjectivist' notions are also, I think, at the root of many philosophical objec-
tions to quantum theories.

The question of where to draw the line between subjective and objective
frames of reference also arises in connection with attempts to link information
theory with thermodynamics so as to make it useful in theoretical molecular
biology. Whatever the merits of the attempts may be, this area of investigation
does bring out rather pointedly the necessity of examining the possibly 'subjec-
tive' postulates underlying the description of the situations studied, indeed, the
philosophical question 'What is a subjective postulate?' comes to the forefront
in the region where thermodynamics, quantum theory and information theory,
meet — a triple point.

There is an area of possible application of information theory, however,
where clearly subjective postulates are not only unavoidable but central. This
is the area of psychology. Psychology is a study of behavior. Since psychology
has gradually outgrown the austere positivistic restrictions of strict behaviorism,
it has become respectable again to include into psychological theory considera-
tions based on how the situation looks from inside the subject. To be sure,
these matters must somehow be inferred from overt behavior, but once they are
inferred there is no reason why these 'subjective variables', for example, sub-
jective probabilities, utility functions, and so on, cannot enter as parameters in
a theory. Indeed, if these parameters are determinable and stable, they serve to
'objectify' the subjective and thus contribute to the success of psychology as a
science.

Information theory was applied from its very inception to psychological
investigations. These applications have often been criticized. The grounds for
criticism have been many, but a recurrent theme has been the failure of many
psychologists to realize that information theory is worthless without an under-
lying set of postulates for each situation. Just as the application of probability
theory to any situation necessitates the determination of a 'sample space', that
is, a set of elementary events with a priori assignment of probabilities or a
probability distribution function, so is the case with information theory.

Yet it was shown by de Finetti (1), Savage (2), and others that a rigorous
theory of probability could be constructed backwards. That is to say, beginning
with certain preferences of individuals for certain outcomes as reflected in their
choices of actions under uncertainty, a set of subjective probabilities of events
could be inferred, provided certain 'rationality criteria' of behavior were satisfied
by the individuals. The question to what degree such rationality criteria are
in actuahty satisfied is another question which has led to many interesting
investigations in their own right; so it is not entirely an unfortunate one. It
must in any case be admitted that the 'subjective probability' of an event can
in principle be defined, and thus statements such as, 'The Democrats will with
probability 0.6 win in I960,' are not wholly devoid of operational sense, pro-
vided the expressed 'subjective' probability is inferrable by explicit rules from
observed behavior and enjoys a certain stability. Such assertions have no
sense in the conceptual framework of the objectivist school, since the election
of 1960 is a unique event whose 'probability' cannot be deduced from a fre-
quency of occurrence.

The operational definition of subjective probability introduces probability

232 A. Rapoport

theory into psychology in a significant way, not as a mere appendage to statistics.
I think the situation is similar in the case of information theory. Instead of
lamenting the ambiguity of the 'universe of discourse' in psychological situations,
which stands in the way of a straight-forward appHcation of infonnation theory,
we may well seek to infer the universe of discourse as it looks from inside the
subject. This is, indeed, a central task of the psychologist, and it is improper
for him to shun it.

It remains true, however (and it is just as it should have been), that the early
psychological experiments based on information-theoretical considerations
were constructed in such a way as to eliminate idiosyncratic subjective probabili-
ties. In memory tasks one starts with some set of thoroughly randomized and
presumably equalized stimuli. One introduces redundancies in terms of actual
biases of occurrence-frequencies objectively determined. The same techniques
prevail in experiments in which the capacity of the individual as a channel is
measured. These are all attempts to translate into experimental psychology
situations occurring in communication engineering. The human being is studied
as a piece of communication apparatus. I beheve this strategy to be entirely
correct as far as it has gone. I am sure, however, that its limitations are apparent
most of all to the investigators who pursue it. Somewhere along the line a
transition must be made which will allow the application of information theory
to psychology as distinct from psychophysics. In other words, the perceptual
world of the subject must eventually become a focus of interest. There is no
reason why information theory should not become a useful tool in such investiga-
tions.

Characteristically, the tasks just described (such as rote learning, multiple
choice responses, and so on) do not involve the deductive process. Indeed,
from the formal information-theoretical point of view, the results of infomiation
theory are not applicable to a deductive process, because there is no 'uncertainty'
in such processes. The solution of a mathematical problem, no matter how
complex, yields no information from the information-theoretical point of view.
From either the common-sense or the psychological point of view such a con-
clusion seems bizarre. The information-theorist can, of course, argue that his
technical definition of information departs from common-sense and psycho-
logical notions of what constitutes infonnation, and he is technically correct.
Yet it might be instructive to try to bring the two concepts of 'information'
into closer agreement.

Formally speaking, no information is gained in the solution of a purely
mathematical or logical problem, because the solution is implicitly contained in
the already known conditions. But the solution is not initially known to the
subject. Is there a way to measure the extent of his ignorance ? There might
be, if we are willing to abandon the omniscient position from which the solution
is seen as a necessary inference, hence of zero uncertainty, and enter the per-
ceptive of the cognitive field of the subject, to whom only a range of possible
solutions and, perhaps, associated subjective probabilities present themselves.
But how does one get into this perceptive field? Obviously by observing the
subject's behavior. But how does one make inferences from the observations to
what that perceptive field may be ? It would be gratifying to be able to say that
for every configuration of the cognitive field, there is a specific behavior pattern,

Quantification of Performance in a Logical Task With Uncertainty 233

but unfortunately this is not the case, as will be seen in the following example.

Suppose we present the subject with the famous coin-weighing problem.
One of twelve coins is of odd weight. It is required to detennine the coin and
whether it is lighter or heavier than the rest in a minimum number of weighings
on a balance using only the coins for weights.

Information theory not only reveals that three weighings are necessary and
sufficient but also indicates the strategy. Obviously there are loga 24 = 4.59
bits of information (uncertainty) in the problem. A weighing can yield a
maximum of logo 3 = 1.59 bits. Therefore, at least three weighings are necessary
and may be sufficient. Further analysis shows that the first weighing can yield
the full 1.59 bits and that only if four coins are weighed against four. The
second weighing must involve six coins chosen in such a way that the three
outcomes have probabihties 3/8, 3/8, 2/8, which yields 1.55 bits. The third
weighing will therefore involve three coins, that is, 1.59 bits, in three
fourths of the cases and two coins or 1 bit in one fourth of the cases, i.e.
an average of 1.45 bits. The total information is 4.59, exactly equal to the
initial uncertainty.

Now the uncertainty in the problem as it is presented is clearly perceived.
At least it is easy to recognize that there are initially twenty-four possibilities.
It takes some effort to determine the remaining uncertainty after each weighing,
but it is none too difficult to do so. We may therefore suppose that in most
instances the 'uncertainty' of the problem is perceived by a fairly intelligent
subject correctly, that is, in accordance with the 'objective' assignment of
uncertainty. However, it is by no means true that the majority of subjects
proceed to the solution in the optimal way. That is, they cannot deduce the
'correct' strategy, even when they perceived the 'actual' amount of uncertainty
in the problem.

It appears, therefore, that it is too much to expect to be able to deduce the
subject's personal evaluation of uncertainty from his strategy in the solution
of a problem in which both the deductive process and resolution of actual
uncertainty must operate. However, this circumstance only reveals the situa-
tions to be more 'psychological' than they appear in the light of the personal
evaluation of uncertainty. Not only is this evaluation personal but also the
choice of strategy is, and the latter is by no means always optimal relative to
the uncertainty perceived. We are reminded of a similar difficulty in the
psychology of decisions in which subjective estimates of probabilities and
subjective utility functions are intimately intertwined.

As pointed out, ours is a similar problem. Assuming that the solution of
a logical task with uncertainty will be determined by two 'subjective' characteris-
tics, namely, (a) the amount of uncertainty perceived by the subject at each
step, and (b) his preference of strategy for a given amount of perceived un-
certainty, then our problem is to determine these subjective characteristics in
the course of a solution of a problem. It should be mentioned that some obvious
techniques for detennining subjective uncertainty are in most cases unusable.
If, for example, the solving process is interrupted to ask the subject what he
does or does not know, the subject may through these questions become
aware of relations he had not been aware of or he may doubt some assumptions
he had been making correctly but with insufficient justification.

234

A. Rapoport

I will now describe a task which has been adapted to an analysis of the
problem-solving process in such a situation.*

The subject is faced with a board on which nine numbered light bulbs are
arranged in a circle, at the center of which is a tenth bulb. Each of the peri-
pheral bulbs may be lit by an adjacent button. Moreover, relays are so arranged
inside the apparatus that lighting of certain lights may result in the lighting
of other lights following a constant 'synaptic delay' of three seconds. A 'prob-
lem' is a programming in the apparatus so that certain causal relations are
established among the lights. These causal relations are only partially represented
by arrows on a chart attached to the mounting board. Examples are given in
Figs. 1 and 2.

Fig. 1. Problem 2 on PSI

Fig. 2. Problem 3 on PSI

The point of the problem is that the meanings of the arrows on the chart
are ambiguous. An arrow from A to B may mean that A is necessary to light
B or sufficient, or both, or that A inhibits B. The subject's task is to obtain
sufficient information about these relations, by pushing any button he chooses,
to be able to cause the center bulb to be lit by manipulating buttons 4, 5, and 6
only. We will refer to these as the circled buttons.

There is a unique solution to each problem, consisting of a certain sequence
of pushes of the circled buttons or of their combinations. For example, the
solution to problem 2 (Fig. 1) is the pushing of buttons 4, 6, 5, 6 in the successive
time periods. The solution to Problem 3 (Fig. 2) is 5, 0, 45, 6, 45.

There are a number of 'rational' approaches to the problem. Let us begin
by making a chart of the connections indicated by the arrows. Figs. 1 and 2
are formally equivalent (as linear graphs) to Figs. 3 and 4. However, many
characteristics of the problems are visually displayed in Figs. 3 and 4, which
immediately suggest various lines of attack. These charts display what the

* The apparatus to be described, 'PSI', based on the isomorphism ofcertain networks of relays
and the calculus of propositions (previously discovered by Shannon (4) and by McCulloch
and Pitts (5)) was developed in Chicago by R. John, J. G. Miller, S. Molnar and H. J. A.
RiMOLDi. The adaptation of the instrument to experiments of the type described is largely due
to John (3), who has listed a great number of performance parameters to be observed in the
problem solving process. Of these the so-called 'inferential lag' (defined below) seems to me of
particular importance. John's terminology and definitions diff"er somewhat from those in this
paper, but the basic ideas (as yet unpublished) have been the point of departure for the present
analysis.

Quantification of Performance in a Logical Task With Uncertainty

235

subject does not know. For example, in Fig. 3, the convergence of arrows
leading from lights I, 2, and 6 upon C (the center light) induces the following
questions: Which combinations of 1, 2, and 6 are necessary or sufficient or
both to light C? Is one or more of them an inhibitor? If so, which one?
Similar ambiguities are apparent at the other three junctures, that is at lights

Fig. 3. Problem 2 displayed in time sequence

1, 2, and 9. A single arrow leading to a light presents no ambiguity. This is
in consequence of the condition explained to the subject that each arrow
'means' something, hence a single arrow can mean only 'necessary and sufficient',
otherwise its presence or absence would make no difference.

The subject can now ask specific questions. He can ask, for example, a
question about each converging juncture. The question can pertain to the

d)—

^c

Fig. 4. Problem 3 displayed in time sequence

meaning of the arrows or to the combinations necessary or sufficient to light
the bulb on which the arrows of the juncture converge. In the first case, he
will be labeling arrows, in the second case the lights. Or he may proceed in a
different way. Noting that all the possibilities of solution are displayed by the
circled buttons in their proper time sequence, he may ask how each button is
involved in the solution when its turn comes, by being pushed or not by being
pushed.

Note that each of these perceptions of the problem implies a different
'information content'. According to one scheme, one seeks a 'yes' or 'no'
answer to every non-null combination at a juncture. There are sixteen such
combinations in all in both problems, hence sixteen bits of uncertainty if the
'yes's' and 'no's' are assumed independent. They are not independent, but
this interdependence can be arrived at a priori only by deduction, wliich may
or may not be made. Thus the uncertainty of the situation depends on the

236 A. Rapoport

State of mind of the subject. According to another scheme (labeHng arrows),
one can assign the values to the arrows in eighteen different ways at the triple
juncture! and in four different ways at each of the three double junctures.
Hence there are 18 x 64 different ways. This gives a little over ten bits of
uncertainty. According to the last scheme, one has to decide whether to push or
not to push each of the circled buttons in the time period when they appear on
the chart. Here Problem 2 seems to have four bits of uncertainty and Problem 3
seems to have six bits. Clearly, the amounts of uncertainty associated with
each scheme are different, but so are the yields of each trial, because one counts
the yield in different kinds of statements, which have different a priori probabili-
ties of being true.

One can push the analysis still further and thus reduce the information
content of each problem by utiHzing the rule that each problem has a unique
solution. In this analysis the 'sample space' v/ould be all possible problems
having unique solutions involving the circled buttons at the proper time periods.
Several of such problems would 'map' on each solution, and since the number
of problems mapping on each solution are not equal, neither are the probabihties
of the respective solutions. The value 4 bits for Problem 2 is a consequence
of the equi-probability of all sixteen solutions (strictly speaking fifteen, barring
the null solution where no button is pushed). If the solutions are not equi-
probable the infonnation content is correspondingly reduced.

This calcu'ation is extremely tedious and has not been carried out. It is
mentioned only to stress the general idea that the information content of the
PSI problems depends significantly on the 'sample space' according to wliich
probabilities are assigned. This sample space is presumably chosen (perhaps
unconsciously) by the subject; hence the amount of uncertainty in the problem
is a 'subjective' quantity, difficult to ascertain but in principle inferrable from a
thoroughgoing analysis of the problem solving process.

One sees thus that even pursuing a far-reaching analysis and assuming
perfect memory, it is not easy to derive the best strategy in the sense of minimiz-
ing exploratory trials. When one takes into consideration the ambiguities
present in the subject's mind, who may not even have the convenient visual
representation of the time sequence in his mind's eye, one realizes that far more
psychology than can be formally treated by information theory at this time is
involved in the problem.

Nevertheless, it is possible to cast the problem into information theoretical
terms. One hopes, at any rate, that the concepts of information theory can be
extended to cover situations where the subject's perception of the problem is
an important unknown, That is, information theory may help formulate such
situations in quantitative and analytic language. We have attempted to do so
in the following way. We record the successive trials. Each trial must yield at
least one of the sixteen 'crude facts', i.e. combinations of lights at each juncture

t In view of the rule that each arrow must have a meaning, the number of ways values can
be assigned to the arrows equals the number of distinct irreducible disjunctions among the
subsets of the arrows. Thus for three converging arrows there are seven non-null subsets
(i.e. 'disjunctions' involving only one subset), tliree disjunctions among the singles involving
two singles, three among the doubles involving two doubles, three involving a single and a
double, one involving all three doubles, and one involving all three singles, eighteen in all.

Quantification of Performance in a Logical Task With Uncertainty 237

w hich do or do not light the node of the juncture. Some trials yield more
than one fact, but some yield no new facts. The fact yield is also recorded,
counting the facts which the subject had the opportunity to observe, but not
counting the inferences which he could have made.

Combinations of these facts make possible inferences about the meanings
of the arrows at each juncture. For example, in Fig. 4, the facts '1 does not
light 8' and '6 does not light 8' allow the inference that the arrows at this
juncture should be labeled as shown in Fig. 5.

1

Fig. 5.

These possible juncture inferences are also recorded, and thus their rate
of accumulation. Finally, the juncture inferences collate into the bits of
infonnation directly related to the solution of the problem — whether or not
to push the circled buttons involved in the successive time periods.

When all this information is available (by inference, of course), there is
no formal uncertainty left in the problem. However, in most cases the problem
is not yet solved. The extra trials made by the subject, who has the solution
available by inference, constitute the 'inferential lag'. We thus have various
possible measures of subjective uncertainty over and above the 'objective'
measures. The most obvious difference is revealed in the repetitions of trials
(ordinary failure to record information obtained). Next we have the explicitly
redundant trials, that is, those which while being new trials yield no new facts.
Next the inferential lag already mentioned. All these can be measured both
in time units and in numbers of trials.

The apparatus and the analysis of the problem solving process offer many
opportunities for elaborate experimental designs, but they all hang on the
question of how 'standard' these tasks are. In other words one needs to answer
the question of whether there is a level of performance on each problem
characteristic of a given subject, so that the variance in performance in a
population of subjects can be adequately accounted for by a variance of some
inherent abihty.

Although this question has not yet been answered definitively, there are
indications of a certain stability of performance. A set of experiments was
performed at the Mental Health Research Institute, University of Michigan,
in which the 'subject' in each case was a group of three students who solved
the problems cooperatively by discussing each move and by coming to unanimous
decisions on which move to make next. Eight such groups solved Problem 2
and then went on to solve Problem 3. The average number of moves for Problem
2 was about thirteen and for Problem 3 about nineteen. This is a first indication
of the relative difficulty of the problems. That this difference is real is indicated

238 A. Rapoport

by the fact that all eight groups increased the number of moves from Problem 2
to Problem 3. When the groups were rank-ordered on their performance on
Problem 2, the rank order was preserved (with just one reversal of two con-
secutive groups) on Problem 3. Another set of eight groups was given Problem
2 and then Problem 3 with a money incentive to minimize the number of
moves on the latter. Under these conditions again all eight groups decreased
the number of moves (averaging only eight on Problem 3). In spite of the
radically changed situation, the rank order of these eight groups was again
preserved from Problem 2 to Problem 3 (again with a reversal of only one
pair of consecutive groups).

When groups are rank-ordered according to time of solution, no discernible
correlation appears from one problem to another. These results point to a
possible stable relation between the complexity of the problem and the effec-
tiveness of solution strategy adopted by each of our trios of subjects. The
lack of correlation in rates of perfonnance points to possible extraneous effects
such as the nature of the discussion process itself. At any rate the fact that
the most prominent regularities are found in the performances as measured
by the number of moves raises the hope that these regularities are the reflections
of the uncertainty content of the problems as perceived by the subjects. It is
noteworthy that, while on the level of observable crude facts and on the level
of inferences about the meanings of the arrows, the two problems have the
same uncertainty contents (about sixteen and ten bits each), on the level of
major inference involving the circled buttons. Problem 2 has four bits of uncer-
tainty while Problem 3 has six. The approximately 50 per cent increase in the
average number of moves from Problem 2 to Problem 3 may well be a reflection
of the increase in uncertainty on that level. Whatever the case may be, the
results warrant further experimentation with a view of establishing the expected
level of performance of a given subject on a given problem, once the set of
uncertainties on various levels of observation and inference characteristic of
the problem and certain factors of strategy efficiency characteristic of the
subject are known. It is evident that the number of various problems which
can be programmed into the PSl apparatus is astronomical.

REFERENCES

1. B. DeFinetti: La Prevision : ses lois logiques, ses sources subjectives. Ann. Inst. Henri
Poincare 7, 1-68 (1937).

2. L. J. Savage: The Foundations of Statistics, J. Wiley and Sons, New York (1954).

3. E. R. John: Contributions to t/ie study of the problem-solving process. Preprint No. 1,
Mental Health Research Institute, University of Michigan, Ann Arbor (1956).

4. C. E. Shannon: A symbolic analysis of relay and switching circuits. Trans. Amer. Inst.
Elect. Eng. 57, 713-723 (1938).

5. W. S. McCuLLOCH and W. Pitts: A logical calculus of the ideas immanent in nervous
activity. Bull. Math. Biophys. 5, 115-133 (1943).

PART IV

DESTRUCTION OF INFORMATION BY
IONIZING RADIATION

The disorganization of highly ordered macromolecules of biological importance
by the action of ionizing radiation is a field of study owning a half-century of
history, a tremendous literature, and possibly a somewhat feeble accom-
plishment in terms of clear and unexceptionable conclusions. With the develop-
ment of information theory, and its subsequent application to biological systems,
there appears to be substantial basis for cherishing the hope that it may constitute
a valuable tool in the analysis of the experimental results of radiobiology and
their translation into knowledge concerning biological phenomena. The present
section of the symposium is dedicated to this goal. The first two papers, by
GoRDY and by Platzman and Franck, explore different aspects of the inter-
pretation of physical and chemical effects of ionizing radiation on proteins and
related substances; for without some measure of fundamental physical insight
into the mechanisms of this action, the utilization of information theory in
radiobiology would appear unlikely to emerge from an ineffectual state of
pleasant vagueness. In the third paper, by Morowitz, positive steps are taken
in the analysis of some relationships between information theory and ionizing-
radiation action. The following two short papers, which stem from discussion
by Koch and by Augenstine, are devoted to the almost perennial question of
the role of sulfur-bonding in radiobiology, as was also, to a large extent, the further
discussion at the symposium, part of which is summarized in the final pages of
the section. It is disquieting to have to record that the views on this perplexing
problem are still seriously discordant.

R. L. P.

239

ELECTRON SPIN RESONANCE IN THE STUDY
OF RADIATION DAMAGE*

Walter Gordy

Department of Physics, Duke University, Durham, North Carolina

Abstract — It has been demonstrated by a Duke University microwave group that the electron
spin resonance of the resuUing unpaired electron can give specific information about the
radiation damage in proteins, nucleic acids, and many other biologically significant chemicals.
The structures of their electron resonances show that free radicals of various types are formed
from the different amino acids and simpler peptides by ionizing radiations. However, in
numerous proteins only two structural patterns are obtained, either separately or in com-
bination. One of these is like the common pattern obtained for cysteine, cystine, and gluta-
thione and is believed to arise from an unpaired electron (electron hole) on the protein sulfur.
The other pattern (obtained alone in proteins which have no sulfur) is a doublet characteristic
of the interaction of the electron spin with the spin of a single proton. The latter appears to
arise from an electron on a carbonyl oxygen interacting with a proton of the hydrogen bridge,
or possibly on a — CH — of the peptide chain which has lost an R side group. There is no
evidence that the ionizing radiation breaks the polypeptide backbone structure of the proteins.
The results seem to require that an electron hole or vacancy created at a given location in the
protein molecule can migrate to other locations where it has lower energy.

I. INTRODUCTION

Yesterday evening when coming over from the airport I discovered that I
was in the car with a biologist. After making this discovery, about half way
over, I asked my new acquaintance what it is that the biologists expect of the
physicists, what help — if any — we physicists can be to them. He told me
that we could give them better instruments. What they need as biologists,
he said, are newer and better instruments to see into things. He made no
mention of information or theory. I didn't ask him whether we were to bring
the instruments or just send them by mail. Nevertheless, I think that a physical
instrument which brings information out of biological things should be accepted
as a ticket of admission to a discussion of infonnation theory in biology, especi-
ally one held under the auspices of physicists !

The instrument which I offer as an admission ticket was not invented by
me. Electron magnetic resonance was discovered in 1945 by a Russian scientist,
Zavoisky (1). Nor can I claim to be the first to apply electron resonance to
the study of radiation damage. That, I believe, was first accomplished by
Hutchison (2), who in 1949 detected /'-center resonance in neutron-irradiated
alkali halides. Our group at Duke University, we are proud to say, was among
the first to show the applicability of electron magnetic resonance in the study
of biological substances, and the first, we think, to detect such resonances in
irradiated proteins. Combrisson and Uebersfeld (3), independently of our

* This research was supported by the United States Air Force through the Air Force Office
of Scientific Research ARDC contract No. AF 18(600)-497.

241

242 Walter Gordy

work, found resonances in certain amino acids. Their results did not agree
with ours, except with those for glycine.

Our group has now obtained electron spin resonances of scores of biological
substances which have been subjected to ionizing radiation. These include
amino acids (4), peptides (5), fatty acids (6), nucleic acids (7), various proteins
(4, 8), enzymes (8), homiones (9), and vitamins (9). Some of these results we
think we understand, at least partially; others we do not pretend to understand.
This does not discourage us, however. Some twenty to thirty years were required
for obtaining reasonably definitive interpretations of x-ray diffraction patterns
of a few of the simpler proteins. Nevertheless, it must have been apparent
from the first that these patterns contained a wealth of information which
would eventually be decoded by the persistent scientist. In electron spin
resonance we now have a direct method for studying radiation damage which is
comparable to the x-ray diffraction method for the study of structures. It is,
in fact, a specific for such studies, for it 'sees' not the normal biological matter
but the radicals, or broken pieces of molecules torn apart by ionizing radiations.

Descriptions of microwave spectrometers for observation of electron
magnetic resonances are available (10, 11). Such spectrometers can now be
obtained commercially. Descriptions of theoretical methods and applications
to chemical and biochemical problems are given in recent publications (11, 12,
13, 14, 15, 16).

In the observation of electron magnetic resonance the sample to be investi-
gated is placed in a microwave cavity at a point where the magnetic component
of the microwave radiation is strongest. The cavity containing the sample is
so placed in a d.c. magnetic field that the lines of the d.c. field lie perpendicular
to the magnetic component of the microwave radiation. When the d.c. field is
adjusted to the proper strength for resonance, microwave radiation will be
absorbed. The value of the field for resonance is:

Numerically,

H (gauss) = 0.7 HSi' (Mc/sec)/^ (2)

where g is the spectroscopic splitting factor for the paramagnetic species.
It is found that for practically all organic free radicals, including those produced
in solids by ionizing radiation, the g value is very close, within a fraction of
a per cent, to the g factor for the free electron spin, 2.0023. This comes about
because possible orbital moments are largely averaged out by the motion of the
unpaired electron, or by the spreading out over a number of atoms (delocali-
zation) of its molecular orbital. The persistent observation of a ^ factor near
that of the free electron spin has led to the designation of this resonance as
electron spin resonance.

In the vector model, the electron spin vector would precess about the direction
of the applied field H. Quantum mechanically there are only two stable orien-
tations for this precessing vector, which represents an average or the 'expectation
value' for the electron spin momentum. These correspond to the two observable
components, +| and — |, of the electron spin vector along a fixed direction
in space. Because of the interaction of the magnetic moment of the spinning

Electron Spin Resonance in the Study of Radiation Damage 243

electron with H, the potential energy of the electron is slightly greater for one
of the orientations than for the other. The difference in energy for the two
orientations is equal to the microwave quantum energy hv which will induce
the spin vector to flip over from one orientation to the other. The classical
Larmor precessional frequency of the electron spin vector about the direction
of Hh equal to the absorbed microwave frequency. Thus the precessing electron
is in tune with, or at resonance with, the microwave radiation.

In normal organic matter about us, the electrons are all — or nearly all —
in the lowest orbital levels, with the maximum limit of two electrons in each
molecular orbital. According to the Pauli principle, two electrons can share
an orbital only if their spins are aligned in an antiparallel manner. If it is
assumed that the spin vector of one electron flips over in an imposed field,
that of its orbital mate must flip in the opposite direction at the same time,
thus preventing any observable absorption or emission of radiation. To produce
an observable electron spin resonance in normal organic matter, one must
by some means lift electrons out of the completely filled orbitals of the ground
level. Strong ionizing quanta, such as those of x-rays, can eject electrons from
ground molecular orbitals with sufficient energy to free them entirely from the
parent molecule. If a molecule loses a single electron through ionizing irradia-
tion, the ionized molecule — if it holds together — will have a single unpaired
electron in one of its orbitals. This electron is now free to flip over in an
external field without the opposite flipping of a partner. The singly ionized
molecule is thus paramagnetic and can execute electron spin resonance. Further-
more, the electron which is knocked away from one molecule may become attached
to a neighboring molecule and thus convert it into a negatively charged radical.
Since the latter molecule is presumed to have all its bonding orbitals filled,
the new arrival must go into an orbital of higher energy and remain unpaired.
Thus resonance of electrons on negatively charged molecules might Hkewise
be detected. If the electron is ejected with sufficient energy it may, of course,
ionize several molecules before coming under the control of a particular molecule.
The end result is the same, however, except that a single quantum has, in
effect, been able to ionize more than one molecule. Two types of charged
radicals are thus produced. If the barrier to the return passage of the electron
between the molecules is high, as is the case in most organic solids, a sufficiently
high concentration of charged radicals can be built up in this way to give a
detectable electron spin resonance. The molecules may be small ones such
as the amino acids or long-chain macromolecules such as the proteins or
nucleic acids. The only requirement is that the separated electrons cannot
easily become paired again, i.e. that the radicals produced by ionizing radiation
have a lifetime sufficiently long for a detectable quantity to be built up.

II. NATURE OF INFORMATION CONTENT IN
ELECTRON SPIN RESONANCE

If the spin of an odd electron of a radical were entirely free from perturbing
influence of its environment, its resonance would be a single, sharp, isotropic
line with a g factor of 2.0023. Not much information is contained in such
a simple signal, although one could measure the lifetime of the radical from

244 Walter Gordy

its rate of decay. Also, the very fact that electrons could achieve such freedom
witliin an organic solid might itself be classed as desirable information. For-
tunately, however, the electron resonance signals are often rich with information
about the environment of the unpaired electrons. Our problem is to decode
their messages. There are at least tliree important sources of information
in these resonances. The first is the hyperfine structure arising from inter-
actions of the electron spin moment with magnetic moments of various nuclei
around or near the unpaired electron. The second is the small residual spin-
orbit interaction which in some instances makes the g factor slightly anisotropic
and different from the free spin value of 2.0023. The third is the information
which can be obtained from the line widths and shapes. The most important
of these sources is the nuclear hyperfine structure.

Most instruments used for detection of electron spin resonance plot the
intensity of absorption at a particular frequency as a function of d.c. magnetic
field. The appearance of the plot depends upon the instrument as well as
upon the actual, intrinsic shape of the resonance. I shall not discuss possible
variations in the actual line-shapes, but shall here assume that the resonances
have gaussian shape when the intensity of absorption at a constant frequency
is plotted as a function of d.c. magnetic field. A high-fidelity receiver and
recorder (or cathode ray scope) would reproduce closely the actual shape of
the resonance curve, as shown in Fig. 1(a). The high-fidelity systems are not,
however, the most sensitive systems. The most sensitive methods of detection
employ modulation of the resonance relative to the observation frequency.
A narrow-band amplifier is tuned either to the modulation frequency or to a
higher harmonic of tliis frequency. If one uses a frequency modulation which
is very small as compared to the width of the resonance and a phase-sensitive
amplifier tuned to the modulation frequency, a curve like that in Fig. 1(b) is
obtained. This curve represents the first derivative of the actual line-shape.
If one uses such a receiver and tunes to the second harmonic of the modulation
frequency, a curve hke that in Fig. 1(c) is obtained. This curve represents
the second derivative of the actual fine-shape. Both the first and second
derivative curves are commonly employed in display of electron spin resonances.
In interpretation of the curves it is desirable to know what method of detection
has been employed, especially when there are structural components incom-
pletely resolved. In the illustrations which follow we shall sometimes use first
and sometimes second derivative displays.

This brief description of the appearance of the signals and the simplified
theory of the structure of the resonance given below will, I hope, make it possible
for you, whether you are a biologist, chemist, physicist, or hybrid, to share
with us some of the fun of trying to decode the complex microwave messages
which we have been receiving from biological substances. You will be able,
I hope, to decide for yourself what is definitely proved by the resonances,
what is strongly suggested but not proved, and what is merely hinted.

1 . Nuclear Hyperfine Structure

The hydrogen nucleus, with a relatively large magnetic moment, 2.79 nm,
and nuclear spin of |, is abundant in all organic matter. The only other nucleus
with a non-zero spin abundantly found in biochemicals is N^^ (/ = 1 and

Electron Spin Resonance in the Study of Radiation Damage

245

jij = 0.40 nm). Carbon, oxygen, and sulfur are of course also prominent
constituents of biochemical matter, but their most abundant isotopes have zero
nuclear spins and hence cannot interact with the electron spin. In strong
resonances one might detect effects caused by C^^ (spin \ and natural abundance
1.12 per cent) or S'^^ (spin 3/2 and natural abundance 0.74 per cent). For some

(o)
ACTUAL LINE SHAPE

(c)

SECOND DERIVATIVE

Fig. 1 . Appearance of resonance signals as detected in various ways : (a) High
fidelity, (b) First derivative curve obtained by small modulation of the resonance
with a phase-sensitive receiver tuned to the modulating frequency, (c) Second
derivative curve obtained by small modulation of the resonance with phase-
sensitive receiver tuned to twice the modulation frequency.

substances one can obtain samples concentrated with C^^, S^ or O^'^. Hyperfine
structure of their miclei thus obtained will greatly augment the information
obtained from proton hyperfine structure, but it is fortunate for these studies
that C^^ is not the more abundant isotope of carbon. If hyperfine structure from
all the nuclei were present at one time, the resulting pattern would often be
unresolvable and its decoding thus more uncertain. As it is, there is seldom

17

246 Walter Gordy

any ambiguity about the identity of the nucleus which gives rise to the nuclear
hyperfine structure of electron resonances in irradiated organic matter. Usually,
it must be hydrogen. By substitution of deuterium for hydrogen, one should
often be able to learn which hydrogens give rise to a particular splitting.

When the electron spin resonances of organic radicals are observed in
the microwave region at frequencies of 30,000 Mc/sec, the corresponding
magnetic field required is 10,700 gauss. A magnetic field of such strength
is usually sufficient to produce the Paschen-Back effect, in which the / • S
coupling is broken down and both / and S precess about the direction of H.
Under these conditions the resonance frequencies of the various components
at constant field strength Hq can be expressed as:

hv = gpoH, + 2 A,m, (3)

i

where A^ is the coupHng constant of the electron for a particular nucleus /
with spin /^ and where the magnetic quantum numbers have the values :

nu = I,, 7,-1, ••• -4 (4)

Usually the resonances are observed at a fixed frequency, Vq, by variation of
the d.c. magnetic field. The resonant field strengths for the various hyperfine
components are then:

//=7/o + ^p,m, (5)

= /^o + 2 Ai/,m, (6)

i

The summation is again taken over all the coupling nuclei for each combination
of the magnetic quantum numbers. All orientations of a given nucleus (all
values of its m) are equally probable and independent of those of the other
nuclei. In this expression Hq = hvjg^ is the resonant field strength for the
central component of the structure at the observation frequency, Vq, or that for
resonance if there were no nuclear perturbation; AH^ is the component
separation (in magnetic field units) caused by a particular nucleus /. Obviously,
A/f. = AJgfi. In these applications we can set g as equal to 2.00 and write :

A/f, (gauss) = Ai (Mc)/2.80. (7)

If all the coupling nuclei in a given free radical have the same coupling
to the electron spin, one can define

7^=2 4 (8)

i

and

mj, = T, r-1, r-2, •••, -T, (9)

and can write equation (6) in the simpler form:

H^Ho + (AH)Mj. (10)

There will be {2T -\- 1) components corresponding to the different values of
M,p. This simplification is often possible in organic free radicals in solids
where the coupling nuclei are all hydrogens. It is apparent that, where all

Electron Spin Resonance in the Study of Radiation Damage 247

the equally coupling nuclei have the same spin, 7= nl, and the total number
N of components of the multiplet will be:

N = 2nl-\\ (11)

or

Thus n equally coupling hydrogens (/ = \) gives n + 1 components. The
intensities of the components are proportional to the number of different
combinations of the /n/s which give the same sum 2 '"j or same value of M^..

i

Because all the -\-h and —\ orientations of n hydrogens are equally probable
and mutually independent, the intensities of a multiplet formed by equally
coupling hydrogens will be gaussian.

The interaction constant A^ of the electron spin with the moment of a
particular nucleus may contain both an isotropic and an anisotropic component.
The isotropic component, the Fermi term, is independent of the orientation
of the sample in the magnetic field and arises from the non- vanishing probability
density, ^'q t/'o*? of the electronic wave function at the nucleus in question.
Since only the s atomic orbitals are non- vanishing at the nucleus (radius r = 0),
the presence of an isotropic coupling tenn for a particular atom in a molecule
generally indicates 5 character in the bonding orbitals of that atom.

For an unpaired electron occupying wholly an s orbital of a particular
atom, the coupling to the nucleus of that atom arises entirely from the non-
vanishing density ipQ i^)q* at the nucleus and has the value (17):

A. = y fif^igi Wo n* = 3 ^^3 (13)

where /9 is the Bohr magneton; /5j, the nuclear magneton; gj, the g factor
(/ij//) of the nucleus; /;, Planck's constant; c, the velocity of light; R, the
Rydberg constant; a, the fine structure constant; Z, the effective nuclear charge;
and «, the total quantum number. For atomic hydrogen in the ground state,
A is known to be 1420 Mc/sec. This value with equation (7) gives A/Z^ = 507
gauss as the expected splitting for the atomic hydrogen doublet for the strong-
field case {H ^ ^H^). The non-isotropic components are zero because of the
spherical symmetry of the s orbital. Thus the isotropic coupling to the nucleus
of a particular atom gives a good measure of the s orbital contribution of that
atom to the molecular wave function of the odd electron in a free radical.
An electron at a fixed distance from a nucleus / with non-zero spin will
experience a magnetic field component arising from the magnetic moment
of the nucleus. If the spin vectors of both the electron and the nucleus precess
about the direction of an applied field H (this corresponds to the strong-field,
Paschen-Back case), the non-vanishing field component at the electron, A//,
caused by the nucleus, will lie along H and will have the value:

(A//) = {jY^.l^^i^y^O C0S2 0 - 1) (14)

248 Walter Gordy

where /, m and ^7 are the spin, magnetic quantum number, and magnetic
moment (in nm units) of the nucleus, f^j is the nuclear magneton, r is the radius
vector from the nucleus to the electron, and d is the angle between r and H.
Although the nucleus may be regarded as located at a fixed point within the
molecule or crystal, the electron definitely cannot be so regarded. Hence,
to find the averaged or effective (A/r)eff acting on the electron in a molecular
orbital ip, we must average the above quantity over the orbital ip. Thus

{^H\s^i^-^[^J^,^w{^J^Oco^''0-\)^*dT . (15)

Since the coordinates are separable, we can write this equation as

Av

(A//)eff = (^- j /^2/^Z^73/^ <3 C0S2 0 - 1 >^„ (16)

where

/'■'K

ipr* d7

m

and (3 cos^ 0 — 1)^^ = WeO cos^ 0 — \)fe* dr .

To attack such a problem one can assume, as is usually done in other calculations
of molecular orbitals, that ip is a linear combination of atomic orbitals, ip^,
tPi, etc. We then readily get a part of the solution for we already know, at

least to a fair approximation, \^/ and (3cos-0— 1>av for electrons

various kinds of atomic orbitals. Expressions for these to various degrees of
approximation together with couphng constants actually measured are available
in standard texts on atomic spectra (17, 18). There is more to the problem than
this, however. Although an overlap or cross temi of the forni y>,lllr^)(3 cos- 0
— 1)^)* may possibly be neglected, an electron in an atomic orbital of atom B
might have a significant interaction with the nucleus of an adjacent atom A.
It is thus necessary to include terms of the form :

Jv.,(;l-J(3cos2 0„,-l)v',r/T, (17)

where /•„;, and O^j, are the coordinates of an electron on atom B referred to
the nucleus of atom A as the origin. The values of these terms are sensitive
functions of the hybridization of the atomic orbitals and of the direction of the
projections of the major lobes of the hybridized orbitals. As we get greater
skill in the procedure, these orientation-dependent couphng terms should give
additional information about orbitals of radicals. Expressed in convenient
numerical units equation (16) becomes:

A// (in gauss) = 5.05 ^ (4) (3 cos^ d - 1>av, (18)

^ X'' / AV

where /Uj is in nm units and r is in A.

Electron Spin Resonance in the Study of Radiation Damage 249

In simple cases where single crystals can be prepared, it should be possible
to measure (1//'^>av for the interaction of an electron in atomic orbital of
atom B interacting with the nucleus of another atom A. Such applications
are made later in the discussion. If (1//'^>av~* is greater than the interatomic
distance, the electron may be in a hybridized orbital of B which projects
away from A. If it is less than the atomic distance, the electron may be in
a hybridized orbital which projects toward A. In some instances {\lr^)A\
may be so large that the field of the electron at the nucleus may be greater
than the applied field. The nucleus would not then necessarily precess about
the direction of H, and the above fommla would not hold for all values of 0.
It should still hold when 0 equals zero or 90°, for then the field of the electron
at the location of the nucleus would have, on the average, the same direction
as H. If the cloud of the electron is symmetrical about the bond axis between
A and B, the angle 6 would, in effect, measure the orientation of the bond
axis in the field H. For this case (3 cos^ d — 1)av equals 2 for (? = 0 (bond
axis parallel to //), and (3 cos^ 0 — l)^^ equals — 1 for 0 = 90° (bond axis
perpendicular to H). Thus the A// should have twice the value for 0 equal
to zero as that for d equal to 90°. The dipole-dipole interaction of the electron
with the nucleus averages to zero when the electron is entirely outside the
nucleus and is moving in such a manner that its averaged density achieves
spherical symmetry about the nucleus during its lifetime in a spin state.

Nuclear hyperfine structure of any type becomes independent of the mag-
netic field strength after the field becomes sufiiciently strong to achieve the
Paschen-Back case, which is assumed in the above treatment. Thus nuclear
hyperfine structure can be readily distinguished from the splitting wliich arises
from anisotropy in the g factor, discussed below, if measurements are made
at two or more frequencies, both with strong fields. Although the direct-
dipole type interaction with the nucleus varies with orientation in the field,
it does not vary with the magnitude of the field after the strong field case is
reached.

Figure 2 shows the type of hyperfine structure theoretically predicted for
the strong field case for various radicals with equally coupling nuclei having
spins of I {H or F, for example). Figure 3 illustrates a few cases where the
coupling of one or two of the nuclei differs from that of the others. It is appa-
rent that these cases are easily distinguishable.

2. Residual Spin-Orbit Coupling

If the odd-electron density of a radical is largely concentrated on a non-5
orbital of a single atom of a radical or is shared mainly by only two atoms, as
it is on the — N — N — group of diphenyl picryl hydrazyl (DPPH), effects of
spin-orbit interaction are not entirely negligible. The orbital momentum will
be oriented by the strong electrical force of the chemical bond and will not be
free to precess about the applied field. Bond-oriented orbital components will
give rise to an observable anisotropy in the magnetic susceptibility and thus in
the observed g factor. If the odd electron wave function is symmetric about a
particular bond as in DPPH, the observed g factor will reflect this symmetry:
if all such bonds in a given sample were oriented along the applied H, the ^n
factor would differ from the g^^ observed when the bonds are all oriented

250

Walter Gordy

perpenidcular to //. For an arbitrary orientation 0 of the bond axis with H,
the observed ge factor would have the value:

ge

V^ii^ cos'^ 0 + g^^^ sin^ 0

(19)

In a sample in which the bond angles have arbitrary orientations in the
field H such as would be true in a powder or polycrystalline sample, the

NO. OF EQUALLY COUPLING
HYDROGEN SPINS

EXPECTED PATTERN OF RESONANCE

Fig. 2. Types of hyperfine structure predicted for strong-field case for various
radicals having ditTerent numbers of equally coupling hydrogens or other nuclei

of spin |.

resonance absorption would spread over all values of the field intermediate
between that corresponding to the resonance value for g,, and g^^. The ^j^
would apply for any orientation of // in a plane perpendicular to the bond axis,
whereas the g,, value would apply only for H along the bond axis. Thus for
random orientations in the polycrystalline samples, the g^^ value has the
greater weight, and the resonance has an asymmetric form with the highest

Electron Spin Resonance in the Study of Radiation Damage

251

peak corresponding to the g^^ value. Such a resonance will have a shoulder or
shelf on one side with the edge of the shoulder corresponding to ^i,. First
derivatives of an asymmetric resonance arising from an anisotropic g factor
in x-irradiated cystine are shown in Fig. 4 for three different observation
frequencies. That the apparent structure in these curves is due to anisotropy

NO OF RELATIVE
HYDROGENS COUPLING

EXPECTED PATTERN OF RESONANCE

Fig. 3. Some illustrative theoretical hyperfine patterns of radicals with two sets

of H nuclei (or other nuclei of spin |). All nuclei of one set have the same

coupling, but those of the two sets dilTer as indicated.

in the g factor has been established by measurements on a single crystal of
cystine at different orientations in the field (19). Such curves show some
differences depending upon amount of modulation, variations in natural line
widths, degree of anisotropy in g, as well as variations in observation frequency
or H value. Nevertheless, there should always be a bend point in the derivative
curves corresponding to the H for resonance at ^^j^ and a lesser one for _^||.
This fortunate circumstance allows measurement of ^^^[ and gj_ even in poly-
crystalline samples. The identity of these bend points, if in doubt, can usually

252 Walter Gordy

be established by variation of the modulation amphtude and observation
frequency. The outermost bend points will in general correspond to g,^ and g^^.

III. FREE RADICALS IN IRRADIATED AMINO
ACIDS AND SIMPLE PEPTIDES

The work of our group at Duke University has revealed that the isotropic
^orbital contributions of hydrogen atoms in aliphatic hydrocarbon radicals are
very significant and that they give rise to hyperfine structure in the spin resonance
of these radicals v/hich is frequently of the order of 100, and sometimes as
much as 200, gauss. This couphng is an order of magnitude greater than that
generally found for the aromatic ringed radicals (14, 15, 20) which can be
prepared chemically and observed in solution. Furthermore, the first measure-
ments indicated, and later work on single crystals (21) confirmed, that the
isotropic j-orbital coupling to the hydrogen nuclei in aliphatic hydrocarbon
radicals is generally much greater than the orientation-dependent, dipole-dipole
component. This very fortunate circumstance makes possible detection and
often identification of the aliphatic hydrocarbon radicals made by irradiation
of solid matter in the polycrystalline powder and even in impure biological
solids. In other words, it seems possible with microwave spectroscopy to
'fingerprint' many of the common radicals produced within soUd matter by
irradiation. I need not emphasize the usefulness of such a set of fingerprints
for the study of radiation damage.

There are two important factors which we beheve to be mainly responsible
for the reduction of the anisotropic nuclear coupling in hydrocarbon radicals.
One of these is the spreading of the odd electron density over a large molecular
orbital so that there is no appreciable fraction of the total density near a parti-
cular nucleus. The other is the twisting, turning, tunneUng, tumbling, or other
motion of the radicals, or their parts, within the solid cages in wliich they are
trapped. The first is generally more important for large radicals than for
small ones, and the latter is generally more important for room temperature
and elevated temperatures than for lower ones.

These properties of aliphatic free radicals and their remarkably long Hfetime
within solids were not predicted by theory. The conclusions were forced upon
us from the experimental evidence for them. Furthermore, this pronounced
isotropic interaction through the 5-orbitals immediately gives much information
about the electronic wave functions and structure of hydrocarbon radicals. The
large coupling to the H nuclei in the CH3 radical (total spread of quartet 70
gauss) indicates that this radical is not planar. Amazingly, the characteristic
pattern of the ethyl free radical, C2H5, is a symmetrical sextet (or approximately
so) of about 130 gauss spread. This indicates equivalent, or nearly equivalent,
coupling to the electron spin of all five protons.

Fig. 5 illustrates some characteristic hyperfine patterns of hydrocarbon
radicals produced by x-irradiation of some simple peptides. Compare these
with the theoretical patterns for different numbers of equally coupling protons
in Fig. 2. Similar patterns have been obtained by irradiation of amino acids (4)
and other compounds (6, 22, 23) with x-rays and with ultraviolet light (24).

Figs. 6 and 7 illustrate somewhat more complex resonances.

Fig. 4. First derivative curves at different frequencies of powdered cystine after
x-irradiation in a vacuum. The markers at the base are 68 gauss apart. The top
curve for 2.7 kMc requires a magnetic field of 960 gauss; the middle curve at 9
kMc, one of 3200 gauss; the bottom curve at 23 kMc, one of 8200 gauss.

to face p. 250

GUYCYL GLYCYL GLYCINE

/

CHuaRACETYL DL ALANINE

Fig. 5. Some illustrative patterns of resonances of x-irradiated peptides (second
derivative curves). The markers at the base are spaced 68 gauss apart. The
observation frequency is 9 kMc. From G. McCormick and W. Gordy (5).)

GLYCYL DL VALINE

\

\

\

Fig. 6. Hyperfine pattern (second derivative curve) of the radical produced by

x-irradiation of glycyl DL-valine. Marker spacing is 68 gauss. Observation

frequency, 9 kMc. (From G. McCormick and W. Gordy (5).)

Fig. 7. Hyperfine pattern (second derivative curve) of the radical produced by

x-irradiation of acetyl DL-valine. Marker spacing, 68 gauss. Observation

frequency, 9 kMc. (From G. McCormick and W. Gordy (5).)

Fig. 8. Resonances (first derivative curves) obtained for \-irradiatcd silk witii

strands oriented parallel and perpendicular to the magnetic field. The obser\ation

frequency is 23 kMc. (From W. Gordy and H. Shiklds (8).)

— - CYSTINE \ \ \— \

Fig. 9. Resonances (first derivative curves) of x-irradiated hair compared with

similar resonances for cystine and cysteine. Mariner spacing at base, 68 gauss.

Observation frequency, 23 kMc. (From W. Gordy and H. Shields (8).)

Fig. 10. Resonance (first derivative curve) of bovine albumin which represents a

combination pattern of the glycyl-glycine (or silk) doublet and cysteine (or hair)

resonance. Observed at 23 kMc. (From W. Gordy and H. Shields (8).)

Fig. 11. Resonances (first derivative curve) of x-irradiated feather quill (of a

goose) at 23 kMc for parallel and perpendicular orientation in the magnetic

field. (From W. Gordy and H. Shields (8).)

Fig. 12. Resonance (first derivative curve) of x-irradiated insulin observed at
23 kMc. (From W. Gordy and H. Shields (8).)

Cholesterol, Cg^H^^OH

X-rayed in vacuum
(indicating the top curve)

X-rayed in air
(indicating the bottom curve)

Fig. 13. Resonance (first derivative curve) of cholesterol at 2.7 kMc, x-irradiated
in a vacuum (upper figure) and in air (lower figure). (From H. N. Rexroad

and W. GoRDY (24).)

Electron Spin Resonance in the Study of Radiation Damage 253

There are far too many radicals already observed in irradiated amino acids
and peptides to discuss them here. I should like to mention one more,
however. The pattern of Fig. 7 for acetyl valine consists mainly of a set of
nine syimTietrical doublets spread over 200 gauss. There is another resonance
near the center of the group which I ignore for the present discussion. Seemingly,
the nine doublets must arise from eight equally-coupling protons and a ninth
with coupling only about half as much as each of the eight at room temperature,
and only about a fourth as much at liquid air temperature. This pattern
requires an almost unimaginable radical. The odd electron must spread
two-fifths of its total density in \s orbitals of the eight equivalent hydrogens.
This indicates a radical with a high concentration of hydrogens. It is
difficult to design a radical with eight equally coupling hydrogens, especially
with a ninth coupling differently. The (CH3)3C radical would have nine
equally coupling hydrogens wliich would be expected to give a hyperfine
spread of the order of 200 gauss. If we should assume that one of the hydrogens
in (CH3)3C is replaced by a group RH with only one coupling hydrogen (such
as OH) and one which does not noticeably disturb the couphng of the other
two, we would have a radical which might account for the acetyl valine pattern
of nine doublets.

IV. RADIATION DAMAGE IN PROTEINS

In contrast to the varied hyperfine patterns found for the resonances of
the x-irradiated amino acids and simple peptides, we have found mainly (but
not exclusively) two patterns either singly or in combination for numerous
proteins. One of these patterns consists of a simple doublet arising from
interaction of the odd electron spin Vv'ith a single proton spin. The other
pattern is a field-dependent one like that of powdered or polycrystalline cystine,
cysteine, or glutathione. Fig. 8 illustrates the first type; Fig. 9, the second;
and Fig. 10 is a combination of the two patterns.

In our first papers on electron resonances in irradiated proteins (4), we
suggested that the doublet pattern in the proteins might arise from an odd
electron localized mainly on an oxygen joined by a hydrogen bridge as indicated
in Structure II.

Model I represents a structural section of the unirradiated /?-keratin protein.
The doublet structure, we thought, might arise from dipole-dipole interaction
of the electron spin with the proton of the hydrogen bridge. Partly to test this
hypothesis, H. W. Shields and the author (25) have made observations on
strands of irradiated silk directed along the applied magnetic field, and also on
strands directed perpendicular to it. It is known from infrared and x-ray
studies (26) that hydrogen bridges in silk he approximately in a plane perpen-
dicular to the direction of the silk strands. If we assume, for simplicity, that
the odd electron density is symmetrically localized on the oxygen, the 0 of
equation (18) would measure the angle of the O — H axis with the magnetic
field. Hence, when the silk strands are along the apphed field, 6 equals 90°
for all hydrogen bridges, and the doublet splitting is the same for all radicals
of the silk. Under these conditions one would expect a clear resolution of the
doublet. When the silk strands are perpendicular to the applied field, the

254

Walter Gordy

hydrogen bridges have all orientations with the field from 0 to 180°. With this
arrangement one would expect the individual components of the doublet to
be broader and less well resolved than for the parallel case. These features are
not completely in accord with the observed results on silk. The doublet
splitting for 0 = 0 (parallel case) is found to be approximately 25 gauss, some-
what larger than that previously estimated from the polycrystalline material,
and also significantly larger than that expected for the hydrogen bonded model.

H

O

C

c

\ / \ /
CRN

O

H

H

O

N R

C

/ \ / \ .
C N

H

O

C

CRN

H

/b

O

I

H

N RIC

/ \\A \

C \ N

+

H

H

H

(I)

H

(II)

Furthermore, the separation of the doublet seems to be greater for the
parallel case.

It should be appreciated that what is proved for silk is simply that the
radical formed is one in which the odd electron interacts with one and only one
proton, and that this interaction is at least partly anisotropic. Later we
hope to obtain more specific evidence from deuterium substitution in glycyl
glycine, which appears to have the same doublet as that for silk.

Irradiated feather quill gives a composite pattern of a doublet and the
cysteine-like resonance. However, the doublet is not as widely spaced as that
for silk and is not resolved for a polyoriented sample. It has been found (19)
that the strong component to the left of the cysteine-like resonance in feather quill
(Fig. 11) is partially resolved into a doublet when the feather quill is arranged
parallel to the applied magnetic field, whereas it has only about half the width
of the unresolved resonance for the perpendicular orientation. Presumably the
structure of the feather quill is that of the alpha helix of Pauling and Corey
(27), with the helix axis along that of the quill. Interestingly, the cysteine-
like component of the resonance is not orientation-dependent. We believe for
reasons given later that this situation indicates that the S — S or the C — S bonds
of the quill have many different orientations with respect to the quill axis.

A resonance found to be prominent in x-irradiated proteins which contain
sulfur is like that of cystine, shown in Fig. 4. Biological substances such as
hair (Fig. 9), hoof, horn, and feather have this as the predominant if not the

Electron Spin Resonance in the Study of Radiation Damage 255

only pattern, despite the fact that the cystine or cysteine content is only a few
percent. The fact that the same pattern, but one very dilTerent from any so
far obtained from non-sulfur compounds, is observed for many sulfur-containing
proteins and for cysteine, cystine, and glutathione convinces us that the odd
electron giving these resonances is essentially localized on sulfur. Whether it
is on a single sulfur or is shared by two sulfurs of the S — S link, as originally
suggested, remains a question to be answered by later work. That the odd
electron is localized mainly on one or two atoms is borne out by the large amount
of residual spin orbit coupling evidenced by the anisotropy in the observed g
factor, as already explained.

Because cysteine with only — SH sulfur gives the same type of resonance
as cystine with — SS — sulfur, it is uncertain whether the electron wliich
gives rise to the characteristic resonance of Figs. 4 and 9 is on a single S or is
shared between two sulfurs to form a 'three-electron bond'. When the plus
charge accompanying the odd character arrives at the S of the — SH of cysteine,
it would probably 'shock' off either the naked proton to leave the neutral free
radical RS-, or the H atom to leave RS+, where R represents the part of the
cysteine exclusive of the SH group. In the latter case, the H atom would
escape through the lattice or react with something. (We have been unable to
detect the free hydrogen radical at room temperature in any irradiated substances.)
We do not know at tliis time which if either of these two events occurs. Inter-
estingly, RS+ is not a free radical, and no resonance would be detected for this
case until further events had transpired. At room temperature, however, the
molecules may flop about sufficiently to allow the RS+ to react with the — SH
of a neighbor and to release another H and form the same charged disulfide
radical which has been postulated for irradiated cystine. The common patterns
of cystine and cysteine might be thus explained. I should say, however, that
the two patterns although alike are not identical: the resonance pattern of
cysteine has a slightly greater over-all width than that of cystine, a variation
which we believe arises from the difference in dielectric medium. If the radicals
were diff'erent — if one were RS- and the other were R • (SS)'" • R — a much
greater diff'erence would be expected.

If the resonance in irradiated cysteine arises from RS- mentioned above,
the resonance of cystine must arise from the same radical, which would result
first from ionization of the cystine molecule and later from rupture of the
S — S bond to leave RS- and RS+. There is no evident mechanism by which
the positive charge could disrupt the S — S bond other than the initial 'shock'
of the sudden arrival of the charge. Such 'shock' effects can be anticipated from
the Franck-Condon principle (28). They would hardly be expected to break
the S — S link, because its potential curve would be lowered and its bond length
shortened by the removal of an anti-bonding electron. The positive charge
would have no preference for either sulfur; and, if the S — S bond holds, the
odd electron would be shared equally by both sulfurs to form an additional
half-bond. The Franck-Rabinowitch caging principle (28) would also tend
to prevent the breaking of the S — S link by the 'shock' efi'ect. The two S atoms
are in a sense caged and hindered from flying apart by the large inert R groups
to which they are attached. Any 'shock' energy would probably be dissipated
as vibrational energy throughout the whole dimeric molecule. Such a charged

256 Walter Gordy

link would of course tend to attract other agents such as O2 or H2O which
might later sever the bond or an electron which would restore the normal
S— S hnk.

Although we are not yet certain whether the cystine or cysteine-hke resonance
arises from radicals of the type R — (S • • • S)+ — R or RS-, we are inclined to
favor the latter. It would seem that the neutral radical would enjoy the longer
life and hence be the more probable one to be detected. Furthennore, in the
RSH compounds the formation of the RS- radical would require the simpler
process. With the present information we are inclined to beheve that
R — (S • • • S)+ — R is the primary radical formed by ionization of the disulfide
compounds but that the healing of the molecule through capture of an electron
or later rupture of the charged link, probably by attraction of other groups, or
molecules, may occur so rapidly that this charged radical is not the one detected,
but rather the neutral radical R — S. However, our interpretations are still
tentative. Because we consider the question an important one we are continuing
to investigate it experimentally. Studies using S^^ can clear up this uncertainty.
What already seems established is that the odd electron giving rise to the pattern
is essentially localized on the sulfur.

The large anisotropy in the g factor for the cystine-type resonance suggests
the potential usefulness of this resonance for obtaining structural information
about the proteins. Studies by Shields and the author on single crystals of
cystine (19) showed a resonance simpler and much narrower than that for
polycrystalline cystine, and one which shifted position sensitively with orienta-
tion in the magnetic field. After this observation the same crystal was crushed
up and found to give the resonance pattern characteristic of polycrystalline
cystine, shown in Fig. 4. Observations (19) on strands of hair and on feather
quill at various orientations in the d.c. magnetic field shovved only the poly-
crystalline type of cystine resonance for all orientations. It is significant, we
think, that the cystine-like resonance in these proteins is not orientation-
dependent, for that fact gives convincing proof that the bonds to sulfur, either
the C — S or S — S links, in the keratins are randomly oriented (in contrast to
hydrogen bridges). We have also made measurements (19) on stretched and
unstretched hair and found no significant variation in its cystine-hke resonance
pattern. In all cases it is like that of the polycrystalline cystine.

The resonance of x-irradiated insuhn may exliibit a third type of protein
resonance (cf. Fig. 12). It has the characteristic sulfur or cystine-like pattern
but with a relatively sharp resonance superimposed (at the left of the pattern).
Although it has the same g factor — that of the free electron spin — this com-
ponent to the left seems too sharp to be classified as an unresolved doublet
like that of feather quill or silk. Possibly this sharp component of the insulin
resonance may arise from an electron trapped in one of the unsaturated ringed
structures known to be on the side chains of this protein. The ringed structure
may act as a sink or trap for the odd electron produced by ionizing radiation.
We have found a similarly sharp resonance (29) for x-irradiated polystyrene,
where the odd electron observed is believed to be trapped in the aromatic rings
attached to the backbone structure.

Considering the varied patterns which we found for the resonances of the
different amino acids and simple peptides, it was at first surprising to us that

Electron Spin Resonance in the Study of Radiation Damage 257

the proteins gave such shnple patterns with the same few features, described
above, repeating so often either singly or together. We were forced to conclude
that the electron hole or vacancy created by an ionizing quantum or particle
at any given locality in the protein can move through the polypeptide chain
until it reaches one of a few traps or sinks where it becomes lodged. One such
low-energy trap we believe is sulfur. Both — SH and — S — S — groups are
effective traps. Possibly the unsaturated rings of certain side chains are an
important trap.

Furthemiore, we must postulate that there are effective traps for the electrons
knocked away in the ionization process since these do not always seem to be
able to return readily to fill the hole. Because they have not given recognizable
resonances, we do not speculate on the negative traps. For most of them, the
resonances may be too broad for detection.

V. PROTECTIVE MECHANISMS

I am sure that there are many who have suspected that some proteins when
ionized can hold together and conduct the electron hole to certain side-chain
groups such as the sulfur link. I think that I have heard Professor E. C.
Pollard, of Yale, and members of his group express such views. However,
from my brief and sketchy acquaintance with the hterature in tliis field I surmise
that this question has been a highly debatable one. In the microwave resonances
we have a new and perhaps more direct type of evidence in favor of the migra-
tion of the electron holes to certain side-chain groups.

Now that there is new evidence for effective resistance to the breaking
of the polypeptide backbone of the proteins by ionization, it is interesting to
speculate on the reasons why this is true. If one of the electrons of a locahzed,
covalent bond between two atoms were suddenly removed, the two atoms
might — according to Franck-Condon principle — become dissociated wliile
trying to adjust to the new and shallower potential curve with the longer
equilibrium distance commensurate with the 'one-electron bond'. It might be
supposed that the Franck-Rabinowitch caging would help to prevent any two
atoms of a protein chain faced with such an emergency from becoming dis-
sociated. However, the evidence which we have obtained for the migration of
the electron vacancy to a sink in the side chains indicates that a particular bond
of the polypeptide chain does not have to face the Franck-Condon catastrophe
because the bonds are not in a strict sense localized. If we imagine that charge
density equivalent to a single electron is removed completely from the localized
region of two adjacent atoms along the main chain, we must, at the same time
imagine that tliis charge density is restored quickly, before the atoms have time
to move significantly apart, by the flow of electronic charge from a side chain
group such as the S— S hnk. It might be better to think of the ionization as
taking place only at these sites where the electron vacancy is detected. A
molecular chain or polymer which can conduct a hole out to a non-essential
side-chain sink or to a point where a simple recapture of an electron restores
the status quo has, in effect, a built-in, remarkably effective method of self-
protection from radiation damage. Such polymers have a high survival value
in a world where ionizing radiations are ever present.

258 Walter Gordy

Although our measurements were made in dry — reasonably dry — samples,
it seems likely that the same transfer of an electron hole to low-energy sites,
such as the side-chain sulfur, would take place in the proteins of living systems.
The better mobility of charges in the more fluid systems should only speed
up the recapture of an electron and hence the recovery of the system. Of course
the attack on the charged radicals such as — (S — S)+ — by molecules like H.2O
would also be speeded up in the living systems, but in the living systems the
electron recovery might well be the more rapid. Even if a break in the S — S
bond should occur, this might be less damaging and more easily healed than
a break in the polypeptide trunk line.

We seem to be proposing here a self-protective mechanism which would
prevent almost any radiation damage whatever to proteins. This is not true
for several reasons, one of which is that not all proteins have — S — S — hnks
in their side chains. There are other traps for the 'hole' where bonds are
probably broken as postulated for silk, or for the sulfhydryl group, where
the hydrogen atom or proton is believed to be freed. A free hydrogen atom
could cause trouble in the living system, even though it could be temporarily
spared from the S — H group of the protein. Moreover, not all damage to proteins
in the hving systems is due to the direct ionization of the protein which we have
been discussing here. Much of the damage (30) is thought to be done by
radicals such as H, OH, and OOH produced by radiation in the inter-pene-
trating fluid, which later attack and damage the protein. These are the so-called
indirect effects.

About the time of our initial experiment on the proteins, a very significant
experiment of an entirely different kind was in progress by Eldjarn, Pihl, and
Shapiro (31) which indicated that the indirect effects are probably not as
significant as had been previously thought, and that a high degree of protection
could be achieved by previously converting the — SH groups in proteins to
— S — S — links. Their experiments are of a chemical nature and employ
tagged sulfur (S^^) in cysteamine (NH2C2H4SH). I shall not attempt to give
the details of their experiments but merely to connect their results with ours.
The interdependence of the two apparently different types of results has been
pointed out in an interesting paper by Ehrenberg and Zimmer (32). Our
results indicate that any ionization of a protein which contains S — H groups
would always tend to dissociate the — SH group through the migration of the
'hole' or positive charge to the S. Because of the large cross-section of the
proteins there would be a large release of H atoms by this mechanism unless
there were many competing — S — ^S — links or other traps in the protein to
protect the — SH. The experiment of Eldjarn et al. would seem to 'protect'
the — SH group by first destroying it! By carrying the hydrogen away
peacefully in a harmless molecule they prevent its being released by the irradia-
tion as a damaging free radical. Later, after the upheaval is past, it can be
restored peacefully if needed.

Our results, as well as those of Eldjarn et al., suggest that some agents may
exert their protective eff'ects by becoming temporarily attached through a
chemical bond to the protein or other thing which they protect. Cystine,
glutathione, or other agent which gives up electrons easily is needed for
protection against the damaging effects of positive holes. Cysteine, glutathione

Electron Spin Resonance in the Study of Radiation Damage 259

in the reduced form, or other — SH agents may exert their protective effects by
forming an — S — S — link with an — SH of the protected molecule, as Eldjarn
ct al. proved for cysteamine. Electron sinks which collect the electrons knocked
out of the holes, and thus prevent them from causing damaging reactions,
would also be protective agents. The most desirable electron storage tank
would be a molecule which would accept the electron without itself becoming
dissociated, would hold it loosely, and would give it up easily when it was
needed elsewhere.

I should like to add that the electron sources (traps for electron holes)
attached to side chains are not necessarily restricted to protective action against
direct hits : they may also protect from some of the indirect effects. Certain
free radicals produced in the medium around the protein might exert their
damage simply by steahng away an electron from some point in the protein.
This would of course be replaced by an electron borrowed from the protective
group, just as if the electron had been removed by irradiation. The effects of
ionized Oo or HoO — if there are such things — would be, I suppose, to ionize
the protein when they came near it. An OH radical might react with the
protein molecule, or it might simply ionize the protein and form 0H~. I do
not know which would happen in a particular case. I simply wish to illustrate a
possible unrecognized protective mechanism against indirect action of the
radiation. Some specialists on radiation effects evidently believe that the
damage to the protein of the cells is due mainly to the indirect effect of radicals
produced in the medium around the protein molecules and that the protective
action of such agents as cystine or glutathione is entirely the elimination of
these radicals before they get to the protein. I do not mean to imply that such
effects and the mechanism proposed to protect against them are not very im-
portant. What seems clear is that protection is also needed against direct hits
as well, and if possible against those radicals or charges produced in the medium
which survive long enough to reach the protein. Because of the ability of the
protein to transfer a charge, it now seems possible to provide this type of pro-
tection too. In fact it has already been achieved in some measure by Eldjarn e/ a/.

The protective mechanism which I have proposed is strikingly related to
enzyme activity. Pollard's group at Yale, and perhaps others, have been
making experiments which show, I beheve, that a single hit in a large enzyme
molecule by an ionizing particle is enough to destroy the enzyme activity of
that molecule. This is not strange if the sensitive sites for the enzyme activity
are synonymous with the sinks or sources for electrons about which we have
been talking, and the ability of the enzyme molecule to conduct a hole or
excitation is required for enzyme action.

I hke to think of the protective agents which are described here as enzymes
which prevent reactions. I know, of course, that the normal function of an
enzyme is to cause reactions. Some enzymes, so I understand, exert their
catalytic action by accepting spare electrons for a time and giving them up
again later. In the vivid language of Professor Henry Eyring, they take over
the unnecessary children (electrons) during the divorce proceedings and give
them back after the remarriages have taken place. One kind of 'protective
enzyme' supplies children to prevent divorces (broken bonds) and then later
recovers children indistinguishable from those given up (electrons all). Another

260 Walter Gordy

kind provides temporary abode for the disrupted children to prevent their
disturbing the neighbors. Our Hving systems probably have already built in
both types of protective agents in sufficient quantity to provide reasonably
good protection from ionizing radiation encountered in normal living of the
past. For the future we may need to add some.

I have not space to discuss radiation damage to other substances — such as
fatty acids, nucleic acids, and hormones — for which our group has obtained
many spin resonance data similar to that described here. I have not space to
discuss the important effects of oxygen on radiation damage to molecules,
about which we have obtained information from spin resonance, of the type
shown in Fig. 13. I hope that I have described enough of the results to convince
you — and the biologist who rode with me in the car — that microwave electron-
spin resonance is an important new way of 'seeing into' biological things.

ACKNOWLEDGEMENTS

The experimental results I have discussed here were obtained largely by
my students — W. B. Ard, H. W. Shields, C. G. McCormick, H. N. Rexroad,
A. VAN RoGGEN and C. F. Luck. Others now active in the project are J. H.
Hadley, F. W. Patten, and Dr. I. Miyagawa. For their valuable assistance I
am grateful. Our research is supported by the Office of Scientific Research,
U.S. Air Force, and the Office of Ordnance Research, U.S. Army.

Without implying that he is to any degree responsible for any misinterpreta-
tions I may have made, I wish to acknowledge with thanks some stimulating
and enlightening discussions with Dr. James Franck during the preparation of
this paper.

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of Spectroscopy, ed. by W. West, chap. 3, Interscience Publishers, New York (1956).

15. J. E. Wertz: Nuclear and electronic spin resonance. Chem. Rev. 55, 829-955 (1955).

16. W. Gordy: Microwave spectroscopy. In: Handbuch der P/iysi/c, ed. by S. Fliigge, Vol.
28, 1-78, Springer- Verlag, Heidelberg (1957).

17. N. F. Ramsey: Nuclear Moments, J. Wiley and Sons, New York (1953).

18. H. E. White: Introduction to Atomic Spectra, McGraw-Hill, New York (1934);

E. U. Condon and G. H. Shortley: Theory of Atomic Spectra, Macmillan, New York
(1935).

19. H. Shields and W. Gordy: unpublished data.

20. H. S. Jarrett and G. J. Sloan: Paramagnetic resonance absorption in triphenylmethyl
and dimesitylmethyl. J. Chem. Phys. 22, 1783-1784 (1954);

G. E. Pake, S. I. Weissman, and J. Townsend: Paramagnetic resonance of free radicals.
Disc. Faraday Soc. 19, 147-158 (1955).

21. A. Van Roggen, L. Van Roggen, and W. Gordy: Electron-spin resonance in x-
irradiated single crystals of amino acids. Bull. Amer. Phys. Soc. 1, 266-267 (1956).

22. C. G. McCoRMiCK and W. Gordy: Microwave investigations of radiation effects in
solids : Methyl and ethyl compounds of Sn, Zn and Hg. /. Amer. Chem. Soc. 78, 3243-
3246 (1956).

23. C. F. Luck and W. Gordy: Effects of x-irradiation upon some substances in solid
state: Simple alcohols, amines, amides and mercaptans. /. Amer. Chem. Soc. 78,
3240-3243 (1956).

24. H. N. Rexroad and W. Gordy: Electron spin resonance of radicals produced by
ultraviolet irradiation. Bull. Amer. Phys. Soc. 2, 227 (1957).

25. H. W. Shields and W. Gordy: details to be published.

26. B. W. Low: The structure and configuration of amino acids, peptides and proteins. In:
The Proteins, ed. by H. Neurath and K. Bailey, Vol. lA, chap. 4, Academic Press, New
York (1953).

27. L. Pauling and R. B. Corey: Two hydrogen-bonded spiral configurations of the poly-
peptide chain. /. Amer. Chem. Soc. 11, 5349 (1950).

28. J. Franck and R. Platzman: Physical principles underlying photochemical, radiation-
chemical, and radiobiological reactions. In: Radiation Biology, ed. by A. Hollaender,
Vol. I, Chap. 3 McGraw-Hill, New York (1954).

29. H. W. Shields, W. B. Ard, and W. Gordy: Electron-spin resonance in x-irradiated
plastics and synthetic fibers. Bull. Amer. Phys. Soc. 2, 227 (1957).

30. W.M.Dale: Basic radiation biochemistry, Chap. 4; and E. S. G. Barron: The effect of
x-rays on systems of biological importance, Chap. 5, In: Radiation Biology, ed. by
A. HoUaender, Vol. I, McGraw-Hill, New York (1954).

31. L. Eldjarn, a. Pihl, and B. Shapiro: Cysteamine-Cystamine : On the mechanism for
the protective action against ionizing radiation. In: Proceedings of the International
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York (1956).

32. L. Ehrenberg and K. G. Zimmer: Die Bedeutung der Mikrowellen-spektroskopie fiir
die Strahlen-biologie. Hereditas 42, 515-521 (1956).

18

A PHYSICAL MECHANISM FOR THE INACTIVATION
OF PROTEINS BY IONIZING RADIATION

Robert Platzman and James Franck

Department of Physics, Purdue University, Lafayette, Indiana and

Research Institutes {Pels Fund), The University of Chicago,

Chicago, Illinois

Abstract — The extraordinary sensitivity of living systems and certain of their components to
ionizing radiation must stem, at least in part, from a great sensitivity of individual molecular
or macromolecular species. Analysis of the interaction of such species and swiftly moving
charged atomic particles shows that the initial events of energy transfer cannot be responsible
for this sensitivity, but that events immediately subsequent to ionization acts definitely can be.
This is because the time scale for the production of new electric charges is so short as to evoke
a violent reaction of the medium, a reaction which is related intimately to the dielectric be-
havior at very great frequencies. Such behavior is not as yet fully explored experimentally,
for many of the frequencies concerned lie between the readily accessible infrared and the
microwave regions, but the known dielectric properties of highly polar systems like protein
and nucleic-acid macromolecules do disclose the existence of regions of strong dielectric
absorption, which are to be identified with dipole oscillations and rotations of polar atoms
and molecular groupings. The wave of polarization to which a sudden production of electric
charge in the interior of the macromolecule gives rise must cause profound degradation of the
molecular organization. This may be viewed as resulting from rupture of many weak polar
bonds (such as hydrogen bonds) which maintain the intricate organization and which are
involved in the above-mentioned dielectric absorption, the ruptures being essentially simul-
taneous. The dynamic effect on the molecular structure therefore is without parallel in any
other variety of action presently accessible to experimental study — for example, thermal,
chemical, or electrochemical action, all of which are in the present context essentially adiabatic
in character. The mechanism clearly explains at once the striking difference in sensitivity of
the media to ionizing radiation and to ultraviolet light. An approximate quantitative analysis
suggests that inactivation of common proteins by a single ionization act is unlikely, but
rather that several may be required. Since the effects of the ionizations in a particle track or
electron spur are additive (these events being virtually simultaneous), the familiar influence of
spatial correlations of ionization is qualitatively explained. The greater radiation sensitivity
at elevated temperatures is another obvious consequence. Other predictions of the theory are
a dependence of radiation sensitivity upon molecular anisotropy, and a wide variation in the
injury to identical molecules exposed to ionizing radiation.

I. INTRODUCTION

Living systems embody two distinct varieties of intricate organization. One is
the complex static structure of the macromolecules which are essential com-
ponents of cells; the other is dynamic and is manifested in the delicate organiza-
tion whereby the functions of the cell and of the organism are achieved.

Living systems are extraordinarily sensitive to ionizing radiation. This is
perhaps the most striking single result of experiments in radiobiology and has
been emphasized repeatedly (1,2, 3, 4). It is customary, and plausible, to identify

262

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 263

this great sensitivity with a disruption of complex organization, but it is not
known which of the two varieties is so highly susceptible. Indeed, both are
likely ultimately to be involved.

In the case of the functional organization, many proposals have been made
concerning the initial point of attack. Thus, the destruction or transformation
of sulfur-containing groups, of critical enzymes, and of various other essential
constituents present in small or in trace amounts, or the production of powerful
poisons, have been implicated. The answer is unlikely to be unique, and from
its pursuit, which must involve biological questions of the highest complexity,
most of the contributions of radiobiology to the science of biology probably will
devolve.

The degradation of crucial macromolecules by ionizing radiation is, on
the other hand, amenable to in vitro experimentation and to purely physico-
chemical theoretical analysis. It is the purpose of this paper to examine the
possible explanations for such disruption from a simple physical point of view,
and to present and investigate one mechanism which is based realistically upon
physical and chemical principles and is in full accord, at least qualitatively,
with the results of experiment.

A paramount experimental fact is the exceedingly great sensitivity of these
macromolecules to ionizing radiation compared to their sensitivity to ultraviolet
light. This fact is without parallel in the radiation chemistry of simple organic
or inorganic systems, and no clue is provided by the conventional theory of
the interaction of swiftly moving charged atomic particles with simple molecules.
It is therefore imperative to reanalyze this interaction, with specific regard to
the character of the absorbing medium.

The primary processes through which the radiation affects the medium cannot
differ qualitatively from those in a simple molecular system. In the case of
proteins, for example, the very weak bonds which bind the polypeptides together,
and even the peptide bonds, must be essentially without influence on the optical
dispersive properties of the medium,* and hence the varieties of energy transfer
from charged particles, their statistical distribution, and even their spatial dis-
tribution will differ only slightly from the corresponding quantities for a simple
mixture of amino acids having the same over-all composition. (This statement
is not correct with respect to the energy dissipated by moderation of the subex-
citation electrons, but that portion of the energy transfer cannot alone be
responsible for the great sensitivity.)

Many of the events immediately subsequent to primary absorption of the
incident radiation, on the other hand, must differ strikingly from those in a
simple system. The reason (5) is that the course of such events is determined
by the dielectric properties of the medium, and these, in contrast to the behavior
at high (optical) frequencies, are profoundly different for a condensed system
composed of highly polar molecules. Ionization in nonpolar substances is
usually followed more or less quickly by recombination, so that the chemical
consequences of absorption of ionizing radiation are very similar to chemical
changes induced by ultraviolet light of appropriate frequency. In a system

* This is even approximately true for the near-ultraviolet absorption spectrum, which is
more sensitive to such bonds than the excitations of greater energy that dominate the phenomena
of energy transfer from ionizing radiations.

264 Robert Platzman and James Franck

having a great dielectric constant, however, most or all of the initial recombina-
tion is inhibited (6), and the chemical effects of ionization stem from interaction
with the medium of spatially separated electric charges. This interaction is
intimately related to the processes of dielectric absorption characteristic of the
medium. It may be noted parenthetically that nonpolar macromolecules, such
as many plastics, display utterly different dielectric behavior — in particular
showing far less dielectric absorption — and, therefore, that discussions of
mechanisms in radiobiology based upon analogies with such polymers, however
attractive and despite their current vogue, are perilous, to say the least.

II. CONSEQUENCES OF IONIZATION IN A POLAR MEDIUM

Before treating the particular case of biologically important macromolecules
it will be useful to consider briefly the general consequences of an ionization
act in a condensed polar medium. By polar medium is meant one with a high
value of the static dielectric constant e^. The condition e^ ^ 1 implies (with
only one exception, which is not germane*) the existence of dipolar molecules,
and these must always possess regions of strong dielectric absorption at greater
frequencies than those at which the dipoles relax. This dielectric absorption
embraces all of the familiar infrared absorption, and more: it includes the
region from about 30 /^ to 1 mm, which at the present time is not accessible with
commercial instruments and is therefore virtually unexplored (although a few
investigations of simple molecules have been made, particularly in recent years,
and more are now under way). The dispersive properties of proteins, for
example, are almost completely unknown in this spectral region. But it is
certain that such absorption must be common and intense among complex
polar substances, for only those resonances arising from strong bonds and
small masses lie in the 1 to 20-/< region ; weaker bonds and greater masses
entail absorption at greater wavelengths.

The production of an electric charge in a medium will ultimately induce a
strong polarization similar to that produced, say, in a condenser filled with the
same substance. Tliis polarization will not grow uniformly, however, but rather
in several stages, each increase in polarization occurring at a time corresponding
in order of magnitude to the reciprocal of its characteristic frequency (7) ; the
entire spectrum of dielectric absorption is, of course, involved. The total energy
transferred to the medium as the result of an ionization act, excluding the
kinetic energy of the ejected electron, can be divided into three parts: that
involved in the polarization about the positive ion, a similar quantity released
about the electron, or the negative ion which it produces, and finally (and
usually much later) the thermal recombination energy of positive and negative
ion. The last of these is small (in the case of liquid water, for example, it
amounts only to a few per cent of the total) and may be ignored.

It merits emphasis that an ionization act per se does not usually cause a mole-
cular dissociation process. Analysis of results from mass-spectrographic
investigations shows that stable parent ions are the rule, and that the dissociation
of ions, which is usually the main subject of such studies, results from additional

* This refers to substances, such as certain semiconductors, in which intense electronic
absorption at comparatively low frequencies gives rise to a high value of e^.

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 265

energy coinmunicated in conjunction with the ionization act in the form oi'
electronic excitation energy of the parent ion. In the vapor phase this additional
energy may have time to be concentrated in a particular degree of freedom, but in
condensed phases it will ordinarily be dissipated by internal conversion and
thermal conduction, leaving the parent ion in its ground electronic state, which
is usually stable. Hence the simple identification of an ionization act with
splitting of a molecule, which is so common in the literature of radiation
chemistry and radiobiology, must be viewed with skepticism in so far as con-
densed phases are concerned. Such rupture may indeed occur, however, during
the growth of polarization about a freshly formed electric charge. It is then
very much a consequence of the interaction of the ion with its environment,
and in the case of valence-bond breakage imposes special energy requirements
with regard to both availability and mode of communication. These require-
ments may be satisfied, for example, in instances where dissociation would
lead to much greater localization of the charge, and therefore to greater polariza-
tion energy.

An important property of the energy transferred to the medium by virtue of
the growing polarization about a freshly produced electric charge is that most
of it is transferred in initial stages, during which the electric field strength is
very great. This follows from the Born formula

^E ^ (^2/2/?)[(l/e(r,)) - (l/e(?2))] (1)

giving the difference in self-energy of the electric field about a charge of magnitude
e outside the sphere of radius R, between instants when the eff'ective dielectric
constant has the values ^{t-^ and €{t<^. Since the electronic polarization
(oj/-^ 10^^ sec~^) is effective virtually instantaneously, the initial value of e is
approximately equal to the square of the ordinary refractive index n, or about 1 .5.
By the time that e has increased to (say) 5, most of the total energy
(e^l2R){lln^ — 1/eJ will have been dissipated. (Paradoxically, if e^,^ 1 the
behavior under discussion is nearly independent of the magnitude of e^.) This
argument has the important consequence that a major portion of energy trans-
ferred to a polar medium by virtue of an ionization act will be communicated,
in a very short time, to degrees of freedom associated with weak polar
('secondary') bonds, and that the region receiving this energy will be considerably
more extensive than that affected by a slow change in electric field intensity. The
total energy so communicated will be of the order of magnitude of 100 kcal/mole
for each (electronic) charge produced, but will depend upon the 'size' of the
positive ion, or, in general, upon the structure at a molecular level. If the bonds
aflTected are very weak, a substantial fraction of them will be broken, so that the
corresponding amount of energy cannot properly be said to have been converted
to heat: a portion of it truly has been used to 'melt' a certain structure;
obviously, subsequent 'resolidification' often will occur and then will release
part or all of the energy as heat.

The fate of the ejected electron is similar. It will progress a distance more
than sufficient for the developing polarization to inhibit initial recombination
(6), and eventually will attach itself to a negative-ion forming group such as
OH, if one is available, or to some other entity capable of binding it. The net

266 Robert Platzman and James Franck

energy released in such an attachment process is small, apart from the contribu-
tion from polarization, and may be positive or negative, since the energy evolved
in negative-ion formation (electron affinity) must, if it is substantial, compensate
for the energy required to rupture a chemical bond. (This is a consequence of
the fact that electron affinities of molecules always are small; the only large
electron aflinities are those of certain atoms and radicals, which by their nature
must be present in bound states.) Thus the effect on the medium will be very
much like that for the positive ion.

III. PHYSICAL CONSEQUENCES OF IONIZATION IN PROTEINS

The ejection of an electron in an ionization act by even a fairly slow secon-
dary electron is an exceedingly quick process and may be considered to have
duration of at most 10~^^ sec. The response of a highly polar medium to such
an event has been analyzed qualitatively above. After subtraction of the
electronic polarization, equation (1) shows that a total amount of energy
approximately equal to e^flrfiR will be dissipated during the several subsequent
stages of polarization ; here R denotes a distance of the order of magnitude of
the mean separation of polar molecular groups, and for proteins must be only
slightly greater than atomic dimensions. A value of R of about 2 A thus
corresponds to an energy dissipation of 60 kcal/mole. If all of this energy were
expended in dissociating secondary bonds, which may be considered to have
dissociation energies of approximately 5 kcal/mole, on the average, a rupture
of some twelve secondary bonds would be expected. A more detailed analysis
for the particular case of proteins, which leads to the same conclusion, will
now be presented. Although it is again based upon the Born formula, which
applies strictly only to a continuous dielectric, the error caused by neglect of
molecular inhomogeneity will not alter the result in order of magnitude.

The development of polarization ensuant to electric charge localization in
the medium may be divided into four stages. These stages, although distinct in
character, are by no means without mutual effects, but such interactions can
be disregarded in the present analysis, which is only semi-quantitative.

1. Electronic Polarization — This effect, in contrast to the others, is strongly
coupled to the physical processes which lead to localization of the charge, and
indeed to the initial ionization act itself (8). Its inffiience on the secondary-bond
structure probably is negligible.

2. 'Infrared', or True Vibrational Polarization — The polarization resulting
from degrees of freedom corresponding to the characteristic infrared oscillations
is developed during a period corresponding to the longest wavelength of such
oscillations, or about 3 X 10"^^ sec. With a plausible value of 1.7 for the
dielectric constant after this stage of polarization, equation (1) yields an energy
dissipation of 1 1 kcal/mole. Thus at most two secondary bonds can be broken,
and more probably none are. -

3. Secondary- Bond Polarization— li has already been emphasized that pro-
teins and similar substances must possess regions of intense dielectric absorp-
tion at frequencies between the accessible infrared and the radiofrequency
or even microwave regions. Part, or the whole of this absorption, which
has yet to be investigated experimentally, stems from the highly polar

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 267

secondary bonds (hydrogen bonds of various sorts, salt linkages, etc.) upon
which in large measure maintenance of the structure of the macromolecule
depends. The polarization corresponding to this absorption is established
during the period of from roughly 10^^ to 10^^ sec following charge localiza-
tion. Information concerning the magnitude of the dielectric constant sub-
sequent to such polarization apparently is lacking, but fortunately, according to
equation (1), the exact value is comparatively unimportant provided that it is
much greater than unity, which is certainly the case. (For water it is approxi-
mately five.) Thus an energy of about 35 kcal/mole is released during this
stage of polarization. It would be erroneous, however, to suppose that this
amount comprises the total effect. The Born energy of polarization is the
electrostatic energy difference between unpolarized and polarized states (free
energy), and this net diminution in energy includes a positive energy of the
various degrees of freedom (active coordinates of secondary bonds) equal in
magnitude to this net energy. Thus about 35 kcal/mole are dissipated to the
medium and 35 kcal/mole reside in the 'bonds' as potential energy resulting
from deformation and cleavage. A maximum of about fourteen secondary
linkages may therefore be broken.

4. Orientation Polarization — This is the type of process usually considered in
studies (9) of dielectric relaxation of proteins (and, regrettably, often imagined
to be the only variety of dielectric absorption). It occurs at far greater wave-
lengths than the preceding types (e.g. at relaxation times of order of magnitude
10"'^ sec) and is without influence on the secondary bonds. (Thus, these electric
waves do not denature proteins, whereas intense irradiation in the 20 to 50-/^
region would very likely do so.)

To summarize, energy sufficient to dissociate about sixteen secondary linkages
will be released within an extremely short time interval after localization of
an electric charge of magnitude e in a protein molecule. Not all of this energy
need be used in bond rupture: a portion will be communicated to heat— for
example, to quantum oscillations, both primary and secondary, and also to
waves of long wavelength. But since the major interaction is with the secondary-
bond degrees of freedom, it is likely that the actual number of broken bonds is a
substantial fraction of the maximum number. A conservative estimate would be
ten.

It is obvious that this consequence of ionization* will have a profound
influence on the structure. It is now universally believed that, as first proposed
by MiRSKY and Pauling (10), the organization of the macromolecules is
achieved and sustained by a very great number of secondary bonds, and that
the primary-bond structure is identical in native and denatured states. Modern
elaborations have refined details while retaining the basic ideas of Mirsky and
Pauling. (Thus Lumry and Eyring (11) distinguish between several different
arrangements of secondary bonds — for example, in the states of reversible and
irreversible denaturation — and propose the useful term conformation changes
for these variations.) In some respects denaturation may be viewed as a quasi
phase-transition, on a submacroscopic level. Although isolated secondary bonds
are continually being opened in random fashion by thermal energy, each bond

* The essential idea was described briefly in a previous publication (5).

268

Robert Platzman and James Franck

is normally re-formed in the same configuration and the structure maintained
by the constraints imposed by neighboring bonds ; only if a number of distur-
bances overlap will there be a chance that closure of the bonds occurs in im-
proper fashion, and that the disorder becomes irreparable. The model makes
possible a satisfactory interpretation of thermodynamic and even kinetic data
for thermal denaturation of many proteins (12). It immediately suggests that
explanation of the great radiation sensitivity of proteins must be sought in a
means of communicating energy from a swiftly moving charged particle to the
secondary bonds. Direct energy transfer is negligible, for the coupling is too
small (6). The process here advanced provides the required mechanism.
Although the analysis given above is admittedly crude (a circumstance for which
the lack of relevant and important information on protein structure is chiefly
responsible) it is certainly not speculative: it is based upon well established
physical principles which are, perhaps, unfamiliar in their present implication.
The simultaneous cleavage* of approximately ten secondary bonds following
charge localization constitutes a violent perturbation of the protein structure,
but probably does not suffice to denature most proteins, at least at ordinary
temperatures. This conclusion is suggested by an examination of representative
data (Table 1) from analysis of thermal-inactivation kinetics, taken from the

Table I. Critical Number of Hydrogen-Bond Ruptures From
Thermal Inactivation Rates

Molecular

^HX

^S%

A'l

N^

WlNi

weight ( W)

Insulin

12,000

35.6

23.8

7

2

1700

Trypsin

24,000

40.2

44.7

8

4

3000

Pepsin

37,000

55.6

113

11

9

3400

Peroxidase (milk)

40,000

185

466

37

39

1100

Ovalbumin

43,000

132

316

26

26

1700

Hemoglobin

68,000

75.6

153

15

13

4500

Yeast invertase

120,000

110

263

22

22

5500

(based chiefly upon reference (12)). A// j is the enthalpy of activation, in kcal/mole, ASJ is the
entropy of activation, in cal/mole deg, and the values of A'' are calculated by: A/^i = A// J/5,

Ni = ASt/12.

work of Stearn (12). Stearn proposed a calculation of N, the number of
secondary bonds which have been ruptured in the activated complex (i.e. the
critical number for disordering of the conformation), by assuming an average
energy requirement of 5 kcal/mole (A^^), or, alternatively, an average entropy
incre'ase of 12 cal/mole deg {N^. The values of N^ and N^ so calculated from
velocities of thermal denaturation are in impressive accord with one another,

* The simultaneity of secondary-bond cleavage, which plays a decisive role in the mecha-
nism here proposed, has not been accorded much attention in radiobiology heretofore. It
necessarily underlies much of the thinking about mechanisms in thermal denaturation, at least
implicitly, and has been invoked, for example, in connection with a model of chemical de-
naturation by Kauzmann (13).

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 269

except in the case of the smaller proteins, for which the energy and entropy
requirements probably do not correspond well with the averages assumed.
However, an entropy increase of 12 cal/mole deg is much greater than would
be expected for simple cleavage of a secondary bond. This suggests the entirely
reasonable conclusion that unfolding occurs when there are broken, not any N
secondary bonds, but a particular selection of A^ of them. Clearly, the selection
must be a very special one, embracing bonds at certain decisive locations.
(Because of cooperative effects this would be true even if all of the bonds were
equivalent in their stabilizing action, which is unlikely to be the case.) In the
case of secondary-bond rupture following ionization, the bonds aff"ected are
more or less localized, and therefore less effective, on the average, than the
numbers A'^ listed in the table. Hence the required number of ruptured bonds
for ionizing radiation, TV,, must substantially exceed A'^. Since A^ is in the
neighborhood of ten for even the smallest enzyme molecules, it is evident that
the effect of a single electronic charge is almost, but not quite violent enough
to inactivate a typical, small protein macromolecule. Even the combined
eff"ects of the positive and negative charges, if they are localized in the same
molecule, which must usually be the case, may be expected to be just 'subcritical'
(except, possibly, in the case of the smallest molecules).

This conclusion leads immediately to the following important consequences.

1 . Variation in the Response of Various Proteins — Because of differences in
structural features among proteins of comparable size, the effectiveness of one
or two charges may have wide variation. Furthermore, Ni would be expected
to increase with the molecular volume, but not necessarily in a simple way.
(Note that A^ in Table I shows a definite correlation with molecular weight
( IV), but that W/N is by no means constant.) In all hkelihood NJN would also
exhibit interesting differences.

2. Effect of Temperature on Radiation Sensitivity — ^In cases in which a
single electric charge (or a pair of them) is subcritical, its effect may be critical
at elevated temperatures, because of the augmented probability that the ambient
thermal disorder can supplement the radiation eflTect and bring it past the
threshold for denaturation. This explains, qualitatively, the pronounced thennal
sensitivity which has been observed for some inactivation cross sections (14,
15) and which apparently has not received a satisfactory interpretation here-
tofore (14).

3. Effect of Anisotropy on Radiation Sensitivity — ^Anisotropy of the structure
(at the microscopic level) may contribute greatly to the radiation sensitivity.
An extreme example would be DNA, which is stabilized by numerous secondary
bonds having a degree of freedom for oscillation with an almost common
direction. Abrupt production of electric charge would rupture many of these
bonds simultaneously, causing a portion of the structure to collapse. It is entirely
possible that the great radiation sensitivity of DNA, which is found in a variety
of experiments (16), may have its origin, at least to some extent, in this effect.
The predicted role of molecular anisotropy might be tested experimentally, since
proteins and allied molecules exhibit interesting differences in this characteristic.

4. Collective Effect of Individual Activations on Radiation Sensitivity —
Although a single electric charge may be insufficient to eff'ect denaturation, a
very small number of them would suffice. This points to the importance of

270 Robert Platzman and James Franck

the analysis of spatial correlations of charge production* (also called 'spur'
or 'cluster' distribution), a subject that has not yet been brought to a
quantitative basis, j (It should be emphasized that the bond ruptures caused
by positive and negative charges arising from a single spur are all essentially
simultaneous.)

If accurate information concerning these correlations were available, the
path would be open for study of A^^-, and it could be anticipated that both N^
and the ratio NJN would prove helpful in the study of protein structure.
A closely related subject is the dependence of denaturation efficiency on the
so-called density of ionization; the mechanism predicts that as this parameter
increases, the effectiveness first rises (as more of the charges are formed in
proximity to one another) but ultimately declines, on an energy basis (as the
number of bonds ruptured in a molecule exceeds the minimum number required
for unfolding). This is indeed observed in many types of experiment, although
the rising or the declining portion of the dependence may be enhanced or
suppressed in individual cases, depending upon the specific effect. Such
behavior should be distinguished from the corresponding one of simple radia-
tion-chemical systems (18, 19), which stem from secondary chemical reactions
occurring subsequent to the primary processes; the distinction is not trivial.
(In the case of complex biological systems, such as whole cells, the dependence,
although it often appears to be similar and may be closely related, must clearly
have a far more complex origin (20).) It may be noted that for large protein
molecules the disorganization about even a densely ionized track may be
insufficiently extensive to produce denaturation. Hence there would be antici-
pated some theiTnal sensitivity, although in general less than in the case of
sparsely ionizing radiations. Combination of the disorder produced by several
localized electric charges is by no means the only possible kind of collective
effect, for contributions may be made by excitation events and even by energy
transfer to valence-bond and secondary-bond oscillations from subexcitation
electrons, both of which must by themselves be minor influences. Changes in
certain molecular properties may indeed demand such collective action. For
example, permanent dissociation of a valence bond following an excitation act
is very unlikely in proteins, but if a dissociative excitation and an ionization
should occur close together, the secondary-bond breakage caused by the
ionization would prevent heahng of the rupture. Subsequent thermal action
would then denature and fragment the molecule. It is a suggestive possibility

* Following Lea (1), many investigators have inferred from their experimental data that
inactivation is accomplished by a single 'average' primary ionization. This is in rough agree-
ment with the general conclusion reached above, but it is not a quantitative statement. Most
analyses of experimental data currently being offered appear to be insufficiently detailed and
accurate to refine it.

t The proposal that Auger cascades may have an important role in the chemical and
biological effectiveness of ionizing radiation (17) is highly relevant to the conclusion that a
single electronic charge will in general be subcritical, for each cascade must unquestionably
result in destruction of the secondary-bond structure on an extensive scale. (One factor is
shown by equation (1): the polarization energy is proportional to the square of the electric
charge.) In this connection it may be mentioned that the detailed calculations in the paper
cited apply only to heavy-particle irradiation; for fast electrons and gamma-rays the yield of
Auger cascades is very much greater, being of the order of magnitude of a few per cent of all
ionization events, in proteins.

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 271

that interchain disulfide bonds may be sensitive regions for such an effect,
especially in view of the prominent contribution made by cystine absorption to
inactivation of proteins by ultraviolet light (21, 22), but there is no convincing
evidence that disulfide-bond cleavage is a major factor in protein denaturation
by ionizing radiation. Even the connection with ultraviolet inactivation is
ambiguous, because of the difTerent character of excitation produced by charged
particles (cf. infra).

5. Ejject of the Environment on Radiation Sensitivity — Since the external
environment of the protein can and does participate in the structural stabiliza-
tion of the molecule, it may alter the effectiveness of the various possible dis-
turbances; the temperature effect already discussed is an instance of this.
For example, the medium can contribute externally and internally attached
water molecules, various interacting ions, and even chemical influences, and
the altered array of secondary bonds may clearly respond differently to the
disturbances caused by irradiation. After irradiation and resultant unfolding
the imposed forces may impede further unfolding and may, indeed, with the
help of thermal agitation, promote healing of the disorganization. On the other
hand they may under certain circumstances enhance the radiation sensitivity.
This accounts in a general way for pH and other solvent effects. There is
in principle no simple way to correlate such solvent influences with their effects
in ordinary thermal or biochemical inactivation, since the response to sudden
charge localization is completely different in character from that involved in
such phenomena.

6. Spectrum of Radiation Injury — The previous considerations show clearly
that in a system of identical protein molecules exposed to any variety of ionizing
radiation, a broad range of effects on the molecules must occur. This variability
has its origin in (a), variations in the disturbance following localization of a
single charge, owing to both the intrinsic variability of the effect of the charge
at a given position, and to its localization at different possible sites (e.g. in
the interior or on the periphery of the molecule); and (b), in variations in the
cooperative effects discussed above, which can differ in number, degree, and
proximity (extent of overlapping of regions of charge-induced disorder is
obviously a cardinal factor). (Thus A'^^ certainly is not unique.) The consequence
is a wide range of change in properties, different molecules exhibiting qualitative
as well as quantitative differences. This spectrum of radiation injury is manifest
when appropriate measures are taken to detect it, and the suspicion arises that
the common conclusion from irradiation experiments that proteins are either
inactivated or unaffected cannot possibly be general, and may often be an
oversimplification or even an artifact imposed either by the conditions of an
experiment or its interpretation. That thermal denaturation is not a unique
transformation is, of course, elementary knowledge; on the basis of the present
analysis it appears likely that radiation denaturation may cover an even broader
range. Ample proof of the spectrum of radiation injury is provided by the work
of Fricke (23, 24). Thus partial unfolding of the main chains, in addition
to denaturation, is indicated by changes in optical rotation, serological response,
and A//:J:, and there is evidence for a small amount of fragmentation, with
formation of a variety of products of lower molecular weight. The so-called
'after-effect', a diminished thennal stability of irradiated proteins, is simply

272 Robert Platzman and James Franck

interpreted as stemming from the portion of the spectrum that is subcritical.
(Butler has shown (3, 16) that DNA is also more sensitive to thermal destruc-
tion after irradiation.) Fricke has even specifically resolved the thermally
labile component into a number of fractions with differing thennal response (23).
In the case of ovalbumin irradiated with gamma-rays he found the denatured
product to be less degraded than the thermally denatured product; this is as
expected, since large-scale unfolding can only occur thermally. Another mani-
festation of the spectrum of radiation injury is the differing reaction to post-
irradiative environment that is occasionally observed. This phenomenon, of
which the after-effect is a special case, is related to the effect of radiative environ-
ment, discussed above, but it clearly involves a later phase of the injury — in
particular, partial damage will have been stabiUzed by closure of many hydrogen
bonds, although often in an incorrect way. (This can be inferred from the very
low values of lieats of denaturation, which show that in thermal denaturation
most of the bonds do fonn again after unfolding.) Such disordered molecules
may be further altered by certain external influences and may be restored, at
least in part, by others. It has been remarked (15) that a dependence of the
inactivation of irradiated hemoglobin (and other proteins) on the pH of the
solvent in which they are dissolved after irradiation is anomalous, but according
to the views set forth here such a dependence is not unexpected.

In the above discussion the term 'localized electric charge' was used in place
of 'ionization act' to denote the center of the polarization wave. The motion
of an electron vacancy produced by ionization in a protein has been the subject
of much conjecture, but a cogent analysis has yet to be made. Although it is
certainly true that in (for example) a simple, isolated organic molecule, the
precise designation of an original site of ejection of a valence electron has little
meaning, this cannot be taken as proof that an electron vacancy has unlimited
ability to migrate along the skeleton of a protein or similar macromolecule.
One reason is the low degree of symmetry of the molecule, and its greatly
differing regions of potential. Another, which often is overlooked, is the
influence of the external polarization on this migration. The electronic part of
the polarization sets in almost immediately at ionization, and the various low-
frequency varieties follow as discussed above. All of them severely limit the
mobility of both positive and negative charges. It therefore appears unlikely
that an electron vacancy can cross a secondary linkage, or possibly, indeed,
even a peptide bond. In the case that several electron vacancies are produced
within the same molecule, whatever motion may be possible must enhance the
potency of the effect for disordering, for the coulomb repulsion will tend to
separate the final sites of localization, thus preventing diminution in effectiveness
by too great confinement.

It should be emphasized that the mechanism developed in this paper applies
strictly only to the effect of radiation on an isolated macromolecule, a somewhat
hypothetical situation approximated in experimental work on 'dry' proteins
(1, 4). Immediate effects of the environment have also been touched upon.
For proteins in solution, or in living cells, indirect effects, of a simple or complex
chemical nature, must also contribute to the observed behavior, and no general-
izations regarding the relative potency of the two, except that neither is likely to
be negligible, seem warranted.

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 273

It may also be noted that the chemical effects may be reversed, but that the
disorganization caused by localization in a macromolecule of several freshly
created electric charges cannot be; hence protection from or cure of radiation
damage at the molecular level cannot possibly be complete, even in principle.

IV. THE ROLE OF EXCITATION

Absorption of ionizing radiation leading to the formation of a certain
number of ion pairs must also produce a comparable number of electronically
excited molecules. This is true for the effects of primary charged particles as
well as for secondary ones, and is an elementary consequence of electromagnetic
theory. Indeed, the ratio of total number of excited to total number of ionized
molecules is, except for slow electrons, simply related to familiar optical pro-
perties of the absorbing matter, and the available evidence shows that this ratio
is unlikely to depart from unity by more than a factor of about 2, even allowing
for the disturbing effects of slow electrons. The ratio is known accurately, at
present, only for the noble gases, for which it is 0.4. For all molecular systems
it must be greater.

Just as in the case of ionization, which was discussed above, excitation —
whether produced by absorption of ionizing radiation or of ultraviolet light —
does not itself 'break bonds'. The initial acts of energy transfer are all* ones
in which energy is communicated to the electronic systems of molecules;
subsequent rearrangement of atomic positions may then result in dissociation.
For polyatomic molecules the probability that bond rupture will follow
excitation is by no means unity, and may be quite small.

In molecules like amino acids, polypeptides, and proteins, excitation
commonly is followed by dissociation or by internal conversion, but only very
rarely by luminescence (5). In general, experimental work (which has usually
been restricted, for practical reasons, to wavelengths greater than about 2200 A)
indicates small quantum yields for inactivation, of order of magnitude 10 "^ to
10"^. Analysis of the absorption processes has not progressed to the stage of
identifying them either with dissociation or with internal conversion, but the
following explanations for the low efficiency seem attractive. In the case of
dissociation, that is, cleavage of a primary (valence) bond, the secondary-bond
structure may prove capable of sustaining the conformation, at least until
activation energy becomes available for healing the rupture. (Thus the cage
effect is enhanced.) This proposal is supported by the fact that dissociation
by moderate or long-wavelength ultraviolet radiation does not provide much
energy in excess of the bond dissociation energy; thus at 2200 A, not more than
several hydrogen bonds could be broken. The structure should therefore remain
otherwise intact, with closure of the bond a much more likely ultimate result than
denaturation. Internal conversion, on the other hand, releases a substantial
quantity of energy to oscillational modes, but the coupling is chiefly with
valence oscillations (C — H, C — C, etc.); by the time the energy reaches the
secondary bonds it will have been dissipated too extensively to have much effect, t

* The only direct bond breakage arises from momentum transfer to atoms from swiftly
mo\ing particles, in so-called nuclear collisions (17). This is usually a minor effect.

t However, individual internal conversion processes may be responsible for isomerization,
and thus for such biological phenomena as gene mutation.

274 Robert Platzman and James Franck

Another factor which diminishes the effectiveness of excitation by uhraviolet
light is the spatial isolation of the individual absorption events. Thus the second-
ary bonds ruptured as a consequence of a single internal conversion process may
heal before serious unfolding occurs. In the case of excitation by charged
particles, however, the excited molecules are often produced in close proximity
(and simultaneity) to other activations, and hence must undoubtedly contribute
to the disorganizing action. Such collective effects have already been discussed.

One characteristic of ionizing radiation which always should be kept in
mind is the difference in nature of the excited molecules produced from those
that have been studied photochemically : they correspond, for the most part, to
radiation in the vacuum ultraviolet region, where most of the optical transition
probability invariably lies. Little is known of polyatomic molecules with regard to
optical phenomena and to processes following excitation in this spectral region.
However, such radiation may have far greater potency than the readily accessible
ultraviolet, for either in dissociation or in internal conversion processes, it always
releases sufficient kinetic energy to break many more secondary bonds.
There is indeed some experimental indication of this in the rise of quantum
yields at the shortest wavelengths studied (25, 22). Thus the role of excitation
in radiobiology probably is greater than usually is (cf., e.g., (14)) supposed.

V. CONCLUSION

The mechanism considered here provides a realistic physical basis for
understanding the remarkable fact that a polar macromolecule of molecular
weight as great as 10^ can be inactivated by only a few ionization acts, and it is
capable of explaining qualitatively a variety of experimental results. It replaces
the notion that ionizing radiation acts merely by breaking chemical bonds
directly, which, apart from its superficiality, does not actually explain denatura-
tion at all. No attempt has been made in the present paper to analyze in detail
the myriad data on numerous kinds of radiation effect for varying quality and
quantity of radiation, varying environment, etc. Indeed, further development
must await, in most points, the further elucidation of protein structure, especially
in its dependence upon the secondary-bond configuration. In particular, the
number, disposition, and mutual dynamical behavior of the secondary bonds,
as well as the character of their large-scale stabilizing action, must be more
fully understood. At some future stage of development radiation studies may
provide a valuable tool in advancing this knowledge, for the action of ionization,
as described here, is completely different in character from other types of
attack which are investigated, such as heat, salts and other chemically inert
solutes, and chemical agents, all of which act essentially adiabatically at the
atomic level. In essence it has been demonstrated that the marvellous stabilizing
action manifested in natural polar macromolecules is intrinsically ineffectual
against the nonadiabatic disturbance of an ionization act.

REFERENCES

1. D. E. Lea: Actions of Radiations on Living Cells, Cambridge University Press, Cambridge,
England (1946).

2. L. H. Gray: The initiation and development of cellular damage by ionizing radiations.
Brit. J. Radiol. 26, 609-618 (1953).

A Physical Mechanism for the Inactivation of Proteins by Ionizing Radiation 275

3. J. A. V. Butler: The action of ionizing radiations on biological materials. Facts and
theories. Radiat. Res. 4, 20-32 (1956).

4. E. Pollard: Primary ionization as a test of molecular organization. In: Advances in
Biological and Medical Physics, ed. by J. H. Lawrence and C. A. Tobias, 3, 153-189 (1953).

5. J. Franck and R. Platzman: Physical principles underlying photochemical, radiation-
chemical, and radiobiological reactions. Radiation Biology, ed. by A. Hollaender, Vol. I,
Chap. 3, McGraw-Hill, New York (1954).

6. R. L. Platzman: Energy transfer from secondary electrons to matter. In: Basic
Mechanisms in Radiobiology , 11-7,1, Nat. Res. Council (U.S.) Publ. No. 305 (1953).

7. R. Platzman and J. Franck : Theory of the absorption spectra of halide ions in solution.
In: L. Farkas Memorial Volume, 21-36, Research Council (Israel), Jerusalem (1952).

8. R. L. Platzman: Influences of details of electronic binding on penetration phenomena.
In: Symposium on Radiobiology, ed. by J. J. Nickson, Chap. 9 (cf. §VIII), J.Wiley
and Sons, New York (1952).

9. J. T. Edsall: The size, shape and hydration of protein molecules. In: The Proteins,
ed. by H. Neurath and K. Bailey, Vol. I-B, 698-712, Academic Press, New York (1953).

10. A. E. Mirsky and L. Pauling: On the structure of native, denatured, and coagulated
proteins. Proc. Nat. Acad. Sci., Wash. 22, 439^W7 (1936).

11. R. LuMRY and H. Eyring: Conformation changes of proteins. /. Phys. Chem. 58,
110-120(1954).

12. A. E. Stearn: Kinetics of biological reactions with special reference to enzymic pro-
cesses. Advances in Enzymology, ed. by F. F. Nord, 9, 25-74 (1949).

13. W. Kauzmann: Denaturation of proteins and enzymes. In: The Mechanism of Enzyme
Action,ed.hy'W. D. McEIroyand B. Glass, 70-110, Johns Hopkins Press, Baltimore (1954).

14. E. C. Pollard, W. R. Guild, F. Hutchinson, and R. B. Setlow: The direct action of
ionizing radiation on enzymes and antigens. In: Progress in Biophysics, ed. by
J, A. V. Butler and J. P. Randall, 5, 72-108, Pergamon Press, London and
New York (1955).

15. R. Setlow: Radiation studies of proteins and enzymes. Ann. N.Y. Acad. Sci. 59,
471^83 (1955).

16. J. A. V. Butler: Effects of x-rays and radiomimetic agents on nucleic acids and nucleo-
proteins. In: Ciba Foundation Symposium on Ionizing Radiations and Cell Metabolism,
ed. by G. E. W. Wolstenholme and C. M. O'Connor, 59-69, Churchill, London (1956).

17. R. L. Platzman: On the primary processes in radiation chemistry and biology. In:
Symposium on Radiobiology, ed. by J. J. Nickson, Chap. 7, J. Wiley and Sons, New York
(1952).

18. E.J. Hart, W.J. Ramler, and S. R. Rocklin: Chemical yields of ionizing particles in aque-
ous solutions : Eff'ect of energy of protons and deuterons. Radiat. Res. 4, 378-393 (1956).

19. R. H. Schuler and A. O. Allen: Radiation chemistry studies with cyclotron beams of
variable energy — yields in aerated ferrous sulfate solution. J. Amer. Chem. Soc. 79,
1565-1572(1957).

20. R. E. Zirkle: The radiobiological importance of linear energy transfer. In: Radiation
Biology, ed. by A. Hollaender, Vol. I, Chap. 6, McGraw-Hill, New York (1954).

21. R. Setlow: A relation between cystine content and ultraviolet sensitivity of proteins.
Biochim. Biophys. Acta 16, 444 445 (1955).

22. R. Setlow and B. Doyle: The action of monochromatic ultraviolet light on proteins.
Biochim. Biophys. Acta 24, 27-41 (1957).

23. H. Fricke: Kinetics of thermal denaturation of x-rayed egg albumin. /. Phys. Chem.
56, 789-795 (1952).

24. H. Fricke, C. Leone, and W. Landmann: The role of molecular degradation in the
loss of serological activity in gamma-irradiated ovalbumin. Radiat. Res. 7, 316 (1957).

25. A. D. McLaren: Photochemistry of enzymes, proteins, and viruses. Advances in
Enzymology, ed. by F. F. Nord, 9, 75-170 (1949).

INFORMATION AND INACTIVATION OF
BIOLOGICAL MATERIAL*

Harold J. Morowitz

Department of Biophysics, Yale University, New Haven, Connecticut

Abstract — An analysis of target theory has been carried out in terms of the language of in-
formation theory. Certain results suggest that radiation and thermal inactivation experiments
can be used to set limits on the values of information content of biological structures. A group
of such limits has been discussed, as well as a suggestion for using 'radioactive suicide' experi-
ments to evaluate information content.

Information theory provides a discipline for quantifying order and specificity
in biological structures. Ionizing radiation and heat provide more or less
random methods of disordering biological structures. Therefore, we may
anticipate that infonnation theory and studies of the biological effects of heat
and ionizing radiation may in some way complement each other. In particular,
if we can make some quantitative statements about the amount of disordering
necessary for loss of biological function, we are then able to say something
about how much order is involved in specifying the system.

The concept of target volume has an analogue in the representation of a
structure in terms of a series of symbols. If inactivation curves are exponential
and the target volume is less than the volume of the structure, we may conclude
that part of the structure (the critical target) has an information density higher
than the rest of the structure. That is, a subset of syinbols in the array require
much closer specification than the rest of the array. If no energy is transferred
and there are b symbols in the subset, the target volume will be bVjM, where V
is the total volume of the structure and M is the total number of symbols of
equal volume needed to specify the structure. If there is energy transfer with
high efficiency over g atoms, the volume will be of the order of bg^VjM,
assuming no overlap of partial volumes.

In this paper we shall be concerned with those biological materials that
can be dried, taken to low temperatures and then returned to a functional
state without appreciable loss of activity. This class of materials includes
enzymes, viruses, spores, and transforming principle. In these entities we
may conclude that the information is contained in the structure. Several
methods have been used to evaluate the information content of these resting
systems.

We shall outline briefly two methods that have been used to evaluate the
infonnation content of biological materials. In both methods it is assumed
that the atomic composition and volume are known. The volume may then
be divided into a number of elementary atomic volumes. To specify the

* Supported by a Research Grant from the John A. Hartford Foundation.

276

Information and Inactivation of Biological Material 277

system completely, we need to state, in some pre-arranged sequence, which
type of atom is present in each elementary volume and the bonds between
that atom and its six nearest neighbors. Our specification then consists of a
message giving the appropriate symbol to each elementary volume. To cal-
culate the average information per symbol, we consider the probability /7,y
of having the /th type of atom in theyth bonding state. The average information
is then given by

H=-lPii\o%2Pii (1)

a

If the/j/s are assumed from the average composition of dry bacteria (hydrogen,
52.2 mole per cent; carbon, 29.9 mole per cent; nitrogen, 7.6 mole per cent;
oxygen, 5.8 mole per cent; phosphorus, 2.9 mole per cent; sulfur, 1.6 mole
per cent), and if we assume that all the types of bonding configurations have
equal a priori probabilities, we can then calculate that H is of the order of
4.0 bits per atom. Since the different bond configurations have rather different
probabilities, our figure is high and 3 bits would probably be a more realistic
estimate.

An alternative but equivalent method of finding the information content
is to assume that all states of the system have equal a priori probability. If
there are A'^ possible states and L of these are biologically functional, the
probability that the system is in a functional state is LjN and the information
is given by

H = -log2 LIN = log2 TV - log2 L (2)

If the system must be completely specified, L equals one and H takes on its
maximum value, log2 A'^. We may then calculate A^ from the number of per-
mutations of the atoms in the elementary atomic volumes and the permutations
of the bond states (1). This leads to the same average information content
per atom as the previous treatment.

However, from a point of view of biology, we would like to know the
actual value of H rather than //,uax- ^^ we consider a large collection of spores
or viruses or enzymes in contact with a thermal reservoir at temperature T
and allow the system to come to thermal equilibrium over a long time, we
may regard the collection as a Gibbsian ensemble, and the ratio of the final
activity to the initial activity is a measure of the a priori probability of finding
the system in a functional state, in general the activity decreases with time
in an exponential fashion. In all the experiments that have been carried out,
the sample is too small and thermal equilibrium is never reached. This enables
us to determine a lower limit of the information content, but the limit is too low
to be of any practical use. For example, dry Bacillus suhtilis spores show an
exponential inactivation over twelve decades. There is no indication that the
system is nearing equilibrium so we may conclude that the a priori probability
of finding the system in a living state is less than 10^^. H is then greater than
— log2 10~^^ or greater than 42. Since the upper limit (based on L = 1) for
this system is of the order of 10^^ bits, the thermal data do not help very much
in bracketing the figure. Experimentally it is not feasible to carry thermal
inactivation studies below an activity of 10^^^ because of difficulties in the

Id

278 Harold J. Morowitz

sample size and the assay in the presence of all the inactivated material.

It may be noted in passing that the consideration of the system in terms of
a Gibbsian ensemble may provide some insight into the origin of life or the
a priori probabihty of a biologically functional structure arising de novo.

In considering the information aspects of ionizing radiation, we shall
confine ourselves to anhydrous systems and consider only the direct action
of radiation. We must then consider the effect of a primary ionization in
altering the structure of biological molecules. Present evidence indicates that
primary ionizations occur in a random fashion along the track of the fast
charged particle. However, the subsequent events are much less clear. It
is difficult to make quantitative statements about the probability of the energy
being transferred from the site of the original ionization to an energy sink
in the material. For purposes of developing the theory, we shall first make
the simplest possible assumption that the result of a primary ionization is a
bond break, or rearrangement of bonds at the site of the ionization. Many
structures are inactivated by a single ionization within the structure. If the
previous hypothesis applies, such structures have an information content
close to //niax5 sincc L must be unity if any rearrangement destroys the functional
integrity of the structure. It should be remembered that //max is the formal
upper limit if the calculation is based on atomic specification. It would be
possible to start from other points of view, such as monomer specification,
functional unit specification, or genetic specification, and arrive at different
values of an H function for use in subsequent analysis.

However, there are many indications that the simple assumption made
above is not valid. For tobacco mosaic virus (2), the target volume is about
half the total volume of the particle, yet the infectious unit is presumably the
RNA which is only six percent of the total volume. Many enzymes show a
target volume equal to the physical volume of the molecule (3), yet recent
evidence suggests that several amino acids can be removed from the enzyme
without loss of activity (4). It is difficult to see why bond rearrangements in
these amino acids should lead to loss of function. Some enzymes show a target
volume larger than the physical size of the molecule.

These factors indicate energy transfer from the site of the ionization to
an energy sink within the molecule. Recent studies by Gordy (5) and Setlow
(6) tend to suggest that sulfur-sulfur bonds are the ionization sinks in protein.
If we assume that this is the case and that the energy of a primary ionization
is transferred with a high efficiency to these bonds, then we can arrive at a
minimum value of the infonuation content of molecules which contain these
bonds and are inactivated by a single ionization. Since about one in every
400 of the atoms is involved in an S-S bond, we may conclude that MH/400
per atom is a crude estimate of the minimum information necessary to specify
the structure of M atoms. In this case radiation experiments would enable
us to set a lower limit to the information content.

Consider next a structure which requires several ionizations to cause an
inactivation. If there are M atoms in the structure, each ionization may trans-
fornn the system from its original state to any one of the MB neighboring
states, where B is the average number of ways in which each atom can be bonded
to its neighbors. If on the average x hits are required to inactivate the structure,

Information and Inactivation of Biological Material

279

then L must be at least

{MBf

H is then given by

H = //max — X logo MB + l0g2 x\

(3)

It was argued above from equation (I) that there are about 3 bits per atom,
so that //,nax is a number of the order of 3A/; thus if x is small in comparison
to M, a structure requiring multiple hits will still have an information content
close to //max* i^ cascs where no energy transfer is assumed.

A

30x10-'°

-

~s20xl0'°
o

-

z

z
o

1-

'^ 10x10-'°

to

to

o

5 X 0

-

e
•

,

1 1 1 1

1

200 600 1000 2000

LET IN EV/ 100 A

3000

4000

Fig. 1

There are cases in which x may be an appreciable fraction of M. If one
plots cross-section as a function of linear energy transfer (LET), the shape
of the curve gives an indication of target thickness and number of ionizations
required. If it can be shown that x ionizations are required in a distance A
for an inactivation, we can divide the structure into sub-structures of volume
A^ in which case H is given by

H = ZA^m - 1022 ^^^' (4)

'- x\

where m is the number of atoms per unit volume. If x is an appreciable fraction
of A^m the substructure may have an information content smaller than the
maximum value. The information content of the entire structure, which is
the sum of that for the substructures, will be correspondingly smaller than
in the case of complete specification.

Let us now consider the specific case of the irradiation of spores of Bacillus
subtilis with fast charged particles. At all values of LET studied the inactivation
curves are exponential functions of the dose. Fig. 1 shows the curve obtained

280 Harold J. Morowitz

by Mr. J. Edward Donnellan of the Yale Biophysics Department, and indicates
inactivation cross-section for colony formation as a function of LET. From
the electron irradiations of Proctor et al. (7), the target volume for these spores
is of the order of 10"^'^ cm^. However, this seems to be the volume of the sub-
structure with the highest information density. For we see that as we increase
the LET the radiation rapidly becomes more efficient in causing inactivation.
What we are doing in increasing LET is to increase the probabihty of several
ionizations in a given substructure of the spore. Since the cross-section then
rises so dramatically, we must conclude that targets of lower information density
than the one originally inactivated at low ion densities are now coming into
play. Since the curves are exponential, the multiple ionizations in any sub-
structure must be coming from the same fast charged particle. Under these
circumstances, x must of necessity be small compared with M, and the secondary
targets must still retain an information content near //max, if we ignore energy
transfer.

We may conclude, in general, that any large structure which is capable
of being inactivated by the passage of a single fast charged particle through
that structure probably has an information content which is an appreciable
fraction of /^max- In general, if information can be transferred with high
efficiency over g atoms, H is probably greater than H^^aJ^lgf.

There seems to be a possibility of reducing energy transfer and thus getting
a better estimate of information content. When enzymes are irradiated with
fast charged particles and the experiments are carried out at different tempera-
tures, the target cross-section is found to be an increasing function of temperature
(3). The possibility exists that energy transfer is being reduced at the low
temperatures, and data taken in this range might provide a better index of
the actual information content. However, considerations of this type demand
a thoroughgoing analysis of the physics of the situation.

Another method of random disordering exists which might provide an
even more powerful tool for the elucidation of information content. It has
been recently shown (8) that viruses labeled with P^^ lose activity on standing,
and the rate of loss is associated with the amount of P^^ incorporated. Now
the decay of a radioactive atom incorporated in a biological structure, and the
consequent transmutation of the atom, represents a random disordering.
If the labeling is random, the rate of decay should provide a measure of the
fraction of atoms of the labeled type which require precise specification in
order for the structure to be functional. Such an information evaluation should
be possible for phosphorus, sulfur, hydrogen, carbon, sodium and calcium.
Thus we may inquire about a complicated structure like a spore: how many
of the phosphorus atoms in the structure are required to specify a functional
unit? Experiments and calculations of this type should serve to limit the value
of the information content of biological structures.

REFERENCES

1. H. J. Morowitz: Some order-disorder considerations in living systems. Bull. Math.
Biophys. 17, 81-86 (1955).

2. E. C. Pollard and A. E. Dimond: The inactivation of tobacco mosaic virus by ionizing
radiation. Phytopathology A6, 214-218 (1956).

Information and Inactivation of Biological Material 281

3. E. C. Pollard, W. R. Guild, F. Hutchinson, and R. B. Setlow: The direct action of
ionizing radiation on enzymes and antigens. In: Progress in Biophysics, 5, 72-108,
Pergamon Press, London and New York (1956).

4. C. B. Anfinsen: The limited digestion of ribonuclease with pepsin. J. Biol. Cliem. 11\,
405^12 (1956).

5. W. GoRDY, W. B. Ard, and H. Shields: Microwave spectroscopy of biological substances.
Proc. Nat. Acad. Sci., Wash. 41, 983-1003 (1955).

6. R. B. Setlow: A relation between cystine content and ultraviolet sensitivity of proteins.
Biochim. Biophys. Acta 16, 444-445 (1955).

7. B. E. Proctor, S. A. Goldblith, E. M. Oberle, and W. C. Miller, Jr.: Radiosensitivity
of 5ac/////5.sM6r///.y under different environmental conditions. Radiat. Res. 3, 295-303 (1955).

8. G. Stent and C. A. Fuerst: Inactivation of bacteriophage by decay of incorporated
radioactive phosphorus. /. Gen. Physiol. 38, 444-457 (1955).

DISCUSSION

Quastler: Dr. Morowitz's analysis of the informational aspects of radiation effects,
and his concept of information density, are very important developments. As a matter of fact,
I believe them to be so important that even small differences in interpretation are worth
mentioning, and this is the reason for making the following comments.

To rephrase the situation: consider a structure (message) consisting of a distinct sub-
structures (words) of b elements (letters) each. Let H' be the information content per letter
and T' the information measure of constraints between letters. Then:

H" = information content per word = b{H' — T')

H" = information content of message = a(H" — T")

(where T" represents the informational aspects of constraints between words) and

H^jab = information density in bits per letter.

If the 'letters' are atoms in living matter, then I suspect the constraints T' and T" to be quite
considerable and to reduce H"'lab to rather less than three bits per atom.

We introduce noise of such a character that a single noise event results in the functional
destruction of a single letter, and examine the functional value of the message after it has
suffered a known number of noise events. If a single event destroys the functional value, then
all letters are functionally essential and the functional information density is H"'lab. If the
number of noise events needed averages more than one, then the informational density must be
less than maximum, and this can occur in two entirely different situations.

(I) A number a^ of the letters in each word (or a number b^ of the words) is either irrelevant
or can be reconstructed, provided every one of the a — a^ essential letters (or b — h^ essential
words) is intact. Then the functional information density is

H" a -ao H" b - bo

ab a ab b

and a single event can cause loss of function but does so only with probability (1 — aja) or
(1 — b^jb), respectively. This is the situation where the target size is less than the total size of
the structure.

(II) Up to «r letters in every word (or up to br words) can be destroyed without loss of
function — and these letters or words do not belong to a predetermined sub-set but can be any
letters (or words). This is the case with error-correcting codes; in this case no single event can
cause loss of function, but Or + 1 events will every time. The functional information density
is again less than maximum, being

H" a- ar H" b - br

ab a ab b

282 Discussion

but it is reduced by the presence of redundant information — not by irrelevant information as in
the first case. These two situations must be sharply distinguished.

With atoms and molecules, the error-correcting mechanism can be a cage effect or some-
thing of the kind. This could be the situation where loss of function is caused by clusters of
events, i.e. passage of a particle of high linear energy transfer. It may be suspected that the
protective effect of redundancy of chemical structure extends only over regions of rather
limited sizes which would imply that the reduction of information density could be rather
substantial.

THE ABSENCE OF RADIATION-INDUCED
DISULFIDE INTERCHANGES*

Arthur L. Koch f

Division of Biological and Medical Research, Argowie National Laboratory,

Lenwnt, Illinois,

and

Department of Biochemistry, University of Florida,

Gainesville, Florida

Abstract — Mixtures of cystine and its 6/i-dinitrophenyl derivative were: (a) irradiated as dry
films, (b) treated in aqueous solution with Fenton's reagent, and (c) irradiated in aqueous
solution. In none of these cases could any of the interchange product, mono-dinitrophenyl
cystine, be detected. It is therefore inferred that disulfide interchange is not a primary cause
of protein denaturation or enzyme inactivation by ionizing radiations.

As a consequence of treatment of proteins and protein solutions with large
doses of ionizing radiations, denaturation, as assessed by decreased solubility
at the isoelectric point, frequently occurs (1). The involvement of sulfur linkages
in these solubihty changes as well as in the concomitant loss of biological
activity has been frequently suggested. The importance of the oxidation of
existing thiol groups to disulfides is well documented (2), but another possi-
bility is that polymerization results from disulfide interchange, in a manner
similar to that postulated by Huggins, Tapley, and Jensen (3) to account
for gel formation in the presence of urea. In their case the initiator of the chain
reaction was assumed to be a sulfhydryl group exposed by the unfolding of
the protein. This unfolding results from the breaking of intramolecular hydro-
gen bonds by the urea. One could, however, conceive of chain reactions
initiated by the free radicals produced by ionizing radiations. For example,
hydroxyl radicals produced by the action of the radiation on water could
react to produce a sulfenic acid and a sulfide radical, which could then react
further:

OH + /?iSS/?.3 > 7?iS0H + S/?2

Si?2 -r /?3SS/?4 >RS^R^ + S/?3 .

Such a mechanism appears attractive in view of the properties of sulfur
compounds as presented by Calvin (4, 5). Further reactions of /^^SOH could
also lead to polymerization as a consequence of dismutation to the sulfide
and sulfinic acid.

In order to investigate these possibilities, a model system was studied.
The system chosen was that utilized by Ryle and Sanger (6). These authors

* This work performed under the auspices of the U.S. Atomic Energy Commission.
t Present address: Department of Biochemistry, University of Florida, Gainesville,
Florida.

283

284

Arthur L. Koch

were particularly interested in the possibility of interchange under strong
aqueous acid conditions that are present during protein hydrolysis. In our
laboratory this system has been used to study the effects of strong anhydrous
acid media (7). In the former case interchange was found and this could be
repressed with thiol compounds; in the latter case no interchange occurs.

The system consists of a mixture of /?/5-2,4-dinitrophenyl-L-cystine {bis-
DNP cystine) and L-cystine. If the interchange occurs, the reaction product,
mono-2,4-dinitrophenyl-L-cystine (mono-DNP cystine) may be readily measured
by removing the bis compound by acid ether extraction, or by chromatography
in a solvent system consisting of aqueous 5 per cent Na2HP04 overlaid with
isoamyl alcohol. The spots can be visualized by observation with near ultra-
violet hght. By a combination of these two techniques additional sensitivity can
be obtained.

Dry Irradiation

Using this system it was quickly established that even with doses as large
as 3 X 10'^ r of Co^° gamma rays no detectable interchange product was produced
in the radiation of dry films of mixed cystine and its /?w-dinitrophenyl derivative.
As very small amounts could be detected by the combination of the extraction
and chromatographic techniques, it is felt that disulfide interchange cannot
be of importance in the denaturation of dry protein samples, as certainly much
less than one interchange per 1000 disulfide bonds could have been detected.

E^ect oj OH Radicals

In aqueous solution the experimental situation is quite different. We first
investigated the effects of hydroxyl radicals by themselves. Experiments (Table
I) with Fenton's reagent (a mixture of Fe++ and H2O2 prepared as described

Table I. The Absence of Interchange Produced by OH Radicals

The complete system contains 1 x 10^ M cystine; 1.25 x
10-* M 6w-DNP cystine; 1.2 x 10"^ M phosphate buffer, pH
7.9; 5 X 10-5 M pe++ (^s FeSOi); 5 x 10^ M H2O2. For
analysis, 0.5 ml aliquots were added to 2.0 ml of 1 N HCl.
The solution was then exhaustively extracted with ether and
read at 350 m/t in the Beckman spectrophotometer.

Complete

Minus Fe++

Minus H2O2*

Minus Fe++ and H2O2*

If interchange is complete

(calculated)

Increase in optical density

5.5 hours

48 hours

0.048

0.062

0.004

-0.006

0.052
0.052
0.084
0.100
0.489

* The interchange observed at 48 hours in absence of H2O2
is caused by thiol compounds produced by the hydrolysis of the
disulfide (6).

The Absence of Radiation-Induced Disulfide Interchanges

285

by CoLLiNSON et al. (8)) did not give any increase in the content of non-ether
soluble chromophoric material as compared with a control containing HaO,
alone. Even at the end of forty-eight hours no increase was apparent, although
ribonuclease would have been destroyed completely at the end of thirty minutes
(8). The increase in optical density in the HgOg control is small but significant
(20 per cent of theoretical at the end of forty-eight hours), and probably
represents oxidation to ether insoluble materials such as dialkyl sulfoxides
and cysteic acids.

Irradiation in Aqueous Solution

When aqueous solutions of mixtures of cystine and its Z)/5-dinitrophenyl
derivative were irradiated with 1 X 10' r, the results obtained were equivocal
because of the influence of side reactions causing change in the chromophoric
moiety.

Possibly this effect is akin to the well known photo-destruction of dinitro-
phenyl derivatives generally. That such a process is occurring follows from
the observations that the samples irradiated with 6 X 10*^ r of Co^" gamma
rays were less intensely colored than the non-irradiated controls; the optical
density at 350 m/^ was reduced to one third that of the controls. The bulk of the
350 mn absorbing material after irradiation was insoluble in ether. This
product was clearly not the interchange product, because it possessed the wrong
spectrum (high absorption at 250 mfx, with only a shoulder at 380 m//, whereas
the wavelength for the maximum absorption of the mono-dinitrophenyl cystine
under these conditions is 360 m//). In addition, the same material was produced
(in higher yield) in the control containing no cystine.

An attempt was made to lower the dose to a point where the above side
reaction would not obscure the possible interchange reaction (see Table II).

Table II. The Effect o/Co^" Gamma-ray Irradiation ofhis-DNP Cystine

The complete system contains 1 x 10"^ M cystine; 1.25 x 10^* M
bis-DNP cystine; 1.2 x 10"- M versene buflFer, pH 7.9; where indi-
cated, 5 x 10"* M A^-ethyl maleimide (nemi) and 5 x 10"* M/7-chloro
mercuri-benzoate (pcmb). The samples were irradiated with 4 x 10* r
of Co*" gamma-rays in a 60-minute period.

Optical density

Before ether After ether Component with
extraction extraction Rp = 0.6

Unirradiated

0.510

0.040

0

Complete

0.220

0.171

0

Plus NEMI

0.255

0.198

0

Plus PCMB

0.281

0.209

0

Minus cystine

0.155

0.106

0

After a dose of 4 X 10^ r no colored material could be detected with the Rp
of 0.6, which is the R^ of mono-dinitrophenyl cystine, although significant

286 Arthur L. Koch

amounts of the reactants were still present. In this experiment the dose was
delivered in a one-hour period. During this time the effect of the spontaneous
interchange catalyzed by thiols produced by hydrolysis of the disulfides is small
(6). In the presence of versene, which prevents metal-catalyzed oxidation
by molecular oxygen, the interchange is greater because of greater persistence
of thiol. For this reason, controls were included containing thiol binding
reagents which completely block thiol catalyzed interchanges.

These preliminary experiments indicate that interchange of disulfide bonds
is not a prominent feature of radiation-induced denaturation. Further work
will be required to assess the role of disulfide linkages in secondary aspects
of denaturation. In addition, further work should be carried out using a
disulfide interchange indicator that is not itself influenced by irradiation in
aqueous solution and thus affords a more sensitive assay for interchange in
aqueous media.

Acknowledgement — The author acknowledges with gratitude the continued
interest and valuable advice of his colleagues Howard S. Ducoff, George A.
Sacher, and Antreen Pfau.

REFERENCES

1. H. Fricke: The denaturation of proteins by high frequency radiation. Cold Spr.
Harb. Symp. Quant. Biol 6, 164-170 (1938).

2. E. S. G. Barron and P. Finkelstein: Studies on the mechanism of action of ionizing
radiations — X. Effect of x-rays on some physicochemical properties of proteins. Arch.
Biochem. Biophys. 41, 212-232 (1952).

3. C. HuGGiNS, D. F. Tapley, and E. V. Jensen: Sulphydryl-disulphide relationships in the
induction of gels in proteins by urea. Nature, Loud. 167, 592-593 (1951).

4. M. Calvin: Mercaptans and disulfides, some physics, chemistry, and speculation. In:
Glutathione, ed. by S. Colowick et al, 3-26. Academic Press, New York (1954).

5. J. A. Barltrop, p. M. Hayes, and M. Calvin: The chemistry of 1,2-dithiolane (tri-
methylene disulfide) as a model for the primary quantum conversion act in photosynthesis.
/. Am2r. Chem. Soc. 76, 4348-4367 (1954).

6. A. P. Ryle and F. Sanger: Bisulphide interchange reactions. Biochem. J. 60, 535-540
(1955).

7. A. L. Koch, W. A. Lamont, and J. J. Katz: The effects of anhydrous strong acid on
ribonuclease and lysozyme. Arch. Biochem. Biophys. 63, 106-117 (1956).

8. E. Collinson, F. W. Dainton, and B. Holmes: Inactivation of ribonuclease in dilute
aqueous solution. Inactivation by hydroxyl radicals. Nature, Lond. 165, 267-269 (1950).

A PROPOSED MECHANISM OF PROTEIN
IN ACTIVATION*

L. G. AUGENSTINE
Brookhaven National Laboratory, Upton, Long Island, New York

Abstract— An hypothesis dealing with the role of disulfide bonds in protein inactivation by
physical agents has been discussed with reference to material presented at this conference.
It is proposed that the critical effect becomes localized at a 'weak-link', causing first the
rupture of a disulfide bond, followed by the breaking of neighboring intramolecular bonds
and finally the rupture of a second disulfide bond. Much of the evidence upon which these
postulates are based is reviewed. The manner in which this model defines a target volume is
indicated and alternative methods of disulfide splitting are discussed.

The author has previously proposed (I) an hypothesis deahng with the general
problems of protein inactivation and the importance of disulfide bonds in
maintaining protein structure. This hypothesis was originally presented to
account for heat denaturation data. It has since been extended in an attempt
to account for inactivation by ultraviolet hght and by ionizing radiation
('direct effect') (2, 3, 4). The model is a special case of more general ones
proposed by Mirsky and Pauling (5), Lumry and Eyring (6) and Platzman
and Franck (7), and would depend for its accomphshment upon physical
processes similar to those described by the latter authors. It is to be emphasized
that this scheme is not advanced as the only mechanism whereby protein
inactivation can occur, but rather as the most likely.

It is proposed that the critical effect of the physical agents mentioned is
not to cause indiscriminate molecular disorganization. Rather, their primary
effect becomes preferentially locaHzed at certain points in the molecule! .
Further, certain of these points (collectively called the 'weak-hnk') are involved
in processes which are characteristic of all proteins and which lead to inactivation.
These processes can be characterized as occurring in three distinct steps.

1. The breaking of an S — S bond;

2. The breaking of a variable number of neighboring intramolecular bonds

(e.g. H-bonds); and

3. The rupture of a second S — S bond.

Step 1 requires about 20 kcal/mole, or 0.9 eV per molecule (8), and a
negligible entropy factor, while an appreciable entropy increase is associated
with step 2. Step 3 allows the spontaneous formation of a structure incom-
patible with further activity. Although irreversibility could result from the

* Research carried out at Brookhaven National Laboratory under the auspices of the U.S.
Atomic Energy Commission.

t For instance, Platzman (4, p. 19) has pointed out that 'the most stable position for a
migrating electron vacancy to become localized is at a site that can be crudely identified with the
atom of lowest ionization potential'.

287

288 L. G. AUGENSTINE

formation of a single new bond (4)*, it is probably produced most often by
the spontaneous breaking of a large number of intramolecular bonds which
is accompanied by a very large increase in entropy. Steps 1 and 2 would
constitute the activated state of physical denaturation, i.e., reversible inacti-
vation, whereas the rupture of the second S — S bond, step 3, allows irreversible
inactivation to proceed. The large entropy change often found to be associated
with irreversible denaturation indicates that a partial unfolding of the molecule
usually occurs, and therefore the 'weak-link' is probably involved in latching
the molecule together. Once the second S — S bond has ruptured, the degree
of denaturation will depend both upon the extent to which unfolding proceeds
and upon subsequent reactions of the newly exposed groups of the altered
molecule. The number and the location of the intramolecular bonds involved
in step 2 is thought to be essentially invariable for a given protein, and to depend
upon its particular structure in the region of the weak link. It is postulated
that a variable number of bonds is involved in step 2 since the enthalpy of
denaturation activation varies widely between different proteins (8, 1).

These generalizations are consistent with a variety of experimental findings,
many of which have been discussed elsewhere (1,2,3), and therefore will be
only mentioned briefly.

(a) Data reported by a number of investigators give a value for the free
energy of denaturation activation of AF* = 24.8 i 1-5 kcal/mole (or 1.1
eV/molecule), which is slightly in excess of that required to rupture an S — S
bond (8).

(b) Mild denaturation is reversible, whereas violent denaturation is not.

(c) Following activation an additional 20 kcal/mole (for trypsin) is necessary
to initiate a large entropy change (about four or five times that for A^* of
activation). This is thought to be a large configurational change.

(d) An average of two to three cysteine equivalents per insuhn molecule
corresponds to a fifty per cent reduction in its biological activity (the present
hypothesis would predict three cysteine equivalents per molecule, i.e. two
for each reversibly inactivated and four for each irreversibly inactivated mole-
cule).

(e) The appearance of the full protein sulhydryl titer is invariably associated
with complete loss in activity.

(f) Disulfide bonds are likely involved in the latching together of large
segments of the insulin molecule, since reoxidation of the reduced insulin
molecule causes aggregation.

(g) The ultraviolet action spectra for the inactivation of trypsin and ribo-
nuclease, both of which have high cystine contents, are peaked at a wavelength
corresponding to maximum cystine absorption, and the quantum efficiency
is strongly correlated to their cystine content (9), (10); however, Setlow and
Doyle (10) found that the action spectra for gramicidin and aldolase, which
had little or no cystine, roughly paralleled the molecular absorption spectra.
They concluded that although there must be more than one inactivation
mechanism, a quantum absorbed by cystine could be as much as twenty-five
times as effective in producing inactivation as one absorbed by an arom.atic

♦ For instance, inactivation due to freezing and drying, which is apparently not accom-
panied by a gross opening of the molecule (5), may depend upon such a process.

A Proposed Mechanism of Protein Inactivation 289

amino acid, and as much as fifteen times as efTective as a quantum which spht
a peptide bond.

(h) The electron spin resonance measurements reported by Gordy (11)
indicate that irradiation of proteins usually converts some of the disulfides
into free radicals.

(i) The native configuration of the ribonuclease molecule can be greatly
disrupted (as indicated by viscosity measurements) by destroying its H-bonds
with urea without destroying its function; however, as soon as the disulfides
are oxidized activity is lost immediately (12).

(j) The recent findings of Leone (13) are in excellent agreement with the
two main aspects of the hypothesis. First, he found that the antigenic properties
of y-irradiated serum albumin were the same whether an average of 9 or 90 eV
per molecule had been absorbed indicating that irradiation caused this protein
to unfold in a characteristic fashion. Second, the single S— S bond of serum
albumin was likely involved since ultracentrifugation patterns of the irradiated
material contained only monomers, dimers and small amounts of di- and
tripeptides, with no evidence of larger aggregates. Setlow and Doyle (10)
also noted smaller fragments produced by ultraviolet irradiation of trypsin,
but found that the degradation components produced by a wavelength very
favorable to a cystine effect were more prominent and homogeneous than those
produced by a less favorable wavelength. They interpreted this as evidence
for more than one inactivation mechanism.

(k) Studies of the inactivation of protein monolayers (2,3,14,15) yielded
results which were consistent with the model; however, the data could only
disprove but not prove the hypothesis. For example, molecules in compressed
monolayers show reduced inactivation from both surface forces (14) and
irradiation (15). This was expected, since the scheme proposed here would
predict that an external force, such as the monolayer film pressure, should
lower the probability of the second S — S bond being ruptured; and even if
step 3 occurred, an external pressure should be able to maintain molecular
structure sufficiently intact so that restitution would be enhanced. However,
it was estimated that the proposed mechanism might account for no more
than two-thirds of the inactivation observed.

Some proteins, such as ovalbumin (16) and serum albumin, contain fewer
than two S — S bonds. In such proteins other bonds which (i) have comparatively
small rupture energies and (ii) are involved in latching large segments of the
molecule together, would assume the functions of the cystine in this scheme.

The present model provides a specification of the 'target volume' for irradia-
tion inactivation. Associated with each atom is a probability that energy
will be absorbed and migrate to the weak link in amounts sufficient to rupture
that structure completely. The sum of these probabilities over the whole
molecule gives the 'effective target volume'. Thus, the actual physical target
need not have sharp boundaries (see also discussions by Lea (17), Burton (18)
and Setlow and Doyle (10) of target elements having probabilities other than
0 or 1).

The probabilities, and thus the 'size' of the target volume, will depend
upon a number of factors. For instance, the possibility— discussed by Platz-
MAN and Franck (7) — of complementary effects between thermal and absorbed

290 L. G. AUGENSTINE

energies suggests that the target volume should decrease as the temperature
at which protein is irradiated is decreased. Consistent with this is the fact
that the x-irradiation cross-section of phage Tl has been found to be a linear
function of the irradiating temperature (19); also the inactivation of trypsin
ultraviolet-irradiated at 300°K is about three times as great as at 90°K (10).
The target volume should also decrease as the quantum of energy absorbed is
decreased: the inactivation cross-section of bovine serum albumin bombarded
with very low energy electrons was found to increase with increasing ^ energy
and a measurable cross-section was obtained with particle energies as low as
10 ev (20).

The recent resuUs and interpretations of Yalov/ (21) are particularly per-
tinent to the hypothesis discussed here. Her irradiations of insuhn, serum
albumin and cystine indicated that disulfide bonds are reduced both under
conditions where direct and indirect effects should predominate. However, she
proposed that the splitting occurred between the C and S (leaving an S — S — C
configuration) rather than between the sulfurs. Although the data cited pre-
viously appear to indicate a splitting of the S — S bond, most of those same
data would be compatible with a reduction of the C — S bond instead. To
select between the two possibilities may be difficult, since the energy required
to spht a given bond in a compound such as cystine may be quite different
than that required in a protein; as Lumry and Eyring (6) point out, various
of the intramolecular bond angles of proteins may be distorted in order to
effect structural compromises which minimize free energy. However, Yalow (21)
has pointed out that the production of a C — S — S- radical is probably more
consistent with Gordy's findings than the other alternative.

The failure of Koch (22) to detect radiation-induced disulfide inter-
changes either in solution or the dry state does not disprove the hypothesis
proposed here. The dosages they used (up to 3 X 10' r) are much larger than
those required by other workers (3 X 10^ r) to liberate sulfur groups (21, 23)
from similar compounds. These results indicate that although the splitting of
disulfide bonds may well be critically involved in protein inactivation, seven
per cent or less* of the liberated — SH groups undergo interchange.

REFERENCES

1. L. Augenstine: Structural interpretations of denaturation data. In: Information Theory
in Biology, ed. by H. Quastler, 119-124, University of Illinois Press, Urbana (1953).

2. L. Augenstine and R.Ray: Trypsin monolayers at the air-water interface. III. Structural
postulates on inactivation. /. Phys. Chem. 61, 1385-1388 (1957).

3. L. Augenstine: Trypsin monolayers at the water-air interface. Ph.D. thesis, University
of Illinois (1956).

4. E. C. Pollard: The direct effect of radiation on proteins, viruses, and other large mole-
cules. In: Biochemical Aspects of Basic Mechanisms in Radiobiology, ed. by Harvey M.
Patt, Nat. Res. Council Washington Publ. no. 367, 1-29 (1954).

* The \le dose, D*, for a spherical molecule of mol. wt. 240 and density 1.35 is 2 x 10* r.
A dose of 3 X 10' r could potentially rupture 1.5 per cent of the S— S bonds (from dNjN =
dNjD* = (3 X 107)/(2 X 109)). If one interchange per 1000 disulfides could have been
detected (22) but none was found, then seven per cent (1/15) or less of the 'hit' molecules were
eventually involved in disulfide interchanges.

A Proposed Mechanism of Protein Inactivation 291

5. A. MiRSKY and L. Pauling: On the structure of native, denatured and coagulated
proteins. Proc. Nat. Acad. Sci., Wash. 22, 439^W7 (1936).

6. R. LuMRY and H. Eyring: Conformation changes of proteins. J. Phys. Chcm. 58,
110-120(1954).

7. R. Platzman and J. Franck: A physical mechanism for the inactivation of proteins by
ionizing radiation. This volume.

8. A. Stearn: Kinetics of biological reactions with special reference to enzymic processes.
Advances in Enzymology ed. by F. F. Nord, 9, 25-74 (1949).

9. R. Setlow: A relation between cystine content and uv sensitivity of proteins. Biochim.
Biophys. Acta 16, 444-445 (1955).

10. R. Setlow and B. Doyle: The action of monochromatic ultraviolet light on proteins.
Biochim. Biophys. Acta 24, 27-41 (1957).

11. W. Gordy: Electron spin resonance in the study of radiation damage. This volume.

12. C. Anfinsen and R. Redfield: Protein structure in relation to function and biosynthesis.
Advances in Protein Chemistry 11, 1-100 (1956).

13. C.Leone: personal communication.

14. R. Ray and L. Augenstine: Trypsin monolayers at the air-water interface. I. Film
characteristics and the recovery of enzymatic activity. /. Phys. Chem. 60, 1 193-1 199 (1956).

15. L. Augenstine and R. Ray: Trypsin monolayers at the air-water interface. II. Effect
of x-ray and uv radiation upon enzymatic activity. J. Phys. Chem. 61, 1380-1384 (1957).

16. G.Tristram: Amino acid composition of purified proteins. Advances in Protein Chemistry
5, 84-148 (1949).

17. D. Lea: Actions of Radiations on Living Cells, Cambridge University Press, Cambridge,
England (1946).

18. M. Burton: Elementary Chemical processes in radiobiological reactions. In: Symposium
on Radiobiology, ed. by J. J. Nickson, 117-138, J. Wiley and Sons, New York (1952).

19. C. Bachofer, C. F. Ehret, S. Mayer, and E. L. Powers: The influence of temperature
upon the inactivation of a bacterial virus by x-rays. Proc. Nat. Acad. Sci., Wash. 39,
744-750 (1953).

20. F. Hutchinson: Energy requirements for the inactivation of bovine serum albumin by
radiation. Radiat. Res. 1, 43-52 (1954).

21. R. Yalow: Cleavage of the disulfide bond as a result of the indirect or direct effect of
ionizing radiation. National Biophysics Conference, Abstract No. 118 (1957).

22. A.L.Koch: The absence of radiation-induced disulfide interchanges. This volume.

23. W. Dale and J. Davies: The liberation of hydrogen sulfide by x-radiation from cysteine
and glutathione. Biochem. J. 48, 129-132 (1951).

DISCUSSION

Platt: This is a tangential comment which may be relevant to the paper by Professor
Gordy and that by Professor Platzman and Professor Franck. It is that Dr. Meyerson*
has recently done some extremely beautiful work on species of various mass fragments that
break up during their flight time in the mass spectrometer, and by isotopic substitution
experiments, checking the species that come out, he has proved that when isopropylbenzene
is bombarded with 50-volt electrons, the side group is changed to a cyclopropyl group in which
all three carbons are equivalent. He has also proved that if a molecule like toluene is bom-
barded, the decay in flight indicates the existence of a species of the form of a tropylium ion,
a Cy ion in which again all the carbons are equivalent. Similar results are obtained down to
zero excess electron energy.

* P. N. Rylander, S. Meyerson, and H. M. Grubb, "I. The Cationated and Cyclo-
propane Ring" /. Amer. Chem. Soc. 78, 5799-5802 (1956): Organic ions in the gas phase.
II. The tropylium ion. J. Amer. Chem. Soc. 79, 842-846 (1957). See also later papers of
this series by same authors in J. Chem. Phys. and /. Phys. Chem.

292 Discussion

The result, I think, is that one should probably not speak about traditional valence bonds
in traditional directions in a molecular species which has been ionized by ions or radiation.
The notion of the classical valence bond is peculiar to a closed shell system, that is, an electroni-
cally closed shell with a filled lower energy band and with a large energy gap between the highest
filled state and the lowest empty state. I think that it might not be possible to attribute the
electrons whose spins Professor Gordy detects to a particular site in the original primitive
molecule, because these bonds may have been completely rearranged. Also it may not be
possible to attribute Professor Platzman's type of damage to a particular section of the
molecule, if this sort of thing, cyclopropyl or tropylium ion, is very common. There may
be a large section of the molecule which is doing a merry-go-round of interchangeable carbon
atoms before the system settles down.

Platzman : I should like to record my skepticism as to the ubiquitous and decisive role of
disulfide-bond cleavage in radiobiology. This is not to question the participation of such
breakage in denaturation by ionizing radiation or any other agent : since disulfide bonds make
an important contribution to the structural stability of many proteins they must certainly be
involved in structural breakdown. Dr. Augenstine has, indeed, attempted here to describe the
relationship between the contribution of secondary bonds and that of disulfide bonds. However,
the argument — frequently heard in recent years — that the great sensitivity of a protein molecule
to ionizing radiation can be understood in terms of migration of an electron vacancy produced
almost anywhere in the molecule to a disulfide bond, with resultant cleavage of that bond and
unfolding of the molecule, is open to most serious objections. In the first place, such long-
range migration is unsupported by independent evidence and, as indicated in my paper, is
likewise unsupported by physical principles. The fact that electron holes are observed to move
freely in certain nonmetallic crystals is of doubtful relevance because of the different dielectric
properties of such crystals, and because of their periodic structure. Moreover, even though
Professor Gordy's proof of the existence of free valences at sulfur atoms is impressive (although
the precise number of such radicals in relation to the radiation dose is still uncertain), a simple
causal connection between formation of the radicals and inactivation of the protein has yet to
be established, and, indeed, may not exist at all. It is quite possible that they are a secondary
factor in denaturation, however conspicuous they may be in the paramagnetic-resonance
spectrum. Furthermore, the logical link between disulfide-bond cleavage and electron-
vacancy migration is also unproven. A simpler and plausible mechanism for a strong
sulfur-atom signal is given by the action of subexcitation electrons : that these can attack the
disulfide bonds effectively even though the latter are present in low concentration is strongly
suggested by the small dissociation energy of such bonds and also by the marked red displace-
ment of the absorption spectrum of cystine in relation to the spectra of most other amino acids.

Gordy : I certainly think that Professor Platzman's suggestion is worthy of consideration.
I try to keep the sulphur-sulphur bonds in my brain open when discussing these complex
systems.

PART V
AGING AND RADIATION DAMAGE

A FEATURE of our timcs is that people are now living long enough so that the prob-
lems and diseases of the aged have become an important medical speciality,
and at the sam.e time we are, of necessity, embarking on the development of civil
and military technology which generates radioactivity, an agent which, uncon-
trolled, will contribute to shortening our lives. There is evidence that these two
attributes of this age are more than incidentally related.

It is well for us to remember that the biological effects of radiation are not
new, for the same radiation by which Becquerel discovered radioactivity very
soon thereafter burned his person. An understanding of these effects has come
slowly. The relationship between aging and radiation damage has been dormant
in the literature for a long time and has come to prominence only recently.

The first papers on the effect of radiation on life span were published by
W. P. Davey (1, 2) in 1917 and 1919. The care exercised in dosimetry and in
showing that the observed effect is due to the x-rays and not to some experi-
mental artifact was most remarkable for the time at which this work was done.
Davey found that the life span of the beetle Tribolhim confusiun was shortened
by large amounts of x-rays and lengthened slightly by small amounts. The first
result seems to be well established today. The second result is still frequently
reported.

GowEN and Stadler (3) in 1952 found an increased life span for male
Drosophila melanogaster given 2500 r, although the life span of the female was
decreased. The effect appeared in Lorentz's data (4) on the LAF^ mouse and
inbred guinea pigs receiving 0.1 1 r per day. He did not consider this statistically
significant, although Sacher (5) later stated that the effect is significant and that
it had been confirmed by himself and D. Grahn. Gowen (6) found a shortening
of the life span in male mice from ten distinct inbred strains — even for small
single doses of x-rays. However, for female mice he found an increase in life
span for doses up to 320 r. But the number of litters produced was reduced even
for small doses. The explanation given was that the semi-sterility induced by
x-rays reduced the hazards of pregnancy. For low doses, it was argued, this
more than compensated for the somatic x-ray damage.

It is not generally accepted that there is a stimulation due to x-rays. Probably
cases where this seems to occur can be explained as an artifact, perhaps following
Gowen's explanation. At any rate further research on this point is well justified.

In 1937 Russ and Scott (7) published a report on the biological effects of
continuous gamma irradiation. They found the significant features known
today, namely, that there is a cumulative permanent damage reflected by a death
rate higher than that of the controls, sterility or semi-sterility, high infant and
prenatal mortality of progeny from both male and female irradiated parents.
They confirmed these results in 1939 and specifically called attention to
accelerated aging in the irradiated rats (8).

The invention of the nuclear reactor in 1942 added immensely to the industrial
and laboratory hazards of radiation and to the concern for evaluating these
hazards. Henshaw (9) in 1944 again called attention to the similarity between
the pathology of aging and the pathology of radiation damage. Sacher (10)

293

20

294 Hubert P. Yockey

in 1950 and Brues and Sacher (11) in 1952 considered radiation injury and
lethality and normal aging from the same point of view and gave an analysis
in terms of survival curves.

In 1953 H. A. Blair (12) emphasized this relationship and extended the notion
to internal emitters. He pointed out that the shortening of life, even with bone
seekers such as Po, Pu and Ra, is not attributable solely to bone pathology since
other tissues are also damaged in a way similar to total body irradiation. Blair's
remark is based on observations by Boyd et al. (13) that tissue changes were
of the type produced in rats by 550 r whole-body irradiation. In 1954 Furth,
Upton, Christenberry, Benedict, and Moshman (14) called attention to this
relationship in the case of LAF^ mice exposed to atomic bomb radiation. In
the same year Upton, Furth, and Christenberry (15) made the same observa-
tion with regard to late effects from thermal-neutron irradiation of RF mice.

The similarity between aging and radiation damage is paralleled by chemical
carcinogens. Cloudman, Hamilton, Clayton, and Brues (16) reported that
mice painted with a carcinogenic agent (methylcholanthrene) exhibited a life
shortening not to be explained by a single pathology. They indicated an analogy
between life shortening from hydrocarbons and total-body irradiation.

Russell (17) has recently found that the increased prenatal and infant
mortality of offspring from irradiated parents continues throughout life and is
reflected by a reduced average life. He studied only the offspring of male mice
irradiated by neutrons from an atomic weapon. Presumably, the effect is
general and applies to offspring of both male and female animals subjected to
any ionizing radiation. The relation of this work to that of Russ and Scott is
clear and the need for detailed study is paramount.

Some may feel that establishing a relation between two unexplained effects
gets one nowhere. However, as Platt (18) points out, such a relationship may
help one effect to explain the other.

The concept of premature aging as a measure of damage from various
deleterious agents seems to be well enough established for practical use in
understanding the nature of biological damage. Information theory may well
have a contribution to make to the elucidation of these problems of our times
which are so important from so many points of view.

H. P. Y.

REFERENCES

1. W. P. Davey: The effect of x-rays on the length of life of Tribolium confusiim. Gen.
Elect. Rev. 20, 174-182 (1917). (An article nearly identical to this is to be found as
follows: W. P. Davey: The effect of x-rays on the length of life of Tribolium confusum.
J. Exp. Zool. 22, 573-592 (1917).)

2. W. P. Davey: Prolongation of life of Tribolium confusum apparently due to small doses
of x-rays. Gen. Elect. Rev. 22, 479^83 (1919).

3. J. W. GowEN and J. Stadler: Irradiation effects on viability of Drosophila melanogaster.
Genetics 31, 586-587 (1952).

4. E. Lorentz: Effects of long-continued total-body gamma irradiation on mice,
guinea pigs, and rabbits. In: Biological Effects of External X and Gamma Radiation,
Il(i-1A1, ed. by R. E. Zirkle, National Nuclear Energy Series IV-22B, McGraw-Hill,
New York (1954).

5. G. A. Sacher: On the statistical nature of mortality, with especial references to
chronic radiation mortality. Radiology 67, 250-258 (1956).

6. J. W. Gowen: private communication (1957).

7. S. Russ and G. M. Scott: Some biological effects of continuous gamma irradiation,
with a note on protection. Brit. J. Radiol. 10, 619-629 (1937).

Aging and Radiation Damage 295

8. S. Russ and G. M. Scott: Biological eflFccts of gamma irradiation. Bril. J. Radiol. 12,
440-441 (1939).

9. P. S. Hensiiaw: Experimental roentgen injury. iV Effects of repeated small doses of
x-rays on blood picture, tissue morphology and life span in mice. /. Nat. Cancer Inst.
4,513-522(1944).

10. G. A. Sacher: The survival of mice under duration-of-life exposure to X-rays at various
dose rates. Argonne Nat. Lab. Report No. ch-3900 (1950).

11. A. M. Brues and G. A. Sacher: Analysis of mammalian radiation injury and lethality.
In : Symposium on Radiobiology, 441-465, ed. by J. J. Nickson, J. Wiley and Sons,
New York (1952).

12. H. A. Blair: The shortening of life span by injected radium, polonium and plutonium.
University of Rochester Atomic Energy Project, Document No. UR-274 (1953).

13. G. A. Boyd, H. E. Silberstein, R. M. Fink, A. Frenkel, W. L. Minto, R. G. Metcalf,
G. Casarett, and G. M. Suter: Pilot studies on the intravenous lethal dosage of
polonium, plutonium, and radium in rats. In: Biological Studies with Polonium, Radium
and Plutonium, ed. by R. M. Fink, Chap. 7, National Nuclear Energy Series vi.-3.
McGraw-Hill, New York (1950).

14. J. Furth, a. C. Upton, K. W. Christenberry, W. H. Benedict, and J. Moshman:
Some late effects in mice of ionizing radiation from an experimental nuclear detonation.
Radiology 63, 562-570 (1954).

15. A. C. Upton, J. Furth, and K. W. Christenberry: Late effects of thermal neutron
irradiation in mice. /. Cancer Res. 14, 682-690 (1954).

16. A. M. Cloudman, K. A. Hamilton, R. S. Clayton, and A. M. Brues: Effects of
combined local treatment with radioactive and chemical carcinogens. J. Nat. Cancer
Inst. 15, 1077-1083 (1955).

17. W. L. Russell: Shortening of life in the offspring of male mice exposed to neutron
radiation from an atomic bomb. Proc. Nat. Acad. Sci., Wash. 43, 324-329 (1957).

18. J. R. Platt: Functional geometry and the determination of pattern in mosaic receptors.
This volume.

A STUDY OF AGING, THERMAL KILLING, AND
RADIATION DAMAGE BY INFORMATION THEORY

Hubert P. Yockey

Health Physics Division,
Oak Ridge National Laboratory, Oak Ridge, Tennessee

Abstract — The information theoretic formahsm developed in the author's paper in Part I
has been applied to the calculation of survival curves. The results have been compared for a
variety of organisms ranging from viruses to mammals. The deleterious agent varied in the
magnitude of its quantum energy from thermal and chemical energies to several Mev.

It should be emphasized that this article says very Uttle about models. In general the
accepted model of the organism is taken and its behavior is calculated from those features
of the model which have the aspects of a communication system.

In spite of the complexity and variety of the organisms and the range of energy in the lethal
agent and without ad hoc assumptions pertaining to models, we were able to account for the
main features and some details of the survivorship curves. Many additional experiments will
be suggested; some of them have been pointed out and some predictions have been made.

The idea of the storage and transfer of information and its destruction by deleterious
agents seems to link the material discussed. Much of this material may otherwise seem
unrelated or only vaguely so.

I. INTRODUCTION

The study of the survivorship curve has contributed to the quantification of
some essential but otherwise quahtative notions in biology. The effect of
various insults such as ionizing radiation, ultraviolet light, temperature, disease,
chemicals, and so forth, is very often measured by survivorship of a suitable
test organism. On the other hand, the experimenter may be interested in the
survival response of a particular organism as a function of maturation, nutrition,
strain difference, or the like, and may use some convenient agent as a test
stimulus.

Survivorship does not contain all we feel intuitively is involved in the concepts
of 'vigor' or 'fitness' but it does contain much of what can be defined and
measured in an unequivocal and operational way that is associated with those
ideas. These facts, together with the application in evaluating quantitatively
hazards to man, make this subject one of great practical and theoretical
interest.

Information theory is peculiarly well qualified to provide a mathematical
treatment of these matters. The survivorship curve is a property of the ensemble
of organisms rather than of the individual. It reflects the generalized decay of
the organization of a system. The central thesis of this paper is that aging,
thennal killing, and radiation damage reflect essentially the same action, namely,
the destruction of the information content of the cell. The ideas discussed in
the author's previous article in this volume will be applied to the calculation of

297

298 Hubert P. Yockey

hapJoid survivorship, diploid survivorship, and to the role of equivocation in
the germ line.

II. SURVIVORSHIP FOR THE HAPLOID CASE

Otto Rahn (1,2) was the first to suggest in two pioneer papers published
in 1929 and 1930 that the genetic structure is the sensitive element in the cell
for radiation damage, thermal killing, and the action of some chemicals. He
later reviewed the data on disinfectant action and confirmed this opinion (3).
Lea (4) was a strong supporter of this idea and used it in his development of
the target theory. This is generally an accepted view today (5) although the
role of gene mutations and chromosome aberrations is a matter of debate (6, 7).

In a previous article in this volume we showed that this notion follows
directly from the application of information theory to the current conception
of the storage and transfer of genetical information in the cell and the synthesis
of proteins. It is therefore of interest to continue the argument and attempt
to calculate survivorship curves. We also showed that error will exist in the
genetical information of all real organisms. The organism will live and multiply
according to Dancoff's principle (8), in spite of these errors. We argued
previously that there must be a distribution of message entropy values among
the elements of the ensemble of organisms. Suppose that the number of errors
in the genetical infoiTnation is increased as a result of, say, radiation. Those
elements of the ensemble near the lethal limit will succumb even though they
were quite viable before irradiation.

This is a notion peculiar to information theory. The communications
analogy is Shannon's channel capacity theorem (9). This theorem shows that
if a channel has a capacity C, it is possible, by proper coding, to send information
at rate C or less through the channel with as small a frequency of errors as desired.
Thus, though the noise level in the channel will affect the channel capacity C,
it will not prevent nearly perfect transmission of information. This can be
assured by proper coding. As long as this limit C is not exceeded, it is impossible
for the recipient to know the noise level in the channel or information source.

With these points in mind, we now return to the suggestions of Rahn and
Lea, keeping further in mind the idea of Watson and Crick that a mutation
is a change in the order of nucleotide bases in DNA (or some other information-
bearing molecule). We have proposed that the action of radiation or other
deleterious agent at the molecular level is such that the nucleotide pair mimes
some other nucleotide pair insofar as protein synthesis and replication are
concerned (10). The action of radiation may therefore be thought of as causing
lethality through gene mutation by decreasing the message entropy of some
members of the ensemble below the lethal limit. This is essentially the suggestion
of Rahn and of Lea phrased in the language of information theory, and it
follows from the argument given in the previous article in this volume. On
this basis we may proceed to calculate the force of mortality on the ensemble.

The distribution of message entropy in the ensemble will be represented
by a probability distribution p(H, A), where A is a measure of the magnitude
of the deleterious agent and the initial distribution is p{H, 0). This distribution
will vary with the genetic character of the ensemble of organisms. It can
probably be derived from first principles, at least for simple cases, when more

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 299

is known about storage and transfer of information in organisms. For the
present it will be necessary to make some simpje assumptions, however.

It was proposed previously (10) that death occurs when the value of //decays
below some limit H^. Let / be the number of organisms in the population
representing the ensemble. The probability per unit I of leaving the population
{\jl){dHdX) is called the force of mortality. The force of mortality will be the
probability density unit per H at //,, after exposure X multiplied by the rate of
decrease of H per unit X at //,^.

\_dl
I dl

p{Ha, A)

dH
~di

(1)

ffrf

The value of p(//, A) varies continuously with A; no organisms leave the
microensemble which at A = 0 lies between H and U + dH.

dX = p{H„ X)

cm

dX

dX

(2)

H.

The relation of p{H^, X) to p{H, 0) is as follows:

piH„ X) = p(H, 0)

i.)

(3)

^o + ^. + iIp(0 logo ;>:(/)

»j

where p'i(j) is the value corresponding to H^.
Equation (1) may be written

p(Ha, X)

ffo~-ffa + iIp(i)\og,Pi(j)

1,3

J{X) dX

(4)

In many cases the action of the deleterious agent will be of the first order
so that J{X) = /„, a constant. Let us assume that p{H, 0) is of such shape that
p{H^i, X) is a constant.

Equation (4) may be integrated :

log, ///o = p{H„ X)

Ho-H,

I lp(i) ^0^2 Pi(j)

J,X

(5)

Equation (5) represents haploid survivorship as a function of X for many
types of destructive influences under many experimental conditions — but not
for all influences, or conditions, or haploid organisms. T. Alper (11) found
the rate of inactivation by gamma rays of dysentery phage SI 3 to increase with
increasing dose at 130 rad/min. At 5.3 rad/min the survival curves departed
markedly from the exponential forni although that form was found when
catalase was present. Watson (12) also reported the same phenomenon with
phage T2. Alper (13) later showed that the gas treatment of phage could result
in departure from the exponential form. A number of cases of a non-exponential
inactivation curve for viruses are discussed by Luria in a recent review (6).

Gates (14) discussed the deviations from an exponential curve for ultra-
violet irradiations of bacteria. Recent work by Uretz (15) has shown that

300 Hubert P. Yockey

inactivatioii of haploid yeast is exponential for x-rays and sigmoid for ultra-
violet. Anderson (16) has irradiated two biochemical mutants of strain B of
E. coli with x-rays, namely, the streptomycin dependent strain and the purine-
less strain. An exponential survival curve is obtained in oxygen while a sigmoid
curve is obtained in nitrogen for each strain. Hollaender, Baker, and
Anderson (17) have discussed the effect of oxygen and other chemicals on the
x-ray sensitivity for mutation production and survival.

Hollaender and Stapleton (18) have shown that many types of survival
curves may be obtained ranging from exponential to a very pronounced sigmoid
shape depending on the experimental conditions.

Stapleton, Sbarra, and Hollaender (7, 19) have studied the nutritional
aspects of survival of bacteria from ionizing radiation. They showed that the
B/r strain of £". co// grown on a complete medium such as nutrient broth exhibited
radiation-induced requirements for nutritional factors. They presented some
evidence showing that such bacteria are not stable auxotrophic mutants.

The dependence of survivorship on nutritional factors is explained by
ZiRKLE and Tobias (20) from hit-theory concepts. They state that : 'Accordingly,
the number n of essential sites in the haploid chromosome set might vary with
the composition of the medium; in general, one would expect that the richer
the medium the fewer would be the observed number of essential sites. On
the other hand, if the 'inactivation' of a 'site' is not a mutation, but a gross
change in chromosome state or configuration, the number of sites would be
independent of the composition of the medium.'

The interpretation of these results given by the authors quoted loses some
force since essentially the same results are found for viruses by Friedewald
and Anderson (21), iDy Luria and Exner (22), and by Dale (23). The explana-
tion offered by Luria and Exner is based on a two-fold action of the radiation,
a direct and an indirect effect.

The case where two deleterious influences operate simultaneously is interest-
ing. Wood (24, 25) has studied the x-ray survival of haploid yeast as a function
of temperature. The curves show a distinct tendency to be concave downward
for temperatures between 45°C and 55°C. He finds a 'softening' or 'memory'
of exposure to temperature and x-rays for the action of the other. Uretz (15)
finds very little 'softening' in his study of the action of x-rays and ultraviolet
on haploid yeast. We are not aware of a study of the ultraviolet survival as a
function of temperature, although such data would be of importance to complete
knowledge of these effects.

Gray (26) has pointed out recently that a view is gaining general acceptance
that a site may be inactivated by a single fast electron, but not by the absorption
of a single photon. The site mentioned by Gray is interpreted as a nucleotide
pair in the present paper. The action of the deleterious effect may be, partly
at least, to throw the nucleotide pair into an excited tautomeric form. In such
a form it may be more easily damaged by a successive interaction. The extent
to which this occurs may very well depend on the chemical environment. At
any rate, for the present purposes, there is reason to believe that J{X) may be
represented by a polynomial in A. The higher order terms represent higher
order reactions.

In that event, it is possible to begin to understand why an exponential

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 301

survival is obtained under some conditions, but not under others. The shape
of the survival ciuve depends on both the environment and on the genetic
character of the organism. Thus, it may be possible to obtain some separation
between purely biological and purely physical or chemical phenomena — in so
far as such a separation has meaning — by means of the present theory. The
function p{H, 0) is related to the distribution of genetical information in the
ensemble and so is characteristic of the biology of these problems. J{X) represents
the interaction of radiation and matter, and will be determined by the physics
and chemistry of the situation. It is in this regard that the current controversy
on the role of direct and indirect action bears on the present theory.

Not all haploid organisms exhibit the exponential survivorship curve.
Nybom (27) reported sigmoid x-ray survival curves for the green algae, Chlamy-
(hmonas euganietos, C. moewusii, and C. reinhardi. Genetic experiments
involving tetrad analysis indicate that the haploid character of these organisms
is reasonably certain. Jacobson (28) has studied C. reinhardi in some detail
and finds a sigmoid survival curve. The mathematical nature of this curve is
such that it does not correspond with target theory calculations. This and other
cases of sigmoid survival curves in haploid organisms will be discussed in the
next section.

III. SURVIVORSHIP FOR DIPLOID

Lea (4) rejected the gene mutation suggestion for 'killing of organisms other
than bacteria or viruses' in favor of the view that chromosome aberrations are
the main cause for lethal effects in polyploid tissue. He did this partly on the
ground that a 'recessive lethal mutation in a diploid cell will not be lethal
unless it is in the X chromosome of the male, owing to the presence of a normal
allelomorph in the same cell'.

ZiRKLE and Tobias (20) retained the recessive lethal mutation hypothesis
in their study of x-ray survival curves in yeast. It was shown by Tobias and
Stepka (29) that irradiated diploid yeast exhibits an inheritable increase in
radiosensitivity presumably because of an increased load of recessive lethal
mutations. Mortimer and Tobias (30) obtained direct experimental evidence
for x-ray induced recessive lethal mutations by demonstrating a reduction in
the fraction of genninating spores produced by x-ray exposed diploid yeast cells.

Mortimer (31) obtained further evidence for the existence of recessive
lethal mutations in studies of the conjugation of yeast cells of opposite mating
type. See results shown in Fig. 1. Mortimer argued, as Lea had, that the
viability of zygotes should be unaltered because of the presence of the normal
allelomorph and that therefore recessive lethal mutations could not be respon-
sible for all the radiation damage.

Chromosome aberrations clearly represent an increase in the equivocation
in the genetic information. It is difficult to see how this is to be calculated at
the present writing. It is unclear also what their role is in insults milder than
damage due to ionizing radiation, such as thermal killing and aging. Sacher
(32) has called attention to the need for cytological investigation of the part
chromosome aberrations play in the development of late effects from radiation
damage. Russell (33) has argued that chromosomal aberrations probably have
little to do with radiation hazards to man. At any rate, one may argue that

302

Hubert P. Yockey

recessive lethal gene mutations play an important role in the lethality of diploid
cells. Since it is possible to present a calculation of the equivocation due to
this process let us calculate the survivorship curve according to this notion and
see how it compares with experiment.

100

50000
X-RAY DOSE.ROENTGENS

75000

100000

Fig. 1 . Percent survival for yeast with one irradiated parent. Haploid x haploid
cross (oo), haploid x diploid cross (oO), etc. The first symbol represents a cell
of the a-mating type, the second one of ^-mating type. A filled letter o designates
the irradiated parent. Haploid dominant lethal curve: Q, 9o; %,o% ; 6, •©;
9,0*. Diploid dominant lethal curve: n^ •O' ■>0*; D, •©; Ho*.
Diploid survival curve: A' • — aa diploid, ^, 9 — aa diploid. Haploid survival
curve: A> • — a haploid; ^,9 — a haploid. (From ref. (61)).

The decay of the correct read-off probability is given by equation (10) of
my paper in Part I :

^^P.(j) = -J(^)Pi(j) + im (6)

In the diploid case J(X) cannot contain a constant tenn because of the protection
afforded by the unaffected allelomorph. Therefore dp/ij)ldX must depend at
least linearly on ?^. The polynomial for J{X) is in this case, where J^ is a
constant:

m = /i^ (7)

Substitute this function in equation (4)
dJ

1 JX = P^^"^ ^^

J,?.

(8)

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 303

The assumption of Section II concerning the nature of pC//^, A) is retained and
the expression for the surxiva! curve is:

log. Ilk = P(^.^ ^)

//o-^. + i>;/Hoiog2/'ay)

^,}

(9)

That some survivorship curves have wholly or substantially the form of
equation (9) for normal aging where A is the time can be shown for a wide
variety of organisms. Some examples are shown in Fig. 2 and also one in

II 27 43 51 59 67 75 83 91 WEEKS •

(TIME UNIT ) AS INDICATED

Fig. 2. Survivorship curves for two insects and two mammals plotted against the
square of the age (see equation (9)). Straight lines for pure vestigial Drosophila
(35) obtained from maximum likelihood estimate. Other straight lines are for

comparison only. (See text.)

Fig. 3. The data for pure vestigial Drosophila are from Pearl and Parker (35)
and represent a life table. The animals are kept under ideal conditions and the
number which die in certain time intervals is recorded. All data on Fig. 2 and
Fig. 3 are obtained this way. The curve has been fitted by these authors to a
function of the following form where a, h, c, d, e are positive constants.

log / = €"^6 - cA + d?? - e)?)

(10)

Pearl and Parker were aware that this description involves too many con-
stants and that irrelevant statistical fluctuations are preserved by equation (10).

304 Hubert P. Yockey

Leslie and Ranson (36) fitted their data on the vole to a function of the
form of equation (9). They give a conventional yj- analysis to justify the
hypothesis. The y^ analysis cannot be applied to data obtained as these life
tables are obtained since the points are not statistically independent. The
random variable is the time of death of each animal, not the number alive at

100

FLIES (days)
25 35 42 50 55 60 65 70 74 78 62

MICE (months)

Fig. 3. Normal aging survivorship of certain strains of mice (52, 53) and Droso-

phila melanogaster (35). Note that the abscissa is plotted as age squared to show

that the dilute brown strain follows equation (9) but that others do not.

a given interval of time. We are unable to justify our hypothesis in any objective
mathematical way. The standard errors given are calculated as follows where
/, is the number in the / interval and /j_,_i the number in the / + 1 interval

(10

The points in Fig. 2 lie very near to a straight line and so it is plausible, at
least, that equation (9) represents the normal aging survivorship for some
organisms.

If the destruction of genetical information is the feature common to the
action of the deleterious agents discussed in this article then the survivorship
curve should be relatively insensitive to the character of the agent except
insofar as reflected by the fonn of J(A). That such is indeed the case is shown

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 305

by the results obtained for x-ray and thermal kilhng of diploid yeast and other
organisms.

T. H. Wood (24, 25, 39) has reported data on the x-ray survival and thermal
killing of yeast, since repeated and verified by Uretz (15). The data for diploid
yeast are given in Fig. 4 and A is the time at the indicated temperature or the

MINUTES AT TEMP
10 15 20

0.002

0.001

60 90 120 180

MINUTES AT 425 r PER MINUTE

240

Fig. 4. Thermal and radiation killing of yeast from Wood (25, 39). Note that the

abscissa is plotted as the square of time at temperature indicated or at 425 r per

min. Straight lines drawn for comparison only.

X-ray dose as the case may be. The data have been fitted, using Kimball's
method (40), to several curves and the results are shown in Table I.

The function log ///q = n log [2e

-M

— e

-2k„X

■'' ] was derived from hit-theory

by LuRiA and Dulbecco (41) and used by Zirkle and Tobias (20) and by
Wood (39). We have fitted Wood's data allowing k^^ to be determined internally
by the diploid data and obtain the values shown. When the haploid value
nkf^ = 2.49 X 10 * r^^ is imposed on the diploid data n = 21.3; x^ = 5.1;
P > 0.5. Wood obtains graphically the slightly different values shown in
Table I. It is clear from Fig. 4 and Table I that the term in ?? represents sub-
stantially, if not completely, the behavior of the survival curve as a function of
dose. The fact that the fit may be made satisfactory by including a small term
in either /.^ or A* supports this conclusion.

306

Hubert P. Yockey

Wood's survivorship curves for thermal killing in yeast (25) are also given
in Fig. 4. The term in X^ again substantially represents the behavior of the
survivorship curve. The curve retains its form when the temperature is changed.
The -f- test shows in each case a very poor fit to A" but this presumably reflects

Table I. Goodness of Fit for Wood's X-rav Survival of Diploid Yeast

Function

Constants

r-

p*

log ///o =

-a^'

a = 0.022

60.

<0.001

log ///o =

~aX' + bX^

a = 0.029;

b = 7.2 X lO--"

5.5

^0.5

log ///„ =

-flP + bX^

0 = 0.025;
* = 3.2 X 10-^

8.3

^0.2

log///o =

/;]og[2t'-M - e-2M]

n = 26.3;
//Atj = 2.20 X 10-* 1-1

(this paper)

n = 30;
nka = 2.41 >: 10^* r-i

(from Wood (39))

3.9

>0.5

* 7 degrees of freedom

the existence of small higher order terms as in the x-ray case. Attention is also
called to the aging of the grain beetle Calandra oryzae at 32.3°C and at 29. TC
shown in Fig. 2. The survivorship curve again retains the same shape, changing
only the coefficient of A^.

The sensitization to thermal killing of Paramecium caudatum following
x-irradiation was first reported by Giese and Heath (42). They found a slow
recovery eff'ect, requiring several days. This parallels the earlier discovery of
Giese and Grossman (43) of sensitization to thermal killing by ultraviolet and
by visible light in the presence of photodynamic dyes (44).

Baldwin (45) has pointed out the similarities between thermal killing and
killing by x-rays for the hymenopterous insect Dahlbominus fuscipennis. The
immediate consequence of both insults is a coma from which the insect may
recover to die later of delayed eflFects. Aging decreases the tolerance for both
temperature and x-rays. The dose-survivorship curve is not given accurately
but it has roughly the same shape for each agent. The diploid females are more
resistant than the haploid males. These observations parallel those of Wood
on yeast.

It was mentioned briefly in the section on haploid organisms that Nybom
(27) has reported sigmoid x-ray survival curves for three species of green
algae, Chlamydomonas eugametas, C. Moewusii, and C. rcinhardi. Jacobson (28)
has studied C reinhardi in some detail and shows that the x-ray survivorship
curve fits accurately an equation of the foitn of equation (9). He points out
that this can 'be explained by a redundancy of genetic information.' Clark
and Herr (46) irradiated the haploid male and diploid female of Habrobracon

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 307

uglandis at three stages of growth in air and nitrogen. Rough survivorship
curves are given using eclosion as the criterion of survival. The haploid males
apparently do not exhibit an exponential survival. This point should be studied
further but it may be that the male haploid insects also exhibit a redundancy
in the genetic information similar to Chlamydonwnas in spite of their haploid
character. The argument used to derive equation (9) applies in these cases
as well as in the diploid case.

So far in the discussion it has been argued that deviations from the ideal
fonn of the survivorship curves were due to the deleterious agent and p{H, 0)
was regarded as having the same form. The fact that many organisms, parti-
cularly hybrids, do not exhibit the survivorship curves corresponding to
equation (9) is shown in Fig. 3. This behavior is closely associated with the
genetic constitution of the organisms. There are a number of facts which
support this conclusion.

Consider the survivorship curves of vestigial Drosophila melanogaster in
Fig. 2 which differs from the wild type, whose survivorship curve is shown in
Fig. 3 by a single gene. The same general effect has been reported by Clarke
and Smith (47) for Drosophila subobscura. The hybrids between two inbred lines
designated 'B' and 'K' exhibit a life span essentially double that of the parent
inbred strains. The data are not sufficiently extensive to determine the mathe-
matical form of the survivorship curve, but the inbred strains seem to have
roughly the same type as the vestigial Drosophila melanogaster of Pearl
and Parker shown in Fig. 2 while the hybrid has the same form as the wild
type shown in Fig. 3. This effect is also shown by mice. The survivorship
curves for nonnal aging are given in Fig. 3 for two hybrid strains and for the
hybrids of each with the C57 strain.

It is therefore a very plausible conclusion that the survivorship curve is
very sensitive to the genetical character of the ensemble and that the change
of shape can be ascribed to the form of p(H, 0).

This function p(H, 0) plays a role in information theory not unlike the
equation of state in thermodynamics. We are at liberty to admit many types
of probability distribution in //but it must be the same one in a given ensemble
of organisms for all experiments. That this is the case is illustrated for mice
by the resemblance between the survivorship curves for gamma- and x-irradia-
tion and those for normal aging. The purposes of most of the work in this
field, particularly in the case of acute killing, are served by obtaining an LDgQ.
The results are ordinarily reported by probit analysis and the life table is not
given. We will not attempt to review the very extensive literature, which was
not developed for the present purpose. Rather we will quote one experiment
which involved a very large number of mice and which has been extensively
studied and reported (48, 49, 50). In Fig. 5 the acute killing from atomic
bomb radiation as a function of dose is shown from Cronkite et al. (51),
on LAFj mice. This is to be compared with the normal aging survivorship
curve obtained from the controls. All curves on this figure are normalized
by being passed through the 3 per cent survivorship point, after the custom
of Pearl. The data of Murray and Hoffman (52) and Murray (53) giving
normal aging life tables for hybrid and in-bred mice are also shown. The
agreement, of course, is not exact but the curves for gamma-ray acute lethality

308

Hubert P. Yockey

agree with the normal aging curves as well as these curves agree with each other.
There are several interesting details which should be pointed out. The
gamma-ray data show a remarkable coUinearity with aging data below the
10 to 20 per cent survivorship value but rise above the aging curve to a much
sharper 'knee'. This effect is probably due to recovery, a phenomenon which
is associated with radiation damage but not with aging. Cronkite et al. noted

« (woeks) 24
100

• r DOSE (r ) 100

300

500

700

900

13

15

17

1100

21 23(months) o

o (months) I

17

Fig. 5. Normalized survivorship of certain strains of mice for normal aging and

acute radiation killing for LAF^ (51, 52, 53). LAFj normal aging curve is due

to A. C. Upton and A. W. Kimball, personal communication (see also (48)).

Radiation dose and age are plotted linearly.

a small mortality below about 600 r and took pains to establish its reality
as a radiation effect. This feature is also present in the aging curves — a bit
more pronounced, to be sure, since there is no recovery. This feature of these
curves, incidentally, fits very well with the present theory, or any theory which
relates aging and radiation damage, but is otherwise quite a puzzle. These
mice were presumed to be as nearly identical as possible and so should have been
killed by nearly the same dose. (A discussion of a possible molecular basis
for recovery has been given (10). This effect is left out of this article for simplicity.)
Cole, Nowell, and Ellis (54) have reported the late survivorship of
LAFj mice protected from 800 r of 250 kVP x-rays by spleen homogenate.
The survivorship curve has the same shape but is shifted so that the mean
age at death is eight months earher than the unirradiated control. This shows
that even if a certain organ system, in this case the hematopoietic system,
is so aided in repair that its role as a cause of death is greatly modified, neverthe-
less, the survivorship curve has the same shape.

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 309

The discussion given above indicates that even though it is necessary to
assume p{H, 0) of different shapes for different ensembles of organisms, once
chosen, the same shape is required to represent survivorship data with httle
regard for the nature of the deleterious agent causing mortality.

The case for loss of information content by action of chemical mutagens
or carcinogens is less clear than that for radiation. Radiation is no respecter
of local chemical detail — it sees only an electron gas held together by positive
charges. Side reactions complicate the experimental problems in obtaining
good survivorship curves for the chemical radiomimetics. In fact, we know of
no such curves at all, although some data of this sort are discussed by Rahn (3).
Nevertheless, there is good reason to believe there is considerable miming
(55, 56, 57) of radiation effects, in general, and of aging in particular.

This is illustrated by a paper by Cloudman, Hamilton, Clayton and
Brues (58). They studied malignant tumors and survival in CF-1 female mice
painted with methylcholanthrene, irradiated with P^^ /? particles, and with
these two insults in combination. A striking decrease in life span was found
in those mice painted with methylcholanthrene. This was not due to any single
pathologic state, not even to the pulmonary tumors generated in these animals.
Survival was also shortened in those mice which did not have pulmonary
tumors. The authors had the impression that life was shortened in a general
way similar to the life shortening effects of total-body irradiation.

The carcinogenic effects of the two agents used in the experiments were
approximately additive. This observation as well as the life shortening and
the carcinogenesis correlates very well with the view that these effects are
manifestations of the destruction of genetic information in the somatic cells.
Since exposure to such chemicals is probably on the increase there is a practical
as well as a theoretical reason for pursuing this matter further.

IV. THE ROLE OF EQUIVOCATION IN THE GERM LINE

It was said in my previous article in this volume that the ideas developed
there should be applicable both to the germ line and to the somatic line. In
this section we shall consider the effect of equivocation on the ability of the
germ line to transmit specificity. We do not have available as much experimental
material as that which pertains to the somatic line but there are several experi-
ments which are very good and are very gennane to the phase of information
theory in biology discussed in this section.

It should be remembered that there are a number of error correction methods
peculiar to the germ line. Among these are fertilization or conjugation and the
selection value of the independent existence of cells in the germ line. The
germ line may therefore be expected to exhibit a recovery from damage to a
degree not found in the soma.

An experiment in which the germ line is propagated parthenogenically
and so resembles very much the somatic line has been reported by Lansing
(59, 60). He studied the effect of parental age on the survivorship of two
species of the rotifer, namely, Euchlanis triquetra, which lives normally about
a week, and Philodina citrina, which survives normally nearly a month.

The method of the experiment was to observe the survivorship curve for

21

310 Hubert P. Yockey

a series of generations each produced from eggs laid on a given day in the
life of the parent. Lansing called such a series an 'orthoclone'. An orthoclone
obtained from a senile stage in the life of the rotifer was designated as an old
orthoclone or a 'geriaclone' whereas an orthoclone from adolescent organisms
was called a young orthoclone or a 'pediaclone'.

For each species it was found that the geriaclone could be followed to
extinction in a few generations. In the case of Philodina citrina even the six-day
orthoclone died out in the seventeenth generation. It was observed that the
longevity of the five-day orthoclone tends to increase. The maximum life span
of that orthoclone was not found but appeared to be indefinite.

It was found for each species of rotifer that the life shortening could be
reversed by starting a pediaclone as an off shoot from a geriaclone. The limit
to the ability to lengthen life seemed to be the fact that egg production does
not appear until about the fifth day for Philodina citrina and about the fourth
day for Euchlanis triquetra.

The number of animals used to establish a life table was sixty, a number too
small to avoid considerable fluctuations. However, the curves shown in
Lansing's papers give the impression that the shape of the survival curves is
maintained. This feature seems to be in common with data discussed above
in Section III, and in particular with the work of Furth et al. (48), on the late
effects of ionizing radiation on mice.

The decline and extinction of viability in the germ line is accounted for
in the present theory by the accumulation of equivocation in the gene code
as it is transmitted in the germ line. The recovery is regarded as being due
to selection and propagation of that portion of the ensemble with a relatively
low amount of equivocation.

The explanation offered by Lansing is quite different from that given here.
He attributes his results to a transmissible factor which appears at cessation
of growth. In particular, his assertion that the factor is non-genic appears
to contradict the point of view adopted here. Actually there is no contradiction
with the latter assertion since Lansing v/as undoubtedly thinking of genetic
factors in terms of the ideas concerning the gene current at the time of writing,
and indeed today. However, as Lansing notes, 'it is striking that the experi-
mental observations on the primitive rotifer as well as conclusions derived
therefrom are entirely compatible with conclusions drawn from mammalian
experiments.' The feature of these and other organisms which is the same
is the chemical composition of the genetic material and for this and other
reasons it seems to me that an explanation for so ubiquitous a phenomenon
as aging must be related to the genome.

The germ line provides an opportunity to study the error correction function
of conjugation. The most extensive data relating damage in the germ line
from one parent or both to survival seem to be due to Mortimer (31, 61).
He obtained survivorship curves for yeast zygotes formed by the conjugation
of cells of opposite mating types. The following crosses were obtained: haploid
X haploid (oo), haploid X diploid (oO), diploid X haploid (Oo), and diploid
X diploid (OO). In the symbolism used a capital O represents a diploid cell,
a lower case o represents a haploid cell; a filled letter (#0) irradiation. The
first symbol indicates the a-mating, the second the a-mating type.

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 311

The survival curve for each haploid type in Fig. 1 is of the usual exponential
form, equation (5). According to the discussion in Section II above, this is
to be understood as the full expression of recessive lethal mutations. The
survival curve for diploid exhibits the sigmoid shape whether the irradiation
is done before or after conjugation (31). Note that the abscissa in Fig. 6 is

«H

100 000

200 000
X-RAY DOSE .ROENTGENS

300 000

Fig. 6. Survivorship for yeast with o'e irradiated parent. Data from ref. (61).
Haploid X haploid cross ( oo ), haploid > diploid cross (oO), etc. The first
symbol represents a cell of the a-mating type, the second one of ^-mating type.
A filled letter o designates the irradiated parent. Haploid dominant lethal
curve: o^ ^q; •, o0; 6 #0; 6- *-**• Diploid dominant lethal curve:
□ , #0; ■. O©; n, 0o; h, oO. Diploid survival curve: A,* — aa diploid,
A, • — aa diploid. Haploid survival curve : ▲, • — a haploid ; ▲, • — a haploid.
Note that abscissa is the square of the dose.

the square of the dose. The straight lines have been drawn for comparison
purposes only, but, as in Figs. 2, 3 and 4, it is clear that log ///q is well
represented by /r.

According to the discussion of Section III, this is to be understood as
indicating that an error is not expressed in the diploid cell except when errors
are paired in the two sets of chromosomes. This follows from the dependence
of log ///o on A^.

The shielding of errors by a normal allele is seen to be very effective in
the (Oo) or the (o©) case so that survival is very much greater than for the

312 Hubert P. Yockey

irradiated diploid (••). This shielding seems to be complete for errors due
to first order damage; that is, damage such that J{X) = /„ in equation (6).
If this shielding were not complete a term in the first power of X would be
apparent in Fig. 6.

Thus far the application of information theory to the currently accepted
model of the diploid cell succeeds very well. We find features we expect and
do not find ones we do not expect. Owen and Mortimer's data on the domi-
nant lethal survival enable one to study second order effects ordinarily sub-
merged in those of the first order discussed in the paragraphs above.

Figure 6 shows that there is a very small dominant lethal expression of
damage but only when the damage is of the second order in the irradiated
parent. That is, a single error or group of errors is shielded but pairs of errors
or pairs of groups of errors are expressed, to some degree at least. This is
evident since log ///q behaves as P. It is to be expected that this higher order
damage exists in the haploid and in the diploid (••) but cannot be observed
because of the lethality due to first order damage.

The survivorship has the same P behavior for the other ploidies, but a
curious feature is that this higher order damage is expressed to a greater degree
in the higher ploidies, contrary to expectation. Perhaps this is a model-sensitive
phenomenon (as higher order phenomena often are). If that is so further
experimentation may tell us more about polyploidy.

It was pointed out in Section II that j{X) is related to the interaction of
radiation and matter. This indicates that repeating Owen and Mortimer's
experiments with other deleterious agents may be very fruitful. For example,
Uretz (15) has shown that the ultraviolet survivorship of haploid yeast is
sigmoidal. If this means in the case of haploid survival /(A) = J^X, these errors
will probably be shielded in the zygote. We choose the next higher term J{X)
= J^X^ so that log JJIq may be expected to behave as X^. Higher powers in X may
be found in the expansion of /(A) depending on the effectiveness of shielding of
recessive lethal mutations in the zygote.

These results should apply to organisms other than yeast and in
particular to the survivorship of F^ progeny in mice. F^ progeny with one
irradiated parent should have a shorter life span than the unirradiated parents.
Fj progeny with two irradiated parents should have a still shorter life span.
That this is at least partly the case is shown by recently reported results by
Russell (34). He reports a life shortening in the offspring of male mice exposed
to neutron irradiation from a nuclear detonation. The dose was rather low;
the highest to the parent was 186 rep, but only two such oflfspring were obtained.
Rather small numbers of individuals were obtained from other parents also
so that the estimate of the magnitude of the effect is rough, although its existence
seems to be established. The life shortening seemed to be of the same order
of magnitude in the father as in the offspring, however.

Wallace (62) has reported work on Drosophila in which he has irradiated
several populations for as many as 150 generations. His criterion of viability
is survival from egg to emergence and this work refers only to the second
chromosome. He finds that the fitness of a population does not necessarily
continue to decrease under the influence of radiation.

These experiments together can be understood from the point of view

A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 3 1 3

developed in my previous article in this volume without aJ hoc assumptions.
Furthermore, certain interesting predictions can be made.

Lansing's remarkable work on the rotifer is a particularly interesting
beginning to understanding the problems discussed in this article, if aging,
thermal killing, and radiation damage are really aspects of the destruction of
information content then there should be, as discussed above, a reciprocity
between the respective agents. It would be particularly interesting to know
if Lansing's results could be obtained by suitable x-, gamma- or ultraviolet-
irradiation, or also by a thermal or chemical treatment. These organisms
should be well adapted to this type of research.

Among the diploid organisms, of course, mice and Drosophila are of para-
mount importance. It would be extremely pertinent to look for the same
reciprocity in this material. In addition, one should expect it to be possible,
given a strain of one of these animals with a rectangular survivorship curve,
see Fig. 5, to change it by irradiation to one of the type corresponding to
equation (9) in several generations.

Acknowledgements — It is a pleasure to acknowledge the help of Dr. A. W.
Kimball in matters concerning the statistics of data analysis. The analysis
of T. H. Wood's data was greatly aided by his sending his exact experimental
values. Thanks are due also to Dr. Arthur C. Upton and Dr. A. W. Kimball
for furnishing the numerical data on the LAF^ normal aging survivorship.
I am very grateful to R. K. Mortimer for the use of his data.

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316 Hubert P. Yockey

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ENTROPIC CONTRIBUTIONS TO MORTALITY

AND AGING*

George A. Sacher

Division of Biolo^^ical and Medical Research,
Argonne National Laboratory, Lemont, Illinois

Abstract — All dynamic physiologic processes are attended by fluctuations. The magnitude of
these fluctuations is determined by the inherent regulatory capacity of the specific process
and by the magnitude of random disturbances arising both in the environment and within the
organism. A system with these characteristics has, in a given environment, a determinate
probability of failure per unit time. As a consequence of the ubiquitous random component
in physiologic performance, a population of individuals that are indistinguishable by any
combination of physiologic measurements will nevertheless manifest time-survival and dosage-
survival curves with finite dispersions. This is illustrated by means of a one-dimensional
model system subjected to a stationary Gaussian random noise disturbance. In real biological
populations, there is a component of variance between individuals. This can be taken into
account by a straightforward generalization of the basic equations for homogeneous popula-
tions.

In this approach, aging is interpreted as a secular change in the values of the parameters
of the regulatory mechanisms. These secular changes are ultimately due to irreversible
changes in permanent or self-reproducing macromolecules. The rate of such irreversible
change is in turn dependent in part on the magnitude of local fluctuations away from
ideal steady state conditions for biochemical syntheses. There are thus two aspects to the
stability of organisms — the probability of mortality per unit time and the rate of increase
of this probability with time (age). Both are intimately dependent on the fluctuation
characteristics of physiologic performances.

I. INTRODUCTION

This paper discusses mortality and aging insofar as they depend on certain
statistical characteristics of organisms and populations. These characteristics,
which may be subsumed under the closely related concepts of fluctuation,
entropy, and information, have their origin in the dynamic nature of physiologic
processes. Much of the current methodology for the analysis of survival
curves is founded on the theory that the observed distributions of survival
are due to the existence of a distribution of sensitivities in the populations
tested. The present discussion is intended to emphasize the statistical nature
of the mortality process within the individual, or in populations of indistinguish-
able individuals. Only those aspects of behavior are considered that have to
do with the establishment and preservation of the steady state of physiologic
function, and that can be described by a set of fixed relations among a finite,
and in fact quite small, number of physiologic processes. Implicit in this
approach is the conception of physiologic process as functional unit rather
than as ultimate enzymatic reaction-step.

* Work performed under the auspices of the U.S. Atomic Energy Commission.

317

318

George A. Sacher

II. PHYSIOLOGIC REGULATIONS

The ability to maintain the physiologic steady state in the face of an unfavor-
able environment is called homeostasis (1). A number of quantitative indices
of homeostatic capacity are in use. In ecological studies the tolerable range
of an environmental variable, such as ambient temperature or salinity (of
sea waters), is widely employed (2). Resistance to transient stresses is a more
common measure in experimental physiology. If the response can be followed
continuously, measures such as the amplitude of displacement of function,
and rate of return to normal may be obtained. The above may be referred
to as determinate measures of homeostatic capacity, for they reflect the fact

Fig. L Schematic representation in two dimensions of the probabihty distri-
bution of physiologic states and their relation to the boundary delimiting viable
from non-viable states. The probability distribution is indicated by elliptical
contours of equal probabihty. The dehmiting boundary (L-L), called the lethal
bound, is indicated as a sharp line, and is treated as a precise value in the derivation
of equation 15. A more realistic representation is given in Fig. 2.

that the homeostatic mechanism, even if it functions perfectly and without
error, has but a finite regulatory capacity, set by the physical limitations of
the mechanism.

In summary, there is a closed region in the physiologic configuration space
within which some degree of stable physiologic function may persist, and beyond
which stable function is impossible. This is indicated schematically in Fig. 1.
The boundary surface of this region will be called the lethal bound, and denoted
byL.

The quantitative properties of the lethal bound diff'er for different physiologic
processes. In the case of white blood cells, the lethal bound on the low side,
either for number of circulating cells or for number of proliferative cells,
is only a small fraction of the normal level. Similarly the lethal range on the
high side is considerably above normal levels. The boundary values for erythro-
cytes lie somewhat closer to the normal values. Blood glucose is rather more

Entropic Contributions to Mortality and Aging 319

sharply limiting on the low side than on the high. Blood pH must be held to
very close tolerances on both sides of normal.

III. SOME PROPERTIES OF FLUCTUATIONS

From a consideration of the components of variation within and between
individuals under different environmental conditions, it can be inferred that
the observed variation can be attributed to (a) random fluctuations in the
common environment that have a uniform influence on all animals maintained
therein and (b) independent random fluctuations of each animal that must
originate either within the animal or in local fluctuations of the environment
that are independent for each animal. The magnitude of the fluctuation arising
within the animal due to internal random noise is reasonably well known in
a few experimental situations of a psychophysical or neurophysiological nature.
Except for certain obvious aspects, such as temperature and humidity, the
nature and properties of the environmental random variables is for the most
part unknown. More significant perhaps than the purely environmental random
variables are these that might be classified as organism-environment inter-
actions. Such relations as pathogenicity, parasitism, dominance-submission,
predator-prey relationships, etc., are in this class, and make contributions
to the variability of individual perfonnance that defy estimation. For the
present purpose, the fact that intra-individual fluctuations exist is sufficient :
the question of their nature can be deferred.

IV. FLUCTUATION AND THE PROBABILITY OF MORTALITY

The set of physiologic processes can be written formally as

^i = ^i k„ ^,;, ^;, /] (/,;■= 1, ..., n) (1)

where the X^ denote the set of physiologic variables, the a,_,- denote internal
parameters, and the A^ external parameters.

The state of an individual at a given moment is specified by the values at
that moment of the n physiologic variables X^. One can conceive of, and in
principle construct, a population made up of indistinguishable individuals,
in which the value of each internal parameter for every member lies within
an arbitrarily small range. In such a population under constant environmental
conditions the time-average of any function of the physiologic variables, X,,
for one individual is equal to the average over the population of the same
function of the A'j at any moment in time.

If we locate a frequency distribution of physiologic states in the configuration
space, the result is as seen in Fig. 1. The contours enclosing percentages of
the distribution (such as 50, 90, 99) are drawn approximately in accord with
the supposition that the bivariate distribution of states is Gaussian, and the
situation is roughly in scale for a 'healthy' population, i.e. there is only a small
probability of observing states near the lethal bound.

Since contact with the lethal bound removes an individual from the popula-
tion, the distribution of states must be modified in the neighborhood of the
boundary. Furthermore, the frequency distribution of states is not by itself

320 George A. Sacher

enough to permit a calculation of the probability per unit time that fluctuations
will reach L. To answer these questions, we turn to a consideration of the
dynamic nature of the fluctuation process within the individual. The complete
description of a fluctuation process is given by specifying its correlation function,
which is in one dimension

P(t) = {X{t)x{t + T)>av/<.v2(r)>av (2)

where x is a deviation from the mean,

^=^0 + ^^ (3)

The correlation function is a measure of the degree to which a fluctuation
present at time t persists at a later time r -\- t, averaged over all values of t.
The nature of p(t) depends on the nature of the system. A process that obeys
the differential equation

^ + ^x = 0 (4)

returns to equilibrium as

X = :Co e-^^ (5)

Corresponding to this, if a stationary pure random Gaussian noise source
f{t) is applied,

^ + ^x =/(/) (6)

the resulting correlation function is

p{r) = e-P^ (7)

It can be shown (3) that if the correlation function in one dimension is given
by equation (7), then the fluctuation process is Markoffian and is completely
described by the joint probability distribution

W.{x^xS = 27ra2 (1 _ p2)*

X exp

2a\\ - p2)

^1^ + -^2^ — 2p.YiX2

(8)

This gives the joint distribution of observations of x separated by time t, where
p is defined by equation (7). The variance, cr^, of the distribution of .y satisfies

a2 = Dl(i (9)

where 4D is the (constant) spectral density of the random noise (white noise)
source. The conditional probability distribution, which describes the distri-
bution of ^2 when x^ is fixed, is

n-Yo/x, /) = [27702(1 - p2)]i

X exp [-(.Y - xfl2a\\ - p"-)] (10)

Entropic Contributions to Mortality and Aging 321

where a~ and p are deiincd as above and

X = x^e'^'^ (11)

As /— > 00, this becomes the stationary distribution of fluctuations,

This distribution is Gaussian because of the linearity of mechanism specified
by equation (4). Fluctuation processes are not in general Gaussian if the
dynamical equations are non-linear.

Equation (12) gives the stationary frequency distribution of fluctuations over
the entire :>c-axis. We now introduce the condition that there is at Xg^ an
absorbing barrier at a distance X from the mean

X— X^ — Xq

An individual remains in the distribution only as long as the path described
by his fluctuation process remains in the region .v < ).. If this situation prevails
for a time sufficiently longer than the relaxation time of fluctuations, 1//?, a
stationary distribution is again established and there will be a stationary
probability q per unit time that the path will intersect x = /I. This 'absorption
rate' is the mortality rate for the model fluctuation process. The stationary
frequency distribution in the presence of an absorbing barrier may be obtained
from equation (12) by the following argument.

In the steady state there is a stationary diffusion current, j, into the barrier.
The desired frequency distribution Q{x) must satisfy the steady state difl'erential
equation for diffusion in the presence of a force field (4). This equation is, in
the notation of equations (6) and (9),

j = KQ{x)-(^a''^^^Q{x) (13)

where K = —fix is the restoring force.

A solution of equation (13) satisfying the boundary condition

Q(x) = 0 (x^ A)
is

3:2 (x-2;)2-l

Q(x)

1

(27702)

2\i

2(72 . ^ 2(T2

(14)

The mortality rate, q, is equal to the diffusion current, j, normalized by the
area under the distribution, Q{x), so that from equation (13) we find the
constant mortality rate to be

A rigorous discussion of this class of stochastic processes (4) indicates that the
validity of equation (15) is subject to the limitation

322 George A. Sacher

This restriction is met if we have X > 3a (as is the case in the appHcations
considered). The normahzing integral in equation (15) is then not appreciably
less than unity, so equation (15) for the mortality rate reduces to

(A>3a) (1-a)

Equation (15) gives the dependence of the mortality rate on the parameters
/?, A and a (or /i, A and D) in the stationary state of a system specified by equation
(6) and subject to a stationary random force function with spectral density 4D.
Although this model is too simple and artificial to be an adequate description of
an actual mortality process, it should be noted that equations equivalent to
equation (4) give an approximate description of a number of different physiologic
mechanisms.

Equation (15) can be extended to the case of time-dependent mortality rates,
as they are observed in animal populations, if the parameters are sufficiently
slowly changing functions of time, so that stationariness of the fluctuation
process is preserved. This is a reasonable assumption with regard to the life
tables of animal populations in their normal environments. It is also considered
for the purpose of this discussion that the fixed and the random components
of environmental forces are stationary throughout life.

Experimental data on homeostatic capacity for a variety of mechanisms
as a function of age indicate that this capacity diminishes during adult life (5).
We therefore expect a steady decrease in the value of />. Since a^ = Djft, the
value of a will be increased by a decrease in /?. The observed dispersion of
physiologic variables does not increase markedly with age. This may imply
that the recovery constant does not diminish much during the life span, but it
may also be due to the eff'ect of the distribution of parameters in the population,
since it can be estimated that about half the total variance in a typical outbred
population is variance between members, and this variance is reduced by selec-
tion, for as mortality proceeds in a heterogeneous population the subpopulations
with the more disadvantageous parameter values will experience heavier
mortality and thus be preferentially eliminated from the surviving population.

We have also examined (6) one simple mathematical model of a homeostatic
mechanism that introduces a plausible type of non-linearity of recovery. In
this model there arises a relation between the location of the mean state and the
value of the recovery constant. In the notation used here, 1 and /9 would
decrease concomitantly.

The methodological difficulty in the study of mortality processes is that
mortality data are not by themselves sufficient for the unique determination of
their parameters, even in the simplest cases. In earlier treatments (7) the
expedient was therefore adopted of assuming that the mean state, X, is the
only parameter that changes with age. There is abundant evidence that the
mean values of physiologic variables change with age (8). Advantage was also
taken of the fact that changes in mean physiologic state with age are usually
small in degree. This justified taking the linear term of the expansion of A^
about the initial value Aq,

A2 = V + 2AoAA (16)

Entropic Contributions to Mortality and Aging 323

Then taking logarithms and collecting the constant terms into lumped constants
the relation was obtained

G(0 — log <7(/) - « -f /> AA (17)

where G(t) is called the Gompertzian.

The linear approximation to A^ is satisfactory for a first-order description
of the relation of injury to age and to dosage of agents that cause permanent
injury, such as x-rays (7).

The fact that /i also tends to decrease with age does not alter the generaliza-
tion made previously (7) that the Gompertzian is a linear measure of mean
physiologic state. The entire exponent

2^2 ~ 2D
can be expanded, yielding an expression of the form

^=^a„ + a,A?. + a.,Aft (18)

Furthemiore if the mechanism depends on several variables, the same expansion
procedure again yields an exponent term that is a linear function of the dis-
placements of all of the parameters. Thus, within the range of parameter values
that occur in the course of natural aging, the Gompertzian is an approximate
linear measure of the mean physiologic state.

V. DESCRIPTION OF THE «-DIMENSIONAL
FLUCTUATION PROCESS

The consideration of the general 77-dimensional case will take as its starting
point the empirical description of the w-variate process in tenns of its moments.
The observational data consist of a large number w of sets of observations
on one individual or on w indistinguishable individuals, where each set is a
measurement of each of n variables at a given time. The first moments are the
n mean values,

1 m

x,o = - 2 X,, (19)

m J = 1

The second central moments are the covariances

m

Vi, = — (20)

The covariances are related to the standard deviations and correlation coefficients
as

Vik = f^i (^k Pik (21)

where c, are the standard deviations and p^,^ is the total correlation coefficient
between the /th and ^th variables. The covariance matrix

nhi • ' • I'm

■ ... p

III '^ II n

(22)

324 George A. Sacher

is a non-negative quadratic form, as is the correlation matrix

iPn • • • Pin

R

(23)

IPnl

Pnn

Given the covariance matrix V, the frequency distribution of the displacements
in n dimensions is determined. In the case that V is positive-definite, so that
the rank is equal to the order n, the distribution is (9)

p(xj_, • • • , x„)

1

T^exp

2K tk ^''"'''"'''

(24)

wherQ V is the determinant of V and K,j. is the cofactor of v,^. in V. The
coefficients, K,JF in the exponent of equation 24 are terms in the inverse of the
covariance matrix,

l7{U=Y-i=A={A,,}

V

(25)

If V is positive semi-definite, the rank r is less than the order n, and the
frequency distribution is an /--dimensional distribution in /• independent linear
functions of the x^ (9)

yx = l ai;,\-, (;. =

1,

•••,/•)

(26)

or

y ^ Ax

(27)

and the moment matrix for y is

M = AVA'

(28)

The frequency distribution for y is then

—

lAfl^^^y^yi

(29)

^Oi, OV) - (.2^y«/2(^^/y/2 exp

The case that the rank of the matrix of covariances is less than the order is
frequently encountered in the initial description of biological systems in terms
of the variables of direct observation.

VI. FLUCTUATION, ENTROPY, AND INFORMATION

The entropy of a system at equilibrium has, in classical thermodynamics, a
precise value, i'oCvjg, • • • , x„q) where the .y,o are the values of the state variables
at equilibrium. However, if thermal agitation or other disturbance causes small
displacements of the state variables, the entropy decreases by an amount, AS.
Expanding AS in a Taylor series in terms of the displacements, .y, (10), we
obtain

(30)

Entropic Contributions to Mortality and Aging 325

plus higher order partials. At equilibrium the first partial is equal to zero, so

^S^lljf^x,x, (31)

= -i2 S,/^x,x, (32)

where 5*,/ is a positive-definite matrix.

There is a formal equivalence between the S^j^ and the /■; defined by equation

(24),

SO = ^A (33)

where k is Boltzmann's constant. Thus the X^j, which we may term the partial
coefficients of the frequency distribution of fluctuations, are proportional to
the coefficients 5",/ of the quadratic form for the mean entropy decrease due to
fluctuation in the system. The physiological systems that are under consideration
and are not completely described by a small number of variables, and accord-
ingly the complete fluctuation distribution and fluctuation entropy would
not be estimated. However, the S^j, or the A,^, are additive, so an initially
incomplete description can be completed as knowledge of the system increases.
From the definition of entropy by Boltzmann

S = k J p{x) log p(x) dx (34)

it follows that the fluctuation entropy coefficient S^^^ in equation (32) can be
written

where /J = p{x^, • • • , x,).

In one dimension this reduces to

S» = -J^%./.v (36)

This is identical with the definition of information given by R.,A. Fisher (11).
The equivalence continues to hold in the n-dimensional case. It should be noted,
however, that the Fisher infoiTnation is a defined quantity, whereas the 5',_,"
are terms in an approximation formula.

There is a close relationship between information theory and the analysis
of fluctuation processes as can be made evident in terms of the equivalences
brought out above. Where there are distinct classes the information is

H=-Y.p,\ogp, (37)

In the one-dimensional continuous case we write

H{x) = -J p{x) log p{x) dx (38)

In a large number of cases, the representation of log/?(.T) in terms of three
terms of a Taylor series is a good or even an exact description. The expression
for the information then becomes

^W = - J /?(a-) log /X'Yo) + \x^ p{x) ^^ log /j(.Vn)

dx (39)

22

326 George A. Sacher

The information function is thereby resolved into separate terms for the expected
values and for the deviations from expectation. The analysis of fluctuation
processes falls into the latter class.

The formal equivalences between fluctuation entropy and Fisher information
does not imply complete equivalence of the concepts. The theory of entropy
fluctuations deals with the stationary fluctuation process in a single individual
or in a group of indistinguishable individuals, where in either case the ergodicity
condition is satisfied. There is no such restriction on the applicability of the
Fisher information. The case of non-ergodic populations (individual differences
in parameters) can be covered by obvious generalizations of the fluctuation
theory, so this distinction is not a permanent one.

Determination of the Lethal Bound

Thus far in the presentation the existence of the lethal boundary surface has
been a postulated property of physiologic mechanisms. In terms of the linear
models of fluctuation processes that have been discussed the lethal bound is
of necessity an arbitrarily assumed property, for a continuous linear process
by its nature has no failure point. The escape from this unsatisfactory situation
is by way of a more thorough mathematical analysis of homeostatic properties.
The lethal boundary has a natural interpretation as a 'divide' on a potential
surface (compare with Fig. 2). When it is possible to discuss the homeostatic
processes as non-linear systems with multiple equilibria, the lethal bound, and
also the boundaries between different viable steady states, will appear as
necessary topological properties of the physiologic mechanisms. We have under
way some investigations of simple non-linear stochastic mortality models, and
the early results are quite interesting (6).

VII. ENTROPIC CONTRIBUTION TO THE AGING PROCESS

Brief consideration was given above to the direction of change of homeo-
static parameters with age. This section will deal with the influence of physiologic
fluctuation on the rate of aging.

It is an intuitive judgment that physiologic steady states of organisms tend
to maximize the efficiency of physiologic function in the environments to which
the organisms are fitted. The approach to greatest efficiency is presumably by
means of natural selection operating on the genetically controllable thermo-
dynamic properties of enzymes. The characteristics of physiologic performance,
and in particular the values of the phenomenological rate constants are ultimately
dependent on the activities, specificities and stabilities of the constituent
enzymes. Thus, to give an account of the age changes in the values of the
phenomenological parameters one must turn to the consideration of function
at the biochemical level. The rate at which irreversible change occurs in a
biological system will be discussed for three situations:

(a) as a function of temperature, independent of metabolic activity;

(b) as a function of metabolic activity in an undisturbed steady-state;

(c) in a steady-state disturbed by ffuctuations much greater than thermal,
i.e. by the fluctuations of physiologic state discussed above.

The analysis of irreversible molecular changes as a function of temperature

Entropic Contributions to Mortality and Aging

327

is a part of the general theory of absolute rate processes, and is also the object
of a great deal of experimental work, particularly on proteins. It is discussed
in another paper in this volume (12).

It has been suggested by a number of investigators that the rate of aging
is a function of the level of metabolic activity. In evidence of this is the relation

m
<

(r
>

<

o

o
o

_i
o

en

>-

X

a.

-2

0 2 4 6 8 10 12

PHYSIOLOGICAL VARIABLE X

Fig. 2. Interpretation of the probability distribution of fluctuation and of the
lethal bound in terms of a potential which is a function of the physiologic state
variables (6). The solid curves are the isopotential contours. The dashed
line L'-L" is the lethal hound. This is the highest point ('divide') on the potential
surface in any direction from the steady state, O. Different parts of the lethal
bound can be at different potentials. If the potential is markedly lower in one
part of the divide, most escapes will occur through this pass. Such preferential
directions of escape may be identified with the occurrence of specific disease
conditions. The contour lines are isopotential contours of the potential function

E = a^x" — biX^ + a^y^ — biV^

A stochastic mortality process has already been investigated for the one-
dimensional case of the cubic potential (6).

between metabolic rate (or body size) and life expectation among the Mammalia,
and the dependence of life expectation on environmental temperature in cold-
blooded forms. However, the relation is not a simple one. Birds, with body
temperatures as much as 5°C higher than mammals (13), tend to have life

328 George A. Sacher

expectations (14) considerably greater than mammals (15) of equal body size
and metabolic rate. Some primates (16) outlive carnivores or herbivores of
equivalent body size by a considerable margin. This is obvious in the case of
man compared with lower animals. In a study on grasshoppers, in which
growth rate and Hfe expectation were investigated as functions of temperature
(17), the Arrhenius coefficient for growth rate was /^ = 18,400 cal and that for
mean death rate was jj, = 6300 cal. Though both are temperature-dependent,
the difference in /j, values suggests that survival is not directly dependent on
metabolic rate.

An association between the level of metabolic activity and the rate of
accumulation of irreversible molecular change is certainly to be expected on
physico-chemical grounds. The presence of poisons in the environment, and
the ever-present possibility of incorrect reactions, imply the existence of a
non-zero error rate per molecular event.

Finally we consider the influence of macroscopic fluctuations in physiologic
state on the rate of accumulation of irreversible molecular changes. The
calculation of the error rate due to fluctuation for a particular biochemical
reaction would require a more detailed specification of the fluctuation process
than is envisaged in the previous development, which dealt with a comparatively
small number of important physiologic functions. This fluctuation in state of
the organism as a whole would certainly play a part, but it would be necessary
to consider in addition the independent fluctuations of small regions. These
would usually have little immediate influence on the state of the whole organism,
but they would be significant for the probabilities of irreversible change within
the regions. The consideration of the problem of local fluctuations cannot be
undertaken here.

It is presumed that the physiological steady state condition is one in which,
through the action of natural selection, the ratio of incorrect to correct reactions
is a minimum. This minimum rate is the metabolic error rate e^i, defined
above. Deviations from the steady state in any direction bring about conditions
in which the probability of incorrect reactions increases. This component of
the error rate is called the fluctuation error rate, e^. The fluctuation error rate
would then in general be a monotone increasing function of the displacement,
and the simplest assumption is that this function is a quadratic.
In one dimension this is

Ej, = /77.\-2 (40)

where x is the displacement from the steady state . Then, for the one-dimensional
model process discussed above, with stationary distribution of displacements
given by equation (12), the mean error incidence per unit time is

r)0-<

■ x^e 2rT2^.v (41)

(2770-

We find

Ep = ma^ (42)

This is not a solution of the problem, for the evaluation of m cannot yet be
carried out. However, the essential point for the present discussion is that
the fluctuation error rate is an increasing function of m and of the dispersion
of displacements, g.

Entropic Contributions to Mortality and Aging 329

The mortality rate for the same model system.

-m

e 2a2,(;>3(;) (15a)

is also an increasing function of a'-, for the exponential factor in equation (15)

varies much more strongly with g than does the constant factor -. The effect

of accumulating errors will be to reduce A and jS and to increase a (see above,
Section IV). All of these changes tend to increase the mortality rate as age
increases. Therefore it is concluded from this quahtative discussion that the
mortality rate of different species, and the rate of increase of mortality rate with
age for the same species are positively correlated. There are too many uncertain-
ties to pemiit a statement of the functional relation between these quantities at
present. However, we have here a possible basis for the relative constancy in the
form of the life table for species as widely different as fruit fly, mouse and man.
The total error rate includes all three terms discussed above

£total = fr + ^.1/ + ^F (43)

where the subscripts denote temperature, metabolic rate and fluctuation,
respectively. The existence of contributions to the error rate arising from back-
ground ionizing radiations and other environmental noxae must also be acknow-
ledged. Perhaps the best viewpoint is that the physical basis for each term
demonstrably exists, but we do not know the absolute contribution of any of
them. This will be a major experimental problem.

All of these contributions arise when the environment and the population
are in a steady state of fluctuation. The course of aging is also influenced to an
important extent by very large disturbances that occur infrequently in the
lifetime of the individual. Illness and crippHng accident are examples, but
changes of nutrition, etc., have equally important effects, as do also insults
such as adventitious poisoning. The unique nature of these events requires
that they be treated historically rather than on the basis of statistical uniformity
of occurrence. Under experimental conditions it can be shown that exposure
of a population to ionizing radiations leaves a pennanent residue of injury (7).
Jones (18) has demonstrated that human sub-populations selected on the basis
of a history of given diseases have a permanent increase in their mortality at
later ages. Some writers have attributed aging in general to the action of such
major disturbances. Against this position it can be argued that the large common
factor in the aging of human or animal populations points to an agency that
acts with comparative uniformity on all members of the population and within
each individual over the course of life. This is compatible with the statistical
uniformities that appear in the summation of a large number of small indepen-
dent events as proposed herein.

REFERENCES

1. W. B. Cannon: Organization and physiological homeostasis. Physiol. Rev. 9, 399-431
(1929).

2. C. L. Prosser: Physiological variation in animals. Biol. Rev. 30, 229-262 (1955).

330 George A. Sacher

3. M. C. Wang and G. E. Uhlenbeck: On the theory of Brownian motion II. Rev. Mod.
Phys. 17, 323-342 (1945).

4. S. Chandrasekhar: Stochastic problems in physics and astronomy. Rev. Mod. Phys.
15, 1-89 (1943).

5. W. B. Cannon: Aging of homeostatic mechanisms. In: Problems of Aging, 2nd ed.
ed. by E. V. Cowdry, Williams and Wilkins, Baltimore (1939).

6. G. A. Sacher: Generation of a model dosage — survival curve from a stochastic hypothesis
(abstract). Radiat. Res. 6, 447 (1957).

7. G. A. Sacher: On the statistical nature of mortality, with especial reference to chronic
radiation mortality. Radiology 67, 250-257 (1956).

8. M. Burger: Altent und Krankheit, Ind ed., G. Thieme, Leipzig (1954).

ed. by A. I. Lansing: Problems of Aging, 3rd ed. Williams and Wilkins, Baltimore (1952),
L. BiNET and F. Bourliere: Precis de gerontologie, Masson et Cie, Paris (1955).

9. H. Cramer: Mathematical Methods of Statistics, Princeton University Press (1946).

10. P. Epstein: Textbook of Thermodynamics, J. Wiley and Sons, New York (1937).

11. R. A. Fisher: Statistical information. In: Information Theory in Biology, 12-13, ed.
by H. Quastler, University of Illinois Press, Urbana (1953).

R. A. Fisher: Probability, likelihood and quantity of information in the logic of uncertain
inference. Proc. Roy. Soc. {A) 146, 1-8 (1934).

M. G. Kendall: The Advanced Theory of Statistics, Vol. II, Chas. Griffin and Co.,
London (1946).

12. H. P. Yockey: A study of aging, thermal killing and radiation damage by information
theory. This volume.

13. S. Brody: Bioeuergetics and Growth, Reinhold Publishing Co., New York (1945).

14. S. S. Flower: Contribution to our knowledge of the duration of life in vertebrate
animals. V. Mammals. Proc. Zool. Soc. Lond. 1931, 145-234 (1931).

F. Bourliere: Natural History of Mammals, Knopf, New York (1954).

15. S. S. Flower: Contributions to our knowledge of the duration of life in vertebrate
animals. Birds. Proc. Zool. Soc. Lond., 1915, U65-\A12{\925).

16. E. P. Walker: The Monkey Book, Macmillan, New York (1954).

R. M. Yerkes and A. W. Yerkes: The Great Apes, Yale University Press, New Haven
(1929).

17. J. R. Parker: Bull. Univ. Mont. Agric. Res. Sta., no. 223 (1930).

18. H. B. Jones: A special consideration of the aging process, disease and life expectancy.
In: Advances in Biological and Medical Physics, ed. by J. H. Lawrence and C. A. Tobias,
4, 281-337, Academic Press, New York (1956).

A QUANTITATIVE DESCRIPTION OF LATENT
INJURY FROM IONIZING RADIATION*

H. A. Blair

Department of Radiation Biology, University of Rochester
School of Medicine and Dentistry

Abstract— A group of hypotheses previously discussed by the writer to account for the kinetics
of radiation injury in mammals is reviewed. That radiation injury is proportional to dose,
is partly irreversible, and that irreversible injury adds to new acute injury to produce lethality,
appear to be vaHd. Recovery is not a single process for the whole animal but proceeds at
different rates in different regions. The lethal threshold diminishes, presumably to zero, in
old animals but not in proportion to life expectancy throughout adult life; rather it changes
more slowly at first and then more rapidly. Irreversibility of injury differs with different
radiations. With x- or gamma-rays it appears to be a similar fraction with doses smaller
than about 100 r, but increases with larger brief single doses. The data in general are not
sufficiently extensive and accurate to test hypotheses critically.

Over the past several years (1, 2, 3, 4, 5) I have discussed the adequacy of
certain hypotheses to provide an empirical mathematical description of radiation
injury and its effect on the duration of life. These hypotheses have been fairly
successful in outlining a broad picture of radiation injury, in correlating many
of the data and in suggesting critical experiments. It has become obvious,
however, that they are deficient in some details and require amplification or
revision. I propose at this time to discuss those changes in these hypotheses
which appear to be necessary and also to point out some of the areas in which
the data are inadequate to form the basis of quantitative correlations.

The hypotheses in question are as follows:

(a) The total injury produced by ionizing radiation is proportional to the
dose.

(b) This injury is reparable in part and irreparable in part.

(c) Recovery from reparable injury occurs at a rate proportional to its
magnitude.

(d) In consequence of (a) and (b), irreparable injury accumulates in pro-
portion to total dose.

(e) Reparable and irreparable injury add in all proportions and death
occurs when their sum attains a level which is proportional to the
remaining life expectancy.

The injury defined here is a latent form observable at present only in terms
of additional radiation dose. With acute exposures this injury has largely
disappeared in most species before the clinical syndrome of radiation sickness
has fully developed. There is presumably a quantitative causal relationship

* This paper is based on work performed under contract with the United States Atomic
Energy Commission at the University of Rochester Atomic Energy Project, Rochester,
New York.

331

332 H. A. Blair

between this latent injury and the clinical syndrome, but this has not yet been
established. The advantages of developing non-lethal methods for detecting
latent injury will be mentioned later.

It should also be remembered in what follows that the minimal lethal injury
to an animal may not initially be manifest clinically at all, and that death occurs
only after many days during which clinical signs develop. Because most
mammals, if they are going to die from irradiation, do so within three or four
weeks, it is customary to describe the lethal dose as that one which will kill
one-half the experimental group within thirty days and to designate it LD50 or
LD5Q 30 days. The events which happen between the time of exposure, when
presumably a lethal threshold for primary injury must be reached, or exceeded,
if death is to occur, and actual death, are outside the scope of this discussion.

The LD50 for most mammals using whole body exposure is within the
range of 400 to 800 roentgens for the young adult.

In accord with the above hypotheses, the rate of development of injury /
under exposure at constant dose rate y is

f =^7-^(/-oc}'0 (1)

in which /> is the rate of recovery per unit injury and A and a are constants.

Integration of equation (1) gives for the level of injury after exposure for

time t

(^ — a) „,

I = ^^—^y{\--e-f^^) + y.yt (2)

If the time of exposure is sufficiently short that no significant recovery
occurs during exposure, as is usual in determining the acute median lethal
dose or LD50, e"''' may be replaced by 1 — /:»/ so that equation (2) becomes

/ = Ayt = Aot.
a being the total dose.

If, now, a is the LD50, the injury / is the lethal injury and according to postu-
late (e)

I=A(x^ So- S (3)

in which 5*0 is the normal life expectancy of the animal and S is its age at
radiation death. The constant of proportionality associated with Sq — S
is taken arbitrarily as unity

For animals irradiated at daily constant rates for periods of some months
e~^^ may be neglected. This reduces equation (2) to

. (A - a)

r + ay/ (4)

or, on using equation (3), to

5*0 — 5" A — a

+ a/ (5)

Because nearly all chronic radiation experiments are begun on the young
adult animal and also because postulate (e) catmot possibly be valid in very
young animals in which the lethal dose rises instead of diminishes with age,

A Quantitative Description of Latent Injury from Ionizing Radiation

333

it is convenient to measure Sq and S from the beginning of irradiation so that
t in equation (5) is replaceable by 5* to give

a

/^

+ OI.S

(6)

This equation represents existing (1, 2) data on chronic irradiation of
mammals well within their possible errors. Such errors may be large in long-
term experiments owing to infections and other accidents. An example of the
fit is given in Fig. 1 for the data in Table I.

IT
bJ
a.

K

cc

tli
a.

o

I-
tr
o

X

in

10 20 30 40

SURVIVAL TIME WEEKS

50

Fig. 1. Data by Henshaw (17) on chronic irradiation of mice plotted according
to equation (6). The data are given in Table I. They cover a wider range than
most. The scatter in such experiments frequently increases as the duration of the

experiment gets long.

Table I.

Data by Henshaw (17) on Mice Irradiated Chronical/}' Five Days
per Week until Death

No. of
animals

Daily
dose (r)

Survival
time (S)
(weeks)

So-S
observed

Total
dose (r)

So-S

y

y{A - a)
(weeks)

aa
(weeks)

So-S
calculated

10

0

45.8

0

0

0

0

15

5

37.0

8.8

925

.352

2

6.2

8.2

15

10

34.6

11.2

1730

.224

4.1

11.7

15.8

15

15

27

18.8

2025

.250

6.1

13.7

19.8

14

20

23.8

22.0

2380

.220

8.1

16.1

24.2

14

25

19.3

26.5

2410

.212

10.1

16.3

26.4

10

40

11

34.8

2200

.174

16.2

14.9

31.1

10

60

7

38.8

2100

.129

24.3

12.1

36.4

10

80

4

41.8

1600

.105

32.4

10.8

43.1

It is obvious now, however, that this equation should fail, providing all the
other postulates are valid, because of the inaccuracy of postulate (e) even in the
region of adult ages. Actually this postulate could have been written: 'LD50
diminishes in proportion to life expectancy.' Consequently it can be tested
directly by measuring LDjo as a function of life expectancy.

In Fig. 2 are plotted LD50 data on Rochester rats (6) as a function of age.
It will be seen that LD50 increases with age in young animals, is maximal in
young adults, then declines slowly with age. As was mentioned above, postulate

334 H. A. Blair

(e) could possibly apply only to the adult stage. It should be noted that this
curve is not convertible into a LDgo-life expectancy relation because, owing
to mortality among the animals, the sample at each succeeding age is different
from those going before. Those dying early have the shortest life expectancies
and presumably the lowest LDgo's, although this latter point cannot be proven
directly.

In the legend to Fig. 2 are also given the days of hfe expectancy for
the adult data only. These are fairly linear but do not extrapolate to LD50 =
0, when Sq — S — 0, but to about 300 r. Presumably later points will diverge

800

£600

3 400

200

0 100 300 500 700

AGE IN DAYS

Fig. 2. Median lethal dose in roentgens as a function of age in rats of the
Rochester strain (6). The animals at different ages are not directly comparable
because, for example, of a group selected at 100 days, only about two-thirds
survive to 500 days. The actual median survival times of control animals for the
groups irradiated at 5, 11 and 16 months, respectively, are 450, 375 and 330 days
after the time of irradiation. Therefore, life expectancy does not decrease as
rapidly as the age of selection increases.

toward zero. Because it requires maintenance of animals for about three years
to obtain data for a point at the advanced ages, it may be some time before
the curves of Fig. 2 are well determined even in short-lived animals. However,
Grahn and associates (7) at Argonne National Laboratory have shown in mice
that the lethal dose as measured by repeated daily doses decreases rapidly from
middle age with an apparent tendency toward zero at old age.

At the present time it is not possible to state the situation more clearly
than that the lethal threshold in the adult is some diminishing function of life
expectancy, not a linear function throughout as required by postulate (e).
This can be expressed also as

LD50 = F(So - S) (7)

and this as yet undetermined function should replace 5*0 — 5" in equation (6).
However, there is considerable indirect evidence which will be discussed later
that

LD50 = k(So - S) (8)

in fairly close approximation,/: being a constant for values of ^q — Sup to 20 per
cent of 5*0. It is important to establish the form of equation (7) in several
species so that estimates can be made of variation of LD50 with age in man.
It is not clear whether equation (6) fits chronic data because equation (7) is
sufficiently linear in the region in which most of the data lie (shortening of life
span by one-half or less) or because of some other compensatory factor. In

A Quantitative Description of Latent Injury from Ionizing Radiation 335

any case putting k from equation (8) equal to unity, as is done in equation (6),
may modify the constants A and a. This possibility should be considered when
comparing the numerical values of these constants in different species and
considering their absolute values.

The constants ft and clJA of equation (1) and their variations with age, if
any, can be determined directly. According to equation (1) the injury /, when
exposure is stopped, should be repaired exponentially between its initial value
and its irreversible residual. This repair was first studied in mammals by
Hagen and Simmons (8) using the rat. They assumed exponential repair to

Radiotion
Injury

/^

~- — -^^^^lethal threshold

( reversible ^^v

injury

\irreverslble injury^*^

N,

AGE S So

Fig. 3. A schematic representation of the LD50, or lethal injury threshold, for an
individual animal with a representation of injury from a single exposure. Data
discussed in the text indicate that the irreversible injury is the same, and remains
constant independent of the adult age at which it is laid down. This threshold
curve cannot be measured directly owing to the change by death of the sample as
the age of selection is made older and older. The related curve which is
measurable is that of LD50 as a function of remaining life expectancy.

zero. Usually in making this determination a single substantial sub-lethal
dose is given to a large group of animals followed by test doses to sub-groups
at increasing intervals. Actually, the residual injury should be determined
separately by testing one group after all repair presumably has taken place as
illustrated in Fig. 3. The test doses less the residual in roentgens should then
demonstrate simple exponential repair according to equation (1). However
there is still another complicating factor in that it has been demonstrated recently
that all parts of the animal do not recover at the same rate. Carsten and
NooNAN (9), for example, have shown that following irradiation of the rat
abdomen alone, recovery occurs with a half time between one and two days
whereas it occurs in the animal with abdomen shielded with a half-time of
about five days, and in the whole animal in about one week according to
Hagen and Simmons (8). Possibly, however, the strain used by Carsten and
Noonan would demonstrate whole-body recovery at the same rate as abdomen-
shielded recovery. In any case we are confronted with the fact that partial
body recovery, at least for some tissues, is different from that for whole body.
We do not yet know whether recovery of the parts is independent of whether
or not other parts have been irradiated. It is fairly certain, however, that
faster abdominal recovery can occur following whole-body irradiation, and
probably accounts for the several observations (10, 11, 12) that recovery
during the first day, as measured by whole-body test doses, is considerably
faster than backward exponential extrapolation of later recovery. Strictly
then equation (1), in some cases, if not in all, should be written with two or
more constants [> and the data analysed appropriately.

It will be seen that the existence of more than one constant, /i, will not alter
the form of equations (4) to (6) but the apparent value of ft determined from

336 H. A. Blair

chronic data will have no exact counterpart in recovery measured directly by test
doses.

According to the hypotheses, recovery should not exceed the irreversible
component ay/. The data confirm that at least after some months following
exposure the irreversible component is demonstrable as a decrease of LD50
and it is ultimately demonstrable as a decrease in life span. Nevertheless,
there are some data on recovery showing that in the first few weeks test doses
for lethality may attain or even exceed values for animals not previously
irradiated. The natural conclusion from these data is that recovery may be
complete or even more than complete in that an apparent tolerance to radiation
is developed. Owing to a number of factors, the nature of this apparent transient
complete or over-recovery is not clear. One of the factors is that if the experi-
ments are done on young animals which have not attained maximal LD50
(Fig. 2), increase of LD5Q during recovery will obviously make recovery appear
greater than it really is. This defect may not be obviated by comparison with
controls at each stage of the experiment, because LD50 may increase differently
with age in the irradiated and control groups.

Another disturbing factor is that fast recovery of the abdominal region
will make the earlier part of the recovery curve fall faster than is appropriate
to the remainder of the body and the later part of the recovery curve will be
lower, because, after the abdomen has recovered considerably, the dose required
to kill will be greater than it would be if the whole body were recovering together.
This factor will tend to obscure an irreversible remainder until all recovery
has proceeded as far as it will.

Another possibility is that the animal may develop a transient physiological
reaction to acute radiation injury which temporarily raises the lethal threshold
for a second dose.

For all these reasons the irreversibility of radiation injury probably cannot
be evaluated properly until at least several weeks after a substantial dose

The question of whether parameters in biological systems are age dependent
should always be raised. In the case of recovery, for the reasons given above,
evaluation of the constants or constant ^ is difficult by direct measurement.
Nevertheless if the unanalysed recovery curve itself is similar at different ages
this is an indication that the constants have not varied. Hursh and Casarett
(13) have shown in the rat that the recovery curve at 546 days (beyond middle
age) is similar to that at 107 days (young adult). More study should be given
this problem, but at present there is no indication that the rate of recovery
is age-dependent.

The problems of whether irreversible injury is the same per unit injury
at all ages, whether it slowly diminishes or increases, whether it gives rise to
shortening of life because it is identical with ordinary aging or because it
promotes ordinary aging, and whether it can be altered in any way, once laid
down, are of considerable interest with respect to the setting of permissible
levels for human exposure. If, for example, the irreversibility of radiation
injury could be reduced the consequences of exposure would be reduced
similarly.

Referring to Fig. 3 the indications at present, though far from complete,
suggest that irreversible injury once laid down remains at constant level,

A Quantitative Description of Latent Injury from Ionizing Radiation 337

as depicted, until it intersects the curve of diminishing lethal threshold to cause
the animal to die prematurely.

One indication of this has been obtained by Baxter (14) in fruit flies.
These flies normally live for about fifty days and lose half their life span if
exposed to 75,000 r in a single dose. They die on day 26 approximately whether
irradiated on day 1, day 25, or any day in between. Presumably recovery
is very rapid in this species, and the irreversible component has the same
eff'ect when laid down at any time which is early enough in life to allow the
whole potential life-shortening to be made manifest.

OSINGLE DOSE
• DIVIDED DOSES

100 200 300 400

DOSE IN PERCENT OF LDsq-SO DAYS

Fig. 4. Life shortening in per cent of normal span as a function of LD50 for
rodents exposed to single doses or divided doses of x- or gamma-radiation.
In the case of divided doses the radiation was stopped sufficiently long before
death, or was at a sufficiently low daily level, that life shortening was caused only
by irreversible injury, all, or nearly all, acute injury presumably having been
repaired. The scatter of data is quite high for low divided doses, there being almost
as many (omitted for simplicity) which show prolongation as shortening of life.
The single dose curve rises more rapidly than linearly as LD50 is approached. The
sources of the data are given in (16). LD50 is from 500 to 700 r for most of these
strains. There is no established reason why data from different species should
form a consistent pattern in this mode of plotting. They are less consistent than

data on single strains.

Incomplete observations by Hursh and Casarett (13) indicate that a
given dose shortens life by about the same fraction of the normal expectancy
in groups of rats exposed in early adult life or beyond middle age.

Direct measurements of residual injury as reduction in LD50 have been
made no later than a few months after an initial dose. Such direct determinations
when extended will be a more satisfactory test of the validity of the hypotheses
depicted in Fig. 3 than the life-span data mentioned above.

Another factor to be discussed is whether the irreversible injury, or the
constant a, is independent of dosage. It appears definitely to be larger with
fast neutrons and alpha rays than with x- or gamma-rays (3). As measured
by life-span shortening, it is also greater for single substantial doses of x- or
gamma-rays than for divided doses even though all are delivered at the same
dose rate in roentgens per minute.

Figure 4 shows the after eff'ects of single and divided doses on life span
in a number of strains of rats and mice. These data are plotted on the assump-
tion that strains of different life spans and different LDjo's will lose the same
fraction of their life spans per unit dose measured in LD5Q. Existing data

338 H. A. Blair

are not sufficiently accurate to decide whether this assumption is more correct
than the one that the effects per roentgen are more similar in going from strain
to strain or species to species.

It will be observed that according to Fig. 4 divided doses cause only about
one-third the life-shortening per unit dose as that produced by single doses.
Because some of the divided doses were given in increments as great as 120 r
and because existing data are not sufficiently accurate to define small effects,
it is probable that the curve for the smaller single doses coincides with that
for multiple doses. It is certain, however, that substantial single doses such
as 200 r (one-third LD50) or more, have considerably more effect than the
same dose in smaller increments.

The reason for this difference that immediately suggests itself, is that the
irreversibility of the injury is some increasing function of its magnitude rather
than the linear function assumed here. That this is not the correct explanation
is indicated by the fact that repeated daily doses calculated to produce as much
injury of the type defined here as a single substantial dose do not have the
same effect on life span. There may be some unidentified dose dependent
concomitant of injury which affects its reversibility. At this time, however,
all that can be said is that a appears to be a constant independent of dose for
doses of daily increments up to about 100 r but that it increases with dose
with greater daily doses. That this larger effect of substantial single doses occurs
at the time of irradiation and is not due to a dose dependent subsequent develop-
ment is indicated by a single set of data (13). Such observations should be
extended.

As predicted, the multiple dose curve of Fig. 4 is probably nearly linear.
The single dose curve increases more rapidly than linearly if carried to higher
doses than those depicted. This is to be expected because, according to the
hypotheses, life shortening will be linear with dose only to the extent that the
threshold curve of Fig. 3 is linear. As irreversible injury becomes substantial
it will have more effect on life span per unit magnitude according to this curve.

YocKEY (15) has postulated the identity of radiation damage with reduction
of somatic genetic information, and has related the present formulation to
the consequences of such damage in tenns of information theory.

CONCLUSIONS

The hypotheses used appear to give a fairly accurate over-all description
of radiation injury. The only one which is definitely known to be inaccurate
is the last, which probably should be restated: Reparable and irreparable injury
add in all proportions and death occurs when their sum attains a level which
is some function, not fully detennined, of the remaining life-expectancy.

Certain details, such as recovery rates, probably must be regarded as tissue-
or region-specific rather than whole-body specific. This may also be true
of irreversibility which has not been systematically studied in this regard.
This latter problem is of particular interest with respect to human exposure,
much of which, especially from internal emitters, is partial-body. However,
even if each tissue, for complete description, requires a different set of constants
A, a and ^, this adds only complexity of detail and not of concept.

A Quantitative Description of Latent Injury from Ionizing Radiation 339

Irreversible radiation injury has the special property that it is closely related
to premature aging abruptly laid down and probably persisting thereafter
at a level constant or nearly so. This suggests the possibility that premature
aging may be studied in young animals without waiting for them to die naturally.
Of special interest is the possibility that irreversible injury may be prevented,
at least in part, or altered once it has been laid down. This possibility should
be studied in relation to exposure problems in man and also with respect to
its bearing on natural aging. If, however, irreversible injury is wholly in the
form of somatic mutations, as is often suggested, the possibility of altering it
or its consequences would presumably be remote.

The acute injury described here in terms of radiation dose has antecedents
in the form of disturbances of cellular structure and function from absorbed
radiation and consequences in the form of the clinical syndrome of radiation
sickness. Only the last stage has been at all well described in physiological
terms, and the connections between the stages has not been elucidated at all.
The ability to measure latent injury in terms of radiation dose should assist
in deriving its description in biochemical or physiological terms. This is also
true of irreversible injury.

Nearly all aspects of the long-term effects of radiation injury are markedly
deficient in data, especially of those based on sufficient numbers of animals
to be reasonably exact.

For this reason no formulation of the kinetics of the injury process can
be adequately tested at present for its quantitative exactness. The virtue of
a particular scheme is measurable rather in its ability to designate the phenomena
involved, to make useful predictions and to serve as a basis for designing
critical experiments.

REFERENCES

1. H. A. Blair: A formulation of the injury, life span, dose relations for ionizing radiations.

I. Application to the mouse. University of Rochester Report UR-206 (1952).

2. H. A. Blair: A formulation of the injury, life span, dose relations for ionizing radiations.

II. Application to the guinea pig, rat and dog. University of Rochester Report UR-207
(1952).

3. H. A. Blair: The shortening of life span by injected radium, polonium and plutonium.
University of Rochester Report UR-274 (1953).

4. H. A. Blair: Recovery from radiation injury in mice and its effects on LD50 for durations
of exposure up to several weeks. University of Rochester Report UR-312 (1954).

5. H. A. Blair: A formulation of the relation between radiation dose and shortening of
life span. Proc. Int. Conf. Peaceful Uses of Atomic Energy 11, 118-120, United Nations,
New York (1956).

6. J. B. Hursh, and George W. Casarett: The lethal effect of acute x-irradiation on rats
as a function of age. Brit. J. Radiol. 29, 169-171 (1956).

7. D. Grahn: Personal communication.

8. C. W. Hagen Jr., and E. L. Simmons: Effects of total body irradiation on rats. Part 1,
Lethal action of single, paired and periodic doses. University of Chicago Metallurgical
Laboratory Report CH-3S15 (1941).

9. A. L. Carsten, and T. R. Noonan: Determination of the recovery from lethal
effects of lower body irradiation in rats. University of Rochester Report UR-455 (1956).

10. J. F. Thomson, and W. W. Tourtellotte: Effect of dose rate on LD50 of mice exposed
to gamma radiation from cobalt 60 sources. Anier. J. Roentgenol. 69, 826-829 (1953).

340 H. A. Blair

11. J. Storer: Personal communication.

12. J. P. Storaasli, S. Rosenberg, J. S. Krohmer, and H. L. Friedell: Effect of short
interval fractionation on the lethal properties of total body radiation in rats. Western
Reserve University Atomic Energy Medical Research Project Report NYO 4919 (1955).

13. J. B. HuRSH, and G. W. Casarett: Unpublished observations.

14. R. Baxter: Unpublished observations.

15. H. P. Yockey: An application of information theory to the physics of tissue damage.
Radiat. Res. 5, 146-155 (1956).

16. H.A.Blair: Data pertaining to shortening of life span by ionizing radiation. University
of Rochester Report UR 442 (1956).

17. P. S. Henshaw: Experimental roentgen injury. IV. Effects of repeated small doses
of x-rays on blood picture, tissue morphology and life span in mice. J. Nat. Cancer
Inst. 4, 513-522(1944).

SOME NOTES ON AGING

Hardin B. Jones

Division of Medical Physics and Donner Laboratory
University of California, Berkeley, California

Abstract — Evidence of physiologic change with age uniformly points to a cumulative deteriora-
tion as age increases. Further degenerative change may occur proportionally to the amount
of change already acquired. As age increases, incidence of degenerative disease and death
increases exponentially. It is pointed out that, whatever aspect of body function is considered,
e.g. functional members, metabolism, cellular activity, or blood flow characteristics, a
relatively exponential increase in degeneration of body function occurs with increasing age
of the individual. It is possible that each of these separately considered systems of aging is
in partial equilibrium with the others, so that all general characteristics of change in functional
vigor with time follow a similar course.

Increments of change in body structure and function occur as a phenomenon
of aging. Usually, the term 'aging' is associated with deteriorative change,
and as such is distinctively set off from those changes with age that are respon-
sible for growth and development. However, even the period of development
may be considered to have associated with every step some hazard that this
step may not be achieved fully, thus adding an increment of imperfect function
to the body. Such a deletion from full function, whether arising from genetic
inheritance, developmental processes, or accidental mishap, may count just
as much toward the accumulated deterioration we can manage to tolerate
as does the deterioration of advanced age.

Experience of mishap accumulates throughout life. Some events, to be
sure, have as little residual effect upon us as the whistle of the wind, but occasion-
ally something of consequence occurs. As an example, it may be the crushing
of a finger; although we usually recover, we can remember the event because
of some persistent change^perhaps a scar, or a distortion of the nail, or even
the loss of the finger.

Since, on the average, we live each day in a situation where there is some
definite but slight chance that an event of misfortune may disturb us, then the
longer we live under this average circumstance of risk, the more likely we are
to find among us individuals showing physical impairment. Inspection of
such a system leads to the probable conclusion that:

Accumulated impairment = Mishap risk x Time of exposure X
Fraction of function lost per mishap.

But, the risk of occurrence of an unfavorable event is subject to increase as
age increases, and the fraction of function lost per mishap may also increase
as age increases. In this system, therefore, we can expect a relatively non-lincrr
accumulation of average physical impairment as age increases; physical impair-
ment may increase as some higher power of time hved than unity. This example

341

23

342 Hardin B. Jones

of a system contributing to aging reflects the exponential increase of morbidity
and mortality that regularly is observed with increasing age.

There are other examples of impairment of body function that depend
upon time lived and upon morbidity experience. A very general theory of
impairment can be argued in which morbidity leads to morbidity, and mortality
risk is some function of the integrated morbidity experience (la). The following
examples of functional disturbances may be cited to illustrate such relationship
between morbidity and morbidity and between morbidity and mortality:

(a) The severity of toxic reaction usually increases more than proportionately
to the poison dose.

(b) Radiation exposure induces ionization in tissues, and this morbidity
in turn can induce morbidity proportional to the dosage. This holds
both for acute effects and for life-span and carcinogenic changes.

(c) Risks of degenerative vascular disease are proportional to the extent
of obesity (5).

(d) Risks of degenerative vascular disease are proportional to the dis-
turbances of serum lipids in individuals followed over a segment of
the adult life span.

(e) Death risks in diabetes throughout the past forty years have been
undergoing a progressive reduction apparently proportional to the
goodness of diabetic control.

(f) Dimming of primary senses (vision, touch, pain, and hearing) is
associated with enhanced risks of trauma.

(g) Susceptibility to infectious disease is believed to be directly propor-
tional to exposure intensity, and inversely proportional to defense
mechanisms such as antibody levels and antibody generating capacity
(lb); also, susceptibility to infectious disease can be quantitatively off'set
by administration of antibiotic agents.

(h) Proportional differences in death-rate risks among population samples
throughout life span are related to sums of environmental and genetic
factors.

Having noted examples of how morbidity and mortahty risk can be depen-
dent upon functional impairment, we can consider in greater detail evidence
pointing to a widespread interdependence of physiologic systems. In vascular
disease, occlusion may directly diminish blood flow in a small but critical
segment of the body, as in coronary thrombosis. However, even though there
is a measure of recovery from the acute episode, there may be a generalized
insufflciency of circulatory function. Changes in blood flow caused by narrowing
of the arterial channels may be expected to exact an effect upon function of
the extremities, and Dobson (2) has recently shown evidence for general
dependence of the body's homeostatic mechanisms upon the proportional
balance of regional blood flow. Thus, especially for the circulatory system,
we can be certain that functional changes can influence the entire quality of
body function.

A similar example of interdependence of disease is in the complications

Some Notes on Aging 343

of diabetes mellitus. This disease is not limited to the classic confines of its
relationship to carbohydrate and intermediary metabolism: serious disturbances
of lipid metabolism may also occur, linked with enhanced tendency for vascular
changes; the term of pregnancy is frequently lengthened in diabetic mothers
retinal changes may occur in diabetics, and the disease in general may be
associated with somewhat early changes related to aging. There seems to be
no reason to suspect that diabetes is a more complicated disease fundamentally
than loss of islet-cell function or absence of insulin; but it does seem that the
results of this functional deficiency can produce several different conditions
that may even interact to compound the pathologic impact of the basic
deficiency.

Another example of general disease being associated with a specific disease
is observed in the follow-up of cancer patients. In cancer of the rectum, death
from intercurrent disease may be just as likely as death from recurrence of
the mahgnancy. There is also general evidence, from comparisons of mortality
from disease in nineteen western countries, that high incidence of any one kind
of disease is associated with high incidence of other diseases (la). Some factors
affecting adult health and life expectancy might be expected to be common
to several kinds of overt disease; other factors influencing health may have
a limited efiTect upon a single system. For example, in overweight individuals
the increased risk of death is attributed to increased incidence of arterio-
sclerosis and hypertensive disease, while the tendency toward cancer is not
significantly changed from the average of the population. In radiation exposure,
all major diseases may be enhanced. Leukemia, however, may be increased
by a factor of 10, while other degenerative diseases are elevated less than
twice. It is quite possible that some kinds of disease are less likely to occur
following radiation exposure, even though the general trend is toward more
severe and earlier degenerative disease following significant radiation exposure.
Similarly, smoking generally enhances degenerative disease by a factor of
2 while lung cancer is increased tenfold. These observations point to the
interrelationships in etiologic factors in disease, and the possibility that causative
factors in development of degenerative disease may have interactions that
accelerate the appearance and consequences of disease change.

Vascular Disease

GoFMAN and associates (3) have been able to show that the change in the
wall of the artery in arteriosclerosis is essentially a linear thickening throughout
aging. Thus, the shift toward occlusive change results from narrowing of a
cylindrical tube by a progressive thickening of the mass, reducing the radius
of the lumen. The function describing the reduction of blood flow in the
artery involves the cross-sectional area of the artery, which is proportional
to the square of the radius of the artery. Since blood flow in the artery is
related to cross-sectional area, blood flow changes in arteriosclerosis are
not proportional to time lived but rather vary as a power function of time.
The fact that elasticity of the artery may fall off" sharply as sclerotic thickening
occurs probably accelerates the process. Thus, from several points of view,
vascular change is not likely to produce a linear accumulation of disturbance
with time lived, even though the basic feature of the disease is reasonably

344 Hardin B. Jones

established as a thickening of the artery wall proportional to lipoprotein
elevation and duration of the condition.

Since vascular disease is a large component of degenerative disease and a con-
tributing cause to other diseases, it is quite possible that exponentially-decUning
blood-flow capacity may in part determine the exponential pattern of increas-
ing incidence of overt disease other than vascular disease.

Cancer and Aging

Throughout adult life, cancer incidence and cancer death rate are increasing
exponentially; in most ways, this increase is remarkably similar to the above-
described increase in heart disease tendency. Armitage and Doll ('4) have
ascribed this property to the fact that a succession of small changes necessarily
precedes cancer. It is of interest to construct population samples of individuals
known to have died of a given kind of cancer. When this is done, the increase
in death rate in the cancer-destined population is remarkably like the increase
in incidence of cancer in the population out of which it was taken (la). Thus,
we can be reasonably certain that the risk of cancer is increasing exponentially
with age.

In contrast to the exponentially-increasing incidence of cancer with increas-
ing age, individuals identified as having overt cancer have a constant death
risk approximately independent of chronologic age. Therefore, it is a reason-
able argument that changes characterizing the period prior to onset of cancer
may be of many different kinds, each making cancer occurrence more likely,
but the change representing incidence of cancer effects a single abrupt decrease
in life expectancy.

It follows from this reasoning that many of the changes that accompany
aging may be of consequence only as they allow a drastic and irreversible
change into overt disease to take place. In vascular disease, the average
degenerative change in the walls of the artery is of less consequence
than the infarctions or vascular occlusive episodes that destroy peripheral tissue.
Death may occur as a consequence of a random occlusive event, even though
average changes in the arterial structure may be minimal.

Cellular Change and Aging

Cancer is usually considered to be an example of cellular change associated
with aging, very possibly upon a basis of somatic mutational change. It should
be noted that evidence for this is based upon an incidence of cancer expon-
entially increasing with age. While I, too, subscribe to this view, a similar
phenomenon is seen in diabetes melHtus, a disease of deletion of function.
It is quite possible that, in addition to changes in the quahty of cells surviving
Vv'ith time, certain kinds of cells may survive aging with different likehhood.
Shock (6) has evidence, for example, for a decline both in functional quality
and numbers of cells in the kidney with age. It is reasonable to explore further
the effects of dechning numbers of cells with age. Instances, as in the case
of disappearance of islet tissue in diabetes, may be observed in various tissues
and are represented by epilation, appearance of channels in the fingernails,
and disappearance of cells supplying sensory function of various kinds. These
cells may disappear, but we do not know why.

Some Notes on Aging 345

In radiation effect, radiation exposure is related directly to enhancement
of degenerative change, thus simulating the effect of aging. The similarity
may be due in part to the random destruction of cells and partly to the alteration
of function of cells. Within certain cells such as the marrow and the lymphatic
tissue, or in embryologic development, radiation over a wide range of dose
and for several species of mammals destroys approximately three cells out
of every 1000 cells per roentgen of whole-body exposure (7c). At less than lethal
exposures, this random destruction of cells proportionally to radiation exposure
does not have a lasting effect upon the blood-forming tissues, since these cells
rapidly regenerate. However, the average lethal dose of whole-body radiation
exposure is estimated to involve a 50 per cent reduction in these cells. Some-
what the same changes occur in other body cells, the degree being dependent
upon radiation sensitivity. (Some cells are known to be much more resistant
to radiation than blood-forming cells.) The effects of radiation in diminishing
the numbers of cells also seem to be about the same upon mammalian germinal
cells as on blood-forming tissues; in both tissues, approximately two to three
cells are affected per 1000 cells per roentgen. Thus it appears that each roentgen
of exposure to tissues like the blood-forming system, the gonads, and the develop-
ing embryo may have about equal probabiUty of either kilhng the cell directly or
altering its chromosomal structure if it survives. Such changes may be sus-
pected as having a role in inducing age change in the somatic tissues.

Leukemia induction by radiation, as evidenced from the analysis of Court-
Brown and Doll and others (7a,b,c,d), is increased proportionally to radiation
exposure. These changes are such that approximately 50 r of whole-body
exposure produces a frequency of leukemia equal to its natural incidence and the
effect is proportional to dose over a wide range. This is in remarkable agreement
with genetic change in mammals ; here, too, an exposure of 50 r produces approxi-
mately the same number of mutations as occur naturally in one generation.

REFERENCES

la. H. B. Jones: A special consideration of the aging process, disease, and life expectancy.

In: Advances in Biological and Medical Physics, 4, 281-337, ed. by J. H. Lawerence and

C. A. Tobias, Academic Press, Inc., New York (1956).
lb. G. A. Sacher: Reference to aging and antibody levels. Donner Laboratory Lecture,

University of California, Feb., 1957.

2. E. L. Dobson: Homeostatic regulation of body fluid volumes: Role of a blood flow
dependent control mechanism. Fed. Proc. 16, 31 (1957).

3. J. W. Gofman: Serum lipoproteins and the evaluation of atherosclerosis. In: Experi-
mental methods for the evaluation of drugs in various diseases. Ann. N. Y. Acad. Sci. 64,
Art. 4, 590-595 (1956).

4. P. Armitage and R. Doll: The age distribution of cancer and a multistage theory of
carcinogenesis. Brit. J. Cancer 8, 1-12 (1954).

5. L. I. Dublin and H. A. Marks: Mortality among insured overweights in recent years.
6th Annual Meeting, Association of Life Insurance Medical Directors. MetropoUtan Life
Insurance Company, October 1951.

6. N. Shock: Physiological aspects of aging. Symposium on Aging, Amer. Assoc. Advanc.
Sci. Meeting, New York, Dec. 1956.

7a. W. M. Court-Brown and R. Doll: The incidence of leukaemia among the survivors
of the atomic bomb explosion at Hiroshima and Nagasaki. In: The Hazards to Man of
Nuclear and Allied Radiations, 84-87, Medical Research Council, London. (1956).

346 Hardin B. Jones

7b. H. B. Jones: A summary and evaluation of the problem with reference to humans of
radioactive fallout from nuclear detonations. In: Hearings before the Special Sub-
committee on Radiation of the Joint Committee on Atomic Energy, Congress of the U.S.,
June 4-7, 1957, 1116-1136 (also discussion, 1100-1108), Government Printing Office,
Washington (1957).

7c. H. B. Jones: Estimation of effect of radiation upon human health and life span. Proc.
Health Physics Soc. 1, 114-126 (1956).

7d. E. B. Lewis: Leukemia and ionizing radiation. Science 125, 965-974 (1957).

CANCER AS A SPECIAL CASE OF A GENERAL
DEGENERATIVE PROCESS*

Harry Auerbach

Division of Biological and Medical Research,
Argonne National Laboratory, Lemont, Illinois

Abstract — Death rates or life table q^^ values for populations throughout the world tend to
exhibit a sixth power linear relationship with age when plotted on a log-log basis.

It is shown that the total deaths can be broadly separated into chronic degenerative causes
and acute causes, with death from the degenerative causes increasing as the sixth power of
age and death from the acute causes increasing in simple exponential fashion.

In many cancer studies at this laboratory and elsewhere, attempts have been
made to discover the underlying mechanism by which tumors come into exis-
tence. While a great many of these studies have been directed toward describing
the process of carcinogenesis in biological terms, the statistical approach
has also been productive. A recent study at Argonne National Laboratory,
using analysis of vital statistics, indicates that cancer has some characteristics
in common with the degenerative diseases.

The study was suggested by observations of others (1, 2, 3) that when the
logarithm of death rate from cancer (either the total or that involving a specific
site) was plotted against the logarithm of age at death, the result was usually
a straight line. The slope of the line indicated a sixth power relationship,
a fact that has been used to support several theories of carcinogenesis. Another
interesting possibility — that the same linear relationship might be present
in other causes of death — was recognized and investigated in the present study.

The question was first examined by analyzing the United States death rates
for the years 1949-1951. Plots were made on the same log-log basis for several
broad groups of causes of death. Five groups (circulatory system, mahgnant
neoplasms, nervous system and sense organs, respiratory system, and genito-
urinary system) showed a relationship of approximately the sixth power of age
to a marked degree for age thirty and older, with departures from linearity
being restricted to ages under thirty. The sum of these groups gave an almost
perfect linear relationship from the age of thirty upwards (Fig. 1). These
five groups represent the overwhelming majority of the chronic degenerative
causes of death. The remaining three (infective and parasitic diseases, digestive
system, and accidents) which did not show the linear relationship, represent
the acute causes of death.

In order to find out whether the same situation obtained in other countries,
a slightly different method had to be used. Life table data, which are available
for most of the countries of the world, were used in the absence of reliable
specific cause death rate statistics. The value used was q^, the proportion of

* Work performed under the auspices of the U.S. Atomic Energy Commission.

347

348

Harry Auerbach

persons alive at the beginning of the year of the specified age, who die during
that year of all causes. The countries tested were United States, Canada,
Israel (Jewish population), India, Union of South Africa (Asian population),
Brazil, Japan, Portugal, Belgian Congo (African population), Costa Rica,
El Salvador, Argentina, Ceylon, Finland, France and Norway. Similar sixth
power relationships were exhibited by all. Deviations from linearity at

10 000 r

5000 -

2000 -

1000 r ^___

o
o
o
o
o

a:

UJ

a.

<

<

UJ

o

500

200 -

100 -

12.5 17.5 22.5 27.5 32.5 42.5 52.5 62.5 72.5 82.5

37.5 47.5 57.5 675 775 675

AGE

Fig. 1 . Log-log plots showing the relationship of death rate to age in United

States white males (1949-1951) for broad groups of causes of death. Solid lines,

chronic causes ; dotted lines, acute causes.

younger ages were always in the direction of the actual figures being higher
than the extrapolated values.

On the basis of the demonstrated log-log sixth power Hnear plot of the
chronic degenerative diseases, and the nonlinearity of the acute causes of
death, an attempt was made to determine the relationship of acute causes to
chronic degenerative causes in the total death rate. Life table values of q^
for United States wliite males for three periods, 1900-1902, 1929-1931, and
1949-1951, were plotted against age on the log-log basis. The usual departures
from linearity at earher ages were marked in the 1900-1902 period, less so in
the 1929-1931 period, and still less in the 1949-1951 period, but all three curves
tended to merge into a common straight sixth power line at the age of forty

Cancer as a Special Case of a General Degenerative Process

349

and older (Fig. 2). This merging of the three plots at the age of forty and older
demonstrates a well-known fact, that chronic degenerative diseases become
most important as cause of death at the older ages; the values show essentially
no change over the period from 1900-1951. On the other hand, at the earlier
ages, the acute causes constitute almost 100 per cent of the total death rate,
and chronic degenerative diseases represent only a minor fraction. Even though

3UU

-

I
□

1 1 I 1 1 1 I
1900-1902

O

1929-1931 n
1949-1951 n-

200

-

X

X

e

100

~

x_
8 -

X

8 -

50

-

X —

8 -

X

K

or

—

8 "

X

o
o

20

-

D
O

o

DO

10

—

° X -
D o"

D

-

D

° Ox :

5

-

o -

Ox

-

0

X

2

X

1

X *■

1 1 1 1 1 1 J

20

40 60 80 100

AGE

Fig. 2. Log-log plot of 1000^^ against age for United States white males for
1900-1902, 1929-1931, and 1949-1951. Lines are omitted in order to show more
clearly the good fit of the three sets of points on the straight portion of the

curve.

it is apparent that acute causes have been decreasing steadily over the fifty-year
period from 1900-1951, their presence is evident as departures from the straight
line in the plots, with highest values at 1900-1902 and lowest at 1949-1951.
The equation of the straight line for the forty years and older group was
calculated on the assumption that the 1949-1951 values represented the least
effect of acute causes of death on the over-all figures. This was regarded as
giving q^ values for the degenerative causes of death which were then subtracted
from the total q^ values for other countries. The resulting numbers were assumed
to represent death rate attributable to acute causes of death.

The ^a,'s associated with these acute causes of death were found to plot
as a simple exponential increase with age. The slopes were equal for the
countries tested, but the intercepts were different and correlated in a general
way with the levels of public health and medical care in the country concerned.
Plots for four of the countries are shown in Fig. 3a. When the sum of the five
major groups of degenerative diseases was similarly subtracted from the total
causes of death in United States white males 1949-1951, leaving a residue

350

Harry Auerbach

representing the acute causes of death, a similar exponential increase with age
was apparent (Fig. 3b).

It therefore appears that the death process in man can be separated broadly

o
o
o

200

— r

~1 1 1 r ■ 1 ' 1 1 1 ' 1 1

— Mauritius (1942-1946)

—

India (1941-1950) ^

—

FnrmnQn flQ'^fi_l94n^ ^

100

^■"■^ ruiriiuau \\^J^~\^*^^] ^ —

70

-

--

Trinidod (1945-1947) ♦^ ,/*

.

•/ ^' ^^

50

—

30

20

—

y'

-'j;>V-'

10

—

-

^ ,•''' :

~

^

7

—

-

^''

5

—

1 , 1 , 1 , L. J — 1,1,

20

(A)

30

40

50 60
AGE

70

80

90

2000

(B)

Fig. 3. a. Typical semi-log plots of acute portions of 1000^^ (total minus
chronic), for four of the countries tested, b. Semi-log plot of death rate per
100,000 population from acute causes of death (total minus chronic), for United

States white males, 1949-1951.

into chronic degenerative causes and acute causes, with death from the degenera-
tive causes increasing as the sixth power of age and death from the acute
causes increasing in simple exponential fashion.

Total and specific causes of death have previously been fitted by the Gom-
pertzian or semi-log plot (4). However, it would appear from this work that
the degenerative causes increase with age not at a constant rate of increase as
predicted by the Gompertzian, and are therefore better fitted by the log-log

Cancer as a Special Case of a General Degenerative Process 351

plot. On the other hand, the acute causes of death clearly are fitted by the
Gompertzian function.

The presence of the sixth power relationship in a large number of different
situations suggests a general underlying principle. Since we have no knowledge
whatever of what this principle is in biological terms, we can only speculate
that it could be a very general organizational scheme which provides about
five redundant elements within each essential unit. An element might be a
molecule, a cell or organelle (internal structural and functional unit of a cell),
a group of cells, or a whole organ. The essential units might be separate or
overlapping. Carcinogenesis may be a special case of this general degenerative
process.

REFERENCES

1. J. C. Fisher and J. H. Holloman: A hypothesis for the origin of cancer foci. Cancer 4
916-918 (1951).

2. C. O. Nordling: A new theory of the cancer inducing mechanism. Brit. J. Cancer 7,
68-72 (1953).

3. P. Armitage and R. Doll: The age distribution of cancer and a multi-stage theory of
carcinogenesis. Brit. J. Cancer 8, 1-12 (1955).

4. H. B. Jones: A special consideration of the aging process, disease and life expectancy.
In: Advances in Biological and Medical Physics 4, 281-337, ed. by J. H. Lawrence and
C. A. Tobias, Academic Press, New York (1956).

DISCUSSION

Quastler: Two ditTerent functions have been proposed as representative of the course of
the Gompertz function, G{t), for the later part of the life span:

Gi(0 = fli + b^t

Gi{t) = ^2 + ^2 In /.

No author claims that either function is a perfect fit even for a limited interval. Still, it is worth
showing that the difference between the two formulae is very small over a limited range. Let
the center of this range be /*; then

and for small values of A//r*,

AGi = ±^1 Ar

.c.^*.,n(q^')

b.

AC,

±^A'

It is said that the mortality rate (in the later part of the life span) doubles about every 8.5 years;
hence b^ ■--= 0.082; and that it increases approximately with the 5.2th power of age, or b., = 5.2.
These two values are compatible around /* = 63 years, which characterizes the neighborhood
in which both are claimed to be valid.

Yockey: If one plots survival data as Auerbach does, one obtains curves which corre-
spond to the Gompertz function for man and for many out bred wild-type organisms. For
some in bred strains, particularly those which have a genetic defect, the survival curve may be
of the form log ///q = — oc/'-.

In Fig. 3 of my paper in Part V, I have plotted log ///o against the square of the age for
several strains of mice. The dilute brown strain reported by Murray and Hoffman follows the

352 Harry Auerbach

above equation quite closely for almost the entire life span, excluding only the first few months.
On the other hand the DBFi hybrids (dilute brown female x C57 male) exhibit the Gompertz
function as may be seen in Fig. 5 of that paper.

The dilute brown strain is characterized by a high rate of mammary cancer, while the hybrid
has a low rate. The Marsh albino is another high-cancer-rate strain, which, although it does
not have a survival curve of the form log ///o = —a.X^, does, when crossed with the C57, produce
hybrids with a much longer life span. The survival curve is of the Gompvertz type. Changes in
the genetic characteristics associated with hybridization do not just change the constants of an
equation of the Gompertz form, but rather the survivorship curve is of a different form.

FREE RADICALS AS A POSSIBLE CAUSE OF
MUTATIONS AND CANCER*

Walter Gordy

Department of Physics, Duke University,
Durham, North Carolina

Abstract — The hypothesis set forth in this note is that free radicals produced outside the body
may find their way into the body and produce mutations and/or cancer. The evidence for
support of this hypothesis is the presence of radicals as detected by microwave paramagnetic
resonance in several carcinogenic agents, and the fact that free radicals are now recognized
by radiobiologists as being responsible for a large portion of mutagenic and carcinogenic
effects of ionizing radiations.

Free radicals may be loosely defined as molecular fragments which are charac-
terized by a free valence or an unpaired electron. Because of their highly
reactive nature they are not thought to exist in any significant quantity within
the organic matter about us, although they are often postulated as important,
transient intermediaries in organic and biochemical reactions. Within the
past few years, however, microwave spectroscopists (I) have shown that free
radicals can be readily detected in organic matter which has been subjected
to some form of pre-treatment that can break chemical bonds. Such free
radicals are produced in the combustion of organic matter — wood, paper,
tobacco, coal, oil. They are produced in excessively cooked foods such as
charred steak or scorched toast. They are produced in various forms of matter
by ultraviolet light, by x-rays, or by atomic radiation.

The radicals are detected through their resonant absorption of microwave
or radio-wave energy when they are placed in a magnetic field of the proper
strength. This type of absorption spectrum is known as paramagnetic resonance
or as electron spin resonance (2). Electrons in normal chemical bonds are
paired in such a manner that their spins and magnetic moments cancel, and
hence they exhibit no paramagnetic absorption. Paramagnetic resonance
occurs only for the unpaired electrons of the disrupted chemical bond. It
therefore provides a specific and powerful means of detecting and studying
reactive free radicals within organic matter without interfering absorption or
confusing signals from the normal stable molecules of the matter.

The surprising new evidence from paramagnetic resonance is not that free
radicals can be easily produced but that they become trapped and stabiUzed
and can be transported from place to place, even through the air within tiny
particles of soUd matter such as those in smoke. The nature of neither the
radicals nor their cages is yet known definitely, although some radicals produced

* This research was supported by the United States Air Force through the Air Force Office
of Scientific Research of the Air Research and Development Command under contract
No. AF18(600)-497. Reproduction in whole or in part is permitted for any purpose of the
United States Government.

353

354 Walter Gordy

in amino acids and proteins by x-irradiation have been tentatively identified
from the fine structure of their microwave resonance patterns (3). The infor-
mation pertinent to the present discussion is that organic radicals produced
by physical forces such as heat or irradiation outside the body can be taken
into the body through the processes of eating, smoking, or normal breathing,
or even by diffusion through the skin. Once inside the body, these radicals
may themselves penetrate the cells or they may be converted to other radicals
which do so. A radical containing an odd number of electrons must, in effect,
meet and react with another radical before its free valence or uncancelled
electronic moment is nullified. If it reacts with a normal organic molecule
(which has an even number of electrons), another radical is produced. In
fact, it is just this odd character which suggests that a lone radical might start
a significant chain of events within a cell.

Many types of radicals which have been detected by microwave resonance
are stabilized mainly within solid particles of matter. Normal chewing and
mixing of food with saliva would tend to destroy them. This destruction may
not always be complete, however. We have made tests which show that ordinary
chewing of charred toast, beef, and other foods does not entirely kill the reso-
nance signal of the radicals. Extremely small solid particles carrying radicals
may diffuse into the tissues of the skin, stomach, or lungs where they would
gradually dissolve and perhaps bring about damaging reactions as their radicals
are released. Furthermore, these radicals are possibly stable in certain organic
solvents which dissolve the solid cages and 'float' the individual radicals
into the tissue. Such a solvent might assist in the production of cancer without
being a primary cause of it. Strong resonances, like that shown in Fig. 1 for
tobacco tar, are found for wood tar, coal tar, and other tars. H. Shields and
the author have dissolved tars in organic solvents including benzene, acetone,
and croton oil, and have found that the resonance of the tar radical remained
strong. The role of agents such as croton oil, which are not themselves carcino-
genic agents but which augment the effects of certain carcinogenic agents,
may be that of facilitating the entrance of carcinogenic radicals into the body.

Radiobiology experiments (4) indicate that much of the effect of ionizing
radiations on the cells themselves may be indirect; that is, irradiation produces
a free radical in one part of the cell which later migrates to a more vital part
of the cell where it may react to bring about a mutation. Alternately, the first
radical formed may react to form a second radical, or a third, which finally
causes the mutation. In particular, OH and OOH radicals have been postulated
as important intermediaries in radiation damage. Of course a mutation might
be brought about by a so-called direct hit, but indirect effects also appear to
have significant consequences. We are proposing an extension of the indirect
effects to include cases where the primary irradiation occurs entirely outside
the injured body, in our laboratory, microwave evidence has been obtained
to indicate that hydrocarbon radicals, R, produced by irradiation, are often
converted to peroxide radicals, ROO, where they come in contact with oxygen.
In the tissue such radicals might be further converted to the OH or OOH
radicals, already under suspicion by radiobiologists.

The striking evidence which prompted this communication is the abundant
paramagnetic resonance data for the existence of free radicals in many agents

y -.-X^

TOBACCO

TAR

~ *•■ 'A

.V ■

CHIMNEY
SOOT

J

SCORCHED
BREAD

X-IRRADIATED
BREAD

Fig. 1. Microwave electron spin resonances of radicals in some common
substances. The tobacco tar was taken from an old pipe stem. Coal, wood, and
other tars give similar resonances. The chimney soot was taken from the flue of
an oil-burning furnace. Similar resonances were obtained for soot taken from the
exhaust pipe of an automobile and from a wood-burning fireplace. Ordinary
bread, unscorched and not irradiated, gave no detectable resonance in the same

spectrometer.

to face p. 354

Free Radicals as a Possible Cause of Mutations and Cancer 355

known or suspected to cause cancer. Among these are cigarette smoke, tobacco
tars, various other tars, exhaust fumes from cars, smoke from home furnaces
or industrial plants, and charred foods. I shall not attempt to cite the literature
references for the various evidences that these are carcinogenic agents. It is
well known that x-rays and other ionizing radiations can cause genetic mutations
and are likewise carcinogenic agents. It is now well known from electron spin
resonance that these ionizing radiations also produce radicals which in many
biochemical solids (3) (including various proteins, carbohydrates, and fats)
persist for long periods after the irradiation.

The carcinogenic effects of severe chemicals which produce burns of the
flesh may possibly result from subsequent diffusion into the healthy cells of
free radicals produced in the original, more violent chemical reaction causing
the burn. It is known that a burn of the flesh from any source of heat has
carcinogenic and mutagenic effects. Since we now know that the charring of any
organic matter produces long-lived radicals, it seems probable that some of
the carcinogenic and mutagenic effects may result from secondary activity
of radicals produced by the burn. Of course chromosome linkages are broken
as direct effects of the heat, but it seems probable that most of the cells exposed
to the elevated temperatures in the burned area would be killed.

Certainly many known carcinogenic chemicals are not radicals, and I
do not suggest that all cancer may be caused by radicals. However, many
chemicals recognized as carcinogenic agents, not themselves radicals, may
exert their carcinogenic activity indirectly through the production of radicals
within the body. This would be analogous to the indirect effects of ionizing
radiations already mentioned and might account for the seemingly parallel
action of certain chemicals with ionizing radiations which has led to their being
caUed radiomimetic chemicals (5). Many carcinogenic chemicals are large,
aromatic, polycyclic hydrocarbons from which it would seem that free radicals
might be easily produced.

The radicals are not convicted from 'guilt by association' with carcinogenic
agents. Our proposal is not intended to be accepted per se, but is offered as a
working hypothesis which can be put to rather objective test because of the
powerful method of electron spin resonance now available for detection of
radicals. That certain radicals are likely to be carcinogenic agents, or that
some types can lead to genetic mutations, probably will not be questioned.
Others, possibly some or all of those which are sufficiently stable in organic
matter to be detected with paramagnetic resonance, may be perfectly harmless.
I do not therefore recommend that we become suddenly alarmed about the
radicals around us. I do think there is some justification for the careful study
of these radicals which can be produced, transported, and taken into the body
so easily. This study is made easier by the powerful new method of paramagnetic
resonance for detection of such radicals.

If externally produced radicals are indeed dangerous, we can fortunately
detect and avoid most of the ones we now are eating, breathing, or rubbing
into our skins. Ingram (1) has shown that the number of radicals produced
by heating organic matter is a sensitive function of temperature. Tests in our
laboratory on common foods such as meat and bread show that those cooked
in a normal manner have no detectable resonances or only very weak resonances,

356 Walter Gordy

whereas burned food, scorched toast, charred steak, etc., have strong radical
resonances. The temperature at which a cigarette is burned should have
significant effect upon the number of radicals produced, although it may be
impossible to produce smoke without producing radicals. If it proves harmful,
we do not have to preserve our food by atomic irradiation.

Acknowledgement — Several of my students, Howard Shields, Harvey N.
Rexroad, Frank Patten, and Gene McCormick, assisted with microwave
magnetic resonance experiments in connection with the hypothesis proposed
here. I am indebted to my wife for encouragement and for assistance with
library reference work.

REFERENCES

1 . See, for example, comments by :

G. E. Pake, J. E. Ingram, J. Cambrisson, and J. Uebersfeld, R. Livingston, W. Gordy
et al.: Disc. Faraday Soc. 19, 179, 184 (1955).

2. General treatments of the subject are given in:

W. Gordy, W. V. Smith, and R. F. Trambarulo: Microwave Spectroscopy, Chap. 5,
J. WUey and Sons, New York (1953).

W. Gordy: Microwave and radio-frequency spectroscopy. In: Techniques of Organic
Chemistry, Vol. 9, 71-185, ed. by A. Weissberger and W. West, Interscience, New York
(1956). D. J. E. Ingram: Spectroscopy at Radio and Microwave Frequencies, Butterworths,
London (1956).

3. W. Gordy, W. B. Ard, and H. Shields: Microwave spectroscopy of biological substances.
I. Paramagnetic resonance in x-irradiated peptides; and 11. Paramagnetic resonance
in x-irradiated carboxylic and hydroxy acids. Proc. Nat. Acad. Sci., Wash. 41, 983-1004
(1955).

4. E. C. Evans: Effects of hydrogen peroxide produced in the medium by radiation on
spermatozoa of Arbocia punctulata. Biol. Bull. 92, 99-109 (1947).

O. Wyss et al. : Role of peroxide in the biological effects of irradiated broth. /. Bact. 56,

51-57 (1948).

W. M. Dale: Some aspects of the biochemical effects of ionizing radiations. In:

Symposium on Radiobiology : The Basic Aspects of Radiation Effects on Living Systems,

177-178, ed. by J. J. Nickson, J. Wiley, New York (1952).

R. E. Zirkle: Speculations on cellular actions of radiations. In: Symposium on

Radiobiology: The Basic Aspects of Radiation Effects on Living Systems, 333-356, ed. by

J. J. Nickson, J. Wiley, New York (1952).

5. A. Haddow: Comparative studies of the biological effects of ionizing radiation and of
radiomimetic chemical agents. Proc. Int. Conf. Peaceful Uses of Atomic Energy, 11
213-218, United Nations, New York (1956).

PART VI

INFORMATION NETWORKS

A PROBABILISTIC MODEL FOR MORPHOGENESIS*

Murray Eden

Laboratory of Technical Development, National Heart Institute,
National Institutes of Health, Bethesda 14, Maryland

Abstract — A program has been outlined for establishing relationships between the form of an
organism and the minimal information content of the germ cell from which the organism was
derived. A simple two-dimensional model has been chosen in order to explore the feasibility
of such a program. A suitable information measure has been defined for this model and
computations of information have been made for small aggregates of cells, as well as estimates
for larger aggregates.

An arbitrary growth process has been formulated which is analogous to an assignment of
virtually no information to the germ cell. The properties of this growth process have been
studied and suggest that even such minimal information content in the germ cell is sufficient to
specify the over-all form of the organism with high probability after a certain number of
divisions have taken place. Possible ways of extending the model and increasing its embryo-
logical relevance have been suggested.

One of the problems that has been touched in this symposium is the particularly
elusive subject that has been with biology since its beginnings as a science;
that is, the general relationship between function and form and between growth
and form. In the particular terms of discourse of this symposium the question
might be phrased in this way: 'What is the minimal amount of information
that is required in a fertilized egg, so that after a certain number of divisions
and a certain length of time the egg will have developed into an organism that
is recognizable as being a member of a certain species?'

A number of workers have estimated the information content of biological
objects. Dancoff and Quastler (1) computed values of information content
relative to four different models; on the basis of atomic orientation, molecular
structure, chromosome volume and a genotype catalogue. These authors were
careful to specify the limitations of their computations. They write, 'We have
arrived, by very tentative methods, to the result that the essential complexity
of a single cell and of a whole man are both not more than 10^^ nor less than
10^ bits; this is an extremely coarse estimate, but is better than no estimate
at all.' LiNSCHiTZ estimated the 'physical entropy' of a bacterial cell as being
10^^ bits (2) and Yockey (3) has computed the information content of DNA
based on its molecular size and on a postulated cryptographic relation between
proteins and nucleic acids. Most of the values obtained have been very large,
and one would presume that they are large enough to describe adequately
the observable properties of a living organism, it may be that the growing
organism requires a lot less information in the germ cell than is indicated by

* The work presented here was begun during the tenure of an United States Public Health
Service Special Fellowship in the Department of Mathematics, Princeton University, Princeton,
New Jersey.

359

360 Murray Eden

estimates made on a molecular level. In the terminology of communication
theory, the redundancy of the source m.ay be extremely high. An examination
of the literature indicates that there is some support for this view. Studies of
properties of monozygotic twins have special relevance to this point. It may
be noted in passing that the existence of twins or high multiplets derived from
a single germ cell is in itself strong evidence of the presence of at least a small
amount of redundancy in the germ cell (4). Monozygotic twins presumably
arise from an identical genetic background and they develop into mature
organisms that can be compared with regard to certain of their properties.

As long ago as 1876 Galton (5) studied what he called 'The History of
Twins as a Criterion of the Relative Power of Nature and Nurture'. Newman,
in a long series of pubhcations begun in 1912 (6) has studied both human twins
and armadillo quadruplets. The nine-banded armadillo is exceptional in that
the female gives birth to monozygotic quadruplets. The scales or scutes on
the back of an armadillo are regular and easily counted, even in the fetus.
Newman prepared a fairly large statistical study on these quadruplets and he
found a correlation coefficient for fifty-six sets of male quadruplets of 0.93 and
for fifty-nine sets of females of 0.91. Still there was no identity in the scute counts.

Work of a similar character has been done by Hancock (7) on mono-
zygotic calf twins, and by Went (8) on genetically identical seedlings. The
conclusion that may be reached on the basis of studies such as these is that
even when embryonic growth starts from genetically isomorphic cells, by the
time the organism has developed to maturity there is, it is true, a great similarity
in the large, but at the cellular level there is very httle similarity.

This would suggest that, aside from the genetic signals or instructions,
there are certain statistical variables or environmental factors operating that
permit the development of an organism to an ultimately recognizable form
but require a good deal less information than would be required if every element
in the structure of the organism had to be specified with microscopic exactitude.

An attempt to construct a theoretical model was made by Turing (9),
who in 1952 posed the following problem. Given a group of identical cells
arranged in some symmetrical configuration, e.g. a ring or a sphere; assume
that each cell contains the same concentrations of certain chemical substrates
and that the laws of diffusion and other classical physical laws hold. How
can one devise a procedure whereby this homogeneous collection of cells
could develop and differentiate so as to produce asymmetric or periodic forms?

Turing proposed accomplishing this in a way that does not do too much
violence to biological understanding. He postulated certain hypothetical
chemical reactions involving substrate, inteiTnediates and enzymes, and built
into this set of hypothetical reactions appropriate reaction rate constants so
that the resulting reaction system would exhibit a special property: namely,
that statistical fluctuations in the concentrations of chemical components
in various cells would increase in amplitude so as to produce an instability
and result in an asymmetric form or a form exhibiting periodicity. By use of
a specific example he showed how a ring of cells might grow into something
more or less petal-shaped with three or four lobes or petals. In another example
he developed a mottled pattern on a two-dimensional surface.

The model described below is entirely mathematical; physical or chemical

A Probabilistic Model for Morphogenesis 361

phenomena are not considered. The principal concern of this model is the
domain of forms an idealized organism can assume and the likelihood of an
egg developing into such a form. Tlie mathematics employed is elementary,
and as in so much of combinatorial analysis, it is ad hoc*. The attempt to
establish a relationship between the form of an organism and the information
content of the germ cell ancestor is treated here from a point of view that has
some resemblance to that of statistical mechanics.

It is assumed here that there are only a finite number of different kinds
of cells in any organism and a finite number of cells of each kind. We neglect
the dynamic processes occurring continuously in an organism: changes within
cells, the migration and movements of cells, the death of certain cells and the
cleavage or maturation of others. If there is some well-defined way of des-
cribing the orientation of each cell in any organism relative to the other cells
in that organism or relative to some arbitrary system of coordinates, then it
is possible, in theory at least, to enumerate all the possible ways of arranging
cells into different configurations. Some of these arrangements would be
recognizable organisms, the overwhelming majority would not. In any case,
these objects, both the recognizable and otherwise, are elements of the set
of all possible configurations. This procedure might represent a means of
defining a given species by certain restrictions on the possible orientations
of cells and thus to identify the given species with a well defined subset of all
possible configurations.

Most multicellular organisms can be said to arise from a single cell resulting
from the fusion of two germ cells. It is true that there are certain biological
objects, of which the slime-mold is a notable example, which take their form
from the migration, coalescence and specialization of a number of free-living
cells. However, such organisms are uncommon and will not be considered
further.

This single germ cell divides into two cells and these cells will divide further
and so on until maturity. Throughout the course of this branching process
the growing organism will pass through a sequence of configurations, each
of which is an element in the set of all possible configurations. If there is a f:

relationship between successive configurations which is recursive, then a
generating function can be constructed to describe the branching process.
Generating functions are useful because they may afford a means of assigning
a probability to each possible configuration. The actual model chosen for
investigation has been simplified to the extent that its relation to biological
reality is largely impressionistic. Its justification is heuristic, for the study of
relatively simple systems may suggest methods of approaching the real systems
which are so very much more complex.

The element of the model is called a cell. All cells are considered to be
identical. We restrict ourselves to the consideration of arrangements of cells
in two dimensions. The shape of the individual cell is unspecified (they may

* I should like to take this opportunity to express my debt to a number of mathematicians
both at Princeton and at the Institute for Advanced Study with whom I have discussed this
problem; and in particular to Professor Valentine Bargmann, Professor William Feller, ij

Dr Hale Trotter and Dr Norman Shapiro for their stimulation and suggestions. Needless to '

say, the results and errors are my own.

362 Murray Eden

be thought of as squares), but their positions are restricted to the points of a
(two-dimensional) square lattice.

Any arrangement of cells on the lattice will be called a configuration, i.e.
an arrangement of k cells will be called a /c-configuration. If each cell in a
configuration is adjacent to at least one other cell then such a configuration
will be called connected. We will be interested only in connected configurations.
The set of all possible (connected) A'-configurations will be called the k-array.
The number of distinct ^-configurations, i.e. configurations that are not iso-
morphic under translations, reflections and rotations, will be called the order
of the ^'-array, symbolized N[k].

Each cell will have four edges, corresponding to the four nearest-neighbor
lattice points. An edge will be called open if its corresponding lattice point
is unoccupied by a cell, otherwise it is covered. Each cell also has four corners
corresponding to points equidistant to four lattice points. A corner will be
called an inner corner if it is at the center of a cluster of four cells.

The problem of enumerating all possible A'-configurations is one that has,
as yet, no easy solution. Similar combinatorial problems, arising in physics
in what is called the order-disorder problem, have been considered by a large
number of workers. Of particular relevance to the above problem is the work
of Van der Waerden (10), Kac and Ward (11), and Humans and de Boer (12).

Certain bounds can be set for the order of the A-array. We can determine
a lower bound for N[k] by enumerating all members of a certain subset of
[k], i.e. the subset in which all save two cells have two edges covered. Two
cells, i.e. the ends, have only one edge covered. It is even easier to enumerate
a smaller subset of this 'two-ended' set. Consider an arbitrary lattice point as
the origin of a random walk. Limit the choices for the first step and each
succeeding step in this random walk to lattice points, either above or to the
right. The k^^^ cell will be added after k — 1 steps are taken. At each point
there are exactly two possible choices, so that in all we have produced 2*^^~^
configurations. Since each configuration (except those that exhibit internal
symmetry, in any case, a small fraction) occurs four times in 2''"^ configurations,
the number of distinct configurations is 2^~^. The restriction to two choice
points is dictated by the necessity of avoiding cross-overs in the random walk.
Obviously, each cross-over would have the effect of decreasing the number
of occupied lattice points by one.

However, if the random walk is permitted three choice points, i.e. above,
to the right and to the left, one can estimate the number of such walks of length,
k, which contain no point adjacent to more than two occupied sites*. Such
walks are isomorphic to the set of 'two-ended' /c-configurations. This estimate
was found to be very close to (1 + \/^)'^~^- I^ consequence the lower bound
for the number of A'-configurations may be raised to this value.

Upper bounds can also be computed using a somewhat diff'erent combina-
torial technique. Consider any A-configuration. Arbitrarily choose one cell
as the origin, and also arbitrarily choose one of the four possible orientations
of the lattice. Identify this cell by 1 if it has a cell beneath, otherwise 0. Further,
this cell may have a cell adjacent to it on the left; if so, assign a 1 to the next

* The mathematical details of the results presented in the text will be the subject of a
separate publication.

A Probabilistic Model for Morphogenesis

363

digit in the identification; a cell above it, and a cell to the right. Thus, tiie
first cell Q in a configuration is identified by four binary digits. Next, identify
the adjacent cell which contributed the first T in the designation of the first
cell, as the second cell Cg, the second '1', as the third cell, C3, etc. Reorient
the lattice so that the first cell is beneath the second. We construct the desig-
nation number of the second cell as we did for the first. However, this time
there are only three binary digits required since the adjacency of C^ to Q is
already determined. Any of the cells adjacent to C^ that have not yet been
assigned a position in the order can be given one now in a perfectly well-defined
way. It is obvious that this procedure can be continued until designation
numbers have been obtained for each cell in the configuration. We thus have
a well-defined word in 3^ + 1 binary digits and a possible 2^''+^ such words.

Since the initial cell and the orientation of the lattice were chosen arbitrarily,
each district configuration (as usual, excepting those exhibiting some internal
symmetry) will be given by Ak such words. Thus an upper bound for TV [A] is
23^-VA:.

It is easily ascertained that a very large proportion of the 2^^^+^ words do
not represent A'-configurations. These forbidden words arise for essentially
the same reason that the unrestricted random walk on the square lattice fails to
serve as an estimate of two-ended configurations. No simple relations have
been found that will indicate which of the 2^'^"+^ words are permissible. However,
one can generate a random sample of these words by a Monte Carlo procedure
and arrive at a statistic that suggests that a satisfactory estimate of N[k'\ is
in the neighborhood of 2-^.

Values of the bounds and the estimate mentioned above have been com-
puted for certain values of k (Table I). This serves to give some idea of the

Table I. Estimate of Configurations for Large Arrays

[k\

Lower bound

Upper bound

Estimate

(1 + V2Y

(2='^)

(22.)

10

2.2 X W

2.4 X 10*

5.8 X 10^

16

4.2 X 10^

6.3 X 10»

2.5 X 101

25

1.1 X 10*

8 X 10^'

6 X 101-

100

1.7 X 101*

3 X 1085

6 X 10"

1000

1.7 X lO^'i

3 X 10««*

6 X lO^"^

magnitudes one might expect for configurations of large numbers of cells. So
long as the number of cells is small, the distinct configurations can be exhibited
with relative ease. This has been done up to A: = 8 and the results are given
in Table II.

In order to establish the assignment of a probability to each of these con-
figurations, a simple and nearly featureless generating function was adopted.
Starting with a single cell, equal probability is assigned to each of the four
possible two-celled configurations. These are all isomorphic. This two-celled
configuration has six open edges. Equal probabilities are assigned to each

364

Murray Eden

edge. This lime, of the six three-celled configurations obtained by adjoining
a cell to an open edge, four are isomorphic to one of two three-celled configura-
tions, and two to the other. Thus, the probability of the first three-celled
configuration is 0.67 and the other 0.33. This procedure can be carried out
indefinitely, in each case assigning equal weight to each open edge and adjoining
a single cell at a time.

Table II. Number of Configurations in Each Array

k

N[k]

N[k]
N[k - 1]

1

1

2

1

1

3

2

2

4

5

2.5

5

12

2.4

6

35

2.9

7

108

3.1

8

367

3.4

While there is no biological organism that exhibits this pattern of growth,
it has certain features in common with some tissue cultures, bacterial colonies
or tumors, in that the cells are more or less undifferentiated. Growth in such

"^-12 7^-10 7rM2 7r^I2 7r-I2 7r=l2 7M4

(1) ^ (I) ^ (2) Ug (1) 4^ (I) ^^ (2) ^ (3) d^
0I1S9 0.0883 0.0817 0.0761 0.0594 0.0511 0.0250

(1) n^ Ocfim '"

7r=I4 Tr=l4

'^' a&n <«' crrxfl <» ^ '^' Bifi

0.0229 0.0203 0.0194 0.0125 0.0111 0.0104 0.00555

TT^U

(I)

6- ARRAY

Fig. 1

biological objects has no preferential direction except that it is peripheral,
a condition due most likely to the fact that diffusion of nutrient is too slow to
permit any large number of cell divisions in the interior of the growth.

Exact computations have been carried out for the probability associated
with each A'-configuration up to k = 8. As before, computations for k > S,
while easily performed in principle, are prohibitively time-consuming. The
configurations for k = 6, 7, 8 and their associated probabilities are assembled
in Fig. 1, 2, 3.

An unanticipated property of the particular generating function employed
was revealed as a consequence of these exact computations. It will be observed
in Fig. 1 to 3 that configurations have been grouped so that each different
value of probability is recorded next to a single prototype configuration.

A Probabilistic Model for Morphogenesis

365

These configurations bearing llic same probability, while they are not isomorphic
in the sense mentioned earlier, have an important property in common. If
each configuration is represented by a graph (13), identifying the cells as nodes

ir, 12 7r_ 12 TT-U ■"•-14 TT-M T'-M '"'U

s s

(2) te (') ft ") ^ (1) t# (1) E§° (2) cfe <') S
9.2642 6 SS30 4.4603 3.S67S 3.3181 3.1906 2.6296

TT- 14 V 14 TT^U Tr=14 TT-H Tr^\t TT^IS

(» #3 (')[ffl3^ Wdffi^ <5)cnrffl (3)%° (') ^ (') P^

25119 2.3261 18499 1.2956 0.7837 0.7730 0.5952

7r= 16 77- 16 7r.i6 7r= 16 '"■=16 "■ 16

'" ^ '" ^' '^''rrftTT. '" 4™' ""rftrrn "' rfWi ^ ''' ^n^

0.5357 0.5060 0.4067 0.3869 0.3075 0.2976 0.2679

TT 16 V 16 TT 16 7r=16 TT; 16 IT 16

S „ S rn rn S S S

(') °#^ (i9)ftTTTn (ugi™ (I) H (luElnfl

H I I I I II
0.2530 0.1587 0.1554 0.1488 0 0794 0.0397

7- ARRAY
Fig. 2

"■=12 rr=i4 ir=u ir=i4 v,u ir=u w-i4 in^u itm ir^n v^u

(">& <'>^ ("^ <«^ 0)^ ">^ ("te^ 0)^ (»fe (l)ffiffl (4)rT4ffl

5-12 3.50 3JS 3J4 3.01 2.61 2J5 2J« 2.19 1.12

■ir=i4 77=14 Tr-14 ir=i4 vm ir=u 7r=i4 v-}i itM ■"■=16

1.66
"■=16

(I)

(1)

1.40 1.30

(1)

"'cfflD '"

(2)

rffFP

(2)

(2)

(I)

(2)

(3)

1.127 1.094 0.9462 0.6456 0.7292 0,7257 0.6841

Wz. 16 7r=)6 ir=i6 Tii6 TTiii Tr=i6 ir=]i

S

<«a& '"^'"'d* '« cP "'-f "'c#^

(3)

(5)

16 _7r=i6 ir=i6

$,

(I)

(IS)

7r=i6
w>cflffl

0.62719 0.6093 0.5960 0J77O 0.5280 OJ20i 0.4716 0.4340 0.3672 0.3480 0.3364

IT: 16 Tr=u "=1« "^16 ir-l« "=i< "^16 ir=.M ir^M itm "=16

s s „„ p n PS

(2)rTffP (l)'#^ (lO)rrTfFP (1) ^ (2) rrFRn (1) #5^ 112) rrrrfB (2) F#P (4)

0^040 0l2920 0J644 0JZ79 02170 Ol20K1 0.1707 0.1649 0.162S ai520 0.I4S8

"=14 "^16 "=14 "=16 V^U ■"=16 "=16 ■"-16 '"=16 "=.16 "-16

(1) ^^ (8) ^ (I) ^' (1) °f°'(13)nflg3 (3) ^ 0) !§: '(15)B^ (i) CdgJ (4) ^ (3) ^ '

ai42l 0.1190 0.1166 0.1116 0.1073 aiOtO 0.1642 0.0043 0.0613 0.0769 0.0744

T»I6 ir=I6 77^16 7r=16 "=16

osi

TT-U ir^M -77=16 ir=16 '"=16 ■"=16

rrrWl (SWrrftrfl (D "^ (2) S=™ (37)^TTTf^ (3) rftrfll (5) Ftfffl 0) M (52) illB O §™^ 0) g^

aOMS 0.0546 0.0531 0.04216 0.0391 0.034« 0.0394 0.019* O.Om 0.0196 0.0192

Tml6 "--16

aoo** 0M496 8 — ARRAY

Fig. 3

and the covered edges as branches between nodes*, it will be seen that all
configurations represented by the same graph have the same probability.
Certain other properties are also suggested by consideration of these small
'organisms'. The configurations with the largest number of inner cornersf are

* This representation is analogous to the graph obtained by identifying countries on a map
with nodes and common frontiers between countries with branches.

t We can use the perimeter, n, i.e. the number of open edges, instead of the inner corner, C,
in describing the property in question since tt ^ 2{k i- 1 — C).

366

Murray Eden

most probable. It also appears that configurations with many short branches
are more probable than those with a few long branches. Finally, it is also
observed that as k increases, a decreasingly small fraction of the A'-array carries
the weight of probability. This is shown in Fig. 4 and in Table III. The k-
configurations have been ranked in order of decreasing probability, that is,

.2 .3 .4 .5 .6

fractional rank
Fig, 4

.8

1.0

Table III.

Probability of

k

Probability of

configuration

of rank 1

least probable
asymmetrical
configuration

Rank at
T.p, = 0.5

Fractional

rank at
•Lp, = 0.5

1

1.00

1.00

2

1.00

1.00

—

—

3

.67

.33

—

—

4

.33

.167

—

—

5

.40

.067

2

.167

6

.12

.011

6

.169

7

.093

.0016

12

.11

8

.051

.0002

24

.067

10

.021

2 ^ 10-«

103

.020

16

.0015

3 X 10-1^

6400

.00002

the most probable configuration was designated 1, the next most probable 2, and
so on, and the cumulative probability (as ordinate) was plotted against the
rank divided by N[k] (number of distinct A'-configurations) as abscissa.

Fig. 5

o face p. 367

A Probabilistic Model for Morphogenesis

367

Since any direct extension of the model to larger values of ^ does not appear
feasible, another procedure was adopted. Starting as before from a single cell,
the edges were numbered, a random number table (14) was consulted to find
a number equal to or less than 4, and then a cell was adjoined to the appro-
priately numbered edge. The open edges were renumbered, another number
equal to or less than the number of open edges obtained from the table, and
a new cell adjoined. In this way samples of 1000 10-configurations and
16-configurations were constructed. A few larger configurations were prepared
by this procedure. One such containing 200 cells is shown in Fig. 5.

In the case of the sample of the 10-array, one configuration was obtained
twenty-two times. Its probability was computed by the exact procedure des-
cribed above and found to be 2.06 per cent. All the configurations containing
four inner corners (77-= 16) (maximal for /: = 10) appeared more than ten
times each. With very few exceptions, in order of occurrence, there followed
the configurations with tt = 18, 20, 22. There were eighty-three occurrences
with 77 = 24 (no inner corners), but none of these was two-ended. Although it
was impossible to enumerate all the configurations, by judicious use of the
equality of probabihties found in configurations with the same graph, estimates
were made of the numbers of configurations of each kind up to rank 1150.
The data were plotted in Fig. 4. It can be seen that the portion of curve
obtainable is very close to the ordinate axis.

A similar procedure was followed in the case of the sample of the 16-array,
Here, estimates v^ere considerably poorer, but the same general features were
revealed (Table IV). The thirty-two possible configurations with 77 = 18

Table IV. Summary

of \6-airay

Monte Carlo Sample

Perimeter

Configura-

Cumulative

Fractional

E(pd

tions

occurrence

rank

xlO*

16

1

0

18

32

.028

1 X 10-«

8.75

20

569

.202

2 X 10-5

3.00

22

6250

.455

4 X 10-*

.40

24

27,300

.728

1.2 X 10-3

.16

26

148,500

.907

6.6 X 10-=»

.012

28

—

.967

30

—

.995

32

—

1.000

34

—

1.000

appeared twenty-eight times, or an expectation of occurrence of a particular
configuration of 8.75 x 10^*. (It is assumed that all configurations with
identical values of tt have approximately equal probabilities of occurrence.)
it was estimated that the expectation of occurrence of a configuration of 77 = 20
was 3 X 10-4; 77 = 22, 4 x 10"^; and 77 = 24, 1.6 X 10~^ In this sample of
1000 there were only five occurrences of configurations with 77 = 32, and no
occurrences of 77 = 34, although a low estimate of the number of distinct

368 Murray Eden

16-configurations with tt ~ 34 would be 250,000. These estimations are plotted
on the same figure as the computations for configurations of up to eight cells
(Fig. 4). It can be seen that none of the estimates obtainable up to a cumulative
probability of 0.907 can be distinguished from the ordinate axis.

The probability of the most probable A-configuration and of the least
probable A-configuration are presented in Table III, for several values of Ar. It
will be noted that the probability of the most probable configuration decreases
slowly with increasing k. While there is no practical way to make exact com-
putations of probability for large values of k, it may be conjectured that the
probabiUty of the first ranked configuration is proportional to 1/2^'. On the
other hand, the probability of the configurations of the lowest ranks falls very
rapidly*. As with the estimates of the number of configurations, exact solutions
for probability are readily obtained only for the two-ended configurations.
As was noted earlier the number of such forms approximates (1 + V^)'' but the
probability associated with each such form is 2^//c !

Information theory (15) suggests methods of defining appropriate measures
for the distribution of probabilities as a function of A'. If 7V[A'] is the number of
distinct configurations containing k cells each, the maximal uncertainty for the
A'-array can be defined as i/^." = — Ig A^[A']t. In a similar manner, an uncer-
tainty can be defined for an arbitrary generating function, Gj, considered as an

N[k]

information source. H{G^^ = ~^Pi Ig/'o ^^ which /?j is the probability that

i = l

the generating function G^ will terminate after k — 1 adjunctions in configura-
tion oj,. Further, a measure of relatedness (16) may be defined as I{Gj^ —
[//,o - H{Gj,,)].

What does this mean in teiTns of information theory? Supposing we had
a generating function or some procedure that produced every one of these
unusual configurations with equal probability. Then the two numbers H^9 and
H(Gjj,) would be identical. The uncertainty of such a generating function
would be maximal. On the other hand, if the generating process were such as
to specify, with probability l,only one out of the total number of configurations,
then the uncertainty of the generating process H{Gj,.) would be 0. As can be
seen, I(Gj^) for a given generating process carried out through k steps has been
defined above simply as the difi'erence of these two quantities. Very briefly
then, this measure would suggest that if a knowledge of the generating process
does not enable us to predict which of the possible configurations to expect
after the process has gone along for k steps, then knowledge of the generating
process provides no information. On the other hand, if one can devise a
mathematical mechanism, that is, a generating process, that can specify the
ultimate form of an organism exactly, then the generating process contains all
the information it possibly can.

Applying this measure to the presently available data and the particular
generating function introduced earlier, it is observed that liGj k) increases with

* It will be noted that the probabihty of the most probable configuration exhibits a maxi-
mum at A; = 5. This is an accident attributable to the fact that this particular 5-configuration is
the only one containing a cluster and it is asymmetric. Such an accident is extremely unlikely to
be found when k is large.

t The symbol 'Ig' is used here to denote 'logarithm to the base 2'.

A Probabilistic Model for Morphogenesis

369

increasing k (Table V). Estimates have been made for A; = 10 and A' ^ 16 from
the Monte Carlo samples. These estimates are certainly lower than the precise
values since an estimate of/?, was not available for every configuration and the
means for rather large groups of configurations were used instead. A functional

Table V. Entropy oj \i-arrays

k

H{G,)

H

KG,)

1

0

0

0

2

0

0

0

3

.92

1.00

.08

4

2.19

2.32

.13

5

2.90

3.59

.69

6

4.54

5.13

.59

7

5.59

6.76

1.17

8

7.00

8.53

1.53

10

10.00

12.29

2.29

16

16.68

21.77

5.09

relationship between liG^^j,) and k has so far not been found. One may con-
jecture that the relatedness increment /(C7y,fc) — I(Gj^j._i) approaches 0.5 as k
increases without limit. This may be interpreted to suggest that the rate of
information accumulation in an organism constructed according to such a plan
is half a bit per cell division.

Other measures have been suggested as being useful to our purposes.
Following the terminology of McGill and Quastler (16), the relative uncertainty

M(C \
of the generating process is Dj^. = — ^ ^^ and the redundancy is Q^^ — \ — D

H,}

},k-

The redundancy evaluated from the results presented in Table V increases
from a value of 0 for A: = 2 to a value of 0.234. As with the measure HGj^j.) —
/(G;j.,_i), it seems plausible to expect that as k increases Q^j. will converge to
some value other than 0 or 1, but no procedure has as yet been found to test
this conjecture and to determine the limit.

In a qualitative way, this increase in /(C7,,fc) may be understood to mean that
the featureless generating function considered above determines the configura-
tions of large numbers of cells with a high degree of specificity. It is virtually
a certainty that large configurations will be essentially circular in outline; that
they will have a high density, i.e. they will contain very few 'holes' and short
'tentacles'. Thus if one considers the most probable outcomes of the generating
procedure in the large, then these configurations appear to resemble one another
very closely even though they exhibit no correspondence in detail.

It is true that the results obtained with such a simple model are far removed
from the intricacy of development of living things. A few regularities in the
most probable forms may be introduced by small modifications of the initial
generating procedure. Objects that are ellipsoidal or cruciform or objects
characterized by large numbers of branches have been developed by such
modifications. However, it is unlikely that further complexity can be introduced

370 Murray Eden

into the growth process without drastic modification of the generating function,
in particular without consideration of the history of a particular growing
configuration. The results of embryology suggest that the generating process
must contain a set of instructions that will alter the pattern of growth on the
condition that a given stage or over-all configuration shall have been reached,
and that such a change in pattern of development may occur a large number of
times during the process of maturation. It is certain that such a modified
generating process will have a higher information content than the process
considered in detail in this paper. It remains to be seen whether modifications
of this character can be fonnulated and whether a mathematical treatment of
the consequences is possible of achievement.

REFERENCES

1. S. M. Dancoff, and H. Quastler: The information content and error rate of living
things. In: Information Theory in Biology, ed. by H. Quastler, 263-273, University of
Illinois Press, Urbana (1953).

2. H. LiNSCHiTz: The information content of a bacterial cell. In: Information Theory in
Biology, ed. by H. Quastler, 251-262, University of Illinois Press, Urbana (1953).

3. H. P. Yockey: An application of information theory to the physics of tissue damage.
Radiat. Res. 5, 146-155 (1956).

4. K. S. Tweedell: Identical twinning and the information content of zygotes. In: Infor-
mation Theory in Biology, ed. by H. Quastler, 215-250, University of Illinois Press,
Urbana (1953).

5. F. G ALTON: The history of twins, as a criterion of the relative powers of nature and
nurture. /. Anthrop. Inst. 5, 391-404 (1876).

6. H. H. Newman: The Biology of Twins {Mammals), University of Chicago Press, Chicago
(1917).

7. J.Hancock: Monozygotic twins in cattle. Advances in Genetics 6, \A\-\1 5 {\95A).

8. F. W. Went: The role of environment in plant growth. Amer. Scient.AA,'il^-'i9i{\956).

9. A.M.Turing: The chemical basis of morphogenesis. Phil. Trans. (B) 237, 37-72 (1952).

10. B. L. Van der Waerden: Die lang reichweite der regelmassigen atomanordnung in
mischkristallen. Z. Physik 118, 473-488 (1941).

11. M. Kac and J. C. Ward: A combinatorial solution of the two-dimensional Ising model.
Inst, for Advanced Study, Princeton, N.J. 1-15 (1954).

12. J. Humans, and J. de Boer: An approximation method for order-disorder problems.
P/?j5/ca 21, 471-516(1955).

13. D. Konig: Theorie der endlichen and unendlichen graphen, Chelsea Publishing Co., New
York (1950).

14. The Rand Corporation: A Million Random Digits with 100,000 Normal Deviates, The
Free Press, Glencoe, 111. (1955).

15. C. E. Shannon, and W. Weaver: The Mathematical Theory of Communication, University
of Illinois Press, Urbana (1949).

16. W. McGiLL, and H. Quastler: Standardized nomenclature: An attempt. In: Information
Theory in Psychology, ed. by H. Quastler, 83-92, The Free Press, Glencoe, 111. (1955).

FUNCTIONAL GEOMETRY AND THE
DETERMINATION OF PATTERN IN MOSAIC

RECEPTORS

John R. Platt

University of Chicago, Chicago, Illinois

Abstract — Every visual pattern element — straight lines, curved lines, parallel lines, angles,
periodicities — shows some self-congruence under translations or rotations. A random mosaic
of detector cells, like the 10* cells of the human eye, can be used as a null detector to indicate
this self-congruence during scanning operations. This operational definition of pattern is called
functional geometry. It underlies the generation of precision optical and machine surfaces by
the Whitworth, Rowland and Strong methods and theoretically can approach infinite precision,
starting from rough materials. It converts a space pattern into time pattern repetitions whose
accuracy is not limited by the mosaic structure. The spherical eyeball shape is generated by
functional geometry, and its almost perfect rotation operations can establish among the
retinal cells an external Euclidean metric of perception-space which is independent of the
distortions of mapping on the retina or the cortex.

A variety of second-stage and higher-stage neuroanatomical structures would have to be
grown for tracking and detecting pattern repetitions. These would almost certainly include
delay lines and null-transmitter cells to transmit only the identical parts of multiple input
patterns.

Such pattern-perception in the mature network is equivalent to determination of the
initially unknown space relationships or addresses of the random detector cells. A non-
addressed mosaic requires much less initial assembly information than a pre-addressed mosaic,
but requires a long learning and growth time for address-determination after operation begins.
It has other quasi-human characteristics, since to determine addresses it consumes information
in abstracting properties, draws analogies, shows closure, may^ts symbols, learns from experience,
incorporates functional memories in the network structure, and apparently might even need
to sleep. But the self-congruences of functional geometry would impose certain paradoxical
and Kantian restrictions on the learning process, such that only certain congruent types of
experience can be learned at all, and only certain congruent types of address-connections can
be formed, regardless of what the experiences are.

This paper revolves around the problem of visual pattern perception by the
human eye and brain. It is an attempt to generalize the problem; to restate
it in a language suitable for electrical networks; and to see what basic physical
principles might be involved, what detailed neural relationships might be
required, and how these principles and relationships restrict and determine the
general properties of such networks.

The eye has millions of simultaneously active photodetectors. The theory of
connections in such a system is still in a primitive state. It is therefore necessary
to begin by introducing and explaining a number of new terms which will be
needed in the analysis.

371

372 John R. Platt

I. MOSAIC RECEPTORS

Single-element and Multiple-element Receptor Systems

A feedback mechanism or a neural network or a social organization is a
decision network connecting sensory-receptor inputs with motor-effector outputs.
The system may have single-element receptors or multiple-element receptors. An
example of a single-element receptor is a phototube. Another is a proprioceptive
muscle spindle cell. In the simplest case each of these might actuate a single-
channel feedback loop or reflex arc leading to a one-coordinate output function
of time. There may be non-linear circuit elements in the loop that pulse or
chop or clip or average or stabilize the input or otherwise transform it. Never-
theless, each feedback signal from a single-element receptor remains a one-
dimensional time signal except as it may be trivially or artificially split into
several components.

Multiple-element receptors consist of many functionally similar single-
element receptors acting simultaneously. If each of these has its own private
reflex arc, independent of the others, to its private motor output, the system is
merely an additive system of single-element receptors. But to avoid conflict
in the motor responses, it is desirable to reduce their independence. In this case,
the simultaneous inputs can be combined in a decision network which selects a
single complex response from the output field, with suppression of conflicting
alternatives. Some of the physical and mathematical relationships in such a
network were discussed earlier (1).

The receptor organ of such a system becomes a mosaic receptor with a
pattern and hierarchy of connections to the decision network. It is an advantage
if the network is concentrated into a compact central switchboard where
extensive interconnections can be made quickly and cheaply.

Examples of mosaic receptors are the 10^-element retina of the human eye,
the basilar membrane of the ear, and the olfactory membrane. The retina will
be treated as the prototype of such systems. Mechanical mosaic receptors have
also been constructed such as the lO^-element assembly of sensory pins in the
reading head of a punch-card sorter or reader. A social mosaic receptor would
be the 10- traveling salesmen sent out by a business organization. The relatively
low complexity of these man-made systems means that they are inferior to their
biological counterparts by more orders of magnitude than almost any other
man-made devices.

It is true that some artificial receptor systems are more elaborate than the two
mentioned. A television camera iconoscope tube with its 1 0^ separate resolvable
spots is an example. But at present, the iconoscope signals are scanned and
sent in sequence into a single output channel, undergoing only the most rudi-
mentary inter-comparisons or decisions, such as stabilization, contrast or color
balance. Likewise the 10^ grains of a photographic emulsion, although they form
a very fine-grained system, do not feed into any decision network until they are
transduced onto the human retina.

Pre-addressed and Non-addressed Mosaics

An address, in computer nomenclature, designates a point in the network at
which a signal may be located. But in a mosaic receptor, the address of an

Functional Geometry and the Determination of Pattern in Mosaic Receptors 373

input element is only partly specified by its network-address. It is incomplete
unless the location in space, or space-address, is also given, at least relative to
the other elements, since both address components efTect the kinds and combina-
tions of messages sent through the network.

Mosaic receptors may be pre-addressed or non-addressed. In a pre-addressed
system, each receptor element has a specified space address and network
address. It is completely connected in a unique and permanent way to the
decision net before the net begins to operate. In a non-addressed system, the
space address of an element, or its network address, or both, may need to be
determined after operation begins.

This may be the main difference between the insect eye and the human eye.
The insect eye consists of a close-packed array of uniform receptor elements.
Because of their uniformity, they lie in long parallel lines. Absolute genetic
determination of the connections from each element to its neighbors and to
the decision net might be easy: a pre-addressed system.

Straight lines in the field of view that fire all elements on one of the principal
lines of such an array should be easy to distinguish from curved lines, if such a
distinction were biologically useful. But straight lines in any other general
direction would be hard to distinguish from curved, without very elaborate
inter-connections in the network; and therein might lie the limitations of a
pre-addressed system.

The human retina escapes this impasse. It appears to make no such dis-
tinction between straight lines in different directions. And indeed under a
microscope the cones in our foveas appear to be close-packed but sufficiently
non-uniform that no straight line arrangements are more than a few cones
long (2).

Assembly Information

This useful randomness seems inevitable from assembly considerations. A
non-random biomechanical assembly of 10^ elements distributed over several
square centimeters of the retina with individual tolerances of better than 1
micron would be almost inconceivable. Even if this could be achieved, the
complexity of a non-random wiring diagram for any system of 10^ input elements,
geometrically regular or irregular, would be almost impossible for the chromo-
somes to specify, as Pitts has emphasized (3).

And so the randomness, if it has solved one dilemma, has evidently created
another. The addresses of the retinal elements are now uncertain. All straight
lines have been made equal by a device which appears to make it impossible
for the eye to identify straight lines at all!

On the other hand, if this new problem could be solved — and the present
paper aims to show that it can — non-addressed systems would evidently have
one tremendous advantage over comparable pre-addressed systems: their
economy of assembly information. In pre-addressed systems, if the inter-
connections among /;; elements are to be specified in advance, the assembly
information must increase with a power of/;? at least as large as two and perhaps
much larger.

This elaboration of initial design specification and mechanical assembly
detail is what makes our artificial electronic networks slow and expensive to

25

374 John R. Platt

manufacture. Sooner or later the increase with increasing m will limit the size
of the pre-addressed systems we can construct, no matter how much the assembly
process is speeded up.

But for a non-addressed system, even with 10^ or 10^ elements, a very few
specifications of the general assembly or growth patterns may suffice (3). The
construction is cheaper, whether measured in assembly information, in time or
money. Obviously there is a price. It is that the addresses of all retinal elements
must now be learned— after operations begin. The construction is speeded up;
the attainment of full operating efficiency is delayed until address-determination
is completed. But the non-addressed system constructed with a given amount
of assembly information can eventually become far more complex and 'intelligent'
than its pre-addressed counterpart.

This initial incompetence may be why, in evolution, the non-addressed
organisms only become prominent when parental care appears in family systems
like those of birds and mammals. The long learning time for large m might be
connected with the long childhood of the more intelligent species.

Actually there may be no sharp boundary in biology between the pre-
addressed and the non-addressed. On evolutionary grounds alone, a vitally
necessary fraction of the human brain must certainly be pre-addressed. The
autonomic nervous system may be largely so constructed. Reflex actions and
probably color vision seem to have this character. The non-addressed sections
of our networks, although perhaps responsible for our most characteristically
human activities, may be a late and still secondary addition to a large pre-
addressed core — as Dr. Sacher stressed in his comments on this paper.

It is often asserted that nerves and synaptic connections do not grow. This
might be true for the pre-addressed sections; but it should be false for the
non-addressed sections. Address-learning in a network necessarily means
creation or change of connections. Change of neural connections means growth
or atrophy or both. If new synaptic connections do not grow, they must at
least be selectively and permanently activated or deactivated during the address-
detennining process.

The Pattern Question

Whatever the economy of assembly, the question remains: Can randomly
arranged elements be used to make discriminations of straight lines or of any
other types of pattern elements ?

There is evidently an intimate connection between the perception of pattern
and the determination of the addresses of the retinal elements. To make the
question more precise, let us number the elements 123 • • -y • • • in as nearly the
same way as possible in all retinas, and set up coordinate axes as nearly alike
as possible. The randomness means that element y will have different address
coordinates, X;, j^ in every retina. Or better, we might specify addresses by
relationships rather than coordinates, giving them forms such as 'Element y is
collinear between elements g and p\ This address might be right in one retina,
wrong in another.

Such an uncertainty of internal pattern has to be resolved within the network.
The question is then: Can the coordinates x^y^ be detennined, or can the
straight-line or other geometrical spatial relations of element j to many other

Functional Geometry and the Determination of Pattern in Mosaic Receptors 375

elements ■ ■ • a • ■ ■ p ■ ■ • be detemiined, within the receptor network and solely
by its normal functional operations? And if so, how?

The present paper aims to show that at least one simple method exists for
this functional detennination of addresses. It can be called the method of
functional geometry. It seems feasible for use at least in an artificial mosaic
system. It may or may not be the method used by the eye or by any other
biological system, although many of the results here strongly suggest that it is.
In any case, its existence removes a principal conceptual difficulty of non-
addressed mosaic receptors. And the examination of one particular method
can help sharpen up our experimental inquiries as to what methods of address-
determination and pattern-perception actually are used in biological systems.

II. FUNCTIONAL GEOMETRY

There is a class of geometrical operations that is of great importance in the
highest precision machine work and in anatomy, especially in the joints of
vertebrates. The operations are related to group theory but, as we shall see,
they might form the axiomatic basis of a separate systematic mathematical
discipline. If this discipline were ever created, an appropriate name for it
would be functional geometry.

Generation of Perfect Surfaces

An illustrative operation of this class is that by which an optician or an
amateur telescope maker grinds and polishes a spherical lens or mirror surface
(4). A rough blank of glass is placed against another rough blank of glass
or metal or pitch, with grinding or polishing powder between them. The blanks
are pressed and rubbed together by hand or by a rather crude and loose grinding
machine, as shown schematically in Fig. 1a. The operation continues with

Fig. 1. Self-congruence of a sphere or a circular arc
under random translation.

successively finer grades of powder. Finally each of the surfaces approaches a
perfectly spherical shape to a precision which may be one-tenth of a wavelength
of light, or better if desired.

Theoretically, if edge effects are neglected, the method can approach infinite
precision. Its practical precision is limited only by the patience of the optician
and the accuracy of available testing methods. The accuracy of approximation
to a perfect sphere can be many orders of magnitude higher than the accuracy

376 John R. Platt

of the initial blanks or the accuracy of construction or operation of the grinding
machine.

Usually the optician also wants a particular curvature, convex or concave,
but this is a separate question which need not concern us here. The curvature
determination is not automatic and it is the automatic approach to perfection
by these methods which is the point of interest.

In order to produce a spherical surface, the motions of the grinding machine
must be (a) relative translation of the blanks in both coordinates along their
surfaces, and (b) relative rotation of the surfaces. Each motion must be randomly
independent of the others, relatively unconstrained by the machine. This is
why the grinding machine must be loosely coupled. A grinding machine that
couples the motions in any regular way or whose translations have some
arbitrary fixed relation to the axis of rotation would 'over-determine' the system
and damage the rate of approach to a spherical surface or the attainable pre-
cision. The surfaces are self-centering, determining their own centers more
and more precisely as the polishing proceeds.

The reason these particular motions generate a spherical surface is that this
is the only surface that satisfies the following functional definition: A spherical
surface is one of two surfaces that is everywhere in contact regardless of relative
translation or rotation against each other.

For one surface alone, this could be made a statement of displacement
congruence: A spherical su face is self-congruent for all translations or rotations
in the surface. A complete sphere is self-congruent for all rotations in the surface ;
that is, about any axis normal to the surface. (Three degrees of freedom. Any
two rotational degrees of freedom imply the third.)

The functional geometry of such definitions is conceptually more funda-
mental than either Euclidean or analytic geometry. To say with Euclid that
'a spherical surface is a surface in which every point is at the same distance
from a fixed point', is to require points, fixity and measures of distance. To
say that 'the equation of a sphere is x^ + y^ -f z^ = 7?^ ' is to require also a
coordinate system. But functional geometry generates perfect surfaces by only
using two of the most primitive notions: identity (congruence) and displacement.

The motions involved in these definitions are those of the continuous transla-
tion and rotation groups of group theory. The definitions can therefore be
generalized to surfaces representing other group operations, including discrete
groups :

Real surfaces approaching indefinitely close to a mathematically perfect
fonn can be generated by mechanical processes that enforce displacement
self-congruence under a particular set of group operations. The set determines
the shape of the surface. The surface is self-centering and defines its own
special centers and axes in space more and more precisely as the operation pro-
ceeds.

In practice, what development of these other operations has been done has
come from the makers of precision screws and ruling-engines, especially
Whitvvorth, Rowland (5) and Strong (6). Strong emphasized the opposi-
tion between these 'inherently precise' methods (self-congruent surfaces) and
the traditional 19th-century semi-precision methods of 'kinematic design' which
he had described earlier (4), and the superiority of the self-congruent method.

Functional Geometry and the Determination of Pattern in Mosaic Receptors 377

'The construction methods of greatest precision are ail primitive methods' (6).
The following are some examples.

A surface of revolution is self-congruent for rotation about its axis. (One
degree of freedom : Strong method for thrust bearings.)

A screw is self-congruent for simultaneous rotation about its axis and trans-
lation along it. (One degree of freedom: Rowland method of lapping.)

A cylinder is self-congruent for all rotations about its axis and translations
along it. (Two degrees of freedom: Strong prescription for lapping a cylinder).
A cylindrical surface section is self-congruent for pure translations in the surface
with no component of rotation about a line normal to the surface.

A gear of n identical teeth, 360^ /n apart in angle, is self-congruent for any
of n different angular displacements about its axis. (One continuous degree of
freedom plus one discrete. In the Strong method, the gear is polished within a
kind of open-ended squirrel cage of n lapping bars or pawls that slide between
the teeth. The cage is rotated by one bar after every stroke, and any initial
irregularity in either the gear or the cage is polished away.) The group operations
are those of the discrete group, C„. Functional geometry can therefore generate
perfect right angles or other angles.

1

Fig. 2. Self-congruence in translational periodicity.

By analogy with the screw and the gear, a cylindrical surface with straight
parallel equally-spaced identical grooves (possibly helical) is self-congruent for
continuous translation in one direction in the surface and discrete translations
in the other, as indicated in Fig. 2. (In principle, the precision ruling of surfaces
might be accomplished in this way.) Perfect translational periodicities in two
or three dimensions might be generated in succession.

There are more sophisticated possibilities on moving beyond ordinary group
theory: A plane is one of three surfaces of which any pair can be placed in
contact everywhere regardless of relative translations or rotations against each
other. (In making optical flats by the Whitworth method of lapping, three
flats are generated simultaneously by being polished against each other, with
frequent interchange of pairs to prevent development of concave or convex
surfaces).

Restated in terms of displacement congruences: A plane is self-congruent
for all translations and rotations in the surface and for two-fold rotations about
an axis in the surface. Note that three-fold rotations about such an axis would
be impossible. This exemplifies a fundamental physical restriction on possible
generating processes, of a kind wc will encounter shortly in the biological cases.

378 John R. Platt

The sophistication of this definition of a plane is that it is antecedent to
the definition of a straight fine in this geometry and requires no definitions of
fines or axes or coordinate systems or rectifinear translations.

Other surfaces can be generated by grinding and lapping operations that
maintain only a line of contact between two self-congruent surfaces, such as
two surfaces of revolution rotating about skew-perpendicular axes.

Biological Examples

Any two physiological surfaces that are pressed and rubbed together con-
tinuously must exhibit displacement congruences approximating mathematical
perfection.

The familiar chicken drumstick has at its lower end a perfect surface of
revolution sweeping through an angle of about 270°. (One degree of freedom.
It may be slightly helical, since the revolution is not complete.) The helical
grooves on the narwhal tusk may be generated by displacement congruences as
it grows from its socket. Ball-and-socket joints are likewise famifiar in anatomy,
with accurately spherical surfaces. (Three degrees of freedom.)

The eyeball-and-socket is perhaps the most perfect instance of this type.
The spheres must be very precise if there are not to be considerable changes of
pressure during normal rotations. The oculomotor musculature provides all
three rotations, about the Z-axis (vertical axis), the 7-axis (transverse horizon-
tal), and the Z-axis (longitudinal horizontal). Functional geometry provides a
precise self-centering specification of the center of the spheres and therefore of
the reference point about which all the operations of the three-dimensional
continuous rotation group can be carried out.

What is more important, these motions provide the necessary displacements
by which the displacement congruences of any pattern in the external field may be
detected by the retina.

To anticipate the results of the next section, if an arc in the external field
produces an excitation pattern on the retina (Fig. 1b), the pattern can remain
unchanged during a displacement of the fixation point along the arc if, and only
if, the arc as seen from the eyeball is either a straight fine or the arc of a perfect
circle, with constant curvature. This is the two-dimensional analogue of the
functional definition of a perfect sphere given above.

Likewise a set of lines in the field is parallel and equidistant if and only
if the excitation pattern can remain unchanged as the fixation point moves from
one line to the next or moves along the lines (Fig. 2). This is the analogue of
the functional definition of a surface with parallel equally-spaced grooves.

These are indeed the kinds of pattern judgment that the human eye makes
most precisely. Our peculiar sensitivity to changes of curvature and to non-
parallelism and non-periodicity is well known in model-making and in pattern
tracing and analysis.

An extreme case is the curvature-continuity judgment involved in 'vernier
acuity'. If two ends of a line join imperfectly in the middle, the eye can still
perceive the break when the lateral displacement is as small as 2 seconds of arc —
l/30th the diameter of a retinal cone (7). Regardless of what neural connections
might be needed to make such a discrimination, it is obvious that the judgment
must depend on a physical operation of inherently high precision, inherently

Functional Geometry and the Determination of Pattern in Mosaic Receptors 379

unlimited by the coarseness of the mosaic structure and the randomness and
uncertainty of cone locations.

Functional geometry offers such a method, since it can generate indefinitely
high precision out of arbitrarily coarse materials crudely manipulated. With it,
the practical limitation in precision could be a very refined signal-to-noise
limitation, that is, an intensity-judgment-time limitation, as we shall see, and
not a coarse mosaic structure limitation. For the internal as well as the external
eye, it would be characteristic of biological systems to make use of such a
method, conceptually simple, operationally precise, making only minimum
demands on the accuracy of assembly, and capable of being driven to higher and
higher precision as needed under the pressure of natural selection.

III. DETERMINATION OF ADDRESSES

A. Scanning in Vision

DiTCHBURN and co-workers (8-10), and Riggs and co-workers (11-12), have
shown that vision disappears unless the field is continuously scanned by the
eye. The scanning is normally provided by 'physiological nystagmus', or 'fixa-
tion tremor.' When a subject is fixating as steadily as possible, the following
eye movements are present :

'(i) a tremor of amphtude of the order of 15 sec arc and frequency ranging
from 30 to 80 c.p.s.

'(ii) a series of 'flicks' of up to 20 min arc occurring at irregular intervals
ranging from 0.03 sec to 5.0 sec.

'(iii) slow drifts in the intervals between flicks.' (Ditchburn (9)).

The movements are involuntary. They continue undiminished even when
an image has been stabilized on the retina, so that they do not seem to have
quantitative feedback character, at least for fixation of a point source ; but the
flicks do tend to produce recentering after the image begins to drift off" the fovea.

The frequency, amplitude and sequence of the movements as presently
known would be consistent with assigning the tremor jerks to the successive
single neural spike inputs in the normal trains of spike pulses to the ocular
muscles ; with assigning drift to the unbalance between these jerks in opposed
muscles at slightly different spike frequencies; and with assigning flick to a
final sudden burst of spikes to the less active muscle which redresses the un-
balance and recenters the system. There is no vision during the flick movement.
This demonstrates an intimate oculomotor interaction with the retinal output,
complementary to the interaction which will be postulated later.

When these movements are stopped by optically stabilizing the retinal image,
vision is lost within a second or two. It can be restored by flicker modulation
of the light intensity or by reintroduction of some image movement.

The necessity for scanning in maintaining vision might have been anticipated.
It is probably no surprise to a biologist to find such a mechanism used to
counteract the effects of adaptation and fatigue in receptors that need to be
continuously sensitive; nor to a biochemist to find that the electrochemical
shock waves corresponding to nerve impulses are reduced in frequency as the
photochemical steady state is approached; nor to a physicist to find that a.c.
operation of a phototube is the best way to avoid d.c. drifting. Many retinal

380 John R. Platt

potential and neural spike results obtained with steady-state illumination may
have to be reexamined for their relevance to the process of vision.

Insects and amphibia and other lower orders seem to hold their heads and
eyes rigid for long periods. The need for scanning suggests this might permit
selective detection of moving objects in the field. (The insect eye perception
problem treated earlier was an artificial way of pointing up the general pattern
problem, and not an attempt to describe the real workings of the insect eye.) At
some point up the scale, a scanning tremor in the eye might have been an
evolutionary predecessor of wide-angle motion.

(It is not only vision that requires 'scanning'. A variation of input stimulus
is needed to maintain sensitivity in touch and in smell. This strongly suggests
that a search be made for a similar mechanism in hearing, by which the 'sound
image' might be scanned up and down the basilar membrane to provide continual
change of stimulation, to prevent local fatigue, and to sharpen tonal discrimina-
tion.)

B. Determination of Addresses

In any field of study, it is always a hopeful sign to find two or more un-
explainable effects and not just one; for this opens up the possibility that the
two will explain each other. In the retina, we are confronted first with the
pattern-perception address-determination problem and then with the strange
importance of scanning. Putting these together, it appears that scanning might
be a particularly straightforward method for functional determination of
addresses in a non-addressed mosaic receptor. And this is functional geometry.
Several theorems suggest themselves.

The Fundamental Operations

1. Sequence of Elements — During random scanning over visual fields con-
taining some structure such as sharp discontinuities or boundaries, if retinal
elements /, y, k are triggered in similar patterns in succession far more often in
the time-sequences ijk or kji than in the sequences y/7:,yA:/, ikj, or kij, then:

(la) there are some boundaries in the external field that are relatively stable

during the scanning motion;
(lb) y lies on the image of a point in the field between the corresponding

points for / and k ; and
(Ic) the eye movement for one of the sequences ijk is opposite to that for

the other kji.

2. Collinearity — During random scanning over visual fields containing sharp
boundaries, if all the elements in a certain large set fgh • • • k are excited simul-
taneously in the same way (d.c. ; or a.c, as by tremor across a boundary) and
if this excitation continues unchanged throughout a short drift movement, then:

(2a) there is a linear boundary in the field;

(2b) elements y^/j • • • A: lie on the image of that boundary; and

(2c) the drift movement is parallel to that boundary.

The photodetector inputs produced by tremor movement could provide a
gradient discrimination across the boundary which, when combined with drift,
as suggested in Fig. 1 for a curved line, could give an especially delicate deter-
mination of addresses (3). Thus, for cells distributed roughly along the image,
one traverse might produce firing in a reproducible sequence fkghjfigf • • •, the

Functional Geometry and the Determination of Pattern in Mosaic Receptors 381

sequence depending on some function of the relative transverse cell displace-
m;nts, sensitivities and repetition rates, and on the image boundary gradient.
'Unchanged excitation' would mean successive recurrences of this same sequence,
and changes in the sequence could correspond to changes in the image
amounting to only a small fraction of a cell diameter. Jhc gradient-discriminating
power would then be limited essentially by signal-to-noise considerations rather
than by mosaic structure and it might be far higher than the static mosaic
resolving power, as numerous authors have suggested. The transmitted self-
congruence signal, whatever it is, need contain no trace of the static mosaic
structural irregularities. It is also independent of differences in the sensitivity of
different receptor cells and could remain unchanged even if a few of them should
fail completely (closure). These would be important biological advantages for
the self-congruence method of address-determination.

2'. Parallelism — If the elements/^/? • • • A' of Operation 2 also are grouped
into /■ subsets each of whose excitations can be duplicated for r different trans-
verse displacements, with a different set of displacements for each subset of
elements, then:

(2a') there are r parallel Hnear boundaries in the field ;
(2b') each subset lies on the image of one of these boundaries; and
(2c') the first drift movement is parallel to the boundaries, while the discrete
transverse displacements are not.

It is typical of functional geometry that it simultaneously limits (2a) the
type of external pattern that can be interpreted (2b), the type of internal relation-
ship that can be organized, and (2c) the operational motions that can produce a
coincidence of the two. This situation for pattern structure is no different
from that for the eyeball, where functional geometry simultaneously limits the
shape of the external socket, the shape of the ball, and the possible movements
and musculatures. We shall see over and over that the functional geometry, if
it is the address-determining method, is neither experience nor structure but
stands outside them both, imposing an inescapably limited selection of forms
on the only experiences we can perceive and the only structures we can create.

Point (2c), the establishment of retinal relationships and proprioceptive
oculomotor signals relative to each other, as suggested by Helmholtz, is not
the least important aspect of address determination, now that proprioceptive
muscle spindles are known to be present (13, 14).

Note that it is the boundaries in the external f eld that are linear, and not their
retinal images, when self-congruence is the method of discrimination. Likewise
the projections on the cerebral cortex can have any kind of twist, distortion or
discontinuity— which they have — without destroying a functional definition of
collinearity and parallelism.

The ambiguous word 'linear' is used in theorems (2) and (2') so as to postpone
for a moment the question of how well these procedures will distinguish a
perfectly straight line from a perfect circular arc of very slight curvature. But
aside from that question, a mosaic detector is seen to be in principle far more
accurate than a single-element detector. With the latter, straight lines could be
discriminated by tracing them out, perhaps using small hunting movements
superimposed on a long sweep, but the accuracy is limited by the accuracy of

382 John R. Platt

the analog position-sensing circuits. With mosaic detectors, the sensitivity to
imperfections in a hne pattern is not affected by analog errors.

In these theorems, a discriminated boundary will be perfectly straight if
the longitudinal Z-axis of the eyeball passes through it and if there is no Z
rotation during the scanning motion. Eye movements about the Z axis during
fixation seem not to have been measured as yet, but it seems unlikely that
physiological tremor about X and Y would be unaccompanied by tremor about
Z. It will be convenient here to consider the analogue of these theorems for
pure rotation about Z, with no X and Y components, and to come back later to
the question of how the present theorems will be changed, and what new theorems
will be valid if all three rotations are present.

3. Circularity — During pure rotational scanning about the Z-axis over visual
fields containing sharp boundaries, if all the elements in a certain large set
fgh • • • k are stimulated in the same way and if the stimulation continues
unchanged throughout this kind of scan, then:

(3a) there is a boundary in the field which is a circle or circular arc as seen

from the eye ;
(3b) elements y^/? • • • k lie on the image of that boundary; and
(3c) the-Z axis of the rotation passes through the center of the circle.

3'. Concentricity — If the elements/g/; • • • A: of Operation 3 are grouped into
/• subsets whose elements can be re-excited in the same local patterns by discrete
sets of X, Y rotations (in analogy with the Operation of 2') then:

(3a') there are r concentric circular boundaries in the field; and so on.

Concentricity is also one of our very delicate discriminations, as is shown
by many gunsight designs.

4. Translational Comparison — During a random scanning drift movement
(in X and Y alone) over visual fields containing sharp boundaries, if a certain
time pattern of excitation of elements bed • • • is repeated after a certain fixed
time-delay (that is, a certain displacement) by elements y^/j • • • in a one-to-one
correspondence with the bed • • • excitation pattern, then :

(4a) there is a stable pattern, fixed or undergoing translation, in the external

field; and
(4b) there is a constant translational separation in the field between points

whose images fall on elements b and/, e and g, d and //; and so on.

4'. Translational Periodicity — If the elements bed • • -fgh • • • of Operation 4
can be divided into r subsets, where r is greater than 2, each of whose excitations
can be duplicated for r different displacements, with the excitations of several
subsets simultaneously duplicated for certain displacements, then

(4a') there is a stable translationally periodic pattern in the field, with r
repetitions; and so on.

Translational comparison is of course the theoretical procedure for estab-
lishing a metric in a space of unknown geometry. The precision of translational
inter-comparisons between the patterns in the two eyes is the basis of depth
perception. Under the most favorable conditions it approaches the same high
angular precision that was found in vernier acuity. This fact alone seems to
require a physical operation that can create a high-precision translational metric

Functional Geometry and the Determination of Pattern in Mosaic Receptors 383

for the retinal elements: an operation for each eye that can translate elements
with fixed relations from one part of the field to another — that is, scan — during
the intercomparison process.

A figure with bilateral symmetry, whenever its median line is defined, has
translational periodicity for lateral scanning. This might be the basis for
whatever accuracy the human eye has in judging such symmetry.

5. Angular Comparison— During pure rotational scanning about the Z-axis
in fields containing sharp boundaries, if a certain time pattern of excitation of
elements bed • • • is repeated after a certain fixed time delay by elementsy^/? • • •,
then :

(5a) there is a stable pattern in the field, fixed or rotating about the Z-axis;

(5b) there is a constant angular separation, with respect to the Z-axis,
between elements b and/, c and g, d and h; and so on.

5. Angular Periodicity — If a relation like 4' is satisfied for pure rotational
Z displacements, then:

(5a') there is a stable angularly periodic pattern in the field, with /• repetitions ;
and so on.

Because of the limited range of Z-rotation in the human eye (about 20°),
our perception of angular periodicities may lose precision rapidly for larger
angles. Some of this acuity may be recovered by treating the angular periodicity
as a bilateral symmetry, converting the judgment into one of lateral translational
periodicity.

The metric of the 'space'' of the addresses established by these operations is
that of the rotation-space of the eyeball and not that of the retina or cortex surface.

All these operations have been internal operations, specified so as to depend
only on the internal properties of the decision net and its scanning system,
and to be as independent as possible of the object and properties of the external
field except for the minimum requirement that there is some variety of structure
and that at least sometimes its changes and motions are slow compared to those
of the eyeball.

Displacements and motions in the external field could lead to another
similar list of theorems which would establish similarly an external metric and
an expected external behavior, whose familiar translational and other con-
stancies— comparable to the congruences produced by the internal operations —
we might finally interpret as invariant 'objects' in the field, uniform motions,
and so on. The external metric may or may not be consistent with the eyeball-
rotational metric. Probably the external metric is the primitive one, with the
scanning metric providing a sophisticated refinement. Inconsistency between the
two may be the source of many optical illusions.

But since theorems (1) to (5) suffice to establish in several different ways
that consistent address determination within the network is at least physically
possible it seems more important to go on now to see how it would be anatomi-
cally possible.

C. Possible Types of Neural Connections Required

Proprioceptive Coordinate Specif cation

What anatomical connections are needed for proprioceptive sensing and
control? The requirements and some possible ways of solving them, at least

384

John R. Platt

for an artificial system witli some quasi-neuronal properties, will be seen if we
consider the problem of scanning along a curved line, with Z-rotation of the
retina to follow the curve, as in Fig. 1.

If the differential muscle stress or strain or rate of change of either (whichever
is the principal sensed variable) about the Y-axis has a fixed ratio r to that about
the Z-axis, the eye will sweep up along a line at an angle arctan r to the horizon.
If the differential neural spike frequencies/^ and/^ from the two muscle pairs
give a quasi-logarithmic representation of the muscle action, a fixed ratio r
corresponds to a fixed frequency difference,/^ — /»> which we can call F. A
subtractive-frequency mixer tube, and perhaps a similar subtractive mixer neuron,
could be devised which would combine two synaptic inputs so that an output
pulse is produced only when the input pulses are simultaneous, as suggested in
Fig. 3. With suitable cell sensitivity and time constant, this output is the beat

f,-AF-R

Fig. 3. Possible proprioceptive analog connections for scanning
along a uniform curve.

frequency, F, the difference of the two input frequencies (1). A neuron used in
this way might be called a difference cell. (Determination of the sign of the
difference might require another cell.) If the output frequency F is fed back
with proper sign to the Jf and 7 muscles, a constant direction of motion can be
stabilized.

The rate of change of direction could be sensed by introducing a time delay
and comparing r{t) with r(/ — A) or F{t) with F{t — A) by a second subtractive
neuron which generates the frequency AF — a time-differential cell. With a
lower sensitivity and a shorter time constant, the same type of cell could be
made to fire only for a certain constant pulse interval in the inputs, equal to
the time delay. This would be a constant-frequency detector, and could be
called a nidi cell.

A constant Z-rotation of the retina to follow the change of X, F direction in
scanning a curve could be detected by a third subtractive neuron which generates
the frequency difference/ — F. Call this frequency R. It can again be held at
a constant value by suitable feed back into the Z motion, as shown at the right
side of Fig. 3. Such a tracking motion permits eeneralization of theorem (3)
and (3'): ^

Functional Geometry and the Determination of Pattern in Mosaic Receptors 385

3". Decentered Circularity — During combined translational and rotational
scanning, if the conditions of theorem (3) or theorem (3') are satisfied, then (3a)
and (3b) or (3a') and (3b') are vaHd; but:

(3c") the Z-axis of the rotation does not pass through the center of curvature
of the boundary or boundaries.

The oculomotor motions that could be directed by this kind of analog
control correspond to the crude motions of the grinding machine in generating
spherical surfaces. They do not need to be exact. They need only to be capable
of making retinal displacements across the field sufficiently good that during
the tremor movements the retinal excitation will have an adequate chance to
signal if it is congruent with the original pattern. This signal could also interact
with the oculomotor system to make the scanning more stable and accurate.
In practice, visual acuity for moving patterns is considerably reduced (15),
presumably because of the increased tracking errors and decreased chance of
a congruence signal.

We can now see the effects of combined motions on theorems (2) and (3).
Evidently Operation (3), the examination of circles, gives a functional self-
centering specification of the axis of rotation, even if it is off the Z-axis, whenever
congruence is maintained. Any tremor about other axes simply provides useful
scanning motions.

But Operations (2) and (2'), the examination of collinearity and parallelism,
cannot discriminate perfect straight lines from perfect circular arcs of large
radius except by invoking the accuracy of the sensing and analogue control, a
discrimination of much lower accuracy than the mosaic self-congruence dis-
criminations. It seems that our perception of such differences is in fact small
unless there are known straight lines nearby permitting a self-congruence test
for parallelism. There is a familiar illusion in which a comparison straight line
appears curved in the opposite direction from a curved line. This shows an
uncertainty in the analogue system, which tends to scan along the bisector so
as to give the figure bilateral symmetry.

The Z rotations of the eyeball during scanning of curved patterns evidently
deserve examination. In the classical ZoUner illusion (parallel lines appear to
be non-parallel when crossed by oblique converging lines) there might also be a
Z-rotation of the retinal coordinate system, perhaps in the sense of stabilizing
the local foveal pattern and the local bilateral symmetry axis as the fixation
point oscillates from one of the parallel lines to the other.

With further combinations of difference cells and time-differentiation cells
and feedbacks, probably the tracing out of any pattern by scanning could be
converted at a high enough stage into a constant output from some subtractive
neuron. If adjustments of the scanning rates at various points in the pattern are
also introduced, probably changes of size and distortions of shape could even
be accommodated in a constant output at a still higher stage neuron. We can
dimly visualize how this might proceed by stages to a neuron capable of producing
a fixed output, or better, a total motion of advance or retreat, whenever so
specific an object as a particular person is scanned, regardless of aspect and
light.

Even if in later life the proprioceptive tracing of patterns by scanning
becomes subordinate to direct mosaic pattern-perception, the long stages of

386

John R. Platt

finger tracing of block letters and large patterns by children and newly-sighted
adults suggests its early importance. Studies of the developmental pathology of
pattern-perception with partial oculomotor paralysis might be instructive.^

Null Detectors and Delay Lines

What kinds of neural connections might be needed in the mosaic to deter-
mine addresses as these operations are performed ?

The discriminating self-congruence information is always of the form
'constant repetition of the same pattern' or 'repetition after a time delay'.
What is needed from the photodetectors is the information 'absence of change'.
They are being used as null detectors. Unstable detector elements in the labora-
tory are often used in the same way whenever the utmost accuracy of measure-
ment and simplicity of interpretation is wanted. The rather complex relation-
ships that can be established when using mosaic receptors as null detectors seem
not to have been explored before.

To signal 'no change' we could use a null cell of the type already described.
But another good way to examine stability of pattern would be to have a cell
with two input channels of different lengths, like two of the channels in Fig. 4,

Image

Fig. 4. Cone addresses from delayed coincident pulses to a
null-transmitting velocity-detector cell.

or of different diameters and travel times, where the cell sensitivity is such as to
require simultaneous spikes from both channels in order to produce an outgoing
spike in its axon. (The word 'channels' is used to avoid the experimentally
unsettled question as to whether these could be all-or-none dendrites of the cell,
if such exist, or two excitatory synapses with different delays in the axons, or
collateral processes from the cells of the preceding stage.)

Such input channels would be delay lines like those used in nuclear physics
to distinguish certain events and particles, to eliminate random spurious
counts, and to measure velocities. They might be used for all these purposes
here. The axon output of such a cell, as shown in Fig. 4, combines three im-
portant properties. It is (a) a null indicator, firing only for those patterns that
are identical in the input channels. It is (b) an indicator of a particular delay
time or difference of times in the channels. And it is (c) a pattern transmitter,
since the pattern is not lost. Let us call this a null transmitter cell, and if the

Functional Geometry and the Determination of Pattern in Mosaic Receptors 387

delay is different from zero, a delay cell. Such cells would have several possible
special applications.

In the auditory system, a delay cell with binaural channels would be a useful
direction-indicator .

In the retina, a second-stage delay cell like that in Fig. 4 would indicate a
particular image velocity-component in the plane of the paper, and could be
called a velocity detector cell. One with several inappropriate delays might be
sensitive to almost any motion or flicker. This may be one of the functions of
the widely branching horizontal cells that are so numerous at the periphery
of the retina, since this is a region particularly sensitive to motion.

Velocity detector cells would give useful correction signals to the oculomotor
system.

Under Operation 1, it is easy to see how delay cells with input channels
from retinal elements /, j, k might be preserved in the organism if their time
lags are in either the spatial sequence ijk or the sequence kji, but might atrophy
from disuse or at least rearrange their channels if their time lags are in any other
sequence. And the ijk delay cells would be a different group from the kji cells.
Such a principle of natural selection and differentiation might be applicable to
all types of second-stage and higher-stage cells.

It may be profitable to examine these or other kinds of time-delay connections
in trying to make a model of color-vision, since it now appears that this may
involve a comparison of signals from cones at different times as the photo-
chemical substance in each one goes through some time sequence of spectral
transformations under illumination and perhaps under scanning.

To summarize these exploratory notions, it appears that the types of neural
connections that would be useful for address determination, at least in an
artificial system, would include: difference cells; time-differential cells; null cells;
null-transmitter cells ; delay lines and delay cells ; and velocity-component cells.

The outputs of such second and third-stage cells apparently can signal all
the self-congruences required in the basic operations of functional geometry.
All the geometrical patterns defined by local group theory congruences can be
signaled without using the retinal elements in any way except as null detectors.

If natural selection favors those cells, together with their oculomotor
connections, which signal repeated self-congruences under scanning; then in the
mature organism each retinal cell will feed into many second-stage cells, each
of which expresses a useful functional relationship between that retinal cell
and some others. The address of the cell has indeed been determined. The
mature network-address becomes an expression cf the space-address.

Evidently the functional geometry of scanning a pattern is a way of con-
verting its space congruences into identical time patterns. It therefore could
be said, as some have said (16), that in the mature organism the appearance
of a certain time pattern at a certain point in the network creates an 'expectation'
of its repetition at an adjacent point, and stimulates oculomotor and other
movements normally appropriate for the accurate fulfillment of this expectation.

The accuracy of address-determination in these operations depends on
the temporal accuracy of the delay lines and not on the spatial structure, which
can be largely eliminated from the congruence signals, and therefore from the
perceived patterns.

388 John R. Platt

In the adult, the need for continuous redetermination of addresses becomes
smaller. As Dr. W. A. Arnold of the Oak Ridge National Laboratory pointed
out when this paper was first given, the words on a printed page that is illuminated
for only 10""* sec, too short for any scanning, can be read (by anyone who
can read) quite normally over an area comparable with the foveal diameter.
The addresses have already been established and need little if any reconfirmation
from the operations that generated them.

How complete and rigid they are might be discovered if we knew the limits
of developmental distortion of the retina after, say, the age of 3. Or if
adults could work with optical systems giving subtle distortions of a few
minutes of arc in the shape and topology of patterns in the foveal region,
to see the effect of the loss of addresses on line, circle and pattern perception,
on reading and the identification of persons, and how soon — and how far
back in the network — a new set of addresses would be learned.

IV. NECESSARY PROPERTIES OF NON-ADDRESSED SYSTEMS

Certain properties would seem to be necessary characteristics of at least
the early stages of all non-addressed and address-determining networks.
What is interesting is that many of these seem to be familiar aspects of higher
human behavior, restated in receptor-network terms. We may properly inquire
how far our more complex activities can be subsumed under a generalized
functional geometry, and how far our more complex experiences are organized
by means of generalized displacement congruences.

A. Operational Characteristics

The null-transmitter delay cell which it seems necessary to invoke for any
network making time-delay comparisons of patterns would be a suitable
prototype for much of our higher neural organization. In the mature organism,
after the structure and connections of such a cell have been stabilized — that
is, after the addresses of its input channels have been determined — the cell
will always collate two or more input patterns in a standard way to produce
a simplified vital output. Let us focus attention, first, on the nature of the
outputs, then on the inputs, and finally on the process as a whole.

Abstraction of Invariant Pattern Properties

The output of each such cell signals to the higher stages the presence of
some particular kind of simple or complex pattern in the lower stages. This
implies in turn a pattern in the first-stage images, representing a pattern in
the external field. The process is abstraction. Pattern is another name for
congruences or invar iances in this field.

At a given instant, some fifth or tenth stage cell may be signaling That
is the letter R'. Simultaneously some other set of elements and delay lines
is abstracting from the same retinal elements the information 'It is in my
wife's handwriting'. A third neuron connected to these elements says, 'It is
black'; a fourth, 'It is large'; and so on, for details and context and background
and all the other components. Perhaps some still higher neuron also signals
the unification of these separate pattern properties and others into a word.

Functional Geometry and the Determination of Pattern in Mosaic Receptors 389

glanced past in a tenth of a second. These signals have a one-to-one corre-
spondence with Platonic properties of 'R-ness', 'Blackness', 'Largeness', and
so on.

Of course, a pre-addressed network, might also give the same kind of infor-
mation that any of these neurons gives. Or it might give information trivial
or inscrutable for us, such as 'Slope of sharpest edge, 103° 8"; or 'Five corners,
two arcs concave to the left'.

In fact, any neuronal output in any connected network could be thought
of as indicating some kind of pattern invariance. Jn this sense there are no
addresses to learn! But most of these invariances in an arbitrary synthetic
network would be worthless for biological survival. A major evolutionary
problem for non-addressed systems must have been the facilitation of principles
of connection leading to the appearance of cells, like the delay cell, capable
of perceiving useful invariances, color, velocity, topology, and so on.

Every internal invariance or imposed relationship of signals in time and
space gives rise to essential redundancies that can be eliminated from the
higher-order signals with no loss of external invariance information. There
is a reduction by a factor of about 10^ between the 10^ elements of the retina
and the 10^ elements of the optic nerve. Possibly this represents the elimination
of some of the redundant scanning constancies of types such as those described
in Section III that are implicit in the oculomotor operations and in the con-
straints of the kinematic rotational metric. These regularities would then
acquire an inescapable a priori character so far as the higher operations of
the network are concerned.

The external field may also contain many redundancies that are not impor-
tant in a given situation. For many purposes it suffices to know that the animal
is a wet, friendly dog, and we do not need the concurrent retinal information
that he is opaque and continuous and in contact with the sidewalk.

We have not considered here how such an 'attention' to certain patterns
and suppression of others might take place. However, the facilitation of
signals through one neuron by means of a change of its sensitivity produced
by feedback from the 'expectations' of a higher-order neuron (representing
an earlier wet-dog experience pattern) may not be different in principle from
the facilitation of oculomotor tracking movements by feedback from the
'expectations' of second-stage or third-stage retinal velocity-detector cells.
It may be helpful in many problems to think of attention and expectation as
generalized tracking devices.

The elimination, first, of field information that does not fit into the familiar
useful second-stage patterns or categories, then of the redundant internal
patterns, and finally of the temporarily unimportant and unattended-to external
patterns, shows qualitatively how and why information is consumed in the
course of abstracting invariances from a mosaic receptor (1). It is not lost
or damaged by transmission in the sense usually considered in single-channel
communication theory. Instead, it is used up, somewhat in the way that energy
is used up in doing mechanical work. More mosaic input information is
consumed in abstracting out a higher-level decision or invariance than in a
lower-level one. It is consumed in the sense that the detailed input information
is irrecoverable, non-reconstructable, from the output. Only by the almost

26

390 John R. Platt

impossible process of applying m independent abstracted relations simul-
taneously could the m independent inputs be inferred. But this consumption
or 'loss' of information is not biological loss but a gain, since it represents
the selection of the biologically relevant item from the confusing irrelevant flux.
After a lifetime of suppression of the less valuable pattern and field details,
adults finally attend only to the later neuron outputs or abstractions and seem
to lose the eidetic ability to bring forth the exact early-stage patterns of instan-
taneous retinal excitation, except as they can reconstruct them approximately
from their appropriate or inappropriate collection of output neurons. This
may show the cessation of early-stage rearrangements, which finally become
completely pre-addressed as far as new experiences are concerned.

Analogy Perception

We may look not only at what has been abstracted — the outputs — but
at what has been compared — the inputs. The elementary process in address-
determination was the comparison of excitation patterns at two different times.
A network whose neurons can signal identities or similarities of pattern — dis-
placement congruences — is an analogy-perceiving network. Much, if not all,
of what we call intelligence may be the abihty to perceive successive analogies
at higher and higher levels of abstraction, a multiple repetition of a single basic
neural process of organization.

Artificial pre-addressed systems are not generally able to perceive any
analogies except between those sets of inputs that they are wired up to treat
as equivalent. The value of mechanical mosaic detectors such as the punch-
card reading-head lies in the fact that they are wired up to perceive obscure
informational analogies and not any of the space or time pattern analogies of the
kind that we perform easily in retinal abstraction.

Thoughts and Symbols

Pattern and analogy perception resemble some important aspects of the
higher-order process we call thought. We might make a limited definition of
a thought as the realization of previously unperceived pattern-relationships.
A thought could then be represented by an operator equation,

where P^" is a pattern of the «th stage of abstraction ; Pg"* is one of the mih.
stage; q is the time delay or other transformation operator which relates
pattern P^ to P^. And Qph the {n + l)st or {m + l)st (whichever is higher)
stage of relationship; it is the pattern of the P's, a pattern of patterns. It is
primarily a realization signal — a displacement-congruence signal — but it
may also contain some or all of the common elements of the P patterns. We
might distinguish if necessary between the possibility of the thought and the
continued existence of the thought-relationship; and between the insight,
or first assertion of the thought, and the repeated use of the established thought.
If P2'"* has no perceivable relationship to P-^", there is no thought,

Po^qP^' = 0 for all q.

Functional Geometry and the Determination of Pattern in Mosaic Receptors 391

The next stage of thought might be to perceive a relationship between two
different g's,

^./'i V^i"+i = RQ

m 12

and so on to stages of any order.

This operator-form of the equation seems to be the simplest familiar form
that expresses all the required relationships. It suggests that Q can be regarded
as a characteristic value or output value of the relationship operator when the
latter connects the state-functions P. Or g is a symbol of the relationship
between P^ and P^. The equations suggest the possible usefulness of a formal
calculus of abstraction.

In the first equation, if either P^ or P^ or q is changed, Q is different and
generally vanishes. A little reflection will show that it is typical of thought,
as it is of such operator equations, that there is only a restricted class of pairs
of P's that have any relation to each other. The ^'s are sharply limited at the
same time as the P's; catalogues of the possible ^'s have been made by various
philosophers. And there is only a restricted class of realization signals, Q,
in any case. If the equation is to have a non-vanishing value, it imposes simul-
taneous restrictions on all four variables. Some /*'s may never show any
congruence. Some ^'s may operate forever in vain. And the Q's may take one
or two values so repeatedly that they become independent of what particular
P's are present.

The significant thing here is that these same equations would also describe
many of the processes and structures in an address-determining network.
So, in the functional determination process, q could be the functional geometry
displacement operation, P^ and P2 the geometrical surfaces or the geometrical
patterns of excited cells before and after the operation, and Q the signal of
self-congruence.

In the velocity-component cell of Fig. 4, q could be the delay operation,
Pi and P2 the pulse patterns in two of the input channels, and Q the coincidence
signal output. In the neuroanatomical structure of the same hypothetical
cell, q represents the delay line or lines, P^ and P, the input cells of the previous
stage, and Q the cell itself or its output axon or other output processes.

At a higher stage of the network, we might imagine that each of these
structural elements in a particular neuron may also be connected to a verbal
motor stage, with the relationships among these structural connections again
represented by the same equations; and probably this structural parallel would
be repeated in the language structure among the words themselves.

An address-detennining system therefore seems to be necessarily a symbol-
creating system. Whether regarded from the process aspect or the signal
aspect or the structure aspect, a relationship or pattern of patterns in each case
becomes represented by a symbol.

The close parallel between neuronal transmission and logical operations
has been discussed for many years and is of great importance in the com-
putational and logical performance of decision nets. But the present equations
and hypothetical models suggest that analogy-perception, 'closure', 'insight'
and other apparent 'extrapolations' from the known — in short, thinking —

392 John R. Platt

may also be a necessary normal and even rather simple aspect of the neural
connection process in any system that can determine its addresses.

B. Growth Characteristics
Learning

We saw earher that a non-addressed system must be initially incompetent
and needs a long learning time. This learning or address-determination requires
inputs containing pattern regularities — that is, experience. For the retina,
the experience may be generated by the external environment alone, or from
this environment as scanned by the eyeball; in either case it is external to the
retina.

In either case it generates spaces and metrics independent of the retina.
Scanning is probably the visual counterpart of exploratory oral and manual
manipulation which defines the 'spaces' of taste and touch. Probably the
'externahty' of the visual metric, plus the simplicity and universal identity
of the scanning operations of all eyeball-spheres about their centers, help to
account both for the Kantian a priori character, and for the pubhc and universal
character, of visual space. This is contrasted with the situation, for example,
in vocal or tone-quality space, which depends on the complex interaction of
hidden muscular movements, and is perhaps the most incommunicable of
our public spaces.

The network can learn only those types of regularities it has experienced.
Two networks should develop somewhat different pattern perceptions if their
environmental regularities or scanning schemes are systematically altered.
A non-addressed network which is forced to operate for a long time in a
structureless environment, like a bhndfolded and insulated animal or human
in the Riesen and Hebb experiments, should and does have seriously defective
pattern-perception and response. One can see how the formation of simple
and accurate early-stage addresses in a network would be very important
in facilitating fast accurate pattern-perception at later stages.

This picture of non-addressed learning exemphfies Hebb's conclusion (17)
that many adult pattern-perceptions having introspectively the most instinctive
and self-evident or necessary character are in fact perceptions that had to be
learned at some very early age. It is early experience that selects the address-
connections that are to be permanent; it is the permanent address-connections
that create expectations and pattern-organizations in later experience.

Nevertheless, there is a double paradox in the present picture, (a) There
are possible external input experiences that cannot determine address connections.
And (b) There are internal pattern-perceptions, just as there are eyeball-shapes,
which have grown or have been learned and yet have not been determined by
the particular experiences or motions that contributed to the learning process.

Both these conclusions would follow from the operator equations of the
last section that were supposed to represent network structure. The first
point is obvious and almost trivial. External field patterns and their images
are usable only if they fall within the limitations set by the network growth
mechanisms and assembly principles. Motions of too high a velocity, patterns
of far too coarse or far too fine a structure, fields of diffuse clouds with no

Functional Geometry and the Determination of Pattern in Mosaic Receptors 393

sharp boundaries, dazzle patterns with the proper kaleidoscopic confusions of
rapidly disappearing and reappearing spots, the diabolical fields of Ditchburn
that refuse to be scanned — in fact, any patterns that deny the analogies that
the network is prepared to detect — are probably all equivalent to a structureless
environment in their failure to produce organization behind the retina.

The second point becomes obvious when we consider functional geometry
and the profound limitations it imposes. Just as the lens-grinding machine
with sufficient freedom of motion necessarily produces spherical surfaces
no matter what it starts with, so the scanning eyeball necessarily generates
'external' space relations or addresses corresponding to the continuous three-
dimensional rotation group, no matter what is the structure of the external
field. Likewise at the retinal level, any scanning retina necessarily acquires
a unique perception for continuous lines of constant curvature and for parallel
lines and lines or points periodically spaced, which it can never accord to
patterns violating these displacement-congruences.

These natural congruence relations may play the same organizing and
aesthetic role in vision that octaves and simple frequency relations play in
hearing.

It is peculiar to functional geometry and it is extremely important for
philosophy that these necessary relations are neither given to the visual system
by any particular external field or experience, nor are they logically implicit
in the structure of the network, even when we include the analogy-detecting
structure. They are Q's that, like spheres, turn up invariably, no matter what
the P's or ^'s. They have rather the character of geometrical preconditions
simultaneously imposed on both the external field and the network organization
if any learning is to be possible. And they are not imposed by the scanning
operation, even though it does mediate between the field and the network —
any more than the spherical shape is imposed on the lens by the loose random
grinding machine, or on the eyeball by the muscles. They are more like a
priori requirements, mathematical absolutes, that determine the only kinds
of experience that can be organized and the only forms that learning can take,
if learning is to be done at all.

Functional geometry thus may be the origin of the Kantian epistemological
limitations on thinking, as represented by 'the synthetic a priori categories of
the apperceptive dialectic' Pitts has described this as 'perhaps the most
fundamental problem of neurophysiology and psychology' (3). It appears
that much, if not all, of Kant's theory of knowledge can be translated word
for word into the language of inputs, structures and geometries in an address-
determining network.

Functional Storage

A neuron that has been selected by experience, so that its output signals
an experienced pattern, constitutes a storage of the experience — a memory.
The storage is not 'dead storage' but a functional link which permanently
changes the operation of the larger net and which remains part of it. The
address-determining connections therefore constitute a functional storage of
experience. At any instant, the net is the memory; the memory is the net.

This kind of storage differs in an essential way from that of a prc-addressed

394 John R. Platt

network, where the inputs do not permanently modify the connections. The
latter must have a separate storage unit capable of modification and isolated
from the main network except for controlled temporary interactions. So our
electronic computers have their fast-access and slow-access storage units.
Our social decision networks have their files and libraries more or less insulated
from the functioning decision-personnel. This necessary but misleading
subdivision of our artificial systems into operating units and storage units
may be the reason why so many investigators in the past have searched —
unsuccessfully — for a special memory organ in the human brain. Functional
storage may be a typical property of biological systems, a further manifestation
of their usual simplicity and efficiency.

As an example, consider the genetic material of the cell, which at the present
time is supposed to consist of a few species-specific macromolecules, such as
DNA or RNA. In a newly-formed cell, such a molecule has two functions
(although they might not be separate functions): to initiate the steps up the
ladder of chemical syntheses of specific cell materials; and to duphcate itself.
But this is functional storage: the chemical structure and reactions are the
expression of the heredity; the heredity is the chemical structure.

Likewise in the production of antibodies by antigens, the chemical record
of the first antigenic experience is preserved in the antibodies (or in the chemical
information in the antibody-producing cells), ready to find instant chemical
expression when a second essentially identical experience occurs. The record
is the specific chemical protection; the protection is the record.

On a grosser scale, evolution is functional storage. The coming of the
cold is shown in our fur and feathers and families. The record of the ancient
temperatures and salinities may be in our blood and tears.

The speed and efficiency of social decision networks might be increased
if they could incorporate this lesson, and replace some of their file cabinets
by continuously repeated appropriate functional modification in the decision
channels.

Time Constants

Address-determination must go on at a certain regulated rate. This is
probably faster for early-stage neurons and slower for later ones, but the order
of magnitude should be well-defined for a given network.

In the adult human brain, the indications are that roughly 50 milhseconds
elapse between distinguishable perceptions or decisions — one 'moment', in
the Stroud terminology. This is of the order of fifty of the milHsecond repetition
intervals or synapse intervals of an individual cell, which seems to be a reasonable
relationship (1). Knowing this time constant, we can make some numerical
estimates of brain rates and capacities. These estimates are naive and probably
false in detail, but they are explicit and rather instructive.

Thus suppose that there is one new perception every moment and that
it may be preserved in a memory, represented by a single changed neural
connection. The now-classical experiment of micro-electrode stimulation
during brain surgery shows at least that if certain points are stimulated, a
complete, detailed and specific memory is indeed evoked. Combining this
with the working hypothesis suggested by Quastler and others (18), that the

Functional Geometry and the Determination of Pattern in Mosaic Receptors 395

waking brain appears to be processing input information at a constant rate,
it would appear that a human brain may be making changed neural connections
at rates up to 10^' per day. The necessary sequential spatial order in these con-
nections might be the origin of our sense of temporal order in our memories.

It may be no accident that this rate adds up to the order of 10^'' to 10"
neurons per lifetime, comparable to the total number of neurons estimated
to be contained in the adult brain; although of course a major fraction of
these may be pre-addressed, unchanging after birth. (This number has also
been computed as the minimum number of neurons required in a fully-
developed decision-net serving 10^ to 10^ input elements (1). But there is
no necessary conflict between these two points of view, since it is a familiar
property of biological systems that they represent simultaneous optimization
of different considerations— as in the two-point resolution of the eye, which
is simultaneously limited by diff"raction, by aberrations, and by the mosaic
cell size.) By this reckoning, less than one neural junction in a thousand would
be changed per week, which might account for the difficulty of detection of
histological changes.

With such a specific moment-by-moment locahzation of new connections,
the increasing loss of memory in older persons might be the result of cumulative
damage to the neurons, such as radiation damage or microhemorrhages ;
or it might be due to a kind of saturation of the address-determining connections,
so that either no new relationships are perceived in the continuing flux of
inputs, or else those that are perceived are no longer able to modify the network.

These numerical estimates are not unreasonable; and even if the one-moment
one-neuron assumption were dropped, it would not be surprising from the
general dimensional considerations in the physics of the problem to find that
that assumption would give correct order-of-magnitude relations between
the time-constant, the lifetime and the number of neurons and its rate of change.
Such a situation is common in order-of-magnitude calculations.

But this estimate of the rates is defended only so that it can be attacked
on other grounds: for it leads to another important biological dilemma, and
one that might have an interesting resolution. For it must be remembered
that the brain is not merely an electrical network; it is also a biological network
— living, breathing, and growing. And a neural connection time of 50 milli-
seconds is orders of magnitude too short for the usual cell growth time or
atrophy time. While electrochemical channels or barriers might be formed
or sudden changes of shape might take place in milliseconds, these can only
occur for cells that are already present.

A few years ago it was supposed that a way out of this dilemma would be
to let the new perception or thought be initially established as a closed self-
maintaining loop of neural electrical excitation, which could persist long enough
afterward for the cell growth and structural change to take place. But a
succession of apparently negative experiments seems to have caused this notion
to be largely abandoned.

There is an alternative. It is to let the neural growth take place, not after,
but before the chemical and electrical connection to the network, as the elec-
trician carries his coils of wire to the site before he hooks them up. The order-
of-magnitude gap between the time constants can be got over by supposing

396 John R. Platt

that the slow growth of new cells or random potential connections occurs in
parallel, thousands or milHons of cells at a time, while the fast new decisions
or perceptions or insights occur sequentially, hooking up one cell at a time or
a small group. Such a sequence might resemble the activity-stimulation-
proliferation-organization sequence in other tissue. And while this specific
suggestion may again be wrong, its accuracy is less important than its general
bearing on the time-constant problem, which suggests that epochs of growth
may need to be separated from epochs of decision in a biological address-
determining network.

This possibility seems to deserve experimental inquiry. Perhaps our limited
time span of intellectual attention, and the 'subconscious' solution of problems,
and the role of sleep, especially in the infant, in preparing new cells to be
ready for new (waking) connections or learning or decisions, should be re-
examined from this point of view.

C. Artificial Non-addressed Systems

The truck driver is trained in cliildhood to perceive and respond appro-
priately to cars, stop-lights and pedestrians of whatever kind. In this pattern
and analogy-perception he excels any arrangement of photocells yet created.

A pre-addressed decision-net might be able to operate with his small high-
way tolerances and high speeds if it had his 10^-element resolving power and
wide tield of view. But it would not be safe in the unpredictabihties of the
open road. For this job, a non-addressed mosaic is needed, capable of learning
new patterns. Otherwise the appearance of a new type of car or a new type
of hazard on the road will cause the machine to be sent back to the factory
for a complete rewiring of the circuits to establish the new invariances and
their analogies with the old cars and the old hazards.

It is important that the new hazard be recognized by analogy and not by
trial and error. Direct highway experience would eliminate quickly a number
of types of 'learning' computers that have recently been devised, in which the
internal strategies are altered according to experienced successes or failures,
but in which there is no pattern-extrapolation or 'insight'.

The possible construction of artificial non-addressed 10"*- to 10^-element
systems with complete decision nets and with 10^- to 10^-element outputs
may deserve consideration. Primitive pattern-perceiving networks might be
useful for narrowing the band-width of communication channels, if not for
crude vehicle guidance. They might be useful internal elements in high-speed
analogue and digital computers, where their stupidity could be partly com-
pensated by the speed of operation. There they might simphfy the presently
elaborate programming operations; and could speed up computations requiring
many simultaneous substages of qualitative judgment or identification under
distortions or transformations, where the total judgment is more elaborate
than can be quickly represented by the coincidence of two digital words.

The complete theory of artificial non-addressed systems with their many
quasi-human characteristics will be fascinating. Evidently in many respects
it may be simpler and more physical than present theories of digital computers
and single-channel systems. It would include questions of optimization of
different aspects of mosaic detection, such as rates and cell sizes, the proper

Functional Geometry and the Determination of Pattern in Mosaic Receptors 397

balance among second-stage detectors of different kinds, and of foveal versus
peripheral vision, the role and mechanism of fixation and attention, and the
whole output-selection problem which has been ignored here. Theoretical
consideration might lead to principles of neural connection, unused in biological
systems, which would produce entirely different kinds of 'intelligence' in the
organization of the input fields.

Actual construction of at least the first stages of a non-addressed system
might even be relatively easy. Since the receptor elements do not need to be
wired individually, they can be laid down en masse, like the 10^ crystals of a
photographic emulsion. The first-stage neuron layer, second-stage layer, and
so on, could be laid down similarly. The crystals could not be compact in
shape, like those of the emulsion, but would have to be interbranching needles.
But the first successful device might be many orders of magnitude more complex
than anything now made.

To create such a device would require a number of really penetrating
chemical or electrical inventions, but perhaps not a prohibitive number.
Oculomotor outputs for scanning and tracking might have solutions close
to the present standard single-element solutions. The main problem would be
to guarantee that the neuron connections will tend to grow in such directions
as to support any congruences in the chemical or electrical time-patterns,
and will tend to be dissolved otherwise.

With elements having 10~^ second time-constants (comparable to transistors)
the potential learning speed of such a device would be 10^ times faster than that
of a human being (2 hours = 20 years). Such speeds could not be fully realized
because the initial address-determination will be limited by scanning speeds
and motor-output speeds and by the chemical speeds of deposition of successive
layers. But these potential speeds and these limitations are comparable to
those of a digital computer; the latter being similarly held back by the slowness
of programming and input and by the slow storage access speeds.

A pattern-perceiving device so much faster than a human being and with
a full range of inputs and outputs would pose grave problems of education,
manipulation and control, problems different from those of a digital computer
and more difficult; but the rewards would be correspondingly greater if these
problems could be solved.

Acknowledgement — This study was stimulated by a number of conversations
with Professor Richard L. Meier, now of the University of Michigan.

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434 (1956).

11. L. A. RiGGS, F. Ratliff, J. C. Cornsweet, and T. N. Cornsweet: The disappearance
of steadily fixated visual test object. /. Opt. Soc. Amer. 43, 495-501 (1953).

12. L. A. Riggs, J. C. Armington, and F. Ratliff: Motions of the retinal image during
fixation. /. Opt. Soc. Amer. 44, 315-321 (1954).

13. S. Cooper and P. M. Daniel: Muscle spindles in human extrinsic eye muscles. Brain
72, 1-24 (1949).

14. a. S. Sunderland: A preliminary note on the presence of neuromuscular spindles in
the extrinsic ocular muscles in man. Anat. Rec. 103, 561-2 (1949).

b. N. C. R. Merrilees, S. Sunderland and W. Mayhow : Neuromuscular spindles in
the extraocular muscles in man. Anat. Rec. 108, 23-30 (1950).

15. E. J. Ludvigh: Symposium on Physiol. Psychology, Pensacola, Mar. 10-11 Office of
Naval Research Symposium Report ACR-\, p. 125 (1955).

16. D. M. Mackay: Towards an information-plan model of human behaviour. Brit. J.
Psychol. 47, 30-43 (1956).

17. D. O. Hebb: The Organization of Behaviour, J. Wiley and Sons, New York (1949).

18. H. Quastler, e/ fl/. : Human Performance in Information Transmission, I-V, Tech.
Report 62, 68, 69, 70, Control Systems Laboratory, Univ. of 111., Urbana, 111.

PART VII

THE STATUS OF INFORMATION THEORY

IN BIOLOGY*

A Round Table Discussion

H. AUERBACH, C. EhRET, S. FrEED, L. S. FrISHKOPF, E. E. jACOBSf, B. N.

Jaroslow, p. D. Klein, A. L. Koch, H. R. Mahler, H. Quastler,

W. S. YAMAMOTOij:

Edited by Henry Quastler

Information theory is very strong on the negative side, i.e. in demonstrating
what cannot be done; on the positive side its apphcation to the study of Hving
things has not produced many results so far; it has not yet led to the discovery
of new facts, nor has its application to known facts been tested in critical
experiments. To date, a definitive and valid judgment of the value of infor-
mation theory in biology is not possible.

The first attempts to apply information theory to biological studies have
been met with varying degrees of enthusiasm, ranging from outright rejection
to statements like : 'Information theory furnishes a person with a sort of thread
which would allow him to sense out a continuum in the order of the universe' ;
'A means of relating the existence of life to the non-existence of fife' ; 'A quest
for regularities in irregular phenomena'. This is an extremely vast span of
reactions to a proposition of admittedly limited scope. Many of the reactions
refer not to information theory as such but more generally to interdisciplinary
endeavours, and to system sciences, both of which are characteristically
represented by information theory.

Interdisciplinary meetings are always, or almost always, an exhilarating
experience to all. They allow some sub-groups of scientists of a number of
breeds to communicate with each other in a way that is in general impossible
with the rest of the breed to which the particular scientist belongs. To put it
another way, interdisciplinary meetings factor out scientists in a different way
than occurs normally, and allow them fruitfully so to aggregate. Information
theory, with its 'interdisciplinary' generalization of the entropy concept,
provides a common meeting group for many disciplines; what is more, it has
in many actual instances provided strong rapport between representatives
of widely separated disciplines. The value of the communications aspects

* On the evening following the Conference, eleven participants gathered for an informal
session to discuss how they felt about the proceedings they had witnessed. The informal debate
which ensued was transcribed and re-arranged into a coherent account. In doing this the
editor tried to be objective.

t Dept. of Physiological Chemistry, University of California.

:|: School of Medicine, University of Pennsylvania.

399

400 Edited by Henry Quastler

of information theory was demonstrated by the apparent harmony that prevailed
at this three-day meeting despite the varied professional disciplines represented
by the papers and the participants. But the devil's advocate will argue that
of potential meeting grounds there are many, and the fact that information
theory actually has provided one does not necessarily imply that it was an
essential ingredient of success. We must not follow the lure of each and every
interdisciplinary beacon; most actual results are still obtained within the safe
limits of the estabhshed discipHnes.

More important is the problem of system sciences in general — that is,
of all sciences that deal with the whole rather than with parts, with general
principles rather than detailed specifications, with patterns rather than specific
mechanisms. This is a many-faceted problem. There are, first of all, the situations
of the 'forest-and-the-trees' type; for instance, in physics: a complete description
of every particle in a gas would contain implicitly all thermodynamic para-
meters— but in this form the information would be useless. Or, to use an
example in biology: if we knew the chemical constitution of all substances
in all cells, together with all details of distribution, chemical kinetics, in brief,
if we had reached the biochemical millenium — then we still would not necessarily
know which of all these details are significant on the next higher level of organi-
zation, although presumably this information must be impHcitly contained
in the known details. Are we simply up against a psychological limitation?
We seem able to think only of so much detail within any single train of thought.
Faced with amounts of detail considerably beyond our mental capacity we
begin to select: in the course of such selection important features are eliminated
almost as readily as unimportant ones. Knowledge is not usable for human
minds unless it is organized in blocks with not too much detail in each.

There is more behind the desire to look at the whole rather than the parts
than just an awareness of psychological limitations. There are relations within
a whole which cannot be expressed in terms of parts alone. This is the fact
expressed in the proposition 'the whole is equal to more than the sum of its
parts'. The very mixed reactions which this proposition elicits are probably
due to a failure to state exactly in what way the whole is more than the sum of
its parts. There should be little disagreement if the 'more' refers to propositions
concerning the whole which are qualitatively different from any proposition
which can be made about any of its parts. Information theory provides a
very convenient formahsm to state this situation : the total information content
of the whole is exactly equal to the sum of the information contents of the
parts — where the description of each part includes all possibiHties of connection
with other parts; the mutual dependency of parts being organized into a whole
causes a mutual reduction of uncertainty; therefore, the amount of non-
redundant information associated with the whole is less than the sum of the
information contents of the parts; the difference is exactly the infonnation
content of the constraints, or all those propositions which apply only to the
whole and not to its parts in isolation. This formulation may be of some help
in making clear a puzzling aspect of the whole-parts relation.

The preference for dealing directly with wholes rather than with parts
is greatly supported by contemplation of the way living things are organized.
The most striking feature is the existence of the organizational pattern with

The Status of Information Theory in Biology: A Round Table Discussion 401

several distinct levels of organization. Some levels are more sharply delined
than others, and the hierarchy of levels is not always unambiguous. Still,
they are pervading enough that the intelligibility and validity of any statement
in biology depends on proper agreement with organizational hierarchy. Now,
one of the outstanding features in biological organization is that quite obviously
only a small amount of the features obtaining at a given level has observable
effects on the next higher level. Hence one of the most urgent problems, on
any level, is that of detennining what details are involved in the communication
to the next higher level — but this is precisely one form of the problem of the
'whole and its parts'. Thus, in studying the whole rather than its parts we
seem to act as organelles, cells, organs do.

So we have good reasons to beHeve in the importance of the systems approach.
Still, it remains no more than a belief — and there exists an equally strong belief
that only intense preservation of details will yield major biological breakthroughs
and that it would be a 'young miracle' if really important contributions would
come to biology without intensive examination of details. So we have extreme
misgivings either way — and those misgivings seem to be destined to be with
us forever. There exists no rigid calculus telhng which formahsm must be
used on what data to achieve a major discovery.

The present conference was arranged to explore the applications of infor-
mation theory to the study of living things. This is a new field, and one cannot
say, at this time, which approach is going to be most successful. Accordingly,
the scope of the program was extremely wide. It was natural to question how
much the various papers had contributed to furthering the purpose of the
meeting. There was general agreement that some papers had contributed
very much, some a moderate amount, some little or nothing; there was however,
notable disagreement about which papers belong in which category.

There exist a few cases where information theory was used in dealing
with problems which could have been solved in other ways; and there are
very many cases where problems have been solved by various methods which
could have been, possibly, solved more easily by using information theory.
The coin problem that Rapoport talked about falls in this category; so do
the cryptographic studies of Gamov/ and YcAS. Information theory is so
general that its domain of applicability is very broad; one cannot name
one situation in which by the use of information theory one cannot get
some understanding on what is happening on an abstract basis. But one
is always beset by the niggling doubt that the application may not be proper.
One can in many situations obtain results which seem to clarify understanding
or increase the sharpness of a description to an extent which was not possible
prior to the use of information theoretic methods. On the other hand, such
results seem often suspended in mid air, away from the results of conventional
disciplines. The important question then, at this nascent stage of affairs, is some-
thing which is repellent to the scientific mind, the assessment of the 'worthwhile-
ness' of the answers information theory seems to give. It seems plausible to
assume that information theory should be useful where communication is
critical, where messages are to be transmitted in the presence of noise, and where
one might assume that some optimization is approximated; biologists are
inclined to invoke the Darwinian mechanism of random trials with perpetuation

402 Edited by Henry Quastler

of successful attempts; one is reluctant to admit any basic element of purpose —
yet it might be better to bring it to the surface for a dispassionate inquiry.
The question arose whether it was preferable to use information theory
only in a semi-quantitative fashion, to account for general trends in observed
data, or buttressed by measurements. The advantage of working with actual
numerical estimates is obvious, but against it is the irreducibly relative
nature of information measures. No unanimity existed concerning this
question. There is general agreement that data properly usable are scarce,
that there is a slight risk involved in using data from the literature which are
inadequate for this purpose, and that the procurement of more pertinent and
better data will yield material which would hardly have been produced otherwise.
Future meetings might be designed to give stimulus and continuity to production
of data which are more cogent and amenable to information theory. There
was general agreement that further meetings should and will be arranged —
and that information theory is here to stay in biology.

AUTHOR INDEX

Abderhalden, E. 81

Abelson, P. H. 83

Acher, R. 80

Ada, G. L. 90

Afzelius, B. A. 222

Akamatsu, N. 148

Alcock, R. S. 125

Allen, A. O. 270

Allmann, D. W. 61,124,126

Alper, T. 299

Anderson, E. 219, 222

Anderson, E. H. 300

Andjus, R. K. 178

Anfinsen, C. B. 80, 109, 113, 114, 116, 125,

126, 278, 289
Ard, W. B. 242, 252, 253, 256, 278, 354, 355
Armington, J. C. 379
Armitage, P. 344, 347
Aschaffenburg, R. 73
Ashby, R. W. 188
Askonas, B. A. 125
Astbury, W. T. 219
Astrachan, L. 139
Atwood, K. C. 309
Aub, J. C. 148
Auerbach, H. 347, 351, 399
Augenstine, L. 51, 61, 103, 106, 109, 114,

116, 120, 193, 194, 202, 218, 239, 287, 288,

289, 292

Bachofer, C. 290

Bahn,A. 81

Baker, W. K. 300

Baldwin, W. F. 306

Balis, M. E. 138

Balser, M. 34

Bang, F. B. 222

Bar-Hillel, Y. 194

Barltrop, J. A. 283

Bamafi, L. 80, 87

Barron, E. S. G. 258, 283

Barry, J. M. 72

Batty, I. 84

Baxter, Robert 337

Beams, H. W. 219, 222

Beerstecher, E., Jr. 207

Behrens, O. K. 79, 87

Bell, P. H. 75

Bellamy, W. D. 298

Bender, M. 86

Benedict, W. H. 294,308,310

Benfrey, B. J. 87

Benzer, S. 76

Berg, P. 131

Berman, M. 181, 182, 183

Bettelheim, F. R. 72

Bier, M. 113

Bigelow, J. N. 226

Binet, L. 322

Birch, L. C. 303

Black, F. L. 90

Blair, E.

A.

154

Blair, H.

A.

188,294,331,

333,

337

Blank, A

. A

. 41,42

Bleaney,

B.

242

Block, R

.J.

90,93

Bollman,

J.

L. 152

Boltman,

E.

T. 83, 138

Boltzmann 4, 325

Bond, V. P. 307, 308

Born, M. 265

Borysko, E. 222

Bourliere, F. 322, 328

Bowers, K. D. 242

Boyd, G. A. 294

Boyd, W. C. 212

Brachet, J. 88

BrambeU, F. W. R. 84

Branson, H. 101, 105, 106, 108, 109, 110

117, 193, 197, 198
Brawerman, G. 88
Brillouin, L. 21,198
Britten, R. J. 83
Brody, S. 327
Bromer, W. W. 79, 87
Brown, D. M. 86
Brues, Austin M. 294, 309
Bruice, T. C. 207
Bucher, N. L. R. 148
Buettner-Janusch, V. 86
Bulbenko, A. 61,124,126
Burdette, W. J. 53
Burger, M. 322
Burnett, G. 72
Burton, M. 289
Butler, J. A. V. 262, 269, 272

Calderon, H. 222, 223
Calkins, G. N. 222, 223
Calvin, M. 283
Cambrisson, J. 353
Campbell, P.N. 125
Cannon, W.B. 318,322

403

404

AUTHOR INDEX

Carlson, J. G. 55

Carnap, R. 194

Carsten, A. L. 335

Carver, E. 106

Casarett, G. 294, 333, 334, 336, 337, 338

Cavallini, D. 86, 94

Chance, B. 180

Chandrasekhar, S. 321

Chantreene, H. 125

Chapman, W. H. 307, 308

Chargaff, E. 63,83,90,91,93,94

Chase, H. H. 39

Chatton, E. 219, 221

Cheng, H.G. 127,131

Christenberry, K. W. 294, 308, 310

Christensen, B. G. 143, 148

Clark, A. M. 306

Clarke, J. M. 307

Clayton, R. S. 294, 309

Cloudman, A. M. 294, 309

Cohen, B. L. 73

Cohen, M. R. 222

Cohn, M. 125

Cole, D. 80

Cole, L. J. 308

Collinson, E. 285

Combrisson, J. 241

Condliffe, P. 113

Condon, E. U. 248, 253, 255

Consden, R. 81

Cooper, G. 114,117,120

Cooper, S. 381

Corey, R. B. 108, 109, 110, 111, 117, 254

Comsweet, J. C. 379

Cornsweet, T. N. 379

Cote, Louis J. 95

Cotter, G. J. 84

Court-Brown, W. M. 345

Cowie, D. B. 83,106,113,131

Cramer, H. 324

Crane, H. 117

Crick, F. H. C. 51, 52, 53, 63, 65, 72, 90,

91,92,95, 117, 141,298
Cronbach, L. J. 192
Cronkite, E. P. 307, 308
Grossman, E. B. 306

Dainton, F. W. 285

Dale, W. M. 258, 290, 300

Dalhamn, T. 219, 222

Danchakoff , V. 126

Dancoff, S. M. 53, 57, 111, 190, 193. 202,

218, 298, 359
Daniel, P. M. 381
Danielli, J. F. 197, 221
Davey, W. P. 293
Davie, E. W. 81
Davies, J. 290

Davis, B. D. 73
Dawson, R. M. C. 126
DeBoer, J. 362
DeBusk, A. G. 88
DeFinetti, B. 231
DeFremery, D. 90
DeGroot, S. R. 198
Deich, T. L. 73, 75, 77
DeMarko, L. 86, 94
DeMoss, J. A. 131
DeRobertis, E. 219, 222
Deutsch, T. 73
Devine, R. L. 219, 222
Dewey, D. L. 71
Diandier, K. M. 132
Dimond, A. E. 278
Dirr, K. 79
Ditchbum, R. W. 379
Dixon, J. J. 75, 79
Dobson, E. L. 342
Dolansky, L. 24
Dolansky, M. 24
Doll, R. 344, 345, 347
Donohue, J. 142,
Dorner, R. W. 90
Dounce, A. L. 71
Doyle, B. 271,274,288,289
Dreyer, W. J. 79
Dublin, L. I. 342
Dulbecco, R. 305
Dunnebacke, T. H. 222, 223
Duryee, W. R. 222, 223
Du Vigneaud, V. 74,80,81,87

Eakin, R. E. 207

Ebert, J. D. 125, 126, 129, 132

Edds, M. v., Jr. 39

Eden, M. A. 188, 359

Edsall, J. T. 267

Ehrenberg, L. 258

Ehret, C. 191, 218, 219, 222, 223, 224,

224-5, 399
Eldjarn, L. 258, 259
Elias, P. 34
Ellis, M. E. 308
Elson, D. 83,90,91,93,94
Ephrussi, B. 125
Epstein, P. 324
Erickson, J. 114,117,120
Erlanger, J. 154
Evans, E. A., Jr. 138
Evans, E. C. 354
Evans, J. V. 73
Exner, F. M. 300
Eyring, H. 117, 120, 267, 287, 290

Fahmy, M. J. 309
Fahmy, O. G. 309

AUTHOR INDEX

405

Falcone, G. 71

Fano, R. M. 11

Farmer, C. J. 130

Fan, P. 159, 160, 161

Fawcett, D. W. 219, 222

Feinstein, R. N. 84

Felix, K. 74, 79

Feller, W. 213, 361

Felton, — . 44

Fender, D. H. 379

Fenton, P. F. 39

Fine, P. C. 198

Fink, R. M. 294

Finkelstein, P. 121,283

Fisher, J. C. 347

Fisher, R. A. 4, 325

Flavin, M. 72, 80, 125, 126

Fleischer, S. 127, 131

Fling, M. 73

Flower, S. S. 328

Fox, S. W. 87, 101

Fraenkel-Conrat, H. 70, 73, 76, 77, 80, 81,

117
Francis, M. D. 125, 131
Franck, J. 239, 255, 257, 262, 263, 264, 267,

273, 287, 289, 291
Freed, S. 171,173
Frenkel, A. 294
Fricke, H. 271,272,283
Friedberg, F. 86
Friedberg, W. 126,127,131
Friedell, H. L. 335
Friedewald, W. F. 300
Frishkopf, L. S. 61, 153, 161, 164, 399
Fritz, F. 44
Fromageot, C. 80, 86
Fuerst, C. A. 280
Furth, J. 294, 308, 310

Gale, E. F. 131

Galton, F. 360

Gamow, G. 8, 51, 52, 61, 63, 71, 78, 83, 91,

92,95, 101, 107, 189, 194,401
Garen, A. 222, 223
Gates, F. L. 299
Gay, H. 219, 222, 223
Gergeley, J. 113
Geschwind, I. I. 75, 79, 80, 87
Gey, G. O. 148
Gierer, A. 70
Giese, A. C. 306
Giles, N. H., Jr. 55
Gladner, J. 113
Glinos, A. D. 61, 148
Godin, C. 125
Gofman, J. W. 343
Golay, J. E. 34
Goldblith, S. A. 280

Goldstein, L. 88

Gordon, A. H. 81

Gordon, W. G. 86

Gordy, W. 239, 241, 242, 251, 252,

252-3, 253, 254, 256, 263, 278, 289,

292, 353, 354, 355
Gowen, J. W. 54, 55, 293
Grahn, D. 293, 334
Gray, L. H. 262, 300
Green, D. E. 219
Green, D. W. 73
Green, F. C. 79
Greenstein, J. 114, 117, 120
Grier, G. W., Jr. 44
Griffith, J. S. 91,92
Grindlay, J. H. 152
Gros, F. 88
Gross, J. 131, 221
Grubb, H. M. 291
Guild, W. R. 269, 274, 278, 280
Gundalch, G. 79
Guthneck, B. T. 94
Guyer, M. G. 214

Haddow, A. 355

Hagen, W., Jr. 335

Hagihara, B. 84

Hald, A. 156

Ham, A. W. 150

Hamilton, K. A. 294, 309

Hampton, M. 84

Hancock, J. 360

Handa, D. T. 101,144

Harkness, R. D. 151

Harrington, W. F. 113,116

Harris, A. 125, 131

Harris, D. G. 174

Han-is, H. 73

Harris, J. 113

Harris, J. I. 74, 75, 79, 80, 87

Hart, E. J. 270

Hartley, R. V. L. 4

Haurowitz, F. 113, 115, 126, 127, 131

Hayes, P. M. 283

Hearon, J. Z. 143

Heath, D. C. 306

Hebb, D. O. 392

Heck, W. W. 72

Heimberg, M. 125

Hemmings, W. A. 84

Henshaw, P. S. 293, 333

Herr, E. B., Jr. 306

Herriott, R. M. 125

Hershey, A. D. 144

Hetzer, H. O. 54

Hijmans, J. 362

Hill, R. 113,116

Hins, C. H. W. 81,86,87

27

406

AUTHOR INDEX

Hinshelwood, C. N. 143

Hirohata, R. 79

Hoagland, M. D. 131

Hodge, A. J. 219, 222

Hodgkin, A. L. 202, 203

Hoffman, J. G. 307, 308, 351

Hogness, D. S. 125

Hollaender, A. 54, 298, 299, 300

Holloman, J. H. 347

Holmes, B. 295

Homeyer, P. G. 87

Honnen, L. 79

Horio, T. 84

Horowitz, N. H. 73

Hough, A. 86

Howatson, A. F. 150

Howe, E. E. 71

Huettner, A. F. 219, 222

Huggins, C. 283

Hughes, W. L. 219

Huisman, T. H. J. 73

Hunt, C. C. 159,160,161

Hursh, J. B. 333, 334, 336, 337, 338

Hutchinson, F. 269, 274, 278, 280, 290

Hutchison, C. A. 241

Hvidt, Aa. 113,116

Ingram, D. J. E. 242, 353, 355
Ingram, J. E. 353
Ingram, V. M. 73, 80
Itano, H. A. 73

Jacobs, E. E. 399

Jacobsen, C. 109

Jacobsen, E. 148

Jacobson, B. S. 301,306

Jager, B. U. 86

Jaroslow, B. N. 211,399

Jarrett, H. S. 252

Jensen, E. V. 283

John, E. R. 234

Johnson, M. P. 131

Jolles, G. 86

Jones, H. B. 188, 329, 341, 342, 343, 344,

345, 350
Jonix, J. H. P. 73
Jordan, D. O. 141
Jutisz, M. 81

Kac, M. 362
Kahn, J. R. 75, 80
Kalman, S. 113
Kalnitsky, G. 113,116
Karreman, G. 191
Katz, B. 159,160,161
Katz, J. J. 178,284
Kaufman, B. P. 55
Kauzman, W. 109, 268
Kay, L. M. 79, 81

Keller, E. B. 131
Kelner, A. 298
Kendell, M. G. 325
Kendrew, J. C. 74
Kennedy, E. P. 72,116
Keynes, R. D. 202, 203
Kharasch, N. 207
Kihlman, B. 146
Kimball, A. W. 55, 305, 308
Kimmel, J. R. 86
King, J. W. B. 73
Kitai, R. 71,80,87
Klein, D. 193, 204, 399
Klemmer, E. 24
Knight, C. A. 90

Koch, A. L. 61, 101, 136, 137, 138, 139, 140,
141, 144, 145, 146, 239, 283, 284, 290, 399
Koechlin, B. A. 86
Komintz, D. R. 86
Konig, D. 365
Korik, S. B. 125
Koros, Z. 73
Koshland, D. 116
Krohmer, J. S. 335
Kroner, T. D. 79
Kunitz, M. 113
Kutsky, R. J. 133

Lagerstedt, S. 150

Laki, K. 86

Lambert, W. V. 54

Lamont, W. A. 139, 141, 144, 146, 284

Lampen, J. O. 139

Landmann, W. A. 271

Landsteiner, K. 215

Lange, K. 86

Lansing, A. I. 309, 310, 313

Lark, C. T. 138

Lark, K. 88

Laurila, U. R. 80

Lawler, H. C. 74,81,87

Lea, D. E. 55, 262, 270, 272, 289, 298, 301

Leak, J. C. 72

Lee, R. H. 307, 308

LeGette, J. 79

Leone, C. 271

Lepper, R. 219

Leslie, P. H. 304

Levinthal, C. 219

Levy, H. R. 101,144

Lewis, E. B. 345

Li, C.H. 75,79,80,87,113

Lietze, A. 127, 131

Linderstrom-Lang, K. 109, 113, 116

Lindgren, F. T. 131

Linschitz, H. 201, 359

Littlefield, J. W. 131

Livingston, R. 353

AUTHOR INDEX

407

Lloyd, D. P. C. 157, 158

Locker, R. H. 79, 81

Lockingen, L. S. 88

Loftfield, R. B. 125, 131

Loiseleur, M. J. 178

Lorand, L. 75, 86

Lorentz, E. 293

Lovelock, J. E. 178

Low, B. W. 253

Lucas, F. 81,87

Luck, C. F. 252

Ludvigh, E. J. 385

Lumry, R. 117, 120, 267, 287, 290

Luria, S. E. 299, 300, 305

Luzzati, D. 138

Lwoff, A. 221,222,223

Maalow, O. 88
Maas, W. K. 73
Mackay, D. M. 387
Magasanik, B. 88
Magdoff, B. S. 90, 93, 95
Mahler, H. R. 61, 124, 126, 180, 399
Marack, J. C. 74
Margenau, H. 182, 183
Markham, R. 90
Marks, H. A. 342
Marsh, W. H. 75, 80
Marshall, W. H. 378
Maylow, W. 381
Mazia, D. 71
Merrilees, N. C. R. 381
Metcald, R. G. 294
Metz, C. B. 219
Michel, R. 72
Middlebrook, W. R. 75
Milhalyi, E. 113
Miller, D. G. 173
Miller, E. C. 94
Miller, J. A. 94
Miller, J. G. 234
Miller, W. C, Jr. 280
Minick, O. T. 219, 222
Minto, W. L. 294
Mirsky, A. E. 267, 287, 288,
Molnar, S. 234
Monier, R. 81
Monne, L. 218
Monod, J. 125
Montagna, W. 39
Montie, D. B. 90, 93
Moore, D. 222, 223
Moore, S. 81,86,87
Morgan, C. 222, 223
Morgenstern, O. 38

Morowitz, H. J. 101, 107, 108, 193, 239,
276, 277, 281

Mortimer, R. K. 301, 302, 310, 311, 312

Moscona, A. 222
Moshman, J. 294,308,310
Muller, H. J. 55
Murai, K. 79
Murphy, G.M. 182,183
Murphy, J. B. 126
Murphy, J. S. 222, 223
Murray, Wm. S. 307, 308, 351
Muus, J. 86
Myerson, S. 291

McConnell, W. B. 73

McCormick, G. 242, 252, 252-3

McCulloch, W. S. 234

McFadden, M. L. 86

McGarr, J. J. 79

McGill, Wm. J. 38, 161, 163, 164, 369

Mclntyre, A. K. 157,158

McLaren, A. D. 121,274

McLean, J. R. 131

McMorris, R. O. 201

Nagel, E. 222

Naughton, M. A. 74

Neumann, J. von 38

Neurath, H. 79, 81, 113, 114, 117, 120

Newman, H. H. 360

Newton, G. 131

Nickerson, W. J. 71

Niu, C. L 76, 80, 81

Noonan, Thomas, R. 335

Nord, F. 113

Nordling, C. O. 347

North, A. C. T. 73

Northrop, J. H. 125, 222, 223

Novelli, G. D. 131

Novick, A. 136, 137, 141, 145, 146

Nowell, P. C. 308

Nozaki, M. 84

Nybom, N. 301,306

Oakley, C. L. 84

Oberle, E. M. 280

Ohno, K. 80, 82

Okunuki, K. 84

Oliff, W. D. 303

Orgel, L. E. 91,92

Orlans, E. S. 74

Ottesen, M. 80,113,116

Ouchterlony, O. 214

Oudin, J. 211,214

Owen, J. 242

Owen, M. E. 302,310,311,312

Ozawa, H. 74, 76, 77, 79, 87

Pake, G. E. 252, 353
Palade, G. E. 219, 222
Paleus, S. 74, 79

408

AUTHOR INDEX

Pappas, G. D. 219, 222

Pardee, A. B. 88, 144

Parish, H. D. 86

Parker, J. R. 328

Parker, S. L. 303, 304, 307

Parkes, A. S. 178

Parrish, R. G. 74

Passman, J. M. 80

Pauling, L. 108, 109, 110, 111, 117, 254,

267, 287, 288
Pearl, R. 54, 303, 304, 307
Peart, W. S. 75

Pecher, C. 154, 155, 156, 157, 159, 160, 161
Perkinson, J. D., Jr. 126
Perlmann, G. 113,116
Perry, B. T. 90
Pihl, A. 258, 259
Pitelka, D. R. 219
Pitts, W. 234

Pitts, W. C. 373, 374, 380, 393
Piatt, J. R. 107, 123, 291, 294, 371, 372, 389,

394, 395
Platzman, R. 239, 255, 262, 263, 264, 265,

266, 267, 268, 270, 273, 287, 289, 291, 292
Plaut, W. 88
Pollaczek, H. 79
Pollard, E. C. 262, 269, 272, 274, 278, 280,

287, 288
Poison, A. 83
Polyak, S. L. 373
Pomper, S. 309
Pon, N. 113
Pontecorvo, G. 76
Popenoe, E. A. 74,81,87
Porter, K. R. 219, 222
Porter, R. R. 79
Posternak, T. 79
Potts, B. P. 222, 224-5
Powers, E. L. 219, 222, 223, 224
Preer, J. R. 226
Prestidge, L. S. 88
Price, J. M. 94
Proctor, B. E. 280
Prosser, C. L. 318
Purvis, J. L. 87
Putnam, F. 114,117,120,138

Quastler, H. 3, 38, 39, 41, 53, 58, 111, 135,
187, 190, 191, 193, 194, 197, 202, 207, 209,
211, 216, 218, 221, 226, 281, 298, 351, 359,
369, 394, 399

Raacke, I. 113
Raacke, 1. D. 75, 79
Rabinowitch, — . 255, 257
Rahn, Otto 54, 298, 309
Rail, W. 159,160
Ramachandran, L. K. 73

Ramasarma, G. B. 90

Ramler, W. J. 270

Ramsey, N. F. 247, 248

Ranson, R. M. 304

Rapaport, A. 196, 230, 401

Rashevsky, N. 193, 222, 223, 225

Ratliff, F. 379

Ray, R. 114,287,289

Rebhun, L. I. 219, 222, 223

Redfield, R. 289

Reed, I. S. 34

Rees, E. D. 178

Ressler, C. 80, 87

Rexroad, H. N. 242, 252, 356, 253-3

Rhondin, J. 219, 222

Rich, A. 71,72,78,83,93,107

Richards, F. 113

Ridenour, L. N. 6

Riggs, L. A. 379

Rimoldi, H. J. A. 234

Robbins, K. C. 74

Roberts, E. 90

Roberts, R. 106, 113

Roberts, R. B. 83

Roche, J. 72

Rocklin, S. R. 270

Rogers, W. 113,116

Romanoff, A. J. 130

Romanoff, A. L. 130,131

Ronzoni, E. 86

Roos, P. 80, 87

Roper, J. H. 76

Rose, H. 222, 223

Rose, I. A. 139

Rosenberg, S. 335

Rosenblith, W. A. 61,153,157

Rossi-Fanelli, A. 86, 94

Rost, G. 94

Roth, L. E. 219, 222, 223, 224-5

Rowland, H. A. 376

Rupe, C. O. 130

Russ, S. 293, 294

Russell, W. L. 55, 294, 301, 312

Rylander, P. N. 291

Ryle, A. P. 71,80,87,283,284,286

Sacher, G. A. 293, 294, 301, 317, 322, 323,

326, 327, 329
Sachs, H. 131

Sanger, F. 71, 74, 80, 87, 283, 284, 286
Satake, K. 74, 76, 77, 79, 87
Savage, L. J. 231
Sayre, E. V. 173
Sbara, A. J. 300
Schellman, J. 113, 116
Schoenfeld, R. 181, 182, 183
Schott, R. G. 54
Schram, G. 70

AUTHOR INDEX

409

Schroeder, W. A. 79, 81

Schroedinger, E. 117,189

Schuler, R. H. 270

Schwartz, D. 71

Schweigert, B. S. 94,139

Scott, G. M. 293, 294

Scott, J. F. 140

Seegers, W. H. 86

Seguela, J. 219

Sekuzu, I. 84

Semmett, W. F., 86

Seno, N. 79

Setlow, R. B. 269, 271, 272, 274, 278, 280,

288, 289
Shannon, C. E. 4, 21, 44, 53, 187, 234, 298,

368
Shapiro, B. 258, 259
Shaw,J.T.B. 81,87
Shields, H. 242, 251, 252, 252-3, 253, 254,

256, 278, 354, 355
Shields, J. 74
Shimura, K. 79
Shive, W. 207
Shock, Nathan 344
Shortley, G. H. 248, 253
Shumway, N. P. 75, 80
Siekevitz, P. 131
Silberstein, H. E. 294
Silverman, R. A. 34
Simmons, Eric L. 335
Simon, H. A. 92, 95, 123
Simpson, M. V. 125, 131
Sinex, F. M. 72
Singer, S. J. 178
Sinn, L. G. 79, 87
Skanidze, I. K. 132
Sleggs, L. T. 75, 80
Sloan, G. J. 252
Smart, H.F. 178
Smellie, R. M. S. 88
Smith, A. U. 178
Smith, E. 113,116
Smith, E. L. 86
Smith, H. 71
Smith, J. D. 90
Smith, L. F. 71,80,87
Smith, M. J. 307
Smith, S.G. 81,87
Smith, W. V. 242, 353
Soreni, E. T. 73, 75, 77
Spiegelman, S. 125
Sri Ram, J. 113
Stacy, R. W. 201
Stadler, J. 55, 293
Stapleton, G. E. 298, 300
Staub, A. 79, 87
Steam, A. 114, 117
Steam, A. E. 268, 287, 288

Stein, W.H. 81,86,87

Steinberg, D. 109, 113, 125, 126

Stent, G. 280

Stepka, B. 301

Stetten, M. R. 72

Stevens, K. W. H. 242

Stockell, A. 86

StoraasU, J. P. 335

Storer, John 335

Strange, R. E. 71

Strong, J. 375, 376, 377

Sunderland, S. 381

Susman, N. 148

Suter, G. M. 294

Swanson, C, P, 55

Swick R. W. 101,144

Swift, H. 219, 222, 223

Symonds, P. 86

Szafarz, D. 88

Szent-Gyorgyi, A. 113

Szilard, L. 4, 136, 137, 141, 145, 196

Szorenyi, E. T. 73

TabrofT, W. 79

Tahmisian, T. N. 219, 222

Talbot, S. A. 378

Tapley, D. F. 283

Tartar, V. 223, 225

Taylor, J. H. 219

Teller, E. 120

Terminiello, L. 113

Thompson, A. R. 80

Thompson, E. O. P. 74, 79, 80, 81, 86

Thompson, W. D'Arcy 191,219,225

Thomson, J. F. 335

Tobias, C. A. 300,301,305

Tolman, R. C. 198

Tourtellotte, W. W. 335

Townsend, J. 252

Trambarulo, R. 242, 353

Trippett, S. 80, 87

Tristram, G. 289

Trucco, E. 191

Tumanishvili, S. 132

Tuppy, H. 74, 79

Turba, F. 79

Turing, A. M. 37, 360

Turner, J. E. 127,131

Tweedell, K. S. 360

Uebersfeld, J. 241,353
Uhlenbek, G. E. 320
Umbarger, H. F. 144
Upton, A. C. 294,308,310
Uretz, R. B. 299,300,305,312

Van Der Schaaf, P. C.
VanderWaals 109

73

410

AUTHOR INDEX

Van der Waerden, B. L. 362
Van Roggen, A. 252
Van Roggen, L. 252
Van Slyke, D. D. 72
Vaughan, M. 109,113,125,126
Velick, J. F. 86
Velick, S. F. 86, 125
Volkin, E. 139

Waelsch, H. 131

Walker, E. P. 328

Wallace, B. 309,312

Waiter, H. 124,126,127,131

Walton, B. P. 131

Wang, M. C. 320

Ward, J. C. 362

Warren, F. L. 73

Wassermann, F. 221

Watson, J. D. 51, 52, 53, 63, 65, 90, 117,

141,298,299
Watson, M. L. 219, 222, 223
Weaver, W. 4, 53, 187, 298, 368
Webster, G. C. 131
Weinstein, H. J. 222
Weiss, P. 125, 126
Weissmann, S. I. 252
Weisz, P. B. 39, 225
Wenneker, A. S. 148
Went, F. W. 360
Wertz, J. E. 242, 252
Westfall, J. A. 219
White, H. E. 248, 253
White, W. F. 74, 75
Wicks, L. F. 86
Wiener, N. 4,21,187
Williams, D. T. 201
Williams, G. R. 180
Williams, R. B. 126
Williams, R. J. 55, 207
WiUiamson, M. B. 80

Wilson, P. W. 144

Windsor, E. 71

Winnick, T. 125,131

Winzler, R. J. 208

Wohlfarth-Bottermann, K. E. 219, 222

Wolf, G. 72

Wolken, J. J. 222

Wollenberg, A. 80

Wood, J. L. 126

Wood, T. H. 300, 305, 306

Woods, P. S. 219

Worden, R. E. 201

Work, E. 71

Work, T. S. 125

Wyatt, G. R. 63

Wyss, O. 354

Yalow, R. 290

Yamamoto, W. S. 399

Yamashita, J. 84

Yates, R. A. 144

Yeas, M. 8, 51, 52, 55, 61, 63, 68, 69, 70,

71, 78, 83, 87, 88, 92, 101, 102, 107, 108,

189, 194,401
Yearkes, A. W. 328
Yearkes, R. M. 328
Yockey, H. P. 50, 54, 55, 188, 297, 298,

299, 308,327,338, 351, 359
Yuasa, Akira 219

Zamecnik, P. C. 131
Zavoisky, E. 241
Zcheile, F. P. 174
Zelle, M. R. 54, 298
Ziegler, J. 86
Zimmer, K. G. 258
Zinder, N. D. 222, 223
Zirkle, R. E. 270,300,301,305
Zwartouw, H. T. 71

SUBJECT INDEX

Acetahularia 88

Acetyl DL-valine 252-3 (Fig. 7)

Acroblast 219, 222

ACTH 69, 75, 76, 104, 107

Actin 79, 86

Additivity, in information functions 21

Address 191, 371

— , determination of 379, 380, 387, 394

Address learning 374

Adenine 63, 90, 136, 137, 138, 141, 145

— deoxyribosidc 1 38, 282, 294
Adenosine deaminase 146, 286
Adenylic acid 70, 90
Adrenocorticotropin 68, 79

Aging 188, 293, 297, 308, 317, 326, 339,

341, 344, 347
— , premature 293
Alanine 70, 90

Albumin 104, 114, 128, 252-3 (Fig. 10)
— ' ^gg ^^^ Ovalbumin

— peptides 128
Alcohol dehydrogenase 86
Aldolase 86, 288

Allele 73,311
Allelic states 190
Allelomorph 301,302
Alphabet 8, 15, 18,211
— , binary 8, 20
Ambiguity 31
Amino acid residues 50

sequence 105,135,194

■ , phylogenetically common ancestral

107
Amino acids 18, 65, 71, 76, 84, 105, 128,

242, 252, 253, 263, 273

, X-irradiated 252

Amino-adipic acid, a 71
Amoeba 88
Amylase 1 14
Analogy perception 390
Anaphe moloneyi 87
Antibodies 192, 342, 394
Antibody formation 211
Antigens 192,211,214,394
Antimetabolites 193
— , artificial 206
— , natural 206
Antimutagens 145
Antiserum 214
Apo-enzyme 204
Arginine 70, 90, 109
Armadillo, nine banded 360

Arrangement, linear 18
Ascorbic acid 208
Asparagine 70
Aspartic acid 70, 90, 109
Auger cascades 270
Averaging, effect of 23
Axon 386

Bacillus sitbtilis 111

Bacterium 136. 178, 215, 277, 299, 301

Binary digits See Bits

Binary symbol 9

Biological material, inactivation of 262, 276

et seq., 287
Bioplast 218
Biosynthesis 117,145
— , of protein 124
— , purine 1 38
Biotin 208
Biotopology 218

bis-2, 4-dinitrophenyl-L-cystine 284
bis-DNP cystine 284

, gamma-ray irradiation of 285

Bits 21

Blepharoplast 219

Bohr magneton 247

Bonds, interhelical 1 10

— , rupture by ionization 269

Born energy of polarization 265 et seq.

Bovine albumin 252-3 (Fig. 10)

CO,, level in blood, as O., regulator 7

— , , as symbolization 7

Caffeine 136, 137

Cage effect 252, 255, 257, 273, 353

Calandra oryzae 303, 306

Cancer 342, 343, 344, 347, 353, 355

Cariboxypeptidase 79, 86

Carcinogenic agents 354, 355

Carcinogens 294, 309, 347, 351

Carotene 173,208

Casein, a 79, 86

Cat, cochlear nucleus 157

Catalase 84

Category 6, 10, 12, 40

Cerebral cortex 381

Channel 30

— capacity 32, 194

theorem 3 1 , 34, 39, 298

Channel communication 31
— , noise-free 31

411

412

SUBJECT INDEX

Chemical potential 199
Chick 208

Chick embryo See Embryos
Chlamydomonas 301, 306
Chloracetyl-DL-alanine 252-3 (Fig. 5)
Chloramphenicol 88
Chlorophyll 174
Choline 208
Chromidion 218

Chromosome 63, 65, 219, 224, 312, 359,
373

— aberrations 55, 298, 301
Chymotrypsin 113
Chymotrypsinogen 79, 87, 104
Cilium 219

Citruline 71
Clupein 79
Coacervation 219
Cocarboxylase 204
Cochlear nucleus 157
Code 30, 34, 219, 298
— , antigen-antibody 211
— , binary 9

— , DNA-protein 52, 67, 194
— , error correcting 32, 281
— , Fano 11, 15, 16, 18
—, Morse 8,10,41,193
— , over-lapping 67, 92

— groups, combination of 10
Coding

— problem, protein text 87
Co-enzymes 192, 204
Co-factors 204
Collagen 72, 79
CoUinearity 380
Communication 25

— channel 3 1

— -engineering 187

— ■ systems 30, 35

Conditioned reflexes 7

Congolese moth See Anaphe maloneyi

Congruence, displacement 376

— , self 376

Conjugation 309, 310

Conservation principle, one-sided 189

— , two-sided 189

Constraint, measures of 27, 188

Constraints 37, 105

Continuity, in information functions 21

Control, in the animal and in the machine

187
Correlation intersymbol 83
Cortex surface 383
Creatine-phosphate-ATP system 225
Cross reaction 212
Cryptography 70
Cybernetics 5
Cysteamine 259

Cysteine 70, 101, 129, (Figs. 9, 10), 253,
255, 258

— residues 109

Cystine 71, 90, 101, 251, 252-3 (Figs. 4,
9), 253, 255, 256, 258, 259, 271, 283,
284, 288, 290, 292

Cystinyl residue 71

Cytidine deaminase 286

Cytidylic acid 70, 90

Cytochrome 74, 79

Cytoplasm 63, 65, 89, 150, 218

Cytosine 63, 142

Dahlbomimis fuscipennis 306

Dancoff's principle 50, 53, 111, 190, 192,

298
Darwinian machines 188
Death, definition of 54
Decision theory 5
Decoding 6, 31

Degenerative diseases, chronic 348
Denaturation 283, 292
— , of proteins 117,267,268,271, 274, 286,

287
Deoxyribonucleic acid See DNA
Diabetes melHtus 342, 344
Diamino pimelic acid 71
Dictyosome 219, 222
Dielectric absorption 264

— properties 263
Differentiation, capacity for 125
Dipeptides, combinations of 78, 82
Diphenyl picryl hydrazyl (DPPH) 249
Diploid survivorship 298, 301

Direct action 253, 258, 272, 276, 300, 301,

354
Disaccharide 212
Displacement congruence 376
Disulfide bond 116, 239, 255, 257, 258,

259, 271, 278, 283, 286, 287 et seq., 292
Disulfide interchanges, radiation-induced

283 et seq.
DNA (deoxyribonucleic acid) 51, 52, 63, 70,

76, 88, 101, 117, 138, 245, 269, 272, 282,

298, 359, 394

— inactivation of by radiation 269, 272

— synthesis, steady-state flux of 142

— Watson and Crick model of 51, 55, 63,
65,90, 142, 189

Drosophila 53, 303, 304, 312

— melatwgaster 293, 304, 307, 337
— • subobscura 307

Earthworm See Lumbricoides terrestris

E. coli See Escherichia coli

Edestin 104

Egg albumin See Ovalbumin

Electrochemical potential 200, 261, 292

I

SUBJECT INDEX

413

Electron-spin resonance 241-261, 292, 353

— hole (electron vacancy) 257, 258, 272, 292

— hole trap 257, 258, 272, 278

— trap 256, 257, 259, 265, 266
Electrophysiology 197
Embryonic protein synthesis 130
Embryos 124

Emulsin 114

Encoding 6, 12, 16, 31

Endoplasm 221, 222

Ensemble 20,191,307

— , Gibbsian 277

— , of genetic messages 53

— , of organisms 51,52,297

— , probability measures of 193

Entropy 21, 44, 52, 1 19, 171, 198, 269, 287,

298, 317,324,359
— , irreversible production of 198

— surface, equilibrium position on 200
Enzymatic inhibition 139

Enzymes 63, 111, 121, 125, 140, 192, 197,

242, 263, 276, 278
Enzyme-substrate complex 171, 180,206
Equilibrium position, on the entropy surface

200
Equivocation 31, 52, 55, 302
— , in the germ line 298, 309
Error detection and detection 32
Escherichia coli 73, 83, 92, 101, 106, 137,

138, 215

, B/r strain of 300

, purine metabohsm in 138,144

Estrogens 208

Euchlanis triquetra 309, 310

Europium chloride 173

Events, groups of 12

— , rare 42

— , real 7, 8

— , symbolic 7

Evolution 112

Excited molecules 273

Experimental design theory 5

Eye, human 373

— , insect 373

— , spot 222

Fano code See Code, Fano

Fatty acids 242

F-center 241

Feather quill, irradiated Fig. 1 1

Feedback 188,223,372,385,389

— , negative 148

Fibrinogen 75, 87

Fission, binary 223

Fixation tremor 379

Flagellum 219

Fluctuations 160, 200, 317, 320, 324, 328

Fluorescence spectrum of solutions 173

"Fluxes" 199

Folic acid 208

Force of mortality 298, 299

"Forces" 199

Formate 1 38

Franck-Condon principle 255, 257

Free energy 1 1 7

— radicals 242, 243, 246, 252 et seq., 258,

259, 283, 353
Frog 208 See Rana pipiens
— , sciatic nerve 154, 155
Fruit fly See Drosophila melanogaster
Functional geometry 375

.^-Factor 243
Game theory 38
y-Globulin 79, 86, 212
Gastrocnemius nerve 1 58

, in decapitated cats 157

Gaunine 63
Gene 73, 88, 224

— code 310

— mutations 298, 301
General systems theory 5

Genetic information 51, 70, 190, 306, 338

, storage and transfer of 298

Genetic locus 190

— noise 52, 55, 189, 298, 309, 313
Genome 53, 54, 55, 310

Germ cell 359

— line, equivocation 298, 309
Giant starfish 215

Gliadin 73, 75, 104

Globulin 79, 129, 212

Glucagon 79, 87

Glutamine 70

Glutamic acid 70, 90, 109, 131

Glutathione 253, 255, 258, 259

Glyceraldehyde dehydrogenase 86

Glycine 70, 90, 138, 242

Gly co-protein 212

Glycyl DL-valine 252-3 (Fig. 6)

Glycyl-glycine 252-3 (Fig. 10)

Glycyl glycine, deuterium substitution 354

Glycyl glycyl glycine 252-3 (Fig. 5)

Golgi apparatus 222

Gompertz function 323, 350, 351

Grain beetle See Calandra oryzae

Gramicidin, action spectra for 288

Grasshopper See Melanoplus differentialis

Green algae 306

Growth hormone 104

Guanine 63, 136, 137, 138, 141

— deoxyriboside 138
Guanosine 138
Guanylic acid 70, 90
Guinea pig 208

414

SUBJECT INDEX

Habrobracon juglandis 306, 307
Haploid 300, 306

— survivorship 298
Heart, chicken 129
Helix 65,110,117,142
— , alpha 254

— , double 141, 190

Hemocyanins 212

Hemoglobin 73, 75, 79, 85, 86, 90, 94, 104,

114, 268, 272
Hepatectomy 148
Heterophile reaction 212
Histidine 70, 90
Hit theory See Target theory
Holo-enzyme 204
Homeostasis 318, 326, 342
Homocysteine 71
Hormones 191,204,242
Horse mussel 215

Humoral system, of communication 148
Hydrogen bond 109, 117, 266, 287 et secj.
Hydroxyglutamic acid 71
Hydroxylysine 70, 72
Hydroxyproline 70, 72
Hyperfine structure 250
Hypertensive peptide 75, 80
Hypoxanthine 137

Immunopolysaccharides 88

Inactivation of proteins, by ionizing radiation

262, 287
Independence 21
Indirect action 258, 300, 301, 354
Individuality 54
Influenza A virus 90
Information 230, 317, 324
— , chemical 394
— , conservation of 189
— , decay of 55

— , destruction of by ionizing radiation 239
— , Fisher 325

— , genetic 51, 70, 190, 306, 338, 359
— , measure of 18, 20, 25, 40, 169, 188
— , rate of production 198,199
—, redundant 33,189,292
Information, replication 87
—, storage 61,87,393
— , transfer 61, 87
— , transmission of 112,211,298

— and entropy 21, 44, 171

— and intelligence 6

— assembly 373

— content 20, 21, 39, 41, 103, 116, 212,
218,235,276, 309, 359,400

, carried by protein sequence 103, 113

, configurational 105,114

, destruction of 297

-. of molecules 193

Information content, of tracer data 181

, per printed letter 44, 281

, structural 1 1 1

, total 105

, total carried by proteins 113

— continuum 6

— functions 26, 31, 43

— measures, Shannon-Wiener 21

— measures 103

, determination of 169

, functions of ensembles 192

, of constraint between letters 281

, relativity of 40, 191, 193, 235

, the search for invariants 190

, topological representation of molecules

193

— representation 6, 7, 8, 9

— theory 5, 7, 50, 230, 276, 399
, domain of in biology 187

— transfer 65, 125

— transmission, by biological co-factors 204

, from genetic to somatic material 189

, process of 1 12, 189

, rate of 44

Inheritance, cytoplasmic 88

Inhibition, enzymatic 139

Inhibitor 208

Injury, irreparable 331

— , irreversible 336

— , radiation 271, 331

— , reparable 331

Inosine arsenolysis, inhibition of 140

— hydrolase 140
Input information 32

Insulin 71,74,104,107,114,125,
252-3 (Fig. 12), 256, 268, 288, 290, 343

— (cattle) 80

— 'A' chain 66, 69, 80, 87

— 'B' chain 69, 80, 87
Intelligence and information 6, 7, 20
Internal emitters 338

Interphase 224

Intersymbol influence 56, 67, 71, 78, 105,

115
Invertase 115

Ionization 243, 255, 264 et seq., 278
Ionization, in proteins 266
Ionizing radiation 252 et seq., 262 et seq.,

273,283,331, 333, 355

• , latent injury from 271, 272, 331

Isoleucine 70, 90
Isopropylbenzene 291

Karyoplasm 221
Keratin protein, /?
Kinetodesma 224
Kinetosome 224

253

SUBJECT INDEX

415

Kinety 224

Lactalbumin, a 86

Lactogenic hormone 104

Lactoglobulin, /5 80, 86, 104

Lacto peroxidase 114

Language 8,44,104,111,193

L-cystine 284

Late eiTects, from radiation damage 301

LD50 332, 333

Learning 392

LET 269, 270, 279 et seq.

Lethal bound, limit 298, 318, 326

Leucine 70, 90

Leucosin 115

Leukemia 343, 345

Life expectancy 333, 334, 344

— span 312,331,334,342
Limitations, of information theory 192
Linear programming theory 5
Lipo-protein 212

Liver, chicken 129

— regeneration 148
Logical machine 37
Longevity 331
Lumbricoides terrestris 215
Lysine 70, 72, 90, 109

Lysozyme, papaya lysozyme 80, 86, 107,
113

Macrostate 118

Malignant neoplasms See Cancer

Markoffian, fluctuation process 320

Mass action, law of 151

Maximum likelihood estimate 213

Maxwell's demon 120, 196

Melanophore 80, 87

Melanopliis differentia/is 215

Membrane phenomena 197

Membranes, exclusive 198

— , indifferent 197

— , responsive 198

Memory 393, 394

Message 30, 33

— , genetical 5 1

— entropy 52, 54, 298

— sets 191

Metabolism, purine 138
Methionine 70, 90
Methylcholanthrene 294, 309
Methyl xanthines 136
Micelle 109,218
Micro-organisms 101,131,208
Microsome 66, 132
Microstate 118

Microtus agrestis 303
Microwave spectroscopy 242, 353
Mitochondrion 132,219

Molecular energy 118

— dissociation process 264
Molecules, irreversibly inactivated 120
Monosaccharide 212
Mono-DNP cystine 284

Mono-2, 4-dinitrophenyl-L-cystine 284

Morbidity 342

Morphogenesis 218, 359

Morse code See Code, Morse

Mortality 317,319,342

Mosaics, non-addressed 372

— , pre-addressed 372

Moth, Congolese (Anaphe maloiwyi) 87

Motoneurons 157

Mouse 293,304,309,333,337,351

— , LAFi 294, 307

— , R.F. 294, 307

Mutagenesis 136

— , chemical 145

Mutagenic agents, chemical 136, 145, 309

, DNA 137

, RNA 137

Mutagenic effects 355

Mutagenicity 137

Mutants, biochemical 300

Mutation rate, spontaneous 58, 136, 141,

145
Mutations 65, 71, 74, 84, 137, 298, 353, 355
— , point 55, 56, 146
— , recessive lethal 301
Myeloma globulin 86
Myoglobin 74, 80, 86, 104
Myosin 104,113

Nebenkern 219

Negentropy, rate of production of 199
Neoplasms, malignant See Cancer
Nerve fiber 153

— membrane 201

— optic 389

- — protein 86
Nervous system 347
Neural connections 383
Neural network 372

— systems 153
Neural thresholds 153
Neurospora 13

Neuron (See also Motoneurons) 384, 389,

393, 395
Nicotinamide 208
Nissl substance 222
Noise 31, 35, 51, 53, 165, 189, 281, 319,

379
— , chemical 172
— , genetic 52, 189, 298, 309, 313
— , measures of 188
— , random Gaussian 320
— , "white" 55, 320

416

SUBJECT INDEX

Noise-and-redundancy-theorem 188, 189,

298
Non-addressed systems 373, 388, 396
Norleucine 71

Nuclear hyperfine structure 244
Nucleic acid metabolism, enzymes of 140

— acid residues 191

— acids {See also DNA, RNA) 18, 138, 144,
209, 242

Nucleolus 219
Nucleotide pairs 51, 52
Nucleotides 8, 18, 65, 70, 76, 91, 298
Nucleus 219

Odd-coin problem 233, 401

OH radicals 258, 259, 284

Operations analysis 5

Order 268, 276, 362

Orderliness, living things feed on 117, 189

— , problem of destruction of 188

Organ, control 191

Organ, target 191

Organelle decision trees 221

Organelles 218

Organization 36, 39, 218, 262

Organ-specific transfer 129

Origin of life 278

Ornithine 71

Output information 32

Ovalbumin (egg albumin) 80, 1 14, 128, 212,

268, 272, 289
— , peptides 128
Ovum, fertilized 51,63
Oxytocine 66, 69, 80, 87

p-Xmmo benzoic acid 208

Pantothenic acid 208

Papain 80,86,113

Parallelism 381

Paramagnetic resonance {See Electron-spin

resonance)
Paramecium 220-225, 306
Paschen-Back effect 246
Pathology of aging 293
Pathology of radiation damage 293
Pattern perception 371, 374, 388
Pauli principle 243
Pellicle unit 224
Peniculus 225

Pepsin 80,104,113,116,268
Pepsinogen 87
Peptide bonds 263
Peptides 215,242,252
— , X-irradiated 253
Peroxidase (milk) 268
Phenylalanine 70, 90

Philodina citrina 309, 310

Phosphoglucomutase 1 1 6

Phosphorylase 86, 144

Phosphorylated derivatives 138

Phosphoserine 70, 72

Physiologic variables 319,322

Plasmagenes 219

Plasmapheresis 148

Ploidy 312

Point mutation 55, 56, 146

Poisson distribution 83, 107

Polarization, electronic 266

— , orientation 267

— , secondary-bond 266

— , vibrational 266

Polypeptides 273

Polypeptide structures, minimum entropy
117

Polystyrene, X-irradiated 256

Pooling, effect of 24

Praseodymium chloride 172

Pre-addressed 373

Preservation, of cells, tissues at low tempera-
tures 178

Probabilities, conditional 28

— , unequal 13

Probability density 247

— distribution 231,298

, joint 320

Problem-solving process 234
Prolactin 80

Proline 70,72,90
Protamine 74

Protein 18, 202, 204, 209, 212, 242, 263,
273, 283, 287

— and peptide chains 87
— , composition of 90, 101

— precursors, incorporation into chick
embryos 128

Proteins, denaturation of, reversible 117,

267, 288
— , genetic determination of 52, 73
— , homologous 74
— , inactivation of 262 et seq., 287
— , ionized 257
— , radiation damage in 253, 262 et seq.,

287
— , terminal residues of 77
Protein specificity 18, 50

— structure 103,111,267
and language 105, 1 12

— synthesis 65, 125, 135, 144, 298

, mechanism for 65, 125

Prothrombin 86

Proto-RNA 89
Pseudo-holo-enzyme 204
Psychology 191,231
Punctuation mark 8, 69, 91

SUBJECT INDEX

417

Purines 63 et seq., 139

— , biosynthesis 138

— , derivatives, structure 136

— , incorporation and mutagenicity 137

— , metabolism 138

— , phosphorylases 140

Purine-purine transglycosidase 140

Purine-pyrimidine transglycosidase 140

Pyridoxine 208

Pyrimidine phosphorylase 140

Pyrimidines 65

Quandrulus 222, 225

Quantum theory 196, 231 , 242, 247

q. 347

Radiation {See Ionizing radiation, Ultraviolet
radiation)

— damage 241, 252 et seq., 262 et seq.,
276 et seq., 283 et seq., 287 et seq., 308,
395

, protection from 273

— exposure 342

— hazards to man 297, 301, 338

— injury 253, 331

, irreversible 273, 339

Radiation sensitivity 269

Radicals, free 259

^, lifetime of 243, 252 et seq.

Radiobiology 190, 239, 252 et seq., 262 et

seq., 276 et seq., 283 et seq., 287 et seq.,

292 et seq., 293, 297
Radiomimetic chemicals 355
Radiomimetics 309
Random networks, theory of 1 88

— variables 230

Rat 148, 208, 293, 335, 337

Rate processes 327

Rattus natalensis 303

Reaction kinetics 56

Receptors 372

Recessive lethal mutations 301, 312

Recovery 308, 322, 335

— , from radiation damage 332

Redundance 3, 33, 111, 116, 369

— , in the germ cell 359, 360

— , measures of 188

Redundant information 3, 33, 189

Rennin 115

Replication, capacity for 125

RepresentabiUty condition 31

Representation, binary 8, 17, 20

— theorem 17, 188

Residues, correlations between adjacent 78
Reticulocytes 94
Retina 383
ReversibiHty 121
Riboflavin 204, 208

Ribonuclease 69, 81, 86, 87, 104, HO, 116,

125, 285, 288
Ribonucleic acid See RNA
Ribonucleoprotein 150
— , associated basophilic bodies 150
RNA 8, 52, 66, 70, 88, 90, 92, 101, 131, 138,

278, 394
Rotifer 178, 309, 313
Ruling engines 376

Salivary amylase 86

Salmine 81, 104

Salmonella gallinarum, typhimurium 54

Salt bridges 109, 267

Sample space 231,235

Sarcosome 222

Sciatic nerve, of frog 154, 155

Screws, precision 376

Sea pen 215

Selection 322

— rules 191

Semantic information 194
Sequence 51, 107, 113, 135, 191, 194
Serine 70, 90, 138
— , protein-bound 72
Serum, normal blood 148

— albumin 74, 81, 86, 104, 128, 150, 289,
290

• , chicken 127

Silk, irradiated 353

— , X-irradiated 252-3 (Fig. 8)

— fibroin (Bombyx) 8 1 , 1 04
Site, sense, non-sense 91
Solanin 115

Somatic line 309

Somatic mutation 344

Soret band 174

Southern bean mosaic virus 90, 93

Specificity See Protein specificity

— , antigenic 211

— , code of 194

Spectroscopic splitting factor, g 242

Spin-orbit coupling 249

Spleen homogenate 308

Spores 276

S-Sbond 116

Staphylococcus aureus 1 3 1

Stentor 223

Stereocilium 222

Stimulus, threshold of 154

— threshold variations, possible sources of
159

Stochastic process 321

S^5 126

Sulphur linkages, in proteins 109, 116, 239,

257, 278, 283, 287, 292
Survival curves, exponential 300
, sigmoid 300

418

SUBJECT INDEX

Survivorship curves 51, 297, 317

Symbol, 8, 30, 390

Symbolic events See Events, symbolic

— representation 7
Symbolization 7
Synapse 157
Synaptic delay 234
System analysis 37

— parameters 182

— theory 5

Systems 36 See also Communication sys-
tems
— , multipart 38
• — , two-part 28, 30

Target 276, 281

— theory 276, 298, 300, 301, 305

— volume 276, 289
Tautomeric form, of purines 141
Temperatures, chemistry and biochemistry

at low 171

Template 67, 71

Theobromine 136, 137

Theophylline 137

Thermal killing 297, 305, 306

Thermodynamics 52, 192, 196

— , equation of state in 307

Thermodynamics, irreversible 194, 198

— , second law of 117, 120, 196

Thiamine 208

Threonine 70, 90

Threshold, fluctuating 153, 161

Thymine 63, 141

Thyroglobulin 72

Thyroxine 72, 207, 208

Tissue homogenates, incorporation of acti-
vity from 130

r-Measure 27, 29

Tobacco mosaic virus 70, 76, 81, 90, 93,
278

Toluene 291

Tomato bushy stunt virus 90

Torulopsis utiUs 126, 131

Transducer 3 1

Transforming principle 276

Transphosphorylase 86

Tribolium confiisum 293

Trichocyst 220, 221

Triticum durum, vulgare 73

Tropomyosin 81, 86, 104

Tropylium ion 291

Trypsin 114,268,288

Trypsinogen 81, 87
Tryptophan 70, 90
Tumors 309

Turnip yellow virus 90, 93
Twins, monozygotic 360
Tyrosine 70, 90, 109
Tyrosine-O-sulfate 72

Uhraviolet radiation 252, 263, 273, 274, 287,

290,297,299, 306, 312, 353
— action spectra 274, 288
Uncertainty 19, 27, 32, 41, 230, 235, 368
— , conditional 28
— , — , average 30
— , functions 207
— , joint 27

— , mappings in generalized space 184
— , measure of 19, 21
— , relative 369
—, unit of 185
Unitization 29, 218
Unsaturated fatty acids 208
Uridylic acid 70, 90
Urosil 66

Valine 70, 90

Van der Waals forces 109

Variables 25

Variance 322

Vascular disease 342, 343

Vasopressin 66,69,74,81,87

Vibriolysin 115

Virus 223, 276, 299, 301

Vitamins 204, 242

— , B 207

— , D 208

Vole 304

Wool 81

Word 8, 107, 212, 363

Xanthine 136, 137

X-rays 243, 252, 290, 293, 300, 305, 337,
353, 355

Yeast 215,300,301,310
—.diploid 301,305
Yeast invertase 268
Yule distributions 123

Zein 104

ZoUner illusion 385