Table Of ContentQuantitative Biology of Metabolism
Quantitative Biology
of Metabolism
Models of Metabolism, Metabolic Parameters, Damage
to Metabolism, Metabolic Control
3rd International Symposium,
Biologische Anstalt Helgoland
September, 26-29, 1967
Organizers
A. Locker and F. Kruger
Editor
A. Locker
With 66 Figures
Springer-Verlag Berlin· Heidelberg. New York 1968
ISBN 978-3-540-04301-0 ISBN 978-3-642-51065-6 (Ebook)
DOl 10.1007/978-3-642-51065-6
All rights reserved. No part of this book may be translated or reproduced in any form without written permissen
from Springer-Verlag. © by Springer-Verlag Berlin·Heidelberg 1968
Library of Congress Catalog Card Number 68-55620
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Title No. 1527
Opening Address
Ladies and Gentlemen,
This is the third time that I have the honour to welcome the participants
of the International Symposium on Ouantitative Biology of Metabolism here on
Helgoland. I cordially welcome you to this big rock of red sandstone in the
North Sea, and to the Marine Station of the Biologische Anstalt Helgoland!
We are very glad that this symposium series has proved a valuable platform
for the exchange of information and ideas concerning quantitative aspects
of metabolism, and that many leading scholars representing a wide variety
of biological and medical disciplines have come again in order to present
and to discuss new scientific results. This third symposium has attracted
the largest number of participants from English-speaking countries yet - an
indication, it seems, of the growing international reputation of this con-
ference.
Please let me say a few words about the history of this symposium
series. The idea to initiate biennial international and interdisciplinary
symposia devoted to the fast developing field of quantitative biology was
put forward in 1962 by Drs A. LOCKER (bsterreichische Studiengesellschaft
fur Atomenergie GmbH, Wicn) and F. KRUGER (Biologische Anstalt
Helgoland, Zentrale, Hamburg). I did not hesitate to support their idea
and to offer the assistance of the Biologische Anstalt Helgoland as spon-
soring institution. Thus the first two symposia of this series were organized
by LOCKER, KRUGER und myself, and held in September 1963 and 1965,
respectively, on Helgoland. All papers and discussions have been published
in volumes 9 and 14 of the "Helgolander wissenschaftliche Meeresunter-
suchungen" .
From the beginning, I intended to devote myself to getting the sym-
posium off the ground. Now that it is flying, I shall restrict myself to
making available, as before, the assistance of our institution. As some of
you may know, I am a marine biologist and experimental ecologist; as such
I should no longer exert influence on an important field which progresses
rapidly beyond my professional horizon. It is also felt that the proceedings
should be published, from now on, in a special publication in order to
do justice to their importance, not only to marine biologists but also to
physiologists, biochemists, radiation biologists, geneticists, biomathe-
VI Opening Address
maticians, theoretical biologists and physicists. Certainly this will make it
easier to reach the great diversity of institutions and individuals interested
in the papers and discussions of this conference. Weare grateful that
Springer-Verlag has agreed to act as publisher, and are convinced that
the proceedings of these international symposia will continue to assist
all colleagues interested in quantitative aspects of metabolism, as well as to
encourage further studies in this exciting new scientific frontier.
I am glad to notice that some of the "old-timers", who attended the
first and second symposia, have returned and equally happy to recognize
several "newcomers"- well-known scholars in their scientific fields-
who have come for the first time thus providing a highly welcome source
of "fresh blood".
May this third symposium enlarge and advance our knowledge on
quantitative aspects of metabolic processes as did the two preceding ones!
I wish all of you rich hours of receiving and giving, and herewith open the
Third International Symposium on Quantitative Biology of Metabolism.
O. KINNE
Biologische Anstalt Helgoland,
Zentrale, Hamburg
Preface
The development of the life sciences may be said to have effected a
gradual transition from a more or less intuitive prescientific approach
based on crude observation, via a more refined type of observation to
experimentation and hence to the level of formal theories. Quantitative
methods are introduced at the second level; they comprise: (a) quantitative
design of experiments; (b) regrouping of experimental results; (c) evalua-
tion of results by means of mathematical or special statistical techniques.
The last step implies the introduction of theoretical concepts, but we are
not justified in speaking of theoretical science unless true theoretical con-
siderations-models or hypotheses-precede experiment, and this is then
followed by an attempt to link results with theory so as to verify the theory.
Biology at present seems to lie somewhere between the second and third
level mentioned above, not yet having achieved the status of a theoretical
science in all its branches. Thus, though the need for quantification and
mathematical formulation is widely recognized, many biologists still believe
that e.g. general systems theory is too abstract to be of use in handling
concrete problems. Those, however, who look critically at the present state
of affairs cannot adopt this attitude.
Here I would like to pay may respects to the founders of theoretical bi-
ology: A. J. LOTKA in his Elements of Physical Biology laid the groundwork for
the theoretical approach to almost all the problems of the life sciences, espe-
cially those of metabolism and related phenomena, such as occur in ecology;
N. RASHEVSKY, in several now classical monographs, in Mathematical
Biophysics, and through the Bulletin of Mathematical Biop~ysics, which he
founded, made a decisive contribution to the subject, and his efforts are
now culminating in a universal theory of "Relational Biology"; L. VON
BERTALANFFY used the term "Theoretical biology" in several monographs,
and we owe to him the concept of steady-state (FlieGgleichgewicht) which,
generalized as an open system, led him to the principal postulate of a
General Systems Theory. The late H. QUASTLER deserves a special mention
for having convinced biologists that information theory may usefully be
applied to biology-and psychology. As a result of this pioneering work,
a world-wide research movement was set off-though the centre of gravity
lies in the United States. The time is now ripe for attempts to bridge the
gap which remains in biology between steps two and three as defined above.
VIII Preface
The chief aim of the S.ymposia on Quantitative Biology of Metabolism,
held every other year at the Biologische Anstalt, Helgoland, is to promote
recognition by producing acceptable results. The first (publ: Helgolander
wiss. Meeresunters., Vol. 9, 1964) comprised 36 papers, most of which dealt
with experimental problems, and included a long discussion on the prob-
lems of metabolism under adaptive conditions. But even in 1963, the
need to define and delimit the subject produced some theoretical contri-
butions. The second (publ: Helgolander wiss. Meeresunters., Vol. 14, 1966)
included 41 papers, many considering the general implications of models
and systems, while several outlined models for metabolic regulation and
control based on differential equations or binary logic.
The lines of investigation pursued at the first two Symposia are found
again at the third, some of the contributions achieving an even higher
level of formalization. Four interrelated themes, chief among them the
application of models to metabolism, can now be distinguished. The
section on models is prefaced by a general review of their role in human
cognition. The two main types of model capable of representing meta-
bolism and the reactions of biosystems in general are, depending on the
mathematics involved, either discrete and continuous or deterministic and
stochastic; examples of both are found here. They show how fruitful purely
theoretical considerations can be when applied to otherwise intractable
problems. Certain limitations inherent in the design of computers exclude
mere representation of all possible reactions in a given system; however,
computer efficiency can be improved by the omission of certain terms. It is
interesting that, for certain systems of differential equations, the solutions
are shown not be to elementary.
Several more or less experimental trends in the quantitative biology of
metabolism are illustrated by papers on the effects of temperature, activity
stage, adaptation to temperature and season, growth and aging. Some of
these problems run parallel in animals and plants. Among noxious influen-
ces, ionizing radiations playa leading role, and the quantitative aspects of
the mechanisms responsible for protection and damage repair are of great
interest. For models of metabolic control, the optimization of reactions is
of fundamental importance and may be based on irreversible thermody-
namics, as well as on the theory of automata. The link with time is of great
importance in the theory of metabolic control and the topic of biological
rhythmicity is also involved. Control mechanisms based on coordination
of elementary reactions display oscillatory features at the cellular, inter-
cellular and systemic levels; the steady state in the central nervous system
is a good example of the power of such coordination. The field of thermo-
regulation requires a special model.
Thus we may say that these papers represent a cross-section through
several of the main lines of advance of quantitative (theoretical) biology;
Preface IX
it is for the reader to decide to what extent they constitute a positive con-
tribution to an ever-growing field of great scientific topicality. This Sym-
posium, like its predecessors, was a truly interdisciplinary occasion, bring-
ing together experts from such diverse fields as mathematics, computer
science, theoretical physics, hiophysics, biochemistry, human, animal and
plant physiology, pharmacology and psychology. The fundamental nature
of the subjects of our common study enables certain general conclusions to
be reached which are of philosophical significance.
The Symposium was held at the Biologische Anstalt Helgoland, Marine
Station, through the kindness of the Leading Director, Prof. O. KINNE,
who made ayailable to us in a most hospitable manner the excellent facilities
of his Institute. The local organization was in the capable hands of Prof.
and Mrs. F. KRUGER, who looked after the accommodation and welfare of
the participants supremely well. I wish, too, to thank the Mayor of Helgo-
land and the municipalit\ for the welcome they extended to us. Grants from
the Federal Ministry of Scientific Research, Bonn-Bad Godesberg, for
which I herewith expre5s my profound gratitude, enabled us to reimburse
some of the participants' tranl expenses. The financial contribution made
by the ()sterreichische Studiengesellschaft fur Atomenergie GmbH,
Vienna, greatly helped me in publishing the program of the Symposium;
this Society also generouslv assumed all the expenses associated with the
editorial work. ?\1 \ special thanks go to Dr. K. F. SPRINGER of Springer-
Verlag, Heidelberg, for agreeing to publish the proceedings of the Sym-
posium. Last but not least, ~fiss H. KRUMPHOLZ assisted me in editing and
retyping some of the manuscripts.
In conclusion, may I express the hope that the material presented here
will come into the hands of all who are interested in quantitative and theore-
tical biolog\'.
Vienna, Noyember, 1968. A. LOCKER
Contents
1. Models of Metabolism
1.1. Models in General
1 A. LOCKER: The Epistemological Significance of Models in Science 1
2 H. KACSER, and J. A. BURNS: Causality, Complexity and Computers 11
1.2. Discrete and Continuous Models
3 R. ROSEN: Discrete and Continuous Representations of Metabolic
Models . . . . . . . . . . . . . . . . . . . . . . . . .. 24
4 M. SUGITA: Interaction of a Digital (Genetic) System with a Con-
tinuous (Enzymatic) One in the Cell ............. 33
5 CH. WALTER: A Model for Sustained Rhythmic Binary Logic in
Biochemical Systems . . . . . . . . . . . . . . .. 38
1.3 Stochastic and Deterministic Models
6 A. F. BARTHOLmIAY: Some General Ideas on Deterministic and
Stochastic Models in Biological Systems . . . . . . . . . . .. 45
7 P.-E. E. BERGNER: Turnover Compartmentalization. An Approach
to Analysis of Whole-body Retention Data .......... 66
1.4 Computer Models of Cell Metabolism
8 Z. SIMON, D. FARCAS, and A. CRISTEA: Functioning of a Cell Model 71
9 J. A. BURNS: A Digital Computer System for the Construction and
Analysis of Steady State Models of Enzyme Catalysed Networks. 75
10 H. J. BRBIERMANN: Computation of Equilibria and Kinetics of
Chemical SYstems with Many Species. . . . . . . . . . . .. 81
2. Metabolic Parameters
2.1 Temperature - Season - Adaptation
11 J. N. R. GRAINGER: The Relation between Heat Production, Oxy-
gen Consumption and Temperature in Some Poikilotherms. . .. 86
12 H.-D. JANKOWSKY: On Structure and Metabolic Rate of the Skeletal
Muscle of the Eel (Anguilla vulgaris L.) . . . . . . . . . . .. 91
13 E. ZERBST: Analvsis of Heart Rate Adaptation to Temperature.. 95
14 S. GELINEO: The Heat Production of Goldfinches and Canaries in
Summer and Winter . . . . . . . . . . . . . . . . . . .. 102
15 R. E. S~IITH, BARBARA A. HORWITZ, and Y. IMAI: Quantitative Ther-
mogenesis of Brown Fat in Hibernation and Cold Adaptation 106
2.2 Growtb - Age
16 F. KRUGER: Contributions to the Energetics of Animal Growth. 113
17 P. R. PAYNE, and ERICA F. WHEELER: Models of the Growth of
Organisms under Nutrient Limiting Conditions . . . . . . .. 127
XII Contents
18 F. COLLOT: Biomathematical Interpretation of Organismic Growth 133
19 L. W. WOODSTOCK: Relationships between Respiration during Imbi-
bition and Subsequent Growth Rates in Germinating Seeds . .. 136
20 D. ADAMIKER: Quantitative Parameters of Rat Liver Mitochondria
in Relation to Age . . . . . . . . . . . . . . . . . . . .. 147
2.3 Cellular Milieu - Experimental Influences
21 E. MeLLER: Enzymes as Indicators of Intracellular Reaction Condi-
tions . . . . . . . . . . . . . . . . . . . . . . . . . 151
22 H. P. T. AMMON: The Influence of Ethanol on Carbohydrate- and
Fat-Metabolism of the Liver . . . . . . . . . . . . . . . 154
3. Damage to Metabolism
3.1 Damage Due to Irradiation
23 N. ARLEY: Application of Quantitative Models for the Analysis
of the Mechanisms of Protection against the Damaging Effects of
Ionizing Radiation . . . . . . . . . . . . . . 157
24 J. KIEFER: Intracellular Recovery after Irradiation . . . . . .. 164
3.2 Damage Due to Radiolytic or Toxic Compounds
25 O. L. KLAMERTH: Inhibitory Action of Radiolytic Compounds on
Cell Function . . . . . . . . . . . . . . . . . . . . . .. 177
26 A. FISCHER, and L. TAKACS: On the Release and Elimination of
Liver Glutamic-Oxalacetic-Transferase . . . . . . . . . . .. 182
3.3 Damage Due to Oxygen Lack
27 A. T. MILLER: Metabolic Effects of Acute Hypoxia on Rat and
Turtle Brain. . . . . . . . . . . . . . . . . . . . . . .. 185
28 H. R. SCHOEN, and R. E. Voss: Changes in Metabolite Concentrations
in Ischemic Kidneys of Rabbits and in Transplanted Kidneys of Dogs 190
4. Metabolic Control
4.1 Metabolic Control and Optimization
29 G. DETCHEV, and A. MOSKONA t: The Mutual Coaction of two Regu-
latory Mechanisms Realizing Optimal Autoregulation of Metabolism 195
30 A. CRISTEA: Optimization of Structure and Metabolism in Cellular
Automata . . . . . . . . . . . . . . . . . . . . . . . .. 202
4.2 Metabolic Control at the Cellular Level
31 A. BETZ: Oscillatory Control of Glycolysis as a Model for Biological
Timing Processes ..................... 205
32 E. L. COE, MARY H. COE, and IN-YOUNG LEE: Evaluation of the Coor-
dinated Control of Activated Glycolysis and Respiration by Ortho-
phosphate and ADP in Ascites Tumor Cells . . . . . . . . .. 217
33 P. ARESE, A. BOSIA, and L. ROSSINI: Profiles of Substrate Levels
of the Central Metabolic Pathways in Frog Heart ....... 221
4.3 Control at the Systemic Level
34 J. KIRK, and J. S. ORR: Analysis by Computer of Some Oscillatory
Features of the Red Cell System . . . . . . . . . . . . . .. 227
