Organisation and Regulation. Hierarchical and Functional Integration

713 Pages·1990·13.817 MB·English

by  G. A. Chauvet (Auth.)

Some related Pergamon titles
Pergamon Studies in Neuroscience Series
No. 1. Function and dysfunction in the basal ganglia ed. A.J. Franks,
J.W. Ironside, R.H.S. Mindham, R.F. Smith, E.G.S. Spokes and
W. Winlow
No. 2. Comparative aspects of neuropeptide function ed. Ernst Florey
and George B. Stefano
No. 3. Neuromuscular transmission: basic and applied aspects
ed. Angela Vincent and Dennis Wray
No. 4. Neurobiology of motor programme selection ed. Jenny Kien,
Catherine R. McCrohan and William Winlow
No. 5. lnterleukin-1 in the brain ed. Nancy Rothwell and Robert Dantzer
No. 6. Neurophysiology of ingestion ed. D. A. Booth
No. 7. A theory of the striatum ed. J. Wickens
No. 8. Neuroregulatory mechanisms in ageing ed. Maynard H. Makman
and George B. Stefano
No. 9. Thalamic networks for relay and modulation ed. Diego
Minciacchi, Marco Molinari, Giorgio Macchi and Edward G. Jones
No. 10. Glycobiology and the brain ed. M. Nicolini and P. F. Zatta
No. 11. Neural modelling and neural networks ed. F. Ventriglia
No. 12. Information processing underlying gaze control ed. J.M.
Delgado-García, Ε. Godaux and P.-P. Vidal
Wenner-Gren International Series
Vol. 60. Neuro-immunology of Fever ed. T. Bartfai and D. Ottoson
Vol.61. Functional Organisation of the Human Visual Cortex
ed. B. Gulyás, D. Ottoson and P. E. Roland
Vol. 62. Trophic Regulation of the Basal Ganglia ed. K. Fuxe, L. F. Agnati,
B. Bjeike and D. Ottoson
Vol. 63. Light and Biological Rhythms in Man ed. L. Wetterberg
Vol. 64. Eye Movements in Reading ed. J. Ygge andG. Lennerstrand
Vol. 65. Active Hearing ed. A. Flock, D. Ottoson and M. Ulfendahl
Vol. 66. Challenges and Perspectives in Neuroscience ed. Ό. Ottoson,
T. Bartfai, T. Hökfelt and K. Fuxe
Vol. 67. Life and Death in the Nervous System ed. C. F. Ibáñez, Τ. Hökfelt,
L. Olson, Κ. Fuxe, Η. Jörnvall and D. Ottoson
IBRO Series
Muscle afferents and spinal control of movement ed. L. Jami,
E. Pierrot-Deseilligny and D. Zytnicki
Theoretical Systems in Biology
Hierarchical and Functional Integration
Volume III Organisation and
Regulation
G. A. Chauvet
Institute of Theoretical Biology,
Faculty of Medicine, University of Angers, France
and
Department of Biomedical Engineering,
University of Southern California,
Los Angeles, California, U.S.A.
translated by
K. Malkani
Department of Histology, Embryology and Cytology,
Faculty of ¡Medicine, University of Angers, France
PERGAMON
UK Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington,
Oxford 0X5 1GB, UK
USA Elsevier Science Inc., 660 White Plains Road,
Tarrytown, New York 10591-5153, USA
JAPAN Elsevier Science Japan, Tsunashima Building Annex,
3-20-12 Yushima, Bunkyo-ku, Tokyo 113, Japan
Copyright © 1990 Massen Editeur, Paris
All Rights Reserved. No part of this publication may be reproduced,
stored In a retrieval system or transmitted In any form or by any
means: electronic, electrostatic, magnetic tape, mechanical, photo­
copying, recording or otherwise, without permission In writing from
the publishers.
First edition published in French by Massen Editeur, Paris 1986
(French edition titled Traite de Physiologie Théorique)
Revised, updated and translated into English for this Elsevier
Science Edition 1996
Library of Congress Cataloging in Publication Data
Chauvet, G.A. (Gilbert)
Theoretical systems in biology: hierarchical and functional
integration/G.A. Chauvet; translated by K. Malkani
Includes bibliographical references and index.
Contents: v. 1. Molecules and cells - v. 2. Tissues and organs -
V. 3. Organisation and regulation
1. Physiology-Mathematical models. 2. Molecular biology-
Mathematical models. I. Title. II. Series.
QP33.6.M36C473 1995 95-30324
574'.01'1-dc20
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
ISBN 0 08 041994 1 (Volume III)
ISBN 0 08 041995 X (3 volume set)
Printed In Great Britain by Alden Press, Oxford
Preface
The use of models in our approach to human physiology is aimed at laying down
the methodological bases for the interpretation of experimental results, both old
and new. True, the title is likely to cause some suφrise, so some justification may
be required: first, we propose to present formalised biological theories at various
levels of description, ranging from the molecular level to that of the whole
organism; and, secondly, we shall consider certain aspects of contemporary
biology, selected not only for their intrinsic importance but also for their capacity
to generate new insights. And all these are, of course, fundamental to theoretical
biology, a discipline analogous in nature to theoretical physics in its relationship
to experimental physics.
Although this work is not meant to be an exhaustive treatise, an attempt has
been made to cover all the subjects of 'classical' biology in a logical manner, going
from the most elementary level — the molecular level — up to the control systems
of the entire organism. Thus, a succinct description of each of the principal
physiological phenomena is followed by a formalised explanation, in so far as this
is possible in the present state of knowledge. The choice of subjects may seem to
be somewhat arbitrary, but the main criterion used has been the didactic aspect of
the topic. For example, certain formalised theories that are now fairly old, such as
those of DNA replication and membrane excitability, have been duly treated in
detail. But very recent theories, such as that of DNA topology, have also been
given careful attention. For how can we be sure which of these approaches will
prove more useful in the future? Similarly, except in a few special cases, we have
preferred the use of deterministic methods to stochastic processes. One reason for
this is that the stochastic formalism is generally less well known and does not
XV
xvi Preface
always carry an obvious advantage, at least for the time being. We have tried —
but perhaps with limited success — to conserve the necessary mathematical rigour
without going into too much detail, and to recall the essentials of biological
phenomenology without striving to explore all the finer points. This is, of course,
a delicately balanced task and the results may annoy 'pure' mathematicians as
well as 'experimental' physiologists. The point of view here is rather that of a
physicist attempting to describe natural phenomena through abstract representa­
tion expressed in concise language. We hope this interdisciplinary approach will
not appear too esoteric to some readers or too lacking in rigour to others. The
basic requirement for understanding the text is a sound knowledge of physics and
mathematics at the undergraduate level, and of physiology as treated in standard
textbooks.
This three-volume work corresponds to the usual levels of structural
organisation in biology. Volume I describes molecular and cellular aspects
(Chapters 1 to 12). Volume II examines the intercellular relationships within
organs (Chapters 1 to 5) as well as the major functional systems of the organism:
energy metabolism, respiration, blood circulation, renal activity (Chapters 6 to 9).
Chapter 10 introduces the important concepts of non-symmetry, non-locality and
structural discontinuity. These concepts are used in Volume III which addresses
the delicate problem of shifting from one biological level to another. Volume III
contains a discussion of the mechanisms of control and regulation exercised by
the nervous and endocrine systems (Chapters 1 and 2). The concluding chapter
proposes a method of vertical functional integration in a multiple-level
hierarchical system (Chapter 6). The formalisation necessary for certain
physiological problems, particularly those involved in the regulation of the
organism, calls for new methods and concepts. Thus, the notion of the integron,
proposed by Jacob in La logique du vivant (1970) has been largely used. The
regulatory functions of respiration, blood circulation and renal activity are
integrated into two major equihbria of the organism: the hydroelectric
equilibrium and the acid-base equilibrium (Chapter 4). Some of the notions of
mathematics and physics used are briefly recalled in the appendices of each
volume. It is hoped that these, together with the comprehensive index and the list
of the principal symbols and units used, will be of some help to the non-
mathematical reader.
Let us now try to justify the choice we have made. Why, indeed, bring up the
idea of theoretical physiology? First, because we are more interested by the
functional than the descriptive aspect of biology; and, secondly because we have
deliberately sought the mathematical formalisation of physiological phenomena.
Here, an obvious difficulty arises since this choice requires the contribution of all
the other sciences — mathematics, physics and chemistry — and demands an
interdisciplinary interpretation. Several reasons lead us to believe that the
evolution of physiology towards greater formalisation is unavoidable: (i) the
rapidly increasing number of experimental results for which no interpretation is
available because of the multiple factors involved; (ii) the continuing technolo-
Preface xvii
gical advances in instrumentation giving finer results than ever before; (iii) the
necessity of integrating the results obtained to counteract the reductionist
tendencies of specialised disciplines with divergent objectives. However, these are
not the only reasons of an epistemological order which we shall now discuss.
Of course, it is possible to explain without formalisation, and indeed up to now
this has been the principal approach in biology. But what is the actual nature of
the 'explanation' in biology? Everybody knows, for example, the theory of
evolution and the theory of gene regulation in procaryotes, to mention only the
best known theories concerning the living world. Clearly, these two qualitative
descriptions cannot be considered to have the same level of intelligibility. The
former rests on observations on the scale of geological timé and on considerations
of a rational order, while the latter stems from rigorous experimentation in a
'molecular' context, the results of which are unanimously accepted. Indeed, the
reticence of many scientists with respect to the Darwinian theory of evolution
contrasts shaφly with the general approval of the model proposed by Jacob and
Monod, at least as far as it applies to procaryotes. These examples are
characteristic of non-formalised theories, even though they describe 'reality' —
or what can so be considered, as we shall see below — at different levels of
'certitude'. As opposed to theoretical concepts which lead to the induction of
theoretical laws capable of generating new empirical laws, non-formalised
theories in fact introduce elementary mechanisms which, taken together, are
difficult to generalise under the form of a theoretical law.
From this point of view, the problem of biological evolution is exemplary and is
considered in detail in Volume I, Part 2. Of course, experimental descriptions and
experimental verifications are indispensable to science, but it has to be admitted
that formalisation is far more useful than rigorous taxonomy. We merely need to
think of the known results of physics and the difficult objective of theoretical
physics (not necessarily the same as in theoretical biology) which is the search for
the great universal laws underlying the reality of the material world. Several
epistemologists have examined this problem, in particular the physicist
d'Espagnat who explains his philosophical point of view in A la recherche du
reel (1979). It may be objected by some that physics, the science of inanimate
matter, is obviously a great deal 'simpler' than physiology, and therefore, even in
the best of cases, the formal description of physics will not be applicable to
biology, so that it may be preferable to give a literary description of biological
phenomena rather than to introduce some useless, esoteric formalism. In answer
to this we would make the following points:
(1) The abundance of experimental results does not in itself lead to a better
understanding of the phenomena studied but rather calls for a synthetic
interpretation. Indeed, new concepts introduced into a theory enhance the
value of the observed results.
(2) A good qualitative or quantitative formalisation permits a synthetic view of
phenomena which are unrelated a priori, thus generating various new laws. It
xviii Preface
leads to the rigorous description of the phenomenon observed in terms of the
hypotheses used.
(3) The enunciation of sufficiently general theoretical laws allows us to imagine
new experiments, and vice versa.
While considering the merits of formalisation in physiology, it would be well
worth bearing in mind the epistemological notions concerning the relationships
between empirical laws and theoretical laws, between theories and models in the
science in which experimentation has always played the foremost role. The reader
may profitably consult some of the excellent contributions to scientific
epistemology dealing with this subject (Delattre, 1981, Volume I).
To illustrate this, let us go back to the two examples above. We know that a
theory of evolution, based on transformism and natural selection, introduces
observable dimensions obtained directly from palaeontological or biological
observation. However, such a theory is practically powerless in the induction of
new empirical laws. But a theory of evolution, formalised in terms of concepts
such as those of self-organisation or of selective value, are seen to be quite potent
(Volume I, Chapter 7). And the theory of gene regulation in bacteria, established
in terms of molecular concepts, reveals a far greater predictive value. Moreover, a
quantitative formalisation of this phenomenon leads to empirical laws which
actually justify the initial hypothesis (Volume I, Chapter 9).
It should, however, be observed that most of the current biological hypotheses,
whether formalised or not, depend on fundamental physico-chemical knowledge.
Such hypotheses therefore rely on already existing theories of matter. We believe
it should be possible to express a fecund biological theory in terms of non-
observables specific to biology, according to theoretical concepts of which the
rules of correspondence with objective reality would be unique and not simply
borrowed from other sciences. As proof of this, we consider two examples in
detail: the morphogenetic field in developmental biology (Chapter 10), and the
neural field in the central nervous system (Volume III, Chapter 2). Working on
this basis, we have tried to develop a theory of functional organisation in
multiple-level hierarchical systems (Volume III, Chapter 6).
Is biological reality 'veiled'?
The problem of biological 'reality', mentioned above, remains to be solved. But
what reality are we actually referring to? We know, of course, what a
controversial subject this has been for philosophers all through the ages.
D'Espagnat (1979) comes to the conclusion that non-physical realism is the only
conception that appears to fit all the facts. The philosophy of a 'veiled' reality
should inspire considerable modesty. However, this is a physicist's point of view
and would therefore need to be qualified in terms of the biological perspective.
Preface xix
But, finally, do we not today perceive fundamental incertitudes in the living as
well as in the non-living world?
Prigogine (1980, Volume I), working on classical dynamic theory and taking
fluctuations into account, has recently added a new indeterminism alongside the
already known indeterminism of quantum theory. Transposed to the biological
world, may not the variabiHty of living organisms be just one form of this
incertitude, or on the contrary could it be our degree of ignorance that leads us to
this postulate? The latest theories of matter seem to answer this important
question through a statistical view of fundamental concepts. We shall have to take
this into account, for example, in considering a formalised theory of the evolution
of the species.
Some comment may be made on the imprecise use of the terms: theories and
models. Mathematical models, physical models, chemical models, and so on, are
being increasingly used in biological work. But when can a model be considered to
constitute a theory? Indeed, if we wish to avoid errors of interpretation of facts —
not to mention the underlying reality — we should be careful to distinguish
between the explicative models, with which we are directly concerned in this work,
and other models that are merely circumstantial. For instance, we refer to a
statistical model when, on the basis of a large number of experimental results, we
seek to verify a hypothetical mathematical relationship between various
dimensions. Although often necessary at the beginning of any scientific
investigation, this kind of analysis does not usually generate a theoretical law.
Theoretical biology is surely not a mere veneer of mathematical methods appHed
to biological observations.
A most interesting analysis of the distinction between theories and models has
been made by Delattre (1981, Volume I), who raises the following questions: Is
there an ideal form for the explanation of phenomena? If there is, can we propose,
within the framework thus defined, a more precise distinction than currently
available between the notions of theories and models? With the same hypothesis,
can we, for a given discipline, claim to achieve right away the best equilibrium
between theoretical endeavour and experimentation, i.e. that capable of leading
the most directly to the best form of theoretical explanation? According to
Delattre the concept of the theory applies best at the level of the general language
of description, the theory then including the inductive synthesis which justifies the
choice of the definitions and their internal coherence. The explanation always
implies the involvement of the constituent parts and of the processes causing
interactions between the parts.
Finally, we may add a few words here on the relationship between formalised
theoretical physiology and medicine. There now exists a considerable gap between
medical care-giving and the increasingly refined and complex knowledge that
underlies medical activity. While the general practitioner can hardly be required
to master the fundamentals indispensable to a formalised understanding of
physiological functions, we beheve that biologists and other users of advanced
techniques in genetic and medical engineering should acquire a sound working
XX Preface
knowledge in this field. Like the experimental physicists, they will soon discover
the advantages of a formalised, synthetic approach. Indeed, the second half of the
twentieth century is a major turning point for biology, just as there was one for
physics some hundreds of years ago. It requires no extraordinary vision to predict
that the unfortunate division between the so-called 'exact sciences' and 'natural
sciences' will continue to decrease, and that the outcome of predictions in biology,
as in physics, will become more and more certain in spite of the multiple levels of
description involved. Does this mean, for example, that we shall succeed in
controlling the conditions of biological variability? Perhaps not, but, like the
fundamental problems concerning reality and interpretation that have appeared
in physics, similar questions are likely to arise in biology, connected with the very
nature of the self-organisation of living organisms and structure-function
relationships. Undoubtedly, the difficulty Hes in the multiple levels of biological
description and the formalism used, but the formidable immensity of the task is
more than compensated by the fascinating beauty of the functioning of living
organisms. In this perspective, and in spite of difficulties of another order due to
the novelty of the discipline, let us hope that more and more biologists will
become interested in these problems since, as a reading will show, our work surely
raises far more questions than it provides answers.
I would like to thank all those who have helped in this long work through their
advice and encouragement: J. A. Jacquez, Professor of Physiology at the
University of Michigan, P. Delattre, who pioneered theoretical biology in France,
T. W. Berger, Professor of Neuroscience at the University of Southern California,
and J. D. Murray, Professor of Mathematical Biology at the University of Seattle.
I am particularly indebted to Dr. A. Tadei, Professor of Cardiology at the
University of Angers, whose dynamism and competence have always been an
outstanding example of the ideal medical research worker, teacher and
practitioner. My wife, with constant understanding, never failed to provide full
moral support. May this work bear witness to our affection.
This edition of Theoretical Systems in Biology, Hierarchical and Functional
Integration contains all the topics presented in the original three-volume French
edition entitled 'Traite de physiologic théorique\ published by Masson & Cie.,
Paris (1987-1989). The EngHsh translation, kindly undertaken by K. Malkani, my
friend and colleague at the University of Angers, has provided an opportunity for
updating some sections, particularly in the chapters on the organisation of
biological systems at the molecular, cellular and organismal levels. Although
Volume I may be read as an independent text, it should be observed that the
mathematical models introduced here, as well as in Volume II, were essentially
chosen with the idea of constructing a theory of functional organisation. A
'bottom-up' approach was initially used to extract properties common to the
models selected so as to draw up the general principles which are finally stated in
an abstract, 'top-down' form in the concluding chapter of Volume III. The
present edition has allowed us to integrate these properties into the discussion of
Preface xxi
the different models. We hope this will make for an easier understanding of the
whole work. Differing considerably from the existing structurally oriented
theories set out in Volume I, Chapter 3, the theory of functional organisation
presented in Volume III views a biological system as consisting of two subsystems,
one describing its topology and the other its dynamics. The stability of the
biological system would thus depend on the conditions of stability of the
corresponding subsystems. Specifically biological concepts, such as those of non-
symmetry and non-locality of the fundamental interaction or functional interac­
tion, or that of structural discontinuity, emerge progressively from the treatment of
the subject in the first two volumes. The most important consequence is that we
are obliged to consider the formaUsm of graphs and fields in hierarchical spaces in
which a parameter such as time defines a particular level of organisation.
Our theory offunctional organisation (Volume I, Chapter 4) may be summed-up
simply as follows. From the diversity of processes occurring in biological
organisms, we have extracted two concepts: on one hand, the concept of a
functional interaction with a property of non-symmetry, and on the other hand, the
concept of a hierarchical system with a property of non-locality. The functioning
of a living organism depends on two types of organisation. The first is the
structural organisation corresponding to the ordered spatial distribution of the
various structural units of the organism, such as cells, tissues and organs. The
second is the functional organisation, resulting from the coordination of a set of
interactions between the structural units. A convenient way of studying the
relations between the structural and functional organisations is by means of a
graphical representation. The points of the graph represent the structural units,
and the arcs represent the elementary physiological functions, i.e. the relations
between the structural units. The graphs may be used in at least two ways. The
first, which scarcely calls for the mathematical properties of graph theory,
depends on a computer programme to organise the physiological functions
between the structural units so that the functional hierarchy is automatically
displayed. The second, however, fully exploits graph theory to search for specific
substructures, such as cyclic subgraphs, the best path in the graph for a given
constraint, and so on. Just as there exists a structural or anatomical hierarchy, i.e.
a group of more or less similar units at different levels of organisation, there also
exists a functional hierarchy. Indeed, it is precisely the existence of interlinked
functional hierarchies that complicates the representation of the functional
organisation of hving organisms. Moreover, in most cases, the functional
hierarchy does not coincide with the structural hierarchy.
In the third part of Volume I (Chapter 12) we examine a property of the
variation of the functional hierarchy during the development of an organism. This
approach is based on a principle of invariance of the physiological function and on
the consequences that may be observed in a given species. For example, an
aerobic organism needs oxygen in order to survive, it has to self-replicate to
peφetuate the species, and so on. This invariance can only be expressed if the
physiological function can be mathematically defined. The presence of the genetic