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TitleMathematical Nature of the Living World: The Power of Integration
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Document Text Contents
Page 2

CONTENTS

Prolog Understanding the Functioning of Living
Organisms 1

Chapter I Physical and Biological Interactions 19

Chapter II The Functional Organization of
Living Organisms 59

Chapter III The Integration of Physiological Functions 95

Chapter IV Structural and Functional Organizations
of Living Organisms 119

Chapter V Physiological Constraints of Biological
Development 153

Chapter VI The Role of Space in Functional Biological
Organization 211

Epilog 251

Plates 271

References 281

Index 287

v

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Page 145

involves all the major systems of the body, i.e. respiratory, cir-
culatory, digestive, excretory, and neurohormonal. A perturba-
tion in any of these systems could affect the cardiovascular
system and produce a state of heart shock characterized by
widespread cell suffering, accompanied by signs of total dise-
quilibrium in the body, leading rapidly to death. Clinical obser-
vations of this condition reveal a vicious circle comprising the
following sequence of events: constriction of blood vessels,
decreased oxygenation of cells, local acidosis, local edema,
decreased blood volume, decreased venous return, heart fail-
ure, and generalized acidosis. In fact, the state of shock is
aggravated by the metabolic, cellular and tissue disorders that
increasingly damage the lungs, the digestive tract, the kidneys,
the heart and the brain. This brief description of heart shock
suggests how difficult it might be for a physician to interpret
the clinical and biological results in such cases. In practice, all
the physiological functions of the organism are so seriously
perturbed that it may be extremely difficult to analyze the syn-
dromes. Since the vicious circle leads spontaneously to death,
it would be important to determine the critical point, i.e. the
crucial instant beyond which all the essential organs will be
irremediably damaged.

Now let us see how an interactive graph could lead to
new insights into the mechanism of the state of heart shock.
Figure IV.8 shows a cyclic sub-graph that emerges from the
interactive graph of the functional organization of the body.
The cyclic sub-graph corresponds to one of the pathways of
the main graph in which, by moving from one summit to
another, we return to the starting point. A more detailed graph,
taking into account a greater number of levels of organization,
would show a greater number of interactions in the form of
cyclic and non-cyclic sub-graphs. This would of course pro-
vide a fuller explanation of the mechanisms underlying the
origin of the state of shock and its consequences.

Thus, an abstract, mathematical representation of biological
reality could lead to a better understanding of the problems
posed by integrative physiology. In fact, the topology of the
organism indicates the localization of the alterations caused by

IV

146

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Page 146

the perturbations; and the dynamics of the processes involved,
which is related to the geometry of the organism, describes the
nature and the course of the resulting alterations. As we shall
see, the time-variation of a biological system is expressed by
two dynamics: one corresponding to the time-variation of its
organization (Chapter V), and the other to the time-variation of
the processes taking place within this organization (Chapter VI).
We propose to deduce a classification of functional interactions
and structural units according to the specialized hierarchical
physiological systems to which they belong. The graphical visu-
alization of the structural and functional organization of the
organism would then allow us to identify particular pathways,

Structural and Functional Organizations of Living Organisms

147

Figure IV.8: The cardiovascular system is represented here in terms of
actions, or fields. The vicious circle of the state of shock appears in the
form of a cyclic sub-graph of the functional interactions in the (�,�)
representation. RS � respiratory system; NS � nervous system; ANS �
autonomous nervous system; ES � endocrine system; m.f. � smooth mus-
cle fiber; f � respiratory frequency; p � pressure gradient; Q

.
� blood

flow; V
.
O2 and V

.
CO2 � ventilatory flow of oxygen and carbon dioxide

respectively.

Filling

Filling

Baro
recep.

m.f.

Veins
(capacitive vessels)

Baro
recep.

m.f.

Left Ventricle
(heart pump)

Adrenalin
Noradrenalin

Filling

O2, CO2

f, p

N.S.

A.N.S.

heart inhibitor
vasomotor center

E.S.

adrenal
Arteries

(resistive vessels)

Baro
recep.

m.f.

f.m.l.
Auricles

(auricle pump)
+ right

ventricle
Baro

recep. Tissue
capillaries

Metabolical
system

Lung
capillaries

Plasma
volume

RS

VO2, VCO2

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Page 290

physiological
function 61, 86, 123, 128, 129
genetics 77

Planck 157
plane wave 220
plasticity 84
Platonic world 56
Poincaré 37
potential 125, 215

barrier 65
energy 39, 64, 182
functional organization 148, 181,

188, 208, 263
organization 13, 182, 209, 233, 247
time dependent 242

prediction 50
Prigogine, Nicolis and Babloyantz 160
Prigogine 99
principle

action and reaction 23
biological evolution 174
conservation 39, 176
evolution 163
least action 13, 38, 43, 149
least time 46
non-locality 66
stabilizing self-association 165
transforming 79
virtual work 40
vital coherence 174, 186, 250, 266

quantum mechanics 260

random walk 55
rate of transfer 140
reaction-diffusion equation 53
recons 78
redistribution 242
regulation 93
relativity 188

hierarchical levels 131
renin-angiotensin-aldosterone (RAA)

system 108
reorganization 35, 198
representation 9, 123, 148

three-dimensional 134
repressor 82
reproductive invariance 79

reservoir 195
respiratory

functional unit 256
system 114, 186

ribosome 131

Schrödinger’s principle 243
selection of structural units 241
self-association 164, 181, 185, 232
self-organization 243, 247, 266
self-reproduction 181
Semmelweiss 62
simplicity 51
sink 12, 25, 213
skeletal muscle fiber 165
source 12, 25, 213
space

neurons 238
scales 232
structural units 225
synapses 238
units 135

special theory of relativity 216
specialization 72, 93, 174,

176, 264
S-propagators 222, 227, 265
stability 12, 37, 62, 92, 124, 150, 156,

163, 168, 193, 232, 262
equilibrium 124
singularity 5

state of organization 191
stationary equilibrium 160
stationary states 99
structure 22, 122, 123

discontinuity 63, 66, 86, 89, 106,
118, 134, 168, 226, 228

equivalence 187
hierarchy 66, 86
organization 156, 205
organizations, functional 121
relationship, functional 121
units 31, 92, 130, 256

superstrings 259
symmetry 26, 205, 219

groups 27
synapses 85

efficacy 90, 137, 228, 237
long-term 228

Index

291

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synapses (continued)
reorganization 203
short-term 228
space 238
synapsons 137

system 122

temporal order 231, 236
theoretical framework 254
theory 8
thermodynamics 156

equilibrium 103
first law 156 (See laws)
non-equilibrium 99
second law 158 (See laws)
theory of irreversible

processes 162
Thom 9
three-body problem 24
three-dimensional graph 137
thyroid system 185
time scale 105, 128, 176, 231, 236
tissue specialization 172

topology 11, 31, 32, 35, 148, 182,
232, 240

entropy 197
“transport” of fluctuations 247
transposons 83

Ullmo 50
unification 5
unifying principles in biology 36

variation 178
calculus 48, 149
principle 39, 42
property 200

ventilation 113
Vesalius 62
virtual particles 261
vitalism 36
Volta 85

Waldeyer 76
Watson and Crick 79
Wells 62

Index

292

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