Self-organization of biological morphogenesis: General approaches and topo-geometrical models

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LevV.Beloussov
Morphomechanics
of Development

Morphomechanics of Development

Lev V. Beloussov
Morphomechanics
of Development
With a contribution by Andrei Lipchinsky
123

Lev V. Beloussov
Department of Embryology
Moscow State University
Moscow
Russia
ISBN 978-3-319-13989-0 ISBN 978-3-319-13990-6 (eBook)
DOI 10.1007/978-3-319-13990-6
Library of Congress Control Number: 2014957132
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Preface
The aim of this book is to outline the contours of a newly emerging approach to the
most complicated and finely regulated successions of events making possible our
very existence: the development of organisms. Because of their ubiquity and
spontaneity, our primary instinct would be to appreciate these events as given, and
simply describe them one after another without asking why they take place at all.
On the other hand, since ancient times human beings have not been satisfied by
only apprehending any natural events, ranging from movements of celestial bodies
to behavior of tiny particles of matter. Instead, people have invented some cognitive
approaches, which created the basis for modern civilization, whether for good or
evil. Our first aim will be to explore whether any of these approaches can help us to
explain the development of organisms. We shall see that in spite of a prolonged
history of the science about development (traditionally called embryology, but now
named developmental biology) and many important discoveries in this field, this
task has still not succeeded. Today, however, due to cooperation between several
newly emerged branches of science, some new and unique possibilities allow
substantial progress in these directions.
Among the approaches used by natural sciences, we start by outlining the two
that have been often regarded as opposites. The first of them is oriented toward
searching for components that are kept unchanged (invariant) among events looking
quite different from each other. The second, on the opposite, is directed toward
outlining reproducible differences between things that are at first glance hardly
discernible. The first approach is directed toward formulation of as broad as pos-
sible invariable laws of nature; this trend dominates in physical sciences since the
times of Galileo and Newton. Its unique advantage is the predictive power. It is this
approach that provided the tremendous technological progress achieved since then
by mankind.
However, not all the sciences followed this path. The second approach, directed
toward classification of events, emphasizing their specificity and internal differences
rather than any common laws that may join them, was long dominant in most of the
natural sciences, and remained so in biology. If we are objective, we must admit
that practically all the achievements of biology and related applied sciences
v

(medicine, agriculture, biotechnology) have been reached within the framework of
this traditional approach, in the sense of remaining almost unconnected with any
general laws. Accordingly, their results continue to be expressed in the form of
specific receipts, instructions, drugs, etc. About a century ago, a German philoso-
pher, Windelband defined this approach as ideographic while the law-oriented
approach as nomothetic.
The contrast between nomothetic and ideographic approaches becomes most
clear when they are applied to more or less prolonged successions of events. For
clarifying this, let us use a simple allegory, or better to say, a kind of a caricature
(Fig. 1). Frame A illustrates a nomothetic tendency directed toward embracing quite
different successions of events by a common law. On the contrary, frame B depicts
an old-fashioned postman whose pathway is determined by the addresses of the
letters he has to hand. For making this allegory closer to conventional views on the
development of organisms, let us assume that by coming to each next address, the
postman receives the instructions of where to move further. Under these conditions,
each next postman’s turn is determined by a specific instruction (which we may call
a“cause”). This displays a principle of a so-called uniform determinism which, as
related to embryology, will be discussed in the text. Frame C gives an example of a
natural periodic process to which a priori any one of the above-mentioned
approaches can be applied: it should be a matter of investigation to make a rea-
sonable choice between them.
Fig. 1 Movements caused by invariable laws (a), by specific causes (b), or suggested to be caused
by any of these components (c). atrajectories of the planets and of a falling apple are determined
by the same law of gravity. ba complicated trajectory of a postman is determined by addresses
written on the envelopes. ca record of a quasi-periodic movement. It is a matter of investigation to
detect whether it may be embraced by a common law or the breaks of trajectories (some of them
shown by arrows) should be ascribed to specific causes
vi Preface

Initially both the approaches looked mutually exclusive. Since the second half
of the previous century, however, a new version of the classificatory approach
emerged, formalized within the framework of so-called systems theory (Bertalanffy
1968; Pattee 1973): it arranged the static events according to their characteristic
dimensions, and the dynamic events according to their rates.
Briefly speaking, this approach invites us to distinguish small things from large
ones and slow processes from fast ones. At first glance, this seems naïve, but is
actually very deep. A use of this approach leads to nontrivial conclusions about the
stratification of our world, both organic and nonorganic, into a restricted number of
discrete levels, each of them populated with events of characteristic linear dimen-
sions and characteristic times (i.e., reversed rates). As we shall see in Chap. 1, such
stratification is indispensable for applying a law-centered approach to any complex
system, whether organic or inorganic. Nevertheless, when taken in isolation, it is
but a preparatory step for doing this.
Which of these approaches—or combination of them—has dominated conven-
tional embryology? Because developmental events lie at the very heart of biology,
it is in no way surprising that the traditional classification approach dominated
throughout the entire history of developmental biology and retained until now the
leading positions. This is true not only for so-called descriptive embryology,
dealing with normal course of development, but also for experimental research,
performing “causal analysis”of developmental mechanisms: this is because the
results of such analysis are usually presented as a set of “specific causes,”having as
a rule nothing in common with each other. Such an approach, seeming at first
glance quite safe, will be shown to involve us into a series of principal uncertainties
and contradictions.
On the other hand, a classification of developmental events according to their
space temporal scale has also been used intuitively for a long time. Already a
century or so ago, embryologists actively disputed the relations between a devel-
oping “whole”and its parts, thus intuitively using what we call today the interlevel
approach. As we shall see later, some of their ideas criticized by contemporaries as
being too vague and even nonscientific previewed in fact some firmly accepted
notions of the present-day knowledge. However, it remains still uncertain whether it
would be reasonable and constructive to transform embryology into a law-centered
science. On the one hand, by referring to a classical Maxwell’sdefinition of physics
[“Physical science is that department of knowledge which relates to the order of
nature, or, in other words, to the regular succession of events”(Maxwell 1871,
1991)], one should immediately regard embryology as but a part of physics: nothing
in nature better represents “the regular succession of events”than the development
of organisms. However, the successions of events which are really taking place
during development of organisms are completely unparalleled in any nonliving
systems, both in their duration and complexity. It is not surprising therefore, that in
spite of isolated, remarkable attempts by certain authors (to be discussed later), the
law-oriented approach in embryology remained marginal, while the majority of
researchers could not believe such complicated chains of events to proceed without
any specific“instructions.”
Preface vii

We suggest that such a situation can be due to a premature use of the law-
oriented approach, rather than by its inherent nonadequacy. Until recently, this
approach was used in the so-called linear approximation, which did not permit to
reproduce unusual dynamic properties of complex multilevel systems; nonlinear
approaches (see Chap. 1) emerged much later.
Before coming to these, it would be desirable to find a common category of
physical events participating in the main, if not all the activities of developing
systems. At first glance, such enterprise looks hopeless. Fortunately, this is not the
case. Both superficial observation of the developmental processes and their refined
analysis up to the molecular level shows that practically all of them are associated
with regular and repeatable deformations of material units ranging roughly from
10
−3
to 10
−9
m, that is, from cell collectives to single molecules. What is called
morphogenesis is actually a succession of such deformations observed at the cel-
lular and supracellular levels. It is but natural to extend this same term to the lower
structural levels as well.
By considering the deformations taking place at any structural level to be the
leading component of development, we take a crucial step toward what we call
morphomechanics. Although nobody can deny that organized deformations are
essential parts of development, most researchers of even a recent past believed them
to be no more than epiphenomena of independent deeply hidden regulatory
mechanisms, nonaffected by deformations themselves. Such views are explicable as
extrapolations from traditional constructions of common man-made devices,
implying a sharp segregation of a macroscopic executive domain from a miniature
regulatory mechanism. We shall see however that in living systems this is not the
case: executive and regulatory mechanisms are mutually dependent. In other words,
we must be ready to accept that morphogenesis can be self-regulated.
Meanwhile before doing this, we would like to see at what point the morp-
homechanics deviates from the ordinary mechanics. Such fundamental notions as
the deformations and mechanical stresses (MS) are common for both. A basic
difference occurs at the next step of our reasoning and is as follows. The ordinary
mechanic does not ask, as a rule, what is the origin of the force(s) producing MS,
taking it as given (under the name of “initial conditions”): its only concern is in
calculating MS as precisely as possible. On the contrary, for morphomechanics the
problem of MS origin is central. Moreover, by dealing with such prolonged suc-
cessions of deformations as those constituting morphogenesis, we cannot be sat-
isfied by discovering the origin of a single force: rather, we must operate with the
chains of forces, each of them creating a basis for the next one to appear. But for
doing this, we have to introduce a distinction between the passive and active forces.
The passive force is that acting to a material element of a biological tissue from
outside, while the active one is that generated as a response within this element,
certainly by spending some of its internal energy. In these terms, we shall consider
morphogenesis as a relay of passive–active forces and corresponding deformations
and shall try to construct an embracing law for this relay.
By focusing itself onto this task, morphomechanics follows a way unusual for
classical mechanics. True, the gap between both trends of mechanics should not be
viii Preface

considered as impassable: the responses of some nonbiological systems to
mechanical forces can be also rather complicated and treated as active ones.
However, what takes place in developing organisms has at least two major features
going far beyond what can be observed in nonbiological systems. The first of them
is the multilevel organization and, the second, a very high diversity and specificity
of the morphological structures. Can these properties be adequately and usefully
treated within the framework of morphomechanics? These are the questions to be
discussed in this book.
The structure of the book is as follows:
In Chap. 1we start from reviewing the main concepts related to morphogenesis.
After doing this, we reformulate developmental events in the language of symmetry
theory, so effectively used in physical sciences. This step is necessary for coming
toward the realm of the self-organization theory (SOT). We hope to demonstrate
that SOT creates an adequate basis for interpreting development but is itself too
general for being applied to concrete processes.
Chapter 2deals with morphomechanical processes related to lower structural
levels, ranging from single macromolecules to entire cells. In recent years, this
research area has been developed in a really explosive way permitting to reach
much more integrated views upon the relations between mechanical events and
those treated traditionally as chemical ones. The dynamic processes belonging to
these levels are treated in terms of symmetry and mechanically based feedbacks.
In Chap. 3we pass toward a supracellular level and review the main modes of
collective cell behavior separately from each other.
The aim of Chap. 4is to integrate these modes into natural developmental
successions, based on morphomechanical feedbacks.
Chapter 5comprises a review of plant morphomechanics, written by Dr. Andrei
Lipchinsky from the Department of Plant Physiology, St. Petersburg University.
The aim of the “Concluding Remarks”is to generalize the beforehand accounted
matters and to outline most important still unsolved problems: the relations between
developmental nomothetics and ideography are here discussed again.
One of the main author’s problems was to trace a border line between the
information to be accounted for reaching the main goal of this book and one that
could be left aside. This task was mostly difficult for the adequate solution as related
to Chap. 2, due to enormous amount of closely interrelated data; we are far from
sure that the optimal balance was achieved. In any case, this monograph in no way
can be regarded as a substitution for regular textbooks on the molecular, cell, and
developmental biology, which are recommended for the interested reader to be
studied beforehand.
To some extent, this book can be considered as an elaborated version of that
published almost two decades ago (Beloussov 1998), but the differences between
them are substantial. To a considerable part they may be ascribed to existing
research progress in related areas, especially in molecular biology of the cell.
However, even most important were not always visible, but in fact quite profound
recent shifts in scientific paradigms. Among these, the first to be mentioned is
extensive penetration of a self-organizing approach in biology accompanied by
Preface ix

increased understanding that so-called “genetic information”is an integral part of
more extensive feedbacks rather than a sole master of development.
There are too many people to which the senior author of this book (LB) is
obliged by everything. The first part of LB’s scientific life which was spent almost
without any contacts with the Western authors provided nevertheless a unique
possibility to assimilate the traditions of the Russian school of “rational morphol-
ogy,”with its attitude to the rejuvenated idea of the primacy of organic forms. The
main person to be mentioned here is Alexander Gurwitsch (1874–1954), who
brought toward the midst of the last century a living spiritual memory of Wilhelm
Roux and Hans Driesch—his teachers and personal friends—but whose ideology he
finally rejected (giving a kind of excuse for making the same with Gurwitsch’s“cell
field”theory). Remembered should be also other bright persons from the same
team: Vladimir Beklemishev, Alexander Liubischev, Sergey Meyen, Pavel Svetlov.
His restricted knowledge of SOT and the related parts of physics LB is owed to
Prof. Chernavskii and his seminar members from Lebedev Physical Institute. More
recently, when a worldwide free exchange became possible, LB got a possibility to
establish contacts with many outstanding persons among whom most influential
were the talks and a real friendship with Albert Harris and Brian Goodwin. The idea
of hyper-restoration emerged in discussions with Jay Mittenthal from Illinois
University.
LB had also the privilege to work together with outstanding representatives
of the next generation—Boris Belintzev, Vladimir Cherdantzev, Vladimir
Mescheryakov, Alexander Stein, and several others. Much of what was taken from
them is incorporated in this book. And last but not least—a view of even younger
population of researchers, now filling our Lab of Developmental Biophysics—gives
the hope that in spite of all the surrounding troubles the great traditions of a
fundamental science about development of organisms will never be broken. LB
thanks a member of this team, Ilya Volodyaev, for critically reading the manuscript
and making valuable remarks.
Moscow Lev V. Beloussov
References
Beloussov LV (1998) The dynamic architecture of a developing organism. Kluwer Academic
Publishers, Dordrecht
Maxwell JC (1871, 1991) Matter and motion. Dover, London
Pattee H (1973) Hierarchy theory: the challenge of complex systems. G. Braziller, New York, p 3
von Bertalanffy L (1968) General systems theory: foundations, development, applications
(Revised edition). George Braziller, New York
x Preface

Contents
1 From Strict Determinism to Self-organization ................ 1
1.1 Deterministic Approaches to Development: Expectations
and Impediments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Lessons from Embryonic Regulations. . . . . . . . . . . . . . . 1
1.1.2 Can Embryonic Inductions Be Regarded
as Cause–Effect Relations? . . . . . . . . . . . . . . . . . . . . . . 8
1.1.3 Genetic Program of Development:
Does It Actually Exist? . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Main Notions and Principles of SOT, Applied
to Developmental Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.1 Translating Developmental Events into
the Language of Symmetry Theory . . . . . . . . . . . . . . . . 11
1.2.2 Parametric and Dynamic Regulations: Several
Basic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.3 Shaping Without Prepatterns . . . . . . . . . . . . . . . . . . . . . 31
1.2.4 Brief Biologically Oriented Exposure of Some
Notions and Principles of Mechanics . . . . . . . . . . . . . . . 36
1.3 Recommended Readings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2 From Molecules to Cells: Machines, Symmetries,
and Feedbacks ....................................... 43
2.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2 Chemo-Mechanical Transduction and Molecular Machines . . . . . 44
2.3 Structures and Actions of Supramolecular Machines,
Treated in Symmetry Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4 Hierarchy of Stressed Networks and the Condition
of Force Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.5 Final Remarks on Supramolecular Machines . . . . . . . . . . . . . . . 52
2.6 From Self-assembly to Self-organization: Temporal
and Spatial Symmetry Breaks . . . . . . . . . . . . . . . . . . . . . . . . . 53
xi

2.7 Metastable (“Glassy”) States of the Cytoskeleton
and Energy Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.8 Cell-Matrix and Cell–Cell Contacts: Mechanodependent
Self-organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.9 Transmission and Regulation of Mechanical Forces
in Cell Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.10 Symmetry Breaks in Entire Cells . . . . . . . . . . . . . . . . . . . . . . . 65
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3 Morphogenesis on the Multicellular Level: Patterns
of Mechanical Stresses and Main Modes of Collective
Cell Behavior ........................................ 75
3.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2 Patterns of Mechanical Stresses (MS) in Developing Embryos . . . 76
3.2.1 MS Patterns in Amphibian Embryos: Methods
of Detection and Mapping . . . . . . . . . . . . . . . . . . . . . . 76
3.2.2 Mechanical Stresses in the Embryos of Other
Taxonomic Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.3 Mechanical Stresses in Post-embryonic Epithelia . . . . . . . 84
3.2.4 Tensile Patterns and Developmental Order . . . . . . . . . . . 86
3.3 Main Modes of Collective Cell Behavior . . . . . . . . . . . . . . . . . 88
3.3.1 Homeostatic Cell Reactions . . . . . . . . . . . . . . . . . . . . . 88
3.3.2 Modes of Cell Alignment . . . . . . . . . . . . . . . . . . . . . . . 90
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4 Morphomechanical Feedbacks ........................... 113
4.1 General Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 Evidences for Hyper-restoration of Mechanical Stresses . . . . . . . 115
4.2.1 Molecular–Supramolecular Levels . . . . . . . . . . . . . . . . . 115
4.2.2 Cellular–Supracellular Levels . . . . . . . . . . . . . . . . . . . . 116
4.3 General Premises and Formulation of HR Model . . . . . . . . . . . . 124
4.4 Some Basic Properties of HR Responses. . . . . . . . . . . . . . . . . . 125
4.5 Main HR-Based Morphomechanical Feedbacks . . . . . . . . . . . . . 128
4.5.1 Contraction–Extension Feedback (CEF) . . . . . . . . . . . . . 128
4.5.2 Curvature-Increasing Feedback (CIF) . . . . . . . . . . . . . . . 129
4.5.3 Extension–Extension Feedback (EEF) . . . . . . . . . . . . . . 130
4.6 Reconstructing Developmental Successions in Terms
of HR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.6.1 Morphomechanics of Zygote. . . . . . . . . . . . . . . . . . . . . 131
4.6.2 Morphomechanics of Cytotomy. . . . . . . . . . . . . . . . . . . 133
4.6.3 Morphomechanics of Blastulation and Gastrulation . . . . . 135
4.6.4 Morphomechanics of the Post-gastrulation Events . . . . . . 144
4.6.5 Morphomechanical Approaches to Cell Differentiation . . . 150
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
xii Contents

5 Morphomechanics of Plants ............................. 157
Andrei Lipchinsky
5.1 An Outline Survey of Self-stressed Plant Architecture
and Its Implications for Plant Mechanobiology . . . . . . . . . . . . . 157
5.2 Organogenetic and Proliferative Events at the Shoot Apex
Are Correlated, but not Coupled, and Are Under Control
by a Non-local Master Field . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.3 Stress Pattern, Cortical Microtubule Dynamics,
and the Orientation of Nascent Cellulose Microfibrils
Are Wired into the Circuitry Modulating Plant
Morphogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.4 Stress-Dependent Polarization of Auxin Transporters
Is Pivotal in Spatiotemporal Patterning of Organ Initiation
at the Shoot Apex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.5 Expansins—Stress-to-Strain Actuators that Play a Preeminent
Role in Plant Morphogenesis. . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.6 A More Detailed Analysis of Tissue Stresses at the Shoot
Apex and Their Significance for Plant Morphogenesis . . . . . . . . 174
5.7 Tissue Stresses and Morphogenesis in Roots . . . . . . . . . . . . . . . 179
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Concluding Remarks ..................................... 191
Contents xiii

Abbreviations
AI Apical index
BM Belintzev’s model
CCP Contact cell polarization
CIF Curvature-increasing feedback
EEF, or EE Extension–extension feedback
GP Growth pulsations
HR Hyper-restoration
MS Mechanical stresses
RAM Root apical meristem
SAM Shoot apical meristem
SBA Suprablastoporal area
SOT Self-organization theory
TIAE Tension-induced active extension
xv

Chapter 1
From Strict Determinism
to Self-organization
Abstract We start from reviewing several ubiquitous approaches to morphogenesis
and argue that for a more adequate presentation of morphogenesis, they should be
replaced by explanatory constructions based upon the self-organization theory
(SOT). The first step on this way will be in describing morphogenetic events in terms
of the symmetry theory, to distinguish the processes driven either toward increase or
toward decrease of the symmetry order and to use Curie principle as a clue. We will
show that the only way to combine this principle with experimental data is to
conclude that morphogenesis passes via a number of instabilities. The latter, in their
turn, point to the domination of nonlinear regimes. Accordingly, we come to the
realm of SOT and give a survey of the dynamic modes which it provides. By
discussing the physical basis of embryonic self-organization, we focus ourselves on
the role of mechanical stresses. We suggest that many (although no all) morpho-
genetic events can be regarded as retarded relaxations of previously accumulated
elastic stresses toward a restricted number of metastable energy wells.
1.1 Deterministic Approaches to Development:
Expectations and Impediments
1.1.1 Lessons from Embryonic Regulations
Please take a look at Fig. 1.1, displaying development of sea urchin embryo from a
non-fertilized egg (Fig. 1.1a) up to a free-swimming larva (Fig. 1.1l, m). This is a
textbook example of embryonic development, known for long ago in great details.
Let us put a naïve question: Why just such a succession is taking place at all and
why it is reproduced for innumerable set of generations? Obviously, our first
suggestion will be that within any stage embryo, a certain set of “causes”is
embedded providing its transition to the next stage. How large should be such a set?
It is easy to see that as the development proceeds, the structure of embryo becomes
ever more complicated: some structures not seen before are emerged. So-called
©Springer International Publishing Switzerland 2015
L.V. Beloussov, Morphomechanics of Development,
DOI 10.1007/978-3-319-13990-6_1
1

arms of free-swimming larvae (Fig. 1.1l, m) are most obvious but not the sole
examples of such a complication. Thus, if being consistent, we should suggest that
any of the newly arisen structures had its own, individual “cause,”settled within an
egg in a definite position even before the start of development.
This is a brief exposition of influential ideology of a so-called preformism which
dominated in embryology for several centuries and is keeping until now (although
in a hidden form) rather strong positions in researchers minds. It is based upon the
principles of a so-called Laplacian, or uniform determinism, ascribed (probably, not
Fig. 1.1 a–mSuccessive stages of sea urchin development. aAn egg within egg membranes;
b–fcleavage; g,hblastula stage, surface view and sagittal section; i–kgastrulation in different
projections; l,mpluteus larva in frontal and sagittal projections, correspondingly
2 1 From Strict Determinism to Self-organization

at all justifiable) to the great French mathematician Pierre Simon Laplace
(1749–1827). By this ideology, the only way for describing and exploring our
world is to split it to such a set of cause–effect links that in each of them, a single
cause cannot produce more than a single effect (the reverse is permitted: A single
effect may require a combination of two or more causes). Until the rise of a
quantum physics in the beginning of twentieth century, this ideology was regarded
as only one compatible with natural sciences. It is worth mentioning, however, that
in physics, it was always more or less shadowed by a law-centered approach (which
puts the “causes”to a category of initial conditions and takes them usually as
granted). However, in biology and the related sciences, the classical deterministic
approach always dominated.
In embryology, it became a basis of one of the most important trends, the so-
called Mechanics of Development (“Entwicklungsmechanik”in German) pro-
claimed by Wilhelm Roux about one and a half century ago (see Moček 1974). By
this view, a developing embryo may be simulated by a clockwork which should be
experimentally split into minor details in order to understand which one of them
“determines”the next part activity; similarly, a task of a researcher would be in
dissecting a developing embryo into single parts in order to see which one of them
contains the “cause”enforcing another to develop further in a regular way.
By evaluating the role played by “Entwicklungsmechanik”in enlarging and
improving our knowledge of development, we come to paradoxical conclusions. On
one hand, by using the recommended analytical tools, we recognized a lot about
interactions of embryo parts of quite different scales, from whole organs to single
cells. But on the other hand—which is often neglected—the conceptual basis of
Roux approach (the idea of a strict cause–effect determination) has been under-
mined already in few years after it was formulated.
This was done by another German embryologist, Hans Driesch, in his experi-
ments on separating from each other two or four blastomeres of sea urchin eggs or
on changing their mutual positions. Although Driesch’s results have been described
virtually in all embryological textbooks, almost never this description was
accompanied by conceptual conclusions, forwarded already by Driesch himself and
elaborated by recent authors.
As it is widely known, the main result of Driesch’s experiments was that fairly
normal (although proportionally diminished) larvae with all of their organs properly
arranged could be obtained from a single embryonic cell (blastomere) containing no
more than ½(if two first blastomeres were separated) or even ¼(in the case of four
blastomeres separation) of the entire egg’s material. Rather soon these effects
(defined by Driesch as “embryonic regulations”) were numerously confirmed and
extended to the species belonging to almost all taxonomic groups of metazoans,
from sponges to mammalians. The only noticed difference was the duration of a
period of an egg/embryo capacity to regulations: In some groups, such as mollusks
or ascidians, this period was rather brief (ending soon after egg’s fertilization),
while in others (flatworms), it extended over the entire living cycle (interesting, in
ascidians, a regulatory capacity is lacking during larva development but restores in
adult state). Importantly, after entire embryos lose their regulatory capacities, these
1.1 Deterministic Approaches to Development: Expectations and Impediments 3

latter are still manifested by their parts: For example, whole limbs or eyes of
Vertebrate embryos can be restored from small fragments of these rudiments, or
even from dissociated cells. Embryonic regulations took place not only after
removal, but also after experimental addition of some excessive amount of
embryonic material.
Besides separating blastomeres, Driesch changed their mutual positions by
compressing cleaving eggs for some time period. After being released, the eggs also
developed in a normal way, although each of the blastomeres became surrounded
by abnormal neighbors. Fairly normal embryos, although not in 100 % of cases
have been obtained later from dissociated-reaggregated masses of sea urchin
blastomeres (Spiegel and Spiegel 1975).
What can these experiments tell us about cause–effect relations? If continuing to
apply deterministic approach to embryonic regulations, we have to conclude that
complete sets of “causes”required for further development are contained not only
within whole eggs/embryos but also in their halves, quarters, etc.; on the other
hand, as a rule, the sets are not increased with the addition of embryonic material.
Moreover, each time (depending upon the type of a disturbance performed) this
hypothetical “set of causes”should change its arrangement for producing the
normal pattern. Obviously, under these circumstances, a concept of an individual
“cause”(precursor) for any embryonic structure becomes meaningless.
Driesch fully recognized this critical situation. So far as in his time scientific
knowledge was in fact identified with strict cause–effect determinism, he concluded
that embryonic regulations undermine the very basis of natural sciences. Such a
position put this outstanding thinker outside the scientific mainstream, which
hampered further study of embryonic regulations for several decades. Driesch
formulated his final conclusion from his regulation studies as a law which in
slightly simplified form sounds like this: “The fate of an embryo part is a function
of its position within a whole”(Driesch 1921). Its idea is in the following. Suggest
that both the normal and experimentally disturbed embryos possess a kind of a
coordinate grid (including, for example, a polar axis and a set of latitudes) which is
each time adjusted to embryo dimensions (being diminished in embryos having a
part of their material removed and enlarged in those getting excessive additional
amount of material). Each part of the embryo is endowed by a capacity to “read”its
own coordinates and to develop accordingly, even if this does not coincide with the
normal fate of this part.
Looking at the first glance as an adequate generalization of embryonic regula-
tions and related phenomena, this statement contains nevertheless some hidden
contradictions and leaves a number of questions unsolved. The first of them is about
the reference points of the postulated coordinate grids. Do they correspond to
certain small previously settled structural elements of otherwise homogeneous
embryo, to entire embryo geometry and/or topology or to something else? How
should the reference points be arranged for providing formation of similar adults
out of differently disturbed eggs/embryos?
The second set of questions relates to the notion of “fate.”So far as during
embryo development any of its parts constantly changes, its position in any system
4 1 From Strict Determinism to Self-organization

of coordinates and the notion of “fate”may include developmental periods of quite
a different longevity—we are urged to define how long should be the develop-
mental period determined by a given position. This question is closely connected
with another, even more important one: What is the nature of the postulated con-
nections between a position and a “fate”of embryonic element, whatever being the
latter? Can we point to any universal dynamic component playing a leading role in
all the position-fate dependencies or each of them has nothing in common with the
others?
The most popular concept pretending to answer these questions is that of
“positional information”(PI) (Wolpert 1969,1996). Appearing after several dec-
ades of almost complete oblivion of Driesch’s ideas, it aimed to modernize them
because the very fact of positional dependencies in embryonic development could
not be further ignored. By doing this, Wolpert started from postulating the existence
of a few (as a rule two) structural elements of embryo acting as reference points for
PI perceived by all the other elements (cells). In more concrete versions of PI
concept, the reference points were identified as the source and the sink of a
chemical substance (called morphogen) which creates concentration gradient
between these points. It is the local morphogen concentration to be “read”and
“interpreted”by any embryonic cell (independently of its neighbors) determining
thus its fate.
If discussing the problem of reference points, the main trouble for PI concept is
lack of robustness to mutual shifts of reference points which inevitably accompany
any of experimental disturbances. Let us trace some examples, starting from the so-
called French Flag (FF) model, a basic one for PI concept.
According to its name, FF model is dealing with 3-stripe axisymmetric pattern. If
putting the “source”and the “sink”to the opposite poles of the main axis and making
removals or additions of tissue pieces precisely axisymmetric, such a reference
system will be formally suitable for preserving the initial pattern (Fig. 1.2a, b).
However, if making tissue removals/additions even slightly asymmetric (which is
almost usually the case), the reference points themselves will be shifted asymmet-
rically, thus distorting the resulting pattern (Fig. 1.2c). Even more important is to
remind that axisymmetric eggs/embryos are rare exceptions among those capable of
regulations: Rather, most of the eggs already soon after fertilization acquire irre-
versible differences [called dorso-ventral (DV)] between opposite sides. In these, any
removals/additions of embryonic material will shift any pair of points into positions
geometrically non-homologous to initial ones (a–a
1
,b–b
1
, Fig. 1.2d), thus inevitably
distorting PI pattern. We can see that any formal way to save PI concept is to suggest
that PI is “emanated”from all the material points of a given stage embryo, rather
than from any previously selected ones. This brings us to the fundamental non-
classical idea of non-locality, associated with collective interactions of a large
number of equivalent elements. The both notions, central for a self-organization
theory (SOT), will be discussed further in this and the next chapters. Meanwhile, if
taken alone, the idea of the multiple PI bearers will be able to interpret embryonic
regulations only if the initial shape of the embryo was not significantly changed after
experimental perturbations. It will not work, for example, when pretty normal shapes
1.1 Deterministic Approaches to Development: Expectations and Impediments 5

will emerge de novo out of completely chaotic cell arrangement, like in the above-
mentioned Spiegel and Spiegel (1975) experiments. Such events belong to a “pure”
self-organization and cannot be explained by any concepts demanding a more or less
precise initial PI, whether it comes either from single elements or their collectives.
Another problem associated with PI concept is that of relations between cell
positions (in any reference system) and their “fates.”Actually, PI concept is rather
uncertain on the exact meaning of the “fate.”Is it identical to the final cell dif-
ferentiation (which is highly improbable if PI is assumed to be set at initial stages),
or just to a next small step of development? In any case, the idea of transformation
of cell position (local morphogen concentration) into its fate raises a number of
problems. Some of them have been discussed by Furusawa and Kaneko (2006). The
authors argue that even in most obvious examples of concentration-dependent
action of certain agents (in their case, activin), “the pattern formation…is not
predetermined from spatial information, but rather through intracellular dynamics
and interaction. Spatial patterns and intracellular states mutually stabilize robust
pattern formation…” They present model data showing that PI itself is not enough
for establishing order in the population of heterogeneous cells, so that such notions
a
a1
b1
b
(a) (b)
(d)(c)
Fig. 1.2 Non-robustness of PI model. Small lilac and blue circles depict hypothetical sources of
PI, the latter shown by arrows at the upper left frame. Following PI model embryonic regulations
will become possible only if (as in frames a,b) embryonic body and PI sources are axisymmetric
and removals (a) or additions (b) of embryonic material do not disturb axial symmetry. If,
however, the pieces of removed or added material are asymmetric (c), or such is the initial shape of
the intact embryo (d), no restoration of geometric similarity viewpoint is possible within the
framework of the PI model
6 1 From Strict Determinism to Self-organization

as nonlinear intracellular dynamics and attractors are required for getting realistic
results. All of these belong to the SOT vocabulary.
By discussing these matters, we come to the most troublesome problem of
development—actually going well beyond PI concept—which can be defined as
that of interpretation.
If we have a certain signal (no matter being located inside of outside of
embryonic body) which generates a definite response from the latter, our main
interest is to know why such a relation between the signal and the response is taking
place. As mentioned in Introduction, we have two epistemological models which
can be used for solving this task: Either there is a reason to postulate each time a
unique one-to-one cause–effect (signal–response) relation—in this case, our work
will consist in compiling a comprehensive list of such relations; or we regard each
relation as a particular manifestation of a general law. For example, if we relate
velocity of a thrown stone to its position, we do not suggest that a new “specific”
force is associated with each next position: Rather, we are searching for a common
law embracing all the positions including those never occupied by the stone.
Fig. 1.3 Random mutual arrangement of transplanted inductor’s tissue (light) and host tissue
(dark) in the first Spemann and Mangold (1924) experiment on embryonic induction, abolishing
the inductor’s capacity to be a PI source. aCross-sectional area of the host embryo with its normal
axial organs to the right and induced organs to the left. bSeveral cross sections of the chimeric
notochord. From Spemann (1936)
1.1 Deterministic Approaches to Development: Expectations and Impediments 7

Considered in this context, PI concept resides a strange intermediate place:
On the one hand, it ascribes that the leading role in development to a largely non-
specific factor of position, which in physical sciences, is always used for con-
structing an embracing law (as a rule, describing certain field); but, on the other
hand, each next position of embryonic elements is claimed to be connected with
quite specific response, having no relations with another one.
1
This, by my view,
makes the entire PI concept tautological, adding nothing to a mere descriptive
approach which takes spatial patterns as given. Let us look now for the situation
with interpretation problem in other branches of developmental biology.
1.1.2 Can Embryonic Inductions Be Regarded
as Cause–Effect Relations?
The discovery and further exploration of embryonic inductions by Hans Spemann
and his followers may look at first glance as a triumph of Wilhelm Roux causal
approach: It was shown indeed that one part of embryo can be a crucial factor for
the development of another. Does it mean, however, that the inductors can be
regarded as a kind of blueprints, or as “PI sources”for induced tissues? It is enough
to have a look to the picture from the famous first Spemann and Mangold paper
(Fig. 1.3) for seeing how far this is from reality. We can see that the inductor’s and
host tissues (discerned by their pigmentation as being taken from two different
Triton species) are mixed at random, both in the notochord and the neural tube.
Nevertheless, the entire structure of the complex of axial organs is perfectly
ordered. It means that the inductor tissue cannot serve not only as a spatial template,
but even as a source of a hypothetical PI gradient for the reacting tissue: Formation
of a proper set of axial organs under the influence of an inductor looks more as
embryonic regulation in Driesch sense rather than a kind of a direct causation. Or, if
speaking in terms of a SOT (to be later on accounted in this chapter), it was the
long-range order, independent from the “micropatterns”of the inductors and host
tissues, to be established in the first Spemann and Mangold experiments. At the
intuitive level, this was perfectly apprehended by Spemann himself who considered
the action of inductor as “abstract,”that is, containing no “information”about
spatial details (Spemann 1936). This conclusion was later on specified by Wadd-
ington as following: “Clearly, the problem [of induction] reduces to that of a
complex response to a simple stimulus …somewhere along the line an increase in
complexity occurs”(Waddington 1962).
Usually, the problem of complication during embryonic induction is resolved in
terms of concentration gradients of inductive substances assumed to be set between
1
My friend, American biologist Albert Harris, liked to compare PI with a price politics in non-
marked economies: The prices (equivalent to local morphologies or cell types) are appointed ad
hoc, without being regulated by any mutual feedbacks.
8 1 From Strict Determinism to Self-organization

animal and vegetal embryo poles, or between its dorsal and ventral sides (e.g., De
Robertis 2009). If accepting the presence of such a macroscopic gradient-like
prepattern, the isolated small pieces of embryonic tissue cannot produce more than
small parts of it. However, already in the old Holtfreter’s(1938) experiment, a
miniature copy of entire embryo was obtained from a piece of embryonic tissue
extirpated from so-called marginal zone. As commented by Gerhardt (1998)
“Holtfreter brought to light an individualistic and anti-authoritarian view of the
embryo in which competent responsive cells interact in a self-organizing commu-
nity, in place of conceptions of the embryo as a collection of naïve passive members
dependent for their future on detailed directions from a central organizer.”
A modern concept of so-called default induction, reducing the inductors’role to
“inhibition of inhibitor”(Hemmati-Brivanloue and Melton 1997) may be regarded
as a next step from the cause–effect ideology toward that of self-organization.
Indeed, the inductors, instead of being the bearers of the positive “information,”
become a kind of releasers (triggers) of the potencies already preexisted in reacting
tissues. As in the cases of embryonic regulations, this situation cannot be ade-
quately described without using such notions belonging to SOT as a nonlinearity,
potential relief (describing a state of embryonic cell), and others. A special question
will be whether such a self-organization can be at least partly based upon morp-
homechanics. Later on, we hope to bring some evidences in favor of such a
suggestion.
1.1.3 Genetic Program of Development: Does It Actually
Exist?
In not so remote past, a claim that the course of development is “genetically
programmed”was accepted as an absolute truth, even in spite of the lack of proper
understanding what the “program of development”actually means. So stunned
were the successes in deciphering the key roles of genes in “controlling”the
development of embryonic rudiments that all the instructions for “making a fly”[a
paraphrase of the title of famous Lawrence (1992) book] looked to be in our hands.
Only closer to our days, it became realized that our believing to govern the
development by switching on or off any genes or signaling pathways is the same as
operating an electronic device by pushing its buttons without having even a slight
idea on how it actually works.
For clarifying the situation, two main groups of evidences have to be mentioned:
one of them related to classical biology and the other recently emerged as a result of
unexpected discoveries in modern molecular genetics.
The first group of evidences claims that the factors determining space–time
schedule of genes expression are non-genetic in their nature and topography. This
statement, which creates the basis of biology for about a century and is supported
by experiments on nuclei transplantations and many others, is on its own enough
1.1 Deterministic Approaches to Development: Expectations and Impediments 9

for concluding that genes themselves should obey outside instructions which are
called epigenetic. Meanwhile, recently it was complemented by numerous obser-
vations showing that relations between genes and signaling pathways on the one
hand and their developmental targets on the other hand turned out to be quite far
from being one to one: The products of activity of the same or closely homologous
genes and/or of the same signaling pathways were found to be involved in quite
different developmental events. Modern textbooks are full of such examples. Here
are just a few of them:
•The interactions between msx-1 and msx-2 homeodomain proteins characterize
the formation of teeth in the jaw field, the progress zone in the limb field, and the
neural retina in the eye (Gilbert 2010).
•The transcription factor Pax-6 is expressed at different times and at different
levels in the telencephalon, hindbrain, and spinal cord of the central nervous
system; in the lens, cornea, neural and pigmented retina, lacrimal gland, and
conjunctiva of the eye; and in the pancreas (Alberts et al. 2003).
•In Drosophila embryos, a gene Engrailed is involved in segmentation of a germ
band, development of intestine, nervous system, and wings. In mouse, same
gene participates in brain and somite development. In Echinodermata, it takes
part in skeleton and nervous system development (Alberts et al. 2003).
•Delta–Notch signaling pathway regulates the following: neuro-epithelial dif-
ferentiation in insects, feather formation in birds, fates of blastomeres in
Nematodes, differentiation of T-lymphocytes, etc. (Alberts et al. 2003).
•Hunchback gene is involved at the early stage of Drosophila development as one
of so-called gap genes and at the later stages participates in development of
neural system.
For the similar conclusions, as related to signaling pathways, see Kupiec (2009).
Shrewd remarks on this topic can be found in (Gordon 1999 V. 1, pp. 59–64).
Anyway, our present-day image on genetic regulation of development contains
two great negations: (1) even complete knowledge of genome structure cannot tell
us what gene will be expressed in a given space/time location; (2) even from
exhaustive knowledge of space/temporal schedule of genes expression, one cannot
predict what morphological structures will be formed in these definite locations.
Certainly, this is not to claim that the genes play no role in development at all. On
the contrary, their role is crucial in permitting or abolishing development of the
single structures and their ensembles; in particular, they may affect shapes of entire
embryos or their parts. A proper conclusion from the above said is that their action
should produce a definite morphological results only if being an integral part of quite
extended and ramified regulatory contours, including the feedbacks coming from the
upper-level events, such as cell shapes and mechanical forces. Actually, such a
situation is in generally acknowledged, but the conclusion is in most cases expressed
in an allegoric form, by claiming that genes action is “context-dependent.”The
urgent aim will be in transforming this vague formulation into a concrete research
program.
10 1 From Strict Determinism to Self-organization

1.2 Main Notions and Principles of SOT, Applied
to Developmental Events
Within one or two last decades, the word “self-organization”became among the
most generally used ones, not only in science, but also in politics and every-day life.
Meanwhile, for most of the users, it remains to be nothing more than a mere word,
or a kind of vague metaphor; only few people knows that it is a designation of a
strict theory, being in its essence mathematical but deeply rooted in physics,
biology, economy, and even humanitarian sciences. SOT is treated in a number of
perfect books ranging from very special to popular ones; among the latter, sim-
plicity and strictness are adequately combined in the book by Capra (1996). For the
readers who do not like math, a very qualified and perfectly illustrated account of
the main SOT principles by Ball (2001) can be recommended. The aim of this
section is more limited: It is in outlining only those notions and concepts of SOT
which are necessary for interpreting adequately development of organisms. The first
of them has been formulated and widely used well before the emergence of SOT:
this is the symmetry theory. In certain sense, the term “symmetry”shares the
destiny of a “self-organization