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# 10 Morphomechanics of cytotomy, applied to early cleavage. a Deformation of the cortical layer by kinesin-mediated pulling apart of the polar microtubules. a 1 Detailed presentation of the pulling apart mechanisms. Mt microtubules, k kinesins moving to +ends of antiparallel microtubules. Red arrows depict active events, and blue ones depict passive shifts. b Convergent flows of cortical material (green) suggested to move uphill the tension gradients born by curvature inequalities. Dynein-mediated shifts of centrioles are shown. c-e Radial, bilateral, and spiral patterns of the first cleavage divisions correspondingly as functions of the cortical flows (dense arrows). From Cherdantzev (2003) with the author's permission

## Citations

... If the discrepancy of this measurement from the referent one is small, we conclude that practically all the forces affecting the given plane cells are located in this very plane (the sum of forces coming from other planes is close to zero) and vice versa. In fact, we found that the deviation from the reference value did not exceed 10 % even if the trip included more than 400 intermediate nodules (Beloussov and Lakirev 1988). ...

... One of the main findings was that within a substantial developmental period from blastula to tail bud stage, the topology of tensions (i.e., the number and mutual Beloussov and Lakirev (1988) arrangement of cross-lines and nodules) is changed for few times only. The changes take no more than few dozens minutes each and exactly fit the transitions between periods outlined already by classical embryologists: blastulation, gastrulation, neurulation, and tail bud formation. ...

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) morphogenetic events can be regarded as retarded relaxations of previously accumulated elastic stresses toward a restricted number of metastable energy wells.

... If the discrepancy of this measurement from the referent one is small, we conclude that practically all the forces affecting the given plane cells are located in this very plane (the sum of forces coming from other planes is close to zero) and vice versa. In fact, we found that the deviation from the reference value did not exceed 10 % even if the trip included more than 400 intermediate nodules (Beloussov and Lakirev 1988). ...

... One of the main findings was that within a substantial developmental period from blastula to tail bud stage, the topology of tensions (i.e., the number and mutual Beloussov and Lakirev (1988) arrangement of cross-lines and nodules) is changed for few times only. The changes take no more than few dozens minutes each and exactly fit the transitions between periods outlined already by classical embryologists: blastulation, gastrulation, neurulation, and tail bud formation. ...

Regular patterns of mechanical stresses are perfectly expressed on the macromorphological level in the embryos of all taxonomic groups studied in this respect. Stress patterns are characterized by the topological invariability retained during prolonged time periods and drastically changing in between. After explanting small pieces of embryonic tissues, they are restored within several dozens minutes. Disturbance of stress patterns in developing embryos irreversibly breaks the long-range order of subsequent development. Morphogenetically important stress patterns are established by three geometrically different modes of cell alignment: parallel, perpendicular, and oblique. The first of them creates prolonged files of actively elongated cells. The second is responsible for segregation of an epithelial layer to the domains of columnar and flattened cells. The model of this process, demonstrating its scaling capacities, is described. The third mode which follows the previous one is responsible for making the curvatures. It is associated with formation of “cell fans,” the universal devices for shapes formation due to slow relaxation of the stored elastic energy.

... If the discrepancy of this measurement from the referent one is small, we conclude that practically all the forces affecting the given plane cells are located in this very plane (the sum of forces coming from other planes is close to zero) and vice versa. In fact, we found that the deviation from the reference value did not exceed 10 % even if the trip included more than 400 intermediate nodules (Beloussov and Lakirev 1988). ...

... One of the main findings was that within a substantial developmental period from blastula to tail bud stage, the topology of tensions (i.e., the number and mutual Beloussov and Lakirev (1988) arrangement of cross-lines and nodules) is changed for few times only. The changes take no more than few dozens minutes each and exactly fit the transitions between periods outlined already by classical embryologists: blastulation, gastrulation, neurulation, and tail bud formation. ...

This book outlines a unified theory of embryonic development, assuming morphogenesis to be a multi-level process including self-organizing steps while also obeying general laws. It is shown how molecular mechanisms generate mechanical forces, which in the long run lead to morphological changes. Questions such as how stress-mediated feedback acts at the cellular and supra-cellular levels and how executive and regulatory mechanisms are mutually dependent are addressed, while aspects of collective cell behavior and the morphogenesis of plants are also discussed. The morphomechanical approach employed in the book is based on the general principles of self-organization theory.

An attempt is made to reconstruct the natural successions of the developmental events on the basis of a common mechanically based trend. It is formulated in terms of a hyper-restoration (HR) hypothesis claiming that embryonic tissue responds to any external deforming force by generating its own one, directed toward the restoration of the initial stress value, but as a rule overshooting it in the opposite side. We give a mathematical formulation of this model, present a number of supporting evidences, and describe several HR-driven feedbacks which may drive forth morphogenesis. We use this approach for reconstructing in greater detail the gastrulation of the embryos from different taxonomic groups. Also, we discuss the application of this model to cytotomy, ooplasmic segregation, and shape complication of tubular rudiments (taking hydroid polyps as examples). In addition, we review the perspectives for applying morphomechanical approach to the problem of cell differentiation.

If you look through a number of contemporary textbooks and introductions of biophysics, in order to find out what exactly biophysics is and what the field covers, you will be quite bewildered. Even the titles of the books with their diversity of names for the field, which include, besides biophysics itself, “Medical Physics ”, “Medical and Biological Physics”, “Physical Biology”,“Physical Bases of Medicine and Biology”, and “Molecular Biology ”, already show the existence of different interpretations and tendencies.

In modern science, a most adequate conceptual framework for treating the behaviour of complex dynamic systems is given by the theory of self-organization (e.g., Prigogine, 1980). The developing organisms may be definitely attributed to self-organizing entities by a number of criteria and, above all, by their capacity for spontaneous breaks of the symmetry order. We define those breaks of macroscopical symmetry as spontaneous which do not imply any definite macroscopical causes (dissymmetrizators), let they be located outside or inside the embryo. As is well established by descriptive and experimental embryology, such symmetry breaks are taking place not only at the level of a visible morphology, but also within the phase space of the developmental potencies. The latter means that embryonic development is always associated with a progressive narrowing and specification of the morphogenetical potencies initially delocalized throughout embryonic space.

Both for an experienced and for a naive observer the development of a living sample, be it plant or animal, looks, first of all, as a regular succession of complicated changes in the shapes and mutual arrangement of its parts; such a succession is usually defined as a morphogenesis while its components as morphogenetic processes. Invaginations, evaginations and the bending of epithelial layers, condensations of freely moving mesenchymal cells, as well as the changes in shapes and overall proportions of the large masses of almost immobile plant cells may serve as the examples of morphogenetic processes. As was shown by the molecular biology within several last decades, all of these processes are based upon a highly regulated motile activity of the molecular and supramolecular components of the living cells. In the first approximation, all of these processes may be considered as mechanical, what means that they are associated with the production of mechanical forces and changes in space positions of the material constituents.

Species-specific morphology in thecate hydroids is considered as a function of 2 fundamental morphogenetic characteristics: parameters of growth pulsations and the relation between the migratory activities of the endo- and ectodermal cells of the growing tips. Comparative, experimental and modelling data are presented suggesting that increases in the values of these parameters lead to gradual transformation of the narrow tubular rudiments of primitive thecates to the more transversely extended and later bilaterally symmetrical morphologies of advanced forms. There is a corresponding change in the mode of branching, from stolonal through alternate to opposite, with densely packed hydranths and hydrothecae. The relations between the traditional systematic approach to this group and the present ontogenetically based interpretation are discussed.

A finite elements model imitating the morphogenesis of smoothly curved tubular epithelial rudiments is suggested. It is based upon the experimentally proved assumption of the lateral (tangential) pressure between adjacent epithelial cells. The main idea of the model is that under a non-zero local curvature the lateral cell-cell pressure acquires the radial components which are absent under zero curvature. In the framework of the model we investigate the roles of initial geometry, the different coefficients relating the local curvatures and radial cell shifts, and of visco-elastical cell-cell linkages in the shaping process. We also employ the different temporal regimes (both periodical and constant) of the lateral pressure exerted and the different overall durations of the modelling. As a result, we get a set of biologically realistical shapes, almost all of them belonging to the same basical "trefoiled" archetype. Among the variables explored, shaping was most affected by the changes in visco-elastical coefficients, in the temporal regimes and in the overall duration of the modelling. The model shows that rather complicated and realistical shapes of epithelial rudiments can be obtained without assuming any initial regional differences inside cell layers. The model may be useful for understanding the principles underlying both genetical and epigenetical regulation of the morphogenesis.