Previous

List of Abstracts

Next

One of the main problem of developmental biology is how an unaccountably infinite number of interactions between potentially morphogenetic processes may unfold regular series of morphological states with a basically simple and reproducible structure. This is rather close to the problem of basic variables (BV) - "parameters of order" - in the general theory of non-linear dynamic systems capable of self-organization. In this theory BV are considered as rate-limiting (slowest) variables with no relevance to their physical nature. Even in more advanced morphomechanical models of the biological self-organization it remains open to question how variables that are no more than characters of form generate the form itself.

A new approach to this question is based on the initial version of the Gurwitsch morphogenetic field. The Gurwitsch field is defined as a vector field of a cell displacement, the value of vectors being proportional to the angle of their deviation from the local curvature radii of the epithelial sheet surface (ESS). Then the cell displacement is inherently connected with the change in ESS curvature with a feedback to the value of displacement vectors. Because of the equivalence between temporal changes in the cell shape and their spatial cell-to-cell spreading the cell displacement and the change in ESS curvature are BV of any dynamic system generating "driving forces" of morphogenesis. In terms of the mathematical theory of self-organization the cell displacement and dynamics of the ESS curvature are analogues of the "local activator" and "distant inhibitor". The dynamics of BV defines smooth mappings of ESS which singularities are identical to the critical points of dynamics.

Using the direction of the cell polar axis as a control parameter of BV dynamics we get an evolutionary unfolding of a structural and dynamic complication of main morphological Bauplans. In the evolutionary initial state the outer ESS surface corresponds to the anterior end of a moving epithelial cell. In hydroids, because of the instability of ESS to the inversion of cell polarity, the morphogenesis of ESS is reduced to the sphericalization, "the hole in a sphere" being the only singularity of the embryo. In sea urchin, because of the origination of a feedback between the centripetal cell movement and the formation of a negative ESS curvature, the inversion of cell polarity generates a differentiation of domains of (+) and (-) curvature. In animals with the spiral cleavage this is added by a feedback between the centrifugal cell movement and the formation of a negative ESS curvature. This leads to a further complication of form and to an origination of new singularities (folds and cusps) which perfectly correspond to loci of a formation of evolutionary new embryonic tissues. In Chordata there appears a feedback between radial and planar cell movements which provides an opportunity of interaction between the centripetal and centrifugal cell movement and leads to the notochord formation. It is the top of the morphogenetic evolution because of making use of all the morphogenetic feedback between movement and geometry which are possible for BV.
 

Previous

List of Abstracts

Next