Topological determination of early morphogenesis in Metazoa

Generic oscillation patterns of the developing systems and their role in the origin and evolution of ontogeny

The role of generic oscillation patterns in embryonic development on a macroscopic scale is discussed in terms of active shell model. These self-oscillations include periodic changes in both the mean shape of the shell surface and its spatial variance. They lead to origination of a universal oscillatory contour in the form of a non-linear dependence of the average rudiment's curvature upon the curvature variance. The alternation of high and low levels of the variance makes it possible to pursue the developmental dynamics irrespective to the spatiotemporal order of development and characters subject to selection and genetic control. Spatially homogeneous and heterogeneous states can alternate in both time and space being the parametric modifications of the same self-organization dynamics, which is a precondition of transforming of the oscillations into spatial differences between the parts of the embryo and then into successive stages of their formation. This process can be explained as a "retrograde developmental evolution", which means the late evolutionary appearance of the earlier developmental stages. The developing system progressively retreats from the initial self-organization threshold replacing the self-oscillatory dynamics by a linear succession of stages in which the earlier developmental stages appear in the evolution after the later ones. It follows that ontogeny is neither the cause, nor the effect of phylogeny: the phenotype development can be subject to directional change under the constancy of the phenotype itself and, vice versa, the developmental evolution can generate new phenotypes in the absence of the external environmental trends of their evolution.

Topological singularities and symmetry breaking in development

The review presents a topological interpretation of some morphogenetic events through the use of well-known mathematical concepts and theorems. Spatial organization of the biological fields is analyzable in topological terms. Topological singularities inevitably emerging in biological morphogenesis are retained and transformed during pattern formation. It is the topological language that can provide strict and adequate description of various phenomena in developmental and evolutionary transformations. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. A topological inevitability of some developmental events through the use of classical topological concepts is discussed. This methodology reveals a topological imperative as a certain set of topological rules that constrains and directs embryogenesis. A breaking of spatial symmetry of preexisting pattern plays a critical role in biological morphogenesis in development and evolution.