The Change of Initial Symmetry in the Pattern-form Interaction Model of Sea Urchin Gastrulation

The characteristic feature of pattern-form interactive models is a feedback loop from biochemical pattern formation to form changes in the developing embryo. The models are directed towards prediction of changes of the embryo surface geometry and biochemical pattern. We deal with an investigation of the mechanisms of "amplification" of non-linear response of a morphogen reaction-diffusion system due to changes of geometry in the developing object. Potentiality of approach is demonstrated by simulation of gastrulation and the following morphogenesis of the sea urchin embryo. Computer experiments with the model at different parameter values reveal three modes of model dynamics, such as invagination with following elongation and then metamerization of a "gut" (1); invagination followed by formation of bilaterally symmetrical "pockets" of the initial invagination (2); "gut" invagination followed by determination of the "oral field" and the beginning phase of "mouth" formation (3).