Dynamic topology of the cephalochordate to amniote morphological transition: a self-organized system of Russian dolls.

This note presents a mechanistic explanation of the transition between the morphology of cephalochordates to that of amniotes. By a careful study of the morphogenetic movements which occur during the early stages of development of a typical amniote (a chicken embryo), we are able to show that the formation of a vertebrate body follows a sequence: first, formation of dorsal folds, then head and heart as dorsal and ventral folds, and finally another dorsal fold, which eventually builds up the chorion. This order has a physical origin linked to the velocity field of the tissue flow. These folds form at right angles to the flow direction, and the topology of the chordates flow is hyperbolic. This mechanism explains the differences between the successive bauplans, by the cumulate forward and backward movement of the flow. Eventually, the entire phenomenon can be described as a self-organized system of Russian dolls, by which the heart finds itself inside the embryo, and the embryo itself inside the chorion. In addition, the phenomenon has a mirror symmetry in the anterior and in the posterior part, thereby explaining naturally the existence of animals having a caudal heart.