Hyperbolic symmetry breaking and its role in the establishment of the body plan of vertebrates

Abstract

This Note presents experimental evidence that a hyperbolic tissue flow plays an important role in the establishment of the organization plan of vertebrates. We have followed the development of chicken embryos from the gastrula stage up to the moment when the body plan is recognizable. We have found that establishment of this plan occurs in the presence of a uniform tissue flow which at all stages presents a hyperbolic pattern. The flow is bidirectional in the antero-posterior direction, with a fixed point (stagnation point of the flow) which is a point of zero speed in all directions, in the reference frame of the egg. This stagnation point of the flow is located at the level of the presumptive yolk stalk of the chicken (analogous to the mammal navel). On either sides (left and right) of the body, the flow is also bidirectional. The antero-posterior bidirectionality and the left-right bidirectionality result in splitting of the embryo into four domains with vortex-like flow, with partial mirror symmetry between the left/right halves and top/bottom ones. The center of symmetry is the stagnation point. The broken symmetry of the flow is up-scaled in the adult animal. Areas with straightforward tissue movement are the ones where axial structures develop. The lateral domains with vortex-like flow colocalize with the future limb plates.