Clarifying tetrapod embryogenesis, a physicist's point of view

Abstract

Abstract. The origin of tetrapods is a complex question that webs together genetic, paleontological, developmental and physical facts. Basically, the development of embryos is described by a complex mix of mechanical movements and biochemical inductions of genetic origin. It is difficult to sort out in this scientific question what are the fundamental features imposed by conservation laws of physics, and by force equilibria, and what can be ascribed to successive, very specific, stop-and-go inductions of genetic nature. A posteriori, evolution selects the parameters of this process as found in the observed species. Whether there is a general law to animal formation seems out of the question. However, several concepts developed in biology, like the concept of "organizer" seem questionable from a physics point of view, since the entire deformation and force field should be the "organizer" of development, and one can hardly ascribe such a role to a single small area of the embryo body. In the same spirit, the concept of "positional information" encapsulated in concentration of chemicals seems questionable since the deformation and force fields in embryonic tissues are tensors. Finally, the concept of a development organized in space along three orthogonal ("Cartesian") axes associated to chemical gradients seems also questionable, since early embryo development is driven by complex vortex fields, with hyperbolic trajectories which span the entire embryo. Such hyperbolic trajectories are best understood by a description in terms of dipolar components of the morphogenetic forces, whose projections along orthogonal axes have no specific meaning except as a mathematical tool. I review here the present state of description of several aspects of tetrapods morphogenesis and evolution, from the point of view of physics. It is getting clear that several basic features of tetrapods body are a direct consequences of fundamental laws of physics. Several lines of work reviewed here show that the topology of the tetrapods may be directly related to the structure of the earliest movements in embryos. The bio-mechanical approach leads to important consequences for the constraints on evolution of the craniates. Such consequences have received a controversial welcome in the last decade, although they may encapsulate the true origin of craniates, esp. simians, and eventually homo.

Limb positioning and shear flows in tetrapods

“…We show that such vortex flows (i.e., streamlines exhibiting closed loops) continue during all stages of embryo morphogenesis, until a vertebrate bauplan starts to be recognizable. In this perspective, we confirm that the limb areas actually form dynamically as a consequence of the vortex flows [2][3][4], because of the strong winding of the tissue sheared along the median axis. The latter behaves as a central elongated element which This article is divided into parts as follows.…”

“…In this view, the mere advection of the entire embryo domain in a hyperbolic pattern would break the symmetry of all concentration fields, thereby generating organs with a partial top-bottom symmetry, in addition to the usual left-right symmetry. In this view, the formation of the animal body amounts qualitatively to an up-scaling of the initial hyperbolic flow pattern towards the final animal shape, which inherits and conserves at all stages the global pattern [4].…”

“…It has been suggested that, at very early stages, embryonic material is viscous and that hydrodynamic laws of viscous flows may apply to the formation of the pattern of embryos [1][2][3][4]. These hydrodynamic laws should help to understand the vortices which are observed in vertebrate development [5,6].…”

Differential Geometry Based Multiscale Models

“…This development is based on the fundamental laws of physics, and has considerably enriched our understanding of biological systems. Recently, Navier–Stokes and Stokes models for visco-elastic systems have yielded impressive successes in the description of tetrapod embryogenesis (Fleury, 2009; le Noble et al, 2005). The construction of multiscale models in the present work follows the same principle, i.e., utilizing the fundamental laws of physics to describe biological phenomena and experimental measurements.…”

De quoi l’extraterrestre est-il le nom ?

“…Puisque toutes ces espèces sont soumises à cette même contrainte, elles ont, chacune de leur côté, évolué vers une solution adaptative très similaire au problème du déplacement dans un milieu dense, comme l'eau. Des chercheurs ont développé une théorie physique de la morphogenèse animale qui contribue à éclairer la nature des contraintes auxquelles la morphologie des animaux est soumise (voir par exemple [5]). Cette théorie applique à l'embryologie les propriétés matérielles de la matière vivante, en particulier sa fluidité.…”