Clock, waves, evolution: geometry of vertebrae patterning

The vertebrate body plan is first built on metameric units called somites, appearing during embryonic development in parallel to tail bud elongation. Oscillatory gene expressions in the tail initiate waves of genetic expression propagating from posterior to anterior. Those waves stabilize into spatial patterns defining somites. In this talk, I will discuss how dynamical system theory can be used in a predictive way to understand this process. I will first describe how unsupervised evolutionary algorithms naturally recover the fundamental dynamical modules driving this system, namely bistability and oscillations. Then, I will further discuss the dynamics and shapes of the experimental wave profiles. Using both gene-network based and gene-free models, I will show that the interplay of two types of enhancers driving the transition from oscillations to pattern formation naturally give rise to two opposite bifurcation scenarios, corresponding to infinite vs finite period bifurcations. I will discuss how one can distinguish experimentally between those dynamical scenarios, and will argue that our new model naturally integrates many aspects of the process, from the shape of the limit cycle and of the waves, to the formation of the final pattern.