A multiscale bio-mathematical point of view on the growth of the vertebrate embryo

During vertebrate embryo elongation, the mesoderm and the neural tube grow in contact while remaining segregated and their live imaging reveals cellular turbulent behavior. They share a boundary with the progenitor zone containing stem-like cells which has drawn a lot of attention amongst developmental biologists.

In the first part of this talk, we will develop mathematical PDE-based models to understand tissue segregation. We introduce two 2D mechanical models reproducing the evolution of two segregated viscous tissues in contact, and displaying swirling cell motions. Segregation is encoded differently in the two models: by passive or active segregation (based on a mechanical repulsion pressure). We formally compute the incompressible limits of the two models to obtain two geometric descriptions of the tissues. The two models at the limit thus obtained are compared and a well-posedness and regularity analysis is conducted. Thanks to a transmission problem formulation, our analysis revealed two striking features: a ghost effect, and the appearance of pressure jumps at the tissues' boundaries. These results are supported by numerical simulations in 2D and confronted to the biological data.
We then extend these models to include terms modeling the effect of the progenitor zone on the mesoderm and the neural tube. We calibrate this model using the biological data at hand, and simulate the elongation of the vertebrate embryo. Interesting biological hypotheses arise from the numerical exploration of the model, which we then confirm experimentally on transgenic quail embryos. -In collaboration with the lab of Bertrand Bénazéraf, Pierre Degond, Sophie Hecht and Ariane Trescases.

In the second part of this talk, we will focus our attention on the progenitor zone. We use immunodetection and electroporation techniques on quail embryos to quantify the expression of these stem cells in two proteins: Sox2 and Brachyury; we then reveal their effect on cell motility and cell destiny. Intrestingly, we discover a zone where cells display a very heterogeneous patterning of protein expression. To understand the role of this cell heterogeneity, we develop and simulate stochastic agent-based models. These models highlight a surprising paradox: chaos (heteroegeneity) sustains an apparently very ordered process (morphogenesis). -In collaboration with the lab of Bertrand Bénazéraf and Ariane Trescases.