Exploring the link between signaling, geometry and information transmission: modeling neural fate induction in ascidian embryonic development

During embryonic development, cells adopt different identities with remarkable spatial and temporal precision. Despite recent progress, the mechanisms governing cell fate inductions remain not completely understood. In particular, the role of the mechanics and geometry of the cells in the embryo has only recently started to be addressed. In this work we investigate the mechanisms regulating ascidian neural induc-tion, especially addressing the impact of cell geometry on this process.During neural induction, which occurs in ascidian embryos at the 32-cell stage, 4 out of 16 ectoderm cells adopt the neural fate, characterized by the expression of the neural marker Otx. This process is initiated at the extracellular level by two signaling molecules, FGF and ephrin, which control the acquisition of neural fate by a two-step process involving first the activation of the ERK pathway and second, the expression of the gene Otx. The combination of the two antagonistic signals (FGF activates the ERK pathway, while ephrin dampens ERK activity) tightly controls the level of Otxexpression in all ectoderm cells. Interestingly, only a fraction of the cells exposed to the inducer FGF acquires the neural fate. We used mathematical modeling to demonstrate that this selectivity is controlled by the quasi-invariant geometry of the embryo, which imposes upon each ectoderm cell a precise area of cell surface contact with underlying FGF-expressing cells. Our model, based on ordinary differential equations, successfully reproduces experimental observations about ERK activation and Otx expression obtained under normal and perturbed conditions. With the model, we investigated the role played by each signaling input as well as the role of two antagonistic transcription factors that regulate Otx expression.We also investigated information transmission in neural induction and how the latter depends on the geometry of the cells. By optimizing information transmission between FGF and the number of active ERK molecules, under the constraint of a restricted total surface area with FGF-emitting cells, we found that the cell surface contacts with FGF that maximize information transmission are compatible with those measured experimentally. Our work suggests that ascidian neural induction might be a consequence of the geometrical constraints imposed on the system via the surfaces of contact between the cells in the embryo.