Shaping fate: geometric methods for cell fate transitions and tissue patterning in stem cells and organoids

Biology currently possesses unprecedented capabilities to generate genome-wide readouts of cells as they develop in embryos. It remains a challenge to parse this data into comprehensible models that can reveal the underlying principles of development and guide methods to engineer target cell and tissue fates. It has recently been demonstrated that Waddington's metaphor of development as downhill flow in an "epigenetic landscape" can be made mathematically rigorous using techniques from differential geometry and dynamical systems. I will discuss applications of these methods to floorplate signaling center self-organization in neuroepithelial cysts and in vitro recapitulations of floorplate induced dorsoventral patterning of the neural tube. In both cases, geometric reasoning simplifies complicated dynamic processes to enable testable predictions in terms of small sets of effective variables. I will show results, from both single-cell assays and whole-tissue live imaging, illustrating how cell signaling coordinates with biochemical and mechanical regulation at the scale of the embryo/organoid to dynamically organize developing tissues.