Towards a mathematical theory of developmental biology:
Analyzing developmental processes with optimal transport
This talk focuses on estimating temporal couplings of stochastic processes with optimal transport (OT), motivated by applications in developmental biology and cellular reprogramming. For nearly a century, the prevailing mathematical theory of developmental biology has been based on Waddington’s epigenetic landscape—a potential energy surface that determines trajectories of cellular development. Now, with the advent of high-throughput measurement technologies like single cell RNA-sequencing (scRNA-seq), the prospect of charting this landscape is within reach. This holds tremendous potential for diverse applications from regenerative medicine (e.g., cellular reprogramming) to agriculture (e.g., predicting impacts of climate change on crops or growing artificial meat). While the problem of recovering the landscape is inherently nonconvex, we demonstrate that the ‘laws on paths’ induced by this potential energy surface can be recovered using convex optimization. Our approach provides a general framework for investigating cellular differentiation.
This talk will be hosted online using Zoom. Please RSVP to obtain a link to the Zoom meeting.