Towards a Mathematical Theory of Development: Analyzing Developmental Stochastic Processes with Optimal Transport

Synopsis

This talk focuses on estimating temporal couplings of stochastic processes with optimal transport (OT), motivated by applications in developmental biology and cellular reprogramming. We present experimental evidence for the fact that the temporal couplings of a developmental stochastic process are well-approximated by (entropic) optimal transport, over short time-scales. We collect 315,000 single cell RNA-seq expression profiles at 40 time points over 18 days of stem cell reprogramming, and we demonstrate that OT can accurately interpolate the distribution of cells at held-out time points. Our analysis leads to new discoveries about cellular reprogramming, including new ways to enhance reprogramming efficiency. Our approach provides a general framework for investigating cellular differentiation, and poses some interesting questions in theoretical statistics.