Inference of stochastic cellular dynamics from time-series data using optimal transport

Cellular and developmental biology presents a wealth of processes that are inherently stochastic in nature, ranging from development to wound healing and carcinogenesis. Modern technologies such as single-cell transcriptomics and epigenomics have enabled interrogation of biological phenomena with unprecedented precision and throughput. These technologies necessarily destroy the cells being measured. Thus, any instance of a biological process can only be measured once to produce a static snapshot, and the underlying behaviour of cells over time is lost. The development of tools for reconstructing temporal dynamics from such snapshots is therefore a major challenge that is crucial to painting an accurate biological picture. We propose a method for inferring governing dynamics from a series of temporal snapshots (such as single-cell transcriptomic profiles) sampled from populations of cells that evolve following some biological stochastic process. Our approach is based on optimal transport, a contemporary mathematical theory at the intersection of analysis, probability and geometry that provides a natural means of comparing probability distributions. Equipped with a corresponding convex optimisation framework, we provide an initial demonstration of accurate recovery of dynamics from simulated data. We also discuss how we tackle the biologically important challenge of dealing with high dimensionality and cellular growth, with a view to application to experimental datasets. This is a joint work with Young-Heon Kim, Hugo Lavenant and Geoffrey Schiebinger.