Inferring stochastic dynamics with growth from cross-sectional data

Stephen Y. Zhang, Suryanarayana Maddu, Xiaojie Qiu, Victor Chardès

Keywords: systems biology, single cell, stochastic dynamics, population dynamics

TL;DR: We consider the problem of learning drift, diffusion and growth rate from snapshot observations of a population of individuals that may divide or die, and propose a novel inference scheme to learn these terms from data.

Abstract: Time-resolved single-cell omics data offers high-throughput, genome-wide measurements of cellular states, which are instrumental to reverse-engineer the processes underpinning cell fate. Such technologies are inherently destructive, allowing only cross-sectional measurements of the underlying stochastic dynamical system. Furthermore, cells may divide or die in addition to changing their molecular state. Collectively these present a major challenge to inferring realistic biophysical models. We present a novel approach, unbalanced probability flow inference, that addresses this challenge for biological processes modelled as stochastic dynamics with growth. By leveraging a Lagrangian formulation of the Fokker-Planck equation, our method accurately disentangles drift from intrinsic noise and growth. We showcase the applicability of our approach through evaluation on a range of simulated and real single-cell RNA-seq datasets. Comparing to several existing methods, we find our method achieves higher accuracy while enjoying a simple two-step training scheme.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Submission Number: 17642