Inferring stochastic dynamics with growth from cross-sectional data

TL;DR

This paper introduces a novel inference method for stochastic biological dynamics with growth, using cross-sectional single-cell data, effectively disentangling drift, noise, and growth effects for more accurate modeling.

Contribution

The paper presents unbalanced probability flow inference, a new approach leveraging a Lagrangian Fokker-Planck formulation to improve modeling of stochastic growth processes from cross-sectional data.

Findings

Higher accuracy than existing methods

Simple two-step training scheme

Effective on simulated and real datasets

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.