Optimal transport analysis reveals trajectories in steady-state systems

Abstract

Understanding how cells change their identity and behaviour in living systems is an important question in many fields of biology. The problem of inferring cell trajectories from single-cell measurements has been a major topic in the single-cell analysis community, with different methods developed for equilibrium and non-equilibrium systems (e.g. haematopoeisis vs. embryonic development). We show that optimal transport analysis, a technique originally designed for analysing time-courses, may also be applied to infer cellular trajectories from a single snapshot of a population in equilibrium. Therefore, optimal transport provides a unified approach to inferring trajectories that is applicable to both stationary and non-stationary systems. Our method, StationaryOT, is mathematically motivated in a natural way from the hypothesis of a Waddington’s epigenetic landscape. We implement StationaryOT as a software package and demonstrate its efficacy in applications to simulated data as well as single-cell data from Arabidopsis thaliana root development.