Optimal transport analysis reveals trajectories in steady-state systems

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, applicable to both stationary and non-stationary systems. Our method, StationaryOT, is mathematically motivated in a natural way from the hypothesis of a Waddingtons epigenetic landscape. We implemented StationaryOT as a software package and demonstrate its efficacy when applied to simulated data as well as single-cell data from Arabidopsis thaliana root development.