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 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. Author summaryMany important biological phenomena involve populations of cells that undergo changes in behaviour over time to achieve a desired state or function. Modern experimental technologies are able to measure aspects of cell state but cannot observe a cell at more than a single instant in time, since the cell is necessarily destroyed in the measurement process. Therefore, the relationship between the present and future states of a cell, which we call its trajectory, must be inferred from observable data. Since biological processes are naturally noisy, we model cells as evolving following a stochastic dynamical system with growth. We show that for datasets drawn from a population of cells in equilibrium and when estimates of cell growth rates are available, cellular trajectories can be estimated by solving an optimal transport problem. We validate our method using simulated data and demonstrate an application to transcriptomic data from Arabidopsis thaliana root development.