Dynamical inference for biological processes through the lens of optimal transport

Understanding how cells change their identity and behaviour over time in living systems is a key question in many fields of biology. Measurement of cell states is inherently destructive, and so the relationship of the current state of a cell to some future state, or ‘fate’, cannot be observed experimentally. Trajectory inference refers to the general problem of trying to estimate various aspects of the state-fate relationship. We discuss optimal transport as a useful analytical tool for trajectory inference, and we develop a mathematical framework for recovering trajectories in both non-equilibrium as well as equilibrium systems.