Stochastic dynamics of single molecules across phase boundaries

Single molecule tracking has been employed to investigate the statistics of molecular components entering and leaving membraneless compartments. These compartments often form in cells by phase separation of proteins and provide centers for a variety of biochemical processes. Interpreting such single molecule data requires a theory that links molecular trajectories to the properties of phase separation at larger scales.
Starting from a continuum theory of macroscopic phase separation we derive a Langevin equation for molecular trajectories that takes into account thermal fluctuations.
We find that a molecule experiences an effective potential, which has a steep gradient at phase boundaries. We obtain the position-dependent diffusion coefficient and the drift velocity, which is caused by concentration fluxes.
We discuss how the physics of phase separation affects the statistics of molecular trajectories. We show that our approach can be used to infer key phase separation parameters from the statistics of single-molecule trajectories.
Finally, we show that, when the system is not at equilibrium, detailed balance is broken at the level of molecular trajectories. Such trajectories can thus be used to characterize non-equilibrium features of intracellular condensates.