We present a method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for time-dependent switching propensities and time-dependent phase space probability densities. It is suitable for equilibrium or non-equilibrium systems, in or out of stationary state, including non-Markovian or externally driven systems. We demonstrate the validity of the technique by applying it to a one-dimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the time-dependent switching of a genetic toggle switch.

J. Chem. Phys.
Biochemical Networks

Becker, N., Allen, R. J., & ten Wolde, P. R. (2012). Non-Stationary Forward Flux Sampling. J. Chem. Phys., 136(Article number: 174118), 1–18. doi:10.1063/1.4704810