Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study,WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ∼10 ¹² to ∼10¹⁸ for characterizing rare states in a distribution, and ∼102 to ∼104 for finding mean first passage times.