Exact Stochastic Simulation of Chemical Reactions with Cycle Leaping

The stochastic simulation algorithm (SSA), first proposed by Gillespie, has become the workhorse of computational biology. It tracks integer quantities of the molecular species, executing reactions at random based on propensity calculations. An estimate for the resulting quantities of the different species is obtained by averaging the results of repeated trials. Unfortunately, for models with many reaction channels and many species, the algorithm requires a prohibitive amount of computation time. Many trials must be performed, each forming a lengthy trajectory through the state space. With coupled or reversible reactions, the simulation often loops through the same sequence of states repeatedly, consuming computing time, but making no forward progress. We propose a algorithm that reduces the simulation time through cycle leaping: when cycles are encountered, the exit probabilities are calculated. Then, in a single bound, the simulation leaps directly to one of the exit states. The technique is exact, sampling the state space with the expected probability distribution. It is a component of a general framework that we have developed for stochastic simulation based on probabilistic analysis and caching