Binomial distribution based τ-leap accelerated stochastic simulation

Recently, Gillespie introduced the tau-leap approximate, accelerated stochastic Monte Carlo method for well-mixed reacting systems J. Chem. Phys. 115, 1716 (2001). In each time increment of that method, one executes a number of reaction events, selected randomly from a Poisson distribution, to enable simulation of long times. Here we introduce a binomial distribution tau-leap algorithm (abbreviated as BD-tau method). This method combines the bounded nature of the binomial distribution variable with the limiting reactant and constrained firing concepts to avoid negative populations encountered in the original tau-leap method of Gillespie for large time increments, and thus conserve mass. Simulations using prototype reaction networks show that the BD-tau method is more accurate than the original method for comparable coarse-graining in time.