Multinomial tau-leaping method for stochastic kinetic simulations

Abstract

We introduce the multinomial tau-leaping (MtauL) method for general reaction networks with multichannel reactant dependencies. The MtauL method is an extension of the binomial tau-leaping method where efficiency is improved in several ways. First, tau-leaping steps are determined simply and efficiently using a priori information and Poisson distribution-based estimates of expectation values for reaction numbers over a tentative tau-leaping step. Second, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant set is found in any other group. Third, product formation is factored into upper-bound estimation of the number of times a particular reaction occurs. Together, these features allow larger time steps where the numbers of reactions occurring simultaneously in a multichannel manner are estimated accurately using a multinomial distribution. Furthermore, we develop a simple procedure that places a specific upper bound on the total reaction number to ensure non-negativity of species populations over a single multiple-reaction step. Using two disparate test case problems involving cellular processes--epidermal growth factor receptor signaling and a lactose operon model--we show that the tau-leaping based methods such as the MtauL algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude.