PNNL

Abstract

We introduce the multinomial tau-leaping (MtL) method, an improved version of the binomial tau-leaping method, for general reaction networks. Improvements in efficiency are achieved in several ways. Firstly, tau-leaping steps are determined simply and efficiently using a-prior information. Secondly, networks are partitioned into closed groups of reactions and corresponding reactants in which no group reactant or reaction is found in any other group. Thirdly, product formation is factored into upper bound estimation of the number of times a particular reaction occurs. Together, these features allow for larger time steps where the numbers of reactions occurring simultaneously in a multi-channel manner are estimated accurately using a multinomial distribution. Using a wide range of test case problems of scientific and practical interest involving cellular processes, such as epidermal growth factor receptor signaling and lactose operon model incorporating gene transcription and translation, we show that tau-leaping based methods like the MtL algorithm can significantly reduce the number of simulation steps thus increasing the numerical efficiency over the exact stochastic simulation algorithm by orders of magnitude. Furthermore, the simultaneous multi-channel representation capability of the MtL algorithm makes it a candidate for FPGA implementation or for parallelization in parallel computing environments.