Stochastic simulation methods for biochemical models with multi-state species

Gillespie's stochastic simulation algorithm (SSA) has been a conventional method for stochastic modeling and simulation of biochemical systems. However, as a population-based algorithm it faces the challenge of combinatorial complexity in many biochemical models where species may present with multiple states. To solve this problem, the rules-based modeling was proposed by Hlavacek's group and the particle-based Network-Free Algorithm (NFA) was used for its simulation. In this paper, we first improve the NFA to efficiently integrate the population-based and particle-based features. Then we propose a population-based SSA scheme for the stochastic simulation of rule-based models. Complexity analysis is presented for the proposed methods. Numerical experiments on two rule-based models demonstrate the power of the proposed methods.