Multistate modeling and simulation for regulatory networks

Many protein regulatory models contain chemical species best represented as having multiple states. Such models stem from the potential for multiple levels of phosphorylation or from the formation of multiprotein complexes. We seek to support such models by augmenting an existing modeling and simulation system. Interactions between multistate species can lead to a combinatorial explosion in the potential state space. This creates a challenge when using Gillespie's stochastic simulation algorithm (SSA). Both the network-free algorithm (NFA) and various rules-based methods have been proposed to more efficiently simulate such models. We show how to further improve NFA to integrate population-based and particle-based features. We then present a population-based scheme for the stochastic simulation of rule-based models. A complexity analysis is presented comparing the proposed simulation methods. We present numerical experiments for two sample models that demonstrate the power of the proposed simulation methods.