Weighted next reaction method and parameter selection for efficient simulation of rare events in biochemical reaction systems

Biochemical reaction systems in living cells exhibit significant stochastic fluctuations due to a small number of molecules involved in processes such as the transcription and translation of genes [1]. A number of exact [2-7] or approximate simulation algorithms [8-19] have been developed for simulating the stochastic dynamics of such systems. Recent research shows that some rare events occurring in biochemical reaction system with an extremely small probability within a specified limited time can have profound and sometimes devastating effects [20,21]. Hence, it is important that computational simulation and analysis of systems with critical rare events can efficiently capture such rare events. However, the existing exact simulation methods such as Gillespie's exact SSA [2,3] often require prohibitive computation to estimate the probability of a rare events, while the approximate methods may not be able to estimate such probability accurately.The weighted stochastic simulation algorithm (wSSA) recently developed by Kuwahara and Mura [22] based on the importance sampling technique enables one to efficiently estimate the probability of a rare event. However, the wSSA does not provide any method for selecting optimal values for importance sampling parameters. More recently, Gillespie et al. [23] analyzed the accuracy of the results yielded from the wSSA and proposed a refined wSSA that employed a try-and-test method for selecting optimal values for importance sampling parameters. It was shown that the refined wSSA could further improve the performance of wSSA. However, the try-and-test method requires some initial guessing for the sets of values from which the parameters can take. If the guessed values do not include the optimal value, then one cannot get appropriate values for the parameters. Moreover, if the number of parameters is greater than one, a very large set of values need to be guessed and tested, which may increase the likelihood of missing the optimal val