Comparison of discrete- and continuous-state stochastic methods to model neuronal signal transduction

Several stochastic methods have been developed for the simulation of biochemical reactions. The best known stochastic reaction method is the Gillespie stochastic simulation algorithm which, in this study, is compared to two types of stochastic differential equation models. As a test case, we use a neuronal signal transduction network of 110 reactions and 63 chemical species. We concentrate on showing when stochastic methods are especially needed and how distributions from different stochastic methods differ. We conclude that stochastic differential equations are not suitable for use in volumes on the order of spines, and that even in dendritic and soma regions a portion of the chemical species will exhibit negative excursions. For this reason, a hybrid deterministic and stochastic method may be most applicable to the larger volumes while the Gillespie stochastic simulation algorithm is needed for spines and subspinal volumes. In addition, a grid computing solution is needed for larger volumes to reduce the computation time to tractable levels.