Modeling Neuronal Signal Transduction Using Itô Stochastic Differential Equations and the Gillespie Stochastic Simulation Algorithm

Several discrete, as well as continuous, stochastic approaches have been developed for the time-series simulation of biochemical systems. Stochastic approaches, in general, are needed because chemical reactions involve discrete, random collisions between individual chemical species. One of the well-known discrete stochastic approaches is the computationally demanding Gillespie stochastic simulation algorithm which is in this work compared to the Itô stochastic differential equations. First, neuronal signal transduction is simulated using two different types of Itô stochastic differential equations and the Gillespie stochastic simulation algorithm. In this work, a large, complex network is for the first time used as a test case, in addition to the previously used less complex pathway. The Itô stochastic differential equation models are found to provide stable solutions and produce similar responses to the Gillespie algorithm also when using the larger network. The Itô stochastic differential equations may be used as a new, computationally fast stochastic modeling tool for studying emergent phenomena in complex neuronal and other signaling networks.