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

T. Manninen, M.-L. Linne, and K. Ruohonen (Finland)


Itˆo stochastic differential equation, Gillespie stochastic simulation algorithm, Neuronal signal transduction


Several discrete, as well as continuous, stochastic ap proaches have been developed for the time-series sim ulation of biochemical systems. Stochastic approaches, in general, are needed because chemical reactions in volve discrete, random collisions between individual chem ical species. One of the well-known discrete stochastic approaches is the computationally demanding Gillespie stochastic simulation algorithm which is in this work com pared to the Itˆo stochastic differential equations. First, neu ronal signal transduction is simulated using two different types of Itˆo stochastic differential equations and the Gille spie 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 Itˆo stochastic differential equation models are found to provide stable solutions and produce similar responses to the Gillespie algorithm also when using the larger net work. The Itˆo 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.

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