Balanced Implicit Methods for Stiff Stochastic Systems
SIAM Journal on Numerical Analysis
Computational Biology and Chemistry
General stochastic hybrid method for the simulation of chemical reaction processes in cells
CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
Review: Stochastic approaches for modelling in vivo reactions
Computational Biology and Chemistry
Research Article: Hybrid stochastic simulations of intracellular reaction-diffusion systems
Computational Biology and Chemistry
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-α method
Journal of Computational Physics
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Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Ito stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Ito stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Ito stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Ito stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The Ito stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values.