Hybrid method for the chemical master equation

Authors:
Andreas Hellander;Per Lötstedt
Affiliations:
Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-75105 Uppsala, Sweden;Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-75105 Uppsala, Sweden
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate equations and the probability distribution for the stochastic variables satisfy a master equation. The probability distribution is obtained by the Stochastic Simulation Algorithm due to Gillespie. The equations are coupled via a summation over the mesoscale variables. This summation is approximated by Quasi-Monte Carlo methods. The error in the approximations is analyzed. The hybrid method is applied to three chemical systems from molecular cell biology.