The two-regime method for optimizing stochastic reaction-diffusion simulations.

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Journal of the Royal Society, Interface, ISSN: 1742-5662, Vol: 9, Issue: 70, Page: 859-68

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Flegg, Mark B; Chapman, S Jonathan; Erban, Radek
The Royal Society
Biochemistry, Genetics and Molecular Biology; Chemical Engineering; Materials Science; Engineering; Hybrid algorithm; Multi-scale simulation; Reaction-diffusion processes; Stochastic modelling; Stochastic Processes; Models, Theoretical; Computer Simulation
article description
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.