Reaction rates for reaction-diffusion kinetics on unstructured meshes

Journal Article · Wed Feb 08 00:00:00 EST 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4975167· OSTI ID:1535296

Hellander, Stefan ^[1]; Petzold, Linda ^[1]

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1. Univ. of California, Santa Barbara, CA (United States). Dept. of Computer Science

The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. Here in this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.

• Research Organization: Univ. of California, Santa Barbara, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC); National Institutes of Health (NIH)
• Grant/Contract Number: SC0008975; R01-EB014877-01; W911NF-09-D-0001
• OSTI ID: 1535296
• Journal Information: Journal of Chemical Physics, Vol. 146, Issue 6; ISSN 0021-9606
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

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