Reaction rates for reaction-diffusion kinetics on unstructured meshes
Abstract
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,more »
- Authors:
-
- Univ. of California, Santa Barbara, CA (United States). Dept. of Computer Science
- Publication Date:
- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Institutes of Health (NIH)
- OSTI Identifier:
- 1535296
- Grant/Contract Number:
- SC0008975; R01-EB014877-01; W911NF-09-D-0001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 146; Journal Issue: 6; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Chemistry; Physics
Citation Formats
Hellander, Stefan, and Petzold, Linda. Reaction rates for reaction-diffusion kinetics on unstructured meshes. United States: N. p., 2017.
Web. doi:10.1063/1.4975167.
Hellander, Stefan, & Petzold, Linda. Reaction rates for reaction-diffusion kinetics on unstructured meshes. United States. https://doi.org/10.1063/1.4975167
Hellander, Stefan, and Petzold, Linda. Wed .
"Reaction rates for reaction-diffusion kinetics on unstructured meshes". United States. https://doi.org/10.1063/1.4975167. https://www.osti.gov/servlets/purl/1535296.
@article{osti_1535296,
title = {Reaction rates for reaction-diffusion kinetics on unstructured meshes},
author = {Hellander, Stefan and Petzold, Linda},
abstractNote = {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.},
doi = {10.1063/1.4975167},
journal = {Journal of Chemical Physics},
number = 6,
volume = 146,
place = {United States},
year = {Wed Feb 08 00:00:00 EST 2017},
month = {Wed Feb 08 00:00:00 EST 2017}
}
Web of Science
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Works referencing / citing this record:
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