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Title: 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 » the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.« less

Authors:
 [1];  [1]
  1. 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}
}

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Cited by: 6 works
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journal, January 2009

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journal, January 2012

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  • Multiscale Modeling & Simulation, Vol. 10, Issue 2
  • DOI: 10.1137/110832148

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text, January 2014


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Works referencing / citing this record:

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning
journal, December 2017

  • Hellander, Stefan; Hellander, Andreas; Petzold, Linda
  • The Journal of Chemical Physics, Vol. 147, Issue 23
  • DOI: 10.1063/1.5002773

Surface reaction-diffusion kinetics on lattice at the microscopic scale
journal, April 2019


Surface reaction-diffusion kinetics on lattice at the microscopic scale
text, January 2018


Effects of different discretisations of the Laplacian upon stochastic simulations of reaction–diffusion systems on both static and growing domains
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  • Bartmanski, Bartosz J.; Baker, Ruth E.
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An unstructured mesh convergent reaction–diffusion master equation for reversible reactions
journal, December 2018