Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm

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We examine an application of the Gillespie algorithm to simulating spatially inhomogeneous reaction-diffusion systems in mesoscopic volumes such as cells and microchambers. The method involves discretizing the chamber into elements and modeling the diffusion of chemical species by the movement of molecules between neighboring elements. These transitions are expressed in the form of a set of reactions which are added to the chemical system. The derivation of the rates of these diffusion reactions is by comparison with a finite volume discretization of the heat equation on an unevenly spaced grid. The diffusion coefficient of each species is allowed to be ... continued below

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Bernstein, David December 12, 2004.

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We examine an application of the Gillespie algorithm to simulating spatially inhomogeneous reaction-diffusion systems in mesoscopic volumes such as cells and microchambers. The method involves discretizing the chamber into elements and modeling the diffusion of chemical species by the movement of molecules between neighboring elements. These transitions are expressed in the form of a set of reactions which are added to the chemical system. The derivation of the rates of these diffusion reactions is by comparison with a finite volume discretization of the heat equation on an unevenly spaced grid. The diffusion coefficient of each species is allowed to be inhomogeneous in space, including discontinuities. The resulting system is solved by the Gillespie algorithm using the fast direct method. We show that in an appropriate limit the method reproduces exact solutions of the heat equation for a purely diffusive system and the nonlinear reaction-rate equation describing the cubic autocatalytic reaction.

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  • Journal Name: Physical Review E; Journal Volume: 71; Journal Issue: 4; Related Information: Journal Publication Date: 04/2005

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  • Report No.: LBNL--56743
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 861306
  • Archival Resource Key: ark:/67531/metadc793629

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  • December 12, 2004

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  • Dec. 19, 2015, 7:14 p.m.

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  • Dec. 11, 2017, 2:33 p.m.

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Bernstein, David. Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm, article, December 12, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc793629/: accessed June 25, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.