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Reaction-diffusion kinetics on lattice at the microscopic scale

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME) can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects...

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Main Authors:	Chew, Wei-Xiang, Kaizu, Kazunari, Watabe, Masaki, Muniandy, Sithi Vinayakam, Takahashi, Koichi, Arjunan, Satya N.V.
Format:	Article
Published:	American Physical Society 2018
Subjects:	Q Science (General) QC Physics
Online Access:	http://eprints.um.edu.my/22225/ https://doi.org/10.1103/PhysRevE.98.032418
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spelling	my.um.eprints.222252019-09-04T07:25:08Z http://eprints.um.edu.my/22225/ Reaction-diffusion kinetics on lattice at the microscopic scale Chew, Wei-Xiang Kaizu, Kazunari Watabe, Masaki Muniandy, Sithi Vinayakam Takahashi, Koichi Arjunan, Satya N.V. Q Science (General) QC Physics Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME) can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in three-dimensional space by employing the spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. The theoretical framework of MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, enhanced Green's function reaction dynamics (egfrd). MLM run time is more than an order of magnitude faster than egfrd when diffusing macromolecules with typical concentrations observed in the cell. MLM also showed good agreements with egfrd and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation-dephosphorylation cycle. In addition, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the nonclassical reaction kinetics caused by anomalous diffusion of reacting molecules. American Physical Society 2018 Article PeerReviewed Chew, Wei-Xiang and Kaizu, Kazunari and Watabe, Masaki and Muniandy, Sithi Vinayakam and Takahashi, Koichi and Arjunan, Satya N.V. (2018) Reaction-diffusion kinetics on lattice at the microscopic scale. Physical Review E, 98 (3). 032418. ISSN 2470-0045 https://doi.org/10.1103/PhysRevE.98.032418 doi:10.1103/PhysRevE.98.032418
institution	Universiti Malaya
building	UM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Malaya
content_source	UM Research Repository
url_provider	http://eprints.um.edu.my/
topic	Q Science (General) QC Physics
spellingShingle	Q Science (General) QC Physics Chew, Wei-Xiang Kaizu, Kazunari Watabe, Masaki Muniandy, Sithi Vinayakam Takahashi, Koichi Arjunan, Satya N.V. Reaction-diffusion kinetics on lattice at the microscopic scale
description	Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME) can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in three-dimensional space by employing the spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about 2% larger than the molecule. The theoretical framework of MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, enhanced Green's function reaction dynamics (egfrd). MLM run time is more than an order of magnitude faster than egfrd when diffusing macromolecules with typical concentrations observed in the cell. MLM also showed good agreements with egfrd and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation-dephosphorylation cycle. In addition, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the nonclassical reaction kinetics caused by anomalous diffusion of reacting molecules.
format	Article
author	Chew, Wei-Xiang Kaizu, Kazunari Watabe, Masaki Muniandy, Sithi Vinayakam Takahashi, Koichi Arjunan, Satya N.V.
author_facet	Chew, Wei-Xiang Kaizu, Kazunari Watabe, Masaki Muniandy, Sithi Vinayakam Takahashi, Koichi Arjunan, Satya N.V.
author_sort	Chew, Wei-Xiang
title	Reaction-diffusion kinetics on lattice at the microscopic scale
title_short	Reaction-diffusion kinetics on lattice at the microscopic scale
title_full	Reaction-diffusion kinetics on lattice at the microscopic scale
title_fullStr	Reaction-diffusion kinetics on lattice at the microscopic scale
title_full_unstemmed	Reaction-diffusion kinetics on lattice at the microscopic scale
title_sort	reaction-diffusion kinetics on lattice at the microscopic scale
publisher	American Physical Society
publishDate	2018
url	http://eprints.um.edu.my/22225/ https://doi.org/10.1103/PhysRevE.98.032418
_version_	1646210180078108672
score	13.211869

Reaction-diffusion kinetics on lattice at the microscopic scale

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