Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The s...
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| Format: | Journal article |
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2009
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| _version_ | 1797090667889950720 |
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| author | Erban, R Chapman, S |
| author_facet | Erban, R Chapman, S |
| author_sort | Erban, R |
| collection | OXFORD |
| description | Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A+B → C, or A+A → C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site). |
| first_indexed | 2024-03-07T03:21:58Z |
| format | Journal article |
| id | oxford-uuid:b7bc0ed5-d541-4106-9e5c-a1856d9215bd |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:21:58Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:b7bc0ed5-d541-4106-9e5c-a1856d9215bd2022-03-27T04:50:49ZStochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b7bc0ed5-d541-4106-9e5c-a1856d9215bdMathematical Institute - ePrints2009Erban, RChapman, SSeveral stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A+B → C, or A+A → C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site). |
| spellingShingle | Erban, R Chapman, S Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions |
| title | Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions
|
| title_full | Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions
|
| title_fullStr | Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions
|
| title_full_unstemmed | Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions
|
| title_short | Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions
|
| title_sort | stochastic modelling of reaction diffusion processes algorithms for bimolecular reactions |
| work_keys_str_mv | AT erbanr stochasticmodellingofreactiondiffusionprocessesalgorithmsforbimolecularreactions AT chapmans stochasticmodellingofreactiondiffusionprocessesalgorithmsforbimolecularreactions |