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Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.

ABSTRACT: Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are 'compartment-based': the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise.

SUBMITTER: Taylor PR

PROVIDER: S-EPMC4971222 | biostudies-literature | 2016 Jul

REPOSITORIES: biostudies-literature

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Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.

Taylor P R PR Baker R E RE Simpson M J MJ Yates C A CA

Journal of the Royal Society, Interface 20160701 120

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are 'compartment-based': the domain is discretized into compartments, and particles can jump between th ...[more]

PMID: 27383421

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Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.

Publications

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.

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