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

Paul Taylor, Ruth E. Baker, Matthew Simpson, Christian Yates

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
136 Downloads (Pure)

Abstract

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) 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-grained models 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 describing 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.
Original languageEnglish
Article number20160336
Number of pages13
JournalJournal of the Royal Society, Interface
Volume13
Issue number120
DOIs
Publication statusPublished - 6 Jul 2016

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