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

• Published in: Journal of the Royal Society interface Vol. 13; no. 120; p. 20160336
• Main Authors: Taylor, P. R., Baker, R. E., Simpson, M. J., Yates, C. A.
• Format: Journal Article
• Language: English
• Published: England The Royal Society 01.07.2016
• Subjects: Compartment-Based Modelling; Diffusion; Hybrid Modelling; Life Sciences–Mathematics interface; Models, Theoretical; Stochastic Processes; Volume Exclusion; hybrid modelling; diffusion; volume exclusion; compartment-based modelling
• ISSN: 1742-5689; 1742-5662
• DOI: 10.1098/rsif.2016.0336

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.