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

TL;DR

This paper develops and compares two hybrid compartment-based models for simulating diffusion with volume exclusion on non-uniform lattices, demonstrating their accuracy and computational efficiency relative to fine-grained models.

Contribution

It introduces two novel approaches for coupling different scales in compartment-based diffusion models with volume exclusion on non-uniform lattices.

Findings

Hybrid models are significantly faster than fine-grained models in certain scenarios.

Both approaches accurately replicate fine-grained model results.

Hybrid models maintain accuracy while improving computational efficiency.

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.