Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning

TL;DR

This paper introduces an automated hybrid simulation method for reaction-diffusion systems that adaptively partitions the system to balance accuracy and efficiency, improving over manual approaches.

Contribution

It presents a novel hybrid simulation algorithm with automatic system partitioning based on error estimates, enhancing usability and performance.

Findings

Accurately simulates diffusion-controlled networks in 3D

Achieves efficiency comparable to coarse mesoscopic methods

Maintains high accuracy for multiscale reaction systems

Abstract

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or Green's Function Reaction Dynamics (GFRD) the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as 'black-box' simulation codes. In this paper we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.