Multi-grid reaction-diffusion master equation: applications to morphogen gradient modelling

TL;DR

The paper introduces the multi-grid reaction-diffusion master equation (mgRDME), a novel approach that enhances the accuracy and efficiency of stochastic reaction-diffusion simulations across different spatial resolutions, applied to morphogen gradient modeling.

Contribution

It presents the mgRDME framework, allowing different lattice resolutions for species with varying diffusion rates, improving simulation accuracy and computational efficiency.

Findings

mgRDME outperforms standard RDME in accuracy.

Error and cost depend on compartment size and are optimized.

Validated against particle-based Brownian dynamics simulations.

Abstract

The multi-grid reaction-diffusion master equation (mgRDME) provides a generalization of stochastic compartment-based reaction-diffusion modelling described by the standard reaction-diffusion master equation (RDME). By enabling different resolutions on lattices for biochemical species with different diffusion constants, the mgRDME approach improves both accuracy and efficiency of compartment-based reaction-diffusion simulations. The mgRDME framework is examined through its application to morphogen gradient formation in stochastic reaction-diffusion scenarios, using both an analytically tractable first-order reaction network and a model with a second-order reaction. The results obtained by the mgRDME modelling are compared with the standard RDME model and with the (more detailed) particle-based Brownian dynamics simulations. The dependence of error and numerical cost on the compartment sizes is defined and investigated through a multi-objective optimization problem.