A Gaussian jump process formulation of the reaction–diffusion master equation enables faster exact stochastic simulations

2022/11/17 by Tina Subic, Ivo F. Sbalzarini · 1 voice · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Evolution and Genetic Dynamics #Gene Regulatory Network Analysis #stochastic dynamics and bifurcation

paper · pdf · doi:10.1063/5.0123073

openalex publication_date 2022/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

We propose a Gaussian jump process model on a regular Cartesian lattice for the diffusion part of the Reaction-Diffusion Master Equation (RDME). We derive the resulting Gaussian RDME (GRDME) formulation from analogy with a kernel-based discretization scheme for continuous diffusion processes and quantify the limits of its validity relative to the classic RDME. We then present an exact stochastic simulation algorithm for the GRDME, showing that the accuracies of GRDME and RDME are comparable, but exact simulations of the GRDME require only a fraction of the computational cost of exact RDME simulations. We analyze the origin of this speedup and its scaling with problem dimension. The benchmarks suggest that the GRDME is a particularly beneficial model for diffusion-dominated systems in three dimensional spaces, often occurring in systems biology and cell biology.

Citations

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Cited by

• Loss of bimolecular reactions in reaction–diffusion master equations is consistent with diffusion limited reaction kinetics in the mean field limit

Discussions

• GRDME (Gaussian Reaction Diffusion Master Equation) is a method that makes exact stochastic simulations of molecular interactions more efficient! It was also the subject of my first PhD paper (doi.org [bsky, 7 points, 1 comments]

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