Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions

TL;DR

This paper analyzes two stochastic simulation algorithms for reaction-diffusion processes, identifies issues with bimolecular reaction implementations, and proposes improvements including a formula for minimal compartment size and reaction rates.

Contribution

It introduces corrections for bimolecular reactions in on-lattice and off-lattice SSAs, enhancing their accuracy for cellular reaction-diffusion modeling.

Findings

Incorrect results can arise from standard bimolecular reaction implementations.

A new formula for the minimal lattice compartment size is proposed.

Improved reaction rate calculations enhance simulation accuracy.

Abstract

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A + B -> C, or A + A -> C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).