Excluded volume effects in on- and off-lattice reaction-diffusion models

TL;DR

This paper compares off-lattice and on-lattice reaction-diffusion models to understand how crowding molecules affect diffusion and reaction rates, highlighting limitations of simplified lattice models at high crowder densities.

Contribution

It evaluates the accuracy of Cellular Automata models in simulating crowded reaction-diffusion systems compared to detailed off-lattice simulations, emphasizing the impact of grid artifacts.

Findings

Off-lattice models show more severe diffusion slowdown due to obstacles.

Grid structure can both increase and decrease reaction rates.

On-lattice models are accurate only at low crowder densities.

Abstract

Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this paper we therefore investigate to which extent on-lattice approximations, so called Cellular Automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. We show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artifacts increase with increasing crowder density and we conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.