Reaction Time for Trimolecular Reactions in Compartment-based Reaction-Diffusion Models

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modelling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae are further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of [Montroll, J.Math.Phys, 1969]. Montroll’s results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.