Efficient Green's Function Reaction Dynamics (GFRD) simulations for diffusion-limited, reversible reactions

Highlights: • Efficient simulation of systems of particles moving by diffusion and reacting with each other. • Probability for chemical reactions is given by Smoluchowski theory. • New Green's function for diffusion limited association and dissociation reactions. • Accuracy and efficiency of the method are shown for bimolecular reactions and a biochemical reaction network. • The computational work is independent of the number of rebindings in the bimolecular reactions. In diffusion controlled reversible bimolecular reactions in three dimensions, a dissociation step is typically followed by multiple, rapid re-association steps slowing down the simulations of such systems. In order to improve the efficiency, we first derive an exact Green's function describing the rate at which an isolated pair of particles undergoing reversible bimolecular reactions and unimolecular decay separates beyond an arbitrarily chosen distance. Then the Green's function is used in an algorithm for particle-based stochastic reaction–diffusion simulations for prediction of the dynamics of biochemical networks. The accuracy and efficiency of the algorithm are evaluated using a reversible reaction and a push–pull chemical network. The computational work is independent of the rates of the re-associations.