Reaction schemes, escape times and geminate recombinations in particle-based spatial simulations of biochemical...

Modeling the spatiotemporal dynamics of biochemical reaction systems at single-molecule resolution has become feasible with the increase of computing power and is applied especially to cellular signal transduction. For an association reaction the two molecules have to be in contact. Hence, a physically faithful model of the molecular interaction assumes non-overlapping molecules that interact at their surfaces (boundary scheme). For performance reasons, this model can be replaced by particles that can overlap and react when they are closer than a certain distance with a reaction probability (volume scheme). Here we present an analytical approximation for the reaction probability in the volume scheme and compare the volume- with the boundary scheme. A dissociation reaction, in contrast, creates two molecules next to each other. If the reaction is reversible, these two products can directly re-bind again, leading to an overestimation of the dimerized state in the simulation. We show how the correct recombination rate can be achieved if the products of the dissociation are placed at identical positions, but cannot react for a certain timespan. This refractory time corresponds to the completion of the diffusion-controlled dissociation of the two molecules to their contact distance r(i)+r(j) at t = τ ×(r(i)+r(j))²/(D(i)+D(j) with τ = 1/10 for molecules with radii r(i) and r(j) and diffusion coefficients D(i) and D(j), respectively.