Exact Green's function of the reversible ABCD reaction in two space dimensions

TL;DR

This paper derives an exact Green's function for the reversible ABCD reaction in two dimensions, providing key formulas for reaction probabilities that aid biological modeling and simulation.

Contribution

It presents the first exact time-domain Green's function for the reversible ABCD reaction in 2D, enabling precise analysis of membrane-bound reactions.

Findings

Exact Green's function derived for the reversible ABCD reaction in 2D.

Expressions for survival and reaction probabilities obtained.

Results applicable to cell biology and stochastic simulations.

Abstract

We derive an exact expression for the Green's functions in the time domain of the reversible diffusion-influenced ABCD reaction $A+B\leftrightarrow C+D$ in two space dimensions. Furthermore, we calculate the corresponding survival and reaction probabilities. The obtained expressions should prove useful for the study of reversible membrane-bound reactions in cell biology and can serve as a useful ingredient of enhanced stochastic particle-based simulation algorithms.