A discrete stochastic formulation for reversible bimolecular reactions via diffusion encounter
Year: 2016
Type: article
Abstract: The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory.As there is a clear corresponding stochastic process, the mathematical description takes both Kolmogorov forward equation for the evolution of the probability distribution function and the stochastic sample trajectories.This dual description is a fundamental characteristic of stochastic processes and allows simple particle-based simulations to accurately match the expected statistical behavior.However, in the traditional theory using the back-reaction boundary condition to model reversible reactions with geminate recombinations, several subtleties arise: It is unclear what the underlying stochastic process is, which causes complications in producing accurate simulations; and it is non-trivial how to perform an appropriate discretization for numerical computations.In this work, we derive a discrete stochastic model that recovers the classical models and their boundary conditions in the continuous limit.In the case of reversible reactions, we recover the back-reaction boundary condition, unifying the back-reaction approach with those of current simulation packages.Furthermore, all the complications encountered in the continuous models become trivial in the discrete model.Our formulation brings to attention the question: With computations in mind, can we develop a discrete reaction kinetics model that is more fundamental than its continuous counterpart? Key words.
Authors: Mauricio J. del Razo, Hong Qian
Institution: University of Washington
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Award: G9000075607
OpenAlex ID: W2271210776