Modeling nanoconfined reaction kinetics: Alternative methodology incorporating equilibrium extent fluctuations

TL;DR

This paper introduces a novel methodology using Equilibrium Constant Differential Equations (ECDE) to model nanoconfined reaction kinetics, enabling efficient stochastic analysis that aligns with traditional master equation results but with reduced computational demands.

Contribution

The paper presents an innovative approach combining ECDE with stochastic kinetics, simplifying calculations compared to Gillespie-based methods for nanoconfined reactions.

Findings

ECDE accurately models stochastic reaction kinetics.

Method reduces computational resources compared to Gillespie algorithm.

Results agree with chemical master equations.

Abstract

This study reveals that Equilibrium Constant Differential Equations (ECDE) for nanoconfined reactions derived recently in the frameworks of statistical mechanics are useful in modeling stochastic chemical kinetics. It is assumed and verified that if the transient value of the nano-reaction quotient is treated as being an equilibrium constant, the corresponding equilibrium reaction extent and its fluctuations (the variance function) coincide with the respective transient values. The ECDE-computed variance function facilitates the solution of the stochastic kinetics equations (SKE), as is demonstrated for a stoichiometric exchange reaction. The results obtained by this original methodology are in full agreement with those provided by the chemical master equations. Contrary to the commonly used approaches based on the latter and the Gillespie algorithm, which need a lot of computer memory and are time-consuming, the proposed SKE-ECDE method requires to solve only the ECDE and a single stochastic kinetics differential equation.