A Macroscopically Consistent Reactive Langevin Dynamics Model

TL;DR

This paper introduces a Reactive Langevin Dynamics model that bridges microscopic reaction models with particle-based stochastic reaction-diffusion models, ensuring physical consistency and detailed balance at equilibrium.

Contribution

It develops a novel RLD model with reactive kernels consistent with detailed balance, linking microscopic Langevin models to volume reactivity PBSRD models.

Findings

Reactive kernels satisfy detailed balance at equilibrium

Overdamped limit corresponds to volume reactivity PBSRD models

Provides a systematic derivation linking microscopic and mesoscopic models

Abstract

Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such models may be inappropriate, necessitating the use of more microscopic Langevin Dynamics models for spatial transport. In this work we develop a novel particle-based Reactive Langevin Dynamics (RLD) model, with a focus on deriving reactive interaction kernels that are consistent with the physical constraint of detailed balance of reactive fluxes at equilibrium. We demonstrate that, to leading order, the overdamped limit of the resulting RLD model corresponds to the volume reactivity PBSRD model, of which the well-known Doi model is a particular instance. Our work provides a step towards systematically deriving PBSRD models from more microscopic reaction models, and suggests possible constraints on the latter to ensure consistency between the two physical scales.