Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations

Abstract

Smoluchowski-type models for diffusion-influenced reactions (A+B -> C) can be formulated within two frameworks: the probabilistic-based approach for a pair A, B of reacting particles and the concentration-based approach for systems in contact with a bath that generates a concentration gradient of B particles that interact with A. Although these two approaches are mathematically similar, it is not straightforward to establish a precise mathematical relationship between them. Determining this relationship is essential to derive particle-based numerical methods that are quantitatively consistent with bulk concentration dynamics. In this work, we determine the relationship between the two approaches by introducing the grand canonical Smoluchowski master equation (GC-SME), which consists of a continuous-time Markov chain that models an arbitrary number of B particles, each one of them following Smoluchowski's probabilistic dynamics. We show that the GC-SME recovers the concentration-based approach by taking either the hydrodynamic or the large copy number limit. In addition, we show that the GC-SME provides a clear statistical mechanical interpretation of the concentration-based approach and yields an emergent chemical potential for nonequilibrium spatially inhomogeneous reaction processes. We further exploit the GC-SME robust framework to accurately derive multiscale/hybrid numerical methods that couple particle-based reaction-diffusion simulations with bulk concentration descriptions, as described in detail through two computational implementations.

References in corpus (14)

• Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
• A Convergent Reaction-Diffusion Master Equation
• A First-Passage Kinetic Monte Carlo Algorithm for Complex Diffusion-Reaction Systems
• Diffusion-limited reactions in crowded environments
• Mesoscopic Model for Diffusion-Influenced Reaction Dynamics
• Mesoscopic Kinetic Basis of Macroscopic Chemical Thermodynamics: A Mathematical Theory
• Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
• Particle-based membrane model for mesoscopic simulation of cellular dynamics
• Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear Chemical Reaction Systems with General Rate Law
• MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
• Multiscale simulations of anisotropic particles combining Brownian Dynamics and Green's Function Reaction Dynamics
• Dynamic Looping of a Free-Draining Polymer
• A Discrete Stochastic Formulation for Reversible Bimolecular Reactions via Diffusion Encounter
• Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

Cited by in corpus (11)

• Modeling of stimuli-responsive nanoreactors: rational rate control towards the design of colloidal enzymes
• A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations
• Diffusion-influenced reaction rates in the presence of pair interactions
• Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics
• Chemical diffusion master equation: formulations of reaction--diffusion processes on the molecular level
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Data-driven dynamical coarse-graining for condensed matter systems
• Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture
• Coupling particle-based reaction-diffusion simulations with reservoirs mediated by reaction-diffusion PDEs
• Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems
• Open reaction-diffusion systems: bridging probabilistic theory and simulations across scales