Reversible Interacting-Particle Reaction Dynamics

TL;DR

This paper develops a reversible interacting-particle reaction dynamics framework that ensures thermodynamic consistency and correct kinetics across different densities, enhancing simulation accuracy for complex biological and chemical systems.

Contribution

It introduces a Monte-Carlo algorithm that enforces detailed balance in iPRD simulations, ensuring physically realistic results at all concentrations.

Findings

Guarantees correct thermodynamics at all densities.

Maintains desired kinetics in dilute limit.

Implemented in ReaDDy 2 for practical use.

Abstract

Interacting-Particle Reaction Dynamics (iPRD) simulates the spatiotemporal evolution of particles that experience interaction forces and can react with one another. The combination of interaction forces and reactions enable a wide range of complex reactive systems in biology and chemistry, but give rise to new questions such as how to evolve the dynamical equations in a computationally efficient and statistically correct manner. Here we consider reversible reactions such as A + B <--> C with interacting particles and derive expressions for the microscopic iPRD simulation parameters such that desired values for the equilibrium constant and the dissociation rate are obtained in the dilute limit. We then introduce a Monte-Carlo algorithm that ensures detailed balance in the iPRD time-evolution (iPRD-DB). iPRD-DB guarantees the correct thermodynamics at all concentrations and maintains the desired kinetics in the dilute limit, where chemical rates are well-defined and kinetic measurement experiments usually operate. We show that in dense particle systems, the incorporation of detailed balance is essential to obtain physically realistic solutions. iPRD-DB is implemented in ReaDDy 2 (https://readdy.github.io).