Reversible Target-Binding Kinetics of Multiple Impatient Particles

TL;DR

This paper derives exact solutions for the distribution of reaction times in biochemical systems with multiple particles that reversibly bind to a target, revealing how unbinding rates influence reaction kinetics.

Contribution

It introduces a novel analytical framework for reversible binding kinetics, extending previous models that only considered irreversible binding, and provides asymptotic analysis and simulation validation.

Findings

Exact solutions for reaction time distribution with reversible binding

Reaction time depends significantly on unbinding rates and particle number

Asymptotic behaviors elucidate short- and long-time dynamics

Abstract

Certain biochemical reactions can only be triggered after binding of a sufficient number of particles to a specific target region such as an enzyme or a protein sensor. We investigate the distribution of the reaction time, i.e., the first instance when all independently diffusing particles are bound to the target. When each particle binds irreversibly, this is equivalent to the first-passage time of the slowest (last) particle. In turn, reversible binding to the target renders the problem much more challenging and drastically changes the distribution of the reaction time. We derive the exact solution of this problem and investigate the short-time and long-time asymptotic behaviors of the reaction time probability density. We also analyze how the mean reaction time depends on the unbinding rate and the number of particles. Our exact and asymptotic solutions are compared to Monte Carlo simulations.