Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control

TL;DR

This paper reveals that in biochemical reactions at nanomolar concentrations, reaction times are complex and defocused due to the interplay of diffusion and reaction limitations, requiring analysis of the full distribution rather than mean times.

Contribution

It introduces a generic, exactly-solvable model demonstrating the complex structure of reaction-time distributions and defines geometry- and reaction-control regimes in biochemical reactions.

Findings

Reaction-times exhibit four distinct regimes with multiple time scales.

Reaction-times are defocused and cannot be characterized by a single time scale.

Full reaction-time distribution is necessary to understand reaction dynamics.

Abstract

Text-book concepts of diffusion- versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants -- the inverse of the mean-first-passage-time to the reaction-event. In contradistinction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly-solvable model we study the conspiratory effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delimited by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.