Geometry-controlled kinetics

TL;DR

This paper analytically derives the first-passage time distribution for various diffusion processes, revealing that geometry significantly influences reaction kinetics and introducing the concept of 'geometry-controlled kinetics' to better understand spatial effects.

Contribution

It provides the first analytical calculation of FPT distribution across different diffusion types, unifying them into universality classes and highlighting geometry's role in reaction kinetics.

Findings

FPT distribution derived analytically for multiple diffusion processes

Transport processes fall into universal classes

Geometry significantly impacts diffusion-limited reactions

Abstract

It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage time (FPT). Although essential to quantify the kinetics of reactions on all time scales, determining the FPT distribution was deemed so far intractable. Here, we calculate analytically this FPT distribution and show that transport processes as various as regular diffusion, anomalous diffusion, diffusion in disordered media and in fractals fall into the same universality classes. Beyond this theoretical aspect, this result changes the views on standard reaction kinetics. More precisely, we argue that geometry can become a key parameter so far ignored in this context, and introduce the concept of "geometry-controlled kinetics". These findings could help understand the crucial role of spatial organization of genes in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions.