Probing microscopic origins of confined subdiffusion by first-passage observables

TL;DR

This paper develops a theoretical framework to analyze first-passage observables in disordered media, enabling discrimination between different microscopic models of subdiffusion, with applications to biological cells.

Contribution

It introduces an analytical approach to calculate first-passage observables for subdiffusive models, aiding in identifying their microscopic origins.

Findings

First-passage observables can distinguish between CTRW and fractal diffusion models.

Analytical formulas for mean first-passage times and occupation times are derived.

Implications for understanding transport and reaction kinetics in cellular environments.

Abstract

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean square displacement (MSD). However, subdiffusive behavior can stem from different microscopic scenarios, which can not be identified solely by the MSD data. In this paper we present a theoretical framework which permits to calculate analytically first-passage observables (mean first-passage times, splitting probabilities and occupation times distributions) in disordered media in any dimensions. This analysis is applied to two representative microscopic models of subdiffusion: continuous-time random walks with heavy tailed waiting times, and diffusion on fractals. Our results show that first-passage observables provide tools to unambiguously discriminate between the two possible microscopic scenarios of subdiffusion. Moreover we suggest experiments based on first-passage observables which could help in determining the origin of subdiffusion in complex media such as living cells, and discuss the implications of anomalous transport to reaction kinetics in cells.