Anomalous Diffusion of Self-Propelled Particles in Directed Random Environments

TL;DR

This paper develops a theoretical framework to analyze the transport behavior of self-propelled particles in complex, directed environments, revealing multiple regimes of anomalous diffusion influenced by network properties and particle dynamics.

Contribution

It introduces a master equation formalism to identify how network heterogeneity and particle parameters induce different anomalous diffusion regimes and crossover times.

Findings

Multiple dynamical regimes of anomalous motion identified

Crossover times and diffusion coefficients can be significantly increased

Interplay between stepping strategy and persistency causes anomalous diffusion

Abstract

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.