Non-Gaussianity and Dynamical Trapping in Locally Activated Random Walks

TL;DR

This paper introduces a minimal model of locally-activated diffusion where the particle's mobility changes upon crossing the origin, leading to non-Gaussian distributions and a transition to static states, relevant for understanding plaque formation.

Contribution

The study presents a novel minimal model demonstrating how local mobility changes induce non-Gaussian diffusion and dynamical transitions, with implications for atherosclerosis.

Findings

Mobility perturbations cause non-Gaussian, multi-peaked distributions.

A dynamical transition to an absorbing static state occurs due to local activation.

Model links local diffusion changes to plaque formation mechanisms.

Abstract

We propose a minimal model of \emph{locally-activated diffusion}, in which the diffusion coefficient of a one-dimensional Brownian particle is modified in a prescribed way --- either increased or decreased --- upon each crossing of the origin. Such a local mobility decrease arises in the formation of atherosclerotic plaques due to diffusing macrophage cells accumulating lipid particles. We show that spatially localized mobility perturbations have remarkable consequences on diffusion at all scales, such as the emergence of a non-Gaussian multi-peaked probability distribution and a dynamical transition to an absorbing static state. In the context of atherosclerosis, this dynamical transition can be viewed as a minimal mechanism that causes macrophages to aggregate in lipid-enriched regions and thereby to the formation of atherosclerotic plaques.