Issue 10, 2014

Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity

Abstract

We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.

Graphical abstract: Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity

Article information

Article type
Paper
Submitted
11 Nov 2013
Accepted
21 Dec 2013
First published
02 Jan 2014
This article is Open Access
Creative Commons BY license

Soft Matter, 2014,10, 1591-1601

Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity

A. G. Cherstvy, A. V. Chechkin and R. Metzler, Soft Matter, 2014, 10, 1591 DOI: 10.1039/C3SM52846D

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