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

  • 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 theWe 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.show moreshow less

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Metadaten
Author:Andrey G. Cherstvy, Aleksei V. ChechkinORCiDGND, Ralf MetzlerORCiDGND
DOI:https://doi.org/10.1039/c3sm52846d
ISSN:2046-2069 (online)
Parent Title (English):Soft matter
Publisher:Royal Society of Chemistry
Document Type:Article
Language:English
Date of first Publication:2014/01/02
Year of Completion:2014
Release Date:2015/03/20
Tag:adenoassociated virus; anomalous diffusion; cytoplasm; endosomal escape; escherichia-coli; infection pathway; intracellular-transport; living cells; models; trafficking
Volume:2014
Issue:10
Pagenumber:11
First Page:1591
Last Page:1601
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 54 Chemie / 540 Chemie und zugeordnete Wissenschaften
Peer Review:Referiert
Publication Way:Open Access
Grantor:RSC
Licence (English):License LogoCreative Commons - Attribution 3.0 unported
Notes extern:Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 168