TY - JOUR A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity JF - Soft matter N2 - 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. KW - anomalous diffusion KW - intracellular-transport KW - adenoassociated virus KW - infection pathway KW - escherichia-coli KW - endosomal escape KW - living cells KW - trafficking KW - cytoplasm KW - models Y1 - 2014 U6 - https://doi.org/10.1039/c3sm52846d SN - 2046-2069 VL - 2014 IS - 10 SP - 1591 EP - 1601 PB - Royal Society of Chemistry ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Ala-Nissila, Tapio A1 - Metzler, Ralf ED - Metzler, Ralf T1 - Polymer translocation: the first two decades and the recent diversification JF - Soft matter N2 - Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous–infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis. KW - solid-state nanopores KW - single-stranded-dna KW - posttranslational protein translocation KW - anomalous diffusion KW - monte-carlo KW - structured polynucleotides KW - dynamics simulation KW - equation approach KW - osmotic-pressure KW - membrane channel Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76266 SN - 1744-683X VL - 45 IS - 10 SP - 9016 EP - 9037 PB - the Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf ED - Metzler, Ralf T1 - Non-universal tracer diffusion in crowded media of non-inert obstacles JF - Physical Chemistry Chemical Physics N2 - We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer–obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer–obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer–crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids. KW - fluorescence correlation spectroscopy KW - single-particle tracking KW - anomalous diffusion KW - living cells KW - physiological consequences KW - langevin equation KW - infection pathway KW - excluded volume KW - brownian-motion KW - random-walks Y1 - 2014 SN - 1463-9076 VL - 3 IS - 17 SP - 1847 EP - 1858 PB - The Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Shin, Jaeoh A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf ED - Metzler, Ralf T1 - Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size JF - Soft Matter N2 - The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping–unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions. KW - gene-regulation kinetics KW - physiological consequences KW - spatial-organization KW - anomalous diffusion KW - folding kinetics KW - living cells KW - dna coiling KW - in-vitro KW - dynamics KW - mixtures Y1 - 2014 SN - 1744-683X SP - 472 EP - 488 PB - The Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Bauer, Maximilian A1 - Godec, Aljaž A1 - Metzler, Ralf T1 - Diffusion of finite-size particles in two-dimensional channels with random wall configurations JF - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies N2 - Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick–Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107]. KW - anomalous diffusion KW - fractional dynamics KW - transport KW - nonergodicity KW - coefficient Y1 - 2014 U6 - https://doi.org/10.1039/C3CP55160A SN - 1463-9084 SN - 1463-9076 VL - 16 IS - 13 SP - 6118 EP - 6128 PB - RSC Publications CY - Cambridge ER -