TY - JOUR A1 - Hou, Ru A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf A1 - Akimoto, Takuma T1 - Biased continuous-time random walks for ordinary and equilibrium cases BT - facilitation of diffusion, ergodicity breaking and ageing JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent alpha are considered for the WTD psi(t) similar to 1/t(1+alpha). We treat continuous-time random walks (CTRWs) with 0 < alpha < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < alpha < 2 and alpha > 2. We demonstrate that in the presence of a drift CTRWs with alpha < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < alpha < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with alpha > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < alpha < 2 and alpha > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with alpha > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent alpha. Y1 - 2018 U6 - https://doi.org/10.1039/c8cp01863d SN - 1463-9076 SN - 1463-9084 VL - 20 IS - 32 SP - 20827 EP - 20848 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Thapa, Samudrajit A1 - Mardoukhi, Yousof A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averages and their statistical variation for the Ornstein-Uhlenbeck process BT - Role of initial particle distributions and relaxation to stationarity JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed. Y1 - 2018 U6 - https://doi.org/10.1103/PhysRevE.98.022134 SN - 2470-0045 SN - 2470-0053 VL - 98 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Aydiner, Ekrem A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Wealth distribution, Pareto law, and stretched exponential decay of money BT - Computer simulations analysis of agent-based models JF - Physica : europhysics journal ; A, Statistical mechanics and its applications N2 - We study by Monte Carlo simulations a kinetic exchange trading model for both fixed and distributed saving propensities of the agents and rationalize the person and wealth distributions. We show that the newly introduced wealth distribution – that may be more amenable in certain situations – features a different power-law exponent, particularly for distributed saving propensities of the agents. For open agent-based systems, we analyze the person and wealth distributions and find that the presence of trap agents alters their amplitude, leaving however the scaling exponents nearly unaffected. For an open system, we show that the total wealth – for different trap agent densities and saving propensities of the agents – decreases in time according to the classical Kohlrausch–Williams–Watts stretched exponential law. Interestingly, this decay does not depend on the trap agent density, but rather on saving propensities. The system relaxation for fixed and distributed saving schemes are found to be different. KW - Econophysics KW - Wealth and income distribution KW - Pareto law KW - Scaling exponents Y1 - 2017 U6 - https://doi.org/10.1016/j.physa.2017.08.017 SN - 0378-4371 SN - 1873-2119 VL - 490 SP - 278 EP - 288 PB - Elsevier CY - Amsterdam ER - TY - GEN A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes N2 - We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 236 KW - anomalous diffusion KW - disordered media KW - fractional dynamics KW - infection pathway KW - inhomogeneous-media KW - intracellular-transport KW - langevin equation KW - living cells KW - random-walks KW - single-particle tracking Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94468 SP - 20220 EP - 20235 ER - TY - JOUR A1 - Metzler, Ralf A1 - Jeon, Jae-Hyung A1 - Cherstvy, Andrey G. A1 - Barkai, Eli T1 - Anomalous diffusion models and their properties BT - non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking JF - physical chemistry, chemical physics : PCCP N2 - Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion. KW - intermittent chaotic systems KW - Fokker-Planck equations KW - time random-walks KW - fluorescence photobleaching recovery KW - fluctuation-dissipation theorem KW - fractional dynamics approach KW - photon-counting statistics KW - weak ergodicity breaking KW - flight search patterns KW - levy flights Y1 - 2014 U6 - https://doi.org/10.1039/c4cp03465a SN - 1463-9076 SN - 1463-9084 VL - 2014 IS - 16 SP - 24128 EP - 24164 ER - TY - GEN A1 - Metzler, Ralf A1 - Jeon, Jae-Hyung A1 - Cherstvy, Andrey G. A1 - Barkai, Eli T1 - Anomalous diffusion models and their properties BT - non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking N2 - Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 174 KW - Fokker-Planck equations KW - flight search patterns KW - fluctuation-dissipation theorem KW - fluorescence photobleaching recovery KW - fractional dynamics approach KW - intermittent chaotic systems KW - levy flights KW - photon-counting statistics KW - time random-walks KW - weak ergodicity breaking Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-74448 SP - 24128 EP - 24164 ER - 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 - GEN 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 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 168 KW - adenoassociated virus KW - anomalous diffusion KW - cytoplasm KW - endosomal escape KW - escherichia-coli KW - infection pathway KW - intracellular-transport KW - living cells KW - models KW - trafficking Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-74021 IS - 168 SP - 1591 EP - 1601 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 - GEN A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Non-universal tracer diffusion in crowded media of non-inert obstacles 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 186 KW - escence 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 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77128 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 - GEN A1 - Shin, Jaeoh A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 185 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 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76961 SP - 472 EP - 488 PB - The Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. A1 - Metzler, Ralf T1 - Interactions of rod-like particles on responsive elastic sheets JF - Soft matter N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed. Y1 - 2016 U6 - https://doi.org/10.1039/C6SM01522K SN - 1744-6848 SN - 1744-683X PB - RSC CY - London ER - TY - GEN A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. A1 - Metzler, Ralf T1 - Interactions of rod-like particles on responsive elastic sheets N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 256 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95882 ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes JF - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion. Y1 - 2016 U6 - https://doi.org/10.1039/C6CP03101C SN - 1463-9084 SN - 1463-9076 VL - 18 SP - 23840 EP - 23852 PB - RSC Publ. CY - Cambridge ER - TY - GEN A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 257 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95901 SP - 23840 EP - 23852 ER - TY - JOUR A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces BT - the nonlinear Poisson–Boltzmann approach JF - New journal of physics : the open-access journal for physics N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems. KW - polyelectrolyte adsorption KW - electrostatic interactions KW - critical phenomena KW - Debye screening Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/8/083037 SN - 1367-2630 VL - 18 PB - IOP Publ. CY - London ER - TY - GEN A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces BT - the nonlinear Poisson–Boltzmann approach N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 292 KW - polyelectrolyte adsorption KW - electrostatic interactions KW - critical phenomena KW - Debye screening Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100295 ER - TY - JOUR A1 - Liu, Lin A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism. Y1 - 2017 U6 - https://doi.org/10.1021/acs.jpcb.6b12413 SN - 1520-6106 VL - 121 SP - 1284 EP - 1289 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Akimoto, Takuma A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed. Y1 - 2018 U6 - https://doi.org/10.1103/PhysRevE.98.022105 SN - 2470-0045 SN - 2470-0053 VL - 98 IS - 2 PB - American Physical Society CY - College Park ER -