@article{HouCherstvyMetzleretal.2018, author = {Hou, Ru and Cherstvy, Andrey G. and Metzler, Ralf and Akimoto, Takuma}, title = {Biased continuous-time random walks for ordinary and equilibrium cases}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {20}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {32}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c8cp01863d}, pages = {20827 -- 20848}, year = {2018}, abstract = {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.}, language = {en} } @article{CherstvyThapaMardoukhietal.2018, author = {Cherstvy, Andrey G. and Thapa, Samudrajit and Mardoukhi, Yousof and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Time averages and their statistical variation for the Ornstein-Uhlenbeck process}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {98}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.98.022134}, pages = {15}, year = {2018}, abstract = {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.}, language = {en} } @article{AydinerCherstvyMetzler2018, author = {Aydiner, Ekrem and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Wealth distribution, Pareto law, and stretched exponential decay of money}, series = {Physica : europhysics journal ; A, Statistical mechanics and its applications}, volume = {490}, journal = {Physica : europhysics journal ; A, Statistical mechanics and its applications}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0378-4371}, doi = {10.1016/j.physa.2017.08.017}, pages = {278 -- 288}, year = {2018}, abstract = {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.}, language = {en} } @misc{CherstvyMetzler2013, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94468}, pages = {20220 -- 20235}, year = {2013}, abstract = {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.}, language = {en} } @article{MetzlerJeonCherstvyetal.2014, author = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli}, title = {Anomalous diffusion models and their properties}, series = {physical chemistry, chemical physics : PCCP}, volume = {2014}, journal = {physical chemistry, chemical physics : PCCP}, number = {16}, issn = {1463-9076}, doi = {10.1039/c4cp03465a}, pages = {24128 -- 24164}, year = {2014}, abstract = {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.}, language = {en} } @misc{MetzlerJeonCherstvyetal.2014, author = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli}, title = {Anomalous diffusion models and their properties}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74448}, pages = {24128 -- 24164}, year = {2014}, abstract = {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.}, language = {en} } @article{CherstvyChechkinMetzler2014, author = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity}, series = {Soft matter}, volume = {2014}, journal = {Soft matter}, number = {10}, publisher = {Royal Society of Chemistry}, issn = {2046-2069}, doi = {10.1039/c3sm52846d}, pages = {1591 -- 1601}, year = {2014}, 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.}, language = {en} } @misc{CherstvyChechkinMetzler2014, author = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity}, number = {168}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74021}, pages = {1591 -- 1601}, year = {2014}, 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.}, language = {en} } @article{GhoshCherstvyMetzler2014, author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Non-universal tracer diffusion in crowded media of non-inert obstacles}, series = {Physical Chemistry Chemical Physics}, volume = {3}, journal = {Physical Chemistry Chemical Physics}, number = {17}, editor = {Metzler, Ralf}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, pages = {1847 -- 1858}, year = {2014}, abstract = {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.}, language = {en} } @misc{GhoshCherstvyMetzler2014, author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Non-universal tracer diffusion in crowded media of non-inert obstacles}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77128}, pages = {1847 -- 1858}, year = {2014}, abstract = {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.}, language = {en} } @article{ShinCherstvyMetzler2014, author = {Shin, Jaeoh and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size}, series = {Soft Matter}, journal = {Soft Matter}, editor = {Metzler, Ralf}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, issn = {1744-683X}, pages = {472 -- 488}, year = {2014}, abstract = {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.}, language = {en} } @misc{ShinCherstvyMetzler2014, author = {Shin, Jaeoh and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76961}, pages = {472 -- 488}, year = {2014}, abstract = {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.}, language = {en} } @article{GhoshCherstvyPetrovetal.2016, author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Petrov, Eugene P. and Metzler, Ralf}, title = {Interactions of rod-like particles on responsive elastic sheets}, series = {Soft matter}, journal = {Soft matter}, publisher = {RSC}, address = {London}, issn = {1744-6848}, doi = {10.1039/C6SM01522K}, year = {2016}, abstract = {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.}, language = {en} } @misc{GhoshCherstvyPetrovetal.2016, author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Petrov, Eugene P. and Metzler, Ralf}, title = {Interactions of rod-like particles on responsive elastic sheets}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95882}, year = {2016}, abstract = {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.}, language = {en} } @article{CherstvyMetzler2016, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes}, series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, volume = {18}, journal = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies}, publisher = {RSC Publ.}, address = {Cambridge}, issn = {1463-9084}, doi = {10.1039/C6CP03101C}, pages = {23840 -- 23852}, year = {2016}, abstract = {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.}, language = {en} } @misc{CherstvyMetzler2016, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95901}, pages = {23840 -- 23852}, year = {2016}, abstract = {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.}, language = {en} } @article{deCarvalhoMetzlerCherstvy2016, author = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.}, title = {Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces}, series = {New journal of physics : the open-access journal for physics}, volume = {18}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ.}, address = {London}, issn = {1367-2630}, doi = {10.1088/1367-2630/18/8/083037}, year = {2016}, abstract = {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-H{\"u}ckel 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-H{\"u}ckel 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.}, language = {en} } @misc{deCarvalhoMetzlerCherstvy2016, author = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.}, title = {Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100295}, pages = {17}, year = {2016}, abstract = {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-H{\"u}ckel 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-H{\"u}ckel 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.}, language = {en} } @article{LiuCherstvyMetzler2017, author = {Liu, Lin and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion}, series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry}, volume = {121}, journal = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry}, publisher = {American Chemical Society}, address = {Washington}, issn = {1520-6106}, doi = {10.1021/acs.jpcb.6b12413}, pages = {1284 -- 1289}, year = {2017}, abstract = {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.}, language = {en} } @article{AkimotoCherstvyMetzler2018, author = {Akimoto, Takuma and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {98}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.98.022105}, pages = {6}, year = {2018}, abstract = {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.}, language = {en} } @article{AydinerCherstvyMetzler2019, author = {Aydiner, Ekrem and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Money distribution in agent-based models with position-exchange dynamics}, series = {The European physical journal : B, Condensed matter and complex systems}, volume = {92}, journal = {The European physical journal : B, Condensed matter and complex systems}, number = {5}, publisher = {Springer}, address = {New York}, issn = {1434-6028}, doi = {10.1140/epjb/e2019-90674-0}, pages = {4}, year = {2019}, abstract = {Wealth and income distributions are known to feature country-specific Pareto exponents for their long power-law tails. To propose a rationale for this, we introduce an agent-based dynamic model and use Monte Carlo simulations to unveil the wealth distributions in closed and open economical systems. The standard money-exchange scenario is supplemented with the position-exchange agent dynamics that vitally affects the Pareto law. Specifically, in closed systems with position-exchange dynamics the power law changes to an exponential shape, while for open systems with traps the Pareto law remains valid.}, language = {en} } @article{CherstvyThapaWagneretal.2019, author = {Cherstvy, Andrey G. and Thapa, Samudrajit and Wagner, Caroline E. and Metzler, Ralf}, title = {Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels}, series = {Soft matter}, volume = {15}, journal = {Soft matter}, number = {12}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1744-683X}, doi = {10.1039/c8sm02096e}, pages = {2526 -- 2551}, year = {2019}, abstract = {Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity', fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.}, language = {en} } @article{ThapaLukatSelhuberUnkeletal.2019, author = {Thapa, Samudrajit and Lukat, Nils and Selhuber-Unkel, Christine and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {150}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {14}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.5086269}, pages = {18}, year = {2019}, abstract = {We perform a detailed statistical analysis of diffusive trajectories of membrane-enclosed vesicles (vacuoles) in the supercrowded cytoplasm of living Acanthamoeba castellanii cells. From the vacuole traces recorded in the center-of-area frame of moving amoebae, we examine the statistics of the time-averaged mean-squared displacements of vacuoles, their generalized diffusion coefficients and anomalous scaling exponents, the ergodicity breaking parameter, the non-Gaussian features of displacement distributions of vacuoles, the displacement autocorrelation function, as well as the distributions of speeds and positions of vacuoles inside the amoeba cells. Our findings deliver novel insights into the internal dynamics of cellular structures in these infectious pathogens. Published under license by AIP Publishing.}, language = {en} } @article{FernandezCharcharCherstvyetal.2020, author = {Fernandez, Amanda Diez and Charchar, Patrick and Cherstvy, Andrey G. and Metzler, Ralf and Finnis, Michael W.}, title = {The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated}, series = {Physical chemistry, chemical physics}, volume = {22}, journal = {Physical chemistry, chemical physics}, number = {48}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/d0cp03849k}, pages = {27955 -- 27965}, year = {2020}, abstract = {In this study we investigate, using all-atom molecular-dynamics computer simulations, the in-plane diffusion of a doxorubicin drug molecule in a thin film of water confined between two silica surfaces. We find that the molecule diffuses along the channel in the manner of a Gaussian diffusion process, but with parameters that vary according to its varying transversal position. Our analysis identifies that four Gaussians, each describing particle motion in a given transversal region, are needed to adequately describe the data. Each of these processes by itself evolves with time at a rate slower than that associated with classical Brownian motion due to a predominance of anticorrelated displacements. Long adsorption events lead to ageing, a property observed when the diffusion is intermittently hindered for periods of time with an average duration which is theoretically infinite. This study presents a simple system in which many interesting features of anomalous diffusion can be explored. It exposes the complexity of diffusion in nanoconfinement and highlights the need to develop new understanding.}, language = {en} } @article{WangCherstvyChechkinetal.2020, author = {Wang, Wei and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thapa, Samudrajit and Seno, Flavio and Liu, Xianbin and Metzler, Ralf}, title = {Fractional Brownian motion with random diffusivity}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {53}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {47}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aba467}, pages = {34}, year = {2020}, abstract = {Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.}, language = {en} } @misc{KindlerPulkkinenCherstvyetal.2019, author = {Kindler, Oliver and Pulkkinen, Otto and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Burst Statistics in an Early Biofilm Quorum Sensing Mode}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {777}, issn = {1866-8372}, doi = {10.25932/publishup-43909}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439099}, pages = {21}, year = {2019}, abstract = {Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called "autoinducers") and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a "cluster" of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get "induced" into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.}, language = {en} } @article{WangCherstvyLiuetal.2020, author = {Wang, Wei and Cherstvy, Andrey G. and Liu, Xianbin and Metzler, Ralf}, title = {Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {102}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {1}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.102.012146}, pages = {012146-1 -- 012146-16}, year = {2020}, abstract = {Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.}, language = {en} } @article{ThapaLomholtKrogetal.2018, author = {Thapa, Samudrajit and Lomholt, Michael Andersen and Krog, Jens and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data}, series = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies}, volume = {20}, journal = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies}, number = {46}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c8cp04043e}, pages = {29018 -- 29037}, year = {2018}, abstract = {We employ Bayesian statistics using the nested-sampling algorithm to compare and rank multiple models of ergodic diffusion (including anomalous diffusion) as well as to assess their optimal parameters for in silico-generated and real time-series. We focus on the recently-introduced model of Brownian motion with "diffusing diffusivity'-giving rise to widely-observed non-Gaussian displacement statistics-and its comparison to Brownian and fractional Brownian motion, also for the time-series with some measurement noise. We conduct this model-assessment analysis using Bayesian statistics and the nested-sampling algorithm on the level of individual particle trajectories. We evaluate relative model probabilities and compute best-parameter sets for each diffusion model, comparing the estimated parameters to the true ones. We test the performance of the nested-sampling algorithm and its predictive power both for computer-generated (idealised) trajectories as well as for real single-particle-tracking trajectories. Our approach delivers new important insight into the objective selection of the most suitable stochastic model for a given time-series. We also present first model-ranking results in application to experimental data of tracer diffusion in polymer-based hydrogels.}, language = {en} } @article{CaetanoCarvalhoMetzleretal.2020, author = {Caetano, Daniel L. Z. and Carvalho, Sidney Jurado de and Metzler, Ralf and Cherstvy, Andrey G.}, title = {Critical adsorption of multiple polyelectrolytes onto a nanosphere}, series = {Interface : journal of the Royal Society}, volume = {17}, journal = {Interface : journal of the Royal Society}, number = {167}, publisher = {Royal Society}, address = {London}, issn = {1742-5689}, doi = {10.1098/rsif.2020.0199}, pages = {10}, year = {2020}, abstract = {Employing extensive Monte Carlo computer simulations, we investigate in detail the properties of multichain adsorption of charged flexible polyelectrolytes (PEs) onto oppositely charged spherical nanoparticles (SNPs). We quantify the conditions of critical adsorption-the phase-separation curve between the adsorbed and desorbed states of the PEs-as a function of the SNP surface-charge density and the concentration of added salt. We study the degree of fluctuations of the PE-SNP electrostatic binding energy, which we use to quantify the emergence of the phase subtransitions, including a series of partially adsorbed PE configurations. We demonstrate how the phase-separation adsorption-desorption boundary shifts and splits into multiple subtransitions at low-salt conditions, thereby generalizing and extending the results for critical adsorption of a single PE onto the SNP. The current findings are relevant for finite concentrations of PEs around the attracting SNP, such as the conditions for PE adsorption onto globular proteins carrying opposite electric charges.}, language = {en} } @article{KarCherstvyMetzler2017, author = {Kar, Prathitha and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Acceleration of bursty multiprotein target search kinetics on DNA by colocalisation}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {20}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {12}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c7cp06922g}, pages = {7931 -- 7946}, year = {2017}, abstract = {Proteins are capable of locating specific targets on DNA by employing a facilitated diffusion process with intermittent 1D and 3D search steps. Gene colocalisation and coregulation-i.e. the spatial proximity of two communicating genes-is one factor capable of accelerating the target search process along the DNA. We perform Monte Carlo computer simulations and demonstrate the benefits of gene colocalisation for minimising the search time in a model DNA-protein system. We use a simple diffusion model to mimic the search for targets by proteins, produced initially in bursts of multiple proteins and performing the first-passage search on the DNA chain. The behaviour of the mean first-passage times to the target is studied as a function of distance between the initial position of proteins and the DNA target position, as well as versus the concentration of proteins. We also examine the properties of bursty target search kinetics for varying physical-chemical protein-DNA binding affinity. Our findings underline the relevance of colocalisation of production and binding sites for protein search inside biological cells.}, language = {en} } @article{CherstvyMetzler2013, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {15}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {46}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c3cp53056f}, pages = {20220 -- 20235}, year = {2013}, abstract = {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.}, language = {en} } @article{CherstvyTeif2013, author = {Cherstvy, Andrey G. and Teif, V. B.}, title = {Structure-driven homology pairing of chromatin fibers the role of electrostatics and protein-induced bridging}, series = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences}, volume = {39}, journal = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences}, number = {3}, publisher = {Springer}, address = {Dordrecht}, issn = {0092-0606}, doi = {10.1007/s10867-012-9294-4}, pages = {363 -- 385}, year = {2013}, abstract = {Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.}, language = {en} } @article{CherstvyMetzler2008, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes}, doi = {10.1039/C3CP53056F}, year = {2008}, abstract = {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.}, language = {en} } @article{PoghossianWeilCherstvyetal.2013, author = {Poghossian, A. and Weil, M. and Cherstvy, Andrey G. and Sch{\"o}ning, M. J.}, title = {Electrical monitoring of polyelectrolyte multilayer formation by means of capacitive field-effect devices}, series = {Analytical \& bioanalytical chemistry}, volume = {405}, journal = {Analytical \& bioanalytical chemistry}, number = {20}, publisher = {Springer}, address = {Heidelberg}, issn = {1618-2642}, doi = {10.1007/s00216-013-6951-9}, pages = {6425 -- 6436}, year = {2013}, abstract = {The semiconductor field-effect platform represents a powerful tool for detecting the adsorption and binding of charged macromolecules with direct electrical readout. In this work, a capacitive electrolyte-insulator-semiconductor (EIS) field-effect sensor consisting of an Al-p-Si-SiO2 structure has been applied for real-time in situ electrical monitoring of the layer-by-layer formation of polyelectrolyte (PE) multilayers (PEM). The PEMs were deposited directly onto the SiO2 surface without any precursor layer or drying procedures. Anionic poly(sodium 4-styrene sulfonate) and cationic weak polyelectrolyte poly(allylamine hydrochloride) have been chosen as a model system. The effect of the ionic strength of the solution, polyelectrolyte concentration, number and polarity of the PE layers on the characteristics of the PEM-modified EIS sensors have been studied by means of capacitance-voltage and constant-capacitance methods. In addition, the thickness, surface morphology, roughness and wettabilityof the PE mono- and multilayers have been characterised by ellipsometry, atomic force microscopy and water contact-angle methods, respectively. To explain potential oscillations on the gate surface and signal behaviour of the capacitive field-effect EIS sensor modified with a PEM, a simplified electrostatic model that takes into account the reduced electrostatic screening of PE charges by mobile ions within the PEM has been proposed and discussed.}, language = {en} } @article{CherstvyChechkinMetzler2013, author = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes}, series = {New journal of physics : the open-access journal for physics}, volume = {15}, journal = {New journal of physics : the open-access journal for physics}, number = {15}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/15/8/083039}, pages = {13}, year = {2013}, abstract = {We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.}, language = {en} } @article{Cherstvy2013, author = {Cherstvy, Andrey G.}, title = {Detection of DNA hybridization by field-effect DNA-based biosensors - mechanisms of signal generation and open questions}, series = {Biosensors and bioelectronics : the principal international journal devoted to research, design development and application of biosensors and bioelectronics}, volume = {46}, journal = {Biosensors and bioelectronics : the principal international journal devoted to research, design development and application of biosensors and bioelectronics}, number = {2}, publisher = {Elsevier}, address = {Oxford}, issn = {0956-5663}, doi = {10.1016/j.bios.2013.02.026}, pages = {162 -- 170}, year = {2013}, abstract = {We model theoretically the electrostatic effects taking place upon DNA hybridization in dense DNA arrays immobilized on a layer of Au nano-particles deposited on the surface of a field-effect-based DNA capacitive biosensor. We consider the influence of separation of a charged analyte from the sensor surface and the salinity of electrolyte solution, in the framework of both linear and nonlinear Poisson-Boltzmann theories. The latter predicts a substantially weaker sensor signals due to electrostatic saturation effects that is the main conclusion of this paper. We analyze how different physical parameters of dense DNA brushes affect the magnitude of hybridization signals. The list includes the fraction of DNA charge neutralization, the length and spatial conformations of adsorbed DNA molecules, as well as the discreteness of DNA charges. We also examine the effect of Donnan ionic equilibrium in DNA lattices on the sensor response. The validity of theoretical models is contrasted against recent experimental observations on detection of DNA hybridization via its intrinsic electric charge. The sensitivity of such biochemical sensing devices, their detection limit, and DNA hybridization efficiency are briefly discussed in the end.}, language = {en} } @misc{WinklerCherstvy2014, author = {Winkler, Roland G. and Cherstvy, Andrey G.}, title = {Strong and weak polyelectrolyte adsorption onto oppositely charged curved surfaces}, series = {Advances in polymer science}, volume = {255}, journal = {Advances in polymer science}, editor = {Muller, M.}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-642-40734-5; 978-3-642-40733-8}, issn = {0065-3195}, doi = {10.1007/12_2012_183}, pages = {1 -- 56}, year = {2014}, abstract = {Polyelectrolytes are macromolecules composed of charged monomers and exhibit unique properties due to the interplay of their flexibility and electrostatic interactions. In solution, they are attracted to oppositely charged surfaces and interfaces and exhibit a transition to an adsorbed state when certain conditions are met concerning the charge densities of the polymer and surface and the properties of the solution. In this review, we discuss two limiting cases for adsorption of flexible polyelectrolytes on curved surfaces: weak and strong adsorption. In the first case, adsorption is strongly influenced by the entropic degrees of freedom of a flexible polyelectrolyte. By contrast, in the strong adsorption limit, electrostatic interactions dominate, which leads to particular adsorption patterns, specifically on spherical surfaces. We discuss the corresponding theoretical approaches, applying a mean-field description for the polymer and the polymer-surface interaction. For weak adsorption, we discuss the critical adsorption behavior by exactly solvable models for planar and spherical geometries and a generic approximation scheme, which is additionally applied to cylindrical surfaces. For strong adsorption, we investigate various polyelectrolyte patterns on cylinders and spheres and evaluate their stability. The results are discussed in the light of experimental results, mostly of DNA adsorption experiments.}, language = {en} } @article{deCarvalhoMetzlerCherstvy2014, author = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.}, title = {Critical adsorption of polyelectrolytes onto charged Janus nanospheres}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {16}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {29}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c4cp02207f}, pages = {15539 -- 15550}, year = {2014}, abstract = {Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption-desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physicochemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.}, language = {en} } @article{CherstvyMetzler2015, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2015/05/P05010}, pages = {20}, year = {2015}, abstract = {We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) similar to D-0x(alpha)t(beta) depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.}, language = {en} } @article{CherstvyMetzler2015, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes}, series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, volume = {142}, journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr}, number = {14}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0021-9606}, doi = {10.1063/1.4917077}, pages = {11}, year = {2015}, abstract = {We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form D(x) similar to D-0 vertical bar x vertical bar (alpha 0) in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent a in time and space. In the case of annealed disorder, for which effectively alpha(0) = alpha(0)(t), we show how the long time scaling of the ensemble mean squared displacement (MSD) and the amplitude variation of individual realizations of the time averaged MSD are affected by the disorder strength. For the case of quenched disorder, the long time behavior becomes effectively Brownian after a number of jumps between the domains of a stratified medium. In the latter situation, the averages are taken over both an ensemble of particles and different realizations of the disorder. As physical observables, we analyze in detail the ensemble and time averaged MSDs, the ergodicity breaking parameter, and higher order moments of the time averages. (C) 2015 AIP Publishing LLC.}, language = {en} } @article{MetzlerJeonCherstvyetal.2014, author = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli}, title = {Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {16}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {44}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c4cp03465a}, pages = {24128 -- 24164}, year = {2014}, abstract = {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.}, language = {en} } @article{BodrovaChechkinCherstvyetal.2015, author = {Bodrova, Anna S. and Chechkin, Aleksei V. and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Ultraslow scaled Brownian motion}, series = {New journal of physics : the open-access journal for physics}, volume = {17}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/17/6/063038}, pages = {16}, year = {2015}, abstract = {We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal to 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.}, language = {en} } @article{AbouzarPoghossianCherstvyetal.2012, author = {Abouzar, Maryam H. and Poghossian, Arshak and Cherstvy, Andrey G. and Pedraza, Angela M. and Ingebrandt, Sven and Sch{\"o}ning, Michael J.}, title = {Label-free electrical detection of DNA by means of field-effect nanoplate capacitors experiments and modeling}, series = {Physica status solidi : A, Applications and materials science}, volume = {209}, journal = {Physica status solidi : A, Applications and materials science}, number = {5}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1862-6300}, doi = {10.1002/pssa.201100710}, pages = {925 -- 934}, year = {2012}, abstract = {Label-free electrical detection of consecutive deoxyribonucleic acid (DNA) hybridization/denaturation by means of an array of individually addressable field-effect-based nanoplate silicon-on-insulator (SOI) capacitors modified with gold nanoparticles (Au-NP) is investigated. The proposed device detects charge changes on Au-NP/DNA hybrids induced by the hybridization or denaturation event. DNA hybridization was performed in a high ionic-strength solution to provide a high hybridization efficiency. On the other hand, to reduce the screening of the DNA charge by counter ions and to achieve a high sensitivity, the sensor signal induced by the hybridization and denaturation events was measured in a low ionic-strength solution. High sensor signals of about 120, 90, and 80 mV were registered after the DNA hybridization, denaturation, and re-hybridization events, respectively. Fluorescence microscopy has been applied as reference method to verify the DNA immobilization, hybridization, and denaturation processes. An electrostatic charge-plane model for potential changes at the gate surface of a nanoplate field-effect sensor induced by the DNA hybridization has been developed taking into account both the Debye length and the distance of the DNA charge from the gate surface.}, language = {en} } @article{Cherstvy2012, author = {Cherstvy, Andrey G.}, title = {Critical polyelectrolyte adsorption under confinement Planar slit, cylindrical pore, and spherical cavity}, series = {Biopolymers}, volume = {97}, journal = {Biopolymers}, number = {5}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0006-3525}, doi = {10.1002/bip.22023}, pages = {311 -- 317}, year = {2012}, abstract = {We explore the properties of adsorption of flexible polyelectrolyte chains in confined spaces between the oppositely charged surfaces in three basic geometries. A method of approximate uniformly valid solutions for the Green function equation for the eigenfunctions of polymer density distributions is developed to rationalize the critical adsorption conditions. The same approach was implemented in our recent study for the inverse problem of polyelectrolyte adsorption onto a planar surface, and on the outer surface of rod-like and spherical obstacles. For the three adsorption geometries investigated, the theory yields simple scaling relations for the minimal surface charge density that triggers the chain adsorption, as a function of the Debye screening length and surface curvature. The encapsulation of polyelectrolytes is governed by interplay of the electrostatic attraction energy toward the adsorbing surface and entropic repulsion of the chain squeezed into a thin slit or small cavities. Under the conditions of surface-mediated confinement, substantially larger polymer linear charge densities are required to adsorb a polyelectrolyte inside a charged spherical cavity, relative to a cylindrical pore and to a planar slit (at the same interfacial surface charge density). Possible biological implications are discussed briefly in the end.}, language = {en} } @article{CherstvyWinkler2012, author = {Cherstvy, Andrey G. and Winkler, R. G.}, title = {Polyelectrolyte adsorption onto oppositely charged interfaces image-charge repulsion and surface curvature}, series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry}, volume = {116}, journal = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry}, number = {32}, publisher = {American Chemical Society}, address = {Washington}, issn = {1520-6106}, doi = {10.1021/jp304980e}, pages = {9838 -- 9845}, year = {2012}, abstract = {We analyze theoretically the influence of low-dielectric boundaries on the adsorption of flexible polyelectrolytes onto planar and spherical oppositely charged surfaces in electrolyte solutions. We rationalize to what extent polymer chains are depleted from adsorbing interfaces by repulsive image forces. We employ the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function of the Edwards equation to determine the adsorption equilibrium. Scaling relations are determined for the critical adsorption strength required to initiate polymer adsorption onto these low-dielectric supports. Image-force repulsion shifts the equilibrium toward the desorbed state, demanding larger surface charge densities and polyelectrolyte linear charge densities for the adsorption to take place. The effect is particularly pronounced for a planar interface in a low-salt regime, where a dramatic change in the scaling behavior for the adsorption-desorption transition is predicted. For the adsorbed state, polymers with higher charge densities are displaced further from the interface by image-charge repulsions. We discuss relevant experimental evidence and argue about possible biological applications of the results.}, language = {en} } @article{BeshnovaCherstvyVainshteinetal.2014, author = {Beshnova, Daria A. and Cherstvy, Andrey G. and Vainshtein, Yevhen and Teif, Vladimir B.}, title = {Regulation of the nucleosome repeat length in vivo by the DNA sequence, protein concentrations and long-range interactions}, series = {PLoS Computational Biology : a new community journal}, volume = {10}, journal = {PLoS Computational Biology : a new community journal}, number = {7}, publisher = {PLoS}, address = {San Fransisco}, issn = {1553-734X}, doi = {10.1371/journal.pcbi.1003698}, pages = {14}, year = {2014}, abstract = {The nucleosome repeat length (NRL) is an integral chromatin property important for its biological functions. Recent experiments revealed several conflicting trends of the NRL dependence on the concentrations of histones and other architectural chromatin proteins, both in vitro and in vivo, but a systematic theoretical description of NRL as a function of DNA sequence and epigenetic determinants is currently lacking. To address this problem, we have performed an integrative biophysical and bioinformatics analysis in species ranging from yeast to frog to mouse where NRL was studied as a function of various parameters. We show that in simple eukaryotes such as yeast, a lower limit for the NRL value exists, determined by internucleosome interactions and remodeler action. For higher eukaryotes, also the upper limit exists since NRL is an increasing but saturating function of the linker histone concentration. Counterintuitively, smaller H1 variants or non-histone architectural proteins can initiate larger effects on the NRL due to entropic reasons. Furthermore, we demonstrate that different regimes of the NRL dependence on histone concentrations exist depending on whether DNA sequence-specific effects dominate over boundary effects or vice versa. We consider several classes of genomic regions with apparently different regimes of the NRL variation. As one extreme, our analysis reveals that the period of oscillations of the nucleosome density around bound RNA polymerase coincides with the period of oscillations of positioning sites of the corresponding DNA sequence. At another extreme, we show that although mouse major satellite repeats intrinsically encode well-defined nucleosome preferences, they have no unique nucleosome arrangement and can undergo a switch between two distinct types of nucleosome positioning.}, language = {en} } @article{CherstvyMetzler2014, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {90}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {1}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.90.012134}, pages = {11}, year = {2014}, abstract = {We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence D(x) similar to vertical bar x vertical bar(alpha) of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on statistical measures such as the amplitude scatter of the time-averaged mean-squared displacement of individual realizations, the ergodicity breaking and non-Gaussianity parameters, as well as the probability density function P(x, t), we analyze the weakly nonergodic character of the heterogeneous diffusion process and, particularly, the degree of irreproducibility of individual realizations. As we show, the fluctuations between individual realizations increase with growing modulus vertical bar alpha vertical bar of the scaling exponent. The fluctuations appear to diverge when the critical value alpha = 2 is approached, while for even larger alpha the fluctuations decrease, again. At criticality, the power-law behavior of the mean-squared displacement changes to an exponentially fast growth, and the fluctuations of the time-averaged mean-squared displacement do not converge for increasing number of realizations. From a systematic comparison we observe some striking similarities of the heterogeneous diffusion process with the familiar subdiffusive continuous time random walk process with power-law waiting time distribution and diverging characteristic waiting time.}, language = {en} } @article{ShinCherstvyKimetal.2015, author = {Shin, Jaeoh and Cherstvy, Andrey G. and Kim, Won Kyu and Metzler, Ralf}, title = {Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles}, series = {New journal of physics : the open-access journal for physics}, volume = {17}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/17/11/113008}, pages = {12}, year = {2015}, abstract = {We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two-dimensional model system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains, while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that higher activities of SPPs yield a higher effective temperature of the bath and thus facilitate the looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or in suspensions of active colloidal particles or bacteria cells.}, language = {en} } @article{ShinCherstvyMetzler2014, author = {Shin, Jaeoh and Cherstvy, Andrey G. and Metzler, Ralf}, title = {Mixing and segregation of ring polymers: spatial confinement and molecular crowding effects}, series = {New journal of physics : the open-access journal for physics}, volume = {16}, journal = {New journal of physics : the open-access journal for physics}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/16/5/053047}, pages = {19}, year = {2014}, abstract = {During the life cycle of bacterial cells the non-mixing of the two ring-shaped daughter genomes is an important prerequisite for the cell division process. Mimicking the environments inside highly crowded biological cells, we study the dynamics and statistical behavior of two flexible ring polymers in the presence of cylindrical confinement and crowding molecules. From extensive computer simulations we determine the degree of ring-ring overlap and the number of inter-monomer contacts for varying volume fractions phi of crowders. We also examine the entropic demixing of polymer rings in the presence of mobile crowders and determine the characteristic times of the internal polymer dynamics. Effects of the ring length on ring-ring overlap are also analyzed. In particular, on systematic variation of the fraction of crowding molecules, a (1 - phi)-scaling is found for the ring-ring overlap length along the cylinder axis, and a non-monotonic dependence of the 3D ring-ring contact number with a maximum at phi approximate to 0.2 is obtained. Our results demonstrate that polymer rings are demixed and separated by particular entropy-favourable partitioning of crowders along the axis of the cylindrical simulation box. These findings help to rationalize the implications of macromolecular crowding for circular DNA molecules in confined spaces inside bacteria as well as in localized cellular compartments inside eukaryotic cells.}, language = {en} } @article{CherstvyChechkinMetzler2014, author = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Ageing and confinement in non-ergodic heterogeneous diffusion processes}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {47}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {48}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/47/48/485002}, pages = {18}, year = {2014}, abstract = {We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.}, language = {en} }