TY - JOUR A1 - Abouzar, Maryam H. A1 - Poghossian, Arshak A1 - Cherstvy, Andrey G. A1 - Pedraza, Angela M. A1 - Ingebrandt, Sven A1 - Schöning, Michael J. T1 - Label-free electrical detection of DNA by means of field-effect nanoplate capacitors experiments and modeling JF - Physica status solidi : A, Applications and materials science N2 - 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. KW - DNA KW - field-effect KW - gold nanoparticle KW - label-free detection KW - nanoplate capacitor Y1 - 2012 U6 - https://doi.org/10.1002/pssa.201100710 SN - 1862-6300 VL - 209 IS - 5 SP - 925 EP - 934 PB - Wiley-VCH CY - Weinheim 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 - 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 - JOUR A1 - Aydiner, Ekrem A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Money distribution in agent-based models with position-exchange dynamics BT - the Pareto paradigm revisited JF - The European physical journal : B, Condensed matter and complex systems N2 - 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. KW - Statistical and Nonlinear Physics Y1 - 2019 U6 - https://doi.org/10.1140/epjb/e2019-90674-0 SN - 1434-6028 SN - 1434-6036 VL - 92 IS - 5 PB - Springer CY - New York ER - TY - JOUR A1 - Beshnova, Daria A. A1 - Cherstvy, Andrey G. A1 - Vainshtein, Yevhen A1 - Teif, Vladimir B. T1 - Regulation of the nucleosome repeat length in vivo by the DNA sequence, protein concentrations and long-range interactions JF - PLoS Computational Biology : a new community journal N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1371/journal.pcbi.1003698 SN - 1553-734X SN - 1553-7358 VL - 10 IS - 7 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Bodrova, Anna A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Quantifying non-ergodic dynamics of force-free granular gases JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient epsilon. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of epsilon on the impact velocity of particles. Y1 - 2015 U6 - https://doi.org/10.1039/c5cp02824h SN - 1463-9076 SN - 1463-9084 VL - 17 IS - 34 SP - 21791 EP - 21798 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Ultraslow scaled Brownian motion JF - New journal of physics : the open-access journal for physics N2 - 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. KW - anomalous diffusion KW - stochastic processes KW - ageing Y1 - 2015 U6 - https://doi.org/10.1088/1367-2630/17/6/063038 SN - 1367-2630 VL - 17 PB - IOP Publ. Ltd. CY - Bristol ER - TY - GEN A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Underdamped scaled Brownian motion BT - (non-)existence of the overdamped limit in anomalous diffusion N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 267 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-97158 ER - TY - JOUR A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Underdamped scaled Brownian motion BT - (non-)existence of the overdamped limit in anomalous diffusion JF - Scientific reports N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. Y1 - 2016 U6 - https://doi.org/10.1038/srep30520 SN - 2045-2322 VL - 6 PB - Nature Publishing Group CY - London ER - TY - JOUR A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion JF - Scientific reports N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. Y1 - 2016 U6 - https://doi.org/10.1038/srep30520 SN - 2045-2322 VL - 6 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Caetano, Daniel L. Z. A1 - Carvalho, Sidney Jurado de A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of multiple polyelectrolytes onto a nanosphere BT - splitting the adsorption-desorption transition boundary JF - Interface : journal of the Royal Society N2 - 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. KW - nanoparticles KW - polyelectrolytes KW - electrostatics KW - critical adsorption KW - phase-transition boundary Y1 - 2020 U6 - https://doi.org/10.1098/rsif.2020.0199 SN - 1742-5689 SN - 1742-5662 VL - 17 IS - 167 PB - Royal Society CY - London ER - TY - JOUR A1 - Caetano, Daniel L. Z. A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of periodic and random polyampholytes onto charged surfaces JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - How different are the properties of critical adsorption of polyampholytes and polyelectrolytes onto charged surfaces? How important are the details of polyampholyte charge distribution on the onset of critical adsorption transition? What are the scaling relations governing the dependence of critical surface charge density on salt concentration in the surrounding solution? Here, we employ Metropolis Monte Carlo simulations and uncover the scaling relations for critical adsorption for quenched periodic and random charge distributions along the polyampholyte chains. We also evaluate and discuss the dependence of the adsorbed layer width on solution salinity and details of the charge distribution. We contrast our findings to the known results for polyelectrolyte adsorption onto oppositely charged surfaces, in particular, their dependence on electrolyte concentration. Y1 - 2017 U6 - https://doi.org/10.1039/c7cp04040g SN - 1463-9076 SN - 1463-9084 VL - 19 SP - 23397 EP - 23413 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Cherstvy, Andrey G. T1 - Shape Morphologies of Icosahedral Two-Component Vesicles JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - What are the features of partitioning of crystalline materials on the surface of a two-component icosahedral vesicle? We model the response of the rigid hardly stretchable crystalline icosahedra upon addition of a softer component on its surface. We demonstrate how the soft phase "invades" the shell regions with the highest elastic energy density around 12 5-fold topological defects. We explore the phase diagram of these inhomogeneous shells as a function of the soft material fraction, shell radius, and elastic moduli of the two phases. The findings are compared with the recent computer simulation findings, and their biological relevance, for example, for the structure of icosahedral viruses, is also discussed. Y1 - 2017 U6 - https://doi.org/10.1021/acs.jpcb.7b02440 SN - 1520-6106 VL - 121 SP - 7484 EP - 7491 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Cherstvy, Andrey G. T1 - Detection of DNA hybridization by field-effect DNA-based biosensors - mechanisms of signal generation and open questions JF - Biosensors and bioelectronics : the principal international journal devoted to research, design development and application of biosensors and bioelectronics N2 - 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. KW - DNA hybridization KW - Au nano-particle KW - Bio-electrochemical sensing KW - Electrostatic screening Y1 - 2013 U6 - https://doi.org/10.1016/j.bios.2013.02.026 SN - 0956-5663 VL - 46 IS - 2 SP - 162 EP - 170 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Cherstvy, Andrey G. T1 - Critical polyelectrolyte adsorption under confinement Planar slit, cylindrical pore, and spherical cavity JF - Biopolymers N2 - 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. KW - polymers KW - adsorption KW - electrostatics KW - confinement Y1 - 2012 U6 - https://doi.org/10.1002/bip.22023 SN - 0006-3525 VL - 97 IS - 5 SP - 311 EP - 317 PB - Wiley-Blackwell CY - Hoboken ER - TY - JOUR A1 - Cherstvy, Andrey G. T1 - Electrostatics and charge regulation in polyelectrolyte multi layered assembly JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - We examine the implications of electrostatic interactions on formation of polyelectrolyte multilayers, in application to field-effect based biosensors for label-free detection of charged macromolecules. We present a quantitative model to describe the experimental potentiometric observations and discuss its possibilities and limitations for detection of polyelectrolyte adsorption. We examine the influence of the ionic strength and pH on the sensor response upon polyelectrolyte layer-by-layer formation. The magnitude of potential oscillations on the sensor-electrolyte interface predicted upon repetitive adsorption charge-alternating polymers agrees satisfactorily with experimental results. The model accounts for different screening by mobile ions in electrolyte and inside tightly interdigitated multilayered structure. In particular, we show that sensors' potential oscillations are larger and more persistent at lower salt conditions, while they decay faster with the number of layers at higher salt conditions, in agreement with experiments. The effects of polyelectrolyte layer thickness, substrate potential, and charge regulation on the sensor surface triggered by layer-by-layer deposition are also analyzed. Y1 - 2014 U6 - https://doi.org/10.1021/jp502460v SN - 1520-6106 VL - 118 IS - 17 SP - 4552 EP - 4560 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes JF - New journal of physics : the open-access journal for physics N2 - 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. Y1 - 2013 U6 - https://doi.org/10.1088/1367-2630/15/8/083039 SN - 1367-2630 VL - 15 IS - 15 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Ageing and confinement in non-ergodic heterogeneous diffusion processes JF - Journal of physics : A, Mathematical and theoretical N2 - 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. KW - stochastic processes KW - anomalous diffusion KW - ageing KW - weak ergodicity breaking Y1 - 2014 U6 - https://doi.org/10.1088/1751-8113/47/48/485002 SN - 1751-8113 SN - 1751-8121 VL - 47 IS - 48 PB - IOP Publ. Ltd. CY - Bristol 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. Y1 - 2014 U6 - https://doi.org/10.1039/c3sm52846d SN - 1744-683X SN - 1744-6848 VL - 10 IS - 10 SP - 1591 EP - 1601 PB - Royal Society of Chemistry CY - Cambridge 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 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes JF - Physical chemistry, chemical physics : a journal of European Chemical Societies 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. Y1 - 2013 U6 - https://doi.org/10.1039/c3cp53056f SN - 1463-9076 SN - 1463-9084 VL - 15 IS - 46 SP - 20220 EP - 20235 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity JF - Journal of statistical mechanics: theory and experiment N2 - 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. KW - diffusion Y1 - 2015 U6 - https://doi.org/10.1088/1742-5468/2015/05/P05010 SN - 1742-5468 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1063/1.4917077 SN - 0021-9606 SN - 1089-7690 VL - 142 IS - 14 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1103/PhysRevE.90.012134 SN - 1539-3755 SN - 1550-2376 VL - 90 IS - 1 PB - American Physical Society CY - College Park 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 : 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 - 1463-9076 SN - 1463-9084 VL - 18 SP - 23840 EP - 23852 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. T1 - Modeling DNA condensation on freestanding cationic lipid membranes JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - Motivated by recent experimental observations of a rapid spontaneous DNA coil-globule transition on freestanding cationic lipid bilayers, we propose simple theoretical models for DNA condensation on cationic lipid membranes. First, for a single DNA rod, we examine the conditions of full wrapping of a cylindrical DNA-like semi-flexible polyelectrolyte by an oppositely charged membrane. Then, for two parallel DNA rods, we self-consistently analyze the shape and the extent of the membrane enveloping them, focusing on membrane elastic deformations and the membrane-DNA embracing angle, which enables us to compute the membrane-mediated DNA-DNA interactions. We examine the effects of the membrane composition and its charge density, which are the experimentally tunable parameters. We show that membrane-driven rod-rod attraction is more pronounced for higher charge densities and for smaller surface tensions of the membrane. Thus, we demonstrate that for a long DNA chain adhered to a cationic lipid membrane, such membrane-induced DNA-DNA attraction can trigger compaction of DNA. Y1 - 2014 U6 - https://doi.org/10.1039/c3cp53433b SN - 1463-9076 SN - 1463-9084 VL - 16 IS - 5 SP - 2020 EP - 2037 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Metzler, Ralf T1 - Anomalous diffusion, nonergodicity, and ageing for exponentially and logarithmically time-dependent diffusivity BT - striking differences for massive versus massless particles JF - Journal of physics. D, Applied physics N2 - We investigate a diffusion process with a time-dependent diffusion coefficient, both exponentially increasing and decreasing in time, D(t)=D-0(e +/- 2 alpha t). For this (hypothetical) nonstationary diffusion process we compute-both analytically and from extensive stochastic simulations-the behavior of the ensemble- and time-averaged mean-squared displacements (MSDs) of the particles, both in the over- and underdamped limits. Simple asymptotic relations derived for the short- and long-time behaviors are shown to be in excellent agreement with the results of simulations. The diffusive characteristics in the presence of ageing are also considered, with dramatic differences of the over- versus underdamped regime. Our results for D(t)=D-0(e +/- 2 alpha t) extend and generalize the class of diffusive systems obeying scaled Brownian motion featuring a power-law-like variation of the diffusivity with time, D(t) similar to t(alpha-1). We also examine the logarithmically increasing diffusivity, D(t)=D(0)log[t/tau(0)], as another fundamental functional dependence (in addition to the power-law and exponential) and as an example of diffusivity slowly varying in time. One of the main conclusions is that the behavior of the massive particles is predominantly ergodic, while weak ergodicity breaking is repeatedly found for the time-dependent diffusion of the massless particles at short times. The latter manifests itself in the nonequivalence of the (both nonaged and aged) MSD and the mean time-averaged MSD. The current findings are potentially applicable to a class of physical systems out of thermal equilibrium where a rapid increase or decrease of the particles' diffusivity is inherently realized. One biological system potentially featuring all three types of time-dependent diffusion (power-law-like, exponential, and logarithmic) is water diffusion in the brain tissues, as we thoroughly discuss in the end. KW - anomalous diffusion KW - scaled Brownian motion KW - stochastic processes KW - nonstationary diffusivity KW - water diffusion in the brain KW - nonergodicity Y1 - 2021 U6 - https://doi.org/10.1088/1361-6463/abdff0 SN - 0022-3727 SN - 1361-6463 VL - 54 IS - 19 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Teif, V. B. T1 - Structure-driven homology pairing of chromatin fibers the role of electrostatics and protein-induced bridging JF - 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 N2 - 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. KW - Chromatin pairing KW - Homology KW - Electrostatics KW - Shape recognition KW - Long-range bridging Y1 - 2013 U6 - https://doi.org/10.1007/s10867-012-9294-4 SN - 0092-0606 SN - 1573-0689 VL - 39 IS - 3 SP - 363 EP - 385 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Teif, Vladimir B. T1 - Electrostatic effect of H1-histone protein binding on nucleosome repeat length JF - Physical biology : a journal for the fundamental understanding of biological systems N2 - Within a simple biophysical model we describe the effect of electrostatic binding of H1 histone proteins on the nucleosome repeat length in chromatin. The length of wrapped DNA optimizes its binding energy to the histone core and the elastic energy penalty of DNA wrapping. The magnitude of the effect predicted from our model is in agreement with the systematic experimental data on the linear variation of nucleosome repeat lengths with H1/nucleosome ratio (Woodcock C L et al 2006 Chromos. Res. 14 17-25). We compare our model to the data for different cell types and organisms, with a widely varying ratio of bound H1 histones per nucleosome. We underline the importance of this non-specific histone-DNA charge-balance mechanism in regulating the positioning of nucleosomes and the degree of compaction of chromatin fibers in eukaryotic cells. KW - electrostatics KW - DNA KW - nucleosome Y1 - 2014 U6 - https://doi.org/10.1088/1478-3975/11/4/044001 SN - 1478-3967 SN - 1478-3975 VL - 11 IS - 4 PB - IOP Publ. Ltd. CY - Bristol 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 - Cherstvy, Andrey G. A1 - Thapa, Samudrajit A1 - Wagner, Caroline E. A1 - Metzler, Ralf T1 - Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels JF - Soft matter N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1039/c8sm02096e SN - 1744-683X SN - 1744-6848 VL - 15 IS - 12 SP - 2526 EP - 2551 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series JF - New journal of physics N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. KW - time averaging KW - diffusion KW - geometric Brownian motion KW - financial time series Y1 - 2017 U6 - https://doi.org/10.1088/1367-2630/aa7199 SN - 1367-2630 VL - 19 SP - 1 EP - 11 PB - IOP CY - London ER - TY - GEN A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 347 KW - diffusion KW - financial time series KW - geometric Brownian motion KW - time averaging Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400541 ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series JF - New journal of physics : the open-access journal for physics N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. KW - time averaging KW - diffusion KW - geometric Brownian motion KW - financial time series Y1 - 2017 U6 - https://doi.org/10.1088/1367-2630/aa7199 SN - 1367-2630 VL - 19 SP - 135 EP - 147 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Scaled geometric Brownian motion features sub- or superexponential ensemble-averaged, but linear time-averaged mean-squared displacements JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Various mathematical Black-Scholes-Merton-like models of option pricing employ the paradigmatic stochastic process of geometric Brownian motion (GBM). The innate property of such models and of real stock-market prices is the roughly exponential growth of prices with time [on average, in crisis-free times]. We here explore the ensemble- and time averages of a multiplicative-noise stochastic process with power-law-like time-dependent volatility, sigma(t) similar to t(alpha), named scaled GBM (SGBM). For SGBM, the mean-squared displacement (MSD) computed for an ensemble of statistically equivalent trajectories can grow faster than exponentially in time, while the time-averaged MSD (TAMSD)-based on a sliding-window averaging along a single trajectory-is always linear at short lag times Delta. The proportionality factor between these the two averages of the time series is Delta/T at short lag times, where T is the trajectory length, similarly to GBM. This discrepancy of the scaling relations and pronounced nonequivalence of the MSD and TAMSD at Delta/T << 1 is a manifestation of weak ergodicity breaking for standard GBM and for SGBM with s (t)-modulation, the main focus of our analysis. The analytical predictions for the MSD and mean TAMSD for SGBM are in quantitative agreement with the results of stochastic computer simulations. Y1 - 2021 U6 - https://doi.org/10.1103/PhysRevE.103.062127 SN - 2470-0045 SN - 2470-0053 VL - 103 IS - 6 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Wang, Wei A1 - Metzler, Ralf A1 - Sokolov, Igor M. T1 - Inertia triggers nonergodicity of fractional Brownian motion JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared displacement (MSD) to the time-averaged MSD (TAMSD) of overdamped or massless FBM, but also dramatically alter the values of the ergodicity-breaking parameter (EB). Our theoretical results for the behavior of EB for underdamped or massive FBM for varying particle mass m, Hurst exponent H, and trace length T are in excellent agreement with the findings of stochastic computer simulations. The current results can be of interest for the experimental community employing various single-particle-tracking techniques and aiming at assessing the degree of nonergodicity for the recorded time series (studying, e.g., the behavior of EB versus lag time). To infer FBM as a realizable model of anomalous diffusion for a set single-particle-tracking data when massive particles are being tracked, the EBs from the data should be compared to EBs of massive (rather than massless) FBM. Y1 - 2021 U6 - https://doi.org/10.1103/PhysRevE.104.024115 SN - 2470-0045 SN - 2470-0053 VL - 104 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Winkler, R. G. T1 - Polyelectrolyte adsorption onto oppositely charged interfaces image-charge repulsion and surface curvature JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1021/jp304980e SN - 1520-6106 VL - 116 IS - 32 SP - 9838 EP - 9845 PB - American Chemical Society CY - Washington 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 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto charged Janus nanospheres JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1039/c4cp02207f SN - 1463-9076 SN - 1463-9084 VL - 16 IS - 29 SP - 15539 EP - 15550 PB - Royal Society of Chemistry CY - Cambridge 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: the nonlinear Poisson-Boltzmann approach JF - NEW JOURNAL OF 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-Huckel 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-Huckel result, such that the required critical surface charge density for polyelectrolyte adsorption sigma(c) 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. Ltd. CY - Bristol ER - TY - JOUR A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Inverted critical adsorption of polyelectrolytes in confinement JF - Soft matter N2 - What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sigma(c)-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sigma(c) for the concave interfaces versus the Debye screening length 1/kappa and the extent of confinement a for these three interfaces for small kappa a values. For large kappa a the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/kappa. We also rationalize how sigma(c)(kappa) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids. Y1 - 2015 U6 - https://doi.org/10.1039/c5sm00635j SN - 1744-683X SN - 1744-6848 VL - 11 IS - 22 SP - 4430 EP - 4443 PB - Royal Society of Chemistry CY - Cambridge ER - TY - GEN A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto charged Janus nanospheres N2 - 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 physico-chemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 278 Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-98783 ER - TY - JOUR A1 - Emanuel, Marc D. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf A1 - Gompper, Gerhard T1 - Buckling transitions and soft-phase invasion of two-component icosahedral shells JF - Physical review / publ. by The American Physical Society. E, Statistical, nonlinear, and soft matter physics N2 - What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.102.062104 SN - 2470-0045 SN - 2470-0053 SN - 2470-0061 SN - 1538-4519 VL - 102 IS - 6 PB - Woodbury CY - New York ER - TY - JOUR A1 - Fernandez, Amanda Diez A1 - Charchar, Patrick A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf A1 - Finnis, Michael W. T1 - The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated JF - Physical chemistry, chemical physics N2 - 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. Y1 - 2020 U6 - https://doi.org/10.1039/d0cp03849k SN - 1463-9076 SN - 1463-9084 VL - 22 IS - 48 SP - 27955 EP - 27965 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Grebenkov, Denis S. A1 - Metzler, Ralf T1 - Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments JF - NEW JOURNAL OF PHYSICS N2 - A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells. KW - anomalous diffusion KW - crowded fluids KW - stochastic processes Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/1/013027 SN - 1367-2630 VL - 18 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Deformation propagation in responsive polymer network films JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr N2 - We study the elastic deformations in a cross-linked polymer network film triggered by the binding of submicron particles with a sticky surface, mimicking the interactions of viral pathogens with thin films of stimulus-responsive polymeric materials such as hydrogels. From extensive Langevin Dynamics simulations we quantify how far the network deformations propagate depending on the elasticity parameters of the network and the adhesion strength of the particles. We examine the dynamics of the collective area shrinkage of the network and obtain some simple relations for the associated characteristic decay lengths. A detailed analysis elucidates how the elastic energy of the network is distributed between stretching and compression modes in response to the particle binding. We also examine the force-distance curves of the repulsion or attraction interactions for a pair of sticky particles in the polymer network film as a function of the particle-particle separation. The results of this computational study provide new insight into collective phenomena in soft polymer network films and may, in particular, be applied to applications for visual detection of pathogens such as viruses via a macroscopic response of thin films of cross-linked hydrogels. (C) 2014 AIP Publishing LLC. Y1 - 2014 U6 - https://doi.org/10.1063/1.4893056 SN - 0021-9606 SN - 1089-7690 VL - 141 IS - 7 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Non-universal tracer diffusion in crowded media of non-inert obstacles JF - Physical chemistry, chemical physics : a journal of European Chemical Societies 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. Y1 - 2015 U6 - https://doi.org/10.1039/c4cp03599b SN - 1463-9076 SN - 1463-9084 VL - 17 IS - 3 SP - 1847 EP - 1858 PB - 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 -