@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}
}
@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}
}
@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}
}
@article{XuZhouMetzleretal.2020,
author = {Xu, Pengbo and Zhou, Tian and Metzler, Ralf and Deng, Weihua},
title = {L{\´e}vy walk dynamics in an external harmonic potential},
series = {Physical review : E, Statistical, nonlinear, and soft matter physics},
volume = {101},
journal = {Physical review : E, Statistical, nonlinear, and soft matter physics},
number = {6},
publisher = {American Physical Society},
address = {College Park},
issn = {2470-0045},
doi = {10.1103/PhysRevE.101.062127},
pages = {12},
year = {2020},
abstract = {Levy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs-their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some longstanding puzzles around LWs.},
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{GodecMetzler2017,
author = {Godec, Aljaž and Metzler, Ralf},
title = {First passage time statistics for two-channel diffusion},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {50},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {8},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8121/aa5204},
pages = {17},
year = {2017},
abstract = {We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes, which is shown to effect a non-trivial first passage behaviour. We also address the scenario of intermittent immobilisation. In both cases we prove that despite the perfectly non-recurrent motion of two-channel Markov additive diffusion in 3 dimensions the first passage statistics at long times do not display Poisson-like behaviour if none of the phases has a vanishing diffusion coefficient. This stands in stark contrast to the standard (one-channel) Markov diffusion counterpart. We also discuss the relevance of our results in the context of cellular signalling.},
language = {en}
}
@article{EstradaDelvenneHatanoetal.2018,
author = {Estrada, Ernesto and Delvenne, Jean-Charles and Hatano, Naomichi and Mateos, Jose L. and Metzler, Ralf and Riascos, Alejandro P. and Schaub, Michael T.},
title = {Random multi-hopper model},
series = {Journal of Complex Networks},
volume = {6},
journal = {Journal of Complex Networks},
number = {3},
publisher = {Oxford Univ. Press},
address = {Oxford},
issn = {2051-1310},
doi = {10.1093/comnet/cnx043},
pages = {382 -- 403},
year = {2018},
abstract = {We develop a mathematical model considering a random walker with long-range hops on arbitrary graphs. The random multi-hopper can jump to any node of the graph from an initial position, with a probability that decays as a function of the shortest-path distance between the two nodes in the graph. We consider here two decaying functions in the form of Laplace and Mellin transforms of the shortest-path distances. We prove that when the parameters of these transforms approach zero asymptotically, the hitting time in the multi-hopper approaches the minimum possible value for a normal random walker. We show by computational experiments that the multi-hopper explores a graph with clusters or skewed degree distributions more efficiently than a normal random walker. We provide computational evidences of the advantages of the random multi-hopper model with respect to the normal random walk by studying deterministic, random and real-world networks.},
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{MardoukhiJeonChechkinetal.2018,
author = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Fluctuations of random walks in critical random environments},
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 = {31},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1463-9076},
doi = {10.1039/c8cp03212b},
pages = {20427 -- 20438},
year = {2018},
abstract = {Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.},
language = {en}
}
@article{KosztolowiczMetzlerWąsiketal.2020,
author = {Kosztolowicz, Tadeusz and Metzler, Ralf and Wąsik, Slawomir and Arabski, Michal},
title = {Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium},
series = {PLoS ONE},
volume = {15},
journal = {PLoS ONE},
publisher = {PLOS},
address = {San Francisco, California, US},
issn = {1932-6203},
doi = {10.1371/journal.pone.0243003},
pages = {14},
year = {2020},
abstract = {We study the experimentally measured ciprofloxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. To quantify the antibiotic diffusion dynamics we employ a phenomenological model using a subdiffusion-absorption equation with a fractional time derivative. This effective equation describes molecular diffusion in a medium structured akin Thompson's plumpudding model; here the 'pudding' background represents the ASM and the 'plums' represent the bacterial biofilm. The pudding is a subdiffusion barrier for antibiotic molecules that can affect bacteria found in plums. For the experimental study we use an interferometric method to determine the time evolution of the amount of antibiotic that has diffused through the biofilm. The theoretical model shows that this function is qualitatively different depending on whether or not absorption of the antibiotic in the biofilm occurs. We show that the process can be divided into three successive stages: (1) only antibiotic subdiffusion with constant biofilm parameters, (2) subdiffusion and absorption of antibiotic molecules with variable biofilm transport parameters, (3) subdiffusion and absorption in the medium but the biofilm parameters are constant again. Stage 2 is interpreted as the appearance of an intensive defence build-up of bacteria against the action of the antibiotic, and in the stage 3 it is likely that the bacteria have been inactivated. Times at which stages change are determined from the experimentally obtained temporal evolution of the amount of antibiotic that has diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and theoretical results and is consistent with the biologically expected biofilm response. We show that an experimental method to study the temporal evolution of the amount of a substance that has diffused through a biofilm is useful in studying the processes occurring in a biofilm. We also show that the complicated biological process of antibiotic diffusion in a biofilm can be described by a fractional subdiffusion-absorption equation with subdiffusion and absorption parameters that change over time.},
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{PadashChechkinDybiecetal.2019,
author = {Padash, Amin and Chechkin, Aleksei V. and Dybiec, Bartlomiej and Pavlyukevich, Ilya and Shokri, Babak and Metzler, Ralf},
title = {First-passage properties of asymmetric Levy flights},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {52},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {45},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8121/ab493e},
pages = {48},
year = {2019},
abstract = {L{\´e}vy flights are paradigmatic generalised random walk processes, in which the independent stationary increments—the 'jump lengths'—are drawn from an -stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of L{\´e}vy flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering L{\´e}vy flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of L{\´e}vy flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index and the skewness (asymmetry) parameter . The other approach is based on the stochastic Langevin equation with -stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times.},
language = {en}
}
@article{VojtaSkinnerMetzler2019,
author = {Vojta, Thomas and Skinner, Sarah and Metzler, Ralf},
title = {Probability density of the fractional Langevin equation with reflecting walls},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {100},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {4},
publisher = {American Physical Society},
address = {College Park},
issn = {2470-0045},
doi = {10.1103/PhysRevE.100.042142},
pages = {11},
year = {2019},
abstract = {We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill the appropriate fluctuation-dissipation relation, the probability density on a finite interval converges for long times towards the expected uniform distribution prescribed by thermal equilibrium. In contrast, on a semi-infinite interval with a reflecting wall at the origin, the probability density shows pronounced deviations from the Gaussian behavior observed for normal diffusion. If the correlations of the random force are persistent (positive), particles accumulate at the reflecting wall while antipersistent (negative) correlations lead to a depletion of particles near the wall. We compare and contrast these results with the strong accumulation and depletion effects recently observed for nonthermal fractional Brownian motion with reflecting walls, and we discuss broader implications.},
language = {en}
}
@article{GranadoAbadMetzleretal.2020,
author = {Granado, Felipe Le Vot and Abad, Enrique and Metzler, Ralf and Yuste, Santos B.},
title = {Continuous time random walk in a velocity field},
series = {New Journal of Physics},
volume = {22},
journal = {New Journal of Physics},
publisher = {Dt. Physikalische Ges.},
address = {Bad Honnef},
issn = {1367-2630},
doi = {10.1088/1367-2630/ab9ae2},
pages = {27},
year = {2020},
abstract = {We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a L{\´e}vy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of L{\´e}vy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter-controlled reactions in real systems are discussed.},
language = {en}
}
@article{Metzler2019,
author = {Metzler, Ralf},
title = {Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion},
series = {Journal of statistical mechanics: theory and experiment},
volume = {2019},
journal = {Journal of statistical mechanics: theory and experiment},
number = {11},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1742-5468},
doi = {10.1088/1742-5468/ab4988},
pages = {18},
year = {2019},
abstract = {Brownian motion is a ubiquitous physical phenomenon across the sciences. After its discovery by Brown and intensive study since the first half of the 20th century, many different aspects of Brownian motion and stochastic processes in general have been addressed in Statistical Physics. In particular, there now exists a very large range of applications of stochastic processes in various disciplines. Here we provide a summary of some of the recent developments in the field of stochastic processes, highlighting both the experimental findings and theoretical frameworks.},
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{KrapfLukatMarinarietal.2019,
author = {Krapf, Diego and Lukat, Nils and Marinari, Enzo and Metzler, Ralf and Oshanin, Gleb and Selhuber-Unkel, Christine and Squarcini, Alessio and Stadler, Lorenz and Weiss, Matthias and Xu, Xinran},
title = {Spectral Content of a Single Non-Brownian Trajectory},
series = {Physical review : X, Expanding access},
volume = {9},
journal = {Physical review : X, Expanding access},
number = {1},
publisher = {American Physical Society},
address = {College Park},
issn = {2160-3308},
doi = {10.1103/PhysRevX.9.011019},
pages = {13},
year = {2019},
abstract = {Time-dependent processes are often analyzed using the power spectral density (PSD) calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble average. Frequently, the available experimental datasets are too small for such ensemble averages, and hence, it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from S(f, T), the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable parametrized by frequency f and observation time T, for a broad family of anomalous diffusions-fractional Brownian motion with Hurst index H-and derive exactly its probability density function. We show that S(f, T) is proportional-up to a random numerical factor whose universal distribution we determine-to the ensemble-averaged PSD. For subdiffusion (H < 1/2), we find that S(f, T) similar to A/f(2H+1) with random amplitude A. In sharp contrast, for superdiffusion (H > 1/2) S(f, T) similar to BT2H-1/f(2) with random amplitude B. Remarkably, for H > 1/2 the PSD exhibits the same frequency dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for H > 1/2 the PSD is ageing and is dependent on T. Our predictions for both sub-and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels and by extensive simulations.},
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}
}
@article{SarabadaniMetzlerAlaNissila2022,
author = {Sarabadani, Jalal and Metzler, Ralf and Ala-Nissila, Tapio},
title = {Driven polymer translocation into a channel: Isoflux tension propagation theory and Langevin dynamics simulations},
series = {Physical Review Research},
volume = {4},
journal = {Physical Review Research},
edition = {3},
publisher = {American Physical Society},
address = {College Park, Maryland, USA},
issn = {2643-1564},
doi = {10.1103/PhysRevResearch.4.033003},
pages = {033003-1 -- 033003-14},
year = {2022},
abstract = {Isoflux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force fc. In the high driving force limit, regardless of the channel width, IFTP theory predicts τ ∝ f βc for the translocation time, where β = -1 is the force scaling exponent. Moreover, LD data show that for a very narrow channel fitting only a single file of monomers, the entropic force due to the subchain inside the channel does not play a significant role in the translocation dynamics and the force exponent β = -1 regardless of the force magnitude. As the channel width increases the number of possible spatial configurations of the subchain inside the channel becomes significant and the resulting entropic force causes the force exponent to drop below unity.},
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{SposiniKrapfMarinarietal.2022,
author = {Sposini, Vittoria and Krapf, Diego and Marinari, Enzo and Sunyer, Raimon and Ritort, Felix and Taheri, Fereydoon and Selhuber-Unkel, Christine and Benelli, Rebecca and Weiss, Matthias and Metzler, Ralf and Oshanin, Gleb},
title = {Towards a robust criterion of anomalous diffusion},
series = {Communications Physics},
volume = {5},
journal = {Communications Physics},
publisher = {Springer Nature},
address = {London},
issn = {2399-3650},
doi = {10.1038/s42005-022-01079-8},
pages = {10},
year = {2022},
abstract = {Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.},
language = {en}
}
@article{SecklerMetzler2022,
author = {Seckler, Henrik and Metzler, Ralf},
title = {Bayesian deep learning for error estimation in the analysis of anomalous diffusion},
series = {Nature Communnications},
volume = {13},
journal = {Nature Communnications},
publisher = {Nature Publishing Group UK},
address = {London},
issn = {2041-1723},
doi = {10.1038/s41467-022-34305-6},
pages = {13},
year = {2022},
abstract = {Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusionmodel and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a wellcalibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.},
language = {en}
}
@article{AwadMetzler2020,
author = {Awad, Emad and Metzler, Ralf},
title = {Crossover dynamics from superdiffusion to subdiffusion},
series = {Fractional calculus and applied analysis : an international journal for theory and applications},
volume = {23},
journal = {Fractional calculus and applied analysis : an international journal for theory and applications},
number = {1},
publisher = {De Gruyter},
address = {Berlin ; Boston},
issn = {1311-0454},
doi = {10.1515/fca-2020-0003},
pages = {55 -- 102},
year = {2020},
abstract = {The Cattaneo or telegrapher's equation describes the crossover from initial ballistic to normal diffusion. Here we study and survey time-fractional generalisations of this equation that are shown to produce the crossover of the mean squared displacement from superdiffusion to subdiffusion. Conditional solutions are derived in terms of Fox H-functions and the dth-order moments as well as the diffusive flux of the different models are derived. Moreover, the concept of the distribution-like is proposed as an alternative to the probability density function.},
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{StojkoskiSandevBasnarkovetal.2020,
author = {Stojkoski, Viktor and Sandev, Trifce and Basnarkov, Lasko and Kocarev, Ljupco and Metzler, Ralf},
title = {Generalised geometric Brownian motion},
series = {Entropy},
volume = {22},
journal = {Entropy},
number = {12},
publisher = {MDPI},
address = {Basel},
issn = {1099-4300},
doi = {10.3390/e22121432},
pages = {34},
year = {2020},
abstract = {Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to irregularities found when comparing its properties with empirical distributions. As a solution, we investigate a generalisation of GBM where the introduction of a memory kernel critically determines the behaviour of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and then obtain the corresponding probability density functions using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) in order to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.},
language = {en}
}
@article{SecklerMetzler2022,
author = {Seckler, Henrik and Metzler, Ralf},
title = {Bayesian deep learning for error estimation in the analysis of anomalous diffusion},
series = {Nature Communications},
volume = {13},
journal = {Nature Communications},
number = {1},
publisher = {Nature portfolio},
address = {Berlin},
issn = {2041-1723},
doi = {10.1038/s41467-022-34305-6},
pages = {13},
year = {2022},
abstract = {Modern single-particle-tracking techniques produce extensive time-series of diffusive motion in a wide variety of systems, from single-molecule motion in living-cells to movement ecology. The quest is to decipher the physical mechanisms encoded in the data and thus to better understand the probed systems. We here augment recently proposed machine-learning techniques for decoding anomalous-diffusion data to include an uncertainty estimate in addition to the predicted output. To avoid the Black-Box-Problem a Bayesian-Deep-Learning technique named Stochastic-Weight-Averaging-Gaussian is used to train models for both the classification of the diffusion model and the regression of the anomalous diffusion exponent of single-particle-trajectories. Evaluating their performance, we find that these models can achieve a well-calibrated error estimate while maintaining high prediction accuracies. In the analysis of the output uncertainty predictions we relate these to properties of the underlying diffusion models, thus providing insights into the learning process of the machine and the relevance of the output.
Diffusive motions in complex environments such as living biological cells or soft matter systems can be analyzed with single-particle-tracking approaches, where accuracy of output may vary. The authors involve a machine-learning technique for decoding anomalous-diffusion data and provide an uncertainty estimate together with predicted output.},
language = {en}
}
@article{GuggenbergerChechkinMetzler2021,
author = {Guggenberger, Tobias and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {54},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {29},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8121/ac019b},
pages = {17},
year = {2021},
abstract = {We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise (FGN) in a superharmonic external potential of the form U(x) proportional to x(2n) (n is an element of N). When the noise is considered to be external, the resulting overdamped motion is described by the non-Markovian Langevin equation for fractional Brownian motion. For this case we show the existence of long time, stationary probability density functions (PDFs) the shape of which strongly deviates from the naively expected Boltzmann PDF in the confining potential U(x). We analyse in detail the temporal approach to stationarity as well as the shape of the non-Boltzmann stationary PDF. A typical characteristic is that subdiffusive, antipersistent (with negative autocorrelation) motion tends to effect an accumulation of probability close to the origin as compared to the corresponding Boltzmann distribution while the opposite trend occurs for superdiffusive (persistent) motion. For this latter case this leads to distinct bimodal shapes of the PDF. This property is compared to a similar phenomenon observed for Markovian Levy flights in superharmonic potentials. We also demonstrate that the motion encoded in the fractional Langevin equation driven by FGN always relaxes to the Boltzmann distribution, as in this case the fluctuation-dissipation theorem is fulfilled.},
language = {en}
}
@article{MattosMejiaMonasterioMetzleretal.2012,
author = {Mattos, Thiago G. and Mejia-Monasterio, Carlos and Metzler, Ralf and Oshanin, Gleb},
title = {First passages in bounded domains When is the mean first passage time meaningful?},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {86},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {3},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.86.031143},
pages = {8},
year = {2012},
abstract = {We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(omega) distribution of the random variable omega = tau(1)/(tau(1) + tau(2)), which is a measure for how similar the first passage times tau(1) and tau(2) are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(omega) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(omega), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.},
language = {en}
}
@article{HerrmannMetzlerEngbert2017,
author = {Herrmann, Carl J. J. and Metzler, Ralf and Engbert, Ralf},
title = {A self-avoiding walk with neural delays as a model of fixational eye movements},
series = {Scientific reports},
volume = {7},
journal = {Scientific reports},
publisher = {Nature Publ. Group},
address = {London},
issn = {2045-2322},
doi = {10.1038/s41598-017-13489-8},
pages = {17},
year = {2017},
abstract = {Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.},
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{XuLiuLietal.2020,
author = {Xu, Yong and Liu, Xuemei and Li, Yongge and Metzler, Ralf},
title = {Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {102},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {6},
publisher = {American Physical Society},
address = {College Park},
issn = {2470-0045},
doi = {10.1103/PhysRevE.102.062106},
pages = {16},
year = {2020},
abstract = {Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent a. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent alpha is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.},
language = {en}
}
@article{CapałaPadashChechkinetal.2020,
author = {Capała, Karol and Padash, Amin and Chechkin, Aleksei V. and Shokri, Babak and Metzler, Ralf and Dybiec, Bartłomiej},
title = {Levy noise-driven escape from arctangent potential wells},
series = {Chaos : an interdisciplinary journal of nonlinear science},
volume = {30},
journal = {Chaos : an interdisciplinary journal of nonlinear science},
number = {12},
publisher = {American Institute of Physics},
address = {Woodbury, NY},
issn = {1054-1500},
doi = {10.1063/5.0021795},
pages = {15},
year = {2020},
abstract = {The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.},
language = {en}
}
@article{LiMeiXuetal.2020,
author = {Li, Yongge and Mei, Ruoxing and Xu, Yong and Kurths, J{\"u}rgen and Duan, Jinqiao and Metzler, Ralf},
title = {Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity},
series = {New Journal of Physics},
volume = {22},
journal = {New Journal of Physics},
publisher = {Dt. Physikalische Ges.},
address = {Bad Honnef},
issn = {1367-2630},
doi = {10.1088/1367-2630/ab81b9},
pages = {27},
year = {2020},
abstract = {This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D ₀), as well as a low (D ₘ) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the It{\^o} calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D ₘ will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D ₘ, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.},
language = {en}
}
@article{MutothyaXuLietal.2021,
author = {Mutothya, Nicholas Mwilu and Xu, Yong and Li, Yongge and Metzler, Ralf},
title = {Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {54},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {29},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8121/abfba6},
pages = {31},
year = {2021},
abstract = {We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments.},
language = {en}
}
@article{EliazarMetzler2013,
author = {Eliazar, Iddo and Metzler, Ralf},
title = {Anomalous statistics of random relaxations in random environments},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {87},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.87.022141},
pages = {12},
year = {2013},
abstract = {We comprehensively analyze the emergence of anomalous statistics in the context of the random relaxation ( RARE) model [Eliazar and Metzler, J. Chem. Phys. 137, 234106 ( 2012)], a recently introduced versatile model of random relaxations in random environments. The RARE model considers excitations scattered randomly across a metric space around a reaction center. The excitations react randomly with the center, the reaction rates depending on the excitations' distances from this center. Relaxation occurs upon the first reaction between an excitation and the center. Addressing both the relaxation time and the relaxation range, we explore when these random variables display anomalous statistics, namely, heavy tails at zero and at infinity that manifest, respectively, exceptionally high occurrence probabilities of very small and very large outliers. A cohesive set of closed-form analytic results is established, determining precisely when such anomalous statistics emerge.},
language = {en}
}
@article{KursaweSchulzMetzler2013,
author = {Kursawe, Jochen and Schulz, Johannes H. P. and Metzler, Ralf},
title = {Transient aging in fractional brownian and langevin-equation motion},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {88},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {6},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.88.062124},
pages = {13},
year = {2013},
abstract = {Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t = 0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.},
language = {en}
}
@article{BauerMetzler2013,
author = {Bauer, Maximilian and Metzler, Ralf},
title = {In vivo facilitated diffusion model},
series = {PLoS one},
volume = {8},
journal = {PLoS one},
number = {1},
publisher = {PLoS},
address = {San Fransisco},
issn = {1932-6203},
doi = {10.1371/journal.pone.0053956},
pages = {8},
year = {2013},
abstract = {Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.},
language = {en}
}
@article{GodecMetzler2013,
author = {Godec, Aljaz and Metzler, Ralf},
title = {Finite-Time effects and ultraweak ergodicity breaking in superdiffusive dynamics},
series = {Physical review letters},
volume = {110},
journal = {Physical review letters},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.110.020603},
pages = {5},
year = {2013},
abstract = {We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement (delta x(2)) over bar around the ensemble value 3 - alpha (1 < alpha < 2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of (delta x(2)) over bar over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.},
language = {en}
}
@article{SchulzBarkaiMetzler2013,
author = {Schulz, Johannes H. P. and Barkai, Eli and Metzler, Ralf},
title = {Aging effects and population splitting in single-particle trajectoryaverages},
series = {Physical review letters},
volume = {110},
journal = {Physical review letters},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.110.020602},
pages = {5},
year = {2013},
abstract = {We study time averages of single particle trajectories in scale-free anomalous diffusion processes, in which the measurement starts at some time t(a) > 0 after initiation of the process at t = 0. Using aging renewal theory, we show that for such nonstationary processes a large class of observables are affected by a unique aging function, which is independent of boundary conditions or the external forces. Moreover, we discuss the implications of aging induced population splitting: with growing age ta of the process, an increasing fraction of particles remains motionless in a measurement of fixed duration. Consequences for single biomolecule tracking in live cells are discussed.},
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{VahabiSchulzShokrietal.2013,
author = {Vahabi, Mahsa and Schulz, Johannes H. P. and Shokri, Babak and Metzler, Ralf},
title = {Area coverage of radial Levy flights with periodic boundary conditions},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {87},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {4},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.87.042136},
pages = {10},
year = {2013},
abstract = {We consider the area coverage of radial Levy flights in a finite square area with periodic boundary conditions. From simulations we show how the fractal path dimension d(f) and thus the degree of area coverage depends on the number of steps of the trajectory, the size of the area, and the resolution of the applied box counting algorithm. For sufficiently long trajectories and not too high resolution, the fractal dimension returned by the box counting method equals two, and in that sense the Levy flight fully covers the area. Otherwise, the determined fractal dimension equals the stable index of the distribution of jump lengths of the Levy flight. We provide mathematical expressions for the turnover between these two scaling regimes. As complementary methods to analyze confined Levy flights we investigate fractional order moments of the position for which we also provide scaling arguments. Finally, we study the time evolution of the probability density function and the first passage time density of Levy flights in a square area. Our findings are of interest for a general understanding of Levy flights as well as for the analysis of recorded trajectories of animals searching for food or for human motion patterns.},
language = {en}
}
@article{JeonLeijnseOddershedeetal.2013,
author = {Jeon, Jae-Hyung and Leijnse, Natascha and Oddershede, Lene B. and Metzler, Ralf},
title = {Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions},
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 = {4},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1367-2630},
doi = {10.1088/1367-2630/15/4/045011},
pages = {16},
year = {2013},
abstract = {We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that the polystyrene tracer beads of size 0.52-2.5 mu m after short-time normal diffusion turn over to perform anomalous diffusion of the form < r(2)(t)> similar or equal to t(alpha) with alpha approximate to 0.3. This free anomalous diffusion is ergodic and consistent with a description in terms of the generalized Langevin equation with a power-law memory kernel. With optical tweezers tracking, we unveil a power-law relaxation over several decades in time to the thermal plateau value under the confinement of the harmonic tweezer potential, as predicted previously (Phys. Rev. E 85 021147 (2012)). After the subdiffusive motion in the millisecond range, the motion becomes faster and turns either back to normal Brownian diffusion or to even faster superdiffusion, depending on the size of the tracer beads.},
language = {en}
}
@article{MaityBandyopadhyayChattopadhyayetal.2013,
author = {Maity, Alok Kumar and Bandyopadhyay, Arnab and Chattopadhyay, Sudip and Chaudhuri, Jyotipratim Ray and Metzler, Ralf and Chaudhury, Pinaki and Banik, Suman K.},
title = {Quantification of noise in bifunctionality-induced post-translational modification},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {88},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {3},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.88.032716},
pages = {7},
year = {2013},
abstract = {We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of a bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase, and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation. The resultant analytical expression of phosphorylated response regulators are then used to quantify the noise profile of biologically motivated single and branched pathways. Enhancement and reduction of noise in terms of extra phosphate outflux and influx, respectively, have been analyzed for the branched system. Furthermore, the role of fluctuations of the network output in the regulation of a promoter with random activation-deactivation dynamics has been analyzed.},
language = {en}
}
@article{JeonBarkaiMetzler2013,
author = {Jeon, Jae-Hyung and Barkai, Eli and Metzler, Ralf},
title = {Noisy continuous time random walks},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {139},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {12},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606},
doi = {10.1063/1.4816635},
pages = {15},
year = {2013},
abstract = {Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.},
language = {en}
}
@article{SchulzChechkinMetzler2013,
author = {Schulz, Johannes H. P. and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Correlated continuous time random walks - combining scale-invariance with long-range memory for spatial and temporal dynamics},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {46},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {47},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8113/46/47/475001},
pages = {22},
year = {2013},
abstract = {Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through scale-free forms of the jump length and/or waiting time distributions by virtue of the generalized central limit theorem. Here we present a modified version of recently proposed correlated CTRW processes, where we incorporate a power-law correlated noise on the level of both jump length and waiting time dynamics. We obtain a very general stochastic model, that encompasses key features of several paradigmatic models of anomalous diffusion: discontinuous, scale-free displacements as in Levy flights, scale-free waiting times as in subdiffusive CTRWs, and the long-range temporal correlations of fractional Brownian motion (FBM). We derive the exact solutions for the single-time probability density functions and extract the scaling behaviours. Interestingly, we find that different combinations of the model parameters lead to indistinguishable shapes of the emerging probability density functions and identical scaling laws. Our model will be useful for describing recent experimental single particle tracking data that feature a combination of CTRW and FBM properties.},
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{LomholtLizanaMetzleretal.2013,
author = {Lomholt, Michael A. and Lizana, Ludvig and Metzler, Ralf and Ambjoernsson, Tobias},
title = {Microscopic origin of the logarithmic time evolution of aging processes in complex systems},
series = {Physical review letters},
volume = {110},
journal = {Physical review letters},
number = {20},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.110.208301},
pages = {5},
year = {2013},
abstract = {There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time tau between clock ticks follows the waiting time density psi (tau). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by psi (tau). For power-law forms psi (tau) similar or equal to tau(-1-alpha) (0 < alpha < 1) we obtain a logarithmic time evolution of the state number < n(t)> similar or equal to log(t/t(0)), while for alpha > 2 the process becomes normal in the sense that < n(t)> similar or equal to t. In the intermediate range 1 < alpha < 2 we find the power-law growth < n(t)> similar or equal to t(alpha-1). Our model provides a universal description for transition dynamics between aging and nonaging states.},
language = {en}
}
@article{PulkkinenMetzler2013,
author = {Pulkkinen, Otto and Metzler, Ralf},
title = {Distance matters the impact of gene proximity in bacterial gene regulation},
series = {Physical review letters},
volume = {110},
journal = {Physical review letters},
number = {19},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.110.198101},
pages = {5},
year = {2013},
abstract = {Following recent discoveries of colocalization of downstream-regulating genes in living cells, the impact of the spatial distance between such genes on the kinetics of gene product formation is increasingly recognized. We here show from analytical and numerical analysis that the distance between a transcription factor (TF) gene and its target gene drastically affects the speed and reliability of transcriptional regulation in bacterial cells. For an explicit model system, we develop a general theory for the interactions between a TF and a transcription unit. The observed variations in regulation efficiency are linked to the magnitude of the variation of the TF concentration peaks as a function of the binding site distance from the signal source. Our results support the role of rapid binding site search for gene colocalization and emphasize the role of local concentration differences.},
language = {en}
}
@article{JeonMetzler2012,
author = {Jeon, Jae-Hyung and Metzler, Ralf},
title = {Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {85},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.85.021147},
pages = {8},
year = {2012},
abstract = {Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.},
language = {en}
}
@article{PalyulinMetzler2012,
author = {Palyulin, Vladimir V. and Metzler, Ralf},
title = {How a finite potential barrier decreases the mean first-passage time},
series = {Journal of statistical mechanics: theory and experiment},
journal = {Journal of statistical mechanics: theory and experiment},
number = {1},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1742-5468},
doi = {10.1088/1742-5468/2012/03/L03001},
pages = {10},
year = {2012},
abstract = {We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.},
language = {en}
}
@article{GodecBauerMetzler2014,
author = {Godec, Aljaz and Bauer, Maximilian and Metzler, Ralf},
title = {Collective dynamics effect transient subdiffusion of inert tracers in flexible gel networks},
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 = {10.1088/1367-2630/16/9/092002},
pages = {13},
year = {2014},
abstract = {Based on extensive Brownian dynamics simulations we study the thermal motion of a tracer bead in a cross-linked, flexible gel in the limit when the tracer particle size is comparable to or even larger than the equilibrium mesh size of the gel. The analysis of long individual trajectories of the tracer demonstrates the existence of pronounced transient anomalous diffusion. From the time averaged mean squared displacement and the time averaged van Hove correlation functions we elucidate the many-body origin of the non-Brownian tracer bead dynamics. Our results shed new light onto the ongoing debate over the physical origin of steric tracer interactions with structured environments.},
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{BlavatskaMetzler2015,
author = {Blavatska, Viktoria and Metzler, Ralf},
title = {Conformational properties of complex polymers: rosette versus star-like structures},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {48},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {13},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8113/48/13/135001},
pages = {14},
year = {2015},
abstract = {Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyse the size and shape characteristics of complex polymer structures, containing in general f(1) loops (petals) and f(2) linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius R-g and asphericity (A) over cap of typical conformation as functions of parameters f(1), f(2). In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight.},
language = {en}
}
@article{MagdziarzMetzlerSzczotkaetal.2012,
author = {Magdziarz, Marcin and Metzler, Ralf and Szczotka, Wladyslaw and Zebrowski, Piotr},
title = {Correlated continuous-time random walks-scaling limits and Langevin picture},
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 = {10.1088/1742-5468/2012/04/P04010},
pages = {18},
year = {2012},
abstract = {In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor. 43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces. Our results are confirmed by Monte Carlo simulations.},
language = {en}
}
@article{LeijnseJeonLoftetal.2012,
author = {Leijnse, N. and Jeon, J. -H. and Loft, S. and Metzler, Ralf and Oddershede, L. B.},
title = {Diffusion inside living human cells},
series = {European physical journal special topics},
volume = {204},
journal = {European physical journal special topics},
number = {1},
publisher = {Springer},
address = {Heidelberg},
issn = {1951-6355},
doi = {10.1140/epjst/e2012-01553-y},
pages = {75 -- 84},
year = {2012},
abstract = {Naturally occurring lipid granules diffuse in the cytoplasm and can be used as tracers to map out the viscoelastic landscape inside living cells. Using optical trapping and single particle tracking we found that lipid granules exhibit anomalous diffusion inside human umbilical vein endothelial cells. For these cells the exact diffusional pattern of a particular granule depends on the physiological state of the cell and on the localization of the granule within the cytoplasm. Granules located close to the actin rich periphery of the cell move less than those located towards to the center of the cell or within the nucleus. Also, granules in cells which are stressed by intense laser illumination or which have attached to a surface for a long period of time move in a more restricted fashion than those within healthy cells. For granules diffusing in healthy cells, in regions away from the cell periphery, occurrences of weak ergodicity breaking are observed, similar to the recent observations inside living fission yeast cells [1].},
language = {en}
}
@article{PalyulinChechkinMetzler2014,
author = {Palyulin, Vladimir V. and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias},
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 = {10.1088/1742-5468/2014/11/P11031},
pages = {32},
year = {2014},
abstract = {Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.},
language = {en}
}
@article{NezhadhaghighiChechkinMetzler2014,
author = {Nezhadhaghighi, M. Ghasemi and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Numerical approach to unbiased and driven generalized elastic model},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {140},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {2},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606},
doi = {10.1063/1.4858425},
pages = {9},
year = {2014},
abstract = {From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent beta characterizing the growth of the mean squared displacement <(delta h)(2)> of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.},
language = {en}
}
@article{PalyulinMetzler2014,
author = {Palyulin, Vladimir V. and Metzler, Ralf},
title = {Speeding up the first-passage for subdiffusion by introducing a finite potential barrier},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {47},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {3},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8113/47/3/032002},
pages = {13},
year = {2014},
abstract = {We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation.},
language = {en}
}
@article{RevereyJeonBaoetal.2015,
author = {Reverey, Julia F. and Jeon, Jae-Hyung and Bao, Han and Leippe, Matthias and Metzler, Ralf and Selhuber-Unkel, Christine},
title = {Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii},
series = {Scientific reports},
volume = {5},
journal = {Scientific reports},
publisher = {Nature Publ. Group},
address = {London},
issn = {2045-2322},
doi = {10.1038/srep11690},
pages = {14},
year = {2015},
abstract = {Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.},
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{MagdziarzMetzlerSzczotkaetal.2012,
author = {Magdziarz, Marcin and Metzler, Ralf and Szczotka, Wladyslaw and Zebrowski, Piotr},
title = {Correlated continuous-time random walks in external force fields},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {85},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {5},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.85.051103},
pages = {5},
year = {2012},
abstract = {We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T-i is equal to the previous waiting time Ti-1 plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.},
language = {en}
}
@article{BauerMetzler2012,
author = {Bauer, Maximilian and Metzler, Ralf},
title = {Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states},
series = {Biophysical journal},
volume = {102},
journal = {Biophysical journal},
number = {10},
publisher = {Cell Press},
address = {Cambridge},
issn = {0006-3495},
doi = {10.1016/j.bpj.2012.04.008},
pages = {2321 -- 2330},
year = {2012},
abstract = {Transcription factors (TFs) such as the lac repressor find their target sequence on DNA at remarkably high rates. In the established Berg-von Hippel model for this search process, the TF alternates between three-dimensional diffusion in the bulk solution and one-dimensional sliding along the DNA chain. To overcome the so-called speed-stability paradox, in similar models the TF was considered as being present in two conformations (search state and recognition state) between which it switches stochastically. Combining both the facilitated diffusion model and alternating states, we obtain a generalized model. We explicitly treat bulk excursions for rodlike chains arranged in parallel and consider a simplified model for coiled DNA. Compared to previously considered facilitated diffusion models, corresponding to limiting cases of our generalized model, we surprisingly find a reduced target search rate. Moreover, at optimal conditions there is no longer an equipartition between the time spent by the protein on and off the DNA chain.},
language = {en}
}
@article{AbdolvahabMetzlerEjtehadi2011,
author = {Abdolvahab, Rouhollah Haji and Metzler, Ralf and Ejtehadi, Mohammad Reza},
title = {First passage time distribution of chaperone driven polymer translocation through a nanopore homopolymer and heteropolymer cases},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {135},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {24},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606},
doi = {10.1063/1.3669427},
pages = {8},
year = {2011},
abstract = {Combining the advection-diffusion equation approach with Monte Carlo simulations we study chaperone driven polymer translocation of a stiff polymer through a nanopore. We demonstrate that the probability density function of first passage times across the pore depends solely on the Peclet number, a dimensionless parameter comparing drift strength and diffusivity. Moreover it is shown that the characteristic exponent in the power-law dependence of the translocation time on the chain length, a function of the chaperone-polymer binding energy, the chaperone concentration, and the chain length, is also effectively determined by the Peclet number. We investigate the effect of the chaperone size on the translocation process. In particular, for large chaperone size, the translocation progress and the mean waiting time as function of the reaction coordinate exhibit pronounced sawtooth-shapes. The effects of a heterogeneous polymer sequence on the translocation dynamics is studied in terms of the translocation velocity, the probability distribution for the translocation progress, and the monomer waiting times. (C) 2011 American Institute of Physics.},
language = {en}
}
@article{SandersLomholtLizanaetal.2014,
author = {Sanders, Lloyd P. and Lomholt, Michael A. and Lizana, Ludvig and Fogelmark, Karl and Metzler, Ralf and Ambjoernsson, Tobias},
title = {Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion},
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 = {10.1088/1367-2630/16/11/113050},
pages = {14},
year = {2014},
abstract = {Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.},
language = {en}
}
@article{MetzlerSandersLomholtetal.2014,
author = {Metzler, Ralf and Sanders, L. and Lomholt, M. A. and Lizana, L. and Fogelmark, K. and Ambjoernsson, Tobias},
title = {Ageing single file motion},
series = {The European physical journal},
volume = {223},
journal = {The European physical journal},
number = {14},
publisher = {Springer},
address = {Heidelberg},
issn = {1951-6355},
doi = {10.1140/epjst/e2014-02333-5},
pages = {3287 -- 3293},
year = {2014},
language = {en}
}
@article{GodecMetzler2015,
author = {Godec, Aljaz and Metzler, Ralf},
title = {Optimization and universality of Brownian search in a basic model of quenched heterogeneous media},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {91},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {5},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.91.052134},
pages = {17},
year = {2015},
abstract = {The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time ( MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.},
language = {en}
}
@article{BarkaiGariniMetzler2012,
author = {Barkai, Eli and Garini, Yuval and Metzler, Ralf},
title = {Strange Kinetics of single molecules in living cells},
series = {Physics today},
volume = {65},
journal = {Physics today},
number = {8},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0031-9228},
pages = {29 -- 35},
year = {2012},
language = {en}
}
@article{AdamcikJeonKarczewskietal.2012,
author = {Adamcik, Jozef and Jeon, Jae-Hyung and Karczewski, Konrad J. and Metzler, Ralf and Dietler, Giovanni},
title = {Quantifying supercoiling-induced denaturation bubbles in DNA},
series = {Soft matter},
volume = {8},
journal = {Soft matter},
number = {33},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1744-683X},
doi = {10.1039/c2sm26089a},
pages = {8651 -- 8658},
year = {2012},
abstract = {In both eukaryotic and prokaryotic DNA sequences of 30-100 base-pairs rich in AT base-pairs have been identified at which the double helix preferentially unwinds. Such DNA unwinding elements are commonly associated with origins for DNA replication and transcription, and with chromosomal matrix attachment regions. Here we present a quantitative study of local DNA unwinding based on extensive single DNA plasmid imaging. We demonstrate that long-lived single-stranded denaturation bubbles exist in negatively supercoiled DNA, at the expense of partial twist release. Remarkably, we observe a linear relation between the degree of supercoiling and the bubble size, in excellent agreement with statistical modelling. Furthermore, we obtain the full distribution of bubble sizes and the opening probabilities at varying salt and temperature conditions. The results presented herein underline the important role of denaturation bubbles in negatively supercoiled DNA for biological processes such as transcription and replication initiation in vivo.},
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{JeonMonneJavanainenetal.2012,
author = {Jeon, Jae-Hyung and Monne, Hector Martinez-Seara and Javanainen, Matti and Metzler, Ralf},
title = {Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins},
series = {Physical review letters},
volume = {109},
journal = {Physical review letters},
number = {18},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.109.188103},
pages = {5},
year = {2012},
abstract = {Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.},
language = {en}
}
@article{JavanainenHammarenMonticellietal.2013,
author = {Javanainen, Matti and Hammaren, Henrik and Monticelli, Luca and Jeon, Jae-Hyung and Miettinen, Markus S. and Martinez-Seara, Hector and Metzler, Ralf and Vattulainen, Ilpo},
title = {Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes},
series = {Faraday discussions},
volume = {161},
journal = {Faraday discussions},
number = {1},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1359-6640},
doi = {10.1039/c2fd20085f},
pages = {397 -- 417},
year = {2013},
abstract = {Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concentration of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is observed to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent associated with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations associated with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically observed in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the physical limits of protein motion. Our results suggest that protein concentration is anything but constant in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.},
language = {en}
}
@article{MetzlerJeon2012,
author = {Metzler, Ralf and Jeon, Jae-Hyung},
title = {The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories},
series = {Physica scripta : an international journal for experimental and theoretical physics},
volume = {86},
journal = {Physica scripta : an international journal for experimental and theoretical physics},
number = {5},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {0031-8949},
doi = {10.1088/0031-8949/86/05/058510},
pages = {5},
year = {2012},
abstract = {Single-particle experiments produce time series x(t) of individual particle trajectories, frequently revealing anomalous diffusion behaviour. Typically, individual x(t) are evaluated in terms of time-averaged quantities instead of ensemble averages. Here we discuss the behaviour of the time-averaged mean squared displacement of different stochastic processes giving rise to anomalous diffusion. In particular, we pay attention to the ergodic properties of these processes, i.e. the (non)equivalence of time and ensemble averages.},
language = {en}
}
@article{GoychukKharchenkoMetzler2014,
author = {Goychuk, Igor and Kharchenko, Vasyl O. and Metzler, Ralf},
title = {How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport},
series = {PLoS one},
volume = {9},
journal = {PLoS one},
number = {3},
publisher = {PLoS},
address = {San Fransisco},
issn = {1932-6203},
doi = {10.1371/journal.pone.0091700},
pages = {7},
year = {2014},
abstract = {Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.},
language = {en}
}
@article{SchulzBarkaiMetzler2014,
author = {Schulz, Johannes H. P. and Barkai, Eli and Metzler, Ralf},
title = {Aging renewal theory and application to random walks},
series = {Physical review : X, Expanding access},
volume = {4},
journal = {Physical review : X, Expanding access},
number = {1},
publisher = {American Physical Society},
address = {College Park},
issn = {2160-3308},
doi = {10.1103/PhysRevX.4.011028},
pages = {24},
year = {2014},
abstract = {We discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long-time properties, this process exhibits aging: events counted initially in a time interval [0, t] statistically strongly differ from those observed at later times [t(a,) t(a) + t]. The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous-time random walk. By this, we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking, along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.},
language = {en}
}
@article{PalyulinChechkinMetzler2014,
author = {Palyulin, Vladimir V. and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Levy flights do not always optimize random blind search for sparse targets},
series = {Proceedings of the National Academy of Sciences of the United States of America},
volume = {111},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = {8},
publisher = {National Acad. of Sciences},
address = {Washington},
issn = {0027-8424},
doi = {10.1073/pnas.1320424111},
pages = {2931 -- 2936},
year = {2014},
abstract = {It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.},
language = {en}
}
@article{TalukderSenChakrabortietal.2014,
author = {Talukder, Srijeeta and Sen, Shrabani and Chakraborti, Prantik and Metzler, Ralf and Banik, Suman K. and Chaudhury, Pinaki},
title = {Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {140},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {12},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606},
doi = {10.1063/1.4869112},
pages = {10},
year = {2014},
abstract = {We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction epsilon(hb)(AT) for an AT base pair and the ring factor. turn out to be the most sensitive parameters. In addition, the stacking interaction epsilon(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization. (c) 2014 AIP Publishing LLC.},
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{EliazarMetzler2012,
author = {Eliazar, Iddo and Metzler, Ralf},
title = {The RARE model a generalized approach to random relaxation processes in disordered systems},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {137},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {23},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606},
doi = {10.1063/1.4770266},
pages = {9},
year = {2012},
abstract = {This paper introduces and analyses a general statistical model, termed the RAndom RElaxations (RARE) model, of random relaxation processes in disordered systems. The model considers excitations that are randomly scattered around a reaction center in a general embedding space. The model's input quantities are the spatial scattering statistics of the excitations around the reaction center, and the chemical reaction rates between the excitations and the reaction center as a function of their mutual distance. The framework of the RARE model is versatile and a detailed stochastic analysis of the random relaxation processes is established. Analytic results regarding the duration and the range of the random relaxation processes, as well as the model's thermodynamic limit, are obtained in closed form. In particular, the case of power-law inputs, which turn out to yield stretched exponential relaxation patterns and asymptotically Paretian relaxation ranges, is addressed in detail.},
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{KruesemannGodecMetzler2015,
author = {Kr{\"u}semann, Henning and Godec, Aljaz and Metzler, Ralf},
title = {Ageing first passage time density in continuous time random walks and quenched energy landscapes},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {48},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {28},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8113/48/28/285001},
pages = {20},
year = {2015},
abstract = {We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function Psi (t) similar or equal to t(-1-alpha) (0 <= alpha <= 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t(a), the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < alpha < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < alpha < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.},
language = {en}
}
@article{BauerRasmussenLomholtetal.2015,
author = {Bauer, Maximilian and Rasmussen, Emil S. and Lomholt, Michael A. and Metzler, Ralf},
title = {Real sequence effects on the search dynamics of transcription factors on DNA},
series = {Scientific reports},
volume = {5},
journal = {Scientific reports},
publisher = {Nature Publ. Group},
address = {London},
issn = {2045-2322},
doi = {10.1038/srep10072},
pages = {13},
year = {2015},
abstract = {Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.},
language = {en}
}
@article{GodecChechkinBarkaietal.2014,
author = {Godec, Aljaz and Chechkin, Aleksei V. and Barkai, Eli and Kantz, Holger and Metzler, Ralf},
title = {Localisation and universal fluctuations in ultraslow diffusion processes},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {47},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {49},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113},
doi = {10.1088/1751-8113/47/49/492002},
pages = {10},
year = {2014},
abstract = {We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.},
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}
}
@article{ShinCherstvyMetzler2014,
author = {Shin, Jaeoh and Cherstvy, Andrey G. and Metzler, Ralf},
title = {Sensing viruses by mechanical tension of DNA in responsive hydrogels},
series = {Physical review : X, Expanding access},
volume = {4},
journal = {Physical review : X, Expanding access},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {2160-3308},
doi = {10.1103/PhysRevX.4.021002},
pages = {13},
year = {2014},
abstract = {The rapid worldwide spread of severe viral infections, often involving novel mutations of viruses, poses major challenges to our health-care systems. This means that tools that can efficiently and specifically diagnose viruses are much needed. To be relevant for broad applications in local health-care centers, such tools should be relatively cheap and easy to use. In this paper, we discuss the biophysical potential for the macroscopic detection of viruses based on the induction of a mechanical stress in a bundle of prestretched DNA molecules upon binding of viruses to the DNA. We show that the affinity of the DNA to the charged virus surface induces a local melting of the double helix into two single-stranded DNA. This process effects a mechanical stress along the DNA chains leading to an overall contraction of the DNA. Our results suggest that when such DNA bundles are incorporated in a supporting matrix such as a responsive hydrogel, the presence of viruses may indeed lead to a significant, macroscopic mechanical deformation of the matrix. We discuss the biophysical basis for this effect and characterize the physical properties of the associated DNA melting transition. In particular, we reveal several scaling relations between the relevant physical parameters of the system. We promote this DNA-based assay as a possible tool for efficient and specific virus screening.},
language = {en}
}
@article{KruesemannGodecMetzler2014,
author = {Kr{\"u}semann, Henning and Godec, Aljaz and Metzler, Ralf},
title = {First-passage statistics for aging diffusion in systems with annealed and quenched disorder},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {89},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {4},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755},
doi = {10.1103/PhysRevE.89.040101},
pages = {5},
year = {2014},
abstract = {Aging, the dependence of the dynamics of a physical process on the time t(a) since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first-passage dynamics. We find that for an aging continuous time random walk process, the scaling exponent of the density of first-passage times changes twice as the aging progresses and reveals an intermediate scaling regime. The first-passage dynamics depends on t(a) differently for intermediate and strong aging. Similar crossovers are obtained for the first-passage dynamics for a confined and driven particle. Comparison to the motion of an aged particle in the quenched trap model with a bias shows excellent agreement with our analytical findings. Our results demonstrate how first-passage measurements can be used to unravel the age t(a) of a physical system.},
language = {en}
}
@article{SereshkiLomholtMetzler2012,
author = {Sereshki, L. E. and Lomholt, M. A. and Metzler, Ralf},
title = {A solution to the subdiffusion-efficiency paradox inactive states enhance reaction efficiency at subdiffusion conditions in living cells},
series = {epl : a letters journal exploring the frontiers of physics},
volume = {97},
journal = {epl : a letters journal exploring the frontiers of physics},
number = {2},
publisher = {EDP Sciences},
address = {Mulhouse},
issn = {0295-5075},
doi = {10.1209/0295-5075/97/20008},
pages = {6},
year = {2012},
abstract = {Macromolecular crowding in living biological cells effects subdiffusion of larger biomolecules such as proteins and enzymes. Mimicking this subdiffusion in terms of random walks on a critical percolation cluster, we here present a case study of EcoRV restriction enzymes involved in vital cellular defence. We show that due to its so far elusive propensity to an inactive state the enzyme avoids non-specific binding and remains well-distributed in the bulk cytoplasm of the cell. Despite the reduced volume exploration capability of subdiffusion processes, this mechanism guarantees a high efficiency of the enzyme. By variation of the non-specific binding constant and the bond occupation probability on the percolation network, we demonstrate that reduced nonspecific binding are beneficial for efficient subdiffusive enzyme activity even in relatively small bacteria cells. Our results corroborate a more local picture of cellular regulation.},
language = {en}
}
@article{GhoshCherstvyMetzler2014,
author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Metzler, Ralf},
title = {Deformation propagation in responsive polymer network films},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {141},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {7},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606},
doi = {10.1063/1.4893056},
pages = {9},
year = {2014},
abstract = {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.},
language = {en}
}
@article{GoychukKharchenkoMetzler2014,
author = {Goychuk, Igor and Kharchenko, Vasyl O. and Metzler, Ralf},
title = {Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion},
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 = {31},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1463-9076},
doi = {10.1039/c4cp01234h},
pages = {16524 -- 16535},
year = {2014},
abstract = {The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.},
language = {en}
}
@article{PulkkinenMetzler2015,
author = {Pulkkinen, Otto and Metzler, Ralf},
title = {Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation},
series = {Scientific reports},
volume = {5},
journal = {Scientific reports},
publisher = {Nature Publ. Group},
address = {London},
issn = {2045-2322},
doi = {10.1038/srep17820},
pages = {11},
year = {2015},
abstract = {Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E. coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.},
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 = {10},
journal = {Soft matter},
number = {10},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1744-683X},
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}
}
@article{SposiniChechkinSenoetal.2018,
author = {Sposini, Vittoria and Chechkin, Aleksei V. and Seno, Flavio and Pagnini, Gianni and Metzler, Ralf},
title = {Random diffusivity from stochastic equations},
series = {New Journal of Physics},
journal = {New Journal of Physics},
publisher = {Deutsche Physikalische Gesellschaft / Institute of Physics},
address = {Bad Honnef und London},
issn = {1367-2630},
doi = {10.1088/1367-2630/aab696},
pages = {1 -- 33},
year = {2018},
abstract = {A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential(Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.},
language = {en}
}
@article{ŚlęzakMetzlerMagdziarz2018,
author = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
title = {Superstatistical generalised Langevin equation},
series = {New Journal of Physics},
volume = {20},
journal = {New Journal of Physics},
number = {023026},
publisher = {Deutsche Physikalische Gesellschaft / Institute of Physics},
address = {Bad Honnef und London},
issn = {1367-2630},
doi = {10.1088/1367-2630/aaa3d4},
pages = {1 -- 25},
year = {2018},
abstract = {Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.},
language = {en}
}
@article{PalyulinBlackburnLomholtetal.2019,
author = {Palyulin, Vladimir V and Blackburn, George and Lomholt, Michael A and Watkins, Nicholas W and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V.},
title = {First passage and first hitting times of L{\´e}vy flights and L{\´e}vy walks},
series = {New Journal of Physics},
volume = {21},
journal = {New Journal of Physics},
publisher = {Dt. Physikalische Ges.},
address = {Bad Honnef},
issn = {1367-2630},
doi = {10.1088/1367-2630/ab41bb},
pages = {24},
year = {2019},
abstract = {For both L{\´e}vy flight and L{\´e}vy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For L{\´e}vy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the L{\´e}vy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.},
language = {en}
}
@article{JeonJavanainenMartinezSearaetal.2016,
author = {Jeon, Jae-Hyung and Javanainen, Matti and Martinez-Seara, Hector and Metzler, Ralf and Vattulainen, Ilpo},
title = {Protein Crowding in Lipid Bilayers Gives Rise to Non-Gaussian Anomalous Lateral Diffusion of Phospholipids and Proteins},
series = {Physical review : X, Expanding access},
volume = {6},
journal = {Physical review : X, Expanding access},
publisher = {American Physical Society},
address = {College Park},
issn = {2160-3308},
doi = {10.1103/PhysRevX.6.021006},
pages = {17},
year = {2016},
abstract = {Biomembranes are exceptionally crowded with proteins with typical protein-to-lipid ratios being around 1:50 - 1:100. Protein crowding has a decisive role in lateral membrane dynamics as shown by recent experimental and computational studies that have reported anomalous lateral diffusion of phospholipids and membrane proteins in crowded lipid membranes. Based on extensive simulations and stochastic modeling of the simulated trajectories, we here investigate in detail how increasing crowding by membrane proteins reshapes the stochastic characteristics of the anomalous lateral diffusion in lipid membranes. We observe that correlated Gaussian processes of the fractional Langevin equation type, identified as the stochastic mechanism behind lipid motion in noncrowded bilayer, no longer adequately describe the lipid and protein motion in crowded but otherwise identical membranes. It turns out that protein crowding gives rise to a multifractal, non-Gaussian, and spatiotemporally heterogeneous anomalous lateral diffusion on time scales from nanoseconds to, at least, tens of microseconds. Our investigation strongly suggests that the macromolecular complexity and spatiotemporal membrane heterogeneity in cellular membranes play critical roles in determining the stochastic nature of the lateral diffusion and, consequently, the associated dynamic phenomena within membranes. Clarifying the exact stochastic mechanism for various kinds of biological membranes is an important step towards a quantitative understanding of numerous intramembrane dynamic phenomena.},
language = {en}
}
@article{GodecMetzler2016,
author = {Godec, Aljaz and Metzler, Ralf},
title = {First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time},
series = {Scientific reports},
volume = {6},
journal = {Scientific reports},
publisher = {Nature Publ. Group},
address = {London},
issn = {2045-2322},
doi = {10.1038/srep20349},
pages = {11},
year = {2016},
abstract = {The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening series of new results focusing mostly on the so-called mean and global first passage time (MFPT and GFPT, respectively) of such processes. Here we push the understanding of first passage processes one step further. For a simple heterogeneous system we derive rigorously the complete distribution of first passage times (FPTs). Our results demonstrate that the typical FPT significantly differs from the MFPT, which corresponds to the long time behaviour of the FPT distribution. Conversely, the short time behaviour is shown to correspond to trajectories connecting directly from the initial value to the target. Remarkably, we reveal a previously overlooked third characteristic time scale of the first passage dynamics mirroring brief excursion away from the target.},
language = {en}
}