@article{CherstvyMetzler2008,
  author    = {Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes},
  doi       = {10.1039/C3CP53056F},
  year      = {2008},
  abstract  = {We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.},
  language  = {en}
}
@article{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{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{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{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{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{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{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{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{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{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{ChechkinZaidLomholtetal.2012,
  author    = {Chechkin, Aleksei V. and Zaid, Irwin M. and Lomholt, Michael A. and Sokolov, Igor M. and Metzler, Ralf},
  title     = {Bulk-mediated diffusion on a planar surface full solution},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {86},
  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.86.041101},
  pages     = {11},
  year      = {2012},
  abstract  = {We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.},
  language  = {en}
}
@article{SandevMetzlerTomovski2012,
  author    = {Sandev, Trifce and Metzler, Ralf and Tomovski, Zivorad},
  title     = {Velocity and displacement correlation functions for fractional generalized Langevin equations},
  series = {Fractional calculus and applied analysis : an international journal for theory and applications},
  volume    = {15},
  journal   = {Fractional calculus and applied analysis : an international journal for theory and applications},
  number    = {3},
  publisher = {Versita},
  address   = {Warsaw},
  issn      = {1311-0454},
  doi       = {10.2478/s13540-012-0031-2},
  pages     = {426 -- 450},
  year      = {2012},
  abstract  = {We study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.},
  language  = {en}
}
@article{TomovskiSandevMetzleretal.2012,
  author    = {Tomovski, Zivorad and Sandev, Trifce and Metzler, Ralf and Dubbeldam, Johan},
  title     = {Generalized space-time fractional diffusion equation with composite fractional time derivative},
  series = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  volume    = {391},
  journal   = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  number    = {8},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2011.12.035},
  pages     = {2527 -- 2542},
  year      = {2012},
  abstract  = {We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).},
  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{TalukderSenMetzleretal.2013,
  author    = {Talukder, Srijeeta and Sen, Shrabani and Metzler, Ralf and Banik, Suman K. and Chaudhury, Pinaki},
  title     = {Stochastic optimization-based study of dimerization kinetics},
  series = {JOURNAL OF CHEMICAL SCIENCES},
  volume    = {125},
  journal   = {JOURNAL OF CHEMICAL SCIENCES},
  number    = {6},
  publisher = {INDIAN ACAD SCIENCES},
  address   = {BANGALORE},
  issn      = {0974-3626},
  pages     = {1619 -- 1627},
  year      = {2013},
  abstract  = {We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end, we study dimerization kinetics of protein as a model system. We follow the dimerization kinetics using a stochastic simulation algorithm and combine it with three different optimization techniques (genetic algorithm, simulated annealing and parallel tempering) to obtain the rate constants involved in each reaction step. We find good convergence of the numerical scheme to the rate constants of the process. We also perform a sensitivity test on the reaction kinetic parameters to see the relative effects of the parameters for the associated profile of the monomer/dimer distribution.},
  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}
}
@misc{BarkaiGariniMetzler2013,
  author    = {Barkai, Eli and Garini, Yuval and Metzler, Ralf},
  title     = {Electrostatic effects in living cells Reply},
  series = {PHYSICS TODAY},
  volume    = {66},
  journal   = {PHYSICS TODAY},
  number    = {7},
  publisher = {AMER INST PHYSICS},
  address   = {MELVILLE},
  issn      = {0031-9228},
  pages     = {11 -- 11},
  year      = {2013},
  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{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{ChechkinZaidLomholtetal.2013,
  author    = {Chechkin, Aleksei V. and Zaid, I. M. and Lomholt, M. A. and Sokolov, Igor M. and Metzler, Ralf},
  title     = {Bulk-mediated surface diffusion on a cylinder in the fast exchange limit},
  series = {Mathematical modelling of natural phenomena},
  volume    = {8},
  journal   = {Mathematical modelling of natural phenomena},
  number    = {2},
  publisher = {EDP Sciences},
  address   = {Les Ulis},
  issn      = {0973-5348},
  doi       = {10.1051/mmnp/20138208},
  pages     = {114 -- 126},
  year      = {2013},
  abstract  = {In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.},
  language  = {en}
}
@article{MetzlerJeonCherstvyetal.2014,
  author    = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli},
  title     = {Anomalous diffusion models and their properties},
  series = {physical chemistry, chemical physics : PCCP},
  volume    = {2014},
  journal   = {physical chemistry, chemical physics : PCCP},
  number    = {16},
  issn      = {1463-9076},
  doi       = {10.1039/c4cp03465a},
  pages     = {24128 -- 24164},
  year      = {2014},
  abstract  = {Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.},
  language  = {en}
}
@article{CherstvyChechkinMetzler2014,
  author    = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity},
  series = {Soft matter},
  volume    = {2014},
  journal   = {Soft matter},
  number    = {10},
  publisher = {Royal Society of Chemistry},
  issn      = {2046-2069},
  doi       = {10.1039/c3sm52846d},
  pages     = {1591 -- 1601},
  year      = {2014},
  abstract  = {We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.},
  language  = {en}
}
@article{PalyulinAlaNissilaMetzler2014,
  author    = {Palyulin, Vladimir V. and Ala-Nissila, Tapio and Metzler, Ralf},
  title     = {Polymer translocation: the first two decades and the recent diversification},
  series = {Soft matter},
  volume    = {45},
  journal   = {Soft matter},
  number    = {10},
  editor    = {Metzler, Ralf},
  publisher = {the Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1744-683X},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76266},
  pages     = {9016 -- 9037},
  year      = {2014},
  abstract  = {Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.},
  language  = {en}
}
@article{JeonChechkinMetzler2014,
  author    = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
  series = {Physical chemistry, chemical physics : PCCP},
  volume    = {30},
  journal   = {Physical chemistry, chemical physics : PCCP},
  number    = {16},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  doi       = {10.1039/C4CP02019G},
  pages     = {15811 -- 15817},
  year      = {2014},
  abstract  = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
  language  = {en}
}
@article{GhoshCherstvyMetzler2014,
  author    = {Ghosh, Surya K. and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Non-universal tracer diffusion in crowded media of non-inert obstacles},
  series = {Physical Chemistry Chemical Physics},
  volume    = {3},
  journal   = {Physical Chemistry Chemical Physics},
  number    = {17},
  editor    = {Metzler, Ralf},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  pages     = {1847 -- 1858},
  year      = {2014},
  abstract  = {We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer-obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer-obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer-crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.},
  language  = {en}
}
@article{ShinCherstvyMetzler2014,
  author    = {Shin, Jaeoh and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size},
  series = {Soft Matter},
  journal   = {Soft Matter},
  editor    = {Metzler, Ralf},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1744-683X},
  pages     = {472 -- 488},
  year      = {2014},
  abstract  = {The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.},
  language  = {en}
}
@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{BauerGodecMetzler2014,
  author    = {Bauer, Maximilian and Godec, Aljaz and Metzler, Ralf},
  title     = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations},
  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    = {13},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c3cp55160a},
  pages     = {6118 -- 6128},
  year      = {2014},
  abstract  = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda},
  language  = {en}
}
@article{JeonChechkinMetzler2014,
  author    = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
  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    = {30},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c4cp02019g},
  pages     = {15811 -- 15817},
  year      = {2014},
  abstract  = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < alpha < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
  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{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 <vertical bar delta h vertical bar(q)> 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}
}
@misc{PalyulinAlaNissilaMetzler2014,
  author    = {Palyulin, Vladimir V. and Ala-Nissila, Tapio and Metzler, Ralf},
  title     = {Polymer translocation: the first two decades and the recent diversification},
  series = {Soft matter},
  volume    = {10},
  journal   = {Soft matter},
  number    = {45},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1744-683X},
  doi       = {10.1039/c4sm01819b},
  pages     = {9016 -- 9037},
  year      = {2014},
  abstract  = {Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.},
  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}
}