@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{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{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{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{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{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{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} }