TY - JOUR A1 - Jeon, Jae-Hyung A1 - Metzler, Ralf T1 - Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.021147 SN - 1539-3755 VL - 85 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Metzler, Ralf T1 - How a finite potential barrier decreases the mean first-passage time JF - Journal of statistical mechanics: theory and experiment N2 - 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. KW - diffusion Y1 - 2012 U6 - https://doi.org/10.1088/1742-5468/2012/03/L03001 SN - 1742-5468 IS - 1 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Magdziarz, Marcin A1 - Metzler, Ralf A1 - Szczotka, Wladyslaw A1 - Zebrowski, Piotr T1 - Correlated continuous-time random walks-scaling limits and Langevin picture JF - Journal of statistical mechanics: theory and experiment N2 - 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. KW - stochastic processes (theory) KW - diffusion Y1 - 2012 U6 - https://doi.org/10.1088/1742-5468/2012/04/P04010 SN - 1742-5468 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Leijnse, N. A1 - Jeon, J. -H. A1 - Loft, S. A1 - Metzler, Ralf A1 - Oddershede, L. B. T1 - Diffusion inside living human cells JF - European physical journal special topics N2 - 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]. Y1 - 2012 U6 - https://doi.org/10.1140/epjst/e2012-01553-y SN - 1951-6355 VL - 204 IS - 1 SP - 75 EP - 84 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Magdziarz, Marcin A1 - Metzler, Ralf A1 - Szczotka, Wladyslaw A1 - Zebrowski, Piotr T1 - Correlated continuous-time random walks in external force fields JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevE.85.051103 SN - 1539-3755 SN - 1550-2376 VL - 85 IS - 5 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Bauer, Maximilian A1 - Metzler, Ralf T1 - Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states JF - Biophysical journal N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1016/j.bpj.2012.04.008 SN - 0006-3495 VL - 102 IS - 10 SP - 2321 EP - 2330 PB - Cell Press CY - Cambridge ER - TY - JOUR A1 - Tomovski, Zivorad A1 - Sandev, Trifce A1 - Metzler, Ralf A1 - Dubbeldam, Johan T1 - Generalized space-time fractional diffusion equation with composite fractional time derivative JF - Physica : europhysics journal ; A, Statistical mechanics and its applications N2 - 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). KW - Fractional diffusion equation KW - Composite fractional derivative KW - Riesz-Feller fractional derivative KW - Mittag-Leffler functions KW - Fox H-function KW - Fractional moments KW - Asymptotic expansions KW - Grunwald-Letnikov approximation Y1 - 2012 U6 - https://doi.org/10.1016/j.physa.2011.12.035 SN - 0378-4371 SN - 1873-2119 VL - 391 IS - 8 SP - 2527 EP - 2542 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Barkai, Eli A1 - Garini, Yuval A1 - Metzler, Ralf T1 - Strange Kinetics of single molecules in living cells JF - Physics today Y1 - 2012 SN - 0031-9228 VL - 65 IS - 8 SP - 29 EP - 35 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Adamcik, Jozef A1 - Jeon, Jae-Hyung A1 - Karczewski, Konrad J. A1 - Metzler, Ralf A1 - Dietler, Giovanni T1 - Quantifying supercoiling-induced denaturation bubbles in DNA JF - Soft matter N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1039/c2sm26089a SN - 1744-683X VL - 8 IS - 33 SP - 8651 EP - 8658 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Jeon, Jae-Hyung A1 - Monne, Hector Martinez-Seara A1 - Javanainen, Matti A1 - Metzler, Ralf T1 - Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins JF - Physical review letters N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.109.188103 SN - 0031-9007 VL - 109 IS - 18 PB - American Physical Society CY - College Park ER -