@misc{ChechkinZaidLomholtetal.2013, author = {Chechkin, Aleksei V. and Zaid, Irwin M. and Lomholt, Michael A. and Sokolov, Igor M. and Metzler, Ralf}, title = {Bulk-mediated surface diffusion on a cylinder in the fast exchange limit}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe}, number = {593}, issn = {1866-8372}, doi = {10.25932/publishup-41548}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-415480}, 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{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{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{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{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{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{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{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{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} }