@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{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{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{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{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{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{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{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{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{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} }