@article{CherstvyThapaMardoukhietal.2018,
  author    = {Cherstvy, Andrey G. and Thapa, Samudrajit and Mardoukhi, Yousof and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Time averages and their statistical variation for the Ornstein-Uhlenbeck process},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {98},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.98.022134},
  pages     = {15},
  year      = {2018},
  abstract  = {How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.},
  language  = {en}
}
@article{AydinerCherstvyMetzler2018,
  author    = {Aydiner, Ekrem and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Wealth distribution, Pareto law, and stretched exponential decay of money},
  series = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  volume    = {490},
  journal   = {Physica : europhysics journal ; A, Statistical mechanics and its applications},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2017.08.017},
  pages     = {278 -- 288},
  year      = {2018},
  abstract  = {We study by Monte Carlo simulations a kinetic exchange trading model for both fixed and distributed saving propensities of the agents and rationalize the person and wealth distributions. We show that the newly introduced wealth distribution - that may be more amenable in certain situations - features a different power-law exponent, particularly for distributed saving propensities of the agents. For open agent-based systems, we analyze the person and wealth distributions and find that the presence of trap agents alters their amplitude, leaving however the scaling exponents nearly unaffected. For an open system, we show that the total wealth - for different trap agent densities and saving propensities of the agents - decreases in time according to the classical Kohlrausch-Williams-Watts stretched exponential law. Interestingly, this decay does not depend on the trap agent density, but rather on saving propensities. The system relaxation for fixed and distributed saving schemes are found to be different.},
  language  = {en}
}
@misc{JavanainenMartinezSearaMetzleretal.2017,
  author    = {Javanainen, Matti and Martinez-Seara, Hector and Metzler, Ralf and Vattulainen, Ilpo Tapio},
  title     = {Diffusion of Proteins and Lipids in Protein-Rich Membranesa},
  series = {Biophysical journal},
  volume    = {114},
  journal   = {Biophysical journal},
  number    = {3},
  publisher = {Cell Press},
  address   = {Cambridge},
  issn      = {0006-3495},
  doi       = {10.1016/j.bpj.2017.11.3009},
  pages     = {551A -- 551A},
  year      = {2017},
  language  = {en}
}
@article{KrapfMarinariMetzleretal.2018,
  author    = {Krapf, Diego and Marinari, Enzo and Metzler, Ralf and Oshanin, Gleb and Xu, Xinran and Squarcini, Alessio},
  title     = {Power spectral density of a single Brownian trajectory},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {20},
  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/aaa67c},
  pages     = {30},
  year      = {2018},
  abstract  = {The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.},
  language  = {en}
}
@misc{GudowskaNowakLindenbergMetzler2017,
  author    = {Gudowska-Nowak, Ewa and Lindenberg, Katja and Metzler, Ralf},
  title     = {Preface: Marian Smoluchowski's 1916 paper—a century of inspiration},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {50},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {38},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aa8529},
  pages     = {8},
  year      = {2017},
  language  = {en}
}
@misc{PalyulinBlackburnLomholtetal.2019,
  author    = {Palyulin, Vladimir V and Blackburn, George and Lomholt, Michael A and Watkins, Nicholas W and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V.},
  title     = {First passage and first hitting times of L{\´e}vy flights and L{\´e}vy walks},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {785},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43983},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439832},
  pages     = {25},
  year      = {2019},
  abstract  = {For both L{\´e}vy flight and L{\´e}vy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For L{\´e}vy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the L{\´e}vy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.},
  language  = {en}
}
@misc{Metzler2020,
  author    = {Metzler, Ralf},
  title     = {Superstatistics and non-Gaussian diffusion},
  series = {The European physical journal special topics},
  volume    = {229},
  journal   = {The European physical journal special topics},
  number    = {5},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2020-900210-x},
  pages     = {711 -- 728},
  year      = {2020},
  abstract  = {Brownian motion and viscoelastic anomalous diffusion in homogeneous environments are intrinsically Gaussian processes. In a growing number of systems, however, non-Gaussian displacement distributions of these processes are being reported. The physical cause of the non-Gaussianity is typically seen in different forms of disorder. These include, for instance, imperfect "ensembles" of tracer particles, the presence of local variations of the tracer mobility in heteroegenous environments, or cases in which the speed or persistence of moving nematodes or cells are distributed. From a theoretical point of view stochastic descriptions based on distributed ("superstatistical") transport coefficients as well as time-dependent generalisations based on stochastic transport parameters with built-in finite correlation time are invoked. After a brief review of the history of Brownian motion and the famed Gaussian displacement distribution, we here provide a brief introduction to the phenomenon of non-Gaussianity and the stochastic modelling in terms of superstatistical and diffusing-diffusivity approaches.},
  language  = {en}
}
@misc{CherstvyMetzler2013,
  author    = {Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94468},
  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{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}
}
@misc{MetzlerJeonCherstvyetal.2014,
  author    = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli},
  title     = {Anomalous diffusion models and their properties},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74448},
  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}
}
@misc{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},
  number    = {168},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74021},
  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}
}
@misc{PalyulinAlaNissilaMetzler2014,
  author    = {Palyulin, Vladimir V. and Ala-Nissila, Tapio and Metzler, Ralf},
  title     = {Polymer translocation: the first two decades and the recent diversification},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76287},
  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{MetzlerBauerRasmussenetal.2015,
  author    = {Metzler, Ralf and Bauer, Maximilian and Rasmussen, Emil S. and Lomholt, Michael A.},
  title     = {Real sequence effects on the search dynamics of transcription factors on DNA},
  series = {Scientific Reports},
  volume    = {5},
  journal   = {Scientific Reports},
  number    = {10072},
  publisher = {Nature Publishing Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep10072},
  year      = {2015},
  abstract  = {Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.},
  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}
}
@misc{GhoshCherstvyMetzler2014,
  author    = {Ghosh, Surya K. and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Non-universal tracer diffusion in crowded media of non-inert obstacles},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77128},
  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}
}
@misc{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},
  publisher = {The Royal Society of Chemistry},
  address   = {Cambridge},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76961},
  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}
}