TY - JOUR
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces
BT - the nonlinear Poisson–Boltzmann approach
JF - New journal of physics : the open-access journal for physics
N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems.
KW - polyelectrolyte adsorption
KW - electrostatic interactions
KW - critical phenomena
KW - Debye screening
Y1 - 2016
U6 - http://dx.doi.org/10.1088/1367-2630/18/8/083037
SN - 1367-2630
VL - 18
PB - IOP Publ.
CY - London
ER -
TY - GEN
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces
BT - the nonlinear Poisson–Boltzmann approach
N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 292
KW - polyelectrolyte adsorption
KW - electrostatic interactions
KW - critical phenomena
KW - Debye screening
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100295
ER -
TY - JOUR
A1 - Bauer, Maximilian
A1 - Metzler, Ralf
T1 - In vivo facilitated diffusion model
JF - PLoS one
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1371/journal.pone.0053956
SN - 1932-6203 (print)
VL - 8
IS - 1
PB - PLoS
CY - San Fransisco
ER -
TY - JOUR
A1 - Godec, Aljaz
A1 - Metzler, Ralf
T1 - Finite-Time effects and ultraweak ergodicity breaking in superdiffusive dynamics
JF - Physical review letters
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1103/PhysRevLett.110.020603
SN - 0031-9007 (print)
VL - 110
IS - 2
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Schulz, Johannes H. P.
A1 - Barkai, Eli
A1 - Metzler, Ralf
T1 - Aging effects and population splitting in single-particle trajectoryaverages
JF - Physical review letters
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1103/PhysRevLett.110.020602
SN - 0031-9007 (print)
SN - 1079-7114 (online)
VL - 110
IS - 2
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Eliazar, Iddo
A1 - Metzler, Ralf
T1 - Anomalous statistics of random relaxations in random environments
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1103/PhysRevE.87.022141
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 87
IS - 2
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
JF - Journal of statistical mechanics: theory and experiment
N2 - Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.
KW - driven diffusive systems (theory)
KW - fluctuations (theory)
KW - stochastic processes (theory)
KW - diffusion
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1742-5468/2014/11/P11031
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Sanders, Lloyd P.
A1 - Lomholt, Michael A.
A1 - Lizana, Ludvig
A1 - Fogelmark, Karl
A1 - Metzler, Ralf
A1 - Ambjoernsson, Tobias
T1 - Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion
JF - New journal of physics : the open-access journal for physics
N2 - Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.
KW - single-file diffusion
KW - continuous time random walks
KW - ageing
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1367-2630/16/11/113050
SN - 1367-2630 (print)
VL - 16
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - GEN
A1 - Talukder, Srijeeta
A1 - Sen, Shrabani
A1 - Chakraborti, Prantik
A1 - Metzler, Ralf
A1 - Banik, Suman K.
A1 - Chaudhury, Pinaki
T1 - Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA
T2 - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction epsilon(hb)(AT) for an AT base pair and the ring factor. turn out to be the most sensitive parameters. In addition, the stacking interaction epsilon(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization.
Y1 - 2014
U6 - http://dx.doi.org/10.1063/1.4871297
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 140
IS - 14
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Krüsemann, Henning
A1 - Godec, Aljaz
A1 - Metzler, Ralf
T1 - First-passage statistics for aging diffusion in systems with annealed and quenched disorder
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - Aging, the dependence of the dynamics of a physical process on the time t(a) since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first-passage dynamics. We find that for an aging continuous time random walk process, the scaling exponent of the density of first-passage times changes twice as the aging progresses and reveals an intermediate scaling regime. The first-passage dynamics depends on t(a) differently for intermediate and strong aging. Similar crossovers are obtained for the first-passage dynamics for a confined and driven particle. Comparison to the motion of an aged particle in the quenched trap model with a bias shows excellent agreement with our analytical findings. Our results demonstrate how first-passage measurements can be used to unravel the age t(a) of a physical system.
Y1 - 2014
U6 - http://dx.doi.org/10.1103/PhysRevE.89.040101
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 89
IS - 4
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Sensing viruses by mechanical tension of DNA in responsive hydrogels
JF - Physical review : X, Expanding access
N2 - The rapid worldwide spread of severe viral infections, often involving novel mutations of viruses, poses major challenges to our health-care systems. This means that tools that can efficiently and specifically diagnose viruses are much needed. To be relevant for broad applications in local health-care centers, such tools should be relatively cheap and easy to use. In this paper, we discuss the biophysical potential for the macroscopic detection of viruses based on the induction of a mechanical stress in a bundle of prestretched DNA molecules upon binding of viruses to the DNA. We show that the affinity of the DNA to the charged virus surface induces a local melting of the double helix into two single-stranded DNA. This process effects a mechanical stress along the DNA chains leading to an overall contraction of the DNA. Our results suggest that when such DNA bundles are incorporated in a supporting matrix such as a responsive hydrogel, the presence of viruses may indeed lead to a significant, macroscopic mechanical deformation of the matrix. We discuss the biophysical basis for this effect and characterize the physical properties of the associated DNA melting transition. In particular, we reveal several scaling relations between the relevant physical parameters of the system. We promote this DNA-based assay as a possible tool for efficient and specific virus screening.
Y1 - 2014
U6 - http://dx.doi.org/10.1103/PhysRevX.4.021002
SN - 2160-3308 (print)
VL - 4
IS - 2
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Talukder, Srijeeta
A1 - Sen, Shrabani
A1 - Chakraborti, Prantik
A1 - Metzler, Ralf
A1 - Banik, Suman K.
A1 - Chaudhury, Pinaki
T1 - Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction epsilon(hb)(AT) for an AT base pair and the ring factor. turn out to be the most sensitive parameters. In addition, the stacking interaction epsilon(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization. (c) 2014 AIP Publishing LLC.
Y1 - 2014
U6 - http://dx.doi.org/10.1063/1.4869112
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 140
IS - 12
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
JF - New journal of physics : the open-access journal for physics
N2 - We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.
Y1 - 2013
U6 - http://dx.doi.org/10.1088/1367-2630/15/8/083039
SN - 1367-2630 (print)
VL - 15
IS - 15
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - GEN
A1 - Barkai, Eli
A1 - Garini, Yuval
A1 - Metzler, Ralf
T1 - Electrostatic effects in living cells Reply
T2 - PHYSICS TODAY
Y1 - 2013
SN - 0031-9228
(print)
SN - 1945-0699
(online)
VL - 66
IS - 7
SP - 11
EP - 11
PB - AMER INST PHYSICS
CY - MELVILLE
ER -
TY - JOUR
A1 - Metzler, Ralf
A1 - Jeon, Jae-Hyung
T1 - The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories
JF - Physica scripta : an international journal for experimental and theoretical physics
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1088/0031-8949/86/05/058510
SN - 0031-8949 (print)
VL - 86
IS - 5
PB - IOP Publ. Ltd.
CY - Bristol
ER -
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 - http://dx.doi.org/10.1103/PhysRevE.85.021147
SN - 1539-3755 (print)
VL - 85
IS - 2
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Schulz, Johannes H. P.
A1 - Barkai, Eli
A1 - Metzler, Ralf
T1 - Aging renewal theory and application to random walks
JF - Physical review : X, Expanding access
N2 - We discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long-time properties, this process exhibits aging: events counted initially in a time interval [0, t] statistically strongly differ from those observed at later times [t(a,) t(a) + t]. The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous-time random walk. By this, we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking, along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.
Y1 - 2014
U6 - http://dx.doi.org/10.1103/PhysRevX.4.011028
SN - 2160-3308 (print)
VL - 4
IS - 1
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Levy flights do not always optimize random blind search for sparse targets
JF - Proceedings of the National Academy of Sciences of the United States of America
N2 - It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.
KW - search optimization
KW - stochastic processes
KW - Levy foraging hypothesis
Y1 - 2014
U6 - http://dx.doi.org/10.1073/pnas.1320424111
SN - 0027-8424 (print)
VL - 111
IS - 8
SP - 2931
EP - 2936
PB - National Acad. of Sciences
CY - Washington
ER -
TY - JOUR
A1 - Goychuk, Igor
A1 - Kharchenko, Vasyl O.
A1 - Metzler, Ralf
T1 - How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport
JF - PLoS one
N2 - Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.
Y1 - 2014
U6 - http://dx.doi.org/10.1371/journal.pone.0091700
SN - 1932-6203 (print)
VL - 9
IS - 3
PB - PLoS
CY - San Fransisco
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 - http://dx.doi.org/10.1016/j.bpj.2012.04.008
SN - 0006-3495 (print)
VL - 102
IS - 10
SP - 2321
EP - 2330
PB - Cell Press
CY - Cambridge
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 - http://dx.doi.org/10.1103/PhysRevE.85.051103
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 85
IS - 5
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Abdolvahab, Rouhollah Haji
A1 - Metzler, Ralf
A1 - Ejtehadi, Mohammad Reza
T1 - First passage time distribution of chaperone driven polymer translocation through a nanopore homopolymer and heteropolymer cases
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - Combining the advection-diffusion equation approach with Monte Carlo simulations we study chaperone driven polymer translocation of a stiff polymer through a nanopore. We demonstrate that the probability density function of first passage times across the pore depends solely on the Peclet number, a dimensionless parameter comparing drift strength and diffusivity. Moreover it is shown that the characteristic exponent in the power-law dependence of the translocation time on the chain length, a function of the chaperone-polymer binding energy, the chaperone concentration, and the chain length, is also effectively determined by the Peclet number. We investigate the effect of the chaperone size on the translocation process. In particular, for large chaperone size, the translocation progress and the mean waiting time as function of the reaction coordinate exhibit pronounced sawtooth-shapes. The effects of a heterogeneous polymer sequence on the translocation dynamics is studied in terms of the translocation velocity, the probability distribution for the translocation progress, and the monomer waiting times. (C) 2011 American Institute of Physics.
Y1 - 2011
U6 - http://dx.doi.org/10.1063/1.3669427
SN - 0021-9606 (print)
VL - 135
IS - 24
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Ageing and confinement in non-ergodic heterogeneous diffusion processes
JF - Journal of physics : A, Mathematical and theoretical
N2 - We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.
KW - stochastic processes
KW - anomalous diffusion
KW - ageing
KW - weak ergodicity breaking
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1751-8113/47/48/485002
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 47
IS - 48
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Godec, Aljaz
A1 - Chechkin, Aleksei V.
A1 - Barkai, Eli
A1 - Kantz, Holger
A1 - Metzler, Ralf
T1 - Localisation and universal fluctuations in ultraslow diffusion processes
JF - Journal of physics : A, Mathematical and theoretical
N2 - We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.
KW - Sinai diffusion
KW - anomalous diffusion
KW - quenched energy landscape
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1751-8113/47/49/492002
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 47
IS - 49
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Metzler, Ralf
A1 - Sanders, L.
A1 - Lomholt, M. A.
A1 - Lizana, L.
A1 - Fogelmark, K.
A1 - Ambjoernsson, Tobias
T1 - Ageing single file motion
JF - The European physical journal
Y1 - 2014
U6 - http://dx.doi.org/10.1140/epjst/e2014-02333-5
SN - 1951-6355 (print)
SN - 1951-6401 (online)
VL - 223
IS - 14
SP - 3287
EP - 3293
PB - Springer
CY - Heidelberg
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Mixing and segregation of ring polymers: spatial confinement and molecular crowding effects
JF - New journal of physics : the open-access journal for physics
N2 - During the life cycle of bacterial cells the non-mixing of the two ring-shaped daughter genomes is an important prerequisite for the cell division process. Mimicking the environments inside highly crowded biological cells, we study the dynamics and statistical behavior of two flexible ring polymers in the presence of cylindrical confinement and crowding molecules. From extensive computer simulations we determine the degree of ring-ring overlap and the number of inter-monomer contacts for varying volume fractions phi of crowders. We also examine the entropic demixing of polymer rings in the presence of mobile crowders and determine the characteristic times of the internal polymer dynamics. Effects of the ring length on ring-ring overlap are also analyzed. In particular, on systematic variation of the fraction of crowding molecules, a (1 - phi)-scaling is found for the ring-ring overlap length along the cylinder axis, and a non-monotonic dependence of the 3D ring-ring contact number with a maximum at phi approximate to 0.2 is obtained. Our results demonstrate that polymer rings are demixed and separated by particular entropy-favourable partitioning of crowders along the axis of the cylindrical simulation box. These findings help to rationalize the implications of macromolecular crowding for circular DNA molecules in confined spaces inside bacteria as well as in localized cellular compartments inside eukaryotic cells.
KW - polymers
KW - confinement
KW - crowding
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1367-2630/16/5/053047
SN - 1367-2630 (print)
VL - 16
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Vahabi, Mahsa
A1 - Schulz, Johannes H. P.
A1 - Shokri, Babak
A1 - Metzler, Ralf
T1 - Area coverage of radial Levy flights with periodic boundary conditions
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1103/PhysRevE.87.042136
SN - 1539-3755 (print)
VL - 87
IS - 4
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Jeon, Jae-Hyung
A1 - Leijnse, Natascha
A1 - Oddershede, Lene B.
A1 - Metzler, Ralf
T1 - Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions
JF - New journal of physics : the open-access journal for physics
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1088/1367-2630/15/4/045011
SN - 1367-2630 (print)
VL - 15
IS - 4
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Javanainen, Matti
A1 - Hammaren, Henrik
A1 - Monticelli, Luca
A1 - Jeon, Jae-Hyung
A1 - Miettinen, Markus S.
A1 - Martinez-Seara, Hector
A1 - Metzler, Ralf
A1 - Vattulainen, Ilpo
T1 - Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes
JF - Faraday discussions
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1039/c2fd20085f
SN - 1359-6640 (print)
VL - 161
IS - 1
SP - 397
EP - 417
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Eliazar, Iddo
A1 - Metzler, Ralf
T1 - The RARE model a generalized approach to random relaxation processes in disordered systems
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - 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.
KW - chemical relaxation
KW - Pareto analysis
KW - reaction kinetics theory
KW - reaction rate constants
KW - stochastic processes
Y1 - 2012
U6 - http://dx.doi.org/10.1063/1.4770266
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 137
IS - 23
PB - American Institute of Physics
CY - Melville
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 - http://dx.doi.org/10.1088/1742-5468/2012/04/P04010
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
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 - http://dx.doi.org/10.1016/j.physa.2011.12.035
SN - 0378-4371 (print)
SN - 1873-2119 (online)
VL - 391
IS - 8
SP - 2527
EP - 2542
PB - Elsevier
CY - Amsterdam
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 - http://dx.doi.org/10.1140/epjst/e2012-01553-y
SN - 1951-6355 (print)
VL - 204
IS - 1
SP - 75
EP - 84
PB - Springer
CY - Heidelberg
ER -
TY - JOUR
A1 - Lomholt, Michael A.
A1 - Lizana, Ludvig
A1 - Metzler, Ralf
A1 - Ambjoernsson, Tobias
T1 - Microscopic origin of the logarithmic time evolution of aging processes in complex systems
JF - Physical review letters
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1103/PhysRevLett.110.208301
SN - 0031-9007 (print)
VL - 110
IS - 20
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Pulkkinen, Otto
A1 - Metzler, Ralf
T1 - Distance matters the impact of gene proximity in bacterial gene regulation
JF - Physical review letters
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1103/PhysRevLett.110.198101
SN - 0031-9007 (print)
VL - 110
IS - 19
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Chechkin, Aleksei V.
A1 - Zaid, Irwin M.
A1 - Lomholt, Michael A.
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Bulk-mediated diffusion on a planar surface full solution
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1103/PhysRevE.86.041101
SN - 1539-3755 (print)
VL - 86
IS - 4
PB - American Physical Society
CY - College Park
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 - http://dx.doi.org/10.1103/PhysRevLett.109.188103
SN - 0031-9007 (print)
VL - 109
IS - 18
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Mattos, Thiago G.
A1 - Mejia-Monasterio, Carlos
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
T1 - First passages in bounded domains When is the mean first passage time meaningful?
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1103/PhysRevE.86.031143
SN - 1539-3755 (print)
VL - 86
IS - 3
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Sereshki, L. E.
A1 - Lomholt, M. A.
A1 - Metzler, Ralf
T1 - A solution to the subdiffusion-efficiency paradox inactive states enhance reaction efficiency at subdiffusion conditions in living cells
JF - epl : a letters journal exploring the frontiers of physics
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1209/0295-5075/97/20008
SN - 0295-5075 (print)
VL - 97
IS - 2
PB - EDP Sciences
CY - Mulhouse
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 - http://dx.doi.org/10.1039/c2sm26089a
SN - 1744-683X (print)
VL - 8
IS - 33
SP - 8651
EP - 8658
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Cherstvy, Andrej G.
A1 - Metzler, Ralf
T1 - Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence D(x) similar to vertical bar x vertical bar(alpha) of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on statistical measures such as the amplitude scatter of the time-averaged mean-squared displacement of individual realizations, the ergodicity breaking and non-Gaussianity parameters, as well as the probability density function P(x, t), we analyze the weakly nonergodic character of the heterogeneous diffusion process and, particularly, the degree of irreproducibility of individual realizations. As we show, the fluctuations between individual realizations increase with growing modulus vertical bar alpha vertical bar of the scaling exponent. The fluctuations appear to diverge when the critical value alpha = 2 is approached, while for even larger alpha the fluctuations decrease, again. At criticality, the power-law behavior of the mean-squared displacement changes to an exponentially fast growth, and the fluctuations of the time-averaged mean-squared displacement do not converge for increasing number of realizations. From a systematic comparison we observe some striking similarities of the heterogeneous diffusion process with the familiar subdiffusive continuous time random walk process with power-law waiting time distribution and diverging characteristic waiting time.
Y1 - 2014
U6 - http://dx.doi.org/10.1103/PhysRevE.90.012134
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 90
IS - 1
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Ghosh, Surya K.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Deformation propagation in responsive polymer network films
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - We study the elastic deformations in a cross-linked polymer network film triggered by the binding of submicron particles with a sticky surface, mimicking the interactions of viral pathogens with thin films of stimulus-responsive polymeric materials such as hydrogels. From extensive Langevin Dynamics simulations we quantify how far the network deformations propagate depending on the elasticity parameters of the network and the adhesion strength of the particles. We examine the dynamics of the collective area shrinkage of the network and obtain some simple relations for the associated characteristic decay lengths. A detailed analysis elucidates how the elastic energy of the network is distributed between stretching and compression modes in response to the particle binding. We also examine the force-distance curves of the repulsion or attraction interactions for a pair of sticky particles in the polymer network film as a function of the particle-particle separation. The results of this computational study provide new insight into collective phenomena in soft polymer network films and may, in particular, be applied to applications for visual detection of pathogens such as viruses via a macroscopic response of thin films of cross-linked hydrogels. (C) 2014 AIP Publishing LLC.
Y1 - 2014
U6 - http://dx.doi.org/10.1063/1.4893056
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 141
IS - 7
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Goychuk, Igor
A1 - Kharchenko, Vasyl O.
A1 - Metzler, Ralf
T1 - Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4cp01234h
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 16
IS - 31
SP - 16524
EP - 16535
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Chechkin, Aleksei V.
A1 - Zaid, I. M.
A1 - Lomholt, M. A.
A1 - Sokolov, I. M.
A1 - Metzler, Ralf
T1 - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
JF - Mathematical modelling of natural phenomena
N2 - 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.
KW - Bulk-mediated diffusion
KW - anomalous diffusion
KW - Levy flights
KW - stochastic processes
Y1 - 2013
U6 - http://dx.doi.org/10.1051/mmnp/20138208
SN - 0973-5348 (print)
VL - 8
IS - 2
SP - 114
EP - 126
PB - EDP Sciences
CY - Les Ulis
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - 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.
Y1 - 2013
U6 - http://dx.doi.org/10.1039/c3cp53056f
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 15
IS - 46
SP - 20220
EP - 20235
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Sandev, Trifce
A1 - Metzler, Ralf
A1 - Tomovski, Zivorad
T1 - Velocity and displacement correlation functions for fractional generalized Langevin equations
JF - Fractional calculus and applied analysis : an international journal for theory and applications
N2 - 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.
KW - fractional generalized Langevin equation
KW - frictional memory kernel
KW - variances
KW - mean square displacement
KW - anomalous diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.2478/s13540-012-0031-2
SN - 1311-0454 (print)
VL - 15
IS - 3
SP - 426
EP - 450
PB - Versita
CY - Warsaw
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 (print)
VL - 65
IS - 8
SP - 29
EP - 35
PB - American Institute of Physics
CY - Melville
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 - http://dx.doi.org/10.1088/1742-5468/2012/03/L03001
SN - 1742-5468 (print)
IS - 1
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Godec, Aljaz
A1 - Bauer, Maximilian
A1 - Metzler, Ralf
T1 - Collective dynamics effect transient subdiffusion of inert tracers in flexible gel networks
JF - New journal of physics : the open-access journal for physics
N2 - Based on extensive Brownian dynamics simulations we study the thermal motion of a tracer bead in a cross-linked, flexible gel in the limit when the tracer particle size is comparable to or even larger than the equilibrium mesh size of the gel. The analysis of long individual trajectories of the tracer demonstrates the existence of pronounced transient anomalous diffusion. From the time averaged mean squared displacement and the time averaged van Hove correlation functions we elucidate the many-body origin of the non-Brownian tracer bead dynamics. Our results shed new light onto the ongoing debate over the physical origin of steric tracer interactions with structured environments.
KW - anomalous diffusion
KW - gel network
KW - van Hove correlation
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1367-2630/16/9/092002
SN - 1367-2630 (print)
VL - 16
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Sandev, Trifce
A1 - Metzler, Ralf
A1 - Tomovski, Zivorad
T1 - Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise
JF - Journal of mathematical physics
N2 - We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.
Y1 - 2014
U6 - http://dx.doi.org/10.1063/1.4863478
SN - 0022-2488 (print)
SN - 1089-7658 (online)
VL - 55
IS - 2
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Vinod, Deepak
A1 - Aghion, Erez
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Time averaging, ageing and delay analysis of financial time series
JF - New journal of physics
N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
KW - time averaging
KW - diffusion
KW - geometric Brownian motion
KW - financial time series
Y1 - 2017
U6 - http://dx.doi.org/10.1088/1367-2630/aa7199
SN - 1367-2630
VL - 19
SP - 1
EP - 11
PB - IOP
CY - London
ER -
TY - GEN
A1 - Cherstvy, Andrey G.
A1 - Vinod, Deepak
A1 - Aghion, Erez
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Time averaging, ageing and delay analysis of financial time series
N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 347
KW - diffusion
KW - financial time series
KW - geometric Brownian motion
KW - time averaging
Y1 - 2017
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400541
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions
JF - New journal of physics : the open-access journal for physics
N2 - We examine by extensive computer simulations the self-diffusion of anisotropic star-like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction phi of the crowders and the crowder-crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, and the effective diffusion coefficient. The diffusion is ergodic in the limit of long traces, such that the mean time averaged MSD converges towards the ensemble averaged MSD, and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales, we quantify the anomalous diffusion in the system. Also, we show that the translational-but not rotational-diffusivity of the particles Dis a nonmonotonic function of the attraction strength between them. Both diffusion coefficients decrease as the power law D(phi) similar to (1 - phi/phi*)(2 ... 2.4) with the area fraction phi occupied by the crowders and the critical value phi*. Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells.
KW - anomalous diffusion
KW - crowded fluids
KW - stochastic processes
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1367-2630/17/11/113028
SN - 1367-2630 (print)
VL - 17
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Kim, Won Kyu
A1 - Metzler, Ralf
T1 - Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles
JF - New journal of physics : the open-access journal for physics
N2 - We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two-dimensional model system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains, while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that higher activities of SPPs yield a higher effective temperature of the bath and thus facilitate the looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or in suspensions of active colloidal particles or bacteria cells.
KW - diffusion
KW - active transport
KW - polymers
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1367-2630/17/11/113008
SN - 1367-2630 (print)
VL - 17
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Sandev, Trifce
A1 - Chechkin, Aleksei V.
A1 - Korabel, Nickolay
A1 - Kantz, Holger
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Distributed-order diffusion equations and multifractality: Models and solutions
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Y1 - 2015
U6 - http://dx.doi.org/10.1103/PhysRevE.92.042117
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 92
IS - 4
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Godec, Aljaz
A1 - Metzler, Ralf
T1 - Optimization and universality of Brownian search in a basic model of quenched heterogeneous media
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time ( MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.
Y1 - 2015
U6 - http://dx.doi.org/10.1103/PhysRevE.91.052134
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 91
IS - 5
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity
JF - Journal of statistical mechanics: theory and experiment
N2 - We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) similar to D-0x(alpha)t(beta) depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.
KW - diffusion
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1742-5468/2015/05/P05010
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size
JF - Soft matter
N2 - 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.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/c4sm02007c
SN - 1744-683X (print)
SN - 1744-6848 (online)
VL - 11
IS - 3
SP - 472
EP - 488
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Inverted critical adsorption of polyelectrolytes in confinement
JF - Soft matter
N2 - What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sigma(c)-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sigma(c) for the concave interfaces versus the Debye screening length 1/kappa and the extent of confinement a for these three interfaces for small kappa a values. For large kappa a the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/kappa. We also rationalize how sigma(c)(kappa) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/c5sm00635j
SN - 1744-683X (print)
SN - 1744-6848 (online)
VL - 11
IS - 22
SP - 4430
EP - 4443
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Ghosh, Surya K.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Non-universal tracer diffusion in crowded media of non-inert obstacles
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - 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.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/c4cp03599b
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 17
IS - 3
SP - 1847
EP - 1858
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Ala-Nissila, Tapio
A1 - Metzler, Ralf
T1 - Polymer translocation: the first two decades and the recent diversification
JF - Soft matter
N2 - 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.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4sm01819b
SN - 1744-683X (print)
SN - 1744-6848 (online)
VL - 10
IS - 45
SP - 9016
EP - 9037
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Metzler, Ralf
A1 - Jeon, Jae-Hyung
A1 - Cherstvy, Andrey G.
A1 - Barkai, Eli
T1 - Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - 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.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4cp03465a
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 16
IS - 44
SP - 24128
EP - 24164
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Metzler, Ralf
T1 - Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
JF - Journal of physics : A, Mathematical and theoretical
N2 - We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation.
KW - first passage
KW - anomalous diffusion
KW - potential landscape
KW - polymer translocation
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1751-8113/47/3/032002
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 47
IS - 3
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Nezhadhaghighi, M. Ghasemi
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Numerical approach to unbiased and driven generalized elastic model
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent beta characterizing the growth of the mean squared displacement <(delta h)(2)> of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.
Y1 - 2014
U6 - http://dx.doi.org/10.1063/1.4858425
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 140
IS - 2
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
JF - Soft matter
N2 - 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.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c3sm52846d
SN - 1744-683X (print)
SN - 1744-6848 (online)
VL - 10
IS - 10
SP - 1591
EP - 1601
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Jeon, Jae-Hyung
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - 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 < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < 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.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4cp02019g
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 16
IS - 30
SP - 15811
EP - 15817
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Critical adsorption of polyelectrolytes onto charged Janus nanospheres
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption-desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physicochemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4cp02207f
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 16
IS - 29
SP - 15539
EP - 15550
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Bauer, Maximilian
A1 - Godec, Aljaz
A1 - Metzler, Ralf
T1 - Diffusion of finite-size particles in two-dimensional channels with random wall configurations
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c3cp55160a
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 16
IS - 13
SP - 6118
EP - 6128
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Sandev, Trifce
A1 - Chechkin, Aleksei V.
A1 - Kantz, Holger
A1 - Metzler, Ralf
T1 - Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel
JF - Fractional calculus and applied analysis : an international journal for theory and applications
N2 - We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
KW - continuous time random walk (CTRW)
KW - Fokker-Planck-Smoluchowski equation
KW - Mittag-Leffler functions
KW - anomalous diffusion
KW - multi-scaling
Y1 - 2015
U6 - http://dx.doi.org/10.1515/fca-2015-0059
SN - 1311-0454 (print)
SN - 1314-2224 (online)
VL - 18
IS - 4
SP - 1006
EP - 1038
PB - De Gruyter
CY - Berlin
ER -
TY - JOUR
A1 - Bauer, Maximilian
A1 - Rasmussen, Emil S.
A1 - Lomholt, Michael A.
A1 - Metzler, Ralf
T1 - Real sequence effects on the search dynamics of transcription factors on DNA
JF - Scientific reports
N2 - 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.
Y1 - 2015
U6 - http://dx.doi.org/10.1038/srep10072
SN - 2045-2322 (print)
VL - 5
PB - Nature Publ. Group
CY - London
ER -
TY - JOUR
A1 - Krüsemann, Henning
A1 - Godec, Aljaz
A1 - Metzler, Ralf
T1 - Ageing first passage time density in continuous time random walks and quenched energy landscapes
JF - Journal of physics : A, Mathematical and theoretical
N2 - We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function Psi (t) similar or equal to t(-1-alpha) (0 <= alpha <= 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t(a), the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < alpha < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < alpha < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
KW - first passage
KW - random walks
KW - anomalous diffusion
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1751-8113/48/28/285001
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 48
IS - 28
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Shin, Jaeoh
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Polymer looping is controlled by macromolecular crowding, spatial confinement, and chain stiffness
JF - ACS Macro Letters
N2 - We study by extensive computer simulations the looping characteristics of linear polymers with varying persistence length inside a spherical cavity in the presence of macromolecular crowding. For stiff chains, the looping probability and looping time reveal wildly oscillating patterns as functions of the chain length. The effects of crowding differ dramatically for flexible versus stiff polymers. While for flexible chains the looping kinetics is slowed down by the crowders, for stiffer chains the kinetics turns out to be either decreased or facilitated, depending on the polymer length. For severe confinement, the looping kinetics may become strongly facilitated by crowding. Our findings are of broad impact for DNA looping in the crowded and compartmentalized interior of living biological cells.
Y1 - 2015
U6 - http://dx.doi.org/10.1021/mz500709w
SN - 2161-1653 (print)
VL - 4
IS - 2
SP - 202
EP - 206
PB - American Chemical Society
CY - Washington
ER -
TY - JOUR
A1 - Pulkkinen, Otto
A1 - Metzler, Ralf
T1 - Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation
JF - Scientific reports
N2 - Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E. coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
Y1 - 2015
U6 - http://dx.doi.org/10.1038/srep17820
SN - 2045-2322 (print)
VL - 5
PB - Nature Publ. Group
CY - London
ER -
TY - JOUR
A1 - Reverey, Julia F.
A1 - Jeon, Jae-Hyung
A1 - Bao, Han
A1 - Leippe, Matthias
A1 - Metzler, Ralf
A1 - Selhuber-Unkel, Christine
T1 - Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii
JF - Scientific reports
N2 - Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.
Y1 - 2015
U6 - http://dx.doi.org/10.1038/srep11690
SN - 2045-2322 (print)
VL - 5
PB - Nature Publ. Group
CY - London
ER -
TY - JOUR
A1 - Bodrova, Anna S.
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Ultraslow scaled Brownian motion
JF - New journal of physics : the open-access journal for physics
N2 - We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal to 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
KW - anomalous diffusion
KW - stochastic processes
KW - ageing
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1367-2630/17/6/063038
SN - 1367-2630 (print)
VL - 17
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Mardoukhi, Yousof
A1 - Jeon, Jae-Hyung
A1 - Metzler, Ralf
T1 - Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law similar to T-h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/c5cp03548a
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 17
IS - 44
SP - 30134
EP - 30147
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Bodrova, Anna
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Quantifying non-ergodic dynamics of force-free granular gases
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient epsilon. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of epsilon on the impact velocity of particles.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/c5cp02824h
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 17
IS - 34
SP - 21791
EP - 21798
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Safdari, Hadiseh
A1 - Cherstvy, Andrey G.
A1 - Chechkin, Aleksei V.
A1 - Thiel, Felix
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Quantifying the non-ergodicity of scaled Brownian motion
JF - Journal of physics : A, Mathematical and theoretical
N2 - We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form D(t) similar or equal to t(alpha-1). We compute the ergodicity breaking parameter EB in the entire range of scaling exponents a, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Delta the EB parameter as function of the scaling exponent a has no divergence at alpha - 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.
KW - scaled Brownian motion
KW - anomalous diffusion
KW - ageing
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1751-8113/48/37/375002
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 48
IS - 37
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form D(x) similar to D-0 vertical bar x vertical bar (alpha 0) in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent a in time and space. In the case of annealed disorder, for which effectively alpha(0) = alpha(0)(t), we show how the long time scaling of the ensemble mean squared displacement (MSD) and the amplitude variation of individual realizations of the time averaged MSD are affected by the disorder strength. For the case of quenched disorder, the long time behavior becomes effectively Brownian after a number of jumps between the domains of a stratified medium. In the latter situation, the averages are taken over both an ensemble of particles and different realizations of the disorder. As physical observables, we analyze in detail the ensemble and time averaged MSDs, the ergodicity breaking parameter, and higher order moments of the time averages. (C) 2015 AIP Publishing LLC.
Y1 - 2015
U6 - http://dx.doi.org/10.1063/1.4917077
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 142
IS - 14
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Safdari, Hadiseh
A1 - Chechkin, Aleksei V.
A1 - Jafari, Gholamreza R.
A1 - Metzler, Ralf
T1 - Aging scaled Brownian motion
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.
Y1 - 2015
U6 - http://dx.doi.org/10.1103/PhysRevE.91.042107
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 91
IS - 4
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Blavatska, Viktoria
A1 - Metzler, Ralf
T1 - Conformational properties of complex polymers: rosette versus star-like structures
JF - Journal of physics : A, Mathematical and theoretical
N2 - Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyse the size and shape characteristics of complex polymer structures, containing in general f(1) loops (petals) and f(2) linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius R-g and asphericity (A) over cap of typical conformation as functions of parameters f(1), f(2). In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight.
KW - polymers
KW - path integration
KW - conformational properties
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1751-8113/48/13/135001
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 48
IS - 13
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Bodrova, Anna S.
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Safdari, Hadiseh
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Underdamped scaled Brownian motion
BT - (non-)existence of the overdamped limit in anomalous diffusion
JF - Scientific reports
N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
Y1 - 2016
U6 - http://dx.doi.org/10.1038/srep30520
SN - 2045-2322
VL - 6
PB - Nature Publishing Group
CY - London
ER -
TY - GEN
A1 - Bodrova, Anna S.
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Safdari, Hadiseh
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Underdamped scaled Brownian motion
BT - (non-)existence of the overdamped limit in anomalous diffusion
N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 267
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-97158
ER -
TY - GEN
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 236
KW - anomalous diffusion
KW - disordered media
KW - fractional dynamics
KW - infection pathway
KW - inhomogeneous-media
KW - intracellular-transport
KW - langevin equation
KW - living cells
KW - random-walks
KW - single-particle tracking
Y1 - 2013
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-94468
SP - 20220
EP - 20235
ER -
TY - JOUR
A1 - Bodrova, Anna
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Quantifying non-ergodic dynamics of force-free granular gases
JF - Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies
N2 - Brownianmotion is ergodic in the Boltzmann–Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann–
Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent (viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/C5CP02824H
SN - 1463-9084 (online)
IS - 17
SP - 21791
EP - 21798
ER -
TY - GEN
A1 - Bodrova, Anna
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Quantifying non-ergodic dynamics of force-free granular gases
N2 - Brownianmotion is ergodic in the Boltzmann–Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent
(viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 206
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-85200
ER -
TY - JOUR
A1 - Mardoukhi, Yousof
A1 - Jeon, Jae-Hyung
A1 - Metzler, Ralf
T1 - Geometry controlled anomalous diffusion in random fractal geometries
BT - looking beyond the infinite cluster
JF - Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies
N2 - We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of
purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/c5cp03548a
SN - 1439-7641 (online)
IS - 17
SP - 30134
EP - 30147
PB - Wiley-VCH Verl.
CY - Weinheim
ER -
TY - GEN
A1 - Mardoukhi, Yousof
A1 - Jeon, Jae-Hyung
A1 - Metzler, Ralf
T1 - Geometry controlled anomalous diffusion in random fractal geometries
BT - looking beyond the infinite cluster
N2 - We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of
purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 207
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-85247
ER -
TY - JOUR
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Inverted critical adsorption of polyelectrolytes in confinement
JF - Soft matter
N2 - What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer–surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sc—defining the adsorption–desorption transition—are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sc for the concave interfaces versus the Debye screening length 1/k and the extent of confinement a for these three interfaces for small ka values. For large ka the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/k. We also rationalize how sc(k) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption—the effect often hard to tackle theoretically—putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/C5SM00635J
SN - 1744-6848 (online)
SN - 1744-683X (print)
IS - 11
SP - 4430
EP - 4443
PB - Royal Society of Chemistry
CY - London
ER -
TY - GEN
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Inverted critical adsorption of polyelectrolytes in confinement
N2 - What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer–surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sc—defining the adsorption–desorption transition—are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sc for the concave interfaces versus the Debye screening length 1/k and the extent of confinement a for these three interfaces for small ka values. For large ka the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/k. We also rationalize how sc(k) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption—the effect often hard to tackle theoretically—putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 214
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-89562
SP - 4430
EP - 4443
ER -
TY - JOUR
A1 - Ghosh, Surya K.
A1 - Cherstvy, Andrey G.
A1 - Petrov, Eugene P.
A1 - Metzler, Ralf
T1 - Interactions of rod-like particles on responsive elastic sheets
JF - Soft matter
N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.
Y1 - 2016
U6 - http://dx.doi.org/10.1039/C6SM01522K
SN - 1744-6848 (online)
SN - 1744-683X (print)
PB - RSC
CY - London
ER -
TY - GEN
A1 - Ghosh, Surya K.
A1 - Cherstvy, Andrey G.
A1 - Petrov, Eugene P.
A1 - Metzler, Ralf
T1 - Interactions of rod-like particles on responsive elastic sheets
N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 256
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95882
ER -
TY - JOUR
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
JF - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies
N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.
Y1 - 2016
U6 - http://dx.doi.org/10.1039/C6CP03101C
SN - 1463-9084 (online)
SN - 1463-9076 (print)
VL - 18
SP - 23840
EP - 23852
PB - RSC Publ.
CY - Cambridge
ER -
TY - GEN
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 257
Y1 - 2016
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95901
SP - 23840
EP - 23852
ER -
TY - GEN
A1 - de Carvalho, Sidney J.
A1 - Metzler, Ralf
A1 - Cherstvy, Andrey G.
T1 - Critical adsorption of polyelectrolytes onto charged Janus nanospheres
N2 - Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption–desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physico-chemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 278
Y1 - 2014
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-98783
ER -
TY - GEN
A1 - Chechkin, Aleksei V.
A1 - Zaid, Irwin M.
A1 - Lomholt, Michael A.
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 593
KW - Bulk-mediated diffusion;
KW - anomalous diffusion
KW - Levy flights
KW - stochastic processes
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-415480
SN - 1866-8372
IS - 593
SP - 114
EP - 126
ER -
TY - GEN
A1 - Ślęzak, Jakub
A1 - Metzler, Ralf
A1 - Magdziarz, Marcin
T1 - Superstatistical generalised Langevin equation
BT - non-Gaussian viscoelastic anomalous diffusion
N2 - Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 413
KW - anomalous diffusion
KW - generalised langevin equation
KW - superstatistics
KW - non-Gaussian diffusion
Y1 - 2018
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409315
ER -
TY - JOUR
A1 - Herrmann, Carl J. J.
A1 - Metzler, Ralf
T1 - A self-avoiding walk with neural delays as a model of fixational eye movements
JF - Scientific reports
N2 - Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
Y1 - 2017
U6 - http://dx.doi.org/10.1038/s41598-017-13489-8
SN - 2045-2322
VL - 7
SP - 1
EP - 17
PB - Springer Nature
CY - London
ER -
TY - GEN
A1 - Herrmann, Carl J. J.
A1 - Metzler, Ralf
T1 - A self-avoiding walk with neural delays as a model of fixational eye movements
N2 - Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 392
Y1 - 2017
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-403742
ER -
TY - JOUR
A1 - Schwarzl, Maria
A1 - Godec, Aljaž
A1 - Metzler, Ralf
T1 - Quantifying non-ergodicity of anomalous diffusion with higher order moments
JF - Scientific reports
N2 - Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
Y1 - 2017
U6 - http://dx.doi.org/10.1038/s41598-017-03712-x
VL - 7
PB - Macmillan Publishers Limited
CY - London
ER -