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 -