arXiv subjects

Ralf Metzler

Publications and source records attributed to Ralf Metzler.

At least 127 records · Page 7Linked to original sources

arXiv2015

Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes

We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form $D(x)\sim D_0|x|^α$ in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent $α$ in time and space. In the case of annealed disorder, for which effectively $α=α(t)$ 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.

cond-mat.stat-mech↗

arXiv2015

Ergodicity breaking, ageing, and confinement in generalised diffusion processes with position and time dependent diffusivity

We study generalised anomalous diffusion processes whose diffusion coefficient $D(x,t)\sim D_0|x|^αt^β$ 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 generalised 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 generalised 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.

cond-mat.stat-mech↗

arXiv2015

Conformational properties of complex polymers: rosette versus star-like structures

Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyze 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 $\hat{A}$ 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.

cond-mat.soft↗

arXiv2015

Nonergodic dynamics of force-free granular gases

We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\varepsilon$ for particle pair collisions. 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 behavior of the ensemble mean squared displacement (MSD) and the velocity correlations in the small dissipation limit. However, we reveal that the time averaged MSD of granular gas particles significantly differs from this effective model due to ballistic correlations for systems with constant $\varepsilon$. For velocity-dependent $\varepsilon$ these corrections become weaker at longer times. Qualitatively the reported non-ergodic behavior is generic for granular gases with any realistic dependence of $\varepsilon$ on the impact velocity.

cond-mat.stat-mech↗

arXiv2015

Signal focusing through active transport

In biological cells and novel diagnostic devices biochemical receptors need to be sensitive to extremely small concentration changes of signaling molecules. The accuracy of such molecular signaling is ultimately limited by the counting noise imposed by the thermal diffusion of molecules. Many macromolecules and organelles transiently bind to molecular motors and are then actively transported. We here show that a random albeit directed delivery of signaling molecules to within a typical diffusion distance to the receptor reduces the correlation time of the counting noise, effecting an improved sensing precision. The conditions for this active focusing are indeed compatible with observations in living cells. Our results are relevant for a better understanding of molecular cellular signaling and the design of novel diagnostic devices.

q-bio.SC↗

arXiv2014

Critical adsorption of polyelectrolytes onto charged Janus nanospheres

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 and the binding energy distributions close to the adsorption-desorption transition for Janus nanoparticles 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.

cond-mat.soft↗

arXiv2014

Non-universal tracer diffusion in crowded media of non-inert obstacles

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 the 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.

cond-mat.soft↗

arXiv2014

Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size

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 slow 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 onto the looping kinetics in terms of an effective solution viscosity and standard excluded volume effects. Thus 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.

cond-mat.soft↗

arXiv2014

Localization and universal fluctuations in ultraslow diffusion processes

We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) $\langle x^2(t)\rangle\simeq\log^γt$. Comparison of annealed continuous time random walks (CTRWs) with logarithmic waiting time distribution $ψ(τ)\simeq1/(τ\log^{1+γ}τ)$ and Sinai diffusion in quenched random landscapes shows striking similarities, despite their very different physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time 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 and time averaged MSD.

cond-mat.stat-mech↗

arXiv2014

Optimization of random search processes in the presence of an external bias

We study the efficiency of random search processes based on L{é}vy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the bias of the searcher based on prior experience. While Lévy flights turn out to be efficient search processes when relative to the starting point the target is upstream, in the downstream scenario regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of L{é}vy flights, due to which L{é}vy flights typically overshoot a point or small interval. Extending our recent work on biased LF search [V. V. Palyulin, A. V. Chechkin, and R. Metzler, Proc. Natl. Acad. Sci. USA, DOI:10.1073/pnas.1320424111] we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favors L{é}vy flights over regular Brownian search. Contrary to the common belief that L{é}vy flights with a L{é}vy index $α=1$ (i.e., Cauchy flights) are optimal for sparse targets, we find that the optimal value for $α$ may range in the entire interval $(1,2)$ and include Brownian motion as the overall most efficient search strategy.

cond-mat.stat-mech↗

arXiv2014

Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion processes

We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence $D(x)\sim|x|^α$ 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 non-ergodic character of the heterogeneous diffusion process and, particularly, the degree of irreproducibility of individual realization. As we show, the fluctuations between individual realizations increase with growing modulus $|α|$ of the scaling exponent. The fluctuations appear to diverge when the critical value $α=2$ is approached, while for even larger $α$ 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 seem to 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.

cond-mat.stat-mech↗

arXiv2014

Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA

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 are 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 fourteen model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction $ε_{hb}(\mathtt{AT})$ for an $\mathtt{AT}$ base pair and the ring factor $ξ$ turn out to be the most sensitive parameters. In addition, the stacking interaction $ε_{st}(\mathtt{TA}-\mathtt{TA})$ for an $\mathtt{TA}-\mathtt{TA}$ 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.

q-bio.BM↗

arXiv2014

Collective dynamics effect transient subdiffusion of inert tracers in gel networks

Based on extensive Brownian dynamics simulations we study the thermally driven motion of a tracer bead in a cross-linked, dynamic gel network in the limit when the tracer bead's size is of the same size or even larger than the equilibrium mesh size of the gel. The analysis of long individual trajectories of the tracer bead demonstrates the existence of pronounced transient anomalous diffusion, accompanied by a drastic slow-down of the gel-bead relaxation dynamics. From the time averaged mean squared displacement and the van Hove cross-correlation function we elucidate the many-body origin of the non-Brownian tracer bead dynamics. Our results shed new light on the ongoing debate over the physical origin of sterical tracer interactions with structured environments.

cond-mat.soft↗

arXiv2014

Deformation propagation in responsive polymer network films

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.

cond-mat.soft↗

arXiv2014

Mixing and segregation of ring polymers: spatial confinement and molecular crowding effects

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 behaviour 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 $ϕ$ of crowders. We also examine the entropic de-mixing 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 analysed. In particular, on systematic variation of the fraction of crowding molecules a $(1-ϕ)$-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 is predicted. Our results help to rationalise the implications of macromolecular crowding for circular DNA molecules in confined spaces inside bacteria as well as in localised cellular compartments inside eukaryotic cells.

cond-mat.soft↗

arXiv2014

First passage statistics for aging diffusion in annealed and quenched disorder

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.

cond-mat.stat-mech↗

arXiv2013

Molecular motors transporting cargos in viscoelastic cytosol: how to beat subdiffusion with a power stroke?

Anomalously slow passive diffusion, $\langle δx^2(t)\rangle\simeq t^α$, with $0<α<1$, of larger tracers such as messenger RNA and endogenous submicron granules in the cytoplasm of living biological cells has been demonstrated in a number of experiments and has been attributed to the viscoelastic physical nature of the cellular cytoplasm. This finding provokes the question to which extent active intracellular transport is affected by this viscoelastic environment: does the subdiffusion of free submicron cargo such as vesicles and organelles always imply anomalously slow transport by molecular motors such as kinesins, that is, directed transport characterized by a sublinear growth of the mean distance, $\langle x(t)\rangle\simeq t^{α_{\rm eff}}$, with $0<α_{\rm eff}<1$? Here we study a generic model approach combining the commonly accepted two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubule driven by a flashing binding potential. The motor is elastically coupled to a cargo particle, which in turn is subject to the viscoelastic cytoplasmic environment. Depending on the physical parameters of cargo size, loading force, amplitude of the binding potential, and the turnover frequency of the molecular motor, the transport can be both normal ($α_{\rm eff}=1$) and anomalous ($α\leq α_{\rm eff}<1$). In particular, we demonstrate in detail how highly efficient normal motor transport can emerge despite the anomalously slow passive diffusion of cargo particles, and how the active motion of the same motor in the same cell may turn anomalously slow when the parameters are changed.

physics.bio-ph↗

arXiv2013

Diffusion of finite-size particles in channels with random walls

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-sized particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. With the application of diffusing pathogens in hydrogels in mind, 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 [J. Chem. Phys., 2012, 137, 024107].

cond-mat.stat-mech↗