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 - https://doi.org/10.1039/C6SM01522K SN - 1744-6848 SN - 1744-683X PB - RSC CY - London 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 - https://doi.org/10.1039/C6CP03101C SN - 1463-9084 SN - 1463-9076 VL - 18 SP - 23840 EP - 23852 PB - RSC Publ. CY - Cambridge ER - 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 - https://doi.org/10.1088/1367-2630/18/8/083037 SN - 1367-2630 VL - 18 PB - IOP Publ. CY - London ER - TY - JOUR A1 - Xu, Pengbo A1 - Zhou, Tian A1 - Metzler, Ralf A1 - Deng, Weihua T1 - Lévy walk dynamics in an external harmonic potential JF - Physical review : E, Statistical, nonlinear, and soft matter physics N2 - Levy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs-their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some longstanding puzzles around LWs. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevE.101.062127 SN - 2470-0045 SN - 2470-0053 SN - 1550-2376 SN - 1063-651X SN - 1539-3755 VL - 101 IS - 6 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Liu, Lin A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion JF - The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces & biophysical chemistry N2 - What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism. Y1 - 2017 U6 - https://doi.org/10.1021/acs.jpcb.6b12413 SN - 1520-6106 VL - 121 SP - 1284 EP - 1289 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Godec, Aljaž A1 - Metzler, Ralf T1 - First passage time statistics for two-channel diffusion JF - Journal of physics : A, Mathematical and theoretical N2 - We present rigorous results for the mean first passage time and first passage time statistics for two-channel Markov additive diffusion in a 3-dimensional spherical domain. Inspired by biophysical examples we assume that the particle can only recognise the target in one of the modes, which is shown to effect a non-trivial first passage behaviour. We also address the scenario of intermittent immobilisation. In both cases we prove that despite the perfectly non-recurrent motion of two-channel Markov additive diffusion in 3 dimensions the first passage statistics at long times do not display Poisson-like behaviour if none of the phases has a vanishing diffusion coefficient. This stands in stark contrast to the standard (one-channel) Markov diffusion counterpart. We also discuss the relevance of our results in the context of cellular signalling. KW - first passage time KW - Markov additive processes KW - Fokker-Planck equation KW - random search processes KW - coupled initial boundary value problem KW - cellular signalling KW - asymptotic analysis Y1 - 2017 U6 - https://doi.org/10.1088/1751-8121/aa5204 SN - 1751-8113 SN - 1751-8121 VL - 50 IS - 8 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Estrada, Ernesto A1 - Delvenne, Jean-Charles A1 - Hatano, Naomichi A1 - Mateos, Jose L. A1 - Metzler, Ralf A1 - Riascos, Alejandro P. A1 - Schaub, Michael T. T1 - Random multi-hopper model BT - super-fast random walks on graphs JF - Journal of Complex Networks N2 - We develop a mathematical model considering a random walker with long-range hops on arbitrary graphs. The random multi-hopper can jump to any node of the graph from an initial position, with a probability that decays as a function of the shortest-path distance between the two nodes in the graph. We consider here two decaying functions in the form of Laplace and Mellin transforms of the shortest-path distances. We prove that when the parameters of these transforms approach zero asymptotically, the hitting time in the multi-hopper approaches the minimum possible value for a normal random walker. We show by computational experiments that the multi-hopper explores a graph with clusters or skewed degree distributions more efficiently than a normal random walker. We provide computational evidences of the advantages of the random multi-hopper model with respect to the normal random walk by studying deterministic, random and real-world networks. Y1 - 2018 U6 - https://doi.org/10.1093/comnet/cnx043 SN - 2051-1310 SN - 2051-1329 VL - 6 IS - 3 SP - 382 EP - 403 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Akimoto, Takuma A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed. Y1 - 2018 U6 - https://doi.org/10.1103/PhysRevE.98.022105 SN - 2470-0045 SN - 2470-0053 VL - 98 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Mardoukhi, Yousof A1 - Jeon, Jae-Hyung A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Fluctuations of random walks in critical random environments JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed. Y1 - 2018 U6 - https://doi.org/10.1039/c8cp03212b SN - 1463-9076 SN - 1463-9084 VL - 20 IS - 31 SP - 20427 EP - 20438 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Kosztolowicz, Tadeusz A1 - Metzler, Ralf A1 - Wąsik, Slawomir A1 - Arabski, Michal T1 - Modelling experimentally measured of ciprofloxacin antibiotic diffusion in Pseudomonas aeruginosa biofilm formed in artificial sputum medium JF - PLoS ONE N2 - We study the experimentally measured ciprofloxacin antibiotic diffusion through a gel-like artificial sputum medium (ASM) mimicking physiological conditions typical for a cystic fibrosis layer, in which regions occupied by Pseudomonas aeruginosa bacteria are present. To quantify the antibiotic diffusion dynamics we employ a phenomenological model using a subdiffusion-absorption equation with a fractional time derivative. This effective equation describes molecular diffusion in a medium structured akin Thompson’s plumpudding model; here the ‘pudding’ background represents the ASM and the ‘plums’ represent the bacterial biofilm. The pudding is a subdiffusion barrier for antibiotic molecules that can affect bacteria found in plums. For the experimental study we use an interferometric method to determine the time evolution of the amount of antibiotic that has diffused through the biofilm. The theoretical model shows that this function is qualitatively different depending on whether or not absorption of the antibiotic in the biofilm occurs. We show that the process can be divided into three successive stages: (1) only antibiotic subdiffusion with constant biofilm parameters, (2) subdiffusion and absorption of antibiotic molecules with variable biofilm transport parameters, (3) subdiffusion and absorption in the medium but the biofilm parameters are constant again. Stage 2 is interpreted as the appearance of an intensive defence build–up of bacteria against the action of the antibiotic, and in the stage 3 it is likely that the bacteria have been inactivated. Times at which stages change are determined from the experimentally obtained temporal evolution of the amount of antibiotic that has diffused through the ASM with bacteria. Our analysis shows good agreement between experimental and theoretical results and is consistent with the biologically expected biofilm response. We show that an experimental method to study the temporal evolution of the amount of a substance that has diffused through a biofilm is useful in studying the processes occurring in a biofilm. We also show that the complicated biological process of antibiotic diffusion in a biofilm can be described by a fractional subdiffusion-absorption equation with subdiffusion and absorption parameters that change over time. KW - Bacterial biofilms KW - Antibiotics KW - Biofilms KW - Cystic fibrosis KW - Absorption KW - Pseudomonas aeruginosa KW - Sputum KW - Biological defense mechanisms Y1 - 2020 U6 - https://doi.org/10.1371/journal.pone.0243003 SN - 1932-6203 VL - 15 PB - PLOS CY - San Francisco, California, US ER -