Refine
Has Fulltext
- no (211)
Year of publication
Document Type
- Article (211) (remove)
Language
- English (211)
Is part of the Bibliography
- yes (211)
Keywords
- anomalous diffusion (28)
- diffusion (27)
- stochastic processes (9)
- ageing (5)
- first passage (5)
- geometric Brownian motion (5)
- Brownian motion (4)
- first passage time (4)
- fractional Brownian motion (4)
- Fokker-Planck equation (3)
- Levy flights (3)
- Mittag-Leffler functions (3)
- first-passage (3)
- first-passage time (3)
- nonergodicity (3)
- polymers (3)
- scaled Brownian motion (3)
- stochastic resetting (3)
- superstatistics (3)
- Boltzmann distribution (2)
- Debye screening (2)
- Fractional moments (2)
- Langevin equation (2)
- Levy walks (2)
- Sinai diffusion (2)
- active transport (2)
- aspect ratio (2)
- continuous time random walk (CTRW) (2)
- critical phenomena (2)
- crowded fluids (2)
- cylindrical geometry (2)
- diffusing diffusivity (2)
- electrostatic interactions (2)
- financial time series (2)
- first-hitting time (2)
- polyelectrolyte adsorption (2)
- power spectral analysis (2)
- probability density function (2)
- protein search (2)
- random diffusivity (2)
- stochastic processes (theory) (2)
- subdiffusion (2)
- time averaging (2)
- transport (2)
- weak ergodicity breaking (2)
- 15 (1)
- 4 (1)
- Absorption (1)
- Adam-Delbruck scenario (1)
- Ageing (1)
- Anomalous diffusion (1)
- Antibiotics (1)
- Asymptotic expansions (1)
- Bacterial biofilms (1)
- Bayesian inference (1)
- Biofilms (1)
- Biological Physics (1)
- Biological defense mechanisms (1)
- Black– Scholes model (1)
- Brownian yet non-Gaussian diffusion (1)
- Cattaneo equation (1)
- Characteristic function (1)
- Chebyshev inequality (1)
- Complete Bernstein function (1)
- Completely monotone function (1)
- Composite fractional derivative (1)
- Cystic fibrosis (1)
- Distributed order diffusion-wave equations (1)
- Econophysics (1)
- Fokker-Planck-Smoluchowski equation (1)
- Fokker– Planck equation (1)
- Fox H-function (1)
- Fox H-functions (1)
- Fractional calculus (primary) (1)
- Fractional diffusion equation (1)
- Grunwald-Letnikov approximation (1)
- Interdisciplinary Physics (1)
- Levy flight (1)
- Levy foraging hypothesis (1)
- Levy walk (1)
- Lévy flights (1)
- Lévy walks (1)
- Markov additive processes (1)
- Mellin transform (1)
- Mittag-Leffler (1)
- Ornstein–Uhlenbeck process (1)
- Pareto analysis (1)
- Pareto law (1)
- Pseudomonas aeruginosa (1)
- Riesz-Feller fractional derivative (1)
- Scaling exponents (1)
- Scher-Montroll transport (1)
- Sputum (1)
- Statistical Physics (1)
- Statistical and Nonlinear Physics (1)
- Wealth and income distribution (1)
- and surface diffusion (1)
- anomalous (or non-Fickian) diffusion (1)
- anomalous heat conduction (1)
- approximate methods (1)
- asymmetric Levy flights (1)
- asymptotic analysis (1)
- autocorrelation function (1)
- autoregressive models (1)
- barrier escape (1)
- behavior (1)
- biological physics (1)
- bulk (1)
- cambridge cb4 0wf (1)
- cambs (1)
- cellular signalling (1)
- channel (1)
- chemical relaxation (1)
- clustering (1)
- codifference (1)
- coefficient (1)
- coefficients (1)
- coloured (1)
- comb-like model (1)
- complex (1)
- confinement (1)
- conformational properties (1)
- conservative random walks (1)
- continuous time random (1)
- continuous time random walk (1)
- continuous time random walks (1)
- correlated noise (1)
- coupled initial boundary value problem (1)
- critical adsorption (1)
- crossover anomalous diffusion dynamics (1)
- crossover dynamics (1)
- crowding (1)
- density (1)
- dimensional reduction (1)
- driven diffusive systems (theory) (1)
- dynamical systems (1)
- dynamics (1)
- dynamics simulation (1)
- ecological (1)
- econophysics (1)
- electrostatics (1)
- england (1)
- ensemble and time averaged mean squared displacement (1)
- equation approach (1)
- exact results (1)
- exclusion process (1)
- exclusion processes (1)
- expanding medium (1)
- extremal values (1)
- fastest first-passage time of N walkers (1)
- first arrival (1)
- first passage process (1)
- first-arrival density (1)
- first-passage time distribution (1)
- first-passage times (1)
- first-reaction time (1)
- fluctuation-dissipation theorem (1)
- fluctuations (theory) (1)
- fractional dynamic equations (1)
- fractional dynamics (1)
- fractional generalized Langevin equation (1)
- frictional memory kernel (1)
- function (1)
- gel network (1)
- gene regulatory networks (1)
- generalised Langevin equation (1)
- generalised langevin equation (1)
- generalized diffusion equation (1)
- heterogeneous diffusion (1)
- heterogeneous diffusion process (1)
- income inequality (1)
- income mobility (1)
- large deviation function (1)
- large-deviation statistic (1)
- lattice gas (1)
- linear response theory (1)
- living cells (1)
- local equilibrium (1)
- maximum and range (1)
- mean square displacement (1)
- mean squared displacement (1)
- mean versus most probable reaction times (1)
- membrane (1)
- membrane channel (1)
- memory kernel (1)
- milton rd (1)
- mixed boundary conditions (1)
- mobile-immobile model (1)
- models (1)
- molecular overcrowding (1)
- monte-carlo (1)
- movement data (1)
- multi-scaling (1)
- multidimensional fractional diffusion equation (1)
- nanoparticles (1)
- narrow escape problem (1)
- noise (1)
- noise in biochemical signalling (1)
- non-Gaussian (1)
- non-Gaussian diffusion (1)
- non-Gaussian distribution (1)
- non-Gaussian probability (1)
- non-Gaussianity (1)
- non-ergodicity (1)
- non-exponential relaxation (1)
- non-extensive statistics (1)
- nonequilibrium stationary state (1)
- nonstationary diffusivity (1)
- option pricing (1)
- osmotic-pressure (1)
- path integration (1)
- persistence (1)
- phase-transition boundary (1)
- polyelectrolytes (1)
- polymer translocation (1)
- posttranslational protein translocation (1)
- potential landscape (1)
- power spectral density (1)
- power spectrum (1)
- predator-prey model (1)
- quenched energy landscape (1)
- random search process (1)
- random search processes (1)
- random walks (1)
- random-walk (1)
- random-walks (1)
- reaction cascade (1)
- reaction kinetics theory (1)
- reaction rate constants (1)
- recurrence (1)
- reflecting boundary conditions (1)
- resetting (1)
- rotational diffusion (1)
- royal soc chemistry (1)
- science park (1)
- search dynamics (1)
- search efficiency (1)
- search optimization (1)
- shell-like geometries (1)
- single particle tracking (1)
- single trajectories (1)
- single trajectory analysis (1)
- single-file diffusion (1)
- single-particle tracking (1)
- single-stranded-dna (1)
- single-trajectory analysis (1)
- solid-state nanopores (1)
- space-dependent diffusivity (1)
- stationary stochastic process (1)
- stochastic dynamics (1)
- structured polynucleotides (1)
- superdiffusion and (1)
- susceptibility (1)
- tau proteins (1)
- telegrapher's equation (1)
- thomas graham house (1)
- time series analysis (1)
- time-averaged mean squared displacement (1)
- time-series analysis (1)
- van Hove correlation (1)
- variances (1)
- walks (1)
- water diffusion in the brain (1)
Institute
- Institut für Physik und Astronomie (211) (remove)
Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states
(2012)
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.
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.
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.
The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories
(2012)
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.
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.
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.
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.
Velocity and displacement correlation functions for fractional generalized Langevin equations
(2012)
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.
Generalized space-time fractional diffusion equation with composite fractional time derivative
(2012)
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).
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.