Refine
Has Fulltext
- yes (55) (remove)
Year of publication
Document Type
- Postprint (55)
Language
- English (55)
Keywords
- anomalous diffusion (16)
- diffusion (14)
- living cells (5)
- infection pathway (3)
- models (3)
- nonergodicity (3)
- random-walks (3)
- single-particle tracking (3)
- dynamics (2)
- first passage time (2)
- first-passage time (2)
- fractional Brownian motion (2)
- fractional dynamics (2)
- intracellular-transport (2)
- langevin equation (2)
- physiological consequences (2)
- random diffusivity (2)
- stochastic processes (2)
- superstatistics (2)
- transport (2)
- Antibiotics (1)
- Bacterial biofilms (1)
- Biofilms (1)
- Biological defense mechanisms (1)
- Brownian motion (1)
- Brownian yet non-Gaussian diffusion (1)
- Bulk-mediated diffusion; (1)
- Chebyshev inequality (1)
- Cystic fibrosis (1)
- Debye screening (1)
- Fokker-Planck equations (1)
- Langevin equation (1)
- Levy flights (1)
- Levy walks (1)
- Lévy flights (1)
- Lévy walks (1)
- Ornstein–Uhlenbeck process (1)
- Pseudomonas aeruginosa (1)
- Sputum (1)
- adenoassociated virus (1)
- ageing (1)
- approximate methods (1)
- aspect ratio (1)
- autoregressive models (1)
- behavior (1)
- biological physics (1)
- brownian-motion (1)
- cambridge cb4 0wf (1)
- cambs (1)
- channel (1)
- codifference (1)
- coefficient (1)
- coefficients (1)
- continuous time random walk (1)
- critical phenomena (1)
- cylindrical geometry (1)
- cytoplasm (1)
- diffusing diffusivity (1)
- disordered media (1)
- dna coiling (1)
- dynamics simulation (1)
- electrostatic interactions (1)
- endosomal escape (1)
- england (1)
- ensemble and time averaged mean squared displacement (1)
- equation approach (1)
- escence correlation spectroscopy (1)
- escherichia-coli (1)
- exact results (1)
- excluded volume (1)
- expanding medium (1)
- extremal values (1)
- fastest first-passage time of N walkers (1)
- financial time series (1)
- first-hitting time (1)
- first-passage (1)
- first-passage time distribution (1)
- first-reaction time (1)
- flight search patterns (1)
- fluctuation-dissipation theorem (1)
- fluorescence photobleaching recovery (1)
- folding kinetics (1)
- fractional dynamics approach (1)
- gene regulatory networks (1)
- gene-regulation kinetics (1)
- generalised langevin equation (1)
- geometric Brownian motion (1)
- in-vitro (1)
- inhomogeneous-media (1)
- intermittent chaotic systems (1)
- large-deviation statistic (1)
- levy flights (1)
- lipid bilayer membrane dynamics (1)
- maximum and range (1)
- mean versus most probable reaction times (1)
- mechanisms (1)
- membrane (1)
- membrane channel (1)
- milton rd (1)
- mixed boundary conditions (1)
- mixtures (1)
- monte-carlo (1)
- motion (1)
- narrow escape problem (1)
- non-Gaussian diffusion (1)
- non-Gaussianity (1)
- osmotic-pressure (1)
- photon-counting statistics (1)
- plasma-membrane (1)
- polyelectrolyte adsorption (1)
- posttranslational protein translocation (1)
- power spectral analysis (1)
- power spectral density (1)
- power spectrum (1)
- probability density function (1)
- protein search (1)
- random-walk (1)
- reaction cascade (1)
- reflecting boundary conditions (1)
- royal soc chemistry (1)
- science park (1)
- shell-like geometries (1)
- single trajectories (1)
- single trajectory analysis (1)
- single-stranded-dna (1)
- single-trajectory analysis (1)
- solid-state nanopores (1)
- space-dependent diffusivity (1)
- spatial-organization (1)
- stationary stochastic process (1)
- stochastic resetting (1)
- stochastic time series (1)
- structured polynucleotides (1)
- subdiffusion (1)
- thomas graham house (1)
- time averaging (1)
- time random-walks (1)
- time series analysis (1)
- time-averaged mean squared displacement (1)
- trafficking (1)
- truncated power-law correlated noise (1)
- weak ergodicity breaking (1)
Institute
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.
Abstract
The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive–diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive–diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion–diffusion and subdiffusion–subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.
Diffusion of finite-size particles in two-dimensional channels with random wall configurations
(2014)
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 [J. Chem. Phys., 2012, 137, 024107].
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
Isoflux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force fc. In the high driving force limit, regardless of the channel width, IFTP theory predicts τ ∝ f βc for the translocation time, where β = −1 is the force scaling exponent. Moreover, LD data show that for a very narrow channel fitting only a single file of monomers, the entropic force due to the subchain inside the channel does not play a significant role in the translocation dynamics and the force exponent β = −1 regardless of the force magnitude. As the channel width increases the number of possible spatial configurations of the subchain inside the channel becomes significant and the resulting entropic force causes the force exponent to drop below unity.
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
(2017)
We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.
For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.