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
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion.
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations (“Joseph effect”), fat-tailed probability density of increments (“Noah effect”), and nonstationarity (“Moses effect”). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.