Extreme heterogeneity in the microrheology of lamellar surfactant gels analyzed with neural networks.

The heterogeneity of the viscoelasticity of a lamellar gel network based on cetyl-trimethylammonium chloride and cetostearyl alcohol was studied using particle-tracking microrheology. A recurrent neural network (RNN) architecture was used for estimating the Hurst exponent, H, on small sections of tracks of probe spheres moving with fractional Brownian motion. Thus, dynamic segmentation of tracks via neural networks was used in microrheology and it is significantly more accurate than using mean square displacements (MSDs).

Modelling Heterogeneous Anomalous Dynamics of Radiation-Induced Double-Strand Breaks in DNA during Non-Homologous End-Joining Pathway.

The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the rare long-range directed motion.

Heterogeneous anomalous transport in cellular and molecular biology.

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport.

Ensemble heterogeneity mimics ageing for endosomal dynamics within eukaryotic cells.

Transport processes of many structures inside living cells display anomalous diffusion, such as endosomes in eukaryotic cells. They are also heterogeneous in space and time. Large ensembles of single particle trajectories allow the heterogeneities to be quantified in detail and provide insights for mathematical modelling.

Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast Moving Endosomes.

Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display switching between persistent and anti-persistent motion, while others jiggle around in one position for the whole measurement time. By splitting the ensemble of endosome trajectories into slow moving subdiffusive and fast moving superdiffusive endosomes, we analyzed them separately.

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption.

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)10.

Deciphering anomalous heterogeneous intracellular transport with neural networks.

Intracellular transport is predominantly heterogeneous in both time and space, exhibiting varying non-Brownian behavior. Characterization of this movement through averaging methods over an ensemble of trajectories or over the course of a single trajectory often fails to capture this heterogeneity. Here, we developed a deep learning feedforward neural network trained on fractional Brownian motion, providing a novel, accurate and efficient method for resolving heterogeneous behavior of intracellular transport in space and time.

Insights into the non-homologous end joining pathway and double strand break end mobility provided by mechanistic in silico modelling.

After radiation exposure, one of the critical processes for cellular survival is the repair of DNA double strand breaks. The pathways involved in this response are complex in nature and involve many individual steps that act across different time scales, all of which combine to produce an overall behaviour. It is therefore experimentally challenging to unambiguously determine the mechanisms involved and how they interact whilst maintaining strict control of all confounding variables.

Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate.

Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate.

Emergence of Lévy walks in systems of interacting individuals.

We propose a model of superdiffusive Lévy walk as an emergent nonlinear phenomenon in systems of interacting individuals. The aim is to provide a qualitative explanation of recent experiments [G. Ariel et al.

Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks.

We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern.

Distributed-order diffusion equations and multifractality: Models and solutions.

We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed.

Cytoskeletal Network Morphology Regulates Intracellular Transport Dynamics.

Intracellular transport is essential for maintaining proper cellular function in most eukaryotic cells, with perturbations in active transport resulting in several types of disease. Efficient delivery of critical cargos to specific locations is accomplished through a combination of passive diffusion and active transport by molecular motors that ballistically move along a network of cytoskeletal filaments. Although motor-based transport is known to be necessary to overcome cytoplasmic crowding and the limited range of diffusion within reasonable timescales, the topological features of the cytoskeletal network that regulate transport efficiency and robustness have not been established.

Subdiffusion in an external potential: Anomalous effects hiding behind normal behavior.

We propose a model of subdiffusion in which an external force is acting on a particle at all times not only at the moment of jump. The implication of this assumption is the dependence of the random trapping time on the force with the dramatic change of particles behavior compared to the standard continuous time random walk model in the long time limit. Constant force leads to the transition from non-ergodic subdiffusion to ergodic diffusive behavior.

Distributions of time averages for weakly chaotic systems: the role of infinite invariant density.

Distributions of time averaged observables are investigated using deterministic maps with N indifferent fixed points and N-state continuous time random walk processes associated with them. In a weakly chaotic phase, namely when separation of trajectories is subexponential, maps are characterized by an infinite invariant density. We find that the infinite density can be used to calculate the distribution of time averages of integrable observables with a formula recently obtained by Rebenshtok and Barkai.

Boundary conditions of normal and anomalous diffusion from thermal equilibrium.

Infiltration of diffusing particles from one material to another, where the diffusion mechanism is either normal or anomalous, is a widely observed phenomenon. Starting with an underlying continuous-time random-walk model, we derive the boundary conditions for the diffusion equations describing this problem. We discuss a simple method showing how the boundary conditions can be determined from equilibrium experiments.

Separation of trajectories and its relation to entropy for intermittent systems with a zero Lyapunov exponent.

One-dimensional intermittent maps with stretched exponential δx(t)∼δx(0)e(λ(α)t(α)) separation of nearby trajectories are considered. When t→∞ the standard Lyapunov exponent λ=∑(i=0)(t-1)ln|M'(x(i))|/t is zero (M' is a Jacobian of the map). We investigate the distribution of λ(α)=∑(i=0)(t-1)ln|M'(x(i))|/t(α), where α is determined by the nonlinearity of the map in the vicinity of marginally unstable fixed points.

Paradoxes of subdiffusive infiltration in disordered systems.

Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behavior: diffusion may lead to an averaged net drift x from one material to another even if all particles eventually flow in the opposite direction. Furthermore, x does not depend on the properties of the medium in which it is situated, indicating nonlocality of the process.

Pesin-type identity for intermittent dynamics with a zero Lyaponov exponent.

Pesin's identity provides a profound connection between the Kolmogorov-Sinai entropy h_{KS} and the Lyapunov exponent lambda. It is well known that many systems exhibit subexponential separation of nearby trajectories and then lambda=0. In many cases such systems are nonergodic and do not obey usual statistical mechanics.

Fractal properties of anomalous diffusion in intermittent maps.

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous time random-walk theory well approximates the coarse behavior of this quantity in terms of a continuous function.