Anomalous diffusion in correlated continuous time random walks

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement ~t^{2/3}. Long-ranged correlations of the waiting times with power-law exponent alpha (0<alpha<=2) give rise to subdiffusion of the form ~t^{alpha/(1+alpha)}. In contrast correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.Comment: 6 pages, 6 figures. Slightly revised version, accepted to J Phys A as a Fast Track Communicatio

Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Levy walks in which the fractional equivalent of the material derivative occurs. Our approach will be useful for the dynamical formulation of Levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited

Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions

We examine by extensive computer simulations the self-diffusion of anisotropic star like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction $\phi$ of the crowders and the crowder-crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, as well as the effective diffusion coefficient. The diffusion appears ergodic in the limit of long traces, such that the time averaged MSD converges towards the ensemble averaged MSD and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales we quantify the anomalous diffusion in the system. Also, we show that the translational---but not rotational---diffusivity of the particles $D$ is a non-monotonic function of the attraction strength between them. Both diffusion coefficients decrease as $D(\phi)\sim (1-\phi/\phi^*)^2$ with the area fraction $\phi$ occupied by the crowders. Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells.Comment: 16 pages, 7 figure

Sensing viruses by mechanical tension of DNA in responsive hydrogels

The rapid worldwide spread of severe viral infections, often involving novel modifications of viruses, poses major challenges to our health care systems. This means that tools that can efficiently and specifically diagnose viruses are much needed. To be relevant for a broad application in local health care centers, such tools should be relatively cheap and easy to use. Here we discuss the biophysical potential for the macroscopic detection of viruses based on the induction of a mechanical stress in a bundle of pre-stretched DNA molecules upon binding of viruses to the DNA. We show that the affinity of the DNA to the charged virus surface induces a local melting of the double-helix into two single-stranded DNA. This process effects a mechanical stress along the DNA chains leading to an overall contraction of the DNA. Our results suggest that when such DNA bundles are incorporated in a supporting matrix such as a responsive hydrogel, the presence of viruses may indeed lead to a significant, macroscopic mechanical deformation of the matrix. We discuss the biophysical basis for this effect and characterize the physical properties of the associated DNA melting transition. In particular, we reveal several scaling relations between the relevant physical parameters of the system. We promote this DNA-based assay for efficient and specific virus screening.Comment: 11 pages, 7 figures, supplementary material included in the source file