Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes

We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.Comment: 16 pages, 20 figures, RevTeX

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

Mixing and segregation of ring polymers: spatial confinement and molecular crowding effects

During the life cycle of bacterial cells the non-mixing of the two ring-shaped daughter genomes is an important prerequisite for the cell division process. Mimicking the environments inside highly crowded biological cells, we study the dynamics and statistical behaviour of two flexible ring polymers in the presence of cylindrical confinement and crowding molecules. From extensive computer simulations we determine the degree of ring-ring overlap and the number of inter-monomer contacts for varying volume fractions $\phi$ of crowders. We also examine the entropic de-mixing of polymer rings in the presence of mobile crowders and determine the characteristic times of the internal polymer dynamics. Effects of the ring length on ring-ring overlap are also analysed. In particular, on systematic variation of the fraction of crowding molecules a $(1-\phi)$-scaling is found for the ring-ring overlap length along the cylinder axis, and a non-monotonic dependence of the 3D ring-ring contact number is predicted. Our results help to rationalise the implications of macromolecular crowding for circular DNA molecules in confined spaces inside bacteria as well as in localised cellular compartments inside eukaryotic cells.Comment: 20 pages, 13 Figures, IOP styl