Weakly anomalous diffusion with non-Gaussian propagators

A poorly understood phenomenon seen in complex systems is diffusion characterized by Hurst exponent H approximate to 1/2 but with non-Gaussian statistics. Motivated by such empirical findings, we report an exact analytical solution for a non-Markovian random walk model that gives rise to weakly anomalous diffusion with H = 1/2 but with a non-Gaussian propagator.

Anomalous diffusion evidenced by particle tracking at high frame rates.

Diffusion is a common phenomenon in nature and generally is associated with a system trying to reach a local or a global equilibrium state, as a result of highly irregular individual particle motion. Therefore it is of fundamental importance in physics, chemistry and biology. Particle tracking in complex fluids can reveal important characteristics of its properties. In living cells, we coat the microbead with a peptide (RGD) that binds to integrin receptors at the plasma membrane, which connects to the CSK. This procedure is based on the hypothesis that the microsphere can move only if the structure where it is attached move as well. Then, the observed trajectory of microbeads is a probe of the cytoskeleton (CSK), which is governed by several factors, including thermal diffusion, pressure gradients, and molecular motors. The possibility of separating the trajectories into passive and active diffusion may give information about the viscoelasticity of the cell structure and molecular motors activity. And also we could analyze the motion via generalized Stokes-Einstein relation, avoiding the use of any active techniques. Usually a 12 to 16 Frames Per Second (FPS) system is used to track the microbeads in cell for about 5 minutes. Several factors make this FPS limitation: camera computer communication, light, computer speed for online analysis among others. Here we used a high quality camera and our own software, developed in C++ and Linux, to reach high FPS. Measurements were conducted with samples for 10£ and 20£ objectives. We performed sequentially images with different intervals, all with 2 ¹s exposure. The sequences of intervals are in milliseconds: 4 5 ms (maximum speed) 14, 25, 50 and 100 FPS. Our preliminary results highlight the difference between passive and active diffusion, since the passive diffusion is represented by a Gaussian in the distribution of displacements of the center of mass of individual beads between consecutive frames. However, the active process, or anomalous diffusion, shows as long tails in the distribution of displacements.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Light scattering on the structural characterization of DMPG vesicles along the bilayer anomalous phase transition

Highly charged vesicles of the saturated anionic lipid dimyristoyl phosphatidylglycerol (DMPG) in low ionic strength medium exhibit a very peculiar thermo-structural behavior. Along a wide gel-fluid transition region, DMPG dispersions display several anomalous characteristics, like low turbidity, high electrical conductivity and viscosity. Here, static and dynamic light scattering (SLS and DLS) were used to characterize DMPG vesicles at different temperatures. Similar experiments were performed with the largely studied zwitterionic lipid dimyristoyl phosphatidylcholine (DMPC). SLS and DLS data yielded similar dimensions for DMPC vesicles at all studied temperatures. However, for DMPG, along the gel-fluid transition region, SLS indicated a threefold increase in the vesicle radius of gyration, whereas the hydrodynamic radius, as obtained from DLS, increased 30% only. Despite the anomalous increase in the radius of gyration, DMPG lipid vesicles maintain isotropy, since no light depolarization was detected. Hence, SLS data are interpreted regarding the presence of isotropic vesicles within the DMPG anomalous transition, but highly perforated vesicles, with large holes. DLS/SLS discrepancy along the DMPG transition region is discussed in terms of the interpretation of the Einstein-Stokes relation for porous vesicles. Therefore, SLS data are shown to be much more appropriate for measuring porous vesicle dimensions than the vesicle diffusion coefficient. The underlying nanoscopic process which leads to the opening of pores in charged DMPG bilayer is very intriguing and deserves further investigation. One could envisage biotechnological applications, with vesicles being produced to enlarge and perforate in a chosen temperature and/or pH value. (C) 2012 Elsevier Ireland Ltd. All rights reserved.