Bounded step superdiffusion in an oriented hexagonal phase

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). An ensemble of 414 particles produces a MSD that is subdiffusive in time, t, with a power law of the form t^{0.74±0.02}, indicating power law viscoelasticity. RNN analysis of the probability distributions of H, combined with detailed analysis of the time-averaged MSDs of individual tracks, revealed diverse diffusion processes belied by the simple scaling of the ensemble MSD, such as caging phenomena, which give rise to the complex viscoelasticity of lamellar gels.

Anisotropic molecular hopping at the solid-nematic interface

Single molecule tracking was used to observe intermittent and anisotropic molecular motion at the solid-nematic interface. Although the interfacial diffusion was dramatically slower than self-diffusion in the nematic, the diffusion anisotropy was the same at the interface and in bulk, supporting the desorption-mediated mechanism of interfacial diffusion, where molecules sample the physical properties of the vicinal fluid phase during flights, and the magnitude of the interfacial diffusion coefficient is primarily determined by the distribution of waiting times between flights.

Transport of particles in liquid crystals

Colloidal particles in a liquid crystal (LC) behave very differently from their counterparts in isotropic fluids. Elastic nature of the orientational order and surface anchoring of the director cause long-range anisotropic interactions and lead to the phenomenon of levitation. The LC environment enables new mechanisms of particle transport that are reviewed in this work. Among them the motion of particles caused by gradients of the director, and effects in the electric field: backflow powered by director reorientations, dielectrophoresis in LC with varying dielectric permittivity and LC-enabled nonlinear electrophoresis with velocity that depends on the square of the applied electric field and can be directed differently from the field direction.

Anisotropic Brownian motion in ordered phases of DNA fragments

Using Fluorescence Recovery After Photobleaching, we investigate the Brownian motion of DNA rod-like fragments in two distinct anisotropic phases with a local nematic symmetry. The height of the measurement volume ensures the averaging of the anisotropy of the in-plane diffusive motion parallel or perpendicular to the local nematic director in aligned domains. Still, as shown in using a model specifically designed to handle such a situation and predicting a non-Gaussian shape for the bleached spot as fluorescence recovery proceeds, the two distinct diffusion coefficients of the DNA particles can be retrieved from data analysis. In the first system investigated (a ternary DNA-lipid lamellar complex), the magnitude and anisotropy of the diffusion coefficient of the DNA fragments confined by the lipid bilayers are obtained for the first time. In the second, binary DNA-solvent system, the magnitude of the diffusion coefficient is found to decrease markedly as DNA concentration is increased from isotropic to cholesteric phase. In addition, the diffusion coefficient anisotropy measured within cholesteric domains in the phase coexistence region increases with concentration, and eventually reaches a high value in the cholesteric phase.

Variation of the lateral mobility of transmembrane peptides with hydrophobic mismatch

A hydrophobic mismatch between protein length and membrane thickness can lead to a modification of protein conformation, function, and oligomerization. To study the role of hydrophobic mismatch, we have measured the change in mobility of transmembrane peptides possessing a hydrophobic helix of various length d(pi) in lipid membranes of giant vesicles. We also used a model system where the hydrophobic thickness of the bilayers, h, can be tuned at will. We precisely measured the diffusion coefficient of the embedded peptides and gained access to the apparent size of diffusing objects. For bilayers thinner than d(pi), the diffusion coefficient decreases, and the derived characteristic sizes are larger than the peptide radii. Previous studies suggest that peptides accommodate by tilting. This scenario was confirmed by ATR-FTIR spectroscopy. As the membrane thickness increases, the value of the diffusion coefficient increases to reach a maximum at h approximately = d(pi). We show that this variation in diffusion coefficient is consistent with a decrease in peptide tilt. To do so, we have derived a relation between the diffusion coefficient and the tilt angle, and we used this relation to derive the peptide tilt from our diffusion measurements. As the membrane thickness increases, the peptides raise (i.e., their tilt is reduced) and reach an upright position and a maximal mobility for h approximately = d(pi). Using accessibility measurements, we show that when the membrane becomes too thick, the peptide polar heads sink into the interfacial region. Surprisingly, this "pinching" behavior does not hinder the lateral diffusion of the transmembrane peptides. Ultimately, a break in the peptide transmembrane anchorage is observed and is revealed by a "jump" in the D values.

Self-diffusion of rodlike viruses through smectic layers

We report the direct visualization at the scale of single particles of mass transport between smectic layers, also called permeation, in a suspension of rodlike viruses. Self-diffusion takes place preferentially in the direction normal to the smectic layers, and occurs by quasiquantized steps of one rod length. The diffusion rate corresponds with the rate calculated from the diffusion in the nematic state with a lamellar periodic ordering potential that is obtained experimentally.

Theoretically predicted effects of Gaussian curvature on lateral diffusion of membrane molecules

Lateral diffusion on curved biological membranes has been studied theoretically and experimentally. However, how membrane geometries influence the diffusion process remains unclear. Here we show the significance of Gaussian curvature by numerically solving the diffusion equation in a geodesic polar coordinate system with regard to several types of surfaces including elliptic and hyperbolic paraboloids. On surfaces where Gaussian curvature has positive and negative values, diffusion is slower and faster than on the plane, respectively. The deviation from the normal diffusion on the plane tends to get larger as the absolute value of Gaussian curvature increases. Diffusion is anisotropic at a surface region where the normal curvature is anisotropic and Gaussian curvature has nonzero values. The anisotropy can be classified into several types according to whether diffusion is the fastest or the slowest in the principal directions. In the case of diffusion on spheroids, the limited area of a closed surface reduces the diffusion rate so greatly that the slowdown effects of positive values of Gaussian curvature are concealed. Analysis of the diffusion equation suggests that Gaussian curvature causes slowed or accelerated diffusion and anisotropic diffusion in any type of surface. Furthermore, it is discussed the degree to which Gaussian curvature influences diffusive phenomena taking place in real membranes through such effects. These results provide a different image of biological membranes that lateral diffusion of membrane molecules is usually anisotropic and the diffusion rate kaleidoscopically changes according to place.

Propagation of fluorescent viruses in growing plaques

To study virus propagation, we have developed a method by which the propagation of the Lambda bacteriophage can be observed and quantified. This is done by creating a fusion protein of the capsid protein gpD and the enhanced yellow fluorescent protein (EYFP). We show that this fusion allows capsid formation and that the modified viruses propagate on a surface covered with host bacteria thus forming fluorescent plaques. The intensity of fluorescence in a growing plaque determines the distribution of phages. This provides a new tool to study the propagation of infection at the microscopic level.

Diffusion in curved fluid membranes

We analyze theoretically the effects of curvature on the diffusion in a fluid membrane, within the Saffman-Delbrück hydrodynamic model. We calculate the effect of curvature on the intrinsic fluidity of a membrane through changes in its thickness, for both static or fluctuating curvature. We treat both thermal curvature fluctuations, and fluctuations due to active processes. Such curvature fluctuations increase the average membrane thickness and diminish the projected area, thereby decreasing the diffusion coefficient. This calculation allows us to predict the effect of shear flow on the membrane diffusion, and to compare to observations on living cells.

Movement of Proteins in an Environment Crowded by Surfactant Micelles: Anomalous versus Normal Diffusion

Small proteins move in crowded cell compartments by anomalous diffusion. In many of them, e.g., the endoplasmic reticulum, the proteins move between lipid membranes in the aqueous lumen. Molecular crowding in vitro offers a systematic way to study anomalous and normal diffusion in a well controlled environment not accessible in vivo. We prepared a crowded environment in vitro consisting of hexaethylene glycol monododecyl ether (C(12)E(6)) nonionic surfactant and water and observed lysozyme diffusion between elongated micelles. We have fitted the data obtained in fluorescence correlation spectroscopy using an anomalous diffusion model and a two-component normal diffusion model. For a small concentration of surfactant (below 4 wt %) the data can be fitted by single-component normal diffusion. For larger concentrations the normal diffusion fit gave two components: one very slow and one fast. The amplitude of the slow component grows with C(12)E(6) concentration. The ratio of diffusion coefficients (slow to fast) is on the order of 0.1 for all concentrations of surfactant in the solution. The fast diffusion is due to free proteins while the slow one is due to the protein-micelle complexes. The protein-micelle interaction is weak since even in a highly concentrated solution (35% of C(12)E(6)) the amplitude of the slow mode is only 10%, despite the fact that the average distance between the micelles is the same as the size of the protein. The anomalous diffusion model gave the anomaly index (r(2)(t) approximately t(alpha)), alpha monotonically decreasing from alpha = 1 (at 4% surfactant) to alpha = 0.88 (at 37% surfactant). The fits for two-component normal diffusion and anomalous diffusion were of equally good quality, but the physical interpretation was only straightforward for the former.

Lateral mobility of proteins in liquid membranes revisited

The biological function of transmembrane proteins is closely related to their insertion, which has most often been studied through their lateral mobility. For >30 years, it has been thought that hardly any information on the size of the diffusing object can be extracted from such experiments. Indeed, the hydrodynamic model developed by Saffman and Delbrück predicts a weak, logarithmic dependence of the diffusion coefficient D with the radius R of the protein. Despite widespread use, its validity has never been thoroughly investigated. To check this model, we measured the diffusion coefficients of various peptides and transmembrane proteins, incorporated into giant unilamellar vesicles of 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC) or in model bilayers of tunable thickness. We show in this work that, for several integral proteins spanning a large range of sizes, the diffusion coefficient is strongly linked to the protein dimensions. A heuristic model results in a Stokes-like expression for D, (D proportional, variant 1/R), which fits literature data as well as ours. Diffusion measurement is then a fast and fruitful method; it allows determining the oligomerization degree of proteins or studying lipid-protein and protein-protein interactions within bilayers.