Numerical study of domain coarsening in anisotropic stripe patterns

We study the coarsening of two-dimensional smectic polycrystals characterized by grains of oblique stripes with only two possible orientations. For this purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close enough to the onset of stripe formation, the average domain size increases with time as $t^{1/2}$. Further from onset, anisotropic pinning forces similar to Peierls stresses in solid crystals slow down defects, and growth becomes anisotropic. In a wide range of quench depths, dislocation arrays remain mobile and dislocation density roughly decays as $t^{-1/3}$, while chevron boundaries are totally pinned. We discuss some agreements and disagreements found with recent experimental results on the coarsening of anisotropic electroconvection patterns.Comment: 8 pages, 11 figures. Phys. Rev E, to appea

Low temperature shape relaxation of 2-d islands by edge diffusion

We present a precise microscopic description of the limiting step for low temperature shape relaxation of two dimensional islands in which activated diffusion of particles along the boundary is the only mechanism of transport allowed. In particular, we are able to explain why the system is driven irreversibly towards equilibrium. Based on this description, we present a scheme for calculating the duration of the limiting step at each stage of the relaxation process. Finally, we calculate numerically the total relaxation time as predicted by our results and compare it with simulations of the relaxation process.Comment: 11 pages, 5 figures, to appear in Phys. Rev.

Elastin-Mediated Choroidal Endothelial Cell Migration: Possible Role in Age-Related Macular Degeneration

PURPOSE. Endothelial cell (EC) migration is a key event in angiogenesis, and is likely to play an important role in choroidal neovascularization in age-related macular degeneration (AMD). Altered elastin metabolism has been described in AMD, and the present study sought to determine the effects of elastin-derived peptides (EDPs) on choroidal EC migration and proliferation. METHODS. Migration of the chorioretinal EC line Rf/6a and a primary culture of human choroidal ECs through polycarbonate membrane inserts was quantified in the presence of elastin bioactive hexapeptides (BPs), EDPs, bovine serum albumin (BSA), or balanced salt solution. Proliferation assays and in vitro wound closure experiments were also performed in the presence of elastin fragments or balanced salt solution (control). Elastin overlay experiments were performed on sections of human eyes. RESULTS. For both Rf/6a and human primary choroidal ECs exposed to EDPs or BPs, the number of ECs that migrated through the polycarbonate membrane was significantly higher than ECs exposed to balanced salt solution alone or to BSA (P Ͻ 0.05) in all experiments. In contrast, the rate of EC proliferation did not significantly change in comparison to controls. Elastin binding sites were identified on choroidal ECs in human eyes. CONCLUSIONS. Elastin fragments increase choroidal EC migration, whereas they do not appear to increase or decrease EC proliferation. Local or systemic abnormalities in elastin physiology may participate in pathologic neovascular membrane formation in AMD. (Invest Ophthalmol Vis Sci. 2008;49: 5574 -5580) DOI:10.1167/iovs. A ge-related macular degeneration (AMD) is a major cause of blindness. The neovascular (wet) form of AMD is characterized by the abnormal growth of choroidal blood vessels into the sub-retinal space of the macula. This multistep process is likely to be initiated by the breakdown of Bruch's membrane which, when intact, prevents pathologic angiogenesis. In this process, choroidal ECs may migrate from the choroid into the sub-RPE and/or sub-retinal space. These ECs proliferate and form tubes (tubulogenesis), ultimately reorganizing their junctions to increase permeability across the newly formed vascular wall. The neovascular process in AMD can result in serous detachment of the retinal pigmented epithelium (RPE) and/or neurosensory retinal detachment, as well as fibrous disciform scarring beneath the retina, causing a catastrophic decrease in visual acuity. 1-5 Current treatments for neovascular AMD are focused primarily on vascular endothelial growth factor (VEGF)-mediated processes. 6 While VEGF is a potent inducer of angiogenesis, understanding the role of additional angiogenic stimuli would be invaluable for the development of improved treatments. 7 Elastin is a glycoprotein consisting of cross-linked 72 kDa tropoelastin subunits and is an abundant component of the extracellular matrix (ECM) of arteries, lung, and skin. 8 Breakdown of elastin results in the formation of elastin-derived peptides (EDPs), cross-linked fragments of tropoelastin of varying sizes. 10 Currently, it is unknown how these peptides are able to activate ECs and whether they are capable of activating ECs from other tissues, such as the choroid. It is plausible that EDPs bind to elastin binding proteins on the cell surface, inducing angiogenic behaviors such as cell migration and/or proliferation. Several lines of evidence suggest abnormal elastin metabolism occurs in Bruch's membrane in AMD. First, early onset choroidal neovascularization has been shown in patients with pseudoxanthoma elasticum. These patients may be at risk for developing choroidal neovascular membranes because of abnormalities in the elastic layer of Bruch's membrane, including breaks, clinically defined as angioid streaks. 11,12 Second, fibulin-5 missense mutations have been identified in association with AMD. 13 This mutation may contribute to AMD development by affecting the elastic layer of Bruch's membrane, since fibulin-5 participates in elastogenesis There is also evidence for abnormal systemic elastin metabolism in AMD. Blumenkranz et al. 11 found a correlation between choroidal neovascularization (CNV) and elastotic degeneration. Patients with exudative AMD demonstrated a greater than twofold increase in their susceptibility to elastotic degeneration of relatively sun-protected areas of the skin in dermal biopsies, suggesting that AMD is associated with systemic elastin abnormalities. 11 Serum levels of EDPs in patients with exudative AMD have also been found to be significantly higher than levels in non-exudative AMD patients and control patients

Changing shapes in the nanoworld

What are the mechanisms leading to the shape relaxation of three dimensional crystallites ? Kinetic Monte Carlo simulations of fcc clusters show that the usual theories of equilibration, via atomic surface diffusion driven by curvature, are verified only at high temperatures. Below the roughening temperature, the relaxation is much slower, kinetics being governed by the nucleation of a critical germ on a facet. We show that the energy barrier for this step linearly increases with the size of the crystallite, leading to an exponential dependence of the relaxation time.Comment: 4 pages, 5 figures. Accepted by Phys Rev Let