On the asymptotic behaviour of elliptic problems with periodic data

We study the asymptotic behaviour of the solution of elliptic problems with periodic data when the size of the domain on which the problem is set becomes unbounded. To cite this article: M. Chipot, Y. Xie, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Exploring the free-energy landscape of a short peptide using an average force

The reversible folding of deca-alanine is chosen as a test case for characterizing a method that uses an adaptive biasing force (ABF) to escape from the minima and overcome the barriers of the free-energy landscape. This approach relies on the continuous estimation of a biasing force that yields a Hamiltonian in which no average force is exerted along the ordering parameter xi. Optimizing the parameters that control how the ABF is applied, the method is shown to be extremely effective when a nonequivocal ordering parameter can be defined to explore the folding pathway of the peptide. Starting from a beta-turn motif and restraining xi to a region of the conformational space that extends from the alpha-helical state to an ensemble of extended structures, the ABF scheme is successful in folding the peptide chain into a compact alpha helix. Sampling of this conformation is, however, marginal when the range of xi values embraces arrangements of greater compactness, hence demonstrating the inherent limitations of free-energy methods when ambiguous ordering parameters are utilized.     

Folding and translocation of the undecamer of poly-L-leucine across the water-hexane interface. A molecular dynamics study.

The undecamer of poly-L-leucine at the water-hexane interface is studied by molecular dynamics simulations. This represents a simple model relevant to folding and insertion of hydrophobic peptides into membranes. The peptide, initially placed in a random coil conformation on the aqueous side of the system, rapidly translocates toward the hexane phase and undergoes interfacial folding into an alpha-helix in the subsequent 36 ns. Folding is nonsequential and highly dynamic. The initially formed helical segment at the N-terminus of the undecamer becomes transiently broken and, subsequently, reforms before the remainder of the peptide folds from the C-terminus. The formation of intramolecular hydrogen bonds during the folding of the peptide is preceded by a dehydration of the participating polar groups, as they become immersed in hexane. Folding proceeds through a short-lived intermediate, a 3(10)-helix, which rapidly interconverts to an alpha-helix. Both helices contribute to the equilibrium ensemble of folded structures. The helical peptide is largely buried in hexane, yet remains adsorbed at the interface. Its preferred orientation is parallel to the interface, although the perpendicular arrangement with the N-terminus immersed in hexane is only slightly less favorable. In contrast, the reversed orientation is highly unfavorable, because it would require dehydration of C-terminus carbonyl groups that do not participate in intramolecular hydrogen bonding. For the same reason, the transfer of the undecamer from the interface to the bulk hexane is also unfavorable. The results suggest that hydrophobic peptides fold in the interfacial region and, simultaneously, translocate into the nonpolar side of the interface. It is further implied that peptide insertion into the membrane is accomplished by rotating from the parallel to the perpendicular orientation, most likely in such a way that the N-terminus penetrates the bilayer.     

The Diffusion of a Population¶Partly Driven by its Preferences

The goal of this paper is to investigate a stationary model for the diffusion of a population when the diffusion coefficient at one location depends on the population at another. This could simulate, for instance, attraction or repulsion between the species considered. Accepted May 29, 2000?Published online November 24, 2000     

The N-membrane problem with nonlocal constraints

In this paper, we study a nonlocal variational inequality. The nonlocality appears both in the coefficients of the operator, through an integral representing some elastic energy, and in the constraints, which are of the type called soft in the literature.     

Structural characterization of micelles formed of cholesteryl-functionalized cyclodextrins

Amphiphilic cholesteryl 2,6-di-O-methyl-β-cyclodextrins (chol-DIMEB) can self-aggregate into spherical micelles of noteworthy potential for drug delivery. All-atom molecular dynamics simulations of chol-DIMEB micelles consisting of 3-24 monomers have been performed in aqueous solution. chol-DIMEB exhibits a pronounced tendency to self-assemble into core-shell structures. van der Waals interactions within the cholesteryl nucleus constitute the main driving force responsible for the formation of the micelle. The calculated radii of the hydrophobic core and of the hydrophilic shell for the micellar structure formed by 24 monomers agree well with the experiment. The cyclodextrin moieties are found to be exposed toward the aqueous medium and possess the appropriate flexibility to capture drugs in an effective fashion. Analysis of the solvent accessible surface area and hydration number indicates that the micelles are highly hydrosoluble species and can, therefore, enhance significantly the aqueous solubility of lipophilic drugs. In addition, the spatial structure of the micelles is suggestive of multiple potential drug binding sites. The present contribution unveils how micelles endowed with specific characteristics can form, while opening exciting perspectives for the design of novel micellar nanoparticles envisioned to be drug carriers of high potential.