CHARMM additive all-atom force field for carbohydrate derivatives and its utility in polysaccharide and carbohydrate-protein modeling

Monosaccharide derivatives such as xylose, fucose, N-acetylglucosamine (GlcNAc), N-acetylgalactosamine (GlaNAc), glucuronic acid, iduronic acid, and N-acetylneuraminic acid (Neu5Ac) are important components of eukaryotic glycans. The present work details development of force-field parameters for these monosaccharides and their covalent connections to proteins via O-linkages to serine or threonine sidechains and via N-linkages to asparagine sidechains. The force field development protocol was designed to explicitly yield parameters that are compatible with the existing CHARMM additive force field for proteins, nucleic acids, lipids, carbohydrates, and small molecules. Therefore, when combined with previously developed parameters for pyranose and furanose monosaccharides, for glycosidic linkages between monosaccharides, and for proteins, the present set of parameters enables the molecular simulation of a wide variety of biologically-important molecules such as complex carbohydrates and glycoproteins. Parametrization included fitting to quantum mechanical (QM) geometries and conformational energies of model compounds, as well as to QM pair interaction energies and distances of model compounds with water. Parameters were validated in the context of crystals of relevant monosaccharides, as well NMR and/or x-ray crystallographic data on larger systems including oligomeric hyaluronan, sialyl Lewis X, O- and N-linked glycopeptides, and a lectin:sucrose complex. As the validated parameters are an extension of the CHARMM all-atom additive biomolecular force field, they further broaden the types of heterogeneous systems accessible with a consistently-developed force-field model.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

The d-Step Conjecture and Gaussian Elimination

The d-step conjecture is one of the fundamental open problems concerning the structure of convex polytopes. Let Δ (d,n) denote the maximum diameter of a graph of a d-polytope that has n facets. The d-step conjecture Δ (d,2d) = d is proved equivalent to the following statement: For each ``general position' real matrix M there are two matrices drawn from a finite group matrices isomorphic to the symmetric group on d letters, such that has the Gaussian elimination factorization L ^-1 U in which L and U are lower triangular and upper triangular matrices, respectively, that have positive nontriangular elements. If #(M) is the number of pairs giving a positive L ^-1 U factorization, then #(M) equals the number of d-step paths between two vertices of an associated Dantzig figure. One consequence is that #(M)≤ d!. Numerical experiments all satisfied #(M) ≥ 2 ^d-1 , including examples attaining equality for 3 ≤ d ≤ 15. The inequality #(M) ≥ 2 ^d-1 is proved for d=3. For d≥ 4, examples with #(M) =2 ^d-1 exhibit a large variety of combinatorial types of associated Dantzig figures. These experiments and other evidence suggest that the d-step conjecture may be true in all dimensions, in the strong form #(M) ≥ 2 ^d-1 . Received April 10, 1995, and in revised form August 23, 1995.     

An algebraic approach to the restoration of images

Two different matrix algorithms are described for the restoration of blurred pictures. These are illustrated by numerical examples.     

Direct measurement of the counterion distribution within swollen polyelectrolyte films

The depth profile of the counterion concentration within thin polyelectrolyte films was measured in situ using contrast variant specular neutron reflectivity to characterize the initial swelling stage of the film dissolution. We find substantial counterion depletion near the substrate and enrichment near the periphery of the film extending into the solution. These observations challenge our understanding of the charge distribution in polyelectrolyte films and are important for understanding film dissolution in medical and technological applications.