Langerin-Heparin Interaction: Two Binding Sites for Small and Large Ligands as revealed by a combination of NMR Spectroscopy and Cross-Linking Mapping Experiments

Langerin is a C-type lectin present on Langerhans cells that mediates capture of pathogens in a carbohydrate-dependent manner, leading to subsequent internalization and elimination in the cellular organelles called Birbeck granules. This mechanism mediated by langerin was shown to constitute a natural barrier for HIV-1 particle transmission. Besides interacting specifically with high mannose and fucosylated neutral carbohydrate structures, langerin has the ability to bind sulfated carbohydrate ligands as 6-sulfated galactosides in the Ca2+ dependent binding site. Very recently langerin was demonstrated to interact with sulfated glycosaminoglycans (GAGs), in a Ca2+ independent way, resulting in the proposal of a new binding site for GAGs. Based on those results, we have conducted a structural study of the interactions of small heparin (HEP) like oligosaccharides with langerin in solution. Heparin-bead cross-linking experiments, an approach specifically designed to identify HEP/HS binding sites in proteins were first carried out and experimentally validated the previously proposed model for the interaction of Lg ECD with 6 kDa HEP. High-resolution NMR studies of a set of 8 synthetic HEP-like trisaccharides harboring different sulfation patterns demonstrated that all of them bound to langerin in a Ca2+ dependent way. The binding epitopes were determined by STD NMR and the bound conformations by transferred NOESY experiments. These experimental data were combined with docking and molecular dynamics and resulted in the proposal of a binding mode characterized by the coordination of calcium by the two equatorial hydroxyl groups OH3 and OH4 at the non-reducing end. The binding also includes the carboxylate group at the adjacent iduronate residue. Such epitope is shared by all the 8 ligands, explaining the absence of any impact on binding from their differences in substitution pattern. Finally, in contrast to the small trisaccharides, we demonstrated that a longer HEP-like hexasaccharide, bearing an additional O-sulfate group at the non-reducing end, which precludes binding to the Ca2+ site, interacts with langerin in the previously identified Ca2+ independent binding site

A path following algorithm for the graph matching problem

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the state-of-the-art.Comment: 23 pages, 13 figures,typo correction, new results in sections 4,5,

Learning Topic Models and Latent Bayesian Networks Under Expansion Constraints

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including probabilistic topic models and latent linear Bayesian networks, using only second-order observed moments. The sufficient conditions for identifiability of these models are primarily based on weak expansion constraints on the topic-word matrix, for topic models, and on the directed acyclic graph, for Bayesian networks. Because no assumptions are made on the distribution among the latent variables, the approach can handle arbitrary correlations among the topics or latent factors. In addition, a tractable learning method via $\ell_1$ optimization is proposed and studied in numerical experiments.Comment: 38 pages, 6 figures, 2 tables, applications in topic models and Bayesian networks are studied. Simulation section is adde

Practical computational toolkits for dendrimers and dendrons structure design

Dendrimers and dendrons offer an excellent platform for developing novel drug delivery systems and medicines. The rational design and further development of these repetitively branched systems are restricted by difficulties in scalable synthesis and structural determination, which can be overcome by judicious use of molecular modelling and molecular simulations. A major difficulty to utilise in silico studies to design dendrimers lies in the laborious generation of their structures. Current modelling tools utilise automated assembly of simpler dendrimers or the inefficient manual assembly of monomer precursors to generate more complicated dendrimer structures. Herein we describe two novel graphical user interface (GUI) toolkits written in Python that provide an improved degree of automation for rapid assembly of dendrimers and generation of their 2D and 3D structures. Our first toolkit uses the RDkit library, SMILES nomenclature of monomers and SMARTS reaction nomenclature to generate SMILES and mol files of dendrimers without 3D coordinates. These files are used for simple graphical representations and storing their structures in databases. The second toolkit assembles complex topology dendrimers from monomers to construct 3D dendrimer structures to be used as starting points for simulation using existing and widely available software and force fields. Both tools were validated for ease-of-use to prototype dendrimer structure and the second toolkit was especially relevant for dendrimers of high complexity and size.Peer reviewe