Van der Waals surface graphs and molecular shape

A van der Waals surface graph is the graph defined on a van der Waals surface by the intersections of the atomic van der Waals spheres. A van der Waals shape graph has a vertex for each atom with a visible face on the van der Waals surface, and edges between vertices representing atoms with adjacent faces on the van der Waals surface. These are discrete invariants of three‐dimensional molecular shape. Some basic properties of van der Waals surface graphs are studied, including their relationship with the Voronoi diagram of the atom centres, and a class of molecular embeddings is identified for which the dual of the van der Waals surface graph coincides with the van der Waals shape graph. This revised version was published online in July 2006 with corrections to the Cover Date.     

Molecular docking using shape descriptors

Molecular docking explores the binding modes of two interacting molecules. The technique is increasingly popular for studying protein-ligand interactions and for drug design. A fundamental problem problem with molecular docking is that orientation space is very large and grows combinatorially with the number of degrees of freedom of the interacting molecules. Here, we describe and evaluate algorithms that improve the efficiency and accuracy of a shape-based docking method. We use molecular organization and sampling techniques to remove the exponential time dependence on molecular size in docking calculations. The new techniques allow us to study systems that were prohibitively large for the original method. The new algorithms are tested in 10 different protein-ligand systems, including 7 systems where the ligand is itself a protein. In all cases, the new algorithms successfully reproduce the experimentally determined configurations of the ligand in the protein.     

Quantum molecular similarity. 3. QTMS descriptors.

Building on the ideas of a previous paper [part 1, J. Phys. Chem. A 1999, 103, 2883] we present a new molecular similarity method based on the topology of the electron density. This method is directly applicable to QSARs and is called quantum topological molecular similarity (QTMS). It has been tested for five sets of carboxylic systems including para- and meta-benzoic acid, para-phenylacetic acid, 4-X-bicyclo[2.2.2]octane-1-carboxylic acids, and polysubstituted benzoic acids. In combination with the partial least squares (PLS) procedure QTMS is able to produce excellent and statistically valid regressions. It is shown that QTMS avoids certain challenges of traditional Carbó-like similarity indices. Finally, QTMS is able to suggest a molecular fragment that contains the active center or the part of the molecule that is responsible for the QSAR.     

Computing a new family of shape descriptors for protein structures

The large-scale 3D structure of a protein can be represented by the polygonal curve through the carbon alpha atoms of the protein backbone. We introduce an algorithm for computing the average number of times that a given configuration of crossings on such polygonal curves is seen, the average being taken over all directions in space. Hereby, we introduce a new family of global geometric measures of protein structures, which we compare with the so-called generalized Gauss integrals.     

On walks in molecular graphs.

Walks in molecular graphs and their counts for a long time have found applications in theoretical chemistry. These are based on the fact that the (i, j)-entry of the kth power of the adjacency matrix is equal to the number of walks starting at vertex i, ending at vertex j, and having length k. In recent papers (refs 13, 18, 19) the numbers of all walks of length k, called molecular walk counts, mwc(k), and their sum from k = 1 to k = n - 1, called total walk count, twc, were proposed as quantities suitable for QSPR studies and capable of measuring the complexity of organic molecules. We now establish a few general properties of mwc's and twc among which are the linear dependence between the mwc's and linear correlations between the mwc's and twc, the spectral decomposition of mwc's, and various connections between the walk counts and the eigenvalues and eigenvectors of the molecular graph. We also characterize the graphs possessing minimal and maximal walk counts.     

PocketPicker: analysis of ligand binding-sites with shape descriptors

Background  

Identification and evaluation of surface binding-pockets and occluded cavities are initial steps in protein structure-based drug design. Characterizing the active site's shape as well as the distribution of surrounding residues plays an important role for a variety of applications such as automated ligand docking or in situ modeling. Comparing the shape similarity of binding site geometries of related proteins provides further insights into the mechanisms of ligand binding.