Michel Petitjean

On the analytical calculation of van der Waals surfaces and volumes: some numerical aspects

A fast computer algorithm is presented for complete analytical calculation of van der Waals surfaces and volumes. Connollys analytical algorithms, computing second‐ and third‐order atomic spheres overlaps, are shown to give insufficient numerical approximations of the exact van der Waals surfaces and volumes. The presented algorithm computes overlaps of any order. Practical situations frequently involve six‐order overlaps. Analytical computed surfaces and volumes of 63 chemicals are compared with Monte Carlo measured values.

On the root mean square quantitative chirality and quantitative symmetry measures

The properties of the root mean square chiral index of a d-dimensional set of n points, previously investigated for planar sets, are examined for spatial sets. The properties of the root mean squares direct symmetry index, defined as the normalized minimized sum of the n squared distances between the vertices of the d-set and the permuted d-set, are compared to the properties of the chiral index. Some most dissymetric figures are analytically computed. They differ from the most chiral figures, but the most dissymetric 3-tuples and the most chiral 3-tuples have a common remarkable geometric property: the squared lengths of the sides are each equal to three times a squared distance vertex to the mean point.

Interactive maximal common 3D substructure searching with the combined SDM/RMS algorithm

Abstract An interactive procedure calling iteratively the sorted distances matrix (SDM) algorithm and the root mean square (RMS) algorithm performs the spatial alignment of two three-dimensional sets of points, and outputs the maximal common subset with the pairwise correspondence between the two common regions.

Geometric molecular similarity from volume-based distance minimization: Application to saxitoxin and tetrodotoxin

The geometric molecular dissimilarity between two molecules is defined as the difference between the volume of their union minus the volume of their intersection. This dissimilarity has the mathematical properties of a distance. This distance is minimized under all rotations and translations using a discrete Broyden, Fletcher, Goldfarb & Shanno (B.F.G.S.) algorithm. The optimal geometric superimposition of saxitoxin and tetrodotoxin is discussed.

About second kind continuous chirality measures. 1. Planar sets

The chirality index of a d-dimensional set of n points is defined as the sum of the n squared distances between the vertices of the set and those of its inverted image, normalized to 4T/d,T being the inertia of the set. The index is computed after minimization of the sum of the squared distances with respect to all rotations and translations and all permutations between equivalent vertices. The properties of the chiral index are examined for planar sets. The most achiral triangles are obtained analytically for all equivalence situations: one, two, and three equivalent vertices. These triangles are different from those obtained by Weinberg and Mislow with distance functions.

The Cytochrome P450 3A4 has three Major Conformations: New Clues to Drug Recognition by this Promiscuous Enzyme

We computed the channels of the 3A4 isoform of the cytochrome P450 3A4 (CYP) on the basis of 24 crystal structures extracted from the Protein Data Bank (PDB). We identified three major conformations (denoted C, O1 and O2) using an enhanced version of the CCCPP software that we developed for the present work, while only two conformations (C and O2) are considered in the literature. We established the flowchart of definition of these three conformations in function of the structural and physicochemical parameters of the ligand. The channels are characterized with qualitative and quantitative parameters, and not only with their surrounding secondary structures as it is usually done in the literature

Chiralité quantitative : le modèle des moindres carrés pondérés

Abstract The continuous measure of quantitative chirality by the least squares method is extended to weighed sets. It is shown that a pairwise correspondence between the atoms of the enantiomers is obtained when all weights are equal.

Ring perception: proof of a formula calculating the number of the smallest rings in connected graphs

A general mathematical proof of a formula proposed and used by Fan et al. for calculating the number of the smallest rings in their smallest set of the smallest rings search algorithm is reported. This proof generalizes this formula to all connected cyclic graphs.

About the Upper Bound of the Chiral Index of Multivariate Distributions

A family of distributions in Rd having a chiral index greater or equal to a constant arbitrarily close to 1/2 is exhibited. It is deduced that the upper bound of the chiral index lies in the interval [1/2; 1], for any dimension d.

MolDIA: XML based system of molecular diversity analysis towards virtual screening and QSPR.

In this paper a new chemoinformatics tool for Molecular Diversity Analysis (MolDIA) is introduced. The objective of this system is the analysis of molecular similarity and diversity through the treatment of structural and physicochemical information. Current needs for chemical databases include the analysis, the management and the retrieval of chemical information. The implementation of eXtended Markup Languages (XML) is proposed as a basis for representing and structuring the chemical information contained in data structures and databases. The adequate descriptor vector and related physicochemical properties have been defined and constructed. The benefits of XML in chemoinformatics are discussed, as well as, the applications of this system in a virtual screening environment. †Presented at CMTPI 2005: Computational Methods in Toxicology and Pharmacology Integrating Internet Resources (Shanghai, China, October 29–November 1, 2005).