Nonatomic solvent‐driven voronoi tessellation of proteins: An open tool to analyze protein folds

Abstract

A three-dimensional Voronoi tessellation of folded proteins is used to analyze geometrical and topological properties of a set of proteins. To each amino acid is associated a central point surrounded by a Voronoi cell. Voronoi cells describe the packing of the amino acids. Special attention is given to reproduction of the protein surface. Once the Voronoi cells are built, a lot of tools from geometrical analysis can be applied to investigate the protein structure; volume of cells, number of faces per cell, and number of sides per face are the usual signatures of the protein structure. A distinct difference between faces related to primary, secondary, and tertiary structures has been observed. Faces threaded by the main-chain have on average more than six edges, whereas those related to helical packing of the amino acid chain have less than five edges. The faces on the protein surface have on average five edges within 1% error. The average number of faces on the protein surface for a given type of amino acid brings a new point of view in the characterization of the exposition to the solvent and the classification of amino acid as hydrophilic or hydrophobic. It may be a convenient tool for model validation.

Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis

“…The Voronoi diagram for ordinary point set has been extensively studied and its properties are well-known in two and higher dimensions. However, Euclidean Voronoi diagrams for circles in two dimensions, spheres in three or higher dimensions have not been as extensively explored even though they have diverse and significant applications in both science and engineering [1,9,15,21,23].…”

Pocket extraction on proteins via the Voronoi diagram of spheres

“…However, the construction of the Voronoi diagram for spheres, often referred to as an additively weighted Voronoi diagram [29], has not been explored sufficiently even though it has significant potential impact on diverse applications in the protein structure [1,12,28,33,35]. Due to the lack of appropriate algorithms and stable running codes for the Voronoi diagrams of spheres, most applications have instead adapted an ordinary Voronoi diagram of points, a power diagram, or an a-shape.…”

From protein sequence space to elementary protein modules

“…This confinement already indicates that, perhaps, the long sequences actually consist of shorter modules. Indeed, the nearly standard size protein units of 25-30 residues have been observed in numerous studies (Benner et al, 1993;Roy et al, 1999;Sato et al, 1999;Berezovsky et al, 2000;Qian and Goldstein, 2001;Angelov et al, 2002;Voigt et al, 2002;Berezovsky et al, 2003a;Berezovsky et al, 2003b;Aharonovsky and Trifonov, 2005;Sobolevsky and Trifonov, 2006;Yew et al, 2007).…”