Eur. Phys. J. B 33, 355-363 (2003)
https://doi.org/10.1140/epjb/e2003-00176-5

The Laguerre polyhedral decomposition: application to protein folds

¹ Laboratoire de Physique des Solides, Université Paris Sud (associé au CNRS), bâtiment 510, Centre d'Orsay, 91405 Orsay, France
² Laboratoire des Verres, Université Montpellier 2 (associé au CNRS), Place E. Bataillon Case 003, 34095 Montpellier, France
³ Laboratoire de Dynamique des Fluides Complexes, Université Louis Pasteur (associé au CNRS), 3 rue de l'Université, 67084 Strasbourg, France

Corresponding author: ^a sadoc@lps.u-psud.fr

Received: 20 November 2002
Revised: 26 March 2003
Published online: 20 June 2003

Abstract

An extension of the Voronoi tessellation, the Laguerre polyhedral decomposition, is introduced and applied to the analysis of the packing geometry of amino-acids in folded proteins. This method considers an ensemble of points with different weights and therefore it is well suited for a geometrical analysis of a set of objects with a wide size distribution. With this method it is shown that the true volumes occupied by the amino-acids inside a protein is better described than with the standard Voronoi procedure. This method allows defining unambiguously (without cut-off distance) the neighborhood for each amino-acid in a given protein and contact matrices can be established which contain all topological informations on the internal structure. Finally, a statistical analysis of the geometrical characteristics of the polyhedra attached to each amino-acid is done over a collection of 35 proteins.