A Novel Evaluation of Residue and Protein Volumes by Means of Laguerre Tessellation

Abstract

Amino acids control the protein folding process and maintain its functional fold. This study underlines the interest of the Laguerre tessellation to determine relevant amino acid volumes in proteins. Previous studies used a limited number of proteins and only buried residues. The present computations improve the method and results on three main points: (i) a large, high-quality updated and refined data bank of proteins is used; (ii) all residues are taken into account, including those at the protein surface, thanks to (iii) the addition of a realistic solvent. The new values of the average and standard deviation of amino acid volumes show significant corrections with respect to previous studies. Another issue of the method is the polyhedral protein/water interface area (PIA) which quantifies the exposure of atoms or residues to the solvent. We propose this PIA as a new, parameter-free, alternative for measuring accessibility. The comparison with NACCESS is satisfactory; however, the methods disagree in pointing out buried residues: where NACCESS evaluates to zero, the exposure given by PIA ranges from 0 to 20%. Variations of average residue volumes have been analyzed under several conditions, e.g., how they depend on protein size and on secondary structure environments. As it is based on strong mathematical grounds and on numerous high-quality protein structures, our work gives a reliable methodology and up-to-date values of amino acid volumes and surface accessibility.

VLDP web server: a powerful geometric tool for analysing protein structures in their environment

“…In a previous work (8), we showed that computations based on tessellations gave a good agreement with experimental results in the evaluation of amino acid volumes, better than the other equivalent methodologies.…”

“…It allows us to take into account all the residues, including the accessible ones at the protein surface. In a previous work (8), we showed that computations based on tessellations gave a good agreement with experimental results in the evaluation of amino acid volumes, better than the other equivalent methodologies.The protein contacts are a crucial feature to analyse protein structures. The usual definition is based only on geometrical parameters, such as distance-threshold (18), and used for instance to identify small compact units (protein units) (19–21).…”

“…Voronoi diagrams and their derived variants have been used often for the study of protein structures, protein–protein interactions, packing of the protein core, packing at the interface with water, protein cavities, assessing the quality of protein crystal structures (8,9). A few studies using Voronoi diagrams were also devoted to nucleic acids (10–12).…”

“…An important point is that VLDPws is the only tessellation approach that includes an effective solvent around the protein. Another improvement is the set of finely tuned weights used in the Laguerre tessellation (8,9). It allows us to take into account all the residues, including the accessible ones at the protein surface.…”

Crystallographic model validation: from diagnosis to healing

“…Steric clashes are a straightforward and sensitive measure of overpacking, but underpacking is more difficult. Although methods exist for identifying cavities, for instance using Voronoi or related volume concepts [38], none have provided practical diagnostics adopted into validation. RosettaHoles [39] is a less mathematically elegant but more practical system of filtered overlapping spheres.…”