Three-dimensional computation of atom depth in complex molecular structures

Motivation: For a complex molecular system the delineation of atom-atom contacts, exposed surface and binding sites represents a fundamental step to predict its interaction with solvent, ligands and other molecules. Recently, atom depth has been also considered as an additional structural descriptor to correlate protein structure with folding and functional properties. The distance between an atom and the nearest water molecule or the closest surface dot has been proposed as a measure of the atom depth, but, in both cases, the 3D character of depth is largely lost. In the present study, a new approach is proposed to calculate atom depths in a way that the molecular shape can be taken into account. Results: An algorithm has been developed to calculate intersections between the molecular volume and spheres centered on the atoms whose depth has to be quantified. Many proteins with different size and shape have been chosen to compare the results obtained from distance-based and volume-based depth calculations. From the wealth of experimental data available for hen egg white lysozyme, H/D exchange rates and TEMPOL induced paramagnetic perturbations have been analyzed both in terms of depth indexes and of atom distances to the solvent accessible surface. The algorithm here proposed yields better correlations between experimental data and atom depth, particularly for those atoms which are located near to the protein surface.