Molecules 3D Delaunay triangulation: a spectral study

Giard, Joachim [UCL] Macq, Benoît [UCL]

Structural features extraction is essential in various molecular biology applications such as functional classification or binding site prediction for molecular docking. In the literature, methods to study the topology and the accessibility of molecule surfaces exist. Some of them are based on the 3D Delaunay triangulation of the set of points formed by the atoms center. In this paper, we propose to investigate the spectral properties of this triangulation by computing and analyzing the first eigenvector of its adjacency matrix. This technique is already used in graph theory to extract core features and to compare networks, 3D meshes, or any set of points and edges. Tests were performed, providing two promising results. First, the correlation between eigenvectors computed from a molecular complex and one of its component is much higher than between structure independent molecules. It allows to find common sub-structures between molecules even after small conformation changes, because no distance is considered, but only the adjacency of the Delaunay triangulation. Second, the value of the eigenvector at indexes corresponding to binding site atoms is higher than for other surface atoms. As this feature is correlated with no other important geometric or physicochemical binding site properties (curvature, depth, hydrogen bonds capacity, ...), it can be integrated in a larger process aiming to localize binding sites.