Graphical Representations of Molecular Surface Properties

The major features of a scalar property P defined on a molecular surface can be captured in the form of a directed graph derived from the gradient flow of P . These molecular surface property graphs (MSPG) have vertices at the critical points (maxima, minima and saddles) of P and edges formed by the trajectories of the gradient flow that pass through the saddles. Techniques developed for the comparison of chemical structure graphs can be adapted to MSPGs to address questions such as the similarity and complementarity of molecular surface properties. This study describes an algorithm to calculate MSPGs in the case where the molecular surface is defined implicitly as the level set of a sum of atom-centred Gaussians. Examples are shown for geometric properties such as the mean and Gaussian curvature of the surface, and two physical properties, a molecular electrostatic potential defined in terms of atom-centred partial charges and a molecular lipophilic potential derived from atomic lipophilic contributions. Maximal common subgraph methods to identify similar or complementary MSPGs are outlined and their utility in QSAR studies and conformational classification are demonstrated.