IU Chemical Informatics Journal Club

Authors: J. Anthony Wilson, Andreas Bender, Taner Kaya and Paul A. Clemons

Source: J. Chem. Inf. Model., Article ASAP, September 23, 2009

Even though multiple molecular shape descriptions have been devised over the paste 20 years, it is still largely an unsolved problem. From early molecular shape descriptions, such as CoMFA, the more recent ROCS (Rapid Overlay of Chemical Structures) to the “ultrafast shape recognition” (USR), none of these descriptions of the molecular shape were ideal, both from a predictive power as well as as ease of handling point of view. This inspite of efforts to create hybrid descriptors, such as thee MACCS/USR, a hybrid of the conventional MACCS keys and the 3D USR descriptor, which outperformed the pure USR descriptors in a series of virtual screening experiments.

The authors therefore propose a novel application of alpha shapes to the description of small molecules. Alpha shapes are parametrized (alpha) generalizations of the convex hull. As alpha approaches infinity, the alpha shape is identical to the convex hull. On the other hand, as alpha decreases, the shape shrinks, gets dents and voids and when alpha corresponds to the spheres of a space filling model, the alpha shape is said to be the geometric dual of the space filling model. Applications of alpha shapes include visualization of irregular shape boundaries of clusters in 3D, characterize simple properties of Brownian motion and the study of protein structures, pockets, surface area and packing.

The investigation of the behavior of the alpha shapes for the description of molecular shape was performed using 3 sets of compounds: multiple conformers of structural isomers of octane, a collection of 388 biologically active compounds and a diverse set of 22,831 compounds from ChemBank. The calculation of comparative descriptors was performed using commercially available software: normalized principal moments-of-inertia (PMIs) ratio method, Ultrafast Shape Recognition (USR), functional class fingerprints (FCFP6s, Pipeline Pilot) and descriptors from MOE.

After the calculation of the alpha shape indices from the 3D coordinates in the SDF file, and resolving the facets of the surface for handedness, the Euclidian distance to all facets was calculated using facet intercentroid distances. Together with the angle between the facet normals, a joint probability function was generated. A method termed Earth-Mover’s distance was used to assess the similarity/dissimilarity among the joint probability functions. These distances were then further used for a pairwise comparison to the calculated reference descriptors.

In general the method is sensitive to resolve constitutional isomers and enantiomers. Even though the proposed method does share information with existing descriptors, the authors found also considerable disagreement for many pairs of molecules, indicating that previously neglected shape information is captured. The proposed method is nearly size independent and more sensitive to changes in the overall shape than the number of atoms. Future optimization will involve hybrid descriptors, combining the alpha shape score with other descriptors that determine molecular size. The authors plan also to investigate how such a method could e applied to the characterization of protein properties, such as the shape of potential binding sites.