Alpha Shapes Applied to Molecular Shape Characterization Exhibit Novel Properties Compared to Established Shape Descriptors
journal contributionposted on 26.10.2009 by J. Anthony Wilson, Andreas Bender, Taner Kaya, Paul A. Clemons
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Despite considerable efforts, description of molecular shape is still largely an unresolved problem. Given the importance of molecular shape in the description of spatial interactions in crystals or ligand-target complexes, this is not a satisfying state. In the current work, we propose a novel application of alpha shapes to the description of the shapes of small molecules. Alpha shapes are parametrized generalizations of the convex hull. For a specific value of α, the alpha shape is the geometric dual of the space-filling model of a molecule, with the parameter α allowing description of shape in varying degrees of detail. To date, alpha shapes have been used to find macromolecular cavities and to estimate molecular surface areas and volumes. We developed a novel methodology for computing molecular shape characteristics from the alpha shape. In this work, we show that alpha-shape descriptors reveal aspects of molecular shape that are complementary to other shape descriptors and that accord well with chemists’ intuition about shape. While our implementation of alpha-shape descriptors is not computationally trivial, we suggest that the additional shape characteristics they provide can be used to improve and complement shape-analysis methods in domains such as crystallography and ligand-target interactions. In this communication, we present a unique methodology for computing molecular shape characteristics from the alpha shape. We first describe details of the alpha-shape calculation, an outline of validation experiments performed, and a discussion of the advantages and challenges we found while implementing this approach. The results show that, relative to known shape calculations, this method provides a high degree of shape resolution with even small changes in atomic coordinates.