Alpha Shapes Applied to Molecular Shape Characterization Exhibit Novel Properties Compared to Established Shape Descriptors

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Abstract

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 alpha, the alpha shape is the geometric dual of the space-filling model of a molecule, with the parameter alpha 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.

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