Superposition-Free Shape Similarity Methods

In the superposition-free category, techniques are typically based on exploiting interatomic distances in a way that is independent of molecular orientation and position. One group of superposition-free methods measuring molecular shape was based on atom triplet distances. Bemis and Kuntz [16] devised a method that considered each molecule as the set of its atom triplets. Molecular shape histograms were calculated with the perimeters of the triangle formed by each atom triplet and 

1) ROCS, OpenEye Scientific Software. Available at http //www.eyesopen.com. 

Ultrafast shape recognition (USR) [19] is a recent and unusually rapid descriptor-based shape similarity technique. USR is based on the observation that the shape of a molecule is determined by the relative positions of its atoms. This 3D spatial arrangement of atoms is accurately described by a set of distributions of interatomic distances measured from four strategically located reference points, which are in turn characterized by its first three statistical moments. The shape similarity of two molecules is Anally calculated through an inverse of the sum of least absolute differences in their respective descriptors (full details about this recent technique along with applications can be found in a recent review [20]). 

Building upon the concept of USR, some extensions and refinements have already been investigated. These are intended to maintain the efficiency of USR, while 

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Methods for molecular shape similarity can be roughly divided into two categories those that require finding the optimal superposition of the molecules being compared (superposition-based) and those that, by contrast, are independent of molecular orientation and position (superposition-free). Here we are restricting our focused review to those techniques that have demonstrated to perform shape similarity and its suitability to bioisosteric replacement in small molecules. 

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