Global Measures for 3D Similarity Searching

Most of the 3D similarity measures that have been described involve the use of interatomic distance information and do not take conformational flexibility into account, other than through storing a compound in the database in 

Given two molecules, A and B, the simplest measure that was tested by Pepperrell and Willett was the distance-distribution measure. Here, an N-element frequency distribution is generated for each molecule, in which the /th element contains the number of interatomic distances in that molecule that lie within the /th distance range (1 N). The resulting frequency 

Nilakantan et al. at Lederle Laboratories have described a similarity measure that is closely related to the Bemis-Kuntz measure, in that it is based 

The 3D similarity measures described thus far are all based on interatomic distance information. Bath et al. have described two measures for 3D similarity searching that are based on angular information and have compared the effectiveness of searches using these measures with those of the atom-triplet measures described in the previous section. It should be noted that all of these angular and atom-triplet measures make use only of geometrical information, that is, distances and angles between the constituent atoms of the pairs of molecules that are being compared, and do not involve chemical information such as atomic type, polarity, hydrophobicity, etc. 

Given a set of four atoms, ABCD, a torsional angle, w, is the angle between the two three-atom planes, ABC and BCD. It describes the twist of the vector AB relative to the vector CD when viewed along the vector BC. A 

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