Graph theoretical study of structural similarity in benzomorphans

Abstract

The existing mathematical models for quantitative structure-activity relationships are normally used to search for additivities of constituent components which contribute to the structure of compounds of interest. Here a distinctive scheme in which we quantify the degree of structural similarity of molecular compounds of interest is considered. The result of our analysis is a numerical index of similarity (or dissimilarity) which can be used for ranking and ordering compounds. The similarity index is derived from comparisons of path sequences in molecular skeletons (that is, sequences of the number of paths of different lengths) as the fundamental graph invariants. Applications to quantitative structure-activity studies follow from the hypothesis that molecules of similar pharmacological activity resemble one another. An examination of the structure-activity relationships among benzomorphins has been selected to illustrate the approach. Among the benzomorphins considered, a few have been selected as standards, and others are “tested” for the degree of skeletal similarity to see if the derived ranking agrees with the experimentally observed properties of these narcotic analgeties. The results support the premise and justify further investigations using the scheme outlined.