A graph theoretical approach to structure-property and structure-activity correlations

Abstract

The structure similarity and dissimilarity implied in many structure-property and structure-activity relationships has been examined from the graph theoretical point of view. The approach outlined is fundamentally different from generally used schemes in that, rather than seeking a new parametrization which will quantitatively fit observed data and trends,similarities among the skeletal forms and connectivities of the compounds of interest are studied quantitatively. The basis of the method is the assumption that skeletal forms of apparent similarity will yield similar enumerations for a number of graph theoretical invariants. In particular, allpaths within molecular skeletons are enumerated and sequences of path numbers (i.e., the number of paths of different length) are compared. The degree of similarity between molecules is proportional to the distance between points in the corresponding “structure space” obtained by interpreting the entries in molecular path sequences as coordinates inn-dimensional space. As anexample of the use of the concept of structural similarity, structure-activity data relating cerebral dopamine agonist properties for a series of N-substituted 2-aminotetralins are considered. The analysis suggests that the method may find wide application in the field of structure-activity correlations and structure-property studies. The data could be mass spectra, the “fingerprint” regions of infrared spectra, optical rotation and circular dichroism measurements, or any of many not fullyunderstood complex experimental findings suspected of having an inherent structural basis.