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

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.

[1]  A. E. Williams,et al.  The mass spectra of organic molecules , 1968 .

[2]  A. Balaban.  Chemical applications of graph theory , 1976 .

[3]  Robin J. Wilson.  Introduction to Graph Theory , 1974 .

[4]  P. Sohár,et al.  Absorption spectra in the infrared region , 1974 .

[5]  J. Platt.  Prediction of Isomeric Differences in Paraffin Properties , 1952 .

[6]  Daniel Laurent,et al.  Système Darc. XVI. Théorie de topologie-information: I. – Méthode de Perturbation d’Environnements Limités Concentriques Ordonnés (PELCO) , 1973 .

[7]  G. Mckenzie,et al.  Synthesis and pharmacology of some 2-aminotetralins. Dopamine receptor agonists. , 1975, Journal of medicinal chemistry.

[8]  S. Free,et al.  A MATHEMATICAL CONTRIBUTION TO STRUCTURE-ACTIVITY STUDIES. , 1964, Journal of medicinal chemistry.

[9]  Theory of Ferromagnetism and the Ordering of Electronic Energy Levels , 1962 .

[10]  A. Cammarata,et al.  Pattern recognition. Classification of therapeutic agents according to pharmacophores. , 1976, Journal of medicinal chemistry.

[11]  H. C. Longuet-Higgins.  The structures of electron-deficient molecules , 1957 .

[12]  R. Muirhead.  Some Methods applicable to Identities and Inequalities of Symmetric Algebraic Functions of n Letters , 1902 .

[13]  Milan Randic,et al.  Use of self-avoiding paths for characterization of molecular graphs with multiple bonds , 1980, Comput. Chem..

[14]  M. Randic.  Characterization of molecular branching , 1975 .

[15]  L. Ruzicka,et al.  Untersuchungen über Organextrakte. (5. Mitteilung). Über zwei moschusartig riechende Steroide aus Schweinetestes-Extrakten , 1944 .

[16]  I︠u︡. A. Shreĭder.  Equality, resemblance, and order , 1975 .

[17]  C. Hansch.  Quantitative approach to biochemical structure-activity relationships , 1969 .

[18]  Milan Randic,et al.  Search for all self-avoiding paths graphs for molecular graphs , 1979, Comput. Chem..

[19]  Milan Randic,et al.  Graph Theoretical Approach to Recognition of Structural Similarity in Molecules , 1979, J. Chem. Inf. Comput. Sci..

[20]  W. A. Beyer,et al.  A molecular sequence metric and evolutionary trees , 1974 .

[21]  L. Hall,et al.  Molecular connectivity in chemistry and drug research , 1976 .

[22]  Charles L. Wilkins,et al.  On a graph theoretical basis for ordering of structures , 1979 .