Chem. Pharm. Bull. 53(6) 611—615 (2005)

tures, that is, chemical compounds, intermediates, changes and mechanisms. Over the past decades graph-based molecular structure descriptors have developed into a quite active field. In these applications a molecular structure is identified to a graph, with vertices representing non-H atoms and edges representing chemical bonds. During the last decade the interest in the problem of computer-aided design of organic structures with prescribed properties has significantly increased. Today, the information feeding the drug design effort is increasingly quantitative, based upon recent developments in molecular structure description, combinatorial mathematics, statistics, and computer simulations. In chemistry, a graph represents the topology of a molecule in the sense that it depicts the pattern of connectedness of atoms in the molecule, being, at the same time, independent of such metric aspects of molecular structure as equilibrium distance between nuclei, bond angles, etc. Topological indices or graph invariants are the single numbers for characterization of molecular structures. In recent years a large number of topological indices have been reported and utilized for chemical documentation, isomer discrimination, study of molecular complexity, chirality, similarity/dissimilarity, QSAR/ QSPR, drug design and database selection, lead optimization, rational combinatorial library design and for deriving multilinear regression models. Though a large number of topological indices have been reported in literature but only some of them have been successfully employed in SAR studies. Notable amongst these are Wiener’s index, Hosoya’s index, Randic’s molecular connectivity index, c , the higher-order connectivity indices, c , for the paths of length n defined by Kier and Hall, Balaban’s index, J, Zagreb group parameters, M1 and M2, 21) eccentric connectivity index, eccentric adjacency index and superpendentic index. Topochemical indices are the topological indices derived from the chemical graphs and modified so as to take into consideration the presence and relative position of heteroatom. Topochemical indices that have been reported and used for SAR studies include atomic molecular connectivity index, eccentric adjacency topochemical index, Wiener’s topochemical index and superadjacency topochemical index. The importance of cyclin-dependent kinases (CDKs) in cell cycle regulation, their interaction with oncogenes and tumor suppressors, and their frequent deregulation in human tumors, has encouraged an active search for agents capable of perturbing the function of CDKs. Therefore, inhibition of cyclin-dependent kinases is a theme of major interest in current anti-cancer agents’ research. Different classes of chemical inhibitors of these enzymes have been identified during the past decade and the structural basis of inhibition has been elucidated by X-ray crystallography studies of one member of the family, CDK2. The CDK2 protein can form complexes with both cyclins E and A, and it is required for the G1/S transition and S phase progression and centrosome duplication. One of the key CDK2 substrates is the E2F-1 protein itself, of which the turnover and activity is induced by phosphorylation by CDK2/cyclin A. This leads to higher than normal levels of E2F, which have been found to induce apoptosis. The series of compounds used in this study is a novel class of CDK2/cyclin A inhibitors which was discovered by HTS and have demonstrated tumor growth inhibition in a xenograft model of human ovarian cancer. Amongst these, the lead compound 41 has been reported to have potential to inhibit CDK2/cyclins E and A in an in vivo setting. Therefore this series of compounds have the potential for optimization and development of a compound as drug for the treatment of human cancers. In the present study three topochemical indices i.e. Wiener’s topochemical index – a distance based topochemical descriptor, atomic molecular connectivity index – an adjacency based topochemical descriptor and superadjacency topochemical index – an adjacency-cum-distance based topochemical descriptor have been used for development of models for prediction of CDK2/cyclin A inhibition by 3aminopyrazoles. June 2005 Chem. Pharm. Bull. 53(6) 611—615 (2005) 611