Simple linear QSAR models based on quantum similarity measures

A novel QSAR approach based on quantum similarity measures was developed and tested in this paper. This approach consists of replacing the usual physicochemical parameters employed in QSAR analysis, such as octanol-water partition coefficient or Hammett sigma constant, by appropriate quantum chemical descriptors. The methodological basis for this substitution is found in recent theoretical studies [J. Comput. Chem. 1998, 19, 1575-1583, J. Comput. -Aided Mol. Des. 1999, 13, 259-270], in which it was demonstrated that both molecular hydrophobic character and electronic substituent effect can be modeled by appropriately chosen quantum self-similarity measures (QS-SM). The most important aim of this study was to prove that selected QS-SM descriptors can be advantageously used in empirical QSAR analysis instead of classical descriptors. For this purpose several QSAR correlations are proposed, in which empirical descriptors such as Hammett sigma constants or log P values are replaced by the appropriate QS-SM. These examples involve: (i) a set of benzenesulfonamides which bind to human carbonic anhydrase, (ii) a set of benzylamines as competitive inhibitors of the enzyme trypsin, and (iii) a set of indole derivatives which are benzodiazepine receptor inverse agonist site ligands. Simple linear QSAR models were developed in order to obtain mathematical relationships between the biological activity and the pertinent quantum chemical descriptors. The validity of the obtained QSAR models is supported by comparison of the observed and predicted values of the biological activity and by a statistical analysis based on a randomization test.