We proposed a novel QSAR (quantitative structure-activity relationship) procedure called LERE (linear expression by representative energy terms)-QSAR involving molecular calculations such as ab initio fragment molecular orbital and generalized Born/surface area ones. We applied LERE-QSAR to two datasets for the free-energy changes during complex formation between carbonic anhydrase and a series of substituted benzenesulfonamides. The first compound set (Set I) and the second one (Set II) include relatively small substituents and alkyl chains of different lengths in the benzene ring, respectively. Variation of the inhibitory activity in Set I is expressed as the combination of Hammett σ and the hydrophobic substituent constant π in classical QSAR, and variation in Set II only by π. LERE-QSAR analyses clearly revealed that effects of σ and π on the activity variations in Sets I and II are consistently explainable with the energy terms in the LERE formulation, and provide more detailed and direct information as to the binding mechanism. The proposed procedure was demonstrated to provide a quantitative basis for understanding ligand-protein interactions at the electronic and atomic levels.
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