QSAR modeling of measured binding affinity for fullerene-based HIV-1 PR inhibitors by CORAL

Abstract

Quantitative structure – activity relationships (QSAR) for prediction of binding affinities (pEC50, i.e., minus decimal logarithm of the 50% effective concentration) of 48 fullerene derivatives inhibitors of the HIV-1 PR (human immunodeficiency virus type 1 protease) have been developed using the software CORAL. CORAL (CORrealtions And Logic) is a freeware aimed to assist QSAR modeling by application of descriptors calculated with SMILES (simplified molecular input line entry system). Three methods of the QSAR modeling of pEC50 have been examined: 1. classic scheme, where model is constructed with a training set and checked up with a validation set; 2. the balance of correlations, where training set is separated into subtraining set and calibration set that is used as a preliminary validation set (the target function provides maximal correlation coefficients for the training and calibration sets with their minimal difference): the final estimation of predictability is based on an external validation set (structures which are not used in building up of the model); and 3. the balance of correlations developed by applying slopes in the plots of the experimental pEC50 versus the calculated pEC50 (separately for the subtraining and the calibration set). A validation set is also used in this case. The best prediction has been obtained for the balance of correlations with ideal slopes. These approaches have been examined for three random splits: into the subtraining set, calibration set, and the validation set. Reliability of the Rm2 criterion, which has been suggested by P.P Roy and K. Roy for estimation of external predictability of QSAR models has been confirmed. Statistical characteristics of the best model are as follows: n = 27, r2 = 0.9030, q2 = 0.8855, s = 0.406, F = 233 (subtraining set); n = 15, r2 = 0.9720, \({{\rm R}^{2}_{\rm pred}=0.9661}\), s = 0.980, F = 451 (calibration set); n = 6, r2 = 0.9224, \({{\rm R}^{2}_{\rm pred}\,{=}\,0.7956}\), s = 0.950, F = 48; Rm2 = 0.7812 (validation set).