Development of Quantitative Structure−Activity Relationship and Classification Models for a Set of Carbonic Anhydrase Inhibitors

Mathematical models are developed to find quantitative structure−activity relationships that correlate chemical structure and inhibition toward three carbonic anhydrase (CA) isozymes:  CA I, II, and IV. Numerical descriptors are generated to encode important topological, geometric, and electronic features of molecular structure. After descriptor generation, multiple linear regression, and computational neural network (CNN) analyses are performed on various descriptor subsets to find superior models for prediction. Committees of five CNNs were utilized to average final predicted values for the 142-compound data set. For inhibitors of CA I, an 8−5−1 CNN committee produced a training set rms error of 0.105 log K_i (r² = 0.994) and prediction set rms error of 0.208 log K_i (r² = 0.980). Training and prediction set rms errors of 0.140 log K_i (r² = 0.992) and 0.231 log K_i (r² = 0.971), respectively, were produced by a 9−5−1 CNN committee for inhibitors of CA II. For prediction of CA IV inhibitors, an 8−5−1 CNN committee produced training and prediction set rms errors of 0.147 log K_i (r² = 0.992) and 0.211 log K_i (r² = 0.991), respectively. In addition, classification models were built using k-nearest neighbor (kNN) analysis to solve two- and three-class problems for inhibitors of CA IV. A three-descriptor classification model proved superior in labeling compounds as active or inactive inhibitors for the two-class problem. Training and prediction set percent classification rates of 100% and 87.1%, respectively, were obtained. For the three-class (active/moderate/inactive) problem, a five-descriptor model was deemed optimal producing a training set percent classification rate of 98.8% and prediction set rate of 79.0%.