The Use of the Ordered Orthogonalized Multivariate Linear Regression in a Structure−Activity Study of Coumarin and Flavonoid Derivatives as Inhibitors of Aldose Reductase

The relationship between molecular descriptors and the inhibitory activity of aldose reductase (AR) for a series of coumarin and flavonoid derivatives has been investigated using a novel multivariate linear regression based on the ordered orthogonalized descriptor set. First, starting from the set of 31 descriptors we produced absolutely the best nonorthogonalized QSAR models with I descriptors (I = 1−7). These models are always better than the models that the most authors achieve by the use of the stepwise inclusion-exclusion procedure. In the next step we realized all possible orthogonalization orderings of a given set of N descriptors (there are N! of these). The key result is that some orthogonalization orderings lead to QSAR models with I ordered orthogonalized descriptors that have higher values of both the correlation coefficient R and cross-validated correlation coefficient R_cv than the corresponding models with the same number of nonorthogonalized descriptors. In order to achieve the highest possible reliability in predicting the inhibition we produced several models that were obtained applying the ordered orthogonalization procedure on one set with five (N = 5) and on two sets with seven (N = 7) descriptors. Then the inhibitory activity for 34 coumarins and 30 flavonoids was predicted, and several compounds were detected with a very high inhibitory activity.