Receptor-independent 4D-QSAR analysis of a set of norstatine derived inhibitors of HIV-1 protease

A training set of 27 norstatine derived inhibitors of HIV-1 protease, based on the 3(S)-amino-2(S)-hydroxyl-4-phenylbutanoic acid core (AHPBA), for which the -log IC(50) values were measured, was used to construct 4D-QSAR models. Five unique RI-4D-QSAR models, from two different alignments, were identified (q(2) = 0.86-0.95). These five models were used to map the atom type morphology of the lining of the inhibitor binding site at the HIV protease receptor site as well as predict the inhibition potencies of seven test set compounds for model validation. The five models, overall, predict the -log IC(50) activity values for the test set compounds in a manner consistent with their q(2) values. The models also correctly identify the hydrophobic nature of the HIV protease receptor site, and inferences are made as to further structural modifications to improve the potency of the AHPBA inhibitors of HIV protease. The finding of five unique, and nearly statistically equivalent, RI-4D-QSAR models for the training set demonstrates that there can be more than one way to fit structure-activity data even within a given QSAR methodology. This set of unique, equally good individual models is referred to as the manifold model.     

Constructing optimum blood brain barrier QSAR models using a combination of 4D-molecular similarity measures and cluster analysis

A new method, using a combination of 4D-molecular similarity measures and cluster analysis to construct optimum QSAR models, is applied to a data set of 150 chemically diverse compounds to build optimum blood-brain barrier (BBB) penetration models. The complete data set is divided into subsets based on 4D-molecular similarity measures using cluster analysis. The compounds in each cluster subset are further divided into a training set and a test set. Predictive QASAR models are constructed for each cluster subset using the corresponding training sets. These QSAR models best predict test set compounds which are assigned to the same cluster subset, based on the 4D-molecular similarity measures, from which the models are derived. The results suggest that the specific properties governing blood-brain barrier permeability may vary across chemically diverse compounds. Partitioning compounds into chemically similar classes is essential to constructing predictive blood-brain barrier penetration models embedding the corresponding key physiochemical properties of a given chemical class.     

External validation and prediction employing the predictive squared correlation coefficient test set activity mean vs training set activity mean

The external prediction capability of quantitative structure-activity relationship (QSAR) models is often quantified using the predictive squared correlation coefficient, q (2). This index relates the predictive residual sum of squares, PRESS, to the activity sum of squares, SS, without postprocessing of the model output, the latter of which is automatically done when calculating the conventional squared correlation coefficient, r (2). According to the current OECD guidelines, q (2) for external validation should be calculated with SS referring to the training set activity mean. Our present findings including a mathematical proof demonstrate that this approach yields a systematic overestimation of the prediction capability that is triggered by the difference between the training and test set activity means. Example calculations with three regression models and data sets taken from literature show further that for external test sets, q (2) based on the training set activity mean may become even larger than r (2). As a consequence, we suggest to always use the test set activity mean when quantifying the external prediction capability through q (2) and to revise the respective OECD guidance document accordingly. The discussion includes a comparison between r (2) and q (2) value ranges and the q (2) statistics for cross-validation.     

On further application of r as a metric for validation of QSAR models

Validation is a crucial aspect for quantitative structure–activity relationship (QSAR) model development. External validation is considered, in general, as the most conclusive proof of predictive capacity of a QSAR model. In the absence of truly external data set, external validation is usually performed on test set compounds, which are members of the original data set but not used in model development exercise. In the case of small data sets, QSAR researchers experience problem in model development due to the fact that the developed models may be less reliable on account of the small number of training set compounds and such models may also show poor external predictability because the models may not have captured all necessary features required for the particular structure–activity relationships. The present paper attempts to show that ‘true r_(LOO)’ statistic calculated based on the model derived from the undivided data set with application of variable selection strategy at each cycle of leave‐one‐out (LOO) validation may reflect external validation characteristics of the developed model thus obviating the requirement of splitting of the data set into training and test sets. This approach may be helpful in the case of small data sets as it uses all available data for model development and validation thus making the resulting model more reliable. Copyright © 2009 John Wiley & Sons, Ltd.     

Rational selection of training and test sets for the development of validated QSAR models

Quantitative Structure–Activity Relationship (QSAR) models are used increasingly to screen chemical databases and/or virtual chemical libraries for potentially bioactive molecules. These developments emphasize the importance of rigorous model validation to ensure that the models have acceptable predictive power. Using k nearest neighbors (kNN) variable selection QSAR method for the analysis of several datasets, we have demonstrated recently that the widely accepted leave-one-out (LOO) cross-validated R² (q²) is an inadequate characteristic to assess the predictive ability of the models [Golbraikh, A., Tropsha, A. Beware of q2! J. Mol. Graphics Mod. 20, 269-276, (2002)]. Herein, we provide additional evidence that there exists no correlation between the values of q ² for the training set and accuracy of prediction (R ²) for the test set and argue that this observation is a general property of any QSAR model developed with LOO cross-validation. We suggest that external validation using rationally selected training and test sets provides a means to establish a reliable QSAR model. We propose several approaches to the division of experimental datasets into training and test sets and apply them in QSAR studies of 48 functionalized amino acid anticonvulsants and a series of 157 epipodophyllotoxin derivatives with antitumor activity. We formulate a set of general criteria for the evaluation of predictive power of QSAR models.     

3D QSAR studies on protein tyrosine phosphatase 1B inhibitors: comparison of the quality and predictivity among 3D QSAR models obtained from different conformer-based alignments

A set of 65 flexible peptidomimetic competitive inhibitors (52 in the training set and 13 in the test set) of protein tyrosine phosphatase 1B (PTP1B) has been used to compare the quality and predictive power of 3D quantitative structure-activity relationship (QSAR) comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) models for the three most commonly used conformer-based alignments, namely, cocrystallized conformer-based alignment (CCBA), docked conformer-based alignment (DCBA), and global minima energy conformer-based alignment (GMCBA). These three conformers of 5-[(2S)-2-({(2S)-2-[(tert-butoxycarbonyl)amino]-3-phenylpropanoyl}amino)3-oxo-3-pentylamino)propyl]-2-(carboxymethoxy)benzoic acid (compound number 66) were obtained from the X-ray structure of its cocrystallized complex with PTP1B (PDB ID: 1JF7), its docking studies, and its global minima by simulated annealing. Among the 3D QSAR models developed using the above three alignments, the CCBA provided the optimal predictive CoMFA model for the training set with cross-validated r2 (q2)=0.708, non-cross-validated r2=0.902, standard error of estimate (s)=0.165, and F=202.553 and the optimal CoMSIA model with q2=0.440, r2=0.799, s=0.192, and F=117.782. These models also showed the best test set prediction for the 13 compounds with predictive r2 values of 0.706 and 0.683, respectively. Though the QSAR models derived using the other two alignments also produced statistically acceptable models in the order DCBA>GMCBA in terms of the values of q2, r2, and predictive r2, they were inferior to the corresponding models derived using CCBA. Thus, the order of preference for the alignment selection for 3D QSAR model development may be CCBA>DCBA>GMCBA, and the information obtained from the CoMFA and CoMSIA contour maps may be useful in designing specific PTP1B inhibitors.