Fuzzy Support Vector Regression for QSAR Modeling of 9,10-Dihydrophenanthrene Derivatives Against SARS-CoV-2 3CLpro

Quantitative Structure-Activity Relationship (QSAR) modeling is a critical computational strategy in drug discovery; however, data heterogeneity and experimental noise frequently compromise model reliability. In this study, QSAR models were developed to predict the inhibitory activity of 9,10-dihydrophenanthrene derivatives against the SARS-CoV-2 3CLpro enzyme using a novel fuzzy Support Vector Regression (FSVR) framework. The proposed approach incorporates a fuzzy membership function to weight activity data according to their reliability and employs both the full molecular descriptor set and a subset refined by Variance Inflation Factor (VIF) analysis.

Four regression models-FSVR-VIF, FSVR-All, SVR-VIF, and SVR-All-were constructed using a radial basis function kernel, with hyperparameters optimized via grid search combined with 10-fold cross-validation. Model performance was evaluated using the coefficient of determination (R²) and the root-mean-square error (RMSE).

FSVR consistently outperformed conventional SVR in terms of accuracy and robustness. Among the four models, FSVR-VIF achieved the best cross-validation performance (R²(CV) = 0.9621). The model also demonstrated good predictive performance on the independent external validation set, yielding an R²(ext) of 0.828. Residual error analyses revealed symmetrically distributed residuals with markedly fewer extreme deviations for the fuzzy-enhanced models. Notably, the FSVR-VIF model exhibited a narrow residual spread, with most compounds falling within ±0.5 units across both the training and test sets.

These findings suggest that the incorporation of fuzzy logic improved model robustness against data uncertainty, while VIF-based descriptor selection enhanced model parsimony and interpretability. Furthermore, descriptor analysis indicated that molecular symmetry and mass distribution (e.g., X23) were positively associated with inhibitory activity, whereas increased methyl substitution and structural branching characteristics (e.g., X7 and X11) tended to be associated with reduced inhibitory potency.

Overall, the integration of fuzzy logic with SVR and VIF-based feature selection provided a parsimonious local QSAR model for the investigated series of 9,10-dihydrophenanthrene derivatives, yielding improved predictive performance and descriptor interpretability while maintaining satisfactory predictive capability on an independent external dataset.