Mathematical Modeling and Computation of NM-Polynomial Indices for Physicochemical Properties Prediction

Mitoxantrone and Doxorubicin are anthracycline-based chemotherapeutic agents widely used in cancer treatment. Mitoxantrone is primarily applied in the treatment of leukemia, lymphoma, and prostate cancer, whereas Doxorubicin is effective against breast cancer, lung cancer, and various solid tumors. Both drugs act by intercalating DNA and inhibiting topoisomerase II, resulting in cell cycle arrest and apoptosis in cancer cells. NM-polynomial indices provide a robust framework for predicting the physicochemical characteristics of drug molecules. In this study, NM-polynomial indices for Mitoxantrone and Doxorubicin were determined using the edge/connectivity partition approach. A comprehensive statistical analysis was performed to evaluate their predictive capability for physicochemical properties of polycyclic drug structures. Lasso, Ridge, Elastic Net, and Multiple Linear Regression models were implemented in Python, and model performance was assessed using correlation coefficients (R, $$R^2$$ ), root mean squared error (RMSE), p-values, and 95% confidence intervals. Cross-validation metrics and external test set evaluations confirmed the predictive strength of the models. The results indicate that key physicochemical characteristics–including flash point, enthalpy of vaporization, boiling point, molar refractivity, molecular complexity, molar volume, surface tension and polarizability–can be accurately predicted using NM-polynomial indices. A Python-based computational tool was developed for efficient calculation of these indices, substantially reducing computation time and minimizing human error. Furthermore, predictive models were proposed, retaining only the most statistically significant ones for estimating uncalculated physicochemical properties.