Topological Indices in QSPR Analysis for Predicting Properties of Migraine Drugs

Introduction: This study aims to elucidate the relationship between molecular structure and the physicochemical properties of triptan drugs used in migraine therapy through Quantitative Structure–Property Relationship (QSPR) analysis. In particular, it investigates the predictive performance of degree-based topological indices, including the recently introduced Elliptic Sombor index, for these properties. Methods: In this study, the molecular graphs of five triptan drugs, Sumatriptan, Rizatriptan, Naratriptan, Eletriptan, and Zolmitriptan, were constructed and analyzed. A custom MATLAB algorithm was developed to compute various degree-based topological indices for these structures. Subsequently, a comprehensive set of regression models, including linear, quadratic, cubic, and logarithmic functions, was employed using SPSS to establish quantitative correlations between the calculated indices and the experimental physicochemical properties of the drugs. Results: The analysis revealed significant correlations between the computed topological indices and key physicochemical properties, including boiling point, enthalpy of vaporization, flash point, molar refractivity, molar volume, and polarizability. Specifically, the Harmonic index exhibited the highest predictive accuracy for boiling point and thermal properties. For volumetric parameters such as molar refractivity, polarizability, and molar volume, the Sombor and Modified Sombor indices emerged as the most reliable predictors. Furthermore, the application of non-linear regression models, particularly quadratic and cubic functions, substantially enhanced prediction accuracy, yielding coefficients of determination (R2 ) approaching unity for several properties. Discussion: These findings confirm the efficacy of topological index-based QSPR models in predicting the physicochemical properties of anti-migraine agents. Such models offer a valuable computational tool for rational drug design, enabling the rapid screening of compounds and potentially accelerating the development pipeline by reducing reliance on costly experimental assays. However, given the limited sample size of this study, it is recommended that future research validate these predictive models on larger and more diverse datasets to ensure their broader applicability Conclusion: In conclusion, this study demonstrates the robust predictive capability of topological index-based QSPR models for estimating the physicochemical properties of triptan derivatives. By providing accurate theoretical predictions, this computational approach holds significant potential for optimizing rational drug design protocols, thereby contributing to substantial reductions in both the time and costs associated with experimental screening in pharmaceutical R&D.