Topological descriptor-driven prediction of physicochemical properties of COVID-19 drugs

Introduction

The emergence of Coronavirus Disease 2019 (COVID19), caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), created a major global health emergency and placed an enormous burden on healthcare systems worldwide. Since it was first identified in late 2019, the virus has spread rapidly across countries, leading to widespread illness, significant mortality, and substantial social and economic disruption. These challenges have stimulated extensive scientific efforts to identify, develop, and evaluate effective therapeutic agents for the prevention and treatment of COVID-19. Although vaccination has substantially reduced disease severity, antiviral drugs continue to play an essential role in the treatment of infected patients, particularly those at high risk of developing severe complications. Consequently, understanding the molecular characteristics and physicochemical properties of COVID-19 drugs has become an aspect of pharmaceutical and medicinal chemistry [1] . Physicochemical properties, including boiling point, enthalpy, polar surface area, molar refractivity, and polarizability, significantly influence the pharmacokinetic and pharmacodynamic behaviour of drug molecules. These properties affect molecular stability, solubility, membrane permeability, and biological activity, thereby contributing to the overall therapeutic performance of pharmaceutical compounds. Experimental determination of these properties is often expensive, labor-intensive, and time-consuming, motivating the development of reliable computational methods for their prediction [2] . Graph-theoretical techniques have become valuable computational tools in mathematical chemistry by representing chemical compounds as molecular graphs, where vertices correspond to atoms and edges represent chemical bonds. Numerical quantities derived from these molecular graphs, known as topological indices, effectively encode structural information and have found extensive applications in QSPR and QSAR investigations [3,6] . Such descriptors enable the prediction of physicochemical and biological properties directly from molecular structures, thereby reducing the need for extensive experimental measurements. Among the numerous degree-based topological descriptors proposed in the literature, the Veerabhadraiah-Lokesha (VL) index has attracted attention because of its ability to characterize molecular connectivity through vertex degrees [9] . In addition to the original descriptor, several transformed forms of the VL index have been explored to investigate their predictive capabilities in QSPR studies. Recent investigations have demonstrated the usefulness of degree-based descriptors for studying graphene, anticancer drugs, triglycerides, and other molecular systems [7,8,12,19] . Evaluating the effectiveness of these descriptors for different classes of pharmaceutical compounds therefore remains an active area of research. Motivated by these considerations, the present study investigates the applicability of the VL index and its variants for predicting the physicochemical parameters of selected COVID-19 drugs. Correlation analysis is employed to examine the relationships among the considered topological descriptors and five important physicochemical properties. Furthermore, simple linear regression models are developed to evaluate the predictive performance of these descriptors. The obtained results provide further evidence that the VL index and its transformed variants can serve as effective molecular descriptors for QSPR modelling and may contribute to the computational characterization of COVID-19 drugs [1,13,16,19] .

Materials and Methods

This section describes the dataset of COVID-19 drugs, the mathematical formulation of the Veerabhadraiah-Lokesha (VL) index and its transformed variants, and the statistical procedures adopted to investigate their applicability in QSPR and QSAR analysis. The physicochemical data were collected from chemical databases and published literature, while the statistical analyses were performed using correlation and regression techniques [1,10,13,16,20] .

Dataset of COVID-19 Drugs

A dataset comprising eight clinically relevant COVID-19 drugs was selected to investigate the predictive capability of the Veerabhadraiah-Lokesha (VL) index and its variants. The selected drugs include Lopinavir, Ritonavir, Arbidol, Thalidomide, Chloroquine, Hydroxychloroquine, Theaflavin, and Remdesivir. The corresponding physicochemical data were compiled from the ChemSpider database and published literature to ensure the accuracy and consistency of the analysis [1,10] . Five physicochemical properties were considered in this investigation, namely boiling point (Bp), enthalpy (E), polar surface area (PSA), molar refractivity (MR), and polarizability (P). These properties are widely employed in Quantitative Structure-Property Relationship studies because of their importance in describing the physicochemical behaviour and molecular characteristics of pharmaceutical compounds [1,13,16,19] .

Veerabhadraiah-Lokesha Index

For a simple graph G with vertex set V(G) and edge set E(G), the VL index is defined by [9] ,

Where 𝑑(𝑢) corresponds to the degree of a vertex 𝑢of vertex set V(G).

The transformed variants of the VL index considered in this study are √VL(𝐺), [VL(𝐺)] 2 , 1/VL(𝐺), and 1/√VL(𝐺). These transformed forms were included to examine whether mathematical transformations of the original descriptor improve its capability to model the selected physicochemical characteristics of COVID-19 drug molecules. Similar transformations of topological descriptors have been successfully employed in recent QSPR investigations involving pharmaceutical compounds [12][13][14][15][16][17][18][19] .

The values of the VL index and its transformed variants computed for the selected COVID-19 drugs are presented in Table 2 and were subsequently used for correlation and regression analyses.

Statistical Analysis

The association between the selected topological descriptors and the physicochemical properties of the COVID-19 drug molecules was examined through Pearson's correlation analysis. Pearson's correlation coefficient (𝑅) was employed to measure the strength and direction of the linear relationship between each topological descriptor and the corresponding physicochemical property. The resulting correlation coefficients were used to assess the predictive relevance of the descriptors and to identify those exhibiting the strongest associations with the selected properties and the associated physicochemical property [15,19] .

To evaluate the predictive capability of the descriptors, simple linear regression analysis was performed. The regression model is expressed as

A=c + dB

where 𝐴 represents the physicochemical property, 𝐵 denotes the topological descriptor, 𝑐 is the intercept, and 𝑑 is the regression coefficient.

The goodness-of-fit of each regression model was assessed using the coefficient of determination (𝑅 2 ), Correlation coefficient (𝑅), residual standard deviation (𝑆 res ), the Fstatistic, and the associated 𝑝-value. These statistical measures were used to evaluate the accuracy, significance, and predictive performance of the developed linear models [13,15,19] .

The correlation coefficients and regression analyses were computed using Google Sheets, and the resulting statistical parameters were employed to assess the predictive performance of the VL index and its transformed variants.

Results and Discussion

The physicochemical parameters of the selected COVID-19 drugs considered in this investigation are presented in Table 1. Five important physicochemical properties, namely boiling point (Bp), enthalpy (E), polar surface area (PSA), molar refractivity (MR), and polarizability (P), were selected to evaluate the predictive capability of the VL index and its transformed variants. The corresponding values of the VL(G) index and its transformed variants are listed in Table 2. These descriptors were subsequently employed to investigate their relationships with the selected physicochemical properties through correlation and regression analyses [1,13,15,19] .

Correlation Analysis

The Pearson correlation coefficients between the considered topological descriptors and the selected physicochemical parameters are presented in Table 3. As shown in Table 3, the original VL(G) exhibits excellent positive correlations with boiling point (𝑅 = 0.9930) and enthalpy (𝑅 = 0.9893). Strong positive correlations are also observed for polar surface area (𝑅 = 0.9000), while molar refractivity (𝑅 = 0.8690) and polarizability (𝑅 = 0.8691) show satisfactory linear relationships. Among the transformed descriptors, [VL(𝐺)] 2 provides the highest correlations with boiling point (𝑅 = 0.9973), enthalpy (𝑅 = 0.9949), and polar surface area (𝑅 = 0.9059). The reciprocal descriptors exhibit negative correlations because they are inversely related to the original VL(G) values [ 13,15,19] .

Regression Analysis

To further investigate the predictive performance of the proposed topological descriptors, simple linear regression analysis was carried out between each descriptor and the selected physicochemical parameters of the COVID-19 drugs. The resulting regression equations, together with the associated statistical parameters, provide a quantitative assessment of the predictive capability of the considered descriptors.

The linear regression model describing the relationship between the boiling point and the VL(G) index is given by Bp = 73.9956 + 3.4894 VL(𝐺).

The regression model exhibits an excellent fit with a coefficient of determination of 𝑅 Overall, the regression analysis demonstrates that the VL(G) index provides excellent predictive performance for boiling point and enthalpy, while yielding satisfactory predictive accuracy for polar surface area, molar refractivity, and polarizability. These findings indicate that VL(G) is a reliable degree-based molecular descriptor for QSPR analysis of the selected COVID-19 drugs.

Regression Analysis of √𝐕𝐋(𝑮) for COVID-19 Drugs

The linear regression model describing the relationship between the boiling point and √VL(𝐺)is given by Bp = -522.8673 + 92.7806√VL(𝐺).

The model exhibits an excellent fit with 𝑅 2 = 0.9774, indicating that 97.7% of the variation in boiling point is explained by √VL(𝐺). Overall, the regression analysis demonstrates that √VL(𝐺) exhibits excellent predictive performance for boiling point and enthalpy, while providing satisfactory prediction of polar surface area, molar refractivity, and polarizability. These findings indicate that the square-root transformation of the VL index is an effective molecular descriptor for QSPR modeling of the selected COVID-19 drugs. Overall, the regression analysis demonstrates that the squared transformation of the VL index provides the strongest predictive performance among the considered descriptors. In particular, the regression models for boiling point and enthalpy exhibit outstanding goodness-of-fit, while satisfactory predictive accuracy is also achieved for polar surface area, molar refractivity, and polarizability. These findings suggest that [VL(𝐺)] 2 is a highly effective transformed descriptor for QSPR studies of the selected COVID-19 drugs.

Regression

Conclusion

This study investigated the applicability of the Veerabhadraiah-Lokesha (VL) index and its transformed variants for predicting the physicochemical properties of selected COVID-19 drugs through QSPR analysis. Correlation analysis revealed that all the considered descriptors exhibited positive associations with boiling point, enthalpy, polar surface area, molar refractivity, and polarizability, with the squared transformation of the VL index showing the strongest correlations for most of the investigated properties. The developed linear regression models further confirmed the predictive capability of the selected descriptors. Among the investigated transformations, [VL(𝐺)] 2 produced the highest predictive accuracy, particularly for boiling point and enthalpy, achieving coefficients of determination of 𝑅 2 = 0.9947 and 𝑅 2 = 0.9897, respectively. The original VL(G) and √VL(𝐺) also demonstrated excellent predictive performance for these properties while providing satisfactory models for polar surface area, molar refractivity, and polarizability. The statistical significance of all regression models indicates that the selected descriptors effectively capture structural information governing the physicochemical characteristics of the studied compounds. Overall, the findings demonstrate that the VL index and its transformed variants constitute reliable molecular descriptors for QSPR investigations of COVID-19 drugs. The proposed approach offers a simple and computationally efficient framework for estimating physicochemical properties and may facilitate the preliminary screening and characterization of pharmaceutical compounds. Future studies may extend this methodology to larger datasets and explore the predictive performance of these descriptors using multiple linear regression and machine learning techniques.

Orcid

Bharathi Shettahalli Nagaraje Urs (Bharathi S N) https://orcid.org/0009-0007-5446-7780.

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