https://orcid.org/0000-0002-1364-5137
Figures
Abstract
COVID-19, which emerged in 2019, is a disease caused by a new coronavirus, severe acute respiratory syndrome coronavirus 2 (SARSCoV-2), and has caused a worldwide epidemic. During and after this outbreak, it has been confirmed once again that finding a drug to prevent and end such diseases as soon as possible is an important issue. However, drug discovery and to determine a molecule’s physical characteristics in a lab takes effort and time and is a costly process. Relevant information about molecules can be obtained by calculating topological indices, which are molecular descriptive numerical values corresponding to the physical properties of the chemical structure of a molecule. In this paper, we consider recently used drugs such as arbidol, chloroquine, hydroxy-chloroquine, lopinavir, remdesivir, ritonavir, thalidomide and theaflavin in treatment of COVID-19. This article examines neighborhood eccentricity-based topological descriptors that are used to analyze the structures of potential drugs against COVID-19. Eccentricity-based topological indices are advancing the field of chem-informatics and helping scientists better understand structure-activity correlations across a wide range of chemical compounds. The purpose is to identify structural components that have a significant impact on physico-chemical properties. In this context, the chemical structure and the corresponding molecular graph of the drugs under consideration are given in order to calculate the neighborhood eccentricity values. QSPR models are studied using linear and cubic regression analysis with topological indices for boiling point, enthalpy of vaporization, flash point, molar refraction, polar surface area, polarizability, molar volume and molecular weight properties of these drugs. Regression analysis is applied to find potential correlation between different drug characteristics such as bio-availability and efficacy. The results show that topological indices and applied regression models are useful in predicting significant characteristics of drugs used for the treatment of COVID-19. Additionally, a comparison of the known values and the calculated values from the regression models discussed is obtained.
Citation: Kara Y, Özkan YS, Ullah A, Hamed YS, Belay MB (2025) QSPR modeling of some COVID-19 drugs using neighborhood eccentricity-based topological indices: A comparative analysis. PLoS One 20(5): e0321359. https://doi.org/10.1371/journal.pone.0321359
Editor: Saba Farooq, International Center For Chemical and Biological Sciences, PAKISTAN
Received: July 6, 2024; Accepted: March 5, 2025; Published: May 20, 2025
Copyright: © 2025 Kara et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All data that support the findings of this study are included within the article.
Funding: This research was funded by Taif University, Saudi Arabia, Project No. (TU-DSPP-2024-47).
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
The disease known as COVID-19 is caused by a novel strain of coronavirus, SARS-CoV-2, which was first identified in China in late 2019. Since then, it has spread to more than 200 countries and territories, resulting in a global pandemic that has affected millions of people and disrupted various aspects of life. The ongoing global pandemic of COVID-19 has undoubtedly been the most significant public health crisis of the 21st century. It has resulted in over 7 million deaths and over 770 million confirmed cases worldwide, creating a significant challenge to global public health [1]. The pandemic has had a profound impact on the physical well-being of millions of people, but it has also affected their psychological, social and economic aspects of life. The World Health Organisation (WHO) and other health authorities have endeavoured to monitor the situation, provide guidance and coordinate the pandemic response. While the development of specific therapeutics and vaccines represents a key objective, achieving mutations of the virus in the world’s population presents a significant challenge. Although some drugs and therapies can help reduce the severity and duration of the disease, it still represents an important target for drug discovery, as the major proteases of the Coronavirus (SARS-CoV-2) play a critical role during the spread of the disease. Since the beginning of this pandemic, hundreds of remarkable papers have been published to justify the cause of viral spread, applicable preventive measures and future therapeutic approaches. In the current era, scientists are engaged in a concerted effort to develop effective diagnostic and therapeutic strategies for the treatment of COVID-19. The high mortality and infection rates associated with this disease have placed new demands on management levels, society, individuals, and researchers in the fight against the pandemic.
The process of discovering and developing new drug molecules is fraught with challenges, including high costs, lengthy periods of time, and limited success in clinical trials. Furthermore, the necessity for new molecules to be more effective, less side-effective and cheaper than existing drugs represents a significant challenge for the pharmaceutical industry, reducing its overall productivity. Despite these challenges, continued drug researches and developments of this field are vital for the quality of life of individuals, public health and governments worldwide.
New variants of the SARS-CoV-2 virus continue to emerge, and there are concerns that these could be resistant to some of the vaccines currently in use for COVID-19. As a result, there is a pressing need to identify a drug that will prevent and halt the spread of this disease as quickly as possible. However, drug discovery is a complex process that requires considerable effort, time, and financial resources. The application of computer-assisted drug design (CADD) has recently been employed to facilitate the process of identifying promising leads, including those with electronic, drug-like, and pharmacokinetic properties. Graph theory, which was first introduced by Euler in 1736, is one of the most widely studied branches of discrete mathematics, with applications across various fields, including physics, biology, computer science, and chemistry [2]. The field of chemical graph theory is a fusion of mathematical modeling of chemical phenomena with graph theory. Relevant information about molecules can be obtained by calculating topological indices, which are molecular descriptive numerical values corresponding to the physical properties of the chemical structure of a molecule and molecule compounds [3]. The primary objective of studying topological indices is to acquire and modify chemical structure data, thereby establishing a mathematical correlation between structures and physico-chemical properties, bio-activities, and other experimental attributes.
In the field of quantitative analysis of the relationships between structure and property, topological indices prove invaluable in elucidating a multitude of physical and chemical properties. Quantitative structure–property relationship (QSPR) analysis is a highly promising approach to the study of structural characteristics and their correlation with the properties of complex materials [4].
The utilization of topological indices has emerged as a pioneering approach in the intricate field of molecular research, offering a quantitative lens through which to interpret the molecular structure subtleties of chemical molecules. In recent times, there has been a great deal of discussion surrounding the use of QSPR models to study the relationships between physico-chemical properties and some topological indices of drugs used in the treatment of COVID-19 [5–13].
Eccentricity-based topological indices [14–16] which represent a class of molecular descriptors, are frequently employed in both analytical and quantitative structure-activity relationship (QSAR) analysis. The eccentricity values of the constituent atoms in a molecular structure are employed in the calculation of these indices. The eccentricity value is the distance between an atom and its nearest neighbor in a molecule. In 2011 [17], Gutman introduced the concept of eccentricity-based topological indices, which established a framework for future studies in the field. The Wiener index is a fundamental eccentricity-based topological index, defined as the total of all the eccentricity of a molecular graph’s vertex combinations. Due to its strong correlation with specific physico-chemical characteristics and bio-activity profiles, the Wiener index has been employed in the fields of drug design and environmental chemistry [18]. The Zagreb indices represent another significant example of an eccentricity-based indicator. The capacity to forecast boiling temperatures, bioavailability, and other molecular features has been demonstrated with the application of these indices. The advancement of cheminformatics and the enhanced comprehension of structure-activity correlations across a diverse array of chemical compounds has been significantly influenced by research on eccentricity-based topological indices [19–31]. Research on eccentricity-based topological indices has been of great significance in advancing the field of cheminformatics and in helping scientists to better comprehend the structure-activity correlations of a wide range of chemical compounds [32–35].
In order to facilitate the analysis of drugs with respect to their physico-chemical properties, particularly in the context of the novel coronavirus (COVID-19), we have selected eight eccentricity-based topological indices. The drugs arbidol, chloroquine, hydroxy-chloroquine, lopinavir, remdesivir, ritonavir, thalidomide, and theaflavin, which are used in the treatment of COVID-19, are discussed in this article.
We introduce a number of neighborhood eccentricity-based topological indices such as first neighborhood eccentricity index, NE1, second neighborhood eccentricity index, NE2, forgotten neighborhood eccentricity index, NFE, reformulate neighborhood eccentricity index, NRE, symmetric degree division neighborhood eccentricity index, NSDdegE, inverse sum indegree neighborhood eccentricity, NISIE, harmonic neighborhood eccentricity, NHE, augmented neighborhood eccentricity, NAE. There are hundreds of topological indices in the literature, and new ones are being created every day. However, it is difficult to perform calculations using formulae each time. To overcome this difficulty, eccentricity based topological indices have been computed by defining the NEC polynomial based on the neighborhood eccentricity of vertices in a graph G in this work. By employing these indices derived from the topological analysis of neighborhood eccentricities, we are able to identify the structural characteristics of the drugs against COVID-19. The selected topological indices, when utilized as quantitative descriptor tools, provide a framework for the examination of the drugs’ molecular environments.
The paper is organized as follows: In Sect 2, we give some basic tools of graph theory and molecular structures of the various COVID-19 drugs. In Sect 3, we calculate the values of topological indices for molecular graph structure of these drugs via NEC-polynomials. In Sect 4, chemical suitability among the physicochemical properties of these drugs and eight topological indices are checked via correlation technique and, make mathematical modeling between them by QSPR analyzing technique. Sect 5 is devoted to comparison and discussions. Finally, we conclude the paper in Sect 6.
2 Material methods
Let G shows the molecular graph. The vertices of a molecular graph, V(G), represented by unsaturated hydrocarbon skeletons of the molecule and molecular compounds, correspond to non-hydrogen atoms. E(G) is a set of bonds is termed as edge sets. The length of the shortest path (the number of edges in it) connecting the vertices u and v of the graph G is equal to the distance d(u, v) between them. Two vertices u and v are connected by an edge of the graph G, i.e.,
. The eccentricity of the atom u in G is the maximum distance from u to all other vertices in G, that is,
. In [16], the EC–polynomial with respect to eccentricity of vertices in a graph G which is defined as
where and
.
The neighborhood eccentricity of a vertex u in a graph G is defined as the sum of eccentricity of the vertices adjacent to u in G and denoted by in [36], that is
, where
. The NEC-polynomial based on the neighborhood eccentricity of vertices in a graph G which is introduced as follows:
where and
.
The following operations are used to find required results for this article:
The topological indices considered in this study are summarized in Table 1.
In this part of the study, structural properties and molecular graphs of arbidol, chloroquine, hydroxy-chloroquine, lopinavir, remdesivir, ritonavir, thalidomide, and theaflavin drugs used to alleviate the COVID-19 pandemic are given [37]. The antiviral agent arbidol is currently being investigated as a potential treatment and prophylactic agent for coronavirus disease 2019 (COVID-19) in conjunction with both existing and investigational antiretroviral therapies for human immunodeficiency virus (HIV). Chloroquine, the most widely used drug against malaria, is also used in the treatment of autoimmune disease. Hydroxy-chloroquine is a medication that has been employed in the treatment of malaria since the Second World War. It is also a common prescription for rheumatoid arthritis, chronic discoid lupus erythematosus and systemic lupus erythematosus. Lopinavir was previously under investigation in combination with ritonavir for the treatment of COVID-19. Remdesivir has been demonstrated to function as a non-obligate chain terminator of RdRp (RNA-dependent RNA polymerase) from SARS-CoV-2 and the related SARS-CoV and MERS-CoV, and has been subjected to investigation within multiple clinical trials for the treatment of COVID-19. Remdesivir is a nucleoside analogue drug that impairs the replication of viral RNA. Thalidomide, which is known to cause congenital defects (phocomelia) in the fetus, is employed in the treatment of numerous autoimmune disorders, including psoriasis and systemic lupus erythematosus. Theaflavin is a pharmaceutical agent employed in the treatment of conditions where absorption is impaired, such as oral health, gastric ulcers, and intestinal or colonic disorders [37].
The molecular structures of the eight drugs used for the treatment of COVID-19 have been taken into consideration and presented in Figs 1,2,3,4,5,6,7, and 8. Indeed, they facilitate the study of reactions, the understanding of structure-activity relationships, and the analysis of molecular characteristics in a manner that would otherwise prove challenging. We employee the edge partitioning technique for eccentric-based indices to calculate the values for the aforementioned topological indices. Note that the neighborhood eccentricity of each vertex of each molecular graphs is written in the Figs 1,2,3,4,5,6,7, and 8.
3 Computation of topological indices
In this section, the NEC-polynomials of the chemical structures of arbidol, chloroquine, hydroxy-chloroquine, lopinavir, remdesivir, ritonavir, thalidomide, and theaflavin drugs are obtained. Using these polynomials, various topological indices depending on the eccentricity are calculated for these structures.
Theorem 1. Let G1 be the graph of arbidol. NEC-polynomial of G1 is given as follows:
Proof: From Fig 1, it is easy to see that and
. The frequencies are given as |E7,22| = 1, |E8,25| = 1, |E10,20| = 1, |E10,30| = 2, |E11,34| = 2, |E14,16| = 1, |E14,21| = 1, |E16,28| = 1, |E18,20| = 1, |E18,24| = 1, |E18,25| = 1, |E18,30| = 1, |E20,22| = 2, |E20,28| = 3, |E20,34| = 1, |E21,22| = 2, |E22,22| = 2, |E22,24| = 2, |E22,25| = 1, |E24,24| = 1, |E24,28| = 1, |E28,30| = 1 and |E30,30| = 1. Then, we have
Theorem 2. Let G1 be the graph of arbidol. Using Fig 1, the various topological indices of the G1 graph are as follows:
- NE1(G1)=1355
- NE2(G1)=14376
- NFE(G1)=32089
- NRE(G1)=664924
- NSDdegE (G1)=72.5912
- NISIE(G1)=318.2806
- NHE(G1)=1.4614
- NAE (G1)=43768.2669
Proof: The following indices can be calculated with the help of the NEC-polynomial obtained in Theorem 1:
Theorem 3. Let G2 be the graph of chloroquine. NEC-polynomial of G2 is given as follows:
Proof: From Fig 2, it is easy to see that and
. The frequencies are given as |E7,23| = 1, |E12,24| = 2, |E12,35| = 1, |E15,23| = 1, |E15,25| = 1, |E16,18| = 1, |E16,23| = 1, |E18,20| = 2, |E18,25| = 1, |E20,20| = 1, |E20,22| = 1, |E20,28| = 1, |E20,31| = 1, |E20,34| = 1, |E22,31| = 1, |E22,35| = 2, |E24,34| = 2, |E25,28| = 1 and |E28,31| = 1. Then, we have
Theorem 4. Let G2 be the graph of chloroquine. Using Fig 2, the various topological indices of the G2 graph are as follows:
- NE1(G2)=1049
- NE2(G2)=11825
- NFE(G2)=26019
- NRE(G2)=580864
- NSDdegE (G2)=52.0127
- NISIE(G2)=248.9108
- NHE(G2)=1.0488
- NAE (G2)=37842.6494
Theorem 5. Let G3 be the graph of hydroxy-chloroquine. NEC-polynomial of G3 is given as follows:
Proof: From Fig 3, it is easy to see that and
. The frequencies are given as |E7,24| = 1, |E12,24| = 1, |E13,26| = 1, |E13,38| = 1, |E16,18| = 1, |E16,24| = 2, |E16,28| = 1, |E18,20| = 1, |E20,22| = 1, |E20,28| = 1, |E20,34| = 1, |E22,22| = 1, |E22,24| = 1, |E22,31| = 1, |E22,34| = 1, |E24,26| = 1, |E24,34| = 3, |E24,38| = 2, |E28,31| = 1 and |E31,34| = 1. Then, we have
Theorem 6. Let G3 be the graph of hydroxy-chloroquine. Using Fig 3, the various topological indices of the G3 graph are as follows:
- NE1(G3)=1168
- NE2(G3)=14092
- NFE(G3)=30898
- NRE(G3)=739548
- NSDdegE (G3)=54.2184
- NISIE(G3)=277.5706
- NHE(G3)=1.0288
- NAE (G3)=47990.9784
Theorem 7. Let G4 be the graph of lopinavir. NEC-polynomial of G4 is given as follows:
Proof: From Fig 4, it is easy to see that and
. The frequencies are given as |E9,30| = 1, |E12,37| = 1, |E13,40| = 1, |E20,30| = 1, |E20,34| = 1, |E28,30| = 2, |E28,40| = 2, |E28,46| = 1, |E30,31| = 1,|E32,34| = 1, |E32,46| = 1, |E40,43| = 1, |E15,46| = 2, |E16,49| = 3, |E22,31| = 2, |E22,37| = 2, |E24,34| = 2, |E24,40| = 2, |E26,28| = 3, |E26,37| = 3, |E28,28| = 2, |E30,30| = 2, |E34,34| = 4, |E34,49| = 3, |E43,46| = 2, and |E46,49| = 3. Then, we have
Theorem 8. Let G4 be the graph of lopinavir. Using Fig 4, the various topological indices of the G4 graph are as follows:
- NE1(G4)=3211
- NE2(G4)=51986
- NFE(G4)=114501
- NRE(G4)=3699994
- NSDdegE (G4)=112.9006
- NISIE(G4)=759.3995
- NHE(G4)=1.5496
- NAE (G4)=235002.9451
Theorem 9. Let G5 be the graph of remdesivir. NEC-polynomial of G5 is given as follows:
Proof: From Fig 5, it is easy to see that and
. The frequencies are given as |E10,42| = 1, |E13,39| = 1, |E13,40| = 1, |E13,53| = 1, |E17,52| = 1, |E20,20| = 1, |E20,34| = 1, |E20,42| = 1, |E24,34| = 1, |E24,53| = 1, |E28,30| = 1, |E28,40| = 1, |E30,31| = 1, |E30,49| = 1, |E30,43| = 1, |E31,48| = , |E32,34| = 1, |E32,46| = 1, |E34,34| = 1, |E34,37| = 1, |E34,52| = 1, |E37,39| = 1, |E37,40| = 1, |E39,53| = 1, |E43,46| = 1, |E43,53| = 1, |E46,48| = 1, |E48,52| = 1, |E12,37| = 2, |E17,34| = 2, |E22,37| = 2, |E22,42| = 2, |E26,28| = 2, |E26,37| = 2, |E28,28| = 2, and |E34,49| = 2. Then, we have
Theorem 10. Let G5 be the graph of remdesivir. Using Fig 5, the various topological indices of the G5 graph are as follows:
- NE1(G5)=2952
- NE2(G5)=48659
- NFE(G5)=109810
- NRE(G5)=3595128
- NSDdegE (G5)=105.4888
- NISIE(G5)=687.5585
- NHE(G5)=1.3713
- NAE (G5)=223477.2482
Theorem 11. Let G6 be the graph of ritonavir. NEC-polynomial of G6 is given as follows:
Proof: From Fig 6, it is easy to see that and
. The frequencies are given as |E12,37| = 1, |E15,46| = 1, |E16,49| = 1, |E17,52| = 1, |E28,40| = 1, |E28,46| = 1, |E34,49| = 1, |E34,55| = 1, |E37,40| = 1, |E38,39| = 1, |E38,60| = 1, |E38,61| = 1, |E39,60| = 1, |E40,43| = 1, |E43,43| = 1, |E43,46| = 1, |E46,49| = 1, |E60,64| = 1, |E14,43| = 3, |E21,64| = 2, |E24,37| = 2, |E26,37| = 2, |E26,43| = 2, |E30,32| = 2, |E30,43| = 2, |E32,32| = 2, |E32,46| = 2, |E32,52| = 2, |E36,38| = 3, |E36,52| = 3, |E38,38| = 2, |E38,55| = 2, |E42,43| = 2 and |E42,61| = 2. Then, we have
Theorem 12. Let G6 be the graph of ritonavir. Using Fig 6, the various topological indices of the G6 graph are as follows:
- NE1(G6)=4134
- NE2(G6)=79061
- NFE(G6)=175662
- NRE(G6)=6636558
- NSDdegE (G6)=123.0674
- NISIE(G6)=973.6367
- NHE(G6)=1.4070
- NAE (G6)=410483.7478
Theorem 13. Let G7 be the graph of thalidomide. NEC-polynomial of G7 is given as follows:
Proof: From Fig 7, it is easy to see that and
. The frequencies are given as |E6,19| = 3, |E8,23| = 1, |E14,23| = 2, |E14,19| = 1, |E12,14| = 1, |E12,17| = 1, |E17,17| = 2, |E17,19| = 3, |E19,21| = 2, |E16,21| = 2, |E16,17| = 2 and |E21,21| = 1. Then, we have
Theorem 14. Let G7 be the graph of thalidomide. Using Fig 7, the various topological indices of the G7 graph are as follows:
- NE1(G7)=706
- NE2(G7)= 5810
- NFE(G7)=12640
- NRE(G7)=204938
- NSDdegE (G7)=48.6270
- NISIE(G7)=167.5911
- NHE(G7)=1.2803
- NAE (G7)=14405.3630
Theorem 15. Let G8 be the graph of theaflavin. NEC-polynomial of G8 is given as follows:
Proof: From Fig 8, it is easy to see that and
. The frequencies are given as |E11,33| = 1, |E11,34| = 1, |E12,37| = 1, |E13,40| = 1, |E15,44| = 1, |E18,27| = 1, |E18,31| = 1, |E20,28| = 1, |E20,32| = 1, |E21,31| = 1, |E21,33| = 1, |E22,31| = 1, |E22,37| = 1, |E24,38| = 1, |E24,40| = 1, |E26,37| = 1, |E26,41| = 1, |E28,38| = 1, |E28,46| = 1, |E34,37| = 1, |E37,38| = 1, |E37,40| = 1, |E40,41| = 1, |E41,46| = 1, |E10,31| = 2, |E11,32| = 1, |E15,46| = 2, |E24,34| = 2, |E27,28| = 2, |E28,31| = 3, |E28,40| = 2, |E28,44| = 2, |E30,46| = 2, |E31,32| = 1, |E31,33| = 1 and |E31,34| = 2. Then, we have
Theorem 16. Let G8 be the graph of theaflavin. Using Fig 8, the various topological indices of the G8 graph are as follows:
- NE1(G8)=2788
- NE2(G8)=41054
- NFE(G8)=92400
- NRE(G8)=2667738
- NSDdegE (G8)=109.8168
- NISIE(G8)=650.1624
- NHE(G8)=1.5703
- NAE (G8)=167520.7917
4 Computation of statistical parameters
Table 2 shows eight physical properties such as boiling point (BP), enthalpy of vaporisation (E), flash point (FP), molar refraction (MR), polar surface area (PSA), polarizability (P), molar volume (MV), and molecular weight (MW), of COVID-19 drugs taken from Chemspider and PubChem databases [37,38], while Table 3 represents the topological indices calculated values in each drug in previous section. The relation between topological indices and physical properties of COVID-19 drugs are found with the help of QSPR modeling.
4.1 Linear regression models
The linear regression models for all the considered topological indices are given in this subsection. The correlation coefficients in linear regression model is presented in Table 4. Tables 5–12 show the statistical parameters used in the QSPR models of topological indices. We have used linear regression model
where, Y is the physical property of drug, B is the regression coefficient, A is the constant and TI is the topological index. R shows the correlation coefficient and p is the p-value. SE and F demonstrate the standard error of the estimates and the Fisher’s statistic [39], respectively. Constant A and regression coefficient B is calculated from SPSS software for eight physical properties and eight based topological indices of molecular structure of eight drugs. The relationship between the topological index and the physico-chemical properties of the drugs and the correlation coefficients associated with them are shown in Fig 1.
Using Eq (20), followings are the linear regression model for the defined based topological indices:
1. Regression models for first neighboorhood eccentricity index NE1:
2. Regression models for second neighboorhood eccentricity index NE2:
3. Regression models for forgotten neighboorhood eccentricity index NFE:
4. Regression models for reformulate neighboorhood eccentricity index NRE:
5. Regression models for symmetric degree division neighboorhood eccentricity index NSDdegE :
6. Regression models for inverse sum indegree neighborhood eccentricity index NISIE:
7. Regression models for harmonic neighborhood eccentricity index NHE:
8. Regression models for augmented neighborhood eccentricity index NAE:
4.2 Cubic regression model
In this part, the cubic regression model is tested. We have used the following cubic regression model
where, Y is the physical property, A is the regression model constant, B, C and D are the coefficients for the individual descriptor. The correlation coefficients in cubic regression model is presented in Table 13. We determine the best possible cubic regression model for predicting physicochemical properties of COVID-19 drugs in Table 14.
From Table 14, NE1 for BP, E and MW; NAE for FP; NISIE for MR, P, MV and MW; NSDdegE for PSA are the best estimator indices in cubic regression model.
5 Comparison and discussions
The molecular topology of the COVID-19 drugs is modeled by means of several topological indices, and a QSPR analysis is carried out to investigate the predictive ability of the topological indices under consideration. We have correlated eight physical properties of drugs used to treat COVID-19 with neighborhood eccentricity based topological indices. This section presents the comparison for known values and calculated values from regression models. Tables 15–22 show the comparison of each physical property for linear regression models, while Tables 23 and 24 give the comparison of actual and calculated values for drugs from cubic regression models for the best predictors.
The linear QSPR analysis (see Table 4) illustrates that NE2 index is the best predictor for MV; NSDdegE index has high correlated value for BP, E, PSA and MW; and NISIE index gives high correlation coefficients for FP, MR and P. On the other hand, in cubic regression model (see Table 13), NE1 index is the best predictor for BP, E and MW; NSDdegE index has high correlated for PSA; NISIE index is the best predictor for MR, P, MV and MW; and NAE index gives best correlation values for FP.
6 Conclusion
In this work, the eight topological indices for eight drugs utilized in the treatment of COVID-19 disease, namely arbidol, chloroquine, hydroxy-chloroquine, lopinavir, remdesivir, ritonavir, thalidomide, and theaflavin, which are shown in Figs 1–8 have been evaluated. The correlation between these indices and eight physico-chemical properties, namely boiling point, enthalpy of vaporization, flash point, molar refraction, polar surface area, polarizability, molar volume, and molecular weight has been analyzed, and correlation coefficients for linear and cubic models have been presented in Tables 4 and 13. The results show that certain topological indices had strong correlations with specific physico-chemical properties. Additionally, SPSS software to fit linear and cubic regression models to predict the physico-chemical properties has been used. All the statistical parameters for linear model have been presented in Tables 5–12.
These analyses represent that the p-value in each case except for FP, MR, PSA, P and MV with harmonic neighborhood eccentricity index is less than 0.05, which indicates the significance of the results. The best predictor indices for each property in the cubic model have been identified (see Table 14). It is observed from Tables 15–24 that the computed values of the properties are found to be close to the actual values, further validating the predictive power of these indices. It is found that the second neighborhood eccentricity index is the best predictor for molar volume in linear regression models. Boiling point, enthalpy, polar surface area and molecular weight properties are best predicted by the symmetric degree division neighborhood eccentricity index in linear regression models. Flash point, molar refraction and polarizability properties are best predicted by inverse sum indegree neighborhood eccentricity in linear regression models.
In cubic regression equations, boiling point, enthalpy vaporization and molecular weight are best predicted by the first neighborhood eccentricity index. The symmetric degree division neighborhood eccentricity index is suitable for polar surface area. The augmented neighborhood eccentricity index is the best predictor for flash point and the other properties such as molar refraction, polarization, molar volume and molecular weight are best predicted by the inverse sum indegree neighborhood eccentricity index. The QSPR analysis of the paper could be helpful in the drug’s development against corona viruses. To our best knowledge, this is the first investigation on various COVID-19 drugs chosen using neighborhood eccentricity-based topological descriptors.
Acknowledgments
The authors extend their appreciation to Taif University, Saudi Arabia, for supporting this work through project number (TU-DSPP-2024-47).
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