On Topological Descriptors and Curvilinear Regression Analysis of Antiviral Drugs Used in COVID-19 Treatment

Molecular networks via reduced reverse degree approach

Porphyrazine and tetrakis porphyrazine are examples of organic compounds with complicated structures of rings. Physicists and chemical researchers have been interested in these structures because of their highly conjugated systems, which lead to peculiar optical and electrical characteristics. These structures are the fundamental components of molecular electronics, sensors, functional materials, and catalysis, among other scientific fields. The idea behind modeling molecules as networks is to calculate the topological index, where atoms are nodes and bonds are links. We can use multiple techniques and algorithms to calculate the topological index. We have used the reduced reverse degree-based approach for estimating the topological indices of the Porphyrazine and Tetrakis porphyrazine structures. The purpose of calculating the reduced reverse degree-based topological indices is to quantify the molecular topology of the mentioned structures. In future research, we can also use these indices in SAR/QSAR modeling of porphyrazine and tetrakis porphyrazine. These indices can also provide comparative analysis and descriptors for predicting chemical behavior, which is useful in material science applications and drug designs. In this study, we present a formula for calculating reduced reverse degree-based topological indices for porphyrazine and tetrakis porphyrazine, including the reduced reverse geometric arithmetic index, reduced reverse general Randić index, reduced reverse Balaban index, reduced reverse redefined Zagreb index, reduced reverse forgotten index, reduced reverse hyper-Zagreb index, and reduced reverse atom-bond connectivity index. Before the conclusion, there is a graph-theoretical analysis and comparison to ascertain the essential significance and validate the obtained results. This research helps to create novel materials for a variety of applications and sheds light on the structural and chemical characteristics of these molecular networks.

Comparative study of degree, neighborhood and reverse degree based indices for drugs used in lung cancer treatment through QSPR analysis

Quantitative structure-property relationship (QSPR) modeling has emerged as a pivotal tool in the field of medicinal chemistry and drug design, offering a predictive framework for understanding the correlation between chemical structure and physicochemical properties. Topological indices are mathematical descriptors derived from the molecular graphs that capture structural features and connectivity, playing a crucial role in QSPR analysis by quantitatively relating chemical structures to their physicochemical properties and biological activities. Lung cancer is characterized by its aggressive nature and late-stage diagnosis, often limiting treatment options and significantly impacting patient survival rates. This study focuses on the selection of drugs used to treat lung cancer, including dacomitinib, selpercatinib, tepotinib, trametinib, sotorasib, etoposide, alectinib, paclitaxel, dabrafenib, entrectinib, crizotinib, ceritinib, lorlatinib, afatinib, pralsetinib, brigatinib, erlotinib, adagrasib, gefitinib, vinorelbine, gemcitabine, docetaxel, and pemetrexed. Using molecular structural measures such as degree, neighborhood degree sum, and modified reverse degree, we have developed QSPR models to predict physicochemical properties through the topological indices derived from these structural measures. We then conducted a comparative analysis, incorporating correlation analysis, to identify the model with the highest predictive accuracy.

QSPR analysis of drugs used for treatment of hepatitis via reduced reverse degree-based topological descriptors

Topological indices refer to numerical values that are structure-invariant and are used to quantify the bonding topology of a molecular graph. 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. Several studies show a high intrinsic correlation between the molecular architectures of pharmaceuticals and their boiling and melting temperatures, as well as other chemical properties. Researchers can discover more about the physical characteristics, chemical stability, and bioactivities of these chemical molecular structures by using topological indices. To compensate for the lack of chemical experiments and to give a theoretical foundation for the production of pharmaceuticals and chemical materials, topological indices on the molecular structure of chemicals/drugs are studied. This study evaluates the chemical structures of medications used to treat hepatitis (A, B, C, D, E and G) based on reduced reverse degree-based topological indices. The success of drug design is influenced by factors such as solubility, metabolic stability, toxicity, permeability, and transporter effects, which are contingent upon the physical and chemical characteristics of the medication. In recent times, computational techniques have gained prominence in the field of hepatitis medication discovery and development. Machine learning is employed by certain systems to assess the effectiveness and adverse effects of medications. The primary focus of this article is to examine the chemical applicability of ten reduced reverse degree-based descriptors in predicting the ten physico-chemical properties for the 16 drugs employed in the treatment of hepatitis.

On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives

This work initiates a concept of reduced reverse degree basedRR D M -Polynomial for a graph, and differential and integral operators by using thisRR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using theRR D M -Polynomial. The topological descriptors, denoted as T D 's, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

Mathematical modeling for prediction of physicochemical characteristics of cardiovascular drugs via modified reverse degree topological indices

Global health concerns persist due to the multifaceted nature of heart diseases, which include lifestyle choices, genetic predispositions, and emerging post-COVID complications like myocarditis and pericarditis. This broadens the spectrum of cardiovascular ailments to encompass conditions such as coronary artery disease, heart failure, arrhythmias, and valvular disorders. Timely interventions, including lifestyle modifications and regular medications such as antiplatelets, beta-blockers, angiotensin-converting enzyme inhibitors, antiarrhythmics, and vasodilators, are pivotal in managing these conditions. In drug development, topological indices play a critical role, offering cost-effective computational and predictive tools. This study explores modified reverse degree topological indices, highlighting their adjustable parameters that actively shape the degree sequences of molecular drugs. This feature makes the approach suitable for datasets with unique physicochemical properties, distinguishing it from traditional methods that rely on fixed degree approaches. In our investigation, we examine a dataset of 30 drug compounds, including sotagliflozin, dapagliflozin, dobutamine, etc., which are used in the treatment of cardiovascular diseases. Through the structural analysis, we utilize modified reverse degree indices to develop quantitative structure-property relationship (QSPR) models, aiming to unveil essential understandings of their characteristics for drug development. Furthermore, we compare our QSPR models against the degree-based models, clearly demonstrating the superior effectiveness inherent in our proposed method.

A QSPR analysis and curvilinear regression models for various degree-based topological indices: Quinolone antibiotics

Topological indices play an essential role in defining a chemical compound numerically and are widely used in QSPR/QSAR analysis. Using this analysis, physicochemical properties of the compounds and the topological indices are studied. Quinolones are synthetic antibiotics employed for treating the diseases caused by bacteria. Across the years, Quinolones have shifted its position from minor drug to a very significant drug to treat the infections caused by bacteria and in the urinary tract. A study is carried out on various Quinolone antibiotic drugs by computing topological indices through QSPR analysis. Curvilinear regression models such as linear, quadratic and cubic regression models are determined for all topological indices. These regression models are depicted graphically by extending for fourth degree and fifth degree models for significant topological indices with its corresponding physical property showing the variation between each model. Various studies have been carried out using linear regression models while this work is extended for curvilinear regression models using a novel concept of finding minimal R M S E . R M S E is a significant measure to find potential predictive index that fits QSAR/QSPR analysis. The goal of R M S E lies in predicting a certain property of a chemical compound based on the molecular structure.

Reduced reverse degree-based topological indices of graphyne and graphdiyne nanoribbons with applications in chemical analysis

Graphyne and Graphdiyne Nanoribbons reveal significant prospective with diverse applications. In electronics, they propose unique electronic properties for high-performance nanoscale devices, while in catalysis, their excellent surface area and reactivity sort them valuable catalyst supports for numerous chemical reactions, contributing to progresses in sustainable energy and environmental remediation. The topological indices (TIs) are numerical invariants that provide important information about the molecular topology of a given molecular graph. These indices are essential in QSAR/QSPR analysis and play a significant role in predicting various physico-chemical characteristics. In this article, we present a formula for computing reduced reverse (RR) degree-based topological indices for graphyne and graphdiyne nanoribbons, including the RR Zagreb indices, RR hyper-Zagreb indices, RR forgotten index, RR atom bond connectivity index, and RR Geometric-arithmetic index. We also execute a graph-theoretical analysis and comparison to demonstrate the critical significance and validate the acquired results. Our findings provide insights into the structural and chemical properties of these nanoribbons and contribute to the development of new materials for various applications.

Predictive ability of physiochemical properties of benzene derivatives using Ve-degree of end vertices-based entropy

Topological indices relate chemical structure to chemical reactivity, physical properties, and biological activity. Quantitative structure-activity relationships (QSPR) are mathematical models proposed for the correlation of various types of chemical reactivity, biological activity, and physical properties with topological indices/entropies. In this article, we have proposed the QSPR between the ve-degree of end vertices of edge based entropies and the physiochemical properties of benzene derivatives. We have designed a Maple-based algorithm for the computation of entropies. The relationship was analyzed using SPSS. We have shown that the physiochemical properties such as critical pressure, Henry's law, critical temperature, Gibb's energy, logP, critical volume, and molar refractivity can be predicted by entropies. All the results were highly positive and significant. The Randić, Balaban, and redefined third Zagreb entropies showed the best relations with physiochemical properties.Communicated by Ramaswamy H. Sarma.

QSPR/QSAR analysis of some eccentricity based topological descriptors of antiviral drugs used in COVID-19 treatment via $ \mathscr{D}\varepsilon $- polynomials

In the field of chemical and medical sciences, topological indices are used to study the chemical, biological, clinical, and therapeutic aspects of pharmaceuticals. The COVID-19 pandemic is largely recognized as the most life-threatening crisis confronting medical advances. Scientists have tested various antiviral drugs and discovered that they help people recover from viral infections like COVID-19. Antiviral medications, such as Arbidol, Chloroquine, Hydroxy-Chloroquine, Lopinavir, Remdesivir, Ritonavir, Thalidomide and Theaflavin, are often used to treat COVID-19. In this paper, we define Diameter Eccentricity Based vertex degree and employ it to introduce a new polynomial called $ D\varepsilon- $ Polynomial. Using the newly introduced polynomial, we derive new topological indices, namely, diameter eccentricity based and hyper diameter eccentricity based indices. In order to check the efficacy of our indices, we derive the $ D\varepsilon- $ polynomials for the eight COVID-19 drugs mentioned above. Using these polynomials, we compute our proposed topological descriptors for the eight COVID-19 drugs. We perform quantitative structure-property relationship (QSPR) analysis by identifying the best fit curvilinear/multilinear regression models based on our topological descriptors for 8 physico- chemical properties of the COVID-19 drugs. We also perform quantitative structure-activity relationship (QSAR) analysis by identifying the best fit multilinear regression model for predicting the $ IC_{50} $ values for the eight COVID-19 drugs. Our findings and models may be useful in the development of new COVID-19 medication.

Curvilinear regression analysis of benzenoid hydrocarbons and computation of some reduced reverse degree based topological indices for hyaluronic acid-paclitaxel conjugates

Graph theoretical molecular descriptors alias topological indices are a convenient means for expressing in numerical form the chemical structure encoded in a molecular graph. The structure descriptors derived from molecular graphs are widely used in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. The reason for introducing new indices is to obtain predictions of target properties of considered molecules that are better than the predictions obtained using already known indices. In this paper, we apply the reduced reverse degree based indices introduced in 2021 by Vignesh et al. In the QSPR analysis, we first compute the reduced reverse degree based indices for a family of benzenoid hydrocarbon molecules and then we obtain the correlation with the Physico-chemical properties of the considered molecules. We show that all the properties taken into consideration for the benzenoid hydrocarbons can be very effectively predicted by the reduced reverse degree based indices. Also, we have compared the predictive capability of reduced reverse degree based topological descriptors against 16 existing degree based indices. Further, we compute the defined reduced reverse degree based topological indices for Hyaluronic Acid-Paclitaxel Conjugates [Formula: see text], [Formula: see text].

Some new results on the face index of certain polycyclic chemical networks

Silicate minerals make up the majority of the earth's crust and account for almost 92 percent of the total. Silicate sheets, often known as silicate networks, are characterised as definite connectivity parallel designs. A key idea in studying different generalised classes of graphs in terms of planarity is the face of the graph. It plays a significant role in the embedding of graphs as well. Face index is a recently created parameter that is based on the data from a graph's faces. The current draft is utilizing a newly established face index, to study different silicate networks. It consists of a generalized chain of silicate, silicate sheet, silicate network, carbon sheet, polyhedron generalized sheet, and also triangular honeycomb network. This study will help to understand the structural properties of chemical networks because the face index is more generalized than vertex degree based topological descriptors.

Quantitative structure-properties relationship analysis of Eigen-value-based indices using COVID-19 drugs structure

Topological indices are an important method for understanding the fundamental topology of chemical structures. Quantitative structure properties relationship (QSPR) is an analytical approach for breaking down a molecule into a sequence of numerical values that describe the chemical and physical characteristics of the molecule. In this article, we have developed the QSPR analysis between eigenvalue-based topological indices and physical properties of COVID-19 drugs to predict the significance level of eigenvalue based indices. We have to use MATLAB for the computation of indices and SPSS for analysis. We show that positive interia index, signless Laplacian Estrada index and Randić energy are the best predictors of molar reactivity, polar surface area and molecular weight, respectively.

Topological Coindices and Quantitative Structure-Property Analysis of Antiviral Drugs Investigated in the Treatment of COVID-19

SARS-CoV-2 is a new strain of coronavirus family that has never been previously detected in humans. This has grown into a huge public health issue that has affected people all around the world. Presently, there is no specific antiviral treatment for COVID-19. To tackle the outbreak, a number of drugs are being explored or have been utilized based on past experience. A molecular descriptor (or topological index) is a numerical value that describes a compound’s molecular structure and has been successfully employed in many QSPR/QSAR investigations to represent several physicochemical attributes. In order to determine topological characteristics of graphs, coindices (topological) take nonadjacent pair of vertices into account. In this study, we introduced CoM-polynomial and numerous degree-based topological coindices for several antiviral medicines such as lopinavir, ritonavir remdesivir, hydroxychloroquine, chloroquine, theaflavin, thalidomide, and arbidol which were studied using the CoM-polynomial approach. In the QSPR model, the linear regression approach is used to analyze the relationships between physicochemical properties and topological coindices. The findings show that the topological coindices under investigation have a substantial relationship with the physicochemical properties of possible antiviral medicines in question. As a result, topological coindices may be effective tools for studying antiviral drugs in the future for QSPR analyses.