Topological Descriptors and QSPR Modelling of HIV/AIDS Disease Treatment Drugs

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Introduction
About 33 million people have died from HIV infection globally, and numerous mathematical models of the human immune system have developed to represent the full range of infection.Human immunodefciency virus (HIV) and the immune system have been shown to interact.According to reports, HIV can cause immunodefciency syndrome (AIDS), which makes it harder for the body to fght of other diseases.About 44,200,000 people have died because of the devastating and incurable HIV virus.According to reports, 1.5 million new HIV infections are reported in 2020, leaving 37.6 million persons worldwide HIV-positive [1].However, people with HIV are now living longer and healthier lives because of efective treatment, care, assessment, and protection.Te HIV virus spreads quickly once it enters the body of a healthy person.Te fu, midnight cravings, coughing, weight loss, diarrhea, body pains, joint pain, and dry mouth are some of the early symptoms and indicators of HIV infection.Te process is still in its early stages, the virus enters the bloodstream more fully, and the HIV infection spreads across the body more readily than at other times.In addition, HIV-infected viruses can infect the uninfected person through bodily fuids like blood, tears, urine, saliva, and others.It belongs to the genus Lentivirus and is responsible for the most serious illness, AIDS (acquired immune defciency syndrome).HIV directly attacks the immune system [2].Tere are numerous recognized targets, and numerous substances have received approval for the treatment of HIV.According to studies, if a single chemical is employed to treat HIV, toxicity and resistance will quickly arise.Te major goal of this study project is to examine the system's most important components for the prevention of this viral infection.Without the need for chemical experimentation, the topological index computing technique is being utilized to assess the medicinal characteristics and biochemical data of novel medications, which is particularly welcomed in underdeveloped nations.Numerous investigations have discovered a clear connection between molecular structure and medications and chemical properties such as boiling and melting points.Gao et al. [3] focused on a family of smart polymers that are frequently employed in the creation of anticancer medications.Te results compensate for the lack of chemical and medical experiments and serve as a theoretical foundation topological index utilizing edge division techniques.In recent years, there has been great curiosity in using these invariants (TIs) in QSPR and quantitative structure activity relationship (QSAR) studies.Te indices have a lot of uses in countless ranges of chemistry, physics, informatics, and biology QSAR [4].Te ABC index, Wiener index, and Randic index can all be used to predict drug bioactivity.QSPR models sustenance in deciding the best association between TIs and physical properties.Research-based medicinal remedies are being tested as medications by scientists.In this paper, we calculated degree-based TIs for HIV drugs.Similarly, HIV drug on which the specifed topological indices are carefully implemented and measured the QSPR technique is performed.With the help of linear regression, the physical characteristic is estimated successfully.It has been discovered that both variables have a good relation.
According to Havare [5], novel medications used in cancer treatment are a costly and complex phenomenon; hence, these are best predicted using this method.QSPR modelling of blood cancer medicines by Nasir et al. [6] demonstrates a signifcant relationship between TIs and pharmacological characteristics.We are working on the current study issue because of improvements in QSPR investigations for diferent topological indices for diferent chemical structures.In order to derive analytically precise equations for particular degree and distance-based topological indices for general networks, Hayat et al. [7] published a computer technique.Experiments are conducted in comparison to the well-known methodologies to show that our method is superior and has a lower level of algorithmic and computing complexity.Antituberculosis drug QSPR modelling is described in [8], and Parveen et al. [9] fnished the QSPR analysis of diabetes therapies and identifed a bestft model for it.Vitiligo disease drug modelling is discussed in [10], and the cardiovascular QSPR ftted model is mentioned in [11].For further investigation, we validate articles [4,5,[11][12][13][14][15] for more information on degree-based topological indices.Our motivation to work on the current research issue came from studies on COVID-19, anticancer, blood cancer, and QSPR investigations of eigenvalue-based, degree-based entropy, and ve-degree-based topological indices for various chemical structures (see [2,[16][17][18]).Tis study's goal is to investigate the usage of TIs in fguring out the physical characteristics and QSPR modelling of the therapeutic management medication regimens for HIV.

Materials and Methods
In this study, the drug's structure is represented as a graph, where each vertex V(G) expresses an atom and each edge E(G) represents a chemical connection between these atoms.All graphs are assumed to be simple and linked.Te numbers of edges that connect a vertex to other edges determine its degree.Please refer to the book [19] in cases where notations and terminologies are unclear.Te degree of a vertex in a graph G is denoted by d u .For further investigation, we refer [4,8,13] and [20] and used the following TIs.Defnition 1. Te ABC index is as follows [15]: Defnition 2. Te Randic index RA(G) calculated by Milan Randic in 1975 [21] is given under the following expression: Defnition 3. Te sum connectivity index [22] is given under the following expression: Defnition 4. Te GA index [23] is given under the following expression: Defnition 5. Zagreb indices [24] are given under the following expression: Defnition 6. Te harmonic index [25] is given under the following expression: Defnition 7. Te hyper Zagreb index [26] is defned as follows: Defnition 8. Te forgotten index [27] is given under the following expression: Tenofovir's antiviral properties were initially noted in 1993, and tenofovir disoproxil, the commercial form of this drug, has been accessible since 2008.Tipranavir is a nonpeptidic protease inhibitor that targets the HIV protease and contains sulfonamides.HIV is treated by the coadministration of ritonavir and tipranavir.Etravirine is a type of antiretroviral medication.

Quantitative Structure Analysis and Regression Model
In this section, TIs are performed on HIV drugs.Te relationship between QSPR analysis and TIs suggests that the physicochemical characteristics of the disease are highly connected.Te thirteen medicines lamivudine, darunavir, Disovey, maraviroc, tenofovir, tipranavir, atazanavir, lopinavir, abacavir, etravirine, nelfnavir, and toreforant are used in the analysis for HIV disease.Te drug edifces are exhibited in Figures 1 and 2. We implement regression analysis calculated for this study.Drug computable structure analysis of nine TIs for QSPR modelling tenacity is performed.Te nine physical properties, molar refractivity (R), polarity, complexity, molar volume (MV), and enthalpy (E) and boiling point (BP) for nine medicines used in HIV treatment are listed in Table 1.We impose the linear model by using the following equation: P denotes the physicochemical property of the given drug.Te term TI stands for the topological index, α stands for constant, and β stands for the regression coefcient.MATLAB and R-language software are helpful for results.A linear model is used to analyze nine TIs of HIV drugs and their properties.
Let G 1 be graph of lamivudine, and then, TIs are as follows: Also, G 2 be a graph of tipranavir, and then, TIs are as follows: Discrete Dynamics in Nature and Society   Discrete Dynamics in Nature and Society Now, for partition of           Tables [4-7, 11-14, 16] represent the statistical parameters used in QSPR models of TIs.

Statistical Parameters Comparison between TIs and Correlation Coefcient of Properties. Te correlation between
Terapeutic Indices (TIs) and the physical properties of drugs used for HIV disease treatment, including medications like lamivudine, darunavir, disovey, maraviroc, tenofovir, tripranavir, atazanavir, lopinavir, abacavir, etravirine, nelfnavir, toreforant, is efectively established through the implementation of Quantitative Structure-Property Relationship (QSPR) modeling.Tis sort of analysis can be useful for the model.It is eminent that the value of p is less than 0.05 and r is greater than 0.6.Hence, it concluded entirely properties given in  which are signifcant.Table 12 lists the correlation coefcients.Figure 3 depicts the graph.

Standard Error of Estimate (SEE), Correlation Determination, and
Comparison.Measure of variation for an observation calculated around the computed regression line is said to be the standard error estimate.It examines the extent of accuracy of predictions made about the calculated regression line in Table 13.Table 14 shows correlation.Tables 15-21 compare the physicochemical properties of the experimental and theoretical calculated tenets of the models.

Conclusions
It is noted harmonic H(G) provides the maximum correlated value of molar polarity r � 0.979.Te ABC(G) index provides a high correlated value for molar volume r � 0.984.Te H(G) index ofers the maximum correlated value of the fash point, i.e., r � 0.882.GA(G) and H(G) indices depict the utmost correlation coefcient of BP r � 0.877.Harmonic H(G) provides the maximum correlated value of molar refractivity r � 0.989.No correlation is present between TIs and density, polar surface area, and surface tension.In this work, the TIs for drugs used to treat HIV disease were computed, and they were contrasted with a linear QSPR model.Using the data gathered in this manner, the pharmaceutical industry will be able to create new medications to discover preventative treatments for the aforementioned illness.Te variety of topological indicators for these medications is strongly afected by the correlation coefcient.Te results ofer a technique to evaluate physicochemical features for new discoveries of other disorders and are eye-opening for researchers working on drug science in the pharmaceutical sector [28].

Figure 4 :
Figure 4: Physicochemical properties and TIs.(a) Complexity on TI.(b) Flash point on TI.(c) Enthalpy on TI.(d) Molar refractivity on TI.(e) Molar volume on TI. (f ) Polarity on TI.(g) Boiling point on TI.

Table 1 :
Physical properties of drugs.

Table 2 :
TIs of drugs.

Table 15 :
Comparison of polarity.

Table 16 :
Comparison of Molar Volume.

Table 19 :
Comparison of Complexity.

Table 20 :
Comparison of Boiling point.

Table 21 :
Comparison of fash point.