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

Farooq, Fozia Bashir; Parveen, Saima; Hassan Awan, Nadeem Ul; Fanja, Rakotondrajao

doi:https://doi.org/10.1155/2023/9963241

Discrete Dynamics in Nature and Society

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Research Article | Open Access

Volume 2023 | Article ID 9963241 | https://doi.org/10.1155/2023/9963241

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

Fozia Bashir Farooq,^1,2Saima Parveen ,²Nadeem Ul Hassan Awan,³and Rakotondrajao Fanja⁴

Academic Editor: Cruz Vargas-De-León

Received21 Apr 2023

Revised23 Jul 2023

Accepted04 Nov 2023

Published25 Nov 2023

Abstract

A topological index is a real number derived from the structure of a chemical graph. It helps determine the physicochemical and biological properties of a wide range of drugs, and it better reflects the theoretical properties of organic compounds. This is accomplished using degree-based topological indices. We examined some of the physiochemical characteristics of thirteen HIV therapy medications and created a QSPR model utilizing nine of the medication’s topological indices. The melting point, boiling point, flash point, complexity, surface tension, etc., of HIV medicines are closely related according to this QSPR model. This work can help to design and synthesize new HIV treatments and other disease drugs.

1. 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 immunodeficiency virus (HIV) and the immune system have been shown to interact. According to reports, HIV can cause immunodeficiency syndrome (AIDS), which makes it harder for the body to fight off 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 effective treatment, care, assessment, and protection. The HIV virus spreads quickly once it enters the body of a healthy person. The flu, midnight cravings, coughing, weight loss, diarrhea, body pains, joint pain, and dry mouth are some of the early symptoms and indicators of HIV infection. The 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 fluids like blood, tears, urine, saliva, and others. It belongs to the genus Lentivirus and is responsible for the most serious illness, AIDS (acquired immune deficiency syndrome). HIV directly attacks the immune system [2]. There 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. The 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. The 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. The indices have a lot of uses in countless ranges of chemistry, physics, informatics, and biology QSAR [4]. The 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 specified 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 significant relationship between TIs and pharmacological characteristics. We are working on the current study issue because of improvements in QSPR investigations for different topological indices for different 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] finished the QSPR analysis of diabetes therapies and identified a best-fit model for it. Vitiligo disease drug modelling is discussed in [10], and the cardiovascular QSPR fitted model is mentioned in [11]. For further investigation, we validate articles [4, 5, 11–15] 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, 16–18]). This study’s goal is to investigate the usage of TIs in figuring out the physical characteristics and QSPR modelling of the therapeutic management medication regimens for HIV.

2. Materials and Methods

In this study, the drug’s structure is represented as a graph, where each vertex expresses an atom and each edge represents a chemical connection between these atoms. All graphs are assumed to be simple and linked. The 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. The degree of a vertex in a graph G is denoted by . For further investigation, we refer [4, 8, 13] and [20] and used the following TIs.

Definition 1. The ABC index is as follows [15]:

Definition 2. The Randic index calculated by Milan Randic in 1975 [21] is given under the following expression:

Definition 3. The sum connectivity index [22] is given under the following expression:

Definition 4. The GA index [23] is given under the following expression:

Definition 5. Zagreb indices [24] are given under the following expression:

Definition 6. The harmonic index [25] is given under the following expression:

Definition 7. The hyper Zagreb index [26] is defined as follows:

Definition 8. The forgotten index [27] is given under the following expression:Tipranavir is a nonpeptidic protease inhibitor that targets the HIV protease and contains sulfonamides. HIV is treated by the coadministration of ritonavir and tipranavir. A nonpeptidic protease inhibitor of HIV is tipranavir. The protease component of HIV is blocked by protease inhibitors. Lamivudine has the molecular formula C₈H₁₁ N₃ O₃S. It is used to treat hepatitis B and type 1 human immunodeficiency virus. It has the molecular formula C₃₁H₃₃ F₃N₂ O₅S. It has the molecular formula C₃₂H₄₅N₃ O₄S. A powerful inhibitor of the HIV-1 protease is nelfinavir. It is used for the treatment of HIV in adults and children. Maraviroc has the molecular formula C₂₉H₄₁ F₂N₅ O₄. It works to combat HIV by obstructing the communication between HIV and CCR5. Emtricitabine is a nucleoside reverse transcriptase inhibitor (NRTI) that is prescribed to treat HIV infection in adults or to prevent HIV infection in high-risk adults and adolescents when taken with tenofovir alafenamide. Emtricitabine is an analogue of cytidine. The medication prevents HIV RNA from being converted to DNA by inhibiting HIV reverse transcriptase. It is identified as a genuine nucleotide analogue in the strictest sense since it has a phosphate group bound to the nitrogenous base. 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.

3. Quantitative Structure Analysis and Regression Model

In this section, TIs are performed on HIV drugs. The relationship between QSPR analysis and TIs suggests that the physicochemical characteristics of the disease are highly connected. The thirteen medicines lamivudine, darunavir, Disovey, maraviroc, tenofovir, tipranavir, atazanavir, lopinavir, abacavir, etravirine, nelfinavir, and toreforant are used in the analysis for HIV disease. The drug edifices 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. The 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:

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(a)

(b)

(c)

(d)

P denotes the physicochemical property of the given drug. The term TI stands for the topological index, stands for constant, and stands for the regression coefficient. 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 be graph of lamivudine, and then, TIs are as follows:(i)(ii)(iii)(iv)(v)(vi)(vii)(viii)(ix)

Now, for partition of , and .(i)Applying Definition 1, we obtain (ii)Applying Definition 2, we obtain (iii)Applying Definition 3, we obtain (iv)Applying Definition 4, we obtain (v)Applying Definition 5, we obtain (vi)Applying Definition 5, we obtain(vii)(viii)Applying Definition 6, we obtain (ix)Applying Definition 7, we obtain (x)Applying Definition 8, we obtain

Also, be a graph of tipranavir, and then, TIs are as follows:(i)(ii)(iii)(iv)(v)(vi)(vii)(viii)(ix)

Now, for partition of and .(i)Applying Definition 1, we obtain (ii)Applying Definition 2, we obtain (iii)Applying Definition 3, we obtain (iv)Applying Definition 4, we obtain (v)Applying Definition 5, we obtain (vi)Applying Definition 5, we obtain (vii)Applying Definition 6, we obtain (viii)Applying Definition 7, we obtain (ix)Applying Definition 8, we obtain

Topological indices of other drugs can be calculated by means of the identical technique as discussed above and Definitions 1 to 8. Table 2 includes calculated tenets for all drugs’ TIs. Figures 3 and 4 depict a graphical representation of calculated TIs for various medicines. Using (1), subsequent diverse linear models to find out other TIs are given as follows:(1)Regression models of ABC(G) are as follows: Boiling point = 346.910 + 13.268 [ABC(G)] Enthalpy = 66.555 + 1.535 [ABC(G)] Flash point = 163.588 + 8.023 [ABC(G)] Molar refractivity = −12.048 + 5.276 [ABC(G)] Polarity = −3.948 + 2.087 [ABC(G)] Molar volume = −101.097 + 17.791 [ABC(G)] Complexity = 15.807 + 26.440 [ABC(G)](2)Regression models of RA(G) are as follows: Boiling point = 345.986 + 21.602 [RA(G)] Enthalpy = 66.296 + 2.509 [RA(G)] Flash point = 163.035 + 13.062 [RA(G)] Molar refractivity = −11.383 + 8.534 [RA(G)] Polarity = −3.724 + 3.377 [RA(G)] Molar volume = −100.628 + 28.88 [RA(G)] Complexity = 18.898 + 42.774 [RA(G)](3)Regression models of S(G) are as follows: Boiling point = 343.313 + 21.044 [S(G)] Enthalpy = 65.953 + 2.446 [S(G)] Flash point = 161.415 + 12.725 [S(G)] Molar refractivity = −12.807 + 8.332 [S(G)] Polarity = −4.191 + 3.294 [S(G)] Molar volume = −103.688 + 28.110 [S(G)] Complexity = 13.333 + 41.709 [S(G)](4)Regression models of GA(G) are as follows: Boiling point = 335.740 + 10.330 [GA(G)] Enthalpy = 64.945 + 1.205 [GA(G)] Flash point = 156.835 + 6.246 [GA(G)] Molar refractivity = −14.735 + 4.051 [GA(G)] Polarity = −4.838 + 1.599 [GA(G)] Molar volume = −107.878 + 13.609 [GA(G)] Complexity = 8.000 + 20.107 [GA(G)](5)Regression models of M1(G) are as follows: Boiling point = 345.584 + 1.993 [M1(G)] Enthalpy = 66.272 + 0.231 [M1(G)] Flash point = 162.775 + 1.205 [M1(G)] Molar refractivity = −13.422 + 0.797 [M1(G)] Polarity = −4.538 + 0.315 [M1(G)] Molar volume = −104.247 + 2.678 [M1(G)] Complexity = 0.879 + 4.042 [M1(G)](6)Regression models of HM(G) are as follows: Boiling point = 359.791 + 0.383 [HM(G)] Enthalpy = 67.889 + 0.045 [HM(G)] Flash point = 171.354 + 0.232 [HM(G)] Molar refractivity = −10.462 + 0.157 [HM(G)] Polarity = −3.571 + 0.062 [HM(G)] Molar volume = −94.808 + 0.527 [HM(G)] Complexity = −2.288 + 0.818 [HM(G)](7)Regression models of M2(G) are as follows: Boiling point = 342.262 + 1.737 [M2(G)] Enthalpy = 65.611 + 0.203 [M2(G)] Flash point = 160.757 + 1.050 [M2(G)] Molar refractivity = −4.752 + 0.695 [M2(G)] Polarity = −5.166 + 0.275 [M2(G)] Molar volume = −107.540 + 2.326 [M2(G)] Complexity = −17.017 + 3.573 [M2(G)](8)Regression models of F(G) are as follows: Boiling point = 375.225 + 0.683 [F(G)] Enthalpy = 69.871 + 0.079 [F(G)] Flash point = 180.685 + 0.413 [F(G)] Molar refractivity = −6.426 + 0.285 [F(G)] Polarity = −2.049 + 0.113 [F(G)] Molar volume = −82.830 + 0.960 [F(G)] Complexity = 12.530 + 1.504 [F(G)](9)Regression models of H(G) are as follows: Boiling point = 341.898 + 22.900 [H(G)] Enthalpy = 65.670 + 2.671 [H(G)] Flash point = 160.565 + 13.847 [H(G)] Molar refractivity = −12.255 + 8.994 [H(G)] Polarity = −3.957 + 3.555 [H(G)] Molar volume = −102.314 + 30.381 [H(G)] Complexity = 18.702 + 44.784 [H(G)]

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Tables [4–7, 11–14, 16] represent the statistical parameters used in QSPR models of TIs.

3.1. Statistical Parameters Comparison between TIs and Correlation Coefficient of Properties

The correlation between Therapeutic 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, nelfinavir, toreforant, is effectively established through the implementation of Quantitative Structure-Property Relationship (QSPR) modeling. This 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 Tables 3–11 which are significant. Table 12 lists the correlation coefficients. Figure 3 depicts the graph.

3.2. 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.

4. Conclusions

It is noted harmonic provides the maximum correlated value of molar polarity r = 0.979. The index provides a high correlated value for molar volume r = 0.984. The index offers the maximum correlated value of the flash point, i.e., r = 0.882. and indices depict the utmost correlation coefficient of BP r = 0.877. Harmonic 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. The variety of topological indicators for these medications is strongly affected by the correlation coefficient. The results offer 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].

Data Availability

The data used to support the findings of this study are available upon reasonable request to the corresponding author.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2023 Fozia Bashir Farooq et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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