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Review Topical Sections

Urinary VPAC1: A potential biomarker in prostate cancer

  • Received: 18 January 2022 Revised: 25 April 2022 Accepted: 10 May 2022 Published: 31 May 2022
  • Prostate cancer is ranked as the fourth most prevalent cancer commonly diagnosed among males over 40 years of age, according to the WHO Cancer Fact Sheet 2020, and it is additionally a leading cause of cancer mortality among males. The incidence of prostate cancer and mortality varied significantly across the globe. Diagnosis of prostate cancer hinders easier management of cases, and prostate-specific antigen (PSA) use for screening of prostate cancer has poor specificity and sensitivity, thereby yielding overdiagnosis and unnecessary biopsies. Radiologically guided (ultrasound/MRI) prostate biopsy, considered the gold standard, is invasive and can miss a significant number of metastatic cancers. Even though mild, other prostate biopsy complications occur on a large scale, and few severe ones are often recorded. Scientists intensify their search for biomarker(s) for non-invasive diagnosis of prostate cancer using proteomics, metabolomics, genomics, and bioinformatics—urinary biomarkers were uniquely on the lookout. Vasoactive intestinal peptide (VIP)/pituitary adenylate cyclase-activating peptide (PACAP) receptor 1 (VPAC1), which is overexpressed (a thousandfold) in prostate cancer at the onset of oncogenesis and is excreted in the urine on tumor cells, is a contender in the prostate cancer biomarker quest. VPAC1 is ubiquitous, expressed by normal and malignant cells, and interwoven in their cell membranes. Therefore, using urine samples limits the possibility of making the wrong diagnosis, since VPAC1 is not normally excreted in the urine. Nevertheless, studying transmembrane receptors is intricate. However, producing monoclonal antibodies against the N-terminal end of VPAC1 can provide a promising target for designing a non-invasive diagnostic assay for early detection of prostate cancer using a urine sample.

    Citation: Mansur Aliyu, Ali Akbar Saboor-Yaraghi, Shima Nejati, Behrouz Robat-Jazi. Urinary VPAC1: A potential biomarker in prostate cancer[J]. AIMS Allergy and Immunology, 2022, 6(2): 42-63. doi: 10.3934/Allergy.2022006

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  • Prostate cancer is ranked as the fourth most prevalent cancer commonly diagnosed among males over 40 years of age, according to the WHO Cancer Fact Sheet 2020, and it is additionally a leading cause of cancer mortality among males. The incidence of prostate cancer and mortality varied significantly across the globe. Diagnosis of prostate cancer hinders easier management of cases, and prostate-specific antigen (PSA) use for screening of prostate cancer has poor specificity and sensitivity, thereby yielding overdiagnosis and unnecessary biopsies. Radiologically guided (ultrasound/MRI) prostate biopsy, considered the gold standard, is invasive and can miss a significant number of metastatic cancers. Even though mild, other prostate biopsy complications occur on a large scale, and few severe ones are often recorded. Scientists intensify their search for biomarker(s) for non-invasive diagnosis of prostate cancer using proteomics, metabolomics, genomics, and bioinformatics—urinary biomarkers were uniquely on the lookout. Vasoactive intestinal peptide (VIP)/pituitary adenylate cyclase-activating peptide (PACAP) receptor 1 (VPAC1), which is overexpressed (a thousandfold) in prostate cancer at the onset of oncogenesis and is excreted in the urine on tumor cells, is a contender in the prostate cancer biomarker quest. VPAC1 is ubiquitous, expressed by normal and malignant cells, and interwoven in their cell membranes. Therefore, using urine samples limits the possibility of making the wrong diagnosis, since VPAC1 is not normally excreted in the urine. Nevertheless, studying transmembrane receptors is intricate. However, producing monoclonal antibodies against the N-terminal end of VPAC1 can provide a promising target for designing a non-invasive diagnostic assay for early detection of prostate cancer using a urine sample.


    Abbreviations

    PSA:

    prostate-specific antigen; 

    VIP:

    vasoactive intestinal peptide; 

    PACAP:

    pituitary adenylate cyclase-activating peptide; 

    VPAC1:

    VIP/PACAP receptor 1; 

    ASR:

    age-standardized rate; 

    BPH:

    benign prostatic hypertrophy; 

    DHT:

    5α-dihydrotestosterone; 

    RTqPCR:

    quantitative reverse transcription polymerase chain reaction; 

    MRI:

    magnetic resonance imaging; 

    mp-MRI:

    multiparametric MRI; 

    DCE-MRI:

    dynamic contrast-enhanced MRI; 

    DWI-MRI:

    diffusion-weighted imaging MRI; 

    TRUS:

    trans-rectal ultrasound scan; 

    ELISA:

    enzyme-linked immunosorbent assay; 

    PCA3:

    prostate cancer antigen 3; 

    TMPRSS2:

    transmembrane protease serine 2; 

    GSTP1:

    glutathione S-transferase P1; 

    DRE:

    digital rectal examination; 

    AUC:

    area under the curve; 

    aHGF:

    hepatocyte growth factor; 

    IGFBP3:

    insulin-like growth factor binding protein 3; 

    OPN:

    Plasma osteopontin; 

    LNCaP:

    lymph node carcinoma of the prostate; 

    GPCRs:

    G protein-coupled receptors; 

    RAMPS:

    receptor activity modifying proteins; 

    7-TMD:

    seven-transmembrane domain; 

    ECD:

    extracellular domain; 

    CHO:

    Chinese hamster ovary; 

    TBP:

    TATA-box binding protein; 

    COX-2:

    cyclooxygenase-2; 

    MMP9:

    metalloproteinase 9; 

    uPA:

    urokinase plasminogen activator; 

    uPAR:

    uPA receptor; 

    DAPI:

    4,6-diamidino-2-phenylindole; 

    AC:

    adenylyl cyclase; 

    CREB:

    cAMP response element-binding protein; 

    PKA:

    phosphokinase A; 

    iNOS:

    inducible nitric oxide synthase; 

    CBP:

    CREB binding protein; 

    NF-κβ:

    nuclear factor-κβ; 

    ERK:

    extracellular signal-regulated kinase; 

    MEKK1:

    MAP/ERK kinase (MEK) kinase 1; 

    IRF-1:

    IFN regulatory factor-1; 

    IKK:

    inhibitory κβ kinase; 

    BB-LP:

    bombesin-like peptides; 

    GRPR:

    gastrin-releasing peptide receptor; 

    PLC:

    phospholipase C; 

    DAG:

    diacylglycerol; 

    IP3:

    1,4,5-triphosphate; 

    PKC:

    protein kinase C; 

    MAPK:

    mitogen-activated protein kinase; 

    MAPKK:

    mitogen-activated protein kinase kinase; 

    ELK:

    ETS like-1 protein; 

    SRE:

    serum response element

    One of the life-threatening diseases world-wide is Malaria caused by the bite of female anopheles’ mosquitoes. There are 5 such parasite species that affect humans of which 2 of these viz., P. falciparum and P. vivax are the greatest threats. These two deadliest parasites are prevalent in African continent and Saharan Africa. It is an acute febrile illness which causes rapid onset of fever with headache and chills only after 10 to 15 days after the mosquito bite. If the symptoms are not treated immediately, it will lead to fatal in just one day [1].

    In the year 2020, there was a high risk for nearly half the world population of contracting malaria. Some population groups with high risk include infants, and young children, pregnant women, and people with low immunity.

    A considerable number of mortality and complications of morbidity is caused by malaria that has become a major health problem globally. As the resistant parasite strains emerge, the therapeutic options are limited which has led to the large spread of malaria. This can be prevented by potential public health emergency in designing new drugs, providing single dose cures and by introducing some novel mechanism of action. New excipients may be included in the medicine that could be effective in fighting the new variants of the strain. Using the available genomic techniques, advancement of the study of biology of the parasites can be developed for the new therapy.

    In recent years, various advanced drug interventions have been revealed. This focusses on the discovery of antimalarial agents using the latest scientific and technological advances. There are many antimalarial targets that include proteins such as proteases, plasmodium sugar, farnesyltransferase inhibitor and DNA replication. World malaria report shows an increase of cases from 2019 to 2020 and an increase of almost 69,000 deaths in 2020 compared to 2019 [2].

    To test the molecular properties in a laboratory consumes more time and money. This inconvenience can be avoided using quantitative structure activity relationship models to forecast different properties of various chemical compounds using topological descriptors. Topological indices find significant applications in various areas of mathematical chemistry [3,4] such as isomer discrimination, chirality, molecular complexity, drug design, selection of database, QSAR/QSPR/QSTR studies in the recent years [5].

    The main objectives of this study are:

    ● QSPR analysis of the properties of the topological indices using regression models for the nine anti-malaria drugs.

    ● Computation of topological indices for the considered drugs.

    ● Comparison of topological indices with correlation coefficients of few physical properties and statistical parameters.

    Identifying drug-like from non-drug-like molecules is very much necessary to reduce the cost and time with failed drug development. There are various approaches that screen chemical databases against biological targets in the progress of new potential leads. QSAR modelling is a significant approach in the discovery of drug that correlates the structure of the molecule with biological activities. There are different methods like 2D (topological indices) and 3D (structure-based) of which 2D requires less calculation time and hence used for the preliminary screening of the drug development. Academia, industry, and research institutions across the globe, widely use 2D approach.

    The principal step involves the selection of the right descriptor for various reasons. Only few descriptorsgive a better understanding of the results and their interpretability, can reduce the risk of overfitting from redundant descriptors, and provides speedy and cost-effective models.

    Topological index represents translations of molecular structures into structural descriptors that are expressed as numerical indices. These topological indices find their applications in drug design where the QSAR/QSPR/QSTR studies are involved. The QSAR/QSPR methods are based on the assumption that the activity or the property, such as a drug binding to DNA or toxic effect, of a certain chemical compound related to its structure through a certain mathematical algorithm.

    For the chemical compound under the study, a series of parameters, called chemical descriptors are computed. Then, an algorithm that provides a quite accurate value, similar to theoretical experimental value is found. The final step is to check if the obtained algorithm is capable of predicting the activity/property values.

    QSAR/QSPR/QSTR models are used to predict the association between the molecular structure and its activity/property/toxicity. Over the years many algorithms have been proposed and applied in QSAR/QSPR studies. The model framework includes molecular structure (graph) representation, calculation of molecular descriptors (graph invariants) and multiple linear regression method. The model will be validated through statistical parameters (r and r2). The same approach is employed in this work and the statistical parameters have shown significant results.

    Recently, Adnan et. al. made a study on the QSPR analysis of anti tuberculosis drugs in which 15 drugs were considered for the regression analysis of 6 physico chemical properties. Eleven topological indices were computed for which the correlation analysis showed a high positive good correlation with all the 6 physico chemical properties. Shanmukha et.al. studied 21 breast cancer drugs for which QSPR analysis were carried out. Eleven topological indices were studied in the study and linear models for each index were carried out. In 2020, Sigarreta [6,7] provided new tools that obtained a unified way inequalities involving many different topological indices. Joseobtained new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Recently, Jose computed new lower and upper optimal bounds for general (exponential) indices of a graph. In the same direction, new inequalities involving some well-known topological indices like the generalized atom-bound connectivity index and the generalized second Zagreb index were shown. Some extremal problems for their corresponding exponential indices were computed.

    The numerical representation of the arrangement of a molecule of a compound refers to topological index. Wiener index was one of the first topological indices proposed by Harold Wiener in 1947 which proved that his index correlated well with the boiling points of alkanes. At present, there are various indices introduced by various researchers which are divided into three categories, namely, degree-based, neighborhood degree-based and distance based topological indices [8,9,10]. Sixty years ago, QSAR was introduced that included modelling of biological activities of molecules which was extended to modelling of few physicochemical properties of molecules leading to QSPR studies. Initially, it was chemical interpretation of topological indices [11,12] which has now extended to modelling of structural characteristics of molecules with their biological activity leading to complex modelling of compounds in QSAR/QSPR/QSTR studies [13,14,15,16,17,18,19,20,21,22,23,24,25].

    This model does not require any lab equipment to perform the analysis. It saves a lot of time and money and the results obtained using the QSPR model are compared with the actual values for further analysis.

    A graph G(V, E) with vertex set V(G) and edge set E(G) is connected if there exists an edge between every pair of vertices in G.

    The graphs used in this work are simple graphs and have no loops and multiple edges. The number of edges incident to vertex v is the degree of the vertex v, denoted by d_v. For graph terminologies and notations refer [26,27].

    Some of the topological descriptors which are used in this work are given below.

    The earliest set of topological indices are the first and the second version of Zagreb indices. They have been found impressive in finding the total π-electron energy of molecules. Gutman and Polansky [28] introduced these indices in the year 1986 and are defined as follows

    M1(G)=vwE(G)(dv+dw) (1)
    M2(G)=vwE(G)(dv×dw) (2)

    Harmonic index is proposed and defined by Fatjlowicz [29] as

    H(G)=vwE(G)2(dv+dw) (3)

    Forgotten index was first defined by Furtula and Gutman [30] in 2015. It became popular as its performance in prediction of the index analogues to that of the original Zagreb index and is defined as

    F(G)=vwE(G)(dv)2+(dw)2 (4)

    A novel graph invariant called the SS index of a graph is proposed by Zhao et al. [31] and is stated as

    SS(G)=vwE(G)dv×dwdv+dw (5)

    Ranjini et al. [32] introduced redefined version of the second and third Zagreb indices and are defined as

    ReZG2(G)=vwE(G)dv×dwdv+dw (6)
    ReZG3(G)=vwE(G)(dv×dw)(dv+dw) (7)

    In this study, anti-malaria drugs are modelled by simple graphs. To compute the TIs of the considered drug's structure, the employed methods are vertex partitioning, edge partitioning, neighbourhood vertex partitioning and computational techniques. For depicting the results in terms of graphs and verification of computed results, the work is equipped with SPSS17 version.

    In this work, degree-based topological indices are computed for the drugs used in the treatment of malaria. The QSPR analysis of the computed indices are discussed, and it is observed that these indices are highly correlated with the physico chemical properties of the drugs that are used in the treatment of malaria.

    The nine drugs viz., Chloroquine, Amodiaquine, Mefloquine, Piperaquine, Primaquine, Lumefrantrine, Atovaquone, Pyrimethamine and Doxycycline used in the malaria treatment are considered for the analysis. The molecular structures of these drugs are shown in Figure 1. It is modelled as a graph where the atoms are referred to as vertices while the bonds by its edges which is represented in Figure 2.

    Figure 1.  Molecular structures of drugs.
    Figure 2.  Molecular graphs.

    The six physical properties of the drugs viz., boiling point, enthalpy, flash point, molar refraction, molar volume and polarizability for the 9 drugs are studied. A linear regression model used in this work is given below.

    P=A+B[TI] (8)

    where P Physical property of the drug, A,B constants, TI topological descriptor.

    Using the linear regression equation discussed, the regression model for the above considered topological indices are defined.

    The physical properties of anti-malaria drugs are considered as dependent variables and the topological indices for molecular graphs of 9 drugs are considered as independent variables. A linear regression model is fitted using SPSS software where the constants A and B in the regression equation (8) are calculated by using the training set in Tables 1 and 2.

    Table 1.  Physical properties of drugs used for the tratment of Malaria.
    Drugs BP (℃ at 760 mmHg) Enthalpy (kj/mol) Flash point (℃) Molar refraction Molar volume (cm3) Polarizability
    Chloroquine 460.6 72.1 232.23 97.4 287.9 38.6
    Amodiaquine 478 77 242.9 105.5 282.8 41.8
    Mefloquine 415.7 70.5 205.2 83 273.4 32.9
    Piperoquine 721.1 105.3 389.9 153.7 414.2 60.9
    Primaquine 451.1 71 226.6 80.5 230.3 31.9
    Lumefrantrine 642.5 99.6 342.3 151 422.3 59.9
    Atovaquine 535 85.4 277.3 99.5 271.8 39.5
    Pyrimethamine 368.4 61.5 176.6 67.1 180.2 26.6
    Doxycycline 762.6 116.5 415 109 271.1 43.2

     | Show Table
    DownLoad: CSV
    Table 2.  The values of the topological indices of the drugs.
    Drugs M1(G) M2(G) H(G) F(G) SS(G) ReZG2(G) ReZG3(G)
    Chloroquine 106 120 10.3 262 23.9599 25.2333 584
    Amodiaquine 128 149 11.7333 324 28.5664 30.5333 742
    Mefloquine 114 137 9.5857 306 24.5829 26.631 728
    Piperoquine 202 240 17.8 510 45.1804 48.9 1200
    Primaquine 92 105 9 226 20.903 22.0833 512
    Lumefrantrine 182 213 16.3666 466 40.3883 43.4333 1090
    Atovaquine 158 194 12.6047 446 33.4116 36.5619 1064
    Pyrimethamine 86 100 7.7667 222 18.9478 20.2167 506
    Doxycycline 200 264 14.4164 608 40.4521 45.55 1594

     | Show Table
    DownLoad: CSV

    Using the linear regression equation discussed, the regression model for the above considered topological indices are defined.

    Boilingpoint=124.096+2.932[M1(G)]
    Enthalpy=49.292+0.228[M1(G)]
    Flashpoint=28.813+1.773[M1(G)]
    MolarRefraction=28.194+0.546[M1(G)]
    MolarVolume=114.389+1.265[M1(G)]
    Polarizability=11.164+0.217[M1(G)]
    Boilingpoint=161.996+2.219[M2(G)]
    Enthalpy=33.198+0.302[M2(G)]
    Flashpoint=51.729+1.342[M2(G)]
    MolarRefraction=41.872+0.374[M2(G)]
    MolarVolume=150.949+0.838[M2(G)]
    Polarizability=16.589+0.148[M2(G)]
    Boilingpoint=87.905+36.905[H(G)]
    Enthalpy=25.031+4.870[H(G)]
    Flashpoint=6.939+22.319[H(G)]
    MolarRefraction=3.348+8.365[H(G)]
    MolarVolume=44.044+20.421[H(G)]
    Polarizability=1.318+3.317[H(G)]
    Boilingpoint=177.821+0.960[F(G)]
    Enthalpy=34.961+0.132[F(G)]
    Flashpoint=61.301+0.581[F(G)]
    MolarRefraction=48.115+0.152[F(G)]
    MolarVolume=167.744+0.334[F(G)]
    Polarizability=19.061+0.060[F(G)]
    Boilingpoint=111.354+13.867[SS(G)]
    Enthalpy=27.343+1.855[SS(G)]
    Flashpoint=21.110+8.387[SS(G)]
    MolarRefraction=18.858+2.811[SS(G)]
    MolarVolume=87.819+6.670[SS(G)]
    Polarizability=7.465+1.115[SS(G)]
    Boilingpoint=123.738+12.440[RezG2(G)]
    Enthalpy=28.782+1.671[RezG2(G)]
    Flashpoint=28.597+7.524[RezG2(G)]
    MolarRefraction=24.545+2.426[RezG2(G)]
    MolarVolume=103.449+5.693[RezG2(G)]
    Polarizability=9.720+0.962[RezG2(G)]
    Boilingpoint=223.151+0.352[RezG3(G)]
    Enthalpy=40.942+0.049[RezG3(G)]
    Flashpoint=88.713+0.213[RezG3(G)]
    MolarRefraction=59.754+0.051[RezG3(G)]
    MolarVolume=196.894+0.107[RezG3(G)]
    Polarizability=23.678+0.020[RezG3(G)]

    In Table 1, six physical properties of the anti-malaria drugs considered in the study are presented. Various degree-based topological indices mentioned above are computed and tabulated in Table 2. The correlation of the indices in this study against all the six physical properties are tabulated in Table 3. It is observed that the indices and their corresponding physical properties are highly correlated for most of the properties and the correlation coefficient of second Zagreb index with enthalpy being the highest value of correlation (0.978). The correlation coefficients of the discussed topological indices with physical properties and graphically presented in Figure 3. The statistical parameters viz., the sample size (N), constant (A), slope (b), correlation coefficient (r), the percentage of the dependent variable r2, and p-value for the QSPR study for all the above seven topological indices are studied. The null hypothesis is tested for p-value of each term is where the coefficient equals zero while the higher the p-value infers those changes in predictor are not related to changes in response. In this case, all the regression coefficients of a null hypothesis are zero while testing gives rise to F value. In such a case, the model does not have predictive capability. Using this test, one can compare their model with zero predictor variables to decide their coefficients improve the model.

    Table 3.  Correlation coefficients of physical properties of drugs.
    Drugs BP Enthalpy Flash point Molar refraction Molar volume Polarizability
    M1(G) 0.961 0.968 0.961 0.838 0.735 0.838
    M2(G) 0.962 0.978 0.963 0.76 0.645 0.76
    H(G) 0.908 0.894 0.908 0.963 0.891 0.964
    F(G) 0.947 0.969 0.947 0.704 0.584 0.704
    SS(G) 0.948 0.945 0.948 0.899 0.809 0.899
    ReZG2(G) 0.957 0.958 0.957 0.873 0.776 0.873
    ReZG3(G) 0.934 0.962 0.934 0.632 0.505 0.633

     | Show Table
    DownLoad: CSV
    Figure 3.  Correlation between physical properties of drugs and Topological indices.

    Tables 410 represent the statistical parameters such as number of drugs considered, constant, regression coefficient, correlation coefficient, Fisher’s statistic, significant value, and standard error denoted by N, A, b, r, r2, F and p respectively, for all the considered topological indices and physical properties. Table 11 denotes the standard error of estimate for physical properties of drugs. Tables 1217 denote the comparison of actual and computed values of all physical properties of anti-malaria drugs. Figure 3 depicts the graphical representation of physical properties and the topological indices.

    Table 4.  Statistical parameters for the linear QSPR model for M1(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 124.096 2.932 0.961 0.923 83.956 0 Significant
    EN 9 28.483 0.396 0.968 0.937 104.502 0 Significant
    FP 9 29.813 1.773 0.961 0.923 83.973 0 Significant
    MR 9 28.194 0.546 0.838 0.702 16.501 0.05 Significant
    MV 9 114.389 1.265 0.735 0.541 8.244 0.02 Significant
    PO 9 11.164 0.217 0.838 0.702 16.529 0 Significant

     | Show Table
    DownLoad: CSV
    Table 5.  Statistical parameters for the linear QSPR model for M2(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 161.996 2.219 0.962 0.926 88.088 0 Significant
    EN 9 33.198 0.302 0.978 0.956 151.468 0 Significant
    FP 9 51.729 1.342 0.963 0.926 88.162 0 Significant
    MR 9 41.872 0.374 0.76 0.578 9.575 0.01 Significant
    MV 9 150.949 0.838 0.645 0.416 4.982 0.06 Significant
    PO 9 16.589 0.148 0.76 0.578 9.588 0.01 Significant

     | Show Table
    DownLoad: CSV
    Table 6.  Statistical parameters for the linear QSPR model for H(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 87.905 36.905 0.908 0.825 33.003 0.01 Significant
    EN 9 25.031 4.87 0.894 0.798 27.731 0 Significant
    FP 9 60939 22.319 0.908 0.825 32.986 0 Significant
    MR 9 3.348 8.365 0.963 0.928 90.501 0 Significant
    MV 9 44.044 20.421 0.891 0.795 27.106 0 Significant
    PO 9 1.318 3.317 0.964 0.928 90.704 0 Significant

     | Show Table
    DownLoad: CSV
    Table 7.  Statistical parameters for the linear QSPR model for F(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 177.821 0.96 0.947 0.897 60.643 0 Significant
    EN 9 34.961 0.132 0.969 0.94 109.495 0 Significant
    FP 9 61.301 0.581 0.947 0.897 60.678 0 Significant
    MR 9 48.115 0.152 0.704 0.495 6.865 0.03 Significant
    MV 9 167.744 0.334 0.584 0.341 3.619 0.09 Significant
    PO 9 19.061 0.06 0.704 0.496 6.877 0.03 Significant

     | Show Table
    DownLoad: CSV
    Table 8.  Statistical parameters for the linear QSPR model for SS(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 111.354 13.867 0.948 0.898 61.748 0 Significant
    EN 9 27.343 1.855 0.945 0.894 58.818 0 Significant
    FP 9 21.11 8.387 0.948 0.898 61.739 0 Significant
    MR 9 18.858 2.811 0.899 0.808 29.522 0 Significant
    MV 9 87.819 6.67 0.809 0.654 13.222 0 Significant
    PO 9 7.465 1.115 0.899 0.809 29.572 0 Significant

     | Show Table
    DownLoad: CSV
    Table 9.  Statistical parameters for the linear QSPR model for ReZG2(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 123.738 12.44 0.957 0.915 75.323 0 Significant
    EN 9 28.782 1.671 0.958 0.918 77.887 0 Significant
    FP 9 28.597 7.524 0.957 0.915 75.331 0 Significant
    MR 9 24.545 2.426 0.873 0.762 22.437 0 Significant
    MV 9 103.449 5.693 0.776 0.603 10.626 0.01 Significant
    PO 9 9.72 0.962 0.873 0.762 22.47 0 Significant

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    Table 10.  Statistical parameters for the linear QSPR model for ReZG3(G).
    Phy. Pro, N A b r r2 F p Indicator
    BP 9 223.151 0.352 0.934 0.873 47.933 0 Significant
    EN 9 40.942 0.049 0.962 0.925 86.586 0 Significant
    FP 9 88.713 0.213 0.934 0.873 47.97 0 Significant
    MR 9 59.754 0.051 0.632 0.4 4.665 0.05 Significant
    MV 9 196.894 0.107 0.505 0.255 2.4 0.05 Significant
    PO 9 23.678 0.02 0.633 0.4 4.671 0.05 Significant

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    Table 11.  Standard error of estimate for physical properties of drugs.
    Drugs BP Enthalpy Flash point Molar refraction Molar volume Polarizability
    M1(G) 41.3818 5.0133 25.0251 17.3965 56.9863 6.8934
    M2(G) 40.4727 402053 24.4681 20.7148 64.279 8.21
    H(G) 62.3993 8.9827 32.985 8.5408 38.0989 3.3828
    F(G) 47.9859 4.9047 29.014 22.6488 68.2796 8.9761
    SS(G) 47.5989 6.6252 28.7891 13.955 49.478 5.5292
    ReZG2(G) 43.4975 5.7457 26.3056 15.5439 52.9971 6.1595
    ReZG3(G) 53.2487 5.4722 32.1935 24.6926 72.5723 9.7875

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    Table 12.  Comparision of actual and computed values for boiling point from regression models of TI.
    Drug Boiling point ℃ (at 760 mmHg) M1(G) M2(G) H(G) F(G)) SS(G) ReZG2(G) ReZG3(G)
    Chloroquine 460.6 ± 40.0 434.88 428.27 468.02 429.341 443.60 437.64 428.71
    Amodiaquine 478.0 ± 45.0 499.39 492.62 520.92 488.861 507.48 503.57 484.33
    Mefloquine 415.7 ± 40.0 458.34 465.99 441.66 471.581 452.24 455.02 479.40
    Piperoquine 721.1 ± 60.0 716.36 694.55 744.81 667.421 737.87 732.05 645.55
    Primaquine 451.1 ± 45.0 393.84 394.99 420.05 394.781 401.21 398.45 403.37
    Lumefrantrine 642.5 ± 55.0 657.72 634.64 691.91 625.181 671.41 664.04 606.83
    Atovaquine 535.0 ± 50.0 587.35 592.48 553.08 605.981 574.67 578.56 597.67
    Pyrimethamine 368.4 ± 52.0 376.24 383.89 374.53 390.941 374.10 375.23 401.26
    Doxycycline 762.6 ± 60.0 710.49 747.81 619.94 761.501 672.30 690.38 784.23

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    Table 13.  Comparison of actual and computed values for enthalpy from regression models of TI.
    Drug Flash point (℃) M1(G) M2(G) H(G) F(G)) SS(G) ReZG2(G) ReZG3(G)
    Chloroquine 232.23 ± 27.3 216.75 212.76 236.82 213.52 222.06 218.45 213.10
    Amodiaquine 242.9 ± 28.7 255.75 251.68 268.81 249.54 260.69 258.32 246.75
    Mefloquine 205.2 ± 27.3 230.93 235.58 220.88 239.08 227.28 228.96 243.77
    Piperoquine 389.9 ± 32.9 386.95 373.80 404.21 357.61 400.03 396.52 344.31
    Primaquine 226.6 ± 28.7 191.92 192.63 207.81 192.60 196.42 194.75 197.76
    Lumefrantrine 342.3 ± 31.5 351.49 337.57 372.22 332.04 359.84 355.38 320.88
    Atovaquine 277.3 ± 30.1 308.94 312.07 288.26 320.42 301.33 303.68 315.34
    Pyrimethamine 176.6 ± 30.7 181.29 185.92 180.28 190.28 180.02 180.70 196.49
    Doxycycline 415.0 ± 32.9 383.41 406.01 328.69 414.54 360.38 371.31 428.23

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    Table 14.  Comparison of actual and computed values for flash point from regression models of TI.
    Drug Enthalpy (kj/mol) M1(G) M2(G) H(G) F(G)) SS(G) ReZG2(G) ReZG3(G)
    Chloroquine 72.1 ± 3.0 73.46 69.438 75.19 69.545 71.78 70.94 69.55
    Amodiaquine 77.0 ± 3.0 78.476 78.19 82.17 77.72 80.33 79.80 77.3
    Mefloquine 70.5 ± 3.0 75.28 74.57 71.71 75.35 72.94 73.28 76.61
    Piperoquine 105.3 ± 3.0 95.34 105.67 111.71 102.28 111.15 110.49 99.74
    Primaquine 71.0 ± 3.0 70.268 64.90 68.86 64.79 66.11 65.68 66.03
    Lumefrantrine 99.6 ± 3.0 90.788 97.52 104.73 96.47 102.26 101.35 94.35
    Atovaquine 85.4 ± 3.0 85.316 91.78 86.41 93.83 89.31 89.87 93.07
    Pyrimethamine 61.5 ± 3.0 68.9 63.39 62.85 64.26 62.48 62.56 65.73
    Doxycycline 116.5 ± 3.0 94.892 112.92 95.23 115.21 102.37 104.89 119.04

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    Table 15.  Comparison of actual and computed values for molar refraction from regression models of TI.
    Drug Molar refraction (cm3) M1(G) M2(G) H(G) F(G)) SS(G) ReZG2(G) ReZG3(G)
    Chloroquine 97.4 ± 0.3 86.07 86.75 89.50 87.93 86.20 85.76 89.53
    Amodiaquine 105.5 ± 0.3 98.08 97.59 101.49 97.36 99.15 98.61 97.59
    Mefloquine 83.0 ± 0.3 90.43 93.11 83.53 94.62 87.96 89.15 96.88
    Piperoquine 153.7 ± 0.3 138.48 131.63 152.24 125.63 145.86 143.17 120.95
    Primaquine 80.5 ± 0.3 78.42 81.14 78.63 82.46 77.61 78.11 85.86
    Lumefrantrine 151.0 ± 0.3 127.56 121.53 140.25 118.94 132.38 129.91 115.34
    Atovaquine 99.5 ± 0.3 114.46 114.42 108.78 115.90 112.77 113.24 114.01
    Pyrimethamine 67.1 ± 0.5 75.15 79.27 68.31 81.85 72.12 73.59 85.56
    Doxycycline 109 ± 0.4 137.39 140.60 123.94 140.53 132.56 135.04 141.04

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    Table 16.  Comparison of actual and computed values for molar volume from regression models of TI.
    Drug Molar volume (cm3) M1(G) M2(G) H(G) F(G)) SS(G) ReZG2(G) ReZzG3(G)
    Chloroquine 287.9 ± 3.0 248.47 251.509 254.38 255.25 247.63 247.10 259.38
    Amodiaquine 282.8 ± 3.0 276.30 275.811 283.64 275.96 278.35 277.27 276.28
    Mefloquine 273.4 ± 3.0 258.59 265.755 239.79 269.94 251.78 255.05 274.79
    Piperoquine 414.2 ± 3.0 369.91 352.069 407.53 338.08 389.17 381.83 325.29
    Primaquine 230.3 ± 3.0 230.76 238.939 227.83 243.22 227.24 229.16 251.67
    Lumefrantrine 422.3 ± 3.0 344.61 329.443 378.26 323.38 357.20 350.71 313.52
    Atovaquine 271.8 ± 3.0 314.25 313.521 301.44 316.70 310.67 311.59 310.74
    Pyrimethamine 180.2 ± 7.0 223.17 234.749 202.64 241.89 214.20 218.54 251.03
    Doxycycline 271.1 ± 5.0 367.38 372.181 338.44 370.81 357.63 362.76 367.45

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    DownLoad: CSV
    Table 17.  Comparison of actual and computed values for polarizability from regression models of TI.
    Drug Polarizability (10-24 cm3) M1(G) M2(G) H(G) F(G)) SS(G) ReZG2(G) ReZG3(G)
    Chloroquine 38.6 ± 0.5 34.16 34.34 35.48 34.78 34.18 33.99 35.35
    Amodiaquine 41.8 ± 0.5 38.94 38.64 40.23 38.50 39.31 39.09 38.51
    Mefloquine 32.9 ± 0.5 35.90 36.86 33.11 37.42 34.87 35.33 38.23
    Piperoquine 60.9 ± 0.5 54.99 52.10 60.36 49.66 57.84 56.76 47.67
    Primaquine 31.9 ± 0.5 31.12 32.12 31.17 32.62 30.77 30.96 33.91
    Lumefrantrine 59.9 ± 0.5 50.65 48.11 55.60 47.02 52.49 51.50 45.47
    Atovaquine 39.5 ± 0.5 45.45 45.30 43.12 45.82 44.71 44.89 44.95
    Pyrimethamine 26.6 ± 0.5 29.82 31.38 27.08 32.38 28.59 29.16 33.79
    Doxycycline 43.2 ± 0.5 54.56 55.66 49.13 55.54 52.56 53.53 55.55

     | Show Table
    DownLoad: CSV

    In this study, seven degree-based topological indices are computed for nine anti-malaria drugs which is presented in Table 2. The coefficient of correlation for the said indices against six physical properties are computed and tabulated in Table 3. It is observed from Table 3 that every topological index shows good correlation with its corresponding physical properties in which, considering second Zagreb index row wise, the correlation coefficient is high with that of enthalpy for M2(G). The first Zagreb index has a high correlation with enthalpy of 0.963. The Harmonic index shows good correlation with polarizability, Forgotten index with enthalpy having r = 0.969, SS index has highest correlation with boiling point and flash point, both being 0.948, while the redefined Zagreb indices with enthalpy having 0.947, 0.958 and 0.962 respectively for the three indices.

    This work focusses on the drugs used for the treatment of malaria which is caused by mosquitoes. The analysis done in this paper may help the chemists and pharmaceutical industry researchers to design novel drugs using various excipients by the values of indices computed here. They may constitute different drugs for various ailments based on the available topological indices in the article. The correlation coefficients of various drugs help the chemists to choose the right composition based on the high correlation value to form a new drug for novel ailments. New tools to obtain a unified way of involving inequalities of various topological indices may be carried out. The extremal values for the considered indices may be computed for exponential version of the indices.

    The author declare that they have no conflict of interest.



    Conflicts of interest



    The authors declare no conflict of interest.

    Author contributions



    MA conceived the idea and drafted the manuscript. MA, AASY, SN, and BRJ searched for the literature, while MA and SN wrote the manuscript and drew the diagrams. MA, AASY, SN, and BRJ revised the manuscript critically and approved the final draft. AASY supervised the whole process.

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