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. 2025 Jan 29;15:3639. doi: 10.1038/s41598-025-88044-x

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

Micheal Arockiaraj 1,✉, J J Jeni Godlin 2, S Radha 2, Tariq Aziz 3, Mitub Al-harbi 4
PMCID: PMC11779869  PMID: 39881149

Abstract

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.

Keywords: Edge partitions, Topological indices, QSPR models, Cancer drug structures

Subject terms: Drug discovery, Chemistry, Mathematics and computing

Introduction

Cancer encompasses a broad category of diseases that can originate in nearly any organ or tissue within the body. It occurs when abnormal cells proliferate uncontrollably, extend beyond their normal boundaries to invade nearby tissues, and may spread to other parts of the body. Lung cancer develops in the tissues of the lungs, typically in the cells lining the air passages. The primary cause of lung cancer is tobacco use, including pipes, cigars, and cigarettes, although it can also affect non-smokers. Additional risk factors include prior chronic lung disorders, air pollution, hereditary cancer syndromes, and exposure to secondhand smoke. Lung cancer is the leading cause of cancer-related deaths globally, resulting in the highest mortality rates among men and women. Early detection and treatment are crucial for improving outcomes and survival rates. If not treated at an early stage, lung cancer can progress to an advanced stage, becoming more challenging to treat and potentially spreading to other parts of the body, significantly reducing the chances of survival1.

The two broad categories for lung cancer are small cell lung cancer (SCLC) and non-small cell lung cancer (NSCLC)2. Approximately 85% of all occurrences of lung cancer are NSCLC, which is mostly detected at an advanced stage, reducing the number of viable treatment options and the chance of survival3. A fatal malignancy that makes up 15% of lung cancer cases is SCLC. This type of lung cancer tends to grow and spread faster than NSCLC. In majority of the patients with SCLC, the cancer has already spread beyond the lungs at the time it is diagnosed. Frequent screenings can help detect early-stage lung cancer and improve treatment outcomes for high-risk individuals, such as chronic smokers4. Additionally, reducing exposure to environmental carcinogens, such as radon and asbestos, can further decrease the risk.

Lung cancer mortality rates are at an all-time high, making it crucial to address this issue by developing and increasing the availability of more effective treatments. This study examines various anti-cancer medications used to treat NSCLC and SCLC types of lung cancer. NSCLC is characterized by several key genetic mutations and alterations, each of which plays a role in cancer progression. These mutations and alterations include anaplastic lymphoma kinase (ALK), B-Raf proto-oncogene (BRAF), epidermal growth factor receptor (EGFR), rearranged during transfection (RET) fusion, mesenchymal epithelial transition (MET), Kirsten rat sarcoma viral oncogene homologue G12C (KRAS G12C), and c-ros oncogene 1 (ROS1) fusion. ALK is treated with drugs such as alectinib, ceritinib, lorlatinib, and brigatinib5,6. BRAF is treated with drugs such as dabrafenib and trametinib6. EGFR is treated with drugs such as dacomitinib, afatinib, gefitinib, and erlotinib6–9. RET fusion is treated with drugs such as selpercatinib and pralsetinib10. MET is treated with drugs such as tepotinib and crizotinib11. KRAS G12C is treated with drugs such as sotorasib and adagrasib12,13. ROS1 fusion is treated with the drug entrectinib14. Paclitaxel, gemcitabine, vinorelbine, docetaxel, and pemetrexed are also used in the treatment of non-small cell lung cancer, but these drugs do not target specific mutations or alterations15–19. Etoposide is used in the treatment of small cell lung cancer20. These drugs specifically target certain types of lung cancer, benefiting patients by improving outcomes and thereby lowering the mortality rate.

Topological indices are numerical values derived from the structure of a molecule or network. In medicinal chemistry, these indices assist in predicting the biological activity of compounds, facilitating drug discovery. In network analysis, topological indices quantify structural properties of graphs, such as connectivity, centrality, and clustering. They are essential for applications like social networks, transportation systems, and biological networks, enabling a better understanding of interactions and system optimization. These indices are widely used in cheminformatics, drug design, and molecular modeling to predict and optimize various chemical properties21–26. Topological indices are cost-effective in drug design, as they enable the rapid screening and evaluation of large compound libraries without the need for expensive, time-consuming laboratory experiments. By predicting the biological activity and properties of compounds through computational models, researchers can focus on the most promising candidates, thus reducing overall development costs.

QSPR is the process of developing and validating quantitative models that relate the topological structure of chemical compounds to its physicochemical properties or biological activities through mathematical, statistical or machine learning techniques27–29. By correlating structural features described by molecular descriptors like topological indices or geometric parameters with observed properties, QSPR enables the prediction of these properties for new or untested molecules. QSPR is widely used in drug discovery, material science, and environmental chemistry to optimize compounds and reduce the need for costly and time-consuming experimental measurements30–34.

Topological descriptors are crucial in QSPR models because they quantitatively capture the structural features of a molecule, allowing for accurate prediction of its properties. These descriptors, derived from the molecular graph, provide a compact and informative representation. Topological indices can be broadly categorized into several types, including distance-based indices, degree-based indices, and others. Degree-based topological descriptors, such as degree-based indices, neighborhood degree sum-based indices, and modified reverse degree-based indices, are crucial in chemistry as they provide insights into molecular connectivity and structure, which are essential for understanding chemical reactivity, stability, and predicting various properties25,35–42. Many QSPR analyses have been conducted recently utilising medications used to treat a variety of illnesses, including cancer43–49, heart disease50, infertility51, malaria52 and HIV53 by which they were able to bring out many best models for predicting the physico chemical properties of the drugs. Advances in these researches can lead to therapies that are more targeted, less toxic, and tailored to the genetic profile of individual illnesses. Developing new medicines offers hope for improving survival rates and quality of life for patients battling these complex and diverse diseases. In particular, in49, QSPR analyses were performed using topological indices via co-index polynomials for 10 lung cancer drugs. Since certain physical attributes can be related with topological structural properties and certain attributes cannot be related, we have chosen physical attributes like molecular weight, heavy atom count, complexity, boiling point, enthalpy of vaporization, molar refractivity, polarizability and molar volume which are closely related with topological structural properties like degree, neighborhood degree sum and modified reverse degree. We then conduct a comparative study by calculating the degree-based, neighborhood degree sum-based, and modified reverse degree-based topological indices of twenty-three lung cancer drugs through QSPR analysis. The indices that we have considered for the QSPR analysis play a vital role in drug discovery40,44,54.

Computation of degree types topological indices

Let G denote the hydrogen-suppressed molecular graph representation of lung cancer drug structures. Let V(G) and E(G) denote the vertex set and edge set of the graph G respectively. The number of vertices in a molecular graph G that are precisely one unit distance away from vertex Inline graphic is known as the degree of that vertex, and is denoted as Inline graphic. The neighborhood degree sum of Inline graphic refers to the sum of the degrees of all vertices that are adjacent to that vertex Inline graphic and is denoted as Inline graphic. The modified reverse degree of Inline graphic with variable parameter k (where Inline graphic) is defined as

graphic file with name M8.gif 1

where Inline graphic is the maximum degree of G. Let Inline graphic = Inline graphic, Inline graphic = Inline graphic, and Inline graphic, where E(G) is the edge set of G. Let Inline graphic, Inline graphic, and Inline graphic.

The conversion of the values of degree, neighborhood degree sum and modified reverse degree into topological indices is done using the index function Inline graphic in the following manner:

graphic file with name M19.gif 2
graphic file with name M20.gif 3
graphic file with name M21.gif 4

where we use Inline graphic for the following indices.

  • Inline graphic (Atom bond connectivity)

  • Inline graphic (Redefined Zagreb-1)

  • Inline graphic (Randić)

  • Inline graphic (Geometric)

  • Inline graphic (Harmonic)

  • Inline graphic (Symmetric division)

  • Inline graphic (Shilpa-Shanmukha)

  • Inline graphic (Geometric-Bi Zagreb)

  • Inline graphic (Tri Zagreb-Harmonic)

  • Inline graphic (Geometric-Arithmetic)

In this paper, we focus on lung cancer drugs such as dacomitinib, selpercatinib, tepotinib, trametinib, sotorasib, etoposide, alectinib, paclitaxel, dabrafenib, entrectinib, crizotinib, ceritinib, lorlatinib, afatinib, pralsetinib, brigatinib, erlotinib, adagrasib, gefitinib, vinorelbine, gemcitabine, docetaxel, and pemetrexed. The molecular structures of these drugs are displayed in Fig. 1, and their degree-based edge partitions are listed in Table 1. The degree based indices discussed above are calculated using Eq. (2) and SAGE software for twenty three lung cancer drugs which are tabulated in Table 2. We now explain the computation of degree-based indices for the ABC index through edge partitions in Table 1 by considering gemcitabine (Inline graphic) as the reference structure.

graphic file with name M34.gif

Fig. 1.

Fig. 1

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Lung cancer drugs: (a) Dacomitinib (b) Selpercatinib (c) Tepotinib (d) Trametinib (e) Sotorasib (f) Etoposide (g) Alectinib (h) Paclitaxel (i) Dabrafenib (j) Entrectinib (k) Crizotinib (l) Ceritinib (m) Lorlatinib (n) Afatinib (o) Pralsetinib (p) Brigatinib (q) Erlotinib (r) Adagrasib (s) Gefitinib (t) Vinorelbine (u) Gemcitabine (v) Docetaxel (w) Pemetrexed.

Table 1.

Degree based bond partitions for lung cancer drug structures.

Graphs Drugs Bond partitions and their frequencies
(1,2) (1,3) (1,4) (2,2) (2,3) (2,4) (3,3) (3,4) (4,4)
Inline graphic Dacomitinib 1 3 0 9 19 0 4 0 0
Inline graphic Selpercatinib 2 0 3 6 25 1 7 0 0
Inline graphic Tepotinib 1 2 0 10 25 0 3 0 0
Inline graphic Trametinib 0 9 0 4 14 0 14 0 0
Inline graphic Sotorasib 1 9 0 5 15 0 15 0 0
Inline graphic Etoposide 2 5 0 4 22 0 15 0 0
Inline graphic Alectinib 2 1 2 7 18 0 9 2 0
Inline graphic Paclitaxel 0 11 4 13 19 3 10 7 1
Inline graphic Dabrafenib 0 4 5 6 13 1 7 2 0
Inline graphic Entrectinib 0 4 0 9 28 0 5 0 0
Inline graphic Crizotinib 0 5 0 7 14 0 7 0 0
Inline graphic Ceritinib 0 6 2 8 18 0 5 2 0
Inline graphic Lorlatinib 1 6 0 2 15 0 9 0 0
Inline graphic Afatinib 0 5 0 8 20 0 4 0 0
Inline graphic Pralsetinib 1 5 0 6 24 3 3 1 0
Inline graphic Brigatinib 1 2 3 9 23 0 5 1 0
Inline graphic Erlotinib 3 0 0 10 15 0 3 0 0
Inline graphic Adagrasib 1 5 0 10 21 0 11 0 0
Inline graphic Gefitinib 1 2 0 10 17 0 4 0 0
Inline graphic Vinorelbine 5 5 1 6 25 4 8 11 0
Inline graphic Gemcitabine 1 3 2 1 7 0 3 2 0
Inline graphic Docetaxel 0 10 7 9 16 4 9 7 1
Inline graphic Pemetrexed 0 7 0 5 16 0 5 0 0
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Table 2.

Degree based indices for lung cancer drug structures.

Graphs Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic 25.62 33 16.03 83.15 15.6 79.67 38.13 8.31 1531 35.16
Inline graphic 31.31 39 18.81 105.89 18.2 100.42 47.43 9.9 2161 42.72
Inline graphic 29.09 37 18.07 95.12 17.67 89.33 43.61 9.44 1733 40.17
Inline graphic 29.41 37 17.58 99.88 16.77 96.33 44.28 9.14 2129 39.51
Inline graphic 32.2 41 19.53 108.75 18.67 105 48.41 10.1 2292 43.43
Inline graphic 33.88 42 20.28 118.38 19.63 107.33 52.43 10.7 2507 46.77
Inline graphic 28.93 36 17.42 100.58 16.9 92 44.65 9.18 2163 39.97
Inline graphic 48.99 62 29.27 166.33 27.78 164.92 73.21 15.14 3871 65.1
Inline graphic 27.7 35 16.38 91.53 15.44 95.42 40.52 8.46 2038 36.12
Inline graphic 32.76 41 19.91 108.51 19.37 102 49.26 10.47 2055 44.9
Inline graphic 23.6 30 14.44 77.95 13.93 75 35.24 7.5 1530 32.05
Inline graphic 29.64 38 18.06 96.41 17.24 97.67 43.45 9.3 1972 39.41
Inline graphic 23.63 30 14.29 79.55 13.67 77 35.47 7.41 1656 31.84
Inline graphic 26.55 34 16.39 85.65 15.83 84 39.14 8.49 1596 35.93
Inline graphic 30.77 39 18.74 101.81 18.05 98.75 45.88 9.75 2049 41.61
Inline graphic 31.54 40 19.21 103.68 18.52 101.83 46.86 10 2063 42.6
Inline graphic 21.8 29 14.25 69.98 14 66 32.56 7.29 1227 30.53
Inline graphic 34.04 43 20.83 114.51 20.23 106.67 51.62 10.9 2269 46.85
Inline graphic 24.1 31 15.14 78.52 14.8 74 36.07 7.86 1434 33.33
Inline graphic 45.67 57 27.38 164.39 26.38 148.5 71.51 14.35 3975 63
Inline graphic 13.84 18 8.37 45.68 7.84 48.33 20.16 4.24 1052 17.98
Inline graphic 45.86 58 26.99 155.07 25.28 160.33 67.67 13.89 3767 59.64
Inline graphic 23.9 31 14.74 76.32 14.07 78 34.71 7.54 1467 31.74
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To compute the neighborhood degree sum-based indices, we considered all the neighborhood degree sum classes of graphs Inline graphic and combined them into a single set Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic. The cardinalities of these classes for the graphs Inline graphic are provided in the order stated below.

  • Inline graphic = {0,1,0,0,1,2,0,0,2,6,0,1,0, 0,0,2,6,2,0,0,0,4,5,1,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,2,0,0,0,0,0,0,0,3,1,1,0, 0,0,5,7,6,0,0,0,3,7,2,0,0,0,1,3,2,0,0,0,1,0,0,0,0,0,0,0}

  • Inline graphic= {0,1,0,0,1,1,0,0,0,4,1,0,0, 0,0,8,9,5,0,0,0,3,6,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,0,2,1,1,5,0,0,2,1,0,0, 0,0,3,2,4,0,0,0,3,3,1,0,0,0,2,1,7,0,0,0,1,0,2,0,0,0,0,0}

  • Inline graphic= {0,1,0,0,2,7,0,0,0,4,1,0,0, 0,0,1,3,1,3,0,0,3,2,6,4,0,0,0,0,0,0,0,3,3,0,1,0,0,0,0,0}

  • Inline graphic= {0,2,0,0,1,1,3,0,0,2,0,2,0, 0,0,3,2,3,1,0,0,0,9,4,1,0,0,5,2,1,0,0,3,2,0,1,0,0,0,0,0}

  • Inline graphic= {0,2,0,0,0,0,1,0,2,2,1,1,2, 0,0,3,1,6,1,0,0,1,3,2,2,0,0,1,4,1,0,0,0,4,0,1,0,0,0,0,0}

  • Inline graphic= {0,0,0,2,0,5,3,1,6,6,0,1,0, 2,2,0,1,6,1,0,0,4,5,3,1,1,0,2,2,0,4,0,1,0,3,0,3,1,0,2,0}

  • Inline graphic= {0,0,0,0,1,2,1,0,0,6,3,2,0, 0,0,1,3,2,1,0,0,0,1,5,0,2,0,3,2,0,1,0,2,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,0,0,3,1,0,0,2,2,0,0,0,0,0,7,5,8,1,0,0,6,5,2,0,0,0,1,3,0,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,0,0,0,4,1,0,2,2,0,0,0,0,0,3,3,5,0,0,0,1,7,0,2,0,0,2,0,1,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,0,2,0,4,0,0,3,4,1,0,2,0,0,1,2,3,0,1,0,3,8,3,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,0,0}

  • Inline graphic= {0,1,0,0,1,4,1,0,0,0,0,0,1,0,0,3,2,1,1,0,0,3,7,3,0,0,0,0,1,2,0,0,1,1,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,0,2,1,2,0,0,1,7,0,0,0,0,0,2,5,2,0,0,0,5,6,1,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,1,0,3,1,1,0,0,0,0,0,0,0,0,6,7,8,0,1,0,6,4,0,2,0,0,2,0,1,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,1,0,0,1,1,0,0,1,2,3,1,0,0,0,8,2,9,0,1,0,2,7,0,1,0,0,3,0,1,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {2,1,0,2,0,0,0,0,2,6,1,0,0,0,0,0,2,4,0,0,0,3,4,1,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {1,0,0,0, 3,2,1,0,0,6,0,0,0,0,0,3,3,8,3,0,0,2,6,1,1,0,0,0,5,1,0,0,1,1,0,0,0,0,0,0,0}

  • Inline graphic= {0,1,0,0,0,2,0,0,3,6,0,1,0,0,0,1,5,3,0,0,0,4,4,1,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,0}

  • Inline graphic= {0,4,1,2,0,0,3,0,1,3,3,3,0,0,1,0,1,3,1,0,1,7,3,2,3,2,1,0,2,1,1,4,1,2,0,0,0,3,2,2,2}

  • Inline graphic= {0,1,0,0,1,1,0,1,0,0,0,1,2,0,0,2,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,0,1,2,0,0,0,0,0,0,0}

  • Inline graphic= {0,0,0,2,1,2,4,1,4,7,0,1,0,2,2,0,2,6,1,0,0,2,4,2,1,1,0,2,3,0,5,0,0,0,2,0,3,1,0,2,0}

  • Inline graphic= {0,0,0,2, 3,2,0,0,0,1,0,0,0,0,0,5,5,7,0,0,0,2,3,0,1,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0}

The neighborhood degree sum based indices are calculated for twenty three drugs using Eq. (3) and SAGE software which are tabulated in Table 3. As discussed for degree indices, the computation of the neighborhood degree ABC index by considering gemcitabine (Inline graphic) as the reference structure, is presented below.

graphic file with name M128.gif

Table 3.

Neighborhood degree based indices for lung cancer drug structures.

Graphs Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic 20.04 14.06 6.94 195.31 6.86 75.05 58.71 4.94 19,770 35.64
Inline graphic 23.71 15.87 7.85 259.13 7.76 91.08 74.81 5.7 30,744 43.63
Inline graphic 22.68 15.64 7.75 223.49 7.67 84.65 67.22 5.57 21,771 40.68
Inline graphic 22.06 14.72 7.2 249.32 7.06 88.16 70.36 5.23 34,193 40.3
Inline graphic 24.38 16.51 8.07 269.76 7.89 97.05 76.6 5.81 36,254 44.17
Inline graphic 25.53 16.83 8.24 298.34 8.08 102.27 83.46 6.01 40,895 47.28
Inline graphic 21.89 14.56 7.15 252.79 7.03 87.06 70.93 5.19 35,089 40.41
Inline graphic 36.55 24.59 12.03 421.14 11.78 147.68 117.19 8.68 65,831 66.68
Inline graphic 20.54 13.69 6.72 225.59 6.61 81.16 64.57 4.89 28,688 37.39
Inline graphic 25.13 16.99 8.42 259.2 8.35 94.86 76.65 6.11 27,437 45.66
Inline graphic 18.08 12.27 6.03 187.51 5.93 70.1 54.99 4.36 20,952 32.52
Inline graphic 22.55 15.5 7.63 231.95 7.52 86.83 68.07 5.48 26,527 40.43
Inline graphic 17.87 12.04 5.88 196.1 5.75 71.01 56.06 4.25 24,666 32.42
Inline graphic 20.53 14.31 7.09 201.59 7.02 76.44 60.53 5.06 20,489 36.71
Inline graphic 23.5 15.88 7.81 245.11 7.69 90.87 71.86 5.66 26,974 42.44
Inline graphic 24.09 16.38 8.09 248.44 7.99 92.04 73.23 5.84 26,888 43.52
Inline graphic 17.58 13.16 6.51 161.82 6.44 64.2 49.39 4.47 16,312 30.73
Inline graphic 26.13 17.8 8.76 278.7 8.64 101.28 80.75 6.31 33,448 47.38
Inline graphic 18.93 13.29 6.56 184.39 6.49 70.85 55.43 4.67 18,719 33.66
Inline graphic 34.24 22.85 11.12 431.21 10.83 141.84 115.58 8 79,300 63.64
Inline graphic 10.36 7.08 3.43 113.46 3.33 42.21 32.17 2.46 15,326 18.52
Inline graphic 33.72 22.43 10.94 394.97 10.69 137.94 109.21 7.94 62,778 61.65
Inline graphic 18.36 12.83 6.33 179.97 6.24 69.35 53.89 4.51 18,787 32.6
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The drugs considered in Fig. 1 have maximum degree 3 and 4, and therefore, the computation of modified reverse degree topological indices is restricted to the cases Inline graphic. The modified reverse degree based indices are calculated using Eq. (4) and SAGE software for twenty three lung cancer drugs and presented in Tables 4, 5 and 6.

Table 4.

Modified reverse degree based indices (Inline graphic) for lung cancer drug structures.

Graphs Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic 22.96 50.33 24.08 56.52 23.07 85.67 31.04 9.92 553 34.49
Inline graphic 31.33 38.08 18.36 107.9 17.77 100.42 47.9 9.8 2284 42.74
Inline graphic 27.09 57 27.24 64.27 26.07 97.33 35.36 11.29 611 39.28
Inline graphic 20.08 65 31.1 57.39 29.83 101 33.12 11.85 519 38.99
Inline graphic 22.2 70.33 33.71 64.25 32.4 109.67 36.74 12.94 604 42.92
Inline graphic 23.88 75.33 36.26 67.67 34.97 114 39.09 13.91 597 46.03
Inline graphic 28.9 36.08 17.53 99.68 17.07 91.17 44.49 9.24 2107 40.04
Inline graphic 47.81 64.25 30.66 160.75 29.37 161.17 72.04 15.5 3484 65.38
Inline graphic 27.53 35.42 16.71 89.72 15.87 93.75 40.18 8.58 1917 36.26
Inline graphic 29.43 66.33 31.61 69.53 30.17 111.33 38.86 12.83 629 43.86
Inline graphic 18.93 48.67 23.29 49.46 22.33 79.67 27.71 9.28 466 31.53
Inline graphic 28.99 35.33 17.05 101.89 16.5 93.5 44.87 9.08 2253 39.78
Inline graphic 17.63 51.33 24.48 47.05 23.4 81.67 26.9 9.45 436 31.32
Inline graphic 23.88 52.67 25.03 56.94 23.83 90.67 31.49 10.23 544 35.19
Inline graphic 30.43 36.83 17.79 107 17.22 97.08 47.14 9.51 2336 41.76
Inline graphic 31.16 37.5 18.09 109.87 17.52 100.17 48.34 9.71 2407 42.75
Inline graphic 19.8 41 19.83 51.56 19.2 70 27.66 8.41 549 30.08
Inline graphic 26.71 71 34.14 71.81 32.9 113.33 40.35 13.57 671 46.11
Inline graphic 21.43 47 22.58 53.96 21.73 79.33 29.54 9.36 530 32.74
Inline graphic 46.01 62.58 30 151.18 28.83 150.17 68.39 15.01 3205 62.79
Inline graphic 13.65 17.83 8.45 44.92 8.05 46.25 20.09 4.31 993 18.16
Inline graphic 45.03 62.42 29.33 144.3 27.7 158.25 65.24 14.49 3093 59.77
Inline graphic 20.56 48.33 22.86 49.75 21.67 83.33 27.66 9.17 485 31.15
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Table 5.

Modified reverse degree based indices (Inline graphic) for lung cancer drug structures.

Graphs Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic 25.2 31.67 15.46 87.51 15.1 78 39.15 8.13 1785 35.31
Inline graphic 29.04 30 14.53 142.67 14.11 96.58 55.18 8.45 5177 43.11
Inline graphic 28.7 34.83 17.03 101.8 16.67 88.5 45.13 9.13 2116.5 40.25
Inline graphic 28.83 41.83 20.41 87.02 19.93 88.83 41.58 9.96 1419.5 40.2
Inline graphic 31.73 45.67 22.23 96.2 21.67 98.33 45.77 10.88 1598 44.05
Inline graphic 34 46.17 22.51 106.42 21.97 104.83 49.81 11.36 1833.5 47
Inline graphic 27.28 28.5 13.75 130.81 13.33 90.67 50.97 7.95 4651 40.13
Inline graphic 46.48 54 25.67 200.16 24.48 156.92 80.43 13.9 6703 65.79
Inline graphic 25.66 30.5 14.6 111.76 14.01 85.75 44.97 7.82 3738 36.95
Inline graphic 32.16 40.33 19.76 111.24 19.37 98.67 49.96 10.42 2221 45.21
Inline graphic 23.05 30.83 15.08 76.36 14.77 70.83 34.99 7.68 1452.5 32.43
Inline graphic 27.58 30.5 14.56 127.47 13.94 92.83 50.03 8.11 4544 39.86
Inline graphic 23.36 33.17 16.11 70.96 15.67 72.83 33.65 7.93 1179.5 32.22
Inline graphic 25.84 33.5 16.37 88.06 16 79.83 39.79 8.47 1746.5 36.31
Inline graphic 28.94 30 14.28 137.73 13.66 98.58 53.37 8.26 4985 41.69
Inline graphic 29.02 30.5 14.74 142.83 14.29 96.5 55.14 8.48 5295 43.1
Inline graphic 21.84 26.17 12.69 77.94 12.33 68.5 34.28 6.83 1672.5 30.3
Inline graphic 33.65 44 21.52 112.24 21.07 103.33 51.2 11.09 2150 47.16
Inline graphic 23.75 29.17 14.27 84.2 13.97 73.17 37.37 7.6 1760.5 33.41
Inline graphic 44.87 49.5 23.38 192.94 22.21 154.33 77.3 13.05 6299 62.57
Inline graphic 13.27 16.5 7.73 52.17 7.28 46.17 21.57 4.02 1588 18.17
Inline graphic 43.44 53.5 25.36 176.11 24.12 147.33 72.36 13.29 5555 60.73
Inline graphic 23.13 32.17 15.65 74.09 15.23 72.17 34.37 7.79 1358.5 32.28
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Table 6.

Modified reverse degree based indices (Inline graphic) for lung cancer drug structures.

Graphs Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic 21.01 50 23.23 62.67 21.7 98.33 31.82 9.45 998 33.34
Inline graphic 30.29 53.58 23.47 95.91 20.78 147.08 42.29 10.2 2864 38.69
Inline graphic 24.53 58.5 26.96 68.61 24.97 116.17 35.4 10.85 1028.5 37.55
Inline graphic 27.13 43.5 20.42 92.29 19.27 102.17 41.96 9.6 1937.5 38.94
Inline graphic 29.32 49 23.04 99.44 21.77 112 45.57 10.67 2058 42.75
Inline graphic 32.91 54.5 25.16 102.18 23.33 127.17 47.36 11.46 2057.5 44.84
Inline graphic 25.93 47.58 21.41 96.48 19.49 124.5 41.37 9.41 3153 37.17
Inline graphic 40.82 75.08 34.61 164.36 32.2 189.5 70.4 15.55 5136 63.02
Inline graphic 24.02 41.42 18.86 92.22 17.35 109.58 39.35 8.59 2903 34.92
Inline graphic 29.02 62 28.47 82.3 26.27 130 41.12 11.82 1350 42.17
Inline graphic 19.63 41.5 19.46 64.5 18.33 85.5 31.12 8.31 1189.5 31.02
Inline graphic 25.6 48.33 21.77 92.8 19.82 126 40.57 9.52 2787 37
Inline graphic 23.2 36.5 16.82 71.09 15.57 87.5 32.82 7.8 1420.5 30.81
Inline graphic 22.53 49.5 22.92 66.89 21.33 101.5 33.35 9.53 1105.5 34.22
Inline graphic 29.96 53.33 23.25 90.22 20.47 147.08 40.45 10.05 2492 37.44
Inline graphic 27.87 55.33 24.68 92.88 22.27 141.83 41.73 10.48 2645 39.16
Inline graphic 16.37 46.5 21.78 49.22 20.5 83.5 26.19 8.49 694.5 28.82
Inline graphic 28.72 61 28.54 93.03 26.83 125.33 45.02 12.13 1715 45.03
Inline graphic 18.67 48.5 22.67 57.76 21.3 91.5 29.7 9.07 901.5 31.62
Inline graphic 44.69 71.08 31.7 156.7 28.54 197.67 66.73 14.53 4915 58.76
Inline graphic 13.43 18.83 8.41 48.73 7.59 56.25 20.3 4.09 1563 17.31
Inline graphic 39.84 65.92 30.31 156.61 28.12 174.08 66.47 14.1 4859 58.48
Inline graphic 21.35 40.5 18.76 64.86 17.47 88.5 31.18 8.18 1168.5 30.71
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To show the computation of modified reverse degree indices for the cases Inline graphic we have considered gemcitabine (Inline graphic) as the reference structure. Since gemcitabine (Inline graphic) drug has Inline graphic, the modified reverse degree obtained through Eq. (1) for Inline graphic is given below.

graphic file with name M168.gif

Hence, the modified reverse degree ABC index of Inline graphic is computed as follows.

graphic file with name M170.gif

When Inline graphic and Inline graphic, the modified reverse degree is given as

graphic file with name M173.gif

Then,

graphic file with name M174.gif

When Inline graphic and Inline graphic, the modified reverse degree is given as

graphic file with name M211.gif

Hence, the modified reverse degree (Inline graphic) based ABC index is calculated as follows for the drug Inline graphic.

graphic file with name M248.gif

QSPR models

QSPR models predict molecular properties or behaviors based on their chemical structure using mathematical and statistical relationships, and is widely applied to identify promising compounds and reduce experimental testing. Table 7 lists the values of the physicochemical characteristics such as molecular weight (MW), heavy atom count (HAC), complexity (CO), boiling point (BP), enthalpy of vaporization (EV), molar refractivity (MR), polarizability (PO) and molar volume (MV) of drug compounds that are gathered from ChemSpider55 and PubChem56. Tables 8, 9, 10, 11 and 12 present the correlation coefficient between indices considered and the physicochemical characteristics of twenty three lung cancer drugs.

Table 7.

Physicochemical properties of lung cancer drugs.

Graphs Drugs MW(g/mol) HAC CO BP(°C) EV( kJ/mol) MR(Inline graphic) PO(Inline graphic) MV(Inline graphic)
Inline graphic Dacomitinib 469.9 33 665 665.7 97.9 129.5 51.3 349.5
Inline graphic Selpercatinib 525.6 39 885 – – 147.5 58.5 383.9
Inline graphic Tepotinib 492.6 37 880 626.5 92.7 144.5 57.3 391.6
Inline graphic Trametinib 615.4 37 1090 – – 141.5 56.1 353.1
Inline graphic Sotorasib 560.6 41 1030 730.5 110.4 150.5 59.6 411.9
Inline graphic Etoposide 588.6 42 969 798.1 121.7 140.1 55.5 378.5
Inline graphic Alectinib 482.6 36 867 722.5 105.5 140.4 55.7 374.7
Inline graphic Paclitaxel 853.9 62 1790 957.1 146 219.3 86.9 610.6
Inline graphic Dabrafenib 519.6 35 817 653.7 96.3 127.4 50.5 359.9
Inline graphic Entrectinib 560.6 41 847 717.5 104.8 156.6 62.1 418.1
Inline graphic Crizotinib 450.3 30 558 599.2 89.2 114.4 45.4 305.2
Inline graphic Ceritinib 558.1 38 835 720.7 105.3 151.5 60.1 446
Inline graphic Lorlatinib 406.4 30 700 675 99.1 108.5 43 285
Inline graphic Afatinib 485.9 34 702 676.9 99.4 131.2 52 352
Inline graphic Pralsetinib 533.6 39 816 799.1 116.2 144.5 57.3 381
Inline graphic Brigatinib 584.1 40 835 781.8 113.8 160.1 63.5 443.6
Inline graphic Erlotinib 393.4 29 525 553.6 83.4 110.1 43.6 315.4
Inline graphic Adagrasib 604.1 43 1060 860.2 125 163.4 64.8 466.2
Inline graphic Gefitinib 446.9 31 545 586.8 87.6 118.8 47.1 337.8
Inline graphic Vinorelbine 778.9 57 1690 – – 214.2 84.9 569.7
Inline graphic Gemcitabine 263.2 18 426 482.7 86.2 52.1 20.6 142.3
Inline graphic Docetaxel 807.9 58 1660 900.5 137.1 205.2 81.4 585.7
Inline graphic Pemetrexed 427.4 31 748 – – 106.3 42.1 268.1
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Table 8.

Correlations between physicochemical properties of lung cancer drugs and degree based indices.

Indices MW HAC CO BP EV MR PO MV
Inline graphic 0.9806 0.999 0.9577 0.9314 0.9249 0.9771 0.9769 0.963
Inline graphic 0.9813 1 0.9578 0.9254 0.9193 0.9784 0.9781 0.9677
Inline graphic 0.9762 0.9985 0.9479 0.9261 0.9128 0.9829 0.9827 0.9704
Inline graphic 0.9728 0.9921 0.9634 0.9357 0.9354 0.9662 0.966 0.9468
Inline graphic 0.969 0.9944 0.9362 0.9237 0.9037 0.9846 0.9844 0.9706
Inline graphic 0.9804 0.9917 0.9703 0.9166 0.9275 0.9561 0.9559 0.947
Inline graphic 0.9733 0.9944 0.9555 0.9358 0.9281 0.974 0.9738 0.9553
Inline graphic 0.9732 0.9965 0.9432 0.929 0.9127 0.9831 0.9829 0.9681
Inline graphic 0.9507 0.9639 0.977 0.9003 0.9338 0.9163 0.916 0.8992
Inline graphic 0.9714 0.9946 0.9459 0.9329 0.9183 0.9797 0.9795 0.962
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Table 9.

Correlations between physicochemical properties and neighborhood degree sum based indices.

Indices MW HAC CO BP EV MR PO MV
Inline graphic 0.976 0.998 0.9458 0.9276 0.9128 0.9834 0.9831 0.9698
Inline graphic 0.9676 0.9932 0.9325 0.9097 0.8896 0.9846 0.9843 0.9754
Inline graphic 0.9646 0.991 0.9253 0.9064 0.8829 0.9851 0.9849 0.9762
Inline graphic 0.9642 0.9819 0.9701 0.9306 0.9418 0.9484 0.9481 0.9269
Inline graphic 0.9613 0.9883 0.9178 0.9027 0.876 0.9851 0.9849 0.9764
Inline graphic 0.978 0.9962 0.9673 0.9324 0.9339 0.969 0.9688 0.9537
Inline graphic 0.9729 0.9924 0.9628 0.9359 0.935 0.9669 0.9666 0.9475
Inline graphic 0.9696 0.994 0.9299 0.916 0.8935 0.9864 0.9861 0.9754
Inline graphic 0.8971 0.9107 0.9564 0.8567 0.9117 0.8564 0.8559 0.8323
Inline graphic 0.9752 0.9969 0.9498 0.9327 0.9205 0.9799 0.9797 0.9634
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Table 10.

Correlations between physicochemical properties and modified reverse degree indices (Inline graphic).

Indices MW HAC CO BP EV MR PO MV
Inline graphic 0.8915 0.9294 0.8798 0.8336 0.8299 0.9237 0.9238 0.9215
Inline graphic 0.5928 0.5867 0.5619 0.5637 0.5351 0.5589 0.5582 0.524
Inline graphic 0.5894 0.5838 0.5566 0.5622 0.5319 0.5581 0.5574 0.523
Inline graphic 0.8291 0.8556 0.8241 0.7973 0.81 0.8462 0.8463 0.848
Inline graphic 0.5878 0.5825 0.5532 0.5625 0.5308 0.5585 0.5579 0.5233
Inline graphic 0.9784 0.9924 0.9637 0.9114 0.9113 0.96 0.9597 0.9438
Inline graphic 0.9118 0.9383 0.899 0.8835 0.8867 0.9266 0.9266 0.9218
Inline graphic 0.8795 0.8906 0.847 0.8224 0.7977 0.8684 0.8679 0.8403
Inline graphic 0.6809 0.7028 0.6915 0.6339 0.6644 0.6908 0.6911 0.7008
Inline graphic 0.9733 0.9957 0.949 0.9364 0.9249 0.9798 0.9796 0.9639
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Table 11.

Correlations between physicochemical properties and modified reverse degree indices (Inline graphic).

Indices MW HAC CO BP EV MR PO MV
Inline graphic 0.9732 0.9936 0.9554 0.9226 0.9163 0.969 0.9687 0.952
Inline graphic 0.8895 0.8854 0.8838 0.8274 0.8337 0.8348 0.8343 0.8128
Inline graphic 0.8727 0.8673 0.8616 0.8145 0.8155 0.8197 0.8191 0.7962
Inline graphic 0.879 0.9109 0.8546 0.8689 0.8583 0.9132 0.9134 0.9071
Inline graphic 0.8557 0.8493 0.8398 0.8015 0.7978 0.8048 0.8042 0.7799
Inline graphic 0.9703 0.9932 0.9657 0.9269 0.933 0.9651 0.9648 0.9515
Inline graphic 0.9414 0.9699 0.9153 0.9201 0.9075 0.9645 0.9645 0.9534
Inline graphic 0.9391 0.9471 0.9189 0.8776 0.8695 0.9139 0.9134 0.8917
Inline graphic 0.6905 0.7206 0.6742 0.6802 0.6802 0.7315 0.7319 0.7351
Inline graphic 0.9757 0.9963 0.949 0.9333 0.92 0.9797 0.9795 0.9628
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Table 12.

Correlations between physicochemical properties and modified reverse degree indices (Inline graphic).

Indices MW HAC CO BP EV MR PO MV
Inline graphic 0.9375 0.9595 0.9396 0.9498 0.9502 0.9275 0.9272 0.8917
Inline graphic 0.8633 0.9072 0.7836 0.8089 0.7456 0.9371 0.9371 0.9277
Inline graphic 0.8588 0.8985 0.7778 0.7886 0.7276 0.926 0.9258 0.92
Inline graphic 0.9442 0.9504 0.9669 0.8949 0.9285 0.903 0.9028 0.8894
Inline graphic 0.8503 0.8856 0.7687 0.7685 0.7102 0.9106 0.9104 0.9082
Inline graphic 0.9072 0.9429 0.8771 0.9252 0.902 0.9439 0.9439 0.9231
Inline graphic 0.9723 0.9823 0.9776 0.924 0.9414 0.9431 0.9428 0.9278
Inline graphic 0.9422 0.9705 0.8907 0.8813 0.846 0.971 0.9708 0.9579
Inline graphic 0.8178 0.8259 0.8643 0.7502 0.8051 0.7792 0.7791 0.7762
Inline graphic 0.9791 0.995 0.9595 0.9216 0.9164 0.9705 0.9702 0.9561
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The simple linear regression is represented by Inline graphic, where P is the property, Inline graphic is the topological index, Inline graphic is the intercept and Inline graphic is the slope. The best predictive linear regression models for physicochemical properties of lung cancer drugs, along with the corresponding r, Inline graphic, F and SE values are calculated by employing SPSS software and tabulated in the Table 13. Each index discussed in our analysis exhibits a positive correlation, with the highest value being 1. Molecular weight and heavy atom count are best predicted using the degree-based redefined Zagreb-1 index. Complexity is best predicted using the modified reverse (Inline graphic) Shilpa-Shanmukha index. Boiling point and enthalpy of vaporization are best predicted using the modified reverse (Inline graphic) atom bond connectivity index. Molar refractivity is best predicted using the neighborhood geometric-Bi Zagreb index, while molar volume is best predicted using the neighborhood harmonic index. In the case of quadratic and logarithmic models, they are represented as Inline graphic and Inline graphic respectively where Inline graphic and Inline graphic are constants.

Table 13.

Best predictive linear regression models for physicochemical properties of drugs.

Properties Regression Equations r Inline graphic F SE
MW MW = 13.38(Inline graphic) + 27.09 0.9813 0.9611 545.015948 26.651656
HAC HAC=(Inline graphic) 1 1 infinity 0
CO CO = 28.1(Inline graphic) - 240.89 0.9776 0.9536 453.238975 77.758046
BP BP = 16.11(Inline graphic) + 292.54 0.9498 0.8964 156.720762 38.649445
EV EV = 2.31(Inline graphic) + 46.3 0.9502 0.8972 158.131996 5.507291
MR MR = 26.94(Inline graphic) - 6.44 0.9864 0.9716 753.664308 6.188667
PO PO = 10.69(Inline graphic) - 2.58 0.9862 0.9712 741.833559 2.474069
MV MV = 56.89(Inline graphic) - 41.24 0.9764 0.9511 428.981034 23.13436
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Comparative analysis

In this section, we discuss the effectiveness of our models in predicting the properties of lung cancer drugs by comparing them with the models proposed in49. In the study49, a QSPR analysis was conducted using ten lung cancer drug molecules, and predictive equations were developed for the physicochemical properties such as EV, MR, PO, and MV using linear, logarithmic, and quadratic regression models, with correlation values provided for their best models based on coindices.

The best predictive linear regression models mentioned in49 are given below:

graphic file with name M382.gif

where Inline graphic represents the inverse Randić coindex, Inline graphic denotes the second Zagreb coindex, and Inline graphic refers to the geometric coindex. When comparing, it is evident that our regression models exhibit higher correlation values than those listed above, as shown below:

graphic file with name M386.gif

Similarly, in49, the proposed quadratic regression models based on the harmonic coindex (Inline graphic) and the second Zagreb coindex (Inline graphic) were

graphic file with name M389.gif

While the quadratic models derived from our considered topological indices provide more accurate predictions than those mentioned above, which are presented below along with their correlation values.

graphic file with name M390.gif

In49, the most suitable logarithmic regression models were identified as

graphic file with name M391.gif

where Inline graphic denotes the symmetric division coindex, and Inline graphic represents the second Zagreb coindex. The logarithmic regression models produced in our study show better correlation values than those listed above. Our logarithmic models, along with their correlation values, are presented as follows.

graphic file with name M394.gif

In addition, we have calculated the quadratic models of four other properties such as molecular weight, heavy atom count, complexity, boiling point, and their corresponding correlation values are given below.

graphic file with name M395.gif

In the case of logarithmic models, we have

graphic file with name M396.gif

While comparing the linear, quadratic, and logarithmic models, quadratic models appear to predict the physical properties in a better way than the rest, having models with the best correlation values. In quadratic models, molecular weight is best predicted using degree based symmetric division index; heavy atom count is best predicted using degree based redefined Zagreb-1 index, complexity is best predicted using modified reverse (Inline graphic) Shilpa-Shanmukha index, boiling point and enthalpy of vaporization are best predicted using modified reverse (Inline graphic) atom bond connectivity index, molar refractivity and polarizability are best predicted using neighbourhood degree based geometric-bi Zagreb index, molar volume is best predicted using neighbourhood degree based Randić index.

Scatter plots comparing linear, quadratic, and logarithmic models of the considered physicochemical properties are shown in Figs. 2, 3, 4, 5, 6, 7, 8 and 9. The comparison of actual values of physicochemical properties and their predicted values using the best predicted quadratic models are tabulated in Tables 14 and 15, with their graphical comparisons shown in Fig. 10.

Fig. 2.

Fig. 2

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Scatter plots comparing the regression models of molecular weight. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 3.

Fig. 3

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Scatter plots comparing the regression models of heavy atom count. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 4.

Fig. 4

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Scatter plots comparing the regression models of complexity. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 5.

Fig. 5

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Scatter plots comparing the regression models of boiling point. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 6.

Fig. 6

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Scatter plots comparing the regression models of enthalpy of vaporization. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 7.

Fig. 7

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Scatter plots comparing the regression models of molar refractivity. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 8.

Fig. 8

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Scatter plots comparing the regression models of polarizability. (a) Linear model (b) quadratic model (c) logarithmic model.

Fig. 9.

Fig. 9

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Scatter plots comparing the regression models of molar volume. (a) Linear model (b) quadratic model (c) logarithmic model.

Table 14.

Comparison of actual values and predicted values by quadratic models.

Properties Molecular weight Heavy atom count Complexity Boiling point
Drugs Actual Predicted Actual Predicted Actual Predicted Actual Predicted
Dacomitinib 469.9 453 33 33 665 661.2 665.7 632.1
Selpercatinib 525.6 559.1 39 39 885 918.6 – 786
Tepotinib 492.6 503.4 37 37 880 745 626.5 693.2
Trametinib 615.4 538.8 37 37 1090 909.9 – 736.1
Sotorasib 560.6 581.5 41 41 1030 1007.3 730.5 771
Etoposide 588.6 592.8 42 42 969 1057.3 798.1 825.5
Alectinib 482.6 517 36 36 867 894.6 722.5 716.4
Paclitaxel 853.9 839.1 62 62 1790 1800.2 957.1 933.6
Dabrafenib 519.6 534.3 35 35 817 842.5 653.7 684.4
Entrectinib 560.6 566.9 41 41 847 887.9 717.5 766.4
Crizotinib 450.3 428 30 30 558 645.4 599.2 607.3
Ceritinib 558.1 545.5 38 38 835 873.6 720.7 711
Lorlatinib 406.4 438.7 30 30 700 684 675 670.4
Afatinib 485.9 475.8 34 34 702 696.5 676.9 658.9
Pralsetinib 533.6 550.9 39 39 816 870.6 799.1 780.9
Brigatinib 584.1 566.1 40 40 835 903.9 781.8 748
Erlotinib 393.4 378.8 29 29 525 538.5 553.6 546.7
Adagrasib 604.1 589.6 43 43 1060 992.2 860.2 761.6
Gefitinib 446.9 422.6 31 31 545 613.7 586.8 589.7
Vinorelbine 778.9 775 57 57 1690 1669.5 – 980.7
Gemcitabine 263.2 277.8 18 18 426 422.2 482.7 489.8
Docetaxel 807.9 821.7 58 58 1660 1660.3 900.5 921.1
Pemetrexed 427.4 444.1 31 31 748 646.7 – 638.1
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Table 15.

Comparison of actual values and predicted values by quadratic models.

Properties Enthalpy of vaporization Molar refractivity Polarizability Molar Volume
Drugs Actual Predicted Actual Predicted Actual Predicted Actual Predicted
Dacomitinib 97.9 94.5 129.5 127.5 51.3 50.5 349.5 349
Selpercatinib – 115 147.5 148.5 58.5 58.9 383.9 400.3
Tepotinib 92.7 101.7 144.5 145 57.3 57.5 391.6 394.7
Trametinib – 107.5 141.5 135.6 56.1 53.8 353.1 364.1
Sotorasib 110.4 112.6 150.5 151.6 59.6 60.1 411.9 412.7
Etoposide 121.7 121.6 140.1 156.9 55.5 62.2 378.5 422.4
Alectinib 105.5 104.7 140.4 134.4 55.7 53.3 374.7 361.1
Paclitaxel 146 144.2 219.3 222.6 86.9 88.2 610.6 620.2
Dabrafenib 96.3 100.6 127.4 126.2 50.5 50 359.9 336.6
Entrectinib 104.8 111.9 156.6 159.6 62.1 63.3 418.1 432.4
Crizotinib 89.2 91.9 114.4 110.8 45.4 43.9 305.2 296.3
Ceritinib 105.3 104 151.5 142.5 60.1 56.5 446 388.3
Lorlatinib 99.1 98.9 108.5 107.6 43 42.6 285 287.6
Afatinib 99.4 97.6 131.2 131 52 51.9 352 357.4
Pralsetinib 116.2 114.2 144.5 147.4 57.3 58.5 381 398.3
Brigatinib 113.8 109.2 160.1 152.4 63.5 60.4 443.6 413.7
Erlotinib 83.4 86.2 110.1 113.8 43.6 45.1 315.4 324
Adagrasib 125 111.2 163.4 164.8 64.8 65.3 466.2 451
Gefitinib 87.6 90.2 118.8 119.8 47.1 47.5 337.8 327.4
Vinorelbine – 156.5 214.2 206.9 84.9 82 569.7 574.9
Gemcitabine 86.2 81.6 52.1 52.1 20.6 20.6 142.3 138
Docetaxel 137.1 141.2 205.2 205.5 81.4 81.5 585.7 565.9
Pemetrexed – 95.2 106.3 115.2 42.1 45.7 268.1 313.6
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Fig. 10.

Fig. 10

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Bar plots comparing actual and predicted values. (a) Comparison of actual and predicted values for MW (b) comparison of actual and predicted values for HAC (c) comparison of actual and predicted values for CO (d) comparison of actual and predicted values for BP (e) comparison of actual and predicted values for EV (f) comparison of actual and predicted values for MR (g) comparison of actual and predicted values for PO (h) comparison of actual and predicted values for MV

Conclusion

This study employed degree-based, neighborhood degree sum, and modified reverse degree edge partitioning approaches to evaluate the associated topological indices of drugs used to treat lung cancer. A QSPR analysis was conducted using these indices, and linear, quadratic, logarithmic models were developed, and their predictive performance was compared. Upon comparison, physicochemical properties are best predicted using quadratic models. In quadratic models, properties such as molecular weight and heavy atom count were best predicted using degree-based indices. Complexity, boiling point, and enthalpy of vaporization were best predicted using modified reverse degree-based indices, while molar refractivity, polarizability and molar volume were best predicted using neighborhood degree sum-based indices. These findings contribute to lung cancer drug development by enabling the prediction of physicochemical properties, thereby supporting more efficient identification and optimization of potential therapeutics. In contrast to models developed using degree-based indices, predictive models can be created in the future using distance-based indices.

Acknowledgements

The authors greatly acknowledge and express their gratitude to research supporting project number (RSP2025R462), King Saud University, Riyadh, Saudi Arabia.

Author contributions

Methodology, M.A., J.J.J.G., and S.R.; validation, J.J.J.G., S.R., T.A., and M.A.; formal analysis, M.A., J.J.J.G., and T.A.; investigation, J.J.J.G., S.R., T.A., and M.A; resources, M.A., S.R., T.A., and M.A.; visualization, J.J.J.G., and S.R.; supervision, M.A. All authors have read and agreed to the current version of the manuscript.

Data availability

All data generated or analyzed during this study are included in this article.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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