The results of various statistical parameters of the selected model are shown in Table 1, therefore, the model satisfies the least required values for the evaluation of a robust QSAR model. Additionally, the selected model was utilized to estimate the inhibitive capacity of the external validation set and it was found to have passed the external validation test with R2ext = 0.655 (Table 2). The structures, experimental as well as predicted inhibitive activities of the compounds in this research work are placed in Table 1 respectively.

A plot of experimental pIC50 against the predicted pIC50 of both the model building as well as the external validation set is shown in Fig. 1, while Fig. 2 represent a plot of experimental Pic50 of both the model building and the external validation set against their residuals. The selected model does not exhibit systematic error since the standardized residuals are randomly dispersed on either side of zero (Ibrahim et al. 2018).

Fig. 1
figure1

Plot of experimental Pic50 against the predicted pIC50 of both the model building as well as the external validation set

Fig. 2
figure2

Plot of experimental Pic50 of both the model building and the external validation set against their residuals

Pearson’s correlation matrix of the selected model indicates that descriptors are not correlated to each other, this illustrates that they are very good (Table 3).

Table 3 Pearson’s correlation matrix of the descriptors in the selected model

Y-randomization test

Result of Y-randomization test is shown in Table 4 and the test is used to confirm that a model was not obtained by coincidental correlation. The coefficient of determination for Y-randomization cR2p is the most crucial parameter for this test and for a robust QSAR model its value must exceed 0.5. Its value in this research work is 0.74, this illustrates that the model is powerful enough and was not purely due to chance and has satisfied the minimal requirement for robustness.

Table 4 Result of Y-randomization test of the selected model

Mean effect of the descriptors in the selected model

The mean effect designate the individual function and the influence of each descriptor in a model, and it is computed for each of the molecular descriptors using the below equation:

$${text{MF}}_{j} = frac{{B_{j} mathop sum nolimits_{j = 1}^{i = n} d_{ij} }}{{mathop sum nolimits_{j}^{m} B_{j} mathop sum nolimits_{i}^{n} d_{ij} }}$$

(7)

MFj denotes the mean effect for the indicated descriptor j, the coefficient of the descriptor j is denoted by βj, dij is the value of the Target descriptor for each molecule and m population of descriptors in the model (Dimić et al. 2015).

The MF value offers essential information on the effect of each molecular descriptors in the picked model; the size and signals of these descriptors combined with their mean effects reveal their stability and path in inducing the activity of a molecule. The mean effect values are presented in Table 5. BCUTc-1l, MATS8c and SpMAD_Dzs were found to possess the most pronounced influence on the model performance due to their large and positive mean effect values. Their positive sign indicated that increase in their value increases the inhibitive activities of a compound against MDA-MB231 breast cancer cell line. The other descriptor, AATSC8c is negatively correlated with the inhibitive activities of the compounds against the breast cancer cell line, higher value of this descriptor will be responsible for hindering the potency of these compound.

Table 5 Descriptors in the selected, their definition, class and Mean effect values

Variance inflation factor (VIF)

The inter-correlation amongst molecular descriptors in a model is detected using their variation inflation factors (VIF), to check whether the descriptors are highly correlated with one another or not. computed VIF values less than 1 illustrates that there is no inter-correlation between the descriptors between 1 and 5, the model can be accepted; and if it is higher than 10, the model cannot be accepted. It can be calculated using the Eq. 8 below. In this research work VIF values for all the descriptors are less than 10, this demonstrates the fitness of the selected model and the descriptors were independent of one another (Table 3).

$${text{VIF}} = frac{1}{{1 – R^{2} }}$$

(8)

Williams’ plot of the selected model

A plot of leverage values against standardized residuals of a particular set of compounds is called Williams plot. It enables the detection of a sample that is outside the defined domain of applicability of a particular model. A compound having a leverage value that exceeds the cut-off leverage is tagged as influential as it may affect the performance of the model. In this research, the Williams plot for model 1 is shown in Fig. 3, the cut-off leverage is 0.833 hence, and only the external validation set compounds lies beyond the defined domain of applicability (leverage values > 0.833). These compounds affects the performance of the model but cannot be tagged as outliers since their standardized residual values lies within ± 3 region.

Fig. 3
figure3

Williams plot of the selected model

Molecular docking studies

Molecular docking studies is performed to have the knowledge on the nature of binding interactions and the amino acid residues that are accounted for inducing the biological activity of a molecule. In this research work docking simulation study was performed between all the studied quinazoline derivatives and the binding pocket of the EGFR protein receptor (pdb id = 3ug2) and the results are placed in Table 2. The reference drug (Gefitinib) was also redocked into the same binding pocket to revalidate the docking results. Eight compounds (6, 10, 13, 16, 17, 18, 19 and 20) were observed to have better docking score as well as experimental and predicted activities than Gefitinib as such they were tagged as potential hit compounds. Various types of Amino acid interactions between the potential hit compounds and the active site of the EGFR receptor are presented in Table 6.

Table 6 various types of Amino acid interactions between the potential hit compounds and the active site of the EGFR receptor

Compound 6 is observed to have interacted with the binding site of the EGFR receptor via one (1) conventional Hydrogen bond, two (2) Carbon-Hydrogen bond, one (1) Pi-sulfur interaction and several Alkyl and Pi-Alkyl Interactions. The Carbonyl Oxygen of the quinazoline ring forms a conventional Hydrogen bond with MET793 at a distance 1.86 Å, and a Carbon-Hydrogen bond with LEU792 at a distance 2.46 Å. Other Carbon-Hydrogen bond is between the Hydrogen atom H8 and GLN791 amino acid residue at a distance 2.85 Å. The benzene ring intercalated in space and forms a π-Sulfur interaction with MET790 at a distance 3.46 Å. ALA743, LEU718, LEU792, CYS775, MET790, MET793, LEU844, VAL726 and LYS745 residues forms Alkyl interactions with the compound and ALA743, LEU844, LEU718, LYS745 and LEU788 amino acid residues forms π-Alkyl interactions. 2D and 3D binding nature of compound 6 in the binding pocket of the EGFR receptor is shown Fig. 4.

Fig. 4
figure4

2D and 3D binding nature of compound 6 in the binding pocket of the EGFR receptor

Compound 10 interacted with the binding pocket of the EGFR receptor through a single Conventional Hydrogen bond, double Carbon-Hydrogen bond, single electrostatic π-Cation Hydrogen bond, Hydrophobic π-Sigma, one π-Sulfur, and several Alkyl and π-Alkyl interactions. The quinazoline group carbonyl oxygen forms a conventional Hydrogen bond with MET793 at a bond distance 2.15 Å, and forms a Carbon-Hydrogen bond with LEU792 at a bond distance 2.79 Å, ALA743 forms the other Carbon-Hydrogen bond with the cyanide carbon at a bond distance 3.14 Å. The phenyl ring intercalated in space and forms a π-cation Hydrogen bond with LYS745 at a bond distance 3.10 Å. LYS745 also forms a single electrostatic π-Sigma with the benzene ring, CYS775 forms a π-Sulfur interaction with the benzene ring of the quinazoline scaffold at a distance 5.58 Å. CYS775, MET790, MET793 and LEU718 residues forms an Alkyl interactions while ALA743, MET790, LEU844, MET793 and LEU844 amino acid residues forms a π-Alkyl interactions with the compound. 2D and 3D binding mode of compound 10 in the binding site of the EGFR receptor is presented in Fig. 5 respectively.

Fig. 5
figure5

2D and 3D binding mode of compound 10 in the binding site of the EGFR receptor

Compound 13 was observed to have interacted with the EGFR receptor via a single conventional Hydrogen bond, three (3) Carbon-Hydrogen bonds, a single π-sigma and π-Sulfur interaction and several hydrophobic alkyl and π-Alkyl interactions. The carbonyl oxygen of the quinazoline group forms a conventional and Carbon-Hydrogen bonds with MET793 and LEU792 at a bond distances 1.61 and 2.45 Å, other Carbon-Hydrogen bond interactions are observed between Methoxy Hydrogen atom and GLU762 at a distance 2.89 Å, Hydrogen atom H8 and GLN791 at a bond distance 2.84 Å. The phenyl ring of the quinazoline scaffold intercalated in space to form a π-sigma hydrophobic interaction with LEU718, a π-Sulfur interaction is observed between the other benzene ring and MET790. LEU718, CYS775, MET790, MET793 and LEU844 residues forms Alkyl interactions while LEU718, VAL726, ALA743, LEU844, LYS745 and LEU788 forms a Pi-Alkyl hydrophobic interactions. 2D and 3D binding mode of compound 13 in the binding site of the EGFR receptor (pdb id = 3ug2) is pictured in Fig. 6.

Fig. 6
figure6

2D and 3D binding mode of compound 13 in the binding site of the EGFR receptor

The binding interactions of compound 16 is through a single conventional and Carbon-Hydrogen bond, one (1) π-Sulfur, and numerous alkyl as well as π-alkyl interactions. The carbonyl oxygen atom of the quinazoline group forms a conventional and Carbon-Hydrogen bond with MET793 and LEU792 at a bond distance 1.65 and 2.55 Å. The phenyl ring of the quinazoline scaffold forms a π-Sulfur interaction with CYS775 at a bond distance 4.35 Å. CYS775, MET793, LYS745, LEU788 and MET790 forms an alkyl interactions while VAL726, ALA743, LYS745, MET790, LEU844, ALA743, MET793 and LEU718 amino acid residues forms a Pi-Alkyl hydrophobic interactions. Figure 7 represent the 2D and 3D binding mode of compound 16 in the binding site of the EGFR receptor (pdb id = 3ug2).

Fig. 7
figure7

2D and 3D binding mode of compound 16 in the binding site of the EGFR receptor

The binding mode of compound 17 is through single conventional Hydrogen bond, triple Carbon-Hydrogen bonds, single Pi-Sulfur interactions and many Alkyl as well as Pi-Alkyl Hydrophobic interactions. The quinazoline carbonyl oxygen interacted with MET793 to form a conventional Hydrogen bond at a distance 2.35 Å, and also forms a carbon-hydrogen bond when interacted with LEU792 at a distance 2.85 Å, the Nitro group oxygen forms another Carbon-Hydrogen bond with ASN842 at a bond distance 2.73 Å, Hydrogen atom of the methyl group that connects the quinazoline scaffold forms the other Carbon-Hydrogen bond with GLN791 at distance 2.69 Å. MET790 forms a Pi-Sulfur interaction, LEU718 and LEU792 forms an Alkyl interaction while LEU844, VAL726, ALA743, LEU718, CYS775, MET790 and MET793 forms a hydrophobic Pi-Alkyl interactions. 3D and 2D Binding interactions of compound 17 in the active site of the EGFR receptor is placed in Fig. 8.

Fig. 8
figure8

3D and 2D Binding interactions of compound 17 in the active site of the EGFR receptor

The binding mode of compound 18 in the active site of the EGFR receptor is through a single conventional Hydrogen bond, an electrostatic π-Anion and π-alkyl interactions. Oxygen atom of the oxadiazole group forms a conventional Hydrogen bond with SER719 at a bond distance 2.88 Å, the quinazoline benzene ring moiety intercalated in space and forms an electrostatic π-Anion interaction with ASP855. LEU844, VAL726, ALA743, LYS745 and MET790 amino acid residues forms Pi- Alkyl hydrophobic interactions. 2D and 3D binding mode of compound 18 in the binding site of the EGFR receptor (pdb id = 3ug2) are shown in Fig. 9.

Fig. 9
figure9

2D and 3D binding mode of compound 18 in the binding site of the EGFR receptor

Compound 19 is bound to the active site of the EGFR receptor via two (2) conventional Hydrogen bonds, a single Pi-cation Hydrogen bond, a hydrophobic Pi-Sigma interaction, a Pi-sulfur and numerous Pi-Alkyl hydrophobic interactions. LYS745 and MET793 forms conventional Hydrogen bonds at bond distances 2.92 and 2.96 Å, LYS745 forms a Pi-Cation Hydrogen bond and Hydrophobic Pi-Sigma interactions at distances 3.33 and 2.57 Å, MET790 forms a Pi-sulfur interaction. VAL726, ALA743, LYS745, MET790, LEU788, LEU718 and LEU792amino acid residues formed Pi- Alkyl hydrophobic interactions. 2D and 3D binding mode of compound 21 in the active site of the EGFR receptor (pdb id = 3ug2) are placed in Fig. 10 respectively.

Fig. 10
figure10

2D and 3D binding mode of compound 19 in the active site of the EGFR receptor

Binding mode of compound 20 is through two (2) conventional Hydrogen bonds, single Carbon-Hydrogen bond, single electrostatic Pi-anion, single Pi-Sulfur and hydrophobic Pi-Alkyl Interactions. Carbonyl Oxygen atoms of the quinazoline scaffold and Isoindoline-1,3-dione group forms conventional Hydrogen bonds with MET793 and LYS745 at distances 2.16 and 1.98 Å, Hydrogen atom of the methyl group that connects the quinazoline scaffold to the phenyl ring forms a Carbon-Hydrogen bond with GLN791 at distance 1.83 Å. ASP855 forms an electrostatic Pi-Anion interaction, MET790 forms a Pi-Sulfur Interaction, while VAL726, ALA743, LEU844, VAL726, CYS775, MET790 and MET793 forms a hydrophobic Alkyl interactions. 3D and 2D binding interactions of compound 20 in the active site of the EGFR receptor is shown in Fig. 11 respectively.

Fig. 11
figure11

3D and 2D binding interactions of compound 20 in the active site of the EGFR receptor

To validate the docking approach the reference drug, Gefitinib was also docked onto the binding pocket of the EGFR receptor and was observed to interact with the protein kinase via a single conventional Hydrogen bond, eight (8) Carbon-Hydrogen bond, single Pi-Sulfur interaction, several Alkyl and Pi-Alkyl hydrophobic interaction. Hydrogen atom attached to the Amino group formed a conventional Hydrogen bond with GLN791 at a bond distance 2.81 Å, Hydrogen atom H3 of the quinazoline group formed a Carbon-Hydrogen bond withALA743 at distance 2.89 Å, Hydrogen atom of the Hydroxyl group attached to the Quinazoline frame forms another Carbon-Hydrogen bond with GLU762 at a distance 3.00 Å, Additionally, Hydrogen atom of the Morpholine group and that of a methyl group adjacent to it forms double Carbon-Hydrogen bonds with ASP855 at a bond distances 2.75 and 2.25 Å respectively, ARG841 forms double Carbon-Hydrogen bonds with two morpholine group Hydrogen atoms at distances 2.76 and 2.61 Å, the last one is with ASN842 at distance 2.95 Å. MET790 forms a Pi-Sulfur interactions, ARG841, LEU718, VAL726, LYS745, MET790, ALA743 and LEU844 forms Alkyl and Pi-Alkyl Interactions. Figure 12 represent the 3D and 2D binding mode of Gefitinb in the active site of EGFR receptor.

Fig. 12
figure12

3D and 2D binding mode of Gefitinib in the active site of EGFR receptor

Structure-based drug design

In this research work, all the quinazoline derivatives were docked on to the binding site of the EGFR (pdb id = 3ug2). Compound 19 (pred pIC50 = 5.67, Residual = − 0.04 and MolDock score = − 123.238) was identified as the best compound since it has the best Moldock score and was excellently predicted by the model selected with least residual value and was within the defined applicability domain, hence, it is adopted as template for the design. Ten (10) novel compounds were designed by addition of various groups on the Meta, Para and Ortho positions of the isoindoline-1, 3-dione phenyl ring. The inhibitive activities of the designed compounds were predicted by the selected model and most of them possess an improved activity relative to the template compound. The structure, predicted activity and MolDock score of the designed compounds are presented in Table 7.

Table 7 Structure, predicted pIC50 and MolDock scores of the designed compounds

Molecular docking studies of the designed compounds

Molecular docking investigation was also performed for the designed compounds and the binding site of the EGFR receptor (pdb id = 3ug2) using Molegro Virtual Docker (MVD) software. The designed compounds were optimized to obtain the most stable and least energy conformer using DFT calculations utilizing B3LYP 631G* basis set and the optimized molecules were saved in pdb format. All the designed compounds displayed better docking scores compared to the Template and the reference drug (Gefitinib) utilized in the design. Types of amino acid interactions of the designed compounds and the active site of the EGFR receptor are presented in Table 8. The results of three (3) compounds with best docking scores are discussed in this research.

Table 8 Types of amino acid interactions of the designed compounds and the active site of the EGFR receptor

Designed compound number three (3) has the best docking score (MolDock score = − 159.63) and it is found to interact with the EGFR receptor via three (3) Carbon-Hydrogen bonds, two (2) Alkyl and many Pi-Alkyl hydrophobic interactions. GLU762 forms two (2) Carbon-Hydrogen bonds with dimethyl amine Hydrogen atoms at a distance 2.64 and 2.98 Å, THR854 residue forms the other Carbon-Hydrogen bond with the Hydrogen atom of the methyl benzene that is directly attached to the Quinazoline scaffold at a distance 2.51 Å. LYS745 and LEU788 forms the alkyl interactions while ALA743, LYS745, LEU788, MET790, CYS775, MET793, LEU844 and LYS852 residues forms the Pi-Alkyl interactions. The 3D and 2D binding mode of designed compound 3 in the active pocket of the EGFR receptor is shown in Fig. 13.

Fig. 13
figure13

3D and 2D binding mode of designed compound 3 in the active pocket of the EGFR receptor

Designed compound 2 has the second best docking score (− 152.085) and it is found to have interacted with the EGFR receptor through three (3) conventional Hydrogen bonds, three (3) Carbon-Hydrogen bonds, single electrostatic Pi-Cation, Pi-Anion and Hydrophobic Pi-Sigma, two (2) Pi-Sulfur, single Alkyl and many Pi-Alkyl hydrophobic interactions. The Oxygen atom of the Isoindoline-1,3-dione forms a conventional Hydrogen bond with MET793 at a bond distance 1.66 Å, ASP855 forms another conventional Hydrogen bond with Hydrogen atom of the OH- group attached to the amino benzene group at a bond distance 1.87 Å, Carbonyl Oxygen of the quinazoline scaffold forms the other Conventional Hydrogen bond with CYS797 at a distance 2.26 Å. Similarly, Oxygen atom of the Isoindoline-1, 3-dione forms a Carbon-Hydrogen bond with LEU792 at a distance 2.77 Å, Methyl group Hydrogen atom attached to the Isoindoline-1,3-dione forms another Carbon-Hydrogen bond with MET793 at a distance 2.92 Å and the last one is between ASP800 and the Hydrogen atom of the methyl group that connects the phenyl ring to the main Quinazoline scaffold at a distance 2.87 Å. Additionally, the para-Hydroxy amino benzene intercalated in space to form an electrostatic Pi-Anion interaction with LYS745, ASP800 forms a Pi-Anion electrostatic interaction, GLY796 forms a Hydrophobic Pi-Sigma, MET790 and CYS797 forms a Pi-Sulfur interaction, LEU844 forms Alkyl and VAL726, ALA743 and LEU844 residues formed a hydrophobic Pi-Alkyl interactions. 3D and 2D binding pattern of designed compound 2 in the active site of the EGFR receptor (pdb id = 3ug2) is presented in Fig. 14.

Fig. 14
figure14

3D and 2D binding pattern of designed compound 2 in the active site of the EGFR receptor

Designed compound 6 also having a promising docking score (MolDock score = − 146.947) interacted with the active pocket of the EGFR receptor via two (2) conventional Hydrogen bonds, four (4) Carbon-Hydrogen bonds, two (2) Pi-Anion electrostatic interactions, and Pi-Alkyl hydrophobic interactions. LYS745 and ASP855 forms a conventional Hydrogen bonds with the Oxygen atoms of the Isoindoline-1,3-dione at a distances 1.54 Å and 2.68 Å, GLU762 forms a Carbon-Hydrogen bond with methyl group Hydrogen atoms attached directly to the Isoindoline group at distances 2.63 Å and 2.73 Å, Oxazolidine Hydrogen atoms forms another Carbon-Hydrogen bonds with ASN842 and ARG841 at distances 2.97 Å and 2.49 Å respectively. ASP855 forms double Pi-Anion electrostatic interactions, and lastly, VAL726, LYS745 and ALA743 forms a hydrophobic Pi-Alkyl interactions. 3D and 2D binding pattern of designed compound 6 in the active site of the EGFR receptor (pdb id = 3ug2) is presented in Fig. 15.

Fig. 15
figure15

3D and 2D binding pattern of designed compound 6 in the active site of the EGFR receptor

ADMET and pharmacokinetics studies of the designed compounds

The results of ADMET and Pharmacokinetics of the designed compounds are depicted in Tables 9 and 10 respectively. None of the compounds designed violate greater than two of the acceptable thresholds established by Lipinski’s rule of five filters for tiny molecules. Accordingly, they were expected to be permeable across the cell membrane, easily absorbed, transported and diffused (Ibrahim et al. 2020). In addition, the designed compounds were further evaluated for their synthetic accessibility, testing on a scale between 1 (simply synthesizable) to 10 (tediously synthesizable).The designed compound’s synthetic accessibility values ranges 3–4 (Table 10), consequently, they are easily synthesizable. Furthermore, all the designed compounds displayed excellent intestinal (human) absorbance values from 81 to 100% (Table 9). The results of ADMET studies of the designed compounds illustrates that they have the potential of crossing blood brain barrier and central nervous system since for a molecule, blood–brain barrier (BBB), and the penetrability of central nervous system (CNS) approved values are > 0.3 to <  − 1 log BB and >  − 2 to <  − 3 log PS respectively (Clark 2003).

Table 9 Predicted ADMET properties of the designed compounds
Table 10 Predicted Drug-likeness properties of the designed compounds

The class of super enzymes Cytochrome P450 (CYP450) have a vigorous role in drug metabolism since it is the key liver protein system responsible for phase-1 metabolism (oxidation). Up to today, only seventeen CYP families were recognized in humans, among which only (CYP1, CYP2, CYP3, and CYP4, respectively) are involved in the drug metabolism, with a CYP (1A2, 2C9, 2C19, 2D6 and 3A4, respectively) were known to be accountable for the biotransformation of at least 90% of the drugs that undertake phase-I metabolism (Šrejber et al. 2018), and have been predicted and presented in Table 9. Moreover, cytochrome CYP3A4 inhibition is the most important principle in the current study. The results of this research indicated that all the designed compounds are the substrates of CYP3A4 as well as inhibitors of CYP3A4, respectively (Table 9). Clearance designates the correlation between the body’s drug levels to its elimination per unit time. A minimal value of the total clearance suggests good perseverance of the drugs in the human body, and all the designed compounds displayed a promising persistence in the body for the drug. Additionally, it is advisable to explore the toxicity level of the designed compounds as it plays an important part in screening of drugs candidates. Based on the results of this research, all the designed compounds are found to be non-toxic (Table 9).

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