The four developed QSAR models passed the minimum requirement for an acceptable model, as illustrated by their statistical parameters (Table 1). Model 1 was selected as the most relevant model as it has the best statistical significance. Its internal R2 value close to unity is an indicator that the selected model clarified an excessive proportion of the independent variable (molecular descriptor), sufficiently enough for a powerful QSAR model. A value of 0.919 suggests that 91.9% of the disparity lies in the residual, suggesting a very good model [23, 30]. Additionally, adjusted R2 has a very high value that is close to the internal R2 value for the selected model. This affirmed that the model possessed exceptional descriptive power for the response variables it contained and also illustrated the actual impact of the descriptors on the anti-cancer activities of the compounds. Additionally, to further confirm the robustness of the selected model, it was validated externally (Table 2), and the external validation correlation coefficient (R2pred) was found to be 0.791. This value exceeds the minimum recommended value of ≥ 0.6 for an acceptable model [16]. A high external prediction correlation coefficient (R2pred) indicates that the model can effectively predict the activities of new molecules. Hence, we can confidently conclude that the selected model will predict the anti-breast cancer activity of the quinazolin-4-one molecules accurately. Moreover, the selected model was utilized to predict the activity of both the training and test sets; the result is shown in Table 3. The experimental pIC50 of both the training and test sets were plotted against their predicted activities (Fig. 1), and a plot of experimental activities for the MCF-7 cell line against their residuals was presented in Fig. 2.

Fig. 1

Plot of experimental pIC50 of the training and test sets against their predicted activities

Fig. 2

Plot of experimental activities of the training and test set against their residuals

Y-scrambling test

The result of the Y-scrambling test is shown in Table 4. The coefficient of determination for the Y-scrambling test cR2p was found to be 0.7049 for this test, which suggested that the model was not obtained by chance correlation and that it is powerful enough for the prediction of anti-breast cancer activities of molecules [20].

Mean effect

The impact and contribution of each descriptor in a QSAR model were measured by computing its mean effect value (MF) [25]. The mean effect values of the selected descriptors are depicted in Fig. 3, respectively. The magnitude and signal of a descriptor are related to the biological activity of a compound [16]. A descriptor with a negative sign illustrates that the biological activity of a compound decreases by increasing its value, while a positive signal suggests that biological activity increases by increasing its value. In this study, the most important molecular descriptor is ZMIC3, a 2D class descriptor defined as a Z-modified information content index (neighborhood symmetry of 3-order). It has a mean effect value of 4.975, which suggests that an increase in its value affects the anti-cancer activities of the compounds positively. The least important descriptor is ZMIC4, another 2D class descriptor Z-modified information content index (neighborhood symmetry of 4-order); it has a mean effect value of -4.309, suggesting that the anti-cancer activities of the compounds can only be affected positively when its value is decreased. Another important descriptor that appears in the model is GATS7e, which is a 2D class autocorrelation descriptor defined as Geary autocorrelation—lag 7/ weighted by Sanderson electro negativities. Its positive mean effect value (0.624) suggested that the increasing biological activity of the compounds is related to the rise in the value of this descriptor. The value of this descriptor is increased by introducing groups with electronegative atoms to the main scaffold structure of the compound. Other descriptors that appear in the model are ATSC5p and VR2_Dzs, their negative mean effect values suggest that they are negatively related to the biological activities of the compounds. A chart showing the mean effect values of the descriptors that appear in the model is shown in Fig. 3.

Fig. 3

Mean effect values of the relevant descriptors

William’s plot of the selected model

The Williams plot for the model selected is shown in Fig. 4. The threshold leverage was found to be 0.72, and as such, only five compounds from the test set data lie beyond the defined AD (i.e., having h > h*). These compounds are labeled as influentials since the model performance is affected by them, but they may not be regarded as structural outliers since their residual values lie within the ± 3 region, which covers up to 99% of the uniformly distributed data [25].

Fig. 4

William’s plot of the selected model

Ligand-based drug design

An in-silico screening approach was used for the design of novel quinazolin-4-ones with pIC50 activities against the MCF-7 cell line based on the selected QSAR model. Compound 4 from the training set samples was selected as a template for the design due to its high inhibitory activity (pIC50 = 5.18) and low standardized residual value (-0.01), which are within the defined domain of applicability. The structure of compound 4 and the template used for the design are shown in Figs. 5 and 6, respectively. The adjustment of the compound was done so that its synthesis experimentally would be easy and feasible. Virtual screening was applied by the addition and replacement of several entities at X and Y positions, as shown in Figs. 5 and 6. Seven (7) new potent compounds with improved activities which ranged from pIC50 = 5.43 to 5.91 compared to the template and Doruxybucin (pIC50 = 5.35) were designed. The structures of the designed compounds and their predicted activities are shown in Table 5.

Fig. 5Fig. 6

Structure of the template used for the design

Result of Molecular docking studies

The designed quinazoline-4-one derivatives were docked onto the active site of the EGFR receptor to explore the nature of interactions between the ligand and the target receptor. The template and the reference drug (DOX) were also docked on the same binding site to validate the docking studies. All the designed compounds were found to have better docking scores which ranged from -137.652 to -162.572 MolDock score and -53.2419 to -127.635 Re-rank score compared to the template (MolDock score = -133.711, Re-rank score = -103.969) and Doruxybucin (MolDock score = -104.364, Re-rank score = .-29.958). The higher binding affinities of the designed compounds disclosed that they binds more effectively with the EGFR target compared to Doruxybucin. The 3D structures of the template and prepared EGFR receptor are shown in Figures. 7 and 8, respectively, while the docking scores and various kinds of amino acid interactions between the designed quinazoline-4-ones and the active site of the EGFR receptor are presented in Table 6.

Fig. 7

3D structure of the Template

Fig. 8

3D structure of the prepared EGFR receptor (pdb id = 2ITO)

Interpretation of the docking results

Designed analogue 7 had the best docking scores (MolDock score = -162.572, Rerank score = -127.635), and it is found to have interacted with the active site of the EGFR receptor through two (2) conventional hydrogen bonds, a single Pi-cationic hydrogen bond, a single electrostatic Pi-anion interaction, a hydrophobic Pi-Sigma and Pi-Pi T-shaped interaction, and several hydrophobic Pi-Alkyl interactions. GLY247 forms a conventional hydrogen bond with the hydrogen atom of the ortho-hydroxyl group attached to the benzene ring; another conventional hydrogen bond is between the amino group hydrogen atom attached to the furyl group. The β-position benzene ring is intercalated in space and forms a Pi-cationic hydrogen bond with LYS745 residue, an electrostatic Pi-anionic interaction with GLU762 residue, and hydrophobic Pi-Sigma and Pi-Pi T-shaped interactions with PHE723. LEU718, VAL726, ALA743, LEU844, LYS745, VAL726, LEU747, and ILE759 residues form pi-alkyl interactions with the ligand. 3D and 2D interactions of designed molecule 7 in the active site of the EGFR receptor are presented in Fig. 9.

Fig. 9

2D and 3D interactions of designed analogue 7 with the active site of the in the active site of the EGFR receptor

Designed compound 6 has the second-best docking score (MolDock score = -161.369, Rerank score = -117.521). It is observed to have interacted with the active site of the EGFR receptor via conventional and pi-cationic hydrogen bonds, two electrostatic pi-anion interactions, hydrophobic pi-sigma and pi-pi T-shaped interactions, two alkyl and several pi-alkyl interactions. GLY724 forms a conventional hydrogen bond with a hydrogen atom attached to the ortho-hydroxyl group of the β-Benzene ring, which is further intercalated in space to form a pi-cationic hydrogen bond with LYS745 and an electrostatic pi-anionic interaction with the GLU762 residue. Furyl ring moiety is intercalated in space and forms an electrostatic Pi-Anion interaction with ASP855. PHE723 forms hydrophobic Pi-sigma and Pi-Pi T-shaped interactions with the β-Benzene ring moiety. ALA755 and LEU747 form alkyl interactions with the chlorine atom attached to the furyl ring. ALA743, LEU844, LEU718, LEU792, VAL726, LYS745, LEU747, and ILE759 form pi-alkyl interactions with the compound. Fig. 10 represents the 2D and 3D interactions of designed compound 6 in the active site of the EGFR receptor.

Fig. 10

3D and 2D Interactions of designed compound 6 with the active site of the EGFR receptor

Designed compound 2 also has the third best docking score (MolDock score = -157.482 Rerank score = -119.221) and was found to interact with the active pocket of the receptor via a conventional hydrogen bond, two carbon-hydrogen bonds, electrostatic Pi-cation and Pi-anion interactions, hydrophobic Pi-Pi stacked interactions, and Pi-alkyl interactions. Carbonyl oxygen attached to the phenyl ring forms conventional and carbon-hydrogen bonds with GLY857; other carbon-hydrogen bonds are formed between the hydrogen atom (H17) of the furyl ring and GLU762. β-Benzene ring intercalated in space and forms an electrostatic Pi-cation interaction with ARG841 and a Pi-anion interaction with ASP837; other electrostatic Pi-anion interactions are between GLU758 and quinazoline scaffold. PHE723 forms a hydrophobic Pi-Pi stack, while ALA755, LEU747, ILE759, and PRO877 form Pi-Alkyl interactions. 3D and 2D interactions of compound 2 with the active sites of the EGFR receptor are shown in Fig. 11, respectively.

Fig. 11

2D and 3D Interactions of designed compound 2 with the active site of the EGFR receptor

Designed compound 4 also has promising docking scores (MolDock score = -156.961, Rerank score = -53.2419). It is found to interact with the active site of the EGFR receptor via a single conventional hydrogen bond, two carbon-hydrogen bonds, three hydrophobic alkyls, and several pi-alkyl interactions. The oxygen atom of the ortho-hydroxyl group attached to the β-phenyl ring forms a conventional hydrogen bond with LYS745. MET793 forms double Pi-donor hydrogen bonds with the quinazoline scaffold. CYS775, MET793, and LEU844 form alkyl interactions, while VAL726, LYS745, LEU718, ALA743, MET793, and LEU844 residues form hydrophobic pi-alkyl interactions. Fig. 12 shows the 2D and 3D interactions of designed compound 4 in the active site of the EGFR receptor.

Fig.12

2D and 3D Interactions of designed compound 4 with the active site of the EGFR receptor

Designed compound 3 (Moldock score = -153.96, Rerank score = -105.477) is found to interact with the binding pocket of the EGFR receptor through single conventional hydrogen bonds, four (4) carbon-hydrogen bonds, an electrostatic Pi-cation interaction, three (3) Pi-sulfur interactions, and several alkyl and pi-alkyl hydrophobic interactions. The THR845 residue forms a conventional hydrogen bond with the hydrogen atom of the ortho-hydroxyl group attached to the β-benzene ring. THR790 forms carbon-hydrogen bonds with a chlorine atom attached to the naphthalene group; GLY796 forms two carbon-hydrogen bonds with oxygen and hydrogen atoms of the furyl group; and ASP800 forms the remaining carbon-hydrogen bond with a hydrogen atom of the furyl group. Phenyl rings of the Naphthalene group intercalated in space to form an electrostatic Pi-Cation interaction with LYS745, two (2) Pi-Sulfur interactions with MET766, and CYS797 forms the other Pi-Sulfur interaction with the Furyl ring moiety. LYS745, MET766 and LEU788 form alkyl hydrophobic interactions, while LEU718, LYS728, LEU792, VAL726, ALA743, and LYS745 residues form several pi-alkyl hydrophobic interactions. Fig. 13 shows the 2D and 3D interactions of designed compound 3 in the active site of the EGFR receptor.

Fig. 13

2D and 3D Interactions of designed compound 3 with the active site of the EGFR receptor

Designed compound 5 (MolDock score = -150.758, Rerank score = -84.7712) interacted with the active site of the EGFR receptor via a single conventional and carbon-hydrogen bond, two (2) electrostatic Pi-anion, one hydrophobic Pi-Sigma, and several alkyl and Pi-Alkyl interactions. LYS745 forms a conventional hydrogen bond with the carbonyl oxygen of the quinazoline group. SER719 forms a carbon-hydrogen bond with a chlorine atom attached to the benzofuran group. Benzene rings adjacent to the carbonyl group and the other at the -position are intercalated in space to form electrostatic Pi-anion interactions with ASP855 and ASP800. LEU718 forms a Pi-Sigma hydrophobic interaction with the benzofuran moiety; LEU718 and VAL726 residues form alkyls, while VAL726, ALA743, LYS745, MET766, LEU788, LEU844, CYS797, and LEU718 form hydrophobic Pi-Alkyl interactions. Fig. 14 shows the 2D and 3D interactions of designed compound 5 in the active site of the EGFR receptor.

Fig. 14

2D and 3D Interactions of designed compound 5 with the active site of the EGFR receptor

Designed compound 1 (MolDock score = -137.652; Rerank score = -100.296) interacted with the EGFR receptor through electrostatic Pi-cations and Pi-anion interactions and hydrophobic alkyl and Pi-alkyl interactions. The benzene rings of the compounds intercalate in space and form electrostatic Pi-cation and Pi-anion interactions with LYS745, ARG841, and ASP837. VAL726 and LYS745 residues form alkyl interactions, while PRO877, LYS745, LEU747, ILE759, and ALA722 form hydrophobic pi-alkyl interactions. Fig. 15 shows the 2D and 3D interactions of design compound 1 in the active site of the EGFR receptor.

Fig. 15

2D and 3D Interactions of designed compound 1 with the active site of the EGFR receptor

This research revealed that Hydrogen bond is the main driving force that regulates the interactions existing between the designed inhibitors and the binding pocket of the EGFR receptor. Low Docking scores exhibited by designed compound 1 is due to the absence of Hydrogen bond interactions between the compound and the protein receptor while higher binding scores of the other designed analogues is due to the presence of several Hydrogen bond interactions between the compounds and the target receptor [13].

Furthermore, to validate the docking studies, the lead compound (5) and the reference drug (DOX) were also docked onto the same binding pocket of the EGFR receptor and it was affirmed that their docking scores is lower than that of the designed compounds. Thus, the designed compounds might serve as novel candidates of EGFR inhibition displaying better capacity than DOX as observed from the docking simulation results.

Result of Pharmacokinetics and ADMET properties

The results of the pharmacokinetic and ADMET properties studies of the designed quinazoline-4-ones are presented in Tables 7 and 8, respectively. There are high expectations that the designed analogues might possess drug-like properties since they all passed Lipinski’s rule of five (they violate only one of the rules, MW > 500). Synthetic accessibility values of compounds are scaled from 1 (simple to synthesize) to 10 (very difficult to synthesize); their synthetic accessibility values range from 3.74 to 4.06, which suggests that they can be easily synthesized [22]. The designed compounds have a high bioavailability score of 0.55, which indicates that they are well absorbed by the blood plasma. Additionally, the designed compounds displayed high human intestinal absorption, which ranges from 96.265 to 100%, these values exceed the minimal satisfactory absorbance value of 30% [27, 28]. The values of LogBB and LogPS for the designed compounds indicate that they are dispersed uniformly to the brain and are deemed to permeate the central nervous system [24, 25]. Furthermore, they are both substrates and inhibitors of the most crucial class of superenzyme 3A4, which plays a critical role in drug metabolism. A parameter that expresses the linkage between the elimination of a drug per unit time and its amount in the body is the total clearance (TC). These designed inhibitors show reasonable values of TC, which are within the acceptable range of a drug composite in the body. AMES toxicity studies revealed that they are non-toxic [29, 30].