## 3 Results and Discussion
### Molecular Docking  
Encouraged by previous reports from our group where docking techniques were applied with good results [47; 48], in the present work, docking was employed to search possible imidazole receptors. Many solid tumors are characterized by aberrant signal transduction through different receptors belonging to the ErbB family of receptor tyrosine kinases, where the EGFR and HER2 receptors belong; therefore, one therapeutic approach in onotherapy is the inhibition of one or both of these receptors [49; 50]. The ErbB receptors and their ligands are overexpressed in the majority of solid neoplasms; EGFR and ErbB-3 are found on average in 50% to 70% of lung, colon, and breast carcinomas [51]. HER2 is mainly related with breast cancer (is expressed in 30% of primary breast carcinomas [51]), but is also related with ovary, colon, lung, uterine cervix, and esophagus cancers, amongst others [52]. As co-expression of different ErbB receptors occurs commonly, 87% of EGFR positive tumors also express HER2 [51]. Due to all of the above, EGFR and HER2 receptors have been selected in the literature [53] to relate in vitro anti-cancer activity to in silico docking calculations. In this last reference, the results from the docking of imidazole derivatives against EGFR and HER2 showed a general good agreement with their cytotoxic results. They evaluated two imidazoles that are reported in the presented work, **11** and **12**, with generally closely related results; having the same docking algorithm and protocol, differences may arise due to different ligand preparation as this step can influence the final result [54]. In the present work, the proposed docking protocol was employed for an initial screening for both EGFR and HER2 as potential cancer-mediated receptors for the synthesized imidazole derivatives. The binding energies results from the docking analysis are shown in Table 3, which includes imidazole as a negative control and lapatinib, an EGFR and HER2 inhibitor [55], as the positive control. All synthesized compounds showed better results than the imidazole, suggesting the derivatization improved their affinity for these receptors. Although lapatinib showed the best result against both enzymes compared to our compounds, it was closely followed by some products. From the synthesized compounds, **11**, **12**, **5**, **9**, and **7** presented the best results interacting with both EGFR and HER2, as they were in the first five places with lower binding energies. After that, there were variations in the order in which the synthesized products interacted with the selected receptors. Comparing the results for the docking in each receptor, against the in vitro results for each of the evaluated cell lines, there was little agreement between them. This can be explained in several ways, one could be the use of a specific docking algorithm, while each one presents differences in the way results are achieved. The employment of different algorithms with the present work dataset of ligand structures and GI\({}_{50}\) values could be further explored to find the most suitable algorithm for the synthesized ligands. On other hand, it could be possible that the biological receptors where the compounds interact are different to EGFR and HER2, explaining the little correlation shown. Additionally, it has been reported that docking results could be significantly improved with post-docking energy refining through semi-empirical methods such as PM7 [56]. The compound that represented good agreement between its in vitro and in silico results was **11**, bearing a \(p\)-nitro substitution (Figure 4). It showed \(-9.11\) and \(-9.19\) kcal/mol binding energy with EGFR and HER2, respectively, having the second-best affinity with both receptors. On the other hand, it was the first or second most active compound against the six evaluated cell lines. This suggests that **11** could be one potential lead compound for further derivatization in the search for new active antiproliferative agents.