## 3 Results and Discussion
### Binding Free Energy Calculation  
The MM-PBSA method has been successfully applied to various protein-ligand complexes [74; 75; 76]. This method is sensitive to simulation protocols, such as the sampling strategy of generating snapshots [65]. Hence, in order to obtain a reliable calculation of the binding free energy, a convergence analysis was performed. A correct G\({}_{\text{bind}}\) calculation implies the evaluation over many MD snapshots. For the sampling, the last 50 ns were considered. Figure 9 shows the resulting G\({}_{\text{bind}}\) for the case of Luteolin. As can be seen, the variation in energy values was very small (0.012 kcal/mol) from 450 to 500 MD snapshots. Therefore, unlike the rest of the properties, 500 MD snapshots--saved every 100 ps--were considered statistically representative for the calculation of G\({}_{\text{bind}}\). Once the calculation parameters were defined, the binding free energy was calculated for the three studied systems, giving values of \(-18.8903\), \(-5.4931\), and \(-18.1401\) kcal/mol,  
Figure 8: Number of water molecules within a distance of 6 Amstrongs from the Asp443 residue, this graph shows how the number of waters decreases in ACA compared to the control protein, unlike MAY which increases the number of waters. Figure 9: Convergence analysis for the G\({}_{\text{bind}}\) calculation. G\({}_{\text{bind}}\) value versus MD snapshots evaluated for the case of luteolin. for ACA, MAY, and LUT, respectively. These values confirm the order of stability of the complexes deduced from the MD analysis presented above: ACA > LUT > MAY. As mentioned in Section 2.4, the total binding free energy (G\({}_{bind}\)) is the sum of the following terms:  
1. Solvent contribution is the sum of electrostatic solvation energy (polar contribution or PB) and non-electrostatic solvation component (non-polar contribution SA);
2. Gas-phase contribution is the sum of electrostatic (elec) and Van der Waals interaction energies (vdW). The gas-phase binding energies are strongly favorable, while the solvation contribution is considered repulsive, as it includes the energetic cost of desolvating the ligand [77]. Table 5 shows the different contributions to the total binding free energy. The G\({}_{\text{gas}}\) is given by the sum of elec and vdW contributions, and G\({}_{\text{solv}}\) is composed of the sum of PB and SA energies. As can be seen, the G\({}_{\text{solv}}\) and G\({}_{\text{gas}}\) contribution for the MAY molecule presented almost the same absolute value (67.9480 kcal/mol for G\({}_{\text{solv}}\) and \(-\)73.4411 kcal/mol G\({}_{\text{gas}}\)), giving a small total G\({}_{\text{bind}}\). This gives a hint that MAY is more attracted to the outside of the active site than LUT and ACA. The reader may now notice that this explains the behavior of the MAY RMSD (Red curve, Figure 6B) and the difference between the order of stability predicted by MD (ACA > LUT > MAY) and molecular docking (MAY > ACA > LUT), respectively. The change in this order is due to the fact that in molecular docking the solvation contributions are not considered, as is correctly done in MD. The latter, far from indicating that molecular docking calculations are useless, confirms the route proposed here, where molecular docking binding energies give an insight into the stability of the complexes. The evolution from a metastable point found with molecular docking to a lower energy state reached in MD is common in macromolecular studies [26]. Furthermore, molecular docking provides initial configurations for MD simulations. Otherwise, performing MD from an arbitrary initial configuration of the systems under study would be computationally much more demanding. Regarding the inhibition of the \(\alpha\)-glucosidases, the phenolic extracts obtained from maize silks presented similar values of IC\({}_{50}\), however, these values were lower than those obtained for the acarbose [14].