# Identification of Some Glutamic Acid Derivatives with Biological Potential by Computational Methods
## 2 Results and Discussion
### Characterisation of the \"Lead\" Compounds
The inhibition constant (Ki) was calculated using the following formula: Ki = e\({}^{*}\)((\(\Delta\)G \(\times\) 1000)/ (R \(\times\) T)), where e = 2.7182, R = 1.98719 cal/(mol \(\times\) K) (Regnault constant) and T = 298.15 K = 25 \({}^{\circ}\)C [159]. It can be seen that cluster 1 shows the lowest energy according to \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Score** & **Interface Area** & **Coordinates** \\ \hline
1 & 2900 & 318.4 & \(-\)1.34; \(-\)0.09; 1.38; \(-\)22.80; \(-\)22.56; \(-\)39.82 \\
2 & 2858 & 318.3 & 1.02; \(-\)0.08; \(-\)48.08; 21.92; \(-\)56.70 \\
3 & 2834 & 310.4 & \(-\)1.95; 0.16; \(-\)1.70; \(-\)74.21; \(-\)8.23; \(-\)46.64 \\
4 & 2830 & 306 & 1.32; \(-\)2.83; \(-\)44.00; \(-\)28.47; \(-\)52.58 \\
5 & 2814 & 318.5 & \(-\)1.33; \(-\)0.27; 1.59; \(-\)27.20; \(-\)37.47; \(-\)60.51 \\
6 & 2792 & 316.6 & \(-\)1.14; \(-\)0.17; \(-\)1.48; \(-\)66.81; 35.58; \(-\)67.43 \\
7 & 2792 & 308.1 & \(-\)1.78; \(-\)0.03; 2.84; \(-\)41.83; \(-\)45.53 \\
8 & 2790 & 301.5 & \(-\)1.64; 0.44; 1.33; \(-\)71.19; \(-\)15.76; \(-\)81.43 \\
9 & 2786 & 310.8 & 2.09; \(-\)0.02; \(-\)1.89; \(-\)16.57; 19.50; \(-\)51.15 \\
10 & 2786 & 296.7 & \(-\)2.08; 0.27; \(-\)1.76; \(-\)57.26; \(-\)20.74; \(-\)68.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Molecular docking results for the 4 Db6 compound using PatchDock [136; 153; 154]. Figure 4: D subunit (in red) and J subunit (blue) of the bacterial GS enzyme and the 4 Db6 compound docked at the most probable site estimated by PatchDock [136; 153; 154]; viewed with UCSF Chimera 1.15 [144; 145]. the \(\Delta\)G value, but Ki and the maximum FullFitness value belong to complex 33. Visualisation and processing of the results obtained in the molecular docking study (Figure 5) were performed using UCSF Chimera 1.15 [144; 145]. The grid sizes used in SwissDock for cluster 1 are (x, y, z) = (15.5, 15.5, 20.5) with centre coordinates (x, y, z) = (-98, 13.711, -87.161). To perform molecular docking using AutoDock Vina (a new version of the Webina online platform), the exhaustiveness of the search was set to 8 and the maximum energy difference to 3 kcal/mol. The space in which the test took place is represented by the volume of a cube (having the following dimensions: width = 20.4346, length = 27.864, height = 18.3759), and whose centre is defined by the coordinates x = \(-4.86256\), y = \(-15.0503\), z = \(-67.7222\)) [160]. Preparation for docking involves the insertion of hydrogen atoms on the chemical structure of both the ligand and the receptor molecule and the removal of the solvent. The protonation state corresponding to histidine was used, and Gasteiger partial charges were assigned (Figure 6). The molecular docking results performed with AutoDock Vina are shown in Table 15, and the corresponding figures are presented in Figure S2 (Supplementary Materials). We chose to work further with model no.1 due to its low free energy (\(-6.3\) kcal/mol) and root-mean-square deviation (RMSD) values that were below 2 A. The 2 A limit is often used as a criterion for predicting the correct binding site. The RMSD for two structures, a and b, of an identical molecule can be defined as follows:  
Figure 5: Ligand (PPQ and 4 Db6 compound conformers)–receptor (active subunit of GS enzyme) complexes: GS–PPQ; GS–cluster1; GS–cluster6; GS–cluster33. Visualised with UCSF Chimera 1.15 [144; 145]. Figure 6: Hydrogen bonds made between the ligand molecule (4 Db6 compound) and the threonine residue of the receptor molecule. Visualisation of the ligand inserted into the “binding pocket” [144; 150; 151; 152; 155; 157].