## 3 Results and Discussion
### MM-GBSA Free Energy Studies  
The binding energy estimation using the molecular mechanics-generalized Born surface area (MMGBSA) method allows for identifying the ligands that bind efficiently [74] with receptors. The validity of the peptides and conjugates identified by docking and MD simulations was further explored by conducting MMGBSA binding free energy estimation calculations. The major contributors, H-bonding, lipophilic interactions, electrostatic interactions and van der Waals interaction energy calculations were also examined from the trajectories obtained during the simulation. The results obtained for the ligands with each of the receptors are shown in Table 5 and Figure 15. For ER-\(\alpha\), the highest \(\Delta\)G bind was seen for the Mut4 peptide (YHWYGYTPQD) at \(\Delta\)G = \(-\)108.9 kcal/mol. This value is significantly higher than that observed for the original peptide (YHWYGYTPQN). Thus, this single point mutation had a profound effect in enhancing \(\Delta\)G bind for estrogen receptor, likely due to enhanced electrostatic interactions. In addition, CGAMut4 and CGAMut4 also showed high \(\Delta\)G bind at \(-\)80.9 kcal/mol and \(-\)78.3 kcal/mol, respectively, while the lowest \(\Delta\)G bind was observed for Mut 1 (FHWYGYTPQN), indicating that the single point mutation involving alteration of Y to F reduces \(\Delta\)G binding with the estrogen receptor. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{5}{c}{**Estrogen-Alpha Receptor**} \\ \hline
**Compound** & \begin{tabular}{c} **Avg. AG Binding** \\ **Energy (kcal/mol)** \\ \end{tabular}  & \begin{tabular}{c} **Avg. Electrostatic** \\ **Energy (kcal/mol)** \\ \end{tabular}  & \begin{tabular}{c} **Avg. H-Bond** \\ **Energy (kcal/mol)** \\ \end{tabular}  & \ \begin{tabular}{c} **Avg. Lipophilic** \\ **Energy (kcal/mol)** \\ \end{tabular}  & \begin{tabular}{c} **Avg. vdW Energy** \\ **(kcal/mol)** \\ \end{tabular}  \\ \hline Pep & \(-61.90\) & \(-37.11\) & \(-6.40\) & \(-15.94\) & \(-71.33\) \\ \hline Mut1 & \(-37.97\) & \(-24.44\) & \(-2.52\) & \(-11.21\) & \(-36.98\) \\ \hline Mut2 & \(-70.94\) & \(-37.61\) & \(-5.45\) & \(-17.87\) & \(-69.43\) \\ \hline Mut3 & \(-70.62\) & \(-39.03\) & \(-5.48\) & \(-18.91\) & \(-61.08\) \\ \hline Mut4 & \(-108.90\) & \(-54.87\) & \(-6.72\) & \(-32.92\) & \(-98.60\) \\ \hline RMAPep & \(-59.98\) & \(-38.10\) & \(-6.70\) & \(-15.77\) & \(-70.52\) \\ \hline GLAMut1 & \(-45.97\) & \(-23.47\) & \(-2.11\) & \(-8.74\) & \(-45.23\) \\ \hline RMAMut1 & \(-41.62\) & \(-30.82\) & \(-3.29\) & \(-12.04\) & \(-42.22\) \\ \hline GLAMut2 & \(-47.28\) & \(-30.05\) & \(-2.89\) & \(-11.53\) & \(-42.30\) \\ \hline CGAMut4 & \(-80.92\) & \(-61.98\) & \(-6.34\) & \(-18.01\) & \(-72.00\) \\ \hline CSAMut4 & \(-78.35\) & \(-32.18\) & \(-3.71\) & \(-22.93\) & \(-80.60\) \\ \hline \multicolumn{5}{c}{**PPAR-Alpha Receptor**} \\ \hline Pep & \(-69.14\) & \(-18.34\) & \(-4.73\) & \(-20.88\) & \(-64.80\) \\ \hline Mut1 & \(-67.02\) & \(-16.01\) & \(-3.72\) & \(-21.31\) & \(-66.31\) \\ \hline Mut2 & \(-67.78\) & \(-5.03\) & \(-3.37\) & \(-20.63\) & \(-64.29\) \\ \In all cases, van der Waals interactions and electrostatic (coulomb) interactions were found to play a significant role in binding. For PPAR-\(\alpha\), the \(\Delta\)G bind was found to be in the range of \(-63.0\) to \(-71.5\) kcal/mol for all of the peptides and the polyphenol conjugates, except for CSAMut4, which showed the lowest \(\Delta\)G bind at \(-40.2\) kcal/mol. These results indicate that, overall, each of the ligands had a fairly moderate binding energy, and stability. Furthermore, conjugating with the polyphenols did not alter the binding significantly, except with CSA, where the binding affinity was lowered. Overall, these values obtained are similar to those obtained for \(\Delta\)G bind for kaempfer and resveratrol in a recent study that explored binding interactions of polyphenols with PPARy using MMGBSA estimations [75].