## 3 Results and Discussion
### Molecular Dynamics Studies
#### 3.6.1 Analysis of RMSDs and RMSFs for Ligand-Receptor Complexes
The ligand binding domain of ER-\(\alpha\) consists of a triple-layered anti-parallel \(\alpha\)-helical sandwich and a small anti-parallel \(\beta\)-sheet at one end [67; 68]. Through the course of the simulation, the ligand (depicted in red) changes conformation and by the end of the simulation it is attached to the central layer comprised of H3/H6/H9/\(\alpha\)-helices in the region. A slight conformation change is also observed in the receptor where the H4 helix at the bottom changes to a bent shape in order to best fit the ligand. For Mut1, the ligand is seen within the estrogen receptor binding throughout the first 50 ns of the simulation, though it begins to migrate within the receptor and reaches all the way to the top of H6 helix. By 100 ns, the Mut1 peptide has migrated out of the receptor completely, explaining the large RMSD at the end of the simulation. Mut 2 undergoes very minor conformational changes and remains associated with the receptor primarily through Helix 6 and Helix 3. Thus, Mut2 appears stable within the binding site. Mut 3 undergoes conformational changes during the simulation, where it appears to move slightly more toward the Helix 6 region at the 75 ns time point and remains stable at that position for the rest of the simulation. Several residues remain associated with the receptor throughout; it appears that both N-terminal and C-terminal regions of the Mut3 interact with the receptor at the end of the simulation. Mut4 appears to migrate further inward throughout the 100 ns, indicating that further interactions are forming between the peptide and the receptor during the simulation. At 100 ns, Mut4 is nestled tightly within the receptor. The trajectories of the polyphenol-peptide conjugates with ER-\(\alpha\) are shown in Supplementary Information Figure S3. RMAPep moves slightly in relation to ER-\(\alpha\) throughout the simulation and shows conformational changes, appearing to spread more widely to associate with ER-\(\alpha\) by the end of the simulation, at which point it is attached to H3, H6 and H9 helices. GLAMut1, on the other hand, appears to move away from the binding site and moves toward the H9 and H10 helices but remains attached to the receptor throughout the simulation. RMAMut1 also changes position slightly in the first 25 ns, after which minimal change occurs, indicating stability of RMAMut1 in complex with ER. GLAMut2 appears to jump around within the binding pocket at different positions but remains at the same position in the region underneath the binding pocket after 75 ns. CGAMut4 remains in the same position throughout the simulation, appearing elongated and indicating favorable interactions with ER\(\alpha\). CSAMut4 likewise remains in the same position, but starts in a folded conformation, and after 25 ns appears more elongated. Minimal conformation change occurs between 75 ns and 100 ns, implying stability in complex with ER-\(\alpha\). RMSF graphs for PPAR-\(\alpha\) with the peptides (Figure 8e) showed the highest fluctuations with Arg226, Ala250 and Asp418 and Asp466, with Mut3 resulting in the highest fluctuation with Arg226. On the other hand, the peptide-polyphenol conjugates (Figure 8f) showed major fluctuations, particularly residues Lys232, Lys252, Gly262, Leu392, Asp418, Asp453 and Ala685. The highest fluctuations were seen for RMA-Mut1, CSA-Mut4 and GLA-Mut1 indicating higher interactions. To further probe these results, we analyzed the corresponding MD trajectories. Supplementary Information Figure S4 shows the MD trajectory images of each peptide with PPAR-\(\alpha\) at 0 ns, 25 ns, 50 ns, 75 ns, and 100 ns. Each of the peptides bind to the ligand binding domain within the alpha-helices [69]. Pep shows very little change in conformation throughout the simulation whereas parts of Mut1 seem to rotate slightly within the binding pocket. Mut2 shows a significant change between its position at 0 ns and 25 ns but remains very stable from 25 ns till the end of the simulation.