## 3 Results and Discussion
### Molecular Dynamics Studies
#### 3.6.2 Protein-Ligand Interactions
The total number of interactions (Figure 10h) through the course of the simulation was found to be 9 on average, with the highest number of contacts (15) at 25 ns. P-L contacts between CGAMut4 and ER\(\alpha\) are shown in Figure 10i. Significant H-bonding was observed with Glu423D, Lys531B, Asp374B, and Val534B. Hydrophobic interactions occurred with Tyr537B, Tyr526B, and His377B, while Glu423D and Asp538B were involved in ionic interactions. InPLIP results, Glu423D, Lys531B, and Asp374B were involved in H-bonding and Tyr537B and Tyr526B were involved in hydrophobic interactions. The total number of contacts (Figure 10j) was found to be 20 over the course of the entire simulation, which is expected given the RMSD analysis which showed a very stable complex. As shown in the P-L contacts histogram for CSAMut4 (Figure 10k), H-bonding occurred with Glu423D, His516D, Glu523D, and Tyr526B of ER\(\alpha\). Hydrophobic interactions occurred with Lys520D and Tyr526B, while Glu423D was involved in ionic interactions. Glu423D, His516D and Tyr526B were also implicated in H-bonding in PLIP results. The total number of contacts throughout the entire course of simulation (Figure 10l) was found to be 15. Thus, the protein-ligand contact analysis further confirms the role of H-bonding and hydrophobic interactions involved in forming complexes with each of the ligands. The ligand atom interactions with the receptor residues are shown in Supplementary Information Figure S9, which corroborates with the results obtained above. Figure 9: Protein ligand contacts of ER\(\alpha\)-ligand complexes (**a**) with Pep; (**b**) total number of contacts during the simulation with Pep; (**c**) with Mut1; (**d**) total contacts during the simulation with Mut1; (**e**) with Mut2; (**f**) total number of contacts during the simulation with Mut2; (**g**) with Mut3 peptide; (**h**) total number of contacts during the simulation with Mut3; (**i**) with Mut4 peptide; (**j**) total number of contacts during the simulation with Mut4. Overall, MD studies of the ER\(\alpha\)-peptide and polyphenol-peptide conjugate complexes provided valuable insight into the stability of each peptide and polyphenol-peptide construct in complex with the receptor. Of the unconjugated peptides, Mut4 showed the greatest degree of stability with ER-\(\alpha\). Of the polyphenol-peptide conjugates, CGAMut4 and CSAMut4 showed favorable degrees of stability, as did RMAPep, which showed comparable stability compared to Pep. Overall, polyphenols conjugated to the peptides were involved in higher numbers of interactions with the receptor, indicating that conjugation of polyphenols to the targeting peptides could improve ER-\(\alpha\) targeting. PPAR-\(\alpha\)  
We next probed the PPAR-\(\alpha\) receptor residues that were involved in interacting with each of the ligands (Figure 11). As seen in the case of the original peptide and mutations 1-4, H-bonding interactions and water-bridges played a major role in the binding interactions. Pep, Mut1, Mut4 and Mut2 showed significantly more H-bonding interactions. Additionally, Pep, Mut2 and Mut3 showed significant hydrophobic interactions. Figure 10: Protein ligand contacts of ER\(\alpha\)-ligand complexes. (**a**) with RAMMut1; (**b**) total number of contacts with RAMMut1; (**c**) with RMAPep; (**d**) total contacts with RMAPep; (**e**) with GLAMut1; (**f**) total number of contacts with GLAMut1; (**g**) with GLAMut2 conjugate; (**h**) total number of contacts with GLAMut2; (**i**) with CGAMut4; (**j**) total number of contacts with CGAMut4; (**k**) with CSA-Mut4; (**l**) total number of contacts with CSAMut4. In all five peptides, Tyr 334 showed significant H-bonding and hydrophobic interactions. For Pep (Figure 11a), Asn 261, Glu 282, and Tyr 334 showed the most H-bonding. The total protein-ligand contacts steadily fluctuated around 15 for the entire simulation. For Mut1 (Figure 11b), Glu 282 showed significant H-bonding. The total protein-ligand contacts also steadily fluctuated around 15 for the entire simulation.