## 3 Results and Discussion
### Molecular Dynamics Studies  
#### 3.6.1 Analysis of RMSDs and RMSFs for Ligand-Receptor Complexes  
To further elucidate the interactions and examine the stability of the ligands with the receptors, we carried out 100 ns molecular dynamics (MD) simulations. While we conducted MD simulations with all peptides, for the polyphenol-peptide conjugates, only those conjugates that showed significant binding interactions were selected. These include RMAPep, RMAMut1, GLAMut1, GLAMut2, CGAMut4, and CSAMut4. Figure 8a,d,g shows a comparison of RMSDs of ligand bound receptors of each of the peptides and conjugates with the three receptors. The RMSDs are representative of the last 25 ns of 100 ns runs. The RMSDs of the entire runs are shown in Supplementary Information Figure S1. As shown in the figures, among the unconjugated peptides, Pep and Mut4 showed the lowest RMSDs, followed closely by Mut2 and Mut3 (<1.0 nm) in the case of ER-\(\alpha\). However, Mut1 showed a relatively high RMSD (2.4 nm). In comparison, for PPAR-\(\alpha\) the lowest RMSD (0.3 nm) was observed for Mut2, followed by Pep, Mut1, and Mut4. Mut3 had the highest (0.82 nm) RMSD in the case of PPAR-\(\alpha\). In the case of EGFR, Mut3 was lowest (0.6 nm) followed closely by Pep, Mut1, and Mut4. The highest RMSD (0.96 nm) was found to be for Mut2. Thus, in each case the most stable receptor-peptide combination was dependent upon the peptide sequence of the ligand. Furthermore, other than Mut1 (in the case of ER-\(\alpha\)), all of the peptides showed fairly stable binding interactions. Figure 8: Comparison of RMSDs (72 ns-100 ns). (**a**) ER\(\alpha\); (**d**) PPAR\(\alpha\); (**g**) EGFR. RMSFs for the entire 100 ns runs are shown for each of the receptors with (**b**) and (**c**) corresponding to ER\(\alpha\); (**e**,**f**) corresponding to PPAR\(\alpha\); (**h**,**i**) corresponding to EGFR. Amongst the polyphenol-peptide conjugates, RMA-Pep was found to have lower RMSD values (\(\sim\)0.7 nm) in the case of all the three receptors. GLAMut1, was found to have the highest RMSD for ER-\(\alpha\), while CSAMut4 was found to have the highest RMSD for both PPAR-\(\alpha\) and EGFR in this time frame, indicating that toward the end of the simulations those ligands are relatively less tightly-bound to the respective receptors. Interestingly, CSAMut4 was found to have the lowest RMSD for ER-\(\alpha\), indicating that it was the most stable conjugate with ER-\(\alpha\). CGAMut4 showed the lowest RMSD with PPAR-\(\alpha\), while RMAMut1 showed the lowest RMSD with EGFR indicating the formation of highly stable complexes [65]. The RMSF graphs for ER-\(\alpha\) (Figure 8b,c) show the fluctuations of the receptor upon binding with the various ligands. In the case of the peptides (Figure 8b), while several regions showed fluctuations, Mut3 showed highest fluctuations with Leu466 and Asp332, while Mut4 showed the highest fluctuations with Gly494 and Leu497. Mut1 showed the highest fluctuation with Lys467 and Pep showed highest fluctuations with Asp322 and Ala546, indicating the strong involvement of those residues in binding interactions. Comparatively, more fluctuations were observed for the polyphenol-peptide conjugates (Figure 8c). GLAMut2, GLAMut1, RMAMut1, showed the highest fluctuations with Ser305, Tyr331; Lys467 and Glu419 respectively. To further probe these results, we examined the trajectory snap shots of the peptide and conjugate-bound ER-\(\alpha\) at various time points throughout the simulation (Supplementary Information Figure S2). In general, estrogen receptors are composed of two domains, made up mostly of \(\alpha\)-helices. It's native ligand, estradiol, binds within a largely hydrophobic pocket of ER\(\alpha\) through H-bonds with Glu353, Arg394, Phe40, and His524 residues in the ligand binding domain of the receptor [66]. Pep initially has a strong association with the receptor in the binding pocket region encompassing multiple helices.