## 3 Results and Discussion
### Molecular Flexibility Simulations  
The best-performing compounds from molecular docking, PBD-17 and PBD-20, were subjected to 200 ns molecular dynamics (MD) simulations to further evaluate the stability of their complex with ER\(\alpha\). The RMSD parameter was calculated to assess the structural fluctuation of each protein-ligand complex relative to its initial conformation over time. As shown in Figure 5, the RMSD trajectories for all ligands were compared against the reference ligand, 4-OHT. In the PBD-17 system, lasofoxifene exhibited the highest fluctuations during the first 25 ns, stabilizing only later at 0.35 nm. In contrast, 4-OHT and raoxifene maintained lower and more consistent RMSD values between 0.25 and 0.30 nm, throughout the simulation, indicating better structural stability. The PBD-17-raloxifene complex reached equilibrium earlier and maintained a more uniform conformation over time. While the PBD-17- ER\(\alpha\) complex initially showed greater fluctuations, it eventually stabilized, albeit more slowly than the other ligands. These observations suggest that the PBD-17 context, 4-OHT and raoxifene form more stable and conformationally consistent complexes with ER\(\alpha\) than lasofoxifene. A stable RMSD profile general reflects minimal conformational changes, indicating stronger binding accommodation and reduced energetic strain. In contrast, the PBD-20 system shows distinct and more favorable stabilization patterns across all ligands. The 4-OHT- ER\(\alpha\) complex achieved equilibrium rapidly, within the first 10 ns, and remained stable at around 0.27 nm. Complexes of PBD-20 with raoxifene and lasofoxifene also displays consistent RMSD trajectories, although lasofoxifene exhibits a slightly higher plateau near to 0.34 nm. Interestingly, the PBD-20- ER\(\alpha\) complex exhibited only moderate early fluctuation, stabilizing after approximately 27 ns and ultimately  
Figure 5: RMSD values of the protein and ligands during 200 ns of MD simulation. displayed lower RMSD values compared to PBD-17. This may reflect greater plasticity of the binding site, allowing ER\(\alpha\) to accommodate PBD-20 more efficiently. The lower RMSD deviation suggest that the PBD-20 system forms a more rigid and well-fitting complex with ER\(\alpha\), compared to the PBD-17 system. These results suggest that ER\(\alpha\) exhibits more favorable binding characteristics in the present of PBD-20, likely due to enhanced conformational adaptability of the receptor. These flexibility may facilitate stronger and more stable interactions, contributing to the overall stability of the complex. Therefore, PBD-20 appears to better stabilize the ER\(\alpha\) conformation during long-term molecular dynamics simulations compared to PBD-17. The structural alignment of ER\(\alpha\) bound to each ligand was evaluated using average conformations extracted from the 200 ns molecular dynamics simulations. As shown in Figure 6, the 4-OHT complex (a) served as the reference for comparison with lasofoxifene (b), raloxifene (c), PBD-17 (d), and PBD-20 (e). Among all tested complexes, PBD-20 displays the closest structural resemblance to the 4-OHT-bound ER\(\alpha\), with minimal deviations across the ligand-binding domain. In contrast, raloxifene induces visible shifts in loop regions near the C-terminal, particularly around residues 530-550. Lasofoxifene also causes mild conformational changes near the helical region, although the overall fold remains preserved. The PBD-17 complexes, however, displayed more pronounced deviation, especially in the flexible peripheral regions, suggesting a less stable binding conformation. These differences highlight the variable impact of each ligand on receptor structure, depending on binding strength and molecular fit. The preserved structural integrity in PBD-20 suggests stronger accommodation within the binding pocket. Ligands that maintain a conformation closer to the native antagonist structure are more favorable for suppressing ER\(\alpha\) activity.