## 3 Results and Discussion
### Molecular Flexibility Simulations
Therefore, the alignment results emphasize that 4-OHT and PBD-20 induce the most stable and structurally consistent binding to ER\(\alpha\). Figure 6: Conformational overlap of the 3D structure of the ER\(\alpha\) complex with each of its inhibitor ligands against the ER\(\alpha\)-4 OHT complex used as a positive control. The 3D structure is based on the average conformation that occurs throughout 200 ns of molecular dynamics simulation. **(a)** 4-OHT, **(b)** lasofoxifene, **(c)** raloxifene, **(d)** PBD-17, and **(e)** PBD-20. The root mean square fluctuation (RMSF) analysis was conducted to assess the flexibility of individual residue within the ER\(\alpha\) protein during the 200 ns MD simulation. As shown in Figure 7, fluctuations were primarily observed in the terminal and loop regions, particularly between residues 530 and 550. In the PDB-17 system, both lasofoxifene and PBD-17 exhibit slightly higher residue fluctuations, although overall RMSF values remained below 0.4 nm across all ligand. The highest flexibility was observed in the C-terminal region, which is commonly associated with structural arrangements during ligand binding. In comparison, the PBD-20 system shows more pronounced variability. Lasofoxifene and raloxifene induced higher RMSF values exceeding 0.5 nm in certain regions. Meanwhile, the 4-OHT complex maintained the most stable fluctuation profile, with the lowest RMSF across nearly all residues. The bar plots of residues with RMSF \(>\) 0.2 nm clearly demonstrate that PBD-20 has more flexible residues than PBD-17, suggesting looser stabilization in some regions. High flexibility in the binding site may lead to reduced binding affinity or receptor destabilization, particularly in antagonistic contexts. Ligands that induce minimal flexibility are generally associated with tighter, more stable interactions. These findings reinforce that 4-OHT yields the most stable residue dynamics, while PBD-20, despite some flexibility, still maintains favorable fluctuation behavior. To further evaluate the structural integrity of the complexes, the radius of gyration (Rg) and solvent accessible surface area (SASA) were analyzed to assess the compactness and solvent exposure of the ER\(\alpha\)-ligand complexes throughout the 200 ns simulation. As depicted in Figure 8, all systems maintain stable Rg values within the range of 1.86-1.92 nm, indicating no major unfolding events. The 4-OHT complex consistently shows the lowest Rg values in both PBD-17 and PBD-20 systems, reflecting a tightly packed and stable conformation. Raloxifene and lasofoxifene exhibit slightly higher Rg values, especially in the PBD-17 structure, suggesting more relaxed protein packing. SASA profiles further demonstrate that the 4-OHT complex has the lowest solvent exposure over time, reinforcing its stable and compact binding. Lasofoxifene shows greater SASA fluctuation in both systems, with a notable increase in the first 50 ns, indicating transient exposure  
Figure 7: RMSF on 4-OHT, lasofoxifene, raloxifene, PBD-17 and PBD-20 against ER\(\alpha\). of hydrophobic regions. The PBD-20 system generally exhibits lower SASA values than PBD-17, suggesting that ligands were better shielded from the solvent in this conformation. Compact structures with reduced solvent exposure typically correlate with favorable binding and energetic stability. The consistent behavior of 4-OHT in both Rg and SASA analysis supports its role as a structurally stable ER\(\alpha\) antagonist. These results suggest that PBD-20, particularly in complex with 4-OHT, promotes a more compact and less solvent-exposed conformation of ER\(\alpha\). Hydrogen bond analysis was performed to evaluate the stability and persistence of key interactions between ER\(\alpha\) and each ligand during the 200 ns simulation. As shown in Table 6, 4-OHT exhibits the strongest hydrogen bonding profile, with GLU353 forming a stable hydrogen bond for 69.08% of the simulation time.