## 4 Conclusions  
The essential interactions of pyrazoline benzenesulfonamide derivatives (PBDs) with estrogen receptor alpha (ER\(\alpha\)) involve both hydrogen bonding and hydrophobic interactions. Among the 45 designed candidates, PBD-17 and PBD-20 emerged as the most promising compounds based on a comprehensive in silico evaluation involving molecular docking, molecular dynamics simulations, and pharmacophore modeling. These compounds feature modifications at position 3 of the parent structure, replacing the hydroxy group with piperidine (PBD-17) and piperazine (PBD-20), respectively. Both PBD-17 and PBD-20 complied with [PERSON]'s Rule of Five, showed high predicted cytotoxicity against breast carcinoma (MCF-7), and exhibited favorable ADMET profiles. Molecular docking revealed binding free energy (\(\Delta\)G) of 11.21 kcal/mol for PBD-17 and \(-\)11.15 kcal/mol for PBD-20, indicating strong receptor affinity. Molecular dynamics simulation demonstrated that the ER\(\alpha-\)PBD-20 complex was more conformational stable, with lower average RMSD of 0.26 nm (2.6 A) compared to the ER\(\alpha-\)PBD-17 complex, which stabilized around 0.32 nm (3.2 A). PBD-20 achieved equilibrium after 27 ns and maintained a stable conformation throughout the 200 ns simulation, while PBD-17 took longer to stabilize and showed greater early-phase deviations. Structural alignment analysis showed that PBD-20 preserved the ER\(\alpha\) backbone architecture with minimal displacement, closely resembling the reference 4-OHT complex. The residue fluctuation profile (RMSF) indicated that 4-OHT generated the least flexibility, while PBD-20 and lasofoxifene showed higher fluctuations at several loop regions. In terms of compactness, the radius of gyration (Rg) for ER\(\alpha-\)PBD-20 remained consistently around 1.88 nm, suggesting stable packing, whereas solvent-accessible surface area (SASA) values decreased gradually to around 125 nm\({}^{2}\), reflecting reduced solvent exposure. Hydrogen bonding analysis showed that the ER\(\alpha-\)PBD-20 complex maintained interactions such as ARG394-S20553 with an occupancy of 20.68%, while the reference  
Figure 11: Matching characteristics of PBD compounds and reference ligands in the best pharmacophore model. **(a)** 4-OHT, **(b)** raloxifene, **(c)** lasofoxifene, **(d)** PBD-17, and **(e)** PBD-20. Hydrogen bond donor (green sphere), hydrogen bond acceptor (red sphere), and hydrophobic area (yellow spheres) are the properties of the model. 4-OHT-GLU353 interaction was sustained for 69.08% of the time. The MM-PBSA binding free energy (\(\Delta\)GTotal) values derived from the decomposition analysis revealed that PDB-17 and PDB-20 exhibited significantly more favorable binding affinities compared to the reference ligand 4-OHT. Specifically, PDB-20 showed a binding energy of \(-\)139.462 kJ/mol, while PDB-17 had \(-\)58.229 kJ/mol. In contrast, the 4-OHT complex exhibited a binding energy of \(-\)145.307 kJ/mol, slightly more negative than PDB-20 but with greater variation and less favorable supporting energy components. Notably, the van der Waals energy was the most substantial contributor to the binding in PDB-20 (\(-\)269.768 kJ/mol), followed by 4-OHT (\(-\)210.692 kJ/mol), indicating strong non-covalent interactions in these complexes. Electrostatic contributions also favored binding in PDB-20 (\(-\)37.782 kJ/mol) compared to 4-OHT (\(-\)46.459 kJ/mol). Despite incurring higher polar solvation energy (194.421 kJ/mol), PDB-20 maintained favorable total energy due to compensating van der Waals and SASA energy contributions (\(-\)26.333 kJ/mol). These findings suggest that PBD-20 demonstrates a favorable structural and energetic profile when interacting with ER\(\alpha\), as reflected across all dynamic parameters. Based on pharmacophore modeling, PBD-17 and PBD-20 have features that include one hydrogen-bond donor (HBD), one hydrogen bond acceptor (HBA), and two hydrophobic interactions (HI) with a pharmacophore fit score of 45.20%.