## 2 Results
### Comprehensive Review of Molecular Dynamics Simulations  
The 500 ns molecular dynamics (MD) simulation trajectories provide data for analyzing the root mean square deviation (RMSD), root mean square fluctuation (RMSF), radius of gyration (RG), and solvent-accessible surface area (SASA). Additionally, they offer insights into the binding energy of the protein\(-\)ligand complex throughout the MD simulation, calculated using the Molecular Mechanics with Generalized Born and Surface Area Solvation (MM-GBSA) method. These analyses contribute to understanding the stability and dynamic \begin{table}
\begin{tabular}{c c c c c} \hline
**Keap1-Ligand** & **Docking Score** & **Hydrogen-Bond** & **Non-Bond Interaction** & **Docking Orientation** \\
**Complex** & **(kcal/mol)** & **Hydrogen-Bond** & **Non-Bond Interaction** & **Docking Orientation** \\ \hline
4 IQK-kaempfer & \(-6.20\) & A:LEU557:O & A:ARG415 & \\  & & A:ALA510:O & A:ALA556 & \\  & & A:GLY511:CA & & \\  & & A:SER363:OG & A:ALA556:CB & \\  & & A:ASN414:OD1 & A:ARG415 & \\
4 IQK-luteolin & \(-6.45\) & A:VAL604:O & A:ALA556 & \\  & & A:GLY462:CA & A:ARG415 & \\  & & A:GLY509:CA & A:ALA556 & \\  & & A:GLY603:CA & & \\  & & A:ASN382:ND2 & & \\  & & A:ARG415:NE & & \\  & & A:VAL604:O & A:ARG415:NH2 & \\
4 IQK-phoretin & \(-6.30\) & A:SER602:OG & A:ALA556 & \\  & & A:ASN414:OD1 & & \\  & & A:SER363:OG & & \\
4 IQK-quercetin & \(-6.12\) & A:VAL604:O & A:ALA556 & \\  & & A:GLY462:CA & A:ARG415 & \\  & & A:GLY509:CA & A:ALA556 & \\  & & A:GLY603:CA & & \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._behavior of the protein\(-\)ligand complex over time, highlighting their potential interactions and efficacy in pharmacological applications. Overall, the MD simulation offers valuable insights into the molecular mechanisms underlying the binding affinity between the protein and ligand, aiding in rational drug design and optimization [24]. The stability metrics such as RMSD and RMSF help assess the flexibility and conformational stability of the complex, while SASA provides information on the extent of the protein\(-\)ligand interaction surface. Furthermore, the RG analysis complements these findings by offering insights into the compactness and overall shape of the complex throughout the simulation [25]. The root mean square deviation (RMSD) provides insight into the stability of the protein\(-\)ligand complex throughout the simulation. Figure 1a displays the RMSD values for 4 IQK with apigenin, luteolin, omaveloxolone, and the Cpd16 compound, showing average values of 1.62 A, 1.53 A, 1.60 A, and 1.59 A, respectively. While the RMSD for 4 IQK-Cpd16 showed significant fluctuations between 0 ns and 200 ns, the overall average values staying below 2 A suggest that the receptor\(-\)ligand complex remains relatively stable throughout the simulation. After 200 ns, the complex stabilizes, highlighting the robustness of the receptor\(-\)ligand interactions during the simulation. However, the fluctuations that tend to increase are shown by 4 IQK-omaevoloxone between 450 ns until the end of the simulation. Root mean square fluctuation (RMSF) evaluates the mobility and stability of amino acid residues, with higher RMSF values indicating greater instability and rigidity. As shown in Figure 1b, the RMSF values for apigenin, luteolin, omaveloxolone, and Cpd16 are all 0.09 nm, which points to their stability and rigidity within the receptor during the MD simulation. The radius of gyration (RG), illustrated in Figure 1c, reveals the compactness and stability of the structure, with average values consistently around 1.78 nm. Initial fluctuations between 250 ns and 450 ns were observed for 4 IQK-Cpd16, but these stabilize with minimal fluctuations thereafter. This indicates a stable and compact ligand binding within the 4 IQK molecule.