## 3 Results
### Post-Simulation Analysis  
#### 3.10.1 Principal Components and Dynamic Cross-Correlation Matrix Analysis  
PCA was used to assess domain dynamics and motion in the VLP-PGN and VLP-\(\beta\)-glucan docked complexes during 100 ns simulations, with results expressed as a fraction of variance (eigen fraction) derived from a covariance matrix of eigenmodes. The VLP-PGN complex exhibited a sharp 80.8% variance drop at the first four eigenmodes (Figure 11a).  
Figure 10: RMSF of PGN with atom index showing ligand fluctuations (**a**). Analysis of PGN during MDS, including RMSD, intramolecular hydrogen bonds, a radius of gyration, molecular surface area, polar surface area, and solvent-accessible surface area, all indicate the stable interaction of PGN with VLP (**b**). RMSF of \(\beta\)-glucan with atom index showing ligand fluctuations (**c**). Analysis of \(\beta\)-glucan during MDS, including RMSD, intramolecular hydrogen bonds, radius of gyration, molecular surface area, polar surface area, and solvent accessible surface area, all indicate the stable interaction of \(\beta\)-glucan with VLP (**d**).  
Figure 9: RMSF of VLP residues with PGN, indicating structural rigidity and stability (**a**). SSE distribution of alpha helices and beta strands of VLP residues with PGN (**b**). SSE behavior over simulation time, with a total SSE of 9.0%, indicating that structural flexibility facilitates ligand binding of VLP residues to PGN (**c**). RMSF of VLP residues with \(\beta\)-glucan, indicating structural rigidity and stability (**d**). SSE distribution of alpha helices and beta strands of VLP residues with \(\beta\)-glucan (**e**). SSE behavior over simulation time, with a total SSE of 8.75%, indicating structural flexibility that facilitates ligand binding of VLP residues to \(\beta\)-glucan (**f**).  
The VLP-\(\beta\)-glucan complex displayed a similar 80.1% drop but at seven eigenmodes (Figure 11b), indicating significant conformational changes in the VLP active pocket induced by both ligands. After these points, both complexes stabilized, showing no notable variations in eigenvalues from 4 to 20, which supports the stability of the protein-ligand interactions. The initial three eigenfractions revealed clustered motions from the MDS trajectory, with early flexibility transitioning into compact cluster motions as the simulation progressed. Two-dimensional plots illustrated the overall conformational shifts in VLP for both systems, with a color gradient from red to blue reflecting gradual structural changes over time. This comparison highlights that while both ligands induce substantial conformational changes and stabilize the VLP active pocket, their dynamics differ slightly in the number of eigenmodes involved in the initial variance drop. The conformational dynamics of VLP induced by PGN and \(\beta\)-glucan were assessed using DCCM analysis, focusing on the correlated motions of alpha carbon atoms during the simulation (Figure 11c,d). The DCCM analysis revealed significant alterations in the correlated motions and dynamic behavior of the VLP structure when it was docked with PGN compared with \(\beta\)-glucan. These findings align closely with the results observed in the PCA plots, providing consistent evidence of ligand-induced structural changes in VLP.  
Figure 11: PCA and DCCM analysis for the MDS trajectories of VLP-PGN and VLP-\(\beta\)-glucan docked complexes. PCA of VLP-PGN (**a**) and VLP-\(\beta\)-glucan (**b**) docked complexes, the percentage of overall mean square displacement of residue positional fluctuation noted in each dimension is expressed by the corresponding eigenvalue (PCs). The color values, ranging from blue to white to red, represent the periodic jump observed during the 100 ns simulation—dynamic cross-correlation for VLP-PGN (**c**) and VLP-\(\beta\)-glucan (**d**) docked complexes. The positive and negative correlations in the residue movement are represented by cyan and red colors, respectively.