## 3 Results
### Molecular Dynamic Simulation
(**h**) Percentages of ion donors and acceptors in \(\beta\)-glucan, along with amino acids from VLP and water molecules. the types of bonds formed with the amino acids of VLP and \(\beta\)-glucan during the MDS. Figure 8g represents the minimum 0 and maximum 18 total contents between VLP and \(\beta\)-glucan. Similarly, Figure 8g also shows the number of contacts between \(\beta\)-glucan and the amino acids of VLP, ranging from 0 (white) to \(\geq\)4 (brown). Figure 5d illustrates the percentages of ion donors and acceptors in the \(\beta\)-glucan, along with the amino acids of protein and water molecules. The analysis of RMSF and SSE provided insights into the stability, flexibility, and structural behavior of VLP when complexed with PGN and \(\beta\)-glucan. RMSF values, which measure the flexibility and fluctuation of amino acid residues, revealed that most residue indices had lower RMSF values for both complexes, confirming the stability and rigidity of VLP (Figure 9a,d). Similarly, B-factors derived from IC-NMA showed consistent results with RMSF data and experimental B-factors from X-ray crystallography, further supporting the stability of VLP (Figures 6b and 7b). Regarding SSE, the distribution of alpha helices and beta strands was assessed over residue indices and simulation time. For the VLP-PGN complex, the total SSE percentage was 9.0%, with 8.55% alpha helices--indicative of structural rigidity--and 0.45% beta strands, suggesting that minor flexibility aids ligand binding (Figure 9b,c). In comparison, the VLP-\(\beta\)-glucan complex exhibited a slightly lower SSE percentage of 8.75%, with 8.34% alpha helices and 0.41% beta strands, reflecting similar structural stability while maintaining the flexibility required for effective ligand interaction (Figure 9e,f). These results highlight the comparable stability of VLP in both complexes, with subtle differences in flexibility that may influence ligand binding dynamics. ] In parallel, the RMSF value of the ligand fluctuations was calculated with an atom index to check the interaction of PGN and \(\beta\)-glucan fragments with VLP and their entropic role during docking. The fit PGN on the VLP graph (Figure 10a,c) exhibited more fluctuation in RMSF at higher atom indices than the fit \(\beta\)-glucan on the VLP graph. The RMSD, intramolecular hydrogen bonds (IntraHBs), radius of gyration (rGyr), molecular surface area (MolSA), polar surface area (PSA), and solvent accessible surface area (SASA) of PGN and \(\beta\)-glucan in complex with VLP was studied further during the 100 ns-long MDS and the resultant images are presented in Figure 10b,d. The comparative analysis of PGN and \(\beta\)-glucan during MDS highlighted their respective structural stability, conformational spread, and interaction dynamics. The average RMSD value for PGN was 3.61 A. In comparison, \(\beta\)-glucan exhibited a slightly lower RMSD of 2.62 A, indicating robust structural stability in both ligands, with \(\beta\)-glucan marginally more stable. The rGyr, indicative of the ligands' conformational spread, averaged 5.61 A for PGN, with values ranging from 5.2 to 6.4 A, suggesting a more extended conformation compared with \(\beta\)-glucan, which had an average rGyr of 4.93 A and a range of 4.8 to 5.1 A. PGN formed a maximum of 6 IntraHBs during the simulation, while \(\beta\)-glucan formed up to 4, reflecting differences in their intramolecular interactions. The MolSA, which relates to van der Waals interactions, was significantly larger for PGN (630-700 A\({}^{2}\), average 653.3 A\({}^{2}\)) than for \(\beta\)-glucan (384-420 A\({}^{2}\), average 395.89 A\({}^{2}\)), indicating a more incredible spatial occupation for PGN. Similarly, the SASA, representing water exposure, was higher for PGN (150-470 A\({}^{2}\), average 297.95 A\({}^{2}\)) compared with \(\beta\)-glucan (130-450 A\({}^{2}\), average 203 A\({}^{2}\)). This result suggests that PGN is more solvent-exposed than \(\beta\)-glucan.