## 2 Results and Discussion
This computational tool was successfully utilized to design novel Nbs targeting the RBD of many VOCs of SARS-CoV-2 ([PERSON] et al., 2020). The binding postures of the 1.29, C11, and K9 Nbs on the receptor-binding motif (RBM) of the RBD of BA.5 variant are depicted. While the 1.29 Nb exhibited a similar posture to the C11 Nb, the C11 Nb demonstrated a slightly superior binding affinity (\(-10.05\) kcal/mol) than the 1.29 Nb (\(-9.58\) kcal/mol). This phenomenon suggests that the two mutated residues of the C11 Nb might influence conformational changes, leading to an increase in its binding affinity. Both Figure 6 and Figure S5 confirm that the 1.29 and C11 Nbs interacted through similar contributing contact residues on CDR1-3. Although the R38C and V64E mutation residues of the C11 Nb did not interact with the RBD of BA.5 variant, as they were not located in the CDR binding sites, the C11 Nb had more salt bridge interactions, resulting in a stronger affinity (Figure S6). An additional cysteine residue introduced by replication slippage in Framework 2 may promote nanobody multimerization, particularly notable in the VHH subfamily 3, which has contributed to further classification of VHH gene subfamilies in the dromedary genome ([PERSON] et al., 2020). In the conserved framework region responsible for VH/VL interactions, typical hydrophobic amino acids are replaced with hydrophilic hallmarks, enhancing solvent accessibility ([PERSON] et al., 2020). The R38C mutation in Framework 2 packs closely against a conserved hydrophobic core, while the unique hydrophilic hallmarks are oriented outward. This structural configuration introduces steric hindrance, restricting R38C oxidation or covalent bonding with other cysteines. Typically, nanobody multimerization is achieved via genetic fusion or domain linking ([PERSON] et al., 2020). However, connecting the N/C termini directly to the scaffold may weaken binding interactions, potentially diminishing affinity and stability. Notably, serine-to-cysteine mutations at four framework positions have promoted dimerization without compromising antigen binding ([PERSON] et al., 2020). Thus, the R38C mutation in Framework 2 is less likely to cause nanobody multimerization due to steric hindrance, and it retains binding affinity by packing closely against the hydrophobic core without interfering with antigen binding. The binding affinity of the K9 Nb was \(-19.82\) kcal/mol, significantly higher than those of the 1.29 and C11 Nbs. This difference is attributed to the numerous changes in the amino acid residues within the K9 Nb's CDR1-3, contributing to interactions with the RBM of the RBD of BA.5 variant. The optimum posture of the K9 Nb shows many interface residues and a substantial interface area (Figures S6 and S7) including aliphatic and aromatic residues that played a crucial role in these interactions. The insertion mutation \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Physicochemical Properties**} & \multicolumn{3}{c}{**Nb**} \\ \cline{2-4}  & **1.29** & **C11** & **K9** \\ \hline
**Number of amino acids** & 121 & 121 & 126 \\
**Molecular weight (g-mol\({}^{-1}\))** & 12,802.926 & 12,779.86 & 13,673.942 \\
**Charge at pH 7.4** & \(-1.4\) & \(-3.4\) & \(-3.4\) \\
**PI** & 5.31 & 4.77 & 4.93 \\
**GRAVY** & \(-0.378\) & \(-0.378\) & \(-0.513\) \\
**Solubility** & 0.615 & 0.7 & 0.628 \\
**Aliphatic index** & 62.89 & 62.89 & 65.79 \\
**Instability index** & 18.57 & 18.57 & 24.99 \\
**Molar extinction (M\({}^{-1}\)-cm\({}^{-1}\))** & 23,020 & 23,020 & 25,580 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of the physicochemical properties of Nbs. in the K9 Nb, specifically the extension of the CDR3 region with a tyrosine-rich sequence, was a significant factor for RBM interaction (Figure 6 and Figure S7). Remarkably, the amino acid residues on the CDRs of the K9 Nb, such as Val31, Ser99, Thr102, Pro112, and Tyr113, significantly increased hydrogen bond interactions with the RBM of the RBD of BA.5 variant (Figure S5).