## 2 Results and Discussion
At a low expression level using pDD18-Cm, the K9 Nb showed higher solubility than the 1.29 and C11 Nbs (approximately twice that of the 1.29 Nb). However, at a high expression level using pET28a, the solubility of the K9 Nb was much lower than that of the 1.29 Nb expressed using the same system (\(\sim\)100 fold that of the 1.29 Nb). Nonetheless, for the in vitro analysis, Nbs were expressed using pET28a since the overall yield of Nbs was higher when expressed using this system. Figure S4 illustrates the Coomassieie analysis of the purified Nbs, which simply involved batch-mode Ni-NTA affinity purification by gravity flow. It should be noted that the C11 nanobody (Nb) contains the R38C mutation, meaning that the extra cysteine in one nanobody might form a covalent disulfide bond with the extra cysteine in a second nanobody, resulting in a homodimer. The formation of this bond would depend on the expression environment. For example, an oxidizing environment, such as the _E. coli_ periplasm, would be required to efficiently form this bond. However, the strain used to produce the nanobody, BL21(DE3), has a strongly reducing cytoplasm that generally disfavors cysteine oxidation and disulfide bond formation. Thus, this linkage likely forms at some point after the protein is released from the cells, resulting from spontaneous oxidation in air. Nonetheless, a molecular-weight cutoff (MWCO) column was used for buffer exchange, concentrating the protein and removing high-molecular-weight contaminants or multimeric Nbs. **Evaluation of the antigen-binding activity of the Nbs isolated using FLI-TRAP. ** The abilities of the 1.29, C11, and K9 Nbs to bind to a range of RBDs of the Omicron subvariant BA.5 and a few other Omicron variants were examined using enzyme-linked immunosorbent assay (ELISA) and microscale thermophoresis (MST). Redirecting the 1.29 Nb toward the RBD of Omicron subvariant BA.5 revealed a significant increase in binding activities for the C11 (OD\({}_{450}\) = 1.5544 \(\pm\) 0.0619) and K9 Nbs (OD\({}_{450}\) = 1.6508 \(\pm\) 0.0392) compared to the 1.29 Nb (OD\({}_{450}\) = 0.2906 \(\pm\) 0.0312) (Figure 4). Additionally, the binding activities of all Nbs against the Delta and BA.1 variants were also evaluated, as the 1.29 Nb has been reported to bind strongly to Delta but not to BA.1 [9]. The results confirmed that the 1.29 Nb remained functional when expressed in this study since it produced a high ELISA signal to Delta but not to BA.1, as expected. Expanding our analysis to include various Omicron variants, the C11 Nb consistently demonstrated binding across multiple Omicron variants other than Omicron BA.5, surpassing the binding potency observed for the 1.29 Nb. In contrast, the binding capacity of the K9 Nb varied among the Omicron variants, suggesting potential limitations in binding to variants other than Omicron subvariant BA.5. In this study, the MST technique was used to determine the equilibrium dissociation constants (K\({}_{\rm D}\)) of the Nbs (Table 1). This technique has been used in previous studies to identify the binding affinity between human ACE-2 and the RBDs of many variants, including the Omicron B.1.1.529 variant [19]. Notably, the C11 and K9 Nbs had -4.3-fold and 46.5-fold higher binding affinities for Omicron BA.5 compared with the parental 1.29 Nb (K\({}_{\rm D}\) values of 326 and 29.9, respectively, versus 1390 nM). The C11 Nb also bound Omicron XBB.1.5 and XBB.1.16, with affinities in the sub-micromolar range (K\({}_{\rm D}\) values of 569 and 251 nM, respectively). Figure 4: **Binding activities of parental and evolved Nbs to various RBD variants observed using ELISA. ** Binding activity from normalized purified Nbs was measured by ELISA with microtiter plates coated with commercial RBD variants produced in HEK293 cells. Detection was with Mouse Anti-DDDDK tag Monoclonal Antibody, HRP Conjugated, Clone M2 (1:3000; Abcam Cat# ab49763, RRID:AB_869428).