## 4 Discussion
Other than the variation of the cysteine number, the two-cysteine CX\({}_{n}\)C motifs in the CDR3 region are discovered in the variable domain of the antibody heavy chain by NGS analysis [50]. This mega research can be a start point to design a new antibody with long CDR3 or cross-reactive activity. Some studies of synthetic antibody libraries choose to remove cysteines to reduce the formation of disulfide bonds because it will limit the choice of subsequent antibody expression systems [38; 51]. The study of [PERSON] et al. mutated the non-canonical cysteines of CDR1 and CDR3, because they want to improve the likeness to the variable domain of human heavy chains [52]. However, disulfide bonds can form tighter protein structures, increasing protein stability and assisting the finger-like structure formed by CDR3 in recognizing antigenic epitopes deep in protein clefts [53]. Another study also shows that the number of cysteines in the synthetic VNAR antibody library does not affect the screening efficiency, which means that the high-affinity binders can be screened and produced [54]. The diversity of the antibody library is the key to screening high-affinity binders. To yield nM affinity binders, the library capacity must be higher than \(10^{9}\)[55]. But the diversity of a typical yeast-derived library does not exceed \(10^{7}\), becoming the bottleneck of the isolating high-affinity binder. In this study, the method of maximizing the diversity of the VNAR library is based on [PERSON] et al. 's research on the semi-synthetic VNAR phage display library, which contains greater than \(1\times 10^{8}\) unique phage clones [35]. An entirely random NNK trinucleotide combination was used to create different lengths of site mutations in the CDR3 region by PCR, and the theoretical diversity can be as high as \(10^{14}\)-\(10^{27}\) in this study. Although the theoretical diversity is high, many factors will affect the actual diversity. For example, the efficient transformation of foreign DNA into yeast could be a limitation. The library bias created by the NNK mutagenesis also affects the expected diversity with the distorted amino acid frequency. The NNK codon covers 32 codons that include all amino acids, but with redundancy for 8 amino acids (Arg, Ser, Leu, Pro, Ala, Thr, Gly, and Val). The most abundant amino acids observed in our library mostly fit the expected frequency based on the NNK codon which means that the frequency bias does exist in our study (Figure 4). The frequency bias also has impact on the pLogo analysis. The two most frequent amino acids, arginine and proline, occupied almost all the positions of randomized CDR3 before sorting (Figure 4). This phenomenon may hinder the finding of the high-affinity binder because the translation-based bias might force the antigen binds to the less suitable clone. Each NNK mutation site also has a chance of mutating into a stop codon (3%), undesired cysteine (3%), or hydrophobic residues (27%), which may cause the low efficiency of the VNAR display. Therefore, the longer the CDR3 is, the higher the chance of a difficult translation. In our study, for the CDR3 with lengths of 12, 13, 16, 18, 20, or 23 residues, the proportion of complete VNAR sequences decreased with the CDR3 length, suggesting that another translational bias happened in our library. Nevertheless, the actual diversity in this study could still maintain a level of more than \(10^{9}\) after checking the library quality by the NGS assay. Even though the library's capacity is larger than usual, the bio-panning efficiency is low when the input library overreaches the FACS workload [56]. Hence, we employed the strategy of sequential MACS and FACS to process a large quantity of library yeast. At first, the MACS filtered out possible binders from the whole library regardless of the low sorting purity. Next, these MACS-sorted clones, which contained true-positive or false-positive clones, were purified by FACS.