You are working to change the specificity of an antibody fragment using semi-rational design. You have discovered a 3-amino acid stretch in the complimentary determining region 3 (CDR3) that you hypothesize directs the specificity of the antibody. Your goal is to study this region by saturation mutagenesis (substituting all possible amino acids in each position). You design the degenerate primer to contain NNK for each mutated amino acid (N=A,T,G,C; K=G,T).

(a) How large of a library would you need to screen if you wish to have 3-fold library coverage (i.e., measure each mutated sequence 3 times on average)? In other words, you would need to screen 3 times more members than the number of possible sequence variants.

(b) After your first attempt, you decide to screen a similar 3-amino acid region in CDR1 and CDR2. How large of a library would you need to screen to ensure 3-fold coverage for all three CDRs simultaneously?

(c) Why is it necessary to have 3-fold library coverage as opposed to 1-fold coverage?

(d) What fraction of the members in the CDR3 library do you expect to be truncated due to the inclusion of a stop codon? Hint: the three stop codons are UAA, UAG, UGA.