= mRNA display
{c}
\b[mRNA display] is an <in vitro selection> method in which a <peptide> or <protein> is covalently linked to the <messenger RNA> encoding it. Selecting the displayed molecule can therefore retain recoverable sequence information about that same molecule: a physical <genotype-phenotype linkage>.
In the original experiment, synthetic <messenger RNA> carried <puromycin> at its 3′ end. During <translation (biology)>, this peptide acceptor enabled fusion of the message to its encoded <peptide>. <Richard W. Roberts> and <Jack W. Szostak> tested the linkage by selecting an encoded myc <epitope tag> with an antibody.<RNA-peptide fusions for the in vitro selection of peptides and proteins by Richard W. Roberts and Jack W. Szostak>[Abstract; Figures 1 and 4, fusion construction and immunoprecipitation]{ref}
The experimental readout went beyond observing binding. Following <immunoprecipitation>, <reverse transcription> and <polymerase chain reaction> recovered the encoding information. A <restriction enzyme> distinguished the selected myc sequence from background pool sequences, allowing before-and-after enrichment to be measured.<RNA-peptide fusions for the in vitro selection of peptides and proteins by Richard W. Roberts and Jack W. Szostak>[Selective Enrichment of an RNA-Peptide Fusion and Figure 5]{ref} This tests whether selection of a molecular property can recover the associated sequence; it does not establish that every possible sequence displays equally well.
An original <statistical sampling> calculation distinguishes nominal input size from <effective displayed-library coverage>. Suppose $N$ independent input molecules contain a desired sequence class with probability $p$, and each such molecule forms a usable fusion with probability $f$. Before any binding selection,
$$
\mathbb E[K]=Npf,\qquad
\Pr(K=0)=(1-pf)^N\simeq e^{-Npf}.
$$
For $N=10^{12}$, $p=10^{-10}$ and stipulated $f=0.01$, the expected usable desired count is only one and the chance of none is approximately 36.8%. Raising the hypothetical yield to 0.10 raises the expected count to ten and reduces that probability to approximately 0.00454%. These are constructed independent-sampling examples, not fusion yields claimed for the original experiment.
Sequence-dependent translation, fusion formation, recovery and amplification can each change representation. A large input sequence pool is therefore different from a large usable displayed pool. Repeating selection and amplification can enrich retained variants, while an independent functional or <binding affinity> measurement tests whether the recovered sequence has the intended property.
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