= In vitro selection
\b[In vitro selection] enriches a molecular sequence population by repeatedly retaining variants with a desired experimentally tested property and recovering their sequence information for further rounds. The functional test occurs outside a living organism. In <directed evolution>, that enrichment can be combined with sequence diversification; selection itself need not introduce a new mutation in every round.
A primary 1990 experiment by <C. Tuerk> and <L. Gold> alternated binding selection and amplification of <RNA> variants that interacted with <bacteriophage T4 DNA polymerase>. Randomizing eight nucleotide positions defined $4^8=65{,}536$ possible sequences, from which selected ligands were characterized.<Systematic evolution of ligands by exponential enrichment: RNA ligands to bacteriophage T4 DNA polymerase by C. Tuerk and L. Gold>[Abstract]{ref} The experiment connects molecular recognition with sequence recovery; merely measuring total binding would not identify which variant succeeded.
For <protein> selection, a <genotype-phenotype linkage> must preserve the connection between activity and recoverable information. In 1997, <Richard W. Roberts> and <Jack W. Szostak> generated covalent fusions between <messenger RNA> and the peptide it encoded using <puromycin>-bearing RNA during <translation (biology)>. <Immunoprecipitation> enriched a fusion carrying the desired <epitope tag>.<RNA-peptide fusions for the in vitro selection of peptides and proteins by Richard W. Roberts and Jack W. Szostak>[Abstract; introductory rationale]{ref} This supplies a concrete molecular implementation underlying <mRNA display>, rather than requiring the recovered protein itself to be copied.
An original two-class model makes the enrichment quantitative. Let the desired class have initial fraction $p$, with retention probabilities $s_A$ and $s_B$ for desired and other molecules. If subsequent amplification is equal,
$$
p'=\frac{ps_A}{ps_A+(1-p)s_B},\qquad
\frac{p'}{1-p'}=\frac{p}{1-p}\frac{s_A}{s_B}.
$$
For stipulated $p=0.001$, $s_A=0.5$ and $s_B=0.005$, one round raises the fraction to approximately 0.091. A second identical round gives approximately 0.909. These are ideal population calculations, not yields reported by either experiment.
The assumptions matter. Different amplification factors $g_A,g_B$ multiply the odds enrichment by an additional factor $g_A/g_B$, so sequence abundance after a round does not measure binding quality alone. A finite starting sample can also lose a rare class before selection: with $p=0.001$ and 100 independent sampled molecules, the probability of missing it entirely is $(1-p)^{100}\simeq0.905$.
Target binding, retention on support material, sequence recovery and amplification are therefore separate experimental steps. Characterizing recovered variants with an independent <binding affinity> or functional assay helps establish whether enrichment captured the intended property. A large theoretical sequence space and a strongly enriched output are useful observations, but neither alone proves that every retained sequence has the desired molecular function.
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