Theoretical consideration of selective enrichment in in vitro selection: optimal concentration of target molecules.

We considered an in vitro selection system composed of a peptide-ligand library and a single target protein receptor, and examined effective strategies to realize maximum efficiency in selection. In the system, a ligand molecule with sequence s binds to a target receptor with probability of [R]/(K(ds)+[R]) (specific binding) or binds to non-target materials with probability of q (non-specific binding), where [R] and K(ds) represent the free target-receptor concentration at equilibrium and dissociation constant K(d) of the ligand sequence s with the receptor, respectively. Focusing on the fittest sequence with the highest affinity (represented by K(d1) ≡ min{K(ds)|s=1,2,…,M}) in the ligand library with a library size N and diversity M, we examined how the target concentration [R] should be set in each round to realize the maximum enrichment of the fittest sequence. In conclusion, when N >> M (that realizes a deterministic process), it is desirable to adopt [R]=K(d1), and when N=M (that realizes a stochastic process), [R]=[Formula in text] only in the first round (where * represents the population average) and [R]=K(d1) in the subsequent rounds. Based on this strategy, the mole fraction of the fittest increases by (2q)(-r) times after the rth round. With realistic parameters, we calculated several quantities such as the optimal [R] values and number of rounds needed. These values were quite reasonable and consistent with observations, suggesting the validity of our theory.