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 equivalent to min{K-ds vertical bar 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 jiesirable to adopt [R] = K-d1, and when N = M (that realizes a stochastic process), [R] = root K-d1(K-d(-1))(-1)q rig 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. (C) 2012 Elsevier Inc. All rights reserved.