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

• Published in: Mathematical biosciences 2012-12, Vol.240 (2), p.201-211
• Main Authors: Aita, Takuyo, Nishigaki, Koichi, Husimi, Yuzuru
• Format: Article
• Language: English
• Subjects: Aptamers, Peptide - chemistry; Biopanning; Computer Simulation; Directed evolution; Evolutionary design; In vitro evolution; Ligands; Models, Chemical; Selection pressure; SELEX; Stochastic Processes
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2012.07.006

► We considered an in vitro selection system composed of ligands and a target receptor. ► We examined the optimal target concentration to realize maximum efficiency in selection. ► This was analyzed from the viewpoint of the deterministic or stochastic process. ► We made a proposition of the effective strategy for both processes. 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]/(Kds+[R]) (specific binding) or binds to non-target materials with probability of q (non-specific binding), where [R] and Kds represent the free target-receptor concentration at equilibrium and dissociation constant Kd of the ligand sequence s with the receptor, respectively. Focusing on the fittest sequence with the highest affinity (represented by Kd1≡min{Kds|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]=Kd1, and when N=M (that realizes a stochastic process), [R]=Kd1〈Kd-1〉-1q only in the first round (where 〈∗〉 represents the population average) and [R]=Kd1 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.