Fitness loss and library size determination in saturation mutagenesis

Saturation mutagenesis is a widely used directed evolution technique, in which a large number of protein variants, each having random amino acids in certain predetermined positions, are screened in order to discover high-fitness variants among them. Several metrics for determining the library size (the number of variants screened) have been suggested in the literature, but none of them incorporates the actual fitness of the variants discovered in the experiment. We present the results of an extensive simulation study, which is based on probabilistic models for protein fitness landscape, and which investigates how the result of a saturation mutagenesis experiment--the fitness of the best variant discovered--varies as a function of the library size. In particular, we study the loss of fitness in the experiment: the difference between the fitness of the best variant discovered, and the fitness of the best variant in variant space. Our results are that the existing criteria for determining the library size are conservative, so smaller libraries are often satisfactory. Reducing the library size can save labor, time, and expenses in the laboratory.