A mathematical model for experimental gene evolution

The purpose of this paper is to determine the optimal mutation rate for ran dom mutagenesis procedures used to make mutant libraries for subsequent scr eening. When the mutation rate is low, the probability of achieving a rare beneficial mutation is low. When the mutation rate is high, the probability of producing lethal mutations which result in loss of function is also hig h. We demonstrate that between these two extremes, an optimal mutation rate exists for experimental gene improvement. This rate depends strongly on th e number of simultaneous mutations required for a beneficial change of the gene, but only weakly on the number of possible lethal mutations. This mode l predicts that when mutagenesis is performed at the optimum mutation Fate, at least 63% (1 - e(-1)) of the cloned genes in a mutant library will be n on-functional. (C) 2001 Academic Press.