A mathematical model for experimental gene evolution

The purpose of this paper is to determine the optimal mutation rate for random mutagenesis procedures used to make mutant libraries for subsequent screening. 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 high. We demonstrate that between these two extremes, an optimal mutation rate exists for experimental gene improvement. This rate depends strongly on the number of simultaneous mutations required for a beneficial change of the gene, but only weakly on the number of possible lethal mutations. This model predicts that when mutagenesis is performed at the optimum mutation rate, at least 63% (1--e(-1)) of the cloned genes in a mutant library will be non-functional.