Additivity of mutant effects assessed by binomial mutagenesis.

Eleven amino acid positions in the helix-turn-helix of lambda repressor have been mutagenized by using a combinatorial method in which alanine is substituted at each position with a probability of 0.5. Approximately 25% of the 2048 proteins in the resulting binomial library are active, including some variants with as many as seven alanine substitutions. The frequency of alanine substitutions in the set of active variants is a measure of the importance of the wild-type residue at each mutagenized position, and comparison of the frequencies of pairwise mutations with those expected based upon the single-position frequencies allows the additivity of mutant effects to be tested. For the positions examined here, we find that the effects of multiple substitutions are largely additive and are able to predict the activity class of the binomial mutants with 90% accuracy by using a model that simply sums penalty scores derived from the alanine substitution frequencies. We also find, however, that several residue pairs, including some that are distant in the three-dimensional structure, do display nonadditive effects that appear to be statistically significant.