Random mutagenesis of genes followed by positive genetic selection in
bacteria requires that the variant molecules confer biological activit
y, and is thus the most demanding approach for generating new function
ally active molecules. Furthermore, one can learn much about the prote
in in question by comparing the population of selected molecules to th
e library from which they were selected. Described here is a mathemati
cal method designed to guide such comparisons. We use as examples the
results of randomization-selection studies of four different proteins.
There exists, in general, a positive correlation between the number o
f amino acid substitutions in a critical region of a protein and the l
ikelihood of inactivation of that protein; a correlation long suspecte
d, but developed here in detail. At this time, we are comparing region
s in different proteins and our conclusions must be limited. However,
the method presented can serve as a guideline for anticipating the yie
ld of new active mutants in genetic complementation assays based on th
e extent of randomization.