Mathematical expressions useful in the construction, description and evaluation of protein libraries

The creation of protein libraries by random mutagenesis and cassette mutagenesis has proven to be a successful method of protein engineering. Appropriate statistical analysis is important for the proper construction of these libraries and even more important for the interpretation of data from these libraries. We present simple mathematical expressions useful in the creation and evaluation of such libraries. These equations are useful in estimating the distribution of mutations, the degeneracy of the library and the frequency of a particular clone in the library. In addition, general equations addressing the probability that a particular clone is in a library, the probability that a library is complete, and as the consequences of retransformation of the library on these probabilities are presented.