Protein Engineering Protocols - Mycobacteriology research center

128 Denault and Pelletierin the past decade as a result of the creation of better-defined large libraries witha variety of strategies for linking genotype and phenotype, which, in turn, haveallowed for the development of a host of new approaches to functional screeningand selection strategies (see refs. 1 and 2 for more information).The goal of this chapter is to present some of the main statistical and probabilisticcalculations pertinent to protein library creation and to library-basedscreening and selection strategies in the language of the combinatorial biologistto ensure their ease of application. This chapter also aims to reveal the pertinenceof these calculations to the process of library creation and screening. Whendesigning an experiment in library-based protein engineering, one must counterbalancethe scientific value of creating the most diverse protein library with thepractical limitations presented by the screening or selection strategies. The statisticaland probabilistic questions pertaining to library representation are important,and they vary according to the specific application. We also present tests of experimentalbiases, to aid in assessing the library quality and the occurrence of biasesbefore or after selection. As we will illustrate, the information revealed by simpleanalyses of library-based problems can lead to important—and sometimescounter-intuitive—insights, which, in turn, allow rapid improvement of the experimentaldesign and a stronger basis for interpretation of the results.We first discuss some important parameters related to the design of proteinlibraries, such as library size, compositional bias, codon degeneracy, and encodeddiversity. This is followed by the development of a series of commonly encounteredproblems, with discussion of the pertinence of addressing each problemand a clear mathematical development. Numerical examples are provided toclarify the application of the formulae. In cases in which the implementation ofthe mathematical tools is more complex or time consuming, we refer the experimenterto Excel files for input of the appropriate variables. The proposed problemsare intended to be general enough to apply to a diversity of library-basedsystems rather than to any specific subset.It is important to note that many results presented below are suited onlywhen various parameters are sufficiently large or small, and can lead to erroneousconclusions if applied otherwise. Specific conditions are provided.Complementary works on the mathematical treatment of library-based strategiesinclude mathematical modeling of DNA shuffling, specifically treated inthe important work of Moore and of Maranas (3–6) and of Sun (7), and, morerecently, Blackburn and colleagues (8). The latter work also presents a mathematicaltreatment of library representation for libraries of equiprobable outcomes; wepresent the same treatment, as a prelude to the treatment of library representationfor libraries of nonequiprobable outcomes. Reference 8 also presents a methodfor estimation of diversity in libraries generated by error-prone polymerase chainreaction and, importantly, provides simple computer programs for users.