Optimization of combinatorial mutagenesis.

Protein engineering by combinatorial site-directed mutagenesis evaluates a portion of the sequence space near a target protein, seeking variants with improved properties (e.g., stability, activity, immunogenicity). In order to improve the hit-rate of beneficial variants in such mutagenesis libraries, we develop methods to select optimal positions and corresponding sets of the mutations that will be used, in all combinations, in constructing a library for experimental evaluation. Our approach, OCoM (Optimization of Combinatorial Mutagenesis), encompasses both degenerate oligonucleotides and specified point mutations, and can be directed accordingly by requirements of experimental cost and library size. It evaluates the quality of the resulting library by one- and two-body sequence potentials, averaged over the variants. To ensure that it is not simply recapitulating extant sequences, it balances the quality of a library with an explicit evaluation of the novelty of its members. We show that, despite dealing with a combinatorial set of variants, in our approach the resulting library optimization problem is actually isomorphic to single-variant optimization. By the same token, this means that the two-body sequence potential results in an NP-hard optimization problem. We present an efficient dynamic programming algorithm for the one-body case and a practically-efficient integer programming approach for the general two-body case. We demonstrate the effectiveness of our approach in designing libraries for three different case study proteins targeted by previous combinatorial libraries--a green fluorescent protein, a cytochrome P450, and a beta lactamase. We found that OCoM worked quite efficiently in practice, requiring only 1 hour even for the massive design problem of selecting 18 mutations to generate 10⁷ variants of a 443-residue P450. We demonstrate the general ability of OCoM in enabling the protein engineer to explore and evaluate trade-offs between quality and novelty as well as library construction technique, and identify optimal libraries for experimental evaluation.