A divide‐and‐conquer approach to determine the Pareto frontier for optimization of protein engineering experiments

Abstract

In developing improved protein variants by site-directed mutagenesis or recombination, there are often competing objectives that must be considered in designing an experiment (selecting mutations or breakpoints): stability vs. novelty, affinity vs. specificity, activity vs. immunogenicity, and so forth. Pareto optimal experimental designs make the best trade-offs between competing objectives. Such designs are not “dominated”; i.e., no other design is better than a Pareto optimal design for one objective without being worse for another objective. Our goal is to produce all the Pareto optimal designs (the Pareto frontier), in order to characterize the trade-offs and suggest designs most worth considering, but to avoid explicitly considering the large number of dominated designs. To do so, we develop a divide-and-conquer algorithm, PEPFR (Protein Engineering Pareto FRontier), that hierarchically subdivides the objective space, employing appropriate dynamic programming or integer programming methods to optimize designs in different regions. This divide-and-conquer approach is efficient in that the number of divisions (and thus calls to the optimizer) is directly proportional to the number of Pareto optimal designs. We demonstrate PEPFR with three protein engineering case studies: site-directed recombination for stability and diversity via dynamic programming, site-directed mutagenesis of interacting proteins for affinity and specificity via integer programming, and site-directed mutagenesis of a therapeutic protein for activity and immunogenicity via integer programming. We show that PEPFR is able to effectively produce all the Pareto optimal designs, discovering many more designs than previous methods. The characterization of the Pareto frontier provides additional insights into the local stability of design choices as well as global trends leading to trade-offs between competing criteria.

Antibody humanization by structure-based computational protein design

“…The humanization algorithm identifies the Pareto optimal protein designs, 72 i.e., those making the best trade-offs between the 2 competing objectives of HSC score and rotamer-based energy. The algorithm follows a "sweep" approach analogous to that previously developed for enzyme deimmunization.…”

Structure-Guided Deimmunization of Therapeutic Proteins

“…It significantly extends structurebased protein design by accounting for the complementary goal of immunogenicity. It likewise significantly extends our previous work on Pareto optimization for protein engineering in general (Zheng et al, 2009, He et al, 2012 and for deimmunization in particular, which assessed effects on structure and function only according to a sequence potential (Parker et al, 2010;Parker et al, 2011a, Parker et al, 2011b. Inspired by an approach for optimization of stability and specificity of interacting proteins (Grigoryan et al, 2009), we employ a sweep algorithm that minimizes the energy of the design target at decreasing predicted epitope scores.…”

Searching for the Pareto frontier in multi-objective protein design

“…Thus, several groups have developed algorithms for identifying the Pareto frontier in protein design problems. Bailey-Kellogg and colleagues developed PEPFR (Protein Engineering Pareto Frontier), which uses dynamic programming to implement an efficient divideand-conquer approach, and applied it to design problems in therapeutic protein deimmunization, characterizing interacting sets of bZIP helical oligomers and optimizing site-directed recombination protocols for generating diverse libraries that maintain stability and activity (He et al 2012;Salvat et al 2015). Pareto refinement methods have also been computed stability E target target state E gap competing states Fig.…”