Algorithms for Joint Optimization of Stability and Diversity in Planning Combinatorial Libraries of Chimeric Proteins

Abstract

Abstract. In engineering protein variants by constructing and screening combinatorial libraries of chimeric proteins, two complementary and competing goals are desired: the new proteins must be similar enough to the evolutionarily-selected wild-type proteins to be stably folded, and they must be different enough to display functional variation. We present here the first method, Staversity, to simultaneously optimize stability and diversity in selecting sets of breakpoint locations for site-directed recombination. Our goal is to uncover all "undominated" breakpoint sets, for which no other breakpoint set is better in both factors. Our first algorithm finds the undominated sets serving as the vertices of the lower envelope of the two-dimensional (stability and diversity) convex hull containing all possible breakpoint sets. Our second algorithm identifies additional breakpoint sets in the concavities that are either undominated or dominated only by undiscovered breakpoint sets within a distance bound computed by the algorithm. Both algorithms are efficient, requiring only time polynomial in the numbers of residues and breakpoints, while characterizing a space defined by an exponential number of possible breakpoint sets. We applied Staversity to identify 2-10 breakpoint sets for three different sets of parent proteins from the purE family of biosynthetic enzymes. The average normalized distance between our plans and the lower bound for optimal plans is around 1 percent. Our plans dominate most (60-90% on average for each parent set) of the plans found by other possible approaches, random sampling or explicit optimization for stability with implicit optimization for diversity. The identified breakpoint sets provide a compact representation of good plans, enabling a protein engineer to understand and account for the trade-offs between two key considerations in combinatorial chimeragenesis.

Algorithms for optimizing cross-overs in DNA shuffling

“…We have previously developed methods for optimizing the diversity of libraries of chimeras produced by site-directed recombination [13,14]. We showed that the total number of mutations in a library is a constant determined only by the parents, but that by assessing the squared-differences in the numbers, we can optimize for a relatively uniform sampling of sequence space.…”

“…In contrast with stochastic methods, site-directed methods enable the engineer to explicitly choose break-point locations so as to optimize expected library quality (e.g., by employing structural information [10], or by minimizing predicted disruption [11,12], library diversity [13], or both factors [14]). We have developed a site-directed method employing planned ligation of parental fragments by short overhangs [15].…”

Directed evolution of cytochrome P450 enzymes for biocatalysis: exploiting the catalytic versatility of enzymes with relaxed substrate specificity

“…Algorithms to calculate mutations and recombinations that maintain structural integrity and reduce the frequency of nonfunctional mutants are facilitating the construction of smaller targeted libraries, enriched in catalytically active proteins, that can be screened readily using biochemical and biophysical assays [68][69][70]. In particular, the SCHEMA algorithm [68] has yielded a number of practical successes.…”

Optimization of Combinatorial Mutagenesis

“…Computational design of combinatorial libraries (Voigt et al, 2002, Meyer et al, 2003, Pantazes et al, 2007, Treynor et al, 2007, Zheng et al, 2009 provides a middle ground between the primarily experimental and primarily computational approaches to development of improved variants. Library-design strategies seek to experimentally evaluate a diverse but focused region of sequence space in order to improve the likelihood of finding a beneficial variant.…”

“…1). Most library optimization work has focused on recombination (i.e., selecting breakpoints), including approaches by Arnold and co-workers (Voigt et al, 2002, Otey et al, 2004, Meyer et al, 2006, Otey et al, 2006, Maranas and co-workers (Moore and Maranas, 2003, Saraf et al, 2004, Saraf et al, 2005, and us (Ye et al, 2007, Zheng et al, 2007, Zheng et al, 2009. Mayo and co-workers (Treynor et al, 2007) have extended structure-based variant design to structure-based mutagenic library design, and applied it to the design of a library of green fluorescent proteins.…”