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

  • Wei Zheng
  • Alan M. Friedman
  • Chris Bailey-Kellogg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4955)

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Voigt, C., Martinez, C., Wang, Z., Mayo, S., Arnold, F.: Protein building blocks preserved by recombination. Nat. Struct. Biol. 9(7), 553–558 (2002)Google Scholar
  2. 2.
    Meyer, M., Silberg, J., Voigt, C., Endelman, J., Mayo, S., Wang, Z., Arnold, F.: Library analysis of SCHEMA-guided protein recombination. Protein Sci. 12, 1686–1693 (2003)CrossRefGoogle Scholar
  3. 3.
    Otey, C., Landwehr, M., Endelman, J., Hiraga, K., Bloom, J., Arnold, F.: Structure-guided recombination creates an artificial family of cytochromes P450. PLoS Biol. 4(5), e112 (2006)Google Scholar
  4. 4.
    Saftalov, L., Smith, P., Friedman, A., Bailey-Kellogg, C.: Site-directed combinatorial construction of chimaeric genes: general method for optimizing assembly of gene fragments. Proteins 64(3), 629–642 (2006)CrossRefGoogle Scholar
  5. 5.
    Stemmer, W.: Rapid evolution of a protein in vitro by DNA shuffling. Nature 370(6488), 389–391 (1994)CrossRefGoogle Scholar
  6. 6.
    Aguinaldo, A., Arnold, F.: Staggered extension process (StEP) in vitro recombination. Methods Mol. Biol. 231, 105–110 (2003)Google Scholar
  7. 7.
    Coco, W.: RACHITT: Gene family shuffling by random chimeragenesis on transient templates. Methods Mol. Biol. 231, 111–127 (2003)Google Scholar
  8. 8.
    Endelman, J., Silberg, J., Wang, Z., Arnold, F.: Site-directed protein recombination as a shortest-path problem. Protein Eng. Des. Sel. 17, 589–594 (2004)CrossRefGoogle Scholar
  9. 9.
    Ye, X., Friedman, A., Bailey-Kellogg, C.: Hypergraph model of multi-residue interactions in proteins: sequentially-constrained partitioning algorithms for optimization of site-directed protein recombination. In: Apostolico, A., Guerra, C., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2006. LNCS (LNBI), vol. 3909, pp. 777–790. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Zheng, W., Ye, X., Friedman, A., Bailey-Kellogg, C.: Algorithms for selecting breakpoint locations to optimize diversity in protein engineering by site-directed protein recombination. In: Proc. CSB, pp. 31–40 (2007)Google Scholar
  11. 11.
    Meyer, M., Hochrein, L., Arnold, F.: Structure-guided SCHEMA recombination of distantly related beta-lactamases. Protein Engineering, Design & Selection 19, 563–570 (2006)CrossRefGoogle Scholar
  12. 12.
    Landwehr, M., Carbone, M., Otey, C., Li, Y., Arnold, F.: Diversification of catalytic function in a synthetic family of chimeric cytochrome P450s. Chemistry & Biology 14, 269–278 (2007)CrossRefGoogle Scholar
  13. 13.
    Moore, G., Maranas, C.: Identifying residue-residue clashes in protein hybrids by using a second-order mean-field approach. PNAS 100(9), 5091–5096 (2003)CrossRefGoogle Scholar
  14. 14.
    Otey, C., Silberg, J., Voigt, C., Endelman, J., Bandara, G., Arnold, F.: Functional evolution and structural conservation in chimeric cytochromes P450: calibrating a structure-guided approach. Chem. Biol. 11(3), 309–318 (2004)CrossRefGoogle Scholar
  15. 15.
    Saraf, M.C., Gupta, A., Maranas, C.: Design of combinatorial protein libraries of optimal size. Proteins 60(4), 769–777 (2005)CrossRefGoogle Scholar
  16. 16.
    Carter Jr., C., LeFebvre, B., Cammer, S., Tropsha, A., Edgell, M.: Four-body potentials reveal protein-specific correlations to stability changes caused by hydrophobic core mutations. J. Mol. Biol. 311, 621–638 (2001)Google Scholar
  17. 17.
    Krishnamoorthy, B., Tropsha, A.: Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations. Bioinformatics 19, 1540–1548 (2003)CrossRefGoogle Scholar
  18. 18.
    Thomas, J., Ramakrishnan, N., Bailey-Kellogg, C.: Graphical models of residue coupling in protein families. IEEE/ACM Transactions on Computational Biology and Bioinformatics (in press, 2007) (Preprint), http://www.cs.dartmouth.edu/~cbk/papers/tcbb07.pdf
  19. 19.
    Zaccolo, M., Gherardi, E.: The effect of high-frequency random mutagenesis on in vitro protein evolution: a study on TEM-1 beta-lactamase. J. Mol. Biol. 285, 775–783 (1999)CrossRefGoogle Scholar
  20. 20.
    Daugherty, P., Chen, G., Iverson, B., Georgiou, G.: Quantitative analysis of the effect of the mutation frequency on the affinity maturation of single chain Fv antibodies. PNAS 97, 2029–2034 (2000)CrossRefGoogle Scholar
  21. 21.
    Eisner, M., Severance, D.: Mathematical techniques for efficient record segmentation in large shared databases. Journal of the ACM 23, 619–635 (1976)CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Waterman, M.S., Eggert, M., Lander, E.: Parametric sequence comparisons. Proc. Natl. Acad. Sci. USA 89, 6090–6093 (1992)CrossRefGoogle Scholar
  23. 23.
    Gusfield, D., Balasubramanian, K., Naor, D.: Parametric optimization of sequence alignment. Algorithmica 12, 312–326 (1994)CrossRefMathSciNetMATHGoogle Scholar
  24. 24.
    Gusfield, D.: Parametric combinatorial computing and a problem of program module distribution. Journal of the ACM 30, 551–563 (1983)CrossRefMathSciNetMATHGoogle Scholar
  25. 25.
    Bykat, A.: Convex hull of a finite set of points in two dimensions. Info. Proc. Letters 7, 296–298 (1978)CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    Firestine, S., Poon, S., Mueller, E., Stubbe, J., Davisson, V.: Reactions catalyzed by 5-aminoimidazole ribonucleotide carboxylases from Escherichia coli and Gallus gallus: a case for divergent catalytic mechanisms. Biochemistry 33, 11927–11934 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Wei Zheng
    • 1
  • Alan M. Friedman
    • 2
  • Chris Bailey-Kellogg
    • 1
  1. 1.Department of Computer ScienceDartmouth College, 6211 Sudikoff LaboratoryHanoverUSA
  2. 2.Department of Biological Sciences and Purdue Cancer CenterPurdue UniversityWest LafayetteUSA

Personalised recommendations