\(BBK^*\) (Branch and Bound over \(K^*\)): A Provable and Efficient Ensemble-Based Algorithm to Optimize Stability and Binding Affinity over Large Sequence Spaces

  • Adegoke A. Ojewole
  • Jonathan D. Jou
  • Vance G. Fowler
  • Bruce R. Donald
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10229)

Abstract

Protein design algorithms that compute binding affinity search for sequences with an energetically favorable free energy of binding. Recent work shows that the following design principles improve the biological accuracy of protein design: ensemble-based design and continuous conformational flexibility. Ensemble-based algorithms capture a measure of entropic contributions to binding affinity, \(K_a\). Designs using backbone flexibility and continuous side-chain flexibility better model conformational flexibility. A third design principle, provable guarantees of accuracy, ensures that an algorithm computes the best sequences defined by the input model (i.e. input structures, energy function, and allowed protein flexibility). However, previous provable methods that model ensembles and continuous flexibility are single-sequence algorithms, which are very costly: linear in the number of sequences and thus exponential in the number of mutable residues. To address these computational challenges, we introduce a new protein design algorithm, \(BBK^*\), that retains all aforementioned design principles yet provably and efficiently computes the tightest-binding sequences. A key innovation of \(BBK^*\) is the multi-sequence (MS) bound: \(BBK^*\) efficiently computes a single provable upper bound to approximate \(K_a\) for a combinatorial number of sequences, and entirely avoids single-sequence computation for all provably suboptimal sequences. Thus, to our knowledge, \(BBK^*\) is the first provable, ensemble-based \(K_a\) algorithm to run in time sublinear in the number of sequences. Computational experiments on 204 protein design problems show that \(BBK^*\) finds the tightest binding sequences while approximating \(K_a\) for up to \(10^5\)-fold fewer sequences than exhaustive enumeration. Furthermore, for 51 protein-ligand design problems, \(BBK^*\) provably approximates \(K_a\) up to 1982-fold faster than the previous state-of-the-art iMinDEE/\(A^*\)/\(K^*\) algorithm. Therefore, \(BBK^*\) not only accelerates protein designs that are possible with previous provable algorithms, but also efficiently performs designs that are too large for previous methods.

Keywords

Partition Function Protein Design Sequence Space Mutable Residue Backbone Flexibility 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We thank Drs. Mark Hallen and Pablo Gainza for helpful discussions and for providing useful protein-ligand binding problems; Dr. Jeffrey Martin for software optimizations; Hunter Nisonoff, Anna Lowegard and all members of the Donald lab for helpful discussions; and the NSF (GRFP DGF 1106401 to AAO) and the NIH (R01-GM78031 to BRD, R01-HL119648 to VGF) for funding.

References

  1. 1.
    Boas, F.E., Harbury, P.B.: Curr. Opin. Struct. Biol. 17, 199 (2007)CrossRefGoogle Scholar
  2. 2.
    Carmen, S., Jermutus, L.: Brief Funct. Genomic Proteomic 1, 189 (2002)CrossRefGoogle Scholar
  3. 3.
    Chen, C.-Y., et al.: Proc. Natl. Acad. Sci. USA 106, 3764 (2009)CrossRefGoogle Scholar
  4. 4.
    Desmet, J., et al.: Nature 356, 539 (1992)CrossRefGoogle Scholar
  5. 5.
    Donald, B.R.: Algorithms in Structural Molecular Biology. MIT Press, Cambridge (2011)Google Scholar
  6. 6.
    Fleishman, S.J., et al.: Protein Sci. 20, 753 (2011)CrossRefGoogle Scholar
  7. 7.
    Frey, K.M., et al.: Proc. Natl. Acad. Sci. USA 107, 13707 (2010)CrossRefGoogle Scholar
  8. 8.
    Fromer, M., Yanover, C.: Bioinformatics 24, i214 (2008)CrossRefGoogle Scholar
  9. 9.
    Gainza, P., Nisonoff, H.M., Donald, B.R.: Curr. Opin. Struct. Biol. 39, 16 (2016)CrossRefGoogle Scholar
  10. 10.
    Gainza, P., Roberts, K.E., Donald, B.R.: PLoS Comput. Biol. 8, e1002335 (2012)CrossRefGoogle Scholar
  11. 11.
    Gainza, P., et al.: Methods Enzymol 523, 87 (2013). Program, user manual, and source code are available at www.cs.duke.edu/donaldlab/software.php
  12. 12.
    Georgiev, I., et al.: Retrovirology 9(Suppl. 2), P50 (2012)Google Scholar
  13. 13.
    Georgiev, I., Donald, B.R.: Bioinformatics 23, i185 (2007)CrossRefGoogle Scholar
  14. 14.
    Georgiev, I., Lilien, R.H., Donald, B.R.: Bioinformatics 22, e174 (2006)CrossRefGoogle Scholar
  15. 15.
    Georgiev, I., Lilien, R.H., Donald, B.R.: J. Comput. Chem. 29, 1527 (2008)CrossRefGoogle Scholar
  16. 16.
    Georgiev, I.S.: Novel algorithms for computational protein design, with applications to enzyme redesign and small-molecule inhibitor design. Ph.D. thesis, Duke University (2009). http://hdl.handle.net/10161/1113
  17. 17.
    Georgiev, I.S., et al.: J. Immunol. 192, 1100 (2014)CrossRefGoogle Scholar
  18. 18.
    Gilson, M.K., et al.: Biophys. J. 72, 1047 (1997)CrossRefGoogle Scholar
  19. 19.
    Gorczynski, M.J., et al.: Chem. Biol. 14, 1186 (2007)CrossRefGoogle Scholar
  20. 20.
    Hallen, M.A., Donald, B.R.: J. Comput. Biol. 23, 311 (2016)CrossRefGoogle Scholar
  21. 21.
    Hallen, M.A., Gainza, P., Donald, B.R.: J. Chem. Theory. Comput. 11, 2292 (2015)CrossRefGoogle Scholar
  22. 22.
    Hallen, M.A., Jou, J.D., Donald, B.R.: J. Comput. Biol. Epub ahead of print (2016)Google Scholar
  23. 23.
    Hallen, M.A., Keedy, D.A., Donald, B.R.: Proteins 81, 18 (2013)CrossRefGoogle Scholar
  24. 24.
    Hart, P., Nilsson, N., Raphael, B.: IEEE Trans. SSC 4, 100 (1968)Google Scholar
  25. 25.
    Jou, J.D., et al.: J. Comput. Biol. 23, 413 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Kingsford, C.L., Chazelle, B., Singh, M.: Bioinformatics 21, 1028 (2005)CrossRefGoogle Scholar
  27. 27.
    Kuhlman, B., Baker, D.: Proc. Natl. Acad. Sci. USA 97, 10383 (2000)CrossRefGoogle Scholar
  28. 28.
    Leach, A.R., Lemon, A.P.: Proteins 33, 227 (1998)CrossRefGoogle Scholar
  29. 29.
    Leaver-Fay, A., et al.: Methods Enzymol. 487, 545 (2011)CrossRefGoogle Scholar
  30. 30.
    Lee, C., Levitt, M.: Nature 352, 448 (1991)CrossRefGoogle Scholar
  31. 31.
    Leech, J., Prins, J.F., Hermans, J.: Comput. Sci. Eng. 3, 38 (1996)CrossRefGoogle Scholar
  32. 32.
    Lilien, R.H., et al.: J. Comput. Biol. 12, 740 (2005)CrossRefGoogle Scholar
  33. 33.
    Lovell, S.C., et al.: Proteins 40, 389 (2000)CrossRefGoogle Scholar
  34. 34.
    Lower, S.K., et al.: Proc. Natl. Acad. Sci. USA 108, 18372 (2011)CrossRefGoogle Scholar
  35. 35.
    Nisonoff, H., Thesis, B.S.: Department of Mathematics, Duke University (2015). http://hdl.handle.net/10161/9746
  36. 36.
    Ojewole, A.A., et al.: Supplementary information: BBK* (Branch and Bound over K*): a provable and efficient ensemble-based algorithm to optimize stability and binding affinity over large sequence spaces for sparse approximations of computational protein design (2015). http://www.cs.duke.edu/donaldlab/Supplementary/recomb17/bbkstar
  37. 37.
    Ojewole, A., et al.: Methods Mol. Biol. 1529, 291 (2017)CrossRefGoogle Scholar
  38. 38.
    Pál, G., et al.: J. Biol. Chem. 281, 22378 (2006)CrossRefGoogle Scholar
  39. 39.
    Peng, J., et al.: [q-bio.BM] (2015). arXiv:1504.05467
  40. 40.
    Pierce, N.A., Winfree, E.: Protein Eng 15, 779 (2002)CrossRefGoogle Scholar
  41. 41.
    Reeve, S.M., et al.: Proc. Natl. Acad. Sci. USA 112, 749 (2015)CrossRefGoogle Scholar
  42. 42.
    Roberts, K.E., et al.: PLoS Comput. Biol. 8, e1002477 (2012)CrossRefGoogle Scholar
  43. 43.
    Roberts, K.E., Donald, B.R.: Proteins 83, 1151 (2015)CrossRefGoogle Scholar
  44. 44.
    Roberts, K.E., et al.: Proteins 83, 1859 (2015)CrossRefGoogle Scholar
  45. 45.
    Rudicell, R.S., et al.: J. Virol. 88, 12669 (2014)CrossRefGoogle Scholar
  46. 46.
    Sciretti, D., et al.: Proteins 74, 176 (2009)CrossRefGoogle Scholar
  47. 47.
    Silver, N.W., et al.: J. Chem. Theory Comput. 9, 5098 (2013)CrossRefGoogle Scholar
  48. 48.
    Simoncini, D., et al.: J. Chem. Theory. Comput. 11, 5980 (2015)CrossRefGoogle Scholar
  49. 49.
    Stevens, B.W., et al.: Biochemistry 45, 15495 (2006)CrossRefGoogle Scholar
  50. 50.
    Traoré, S., et al.: Bioinformatics 29, 2129 (2013)CrossRefGoogle Scholar
  51. 51.
    Traoré, S., et al.: J Comput. Chem. 37, 1048 (2016)CrossRefGoogle Scholar
  52. 52.
    Valiant, L.G.: Theoret. Comput. Sci. 8, 189 (1979)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Viricel, C., et al.: The 22nd International Conference on Principles and Practice of Constraint Programming (2016)Google Scholar
  54. 54.
    Wainwright, M.J., Jaakkola, T.S., Willsky, A.S.: CoRR abs/1301.0610 (2013)Google Scholar
  55. 55.
    Xu, J.: 9th Annual International Conference, RECOMB, vol. 3500, p. 423 (2005)Google Scholar
  56. 56.
    Xu, J., Berger, B.: J. ACM 53, 533 (2006)MathSciNetCrossRefGoogle Scholar
  57. 57.
    Zheng, F., et al.: J. Am. Chem. Soc. 130, 12148 (2008)CrossRefGoogle Scholar
  58. 58.
    Zhou, J., Grigoryan, G.: Protein Sci 24, 508 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Adegoke A. Ojewole
    • 1
    • 3
  • Jonathan D. Jou
    • 1
  • Vance G. Fowler
    • 4
  • Bruce R. Donald
    • 1
    • 2
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Department of BiochemistryDuke University Medical CenterDurhamUSA
  3. 3.Computational Biology and Bioinformatics ProgramDuke UniversityDurhamUSA
  4. 4.Division of Infectious DiseasesDuke University Medical CenterDurhamUSA

Personalised recommendations