Computational Protein Design Using AND/OR Branch-and-Bound Search

  • Yichao Zhou
  • Yuexin Wu
  • Jianyang ZengEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9029)


The computation of the global minimum energy conformation (GMEC) is an important and challenging topic in structure-based computational protein design. In this paper, we propose a new protein design algorithm based on the AND/OR branch-and-bound (AOBB) search, which is a variant of the traditional branch-and-bound search algorithm, to solve this combinatorial optimization problem. By integrating with a powerful heuristic function, AOBB is able to fully exploit the graph structure of the underlying residue interaction network of a backbone template to significantly accelerate the design process. Tests on real protein data show that our new protein design algorithm is able to solve many problems that were previously unsolvable by the traditional exact search algorithms, and for the problems that can be solved with traditional provable algorithms, our new method can provide a large speedup by several orders of magnitude while still guaranteeing to find the global minimum energy conformation (GMEC) solution.


Protein design AND/OR branch-and-bound Global minimum energy conformation Residue interaction network Mini-bucket heuristic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Althaus, E., Kohlbacher, O., Lenhof, H.-P., Müller, P.: A combinatorial approach to protein docking with flexible side chains. Journal of Computational Biology 9(4), 597–612 (2002)CrossRefGoogle Scholar
  2. 2.
    Chen, C.-Y., Georgiev, I., Anderson, A.C., Donald, B.R.: Computational structure-based redesign of enzyme activity. Proceedings of the National Academy of Sciences 106(10), 3764–3769 (2009)CrossRefGoogle Scholar
  3. 3.
    Allouche, J.D.D., de Givry, G.K.S., Schiex, I.A.T., Barbe, S.T.S., Prestwich, B.O.S.: Computational protein design as an optimization problem. Artificial Intelligence 212, 59–79 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Dechter, R.: Bucket elimination: a unifying framework for probabilistic inference. In: Learning in Graphical Models, pp. 75–104. Springer (1998)Google Scholar
  5. 5.
    Dechter, R., Rish, I.: Mini-buckets: A general scheme for bounded inference. Journal of the ACM (JACM) 50(2), 107–153 (2003)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Desmet, J., Maeyer, M.D., Hazes, B., Lasters, I.: The dead-end elimination theorem and its use in protein side-chain positioning. Nature 356(6369), 539–542 (1992)CrossRefGoogle Scholar
  7. 7.
    Donald, B.R.: Algorithms in structural molecular biology. The MIT Press (2011)Google Scholar
  8. 8.
    Freuder, E.C., Quinn, M.J.: Taking advantage of stable sets of variables in constraint satisfaction problems. In: International Joint Conference on Artificial Intelligence, vol. 85, pp. 1076–1078 (1985)Google Scholar
  9. 9.
    Frey, K.M., Georgiev, I., Donald, B.R., Anderson, A.C.: Predicting resistance mutations using protein design algorithms. Proceedings of the National Academy of Sciences 107(31), 13707–13712 (2010)CrossRefGoogle Scholar
  10. 10.
    Gainza, P., Roberts, K.E., Donald, B.R.: Protein design using continuous rotamers. PLoS Computational Biology 8(1), e1002335 (2012)CrossRefGoogle Scholar
  11. 11.
    Globerson, A., Jaakkola, T.S.: Fixing max-product: convergent message passing algorithms for MAP LP-relaxations. In: Advances in Neural Information Processing Systems, pp. 553–560 (2008)Google Scholar
  12. 12.
    Goldstein, R.F.: Efficient rotamer elimination applied to protein side-chains and related spin glasses. Biophysical Journal 66(5), 1335–1340 (1994)CrossRefGoogle Scholar
  13. 13.
    Gorczynski, M.J., Grembecka, J., Zhou, Y., Kong, Y., Roudaia, L., Douvas, M.G., Newman, M., Bielnicka, I., Baber, G., Corpora, T., et al.: Allosteric inhibition of the protein-protein interaction between the leukemia-associated proteins Runx1 and CBF\(\beta \). Chemistry & Biology 14(10), 1186–1197 (2007)CrossRefGoogle Scholar
  14. 14.
    Hong, E.-J., Lozano-Pérez, T.: Protein side-chain placement through MAP estimation and problem-size reduction. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 219–230. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  15. 15.
    Ihler, A.T., Flerova, N., Dechter, R., Otten, L.: Join-graph based cost-shifting schemes. arXiv preprint arXiv:1210.4878 (2012)
  16. 16.
    Kask, K., Dechter, R.: A general scheme for automatic generation of search heuristics from specification dependencies. Artificial Intelligence 129(1), 91–131 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Keedy, D.A., Chen, C.-Y., Rezam, F., Andersonl, A.C.: OSPREY: Protein design with ensembles, flexibility, and provable algorithms. Methods in Protein Design, 87 (2013)Google Scholar
  18. 18.
    Kingsford, C.L., Chazelle, B., Singh, M.: Solving and analyzing side-chain positioning problems using linear and integer programming. Bioinformatics 21(7), 1028–1039 (2005)CrossRefGoogle Scholar
  19. 19.
    Korkegian, A., Black, M.E., Baker, D., Stoddard, B.L.: Computational thermostabilization of an enzyme. Science 308(5723), 857–860 (2005)CrossRefGoogle Scholar
  20. 20.
    Kuhlman, B., Baker, D.: Native protein sequences are close to optimal for their structures. Proceedings of the National Academy of Sciences 97(19), 10383–10388 (2000)CrossRefGoogle Scholar
  21. 21.
    Leach, A.R., Lemon, A.P., et al.: Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm. Proteins Structure Function and Genetics 33(2), 227–239 (1998)CrossRefGoogle Scholar
  22. 22.
    Lippow, S.M., Tidor, B.: Progress in computational protein design. Current Opinion in Biotechnology 18(4), 305–311 (2007)CrossRefGoogle Scholar
  23. 23.
    Marinescu, R., Dechter, R.: AND/OR branch-and-bound search for combinatorial optimization in graphical models. Artificial Intelligence 173(16), 1457–1491 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Marvin, J.S., Hellinga, H.W.: Conversion of a maltose receptor into a zinc biosensor by computational design. Proceedings of the National Academy of Sciences 98(9), 4955–4960 (2001)CrossRefGoogle Scholar
  25. 25.
    Otten, L., Dechter, R.: Anytime and/or depth-first search for combinatorial optimization. AI Communications 25(3), 211–227 (2012)zbMATHMathSciNetGoogle Scholar
  26. 26.
    Otten, L., Ihler, A., Kask, K., Dechter, R.: Winning the PASCAL 2011 MAP challenge with enhanced AND/OR branch-and-bound. In: DISCML (2012)Google Scholar
  27. 27.
    Pierce, N.A., Winfree, E.: Protein design is NP-hard. Protein Engineering 15(10), 779–782 (2002)CrossRefGoogle Scholar
  28. 28.
    Roberts, K.E., Cushing, P.R., Boisguerin, P., Madden, D.R., Donald, B.R.: Computational design of a PDZ domain peptide inhibitor that rescues CFTR activity. PLoS Computational Biology 8(4), e1002477 (2012)CrossRefGoogle Scholar
  29. 29.
    Robertson, N., Seymour, P.D.: Algorithmic aspects of tree-width. Journal of Algorithms 7(3), 309–322 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Street, A.G., Mayo, S.L.: Computational protein design. Structure 7(5), R105–R109 (1999)CrossRefGoogle Scholar
  31. 31.
    Traoré, S., Allouche, D., André, I., de Givry, S., Katsirelos, G., Schiex, T., Barbe, S.: A new framework for computational protein design through cost function network optimization. Bioinformatics 29(17), 2129–2136 (2013)CrossRefGoogle Scholar
  32. 32.
    Xu, J., Berger, B.: Fast and accurate algorithms for protein side-chain packing. Journal of the ACM (JACM) 53(4), 533–557 (2006)CrossRefMathSciNetGoogle Scholar
  33. 33.
    Zhou, Y., Wu, Y., Zeng, J.: Appendix of “computational protein design using AND/OR branch-and-bound search” (2015).
  34. 34.
    Zhou, Y., Xu, W., Donald, B.R., Zeng, J.: An efficient parallel algorithm for accelerating computational protein design. Bioinformatics 30(12), i255–i263 (2014)CrossRefGoogle Scholar
  35. 35.
    Zhou, Y., Zeng, J.: Massively parallel A* search on a GPU. In: Proceedings of the National Conference on Artificial Intelligence (2015)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.MOE Key Laboratory of BioinformaticsTsinghua UniversityBeijingPeople’s Republic of China

Personalised recommendations