LUTE (Local Unpruned Tuple Expansion): Accurate Continuously Flexible Protein Design with General Energy Functions and Rigid-rotamer-like Efficiency

  • Mark A. Hallen
  • Jonathan D. Jou
  • Bruce R. Donald
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9649)


Most protein design algorithms search over discrete conformations and an energy function that is residue-pairwise, i.e., a sum of terms that depend on the sequence and conformation of at most two residues. Although modeling of continuous flexibility and of non-residue-pairwise energies significantly increases the accuracy of protein design, previous methods to model these phenomena add a significant asymptotic cost to design calculations. We now remove this cost by modeling continuous flexibility and non-residue-pairwise energies in a form suitable for direct input to highly efficient, discrete combinatorial optimization algorithms like DEE/A* or Branch-Width Minimization. Our novel algorithm performs a local unpruned tuple expansion (LUTE), which can efficiently represent both continuous flexibility and general, possibly non-pairwise energy functions to an arbitrary level of accuracy using a discrete energy matrix. We show using 47 design calculation test cases that LUTE provides a dramatic speedup in both single-state and multistate continuously flexible designs.


Energy Function Protein Design Energy Landscape Conformational Space Energy Matrix 
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.



We would like to thank Drs. Kyle Roberts and Pablo Gainza for providing PDB files and scripts for testing; all members of the Donald lab for helpful comments; and the PhRMA and Dolores Zohrab Liebmann foundations (MAH) and NIH (grant R01-GM-78031 to BRD) for funding.

Supplementary material

420109_1_En_9_MOESM1_ESM.pdf (4.5 mb)
Supplementary material 1 (pdf 4588 KB)


  1. 1.
    Chazelle, B., Kingsford, C., Singh, M.: A semidefinite programming approach to side chain positioning with new rounding strategies. INFORMS J. Comput. Comput. Biol. 16(4), 380–392 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Chen, C.-Y., Georgiev, I., Anderson, A.C., Donald, B.R.: Computational structure-based redesign of enzyme activity. Proc. Nat. Acad. Sci. U.S.A. 106(10), 3764–3769 (2009)CrossRefGoogle Scholar
  3. 3.
    Čížek, J.: On the use of the cluster expansion and the technique of diagrams in calculations of correlation effects in atoms and molecules. In: Correlation Effects in Atoms and Molecules. Advances in Chemical Physics, vol. 14, pp. 35–90. Wiley (2009)Google Scholar
  4. 4.
    Desmet, J., de Maeyer, M., Hazes, B., Lasters, I.: The dead-end elimination theorem and its use in protein side-chain positioning. Nature 356, 539–542 (1992)CrossRefGoogle Scholar
  5. 5.
    Donald, B.R.: Algorithms in Structural Molecular Biology. MIT Press, Cambridge (2011)Google Scholar
  6. 6.
    Flocke, N., Bartlett, R.J.: A natural linear-scaling coupled-cluster method. J. Chem. Phys. 121(22), 10935–10944 (2004)CrossRefGoogle Scholar
  7. 7.
    Floudas, C.A., Klepeis, J.L., Pardalos. P.M.: Global optimization approaches in protein folding and peptide docking. In: Mathematical Support for Molecular Biology. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 47, pp. 141–172. American Mathematical Society (1999)Google Scholar
  8. 8.
    Frey, K.M., Georgiev, I., Donald, B.R., Anderson, A.C.: Predicting resistance mutations using protein design algorithms. Proc. Nat. Acad. Sci. U.S.A. 107(31), 13707–13712 (2010)CrossRefGoogle Scholar
  9. 9.
    Gainza, P., Roberts, K., Donald, B.R.: Protein design using continuous rotamers. PLoS Comput. Biol. 8(1), e1002335 (2012)CrossRefGoogle Scholar
  10. 10.
    Gainza, P., Roberts, K.E., Georgiev, I., Lilien, R.H., Keedy, D.A., Chen, C.-Y., Reza, F., Richardson, D.C., Richardson, J.S., Donald, B.R.: osprey: protein design with ensembles, flexibility, and provable algorithms. Methods Enzymol. 523, 87–107 (2013)CrossRefGoogle Scholar
  11. 11.
    Georgiev, I., Acharya, P., Schmidt, S., Li, Y., Wycuff, D., Ofek, G., Doria-Rose, N., Luongo, T., Yang, Y., Zhou, T., Donald, B.R., Mascola, J., Kwong, P.: Design of epitope-specific probes for sera analysis and antibody isolation. Retrovirology 9(Suppl. 2), P50 (2012)CrossRefGoogle Scholar
  12. 12.
    Georgiev, I., Donald, B.R.: Dead-end elimination with backbone flexibility. Bioinformatics 23(13), i185–i194 (2007)CrossRefGoogle Scholar
  13. 13.
    Georgiev, I., Lilien, R.H., Donald, B.R.: The minimized dead-end elimination criterion and its application to protein redesign in a hybrid scoring and search algorithm for computing partition functions over molecular ensembles. J. Comput. Chem. 29(10), 1527–1542 (2008)CrossRefzbMATHGoogle Scholar
  14. 14.
    Georgiev, I., Roberts, K.E., Gainza, P., Hallen, M.A., Donald, B.R.: osprey (\(\underline{\rm O}\)pen \(\underline{\rm S}\)ource \(\underline{\rm P}\)rotein \(\underline{\rm R}\)edesign for \(\underline{\rm Y}\)ou) user manual, p. 94 (2009).
  15. 15.
    Georgiev, I.S., Rudicell, R.S., Saunders, K.O., Shi, W., Kirys, T., McKee, K., O’Dell, S., Chuang, G.-Y., Yang, Z.-Y., Ofek, G., Connors, M., Mascola, J.R., Nabel, G.J., Kwong, P.D.: Antibodies VRC01 and 10E8 neutralize HIV-1 with high breadth and potency even with Ig-framework regions substantially reverted to germline. J. Immunol. 192(3), 1100–1106 (2014)CrossRefGoogle Scholar
  16. 16.
    Gorczynski, M.J., Grembecka, J., Zhou, Y., Kong, Y., Roudaia, L., Douvas, M.G., Newman, M., Bielnicka, I., Baber, G., Corpora, T., Shi, J., Sridharan, M., Lilien, R., Donald, B.R., Speck, N.A., Brown, M.L., Bushweller, J.H.: Allosteric inhibition of the protein-protein interaction between the leukemia-associated proteins Runx1 and CBF\(\beta \). Chem. Biol. 14, 1186–1197 (2007)CrossRefGoogle Scholar
  17. 17.
    Grigoryan, G., Reinke, A.W., Keating, A.E.: Design of protein-interaction specificity affords selective bZIP-binding peptides. Nature 458(7240), 859–864 (2009)CrossRefGoogle Scholar
  18. 18.
    Grigoryan, G., Zhou, F., Lustig, S.R., Ceder, G., Morgan, D., Keating, A.E.: Ultra-fast evaluation of protein energies directly from sequence. PLoS Comput. Biol. 2(6), e63 (2006)CrossRefGoogle Scholar
  19. 19.
    Hallen, M.A., Donald, B.R.: comets (Constrained Optimization of Multistate Energies by Tree Search): a provable and efficient algorithm to optimize binding affinity and specificity with respect to sequence. In: Przytycka, T.M. (ed.) RECOMB 2015. LNCS, vol. 9029, pp. 122–135. Springer, Heidelberg (2015)Google Scholar
  20. 20.
    Hallen, M.A., Gainza, P., Donald, B.R.: A compact representation of continuous energy surfaces for more efficient protein design. J. Chem. Theory Comput. 11(5), 2292–2306 (2015)CrossRefGoogle Scholar
  21. 21.
    Hallen, M.A., Keedy, D.A., Donald, B.R.: Dead-end elimination with perturbations (DEEPer): a provable protein design algorithm with continuous sidechain and backbone flexibility. Proteins: Struct., Funct., Bioinf. 81(1), 18–39 (2013)CrossRefGoogle Scholar
  22. 22.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)CrossRefGoogle Scholar
  23. 23.
    Janin, J., Wodak, S., Levitt, M., Maigret, B.: Conformation of amino acid side-chains in proteins. J. Mol. Biol. 125(3), 357–386 (1978)CrossRefGoogle Scholar
  24. 24.
    Jou, J.D., Jain, S., Georgiev, I.S., Donald, B.R.: BWM*: a novel, provable, ensemble-based dynamic programming algorithm for sparse approximations of computational protein design. J. Comput. Biol., 8 January 2016Google Scholar
  25. 25.
    Karanicolas, J., Kuhlman, B.: Computational design of affinity and specificity at protein-protein interfaces. Curr. Opin. Struct. Biol. 19(4), 458–463 (2009)CrossRefGoogle Scholar
  26. 26.
    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
  27. 27.
    Kuhlman, B., Baker, D.: Native protein sequences are close to optimal for their structures. Proc. Nat. Acad. Sci. U.S.A. 97(19), 10383–10388 (2000)CrossRefGoogle Scholar
  28. 28.
    Lazaridis, T., Karplus, M.: Effective energy function for proteins in solution. Proteins: Struct., Funct., Bioinf. 35(2), 133–152 (1999)CrossRefGoogle Scholar
  29. 29.
    Leach, A.R., Lemon, A.P.: Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm. Proteins: Struct., Funct., Bioinf. 33(2), 227–239 (1998)CrossRefGoogle Scholar
  30. 30.
    Leaver-Fay, A., Jacak, R., Stranges, P.B., Kuhlman, B.: A generic program for multistate protein design. PLoS One 6(7), e20937 (2011)CrossRefGoogle Scholar
  31. 31.
    Lee, C., Levitt, M.: Accurate prediction of the stability and activity effects of site-directed mutagenesis on a protein core. Nature 352, 448–451 (1991)CrossRefGoogle Scholar
  32. 32.
    Lilien, R.H., Stevens, B.W., Anderson, A.C., Donald, B.R.: A novel ensemble-based scoring and search algorithm for protein redesign and its application to modify the substrate specificity of the gramicidin synthetase A phenylalanine adenylation enzyme. J. Comput. Biol. 12(6), 740–761 (2005)CrossRefGoogle Scholar
  33. 33.
    LuCore, S.D., Litman, J.M., Powers, K.T., Gao, S., Lynn, A.M., Tollefson, W.T.A., Fenn, T.D., Washington, M.T., Schnieders, M.J.: Dead-end elimination with a polarizable force field repacks PCNA structures. Biophys. J. 109(4), 816–826 (2015)CrossRefGoogle Scholar
  34. 34.
    Nicholls, A., Honig, B.: A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation. J. Comput. Chem. 12(4), 435–445 (1991)CrossRefGoogle Scholar
  35. 35.
    Pierce, N.A., Winfree, E.: Protein design is NP-hard. Protein Eng. 15(10), 779–782 (2002)CrossRefGoogle Scholar
  36. 36.
    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 Comput. Biol. 8(4), e1002477 (2012)CrossRefGoogle Scholar
  37. 37.
    Roberts, K.E., Gainza, P., Hallen, M.A., Donald, B.R.: Fast gap-free enumeration of conformations and sequences for protein design. Proteins: Struct., Funct., Bioinf. 83(10), 1859–1877 (2015)CrossRefGoogle Scholar
  38. 38.
    Rochia, W., Sridharan, S., Nicholls, A., Alexov, E., Chiabrera, A., Honig, B.: Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: applications to the molecular systems and geometric objects. J. Comput. Chem. 23(1), 128–137 (2002)CrossRefGoogle Scholar
  39. 39.
    Rosenzweig, A.C., Huffman, D.L., Hou, M.Y., Wernimont, A.K., Pufahl, R.A., O’Halloran, T.V.: Crystal structure of the Atx1 metallochaperone protein at 1.02 Å resolution. Structure 7(6), 605–617 (1999)CrossRefGoogle Scholar
  40. 40.
    Rudicell, R.S., Kwon, Y.D., Ko, S.-Y., Pegu, A., Louder, M.K., Georgiev, I.S., Wu, X., Zhu, J., Boyington, J.C., Chen, S., Shi, W., Yang, Z.-Y., Doria-Rose, N.A., McKee, K., O’Dell, S., Schmidt, S.D., Chuang, G.-Y., Druz, A., Soto, C., Yang, Y., Zhang, B., Zhou, T., Todd, J.-P., Lloyd, K.E., Eudailey, J., Roberts, K.E., Donald, B.R., Bailer, R.T., Ledgerwood, J., NISC Comparative Sequencing Program, Mullikin, J.C., Shapiro, L., Koup, R.A., Graham, B.S., Nason, M.C., Connors, M., Haynes, B.F., Rao, S.S., Roederer, M., Kwong, P.D., Mascola, J.R., Nabel, G.J.: Enhanced potency of a broadly neutralizing HIV-1 antibody in vitro improves protection against lentiviral infection in vivo. J. Virol. 88(21), 12669–12682 (2014)Google Scholar
  41. 41.
    Simoncini, D., Allouche, D., de Givry, S., Delmas, C., Barbe, S., Schiex, T.: Guaranteed discrete energy optimization on large protein design problems. J. Chem. Theory Comput. 11(12), 5980–5989 (2015)CrossRefGoogle Scholar
  42. 42.
    Sitkoff, D., Sharp, K.A., Honig, B.: Accurate calculation of hydration free energies using macroscopic solvent models. J. Phys. Chem. 98, 1978–1988 (1994)CrossRefGoogle Scholar
  43. 43.
    Stevens, B.W., Lilien, R.H., Georgiev, I., Donald, B.R., Anderson, A.C.: Redesigning the PheA domain of gramicidin synthetase leads to a new understanding of the enzyme’s mechanism and selectivity. Biochemistry 45(51), 15495–15504 (2006)CrossRefGoogle Scholar
  44. 44.
    Tan, X., Calderón-Villalobos, L.I.A., Sharon, M., Zheng, C., Robinson, C.V., Estelle, M., Zheng, N.: Mechanism of auxin perception by the TIR1 ubiquitin ligase. Nature 446, 640–645 (2007)CrossRefGoogle Scholar
  45. 45.
    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
  46. 46.
    Traoré, S., Roberts, K.E., Allouche, D., Donald, B.R., André, I., Schiex, T., Barbe, S.: Fast search algorithms for computational protein design. J. Comput. Chem. (2016)Google Scholar
  47. 47.
    Vizcarra, C.L., Zhang, N., Marshall, S.A., Wingreen, N.S., Zeng, C., Mayo, S.L.: An improved pairwise decomposable finite-difference Poisson-Boltzmann method for computational protein design. J. Comput. Chem. 29(7), 1153–1162 (2008)CrossRefGoogle Scholar
  48. 48.
    Jinbo, X., Berger, B.: Fast and accurate algorithms for protein side-chain packing. J. ACM 53(4), 533–557 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  49. 49.
    Zhang, D.W., Zhang, J.Z.H.: Molecular fractionation with conjugate caps for full quantum mechanical calculation of protein-molecule interaction energy. J. Chem. Phys. 119(7), 3599–3605 (2003)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mark A. Hallen
    • 1
  • Jonathan D. Jou
    • 1
  • Bruce R. Donald
    • 1
    • 2
    • 3
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA
  2. 2.Department of ChemistryDuke UniversityDurhamUSA
  3. 3.Department of BiochemistryDuke University Medical CenterDurhamUSA

Personalised recommendations