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Licensed Unlicensed Requires Authentication Published by De Gruyter November 27, 2014

Exact methods for lattice protein models

  • Martin Mann EMAIL logo and Rolf Backofen EMAIL logo

Abstract

Lattice protein models are well-studied abstractions of globular proteins. By discretizing the structure space and simplifying the energy model over regular proteins, they enable detailed studies of protein structure formation and evolution. However, even in the simplest lattice protein models, the prediction of optimal structures is computationally difficult. Therefore, often, heuristic approaches are applied to find such conformations. Commonly, heuristic methods find only locally optimal solutions. Nevertheless, there exist methods that guarantee to predict globally optimal structures. Currently, only one such exact approach is publicly available, namely the constraint-based protein structure prediction method and variants. Here, we review exact approaches and derived methods. We discuss fundamental concepts like hydrophobic core construction and their use in optimal structure prediction, as well as possible applications like combinations of different energy models.


Corresponding authors: Martin Mann, Bioinformatics Group, Department of Computer Science, University of Freiburg, Georges-Köhler-Allee 106, 79110 Freiburg, Germany, E-mail: ; and Rolf Backofen, Bioinformatics Group, Department of Computer Science, University of Freiburg, Freiburg, Germany; Center for Biological Signaling Studies (BIOSS), University of Freiburg, Freiburg, Germany; Center for Biological Systems Analysis (ZBSA), University of Freiburg, Freiburg, Germany; and Center for Non-coding RNA in Technology and Health, University of Copenhagen, Frederiksberg C, Denmark, E-mail:

References

1. Tyers M, Mann M. From genomics to proteomics. Nature 2003;422:193–7.10.1038/nature01510Search in Google Scholar PubMed

2. Anfinsen CB. Principles that govern the folding of protein chains. Science 1973;181:223–30.10.1126/science.181.4096.223Search in Google Scholar PubMed

3. Crippen GM. Prediction of protein folding from amino acid sequence over discrete conformation spaces. Biochemistry 1991;30:4232–7.10.1021/bi00231a018Search in Google Scholar PubMed

4. Jefferys B, Kelley L, Sternberg MJ. Protein folding requires crowd control in a simulated cell. J Mol Biol 2010;397:1329–38.10.1016/j.jmb.2010.01.074Search in Google Scholar PubMed PubMed Central

5. Wittung-Stafshede P. Role of cofactors in protein folding. Acc Chem Res 2002;35:201–8.10.1021/ar010106eSearch in Google Scholar PubMed

6. Ying BW, Taguchi H, Ueda T. Co-translational binding of groel to nascent polypeptides is followed by post-translational encapsulation by GroES to mediate protein folding. J Biol Chem 2006;281:21813–9.10.1074/jbc.M603091200Search in Google Scholar PubMed

7. Clark PL. Protein folding in the cell: reshaping the folding funnel. Trends Biochem Sci 2004;29:527–34.10.1016/j.tibs.2004.08.008Search in Google Scholar PubMed

8. Rose GD, Fleming PJ, Banavar JR, Maritan A. A backbone-based theory of protein folding. Proc Natl Acad Sci USA 2006;103:16623–33.10.1073/pnas.0606843103Search in Google Scholar PubMed PubMed Central

9. Smith A. Protein misfolding. Special Insight issue on protein misfolding edited by A. Smith. Nature 2003;426:883–909.10.1038/426883aSearch in Google Scholar

10. Laurèn J, Gimbel DA, Nygaard HB, Gilbert JW, Strittmatter SM. Cellular prion protein mediates impairment of synaptic plasticity by amyloid-β oligomers. Nature 2009;457:1128–32.10.1038/nature07761Search in Google Scholar PubMed PubMed Central

11. Nunnally BK, Krull IS, editors. Prions and mad cow disease. New York: CRC Press, 2003.10.1201/9780203912973Search in Google Scholar

12. Prusiner SB. Prions. Proc Natl Acad Sci USA 1998;95:13363–83.10.1073/pnas.95.23.13363Search in Google Scholar

13. Scott MD, Frydman J. Aberrant protein folding as the molecular basis of cancer. In: Bross, Peter and Gregersen, Niels, editors. Protein misfolding and disease, vol. 232 of Methods in molecular biology. San Francisco, California: Humana Press, 2003:67–76.Search in Google Scholar

14. Karplus M, Kuriyan J. Molecular dynamics and protein function. Proc Natl Acad Sci USA 2005;102:6679–85.10.1073/pnas.0408930102Search in Google Scholar

15. Angelani L, Ruocco G. Saddles of the energy landscape and folding of model proteins. Europhys Lett 2009;87:18002.10.1209/0295-5075/87/18002Search in Google Scholar

16. Lau KF, Dill KA. A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 1989;22:3986–97.10.1021/ma00200a030Search in Google Scholar

17. Finkelstein AV, Badretdinov AY. Rate of protein folding near the point of thermo-dynamic equilibrium between the coil and the most stable chain fold. Fold Des 1997;2:115–21.10.1016/S1359-0278(97)00016-3Search in Google Scholar

18. Berger B, Leighton T. Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete. J Comp Biol 1998;5:27–40.10.1089/cmb.1998.5.27Search in Google Scholar

19. Crescenzi P, Goldman D, Papadimitriou C, Piccolboni A, Yannakakis M. On the complexity of protein folding. J Comput Biol 1998;5:423–65.10.1089/cmb.1998.5.423Search in Google Scholar

20. Irbäck A, Sandelin E. On hydrophobicity correlations in protein chains. Biophys J 2000;79:2252–8.10.1016/S0006-3495(00)76472-1Search in Google Scholar

21. Ullah AD, Kapsokalivas L, Mann M, Steinhöfel K. Protein folding simulation by two-stage optimization. In: Cai, Zhihua and Li, Zhenhua and Kang, Zhuo and Liu, Yong, editors. Proc. of ISICA’09, vol. 51 of CCIS, Wuhan, China. Heidelberg, Berlin: Springer, 2009:138–45.Search in Google Scholar

22. Ullah AD, Steinhöofel K. A hybrid approach to protein folding problem integrating constraint programming with local search. BMC Bioinform 2010;11:S39.10.1186/1471-2105-11-S1-S39Search in Google Scholar PubMed PubMed Central

23. Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G, Aspuru-Guzik A. Finding low-energy conformations of lattice protein models by quantum annealing. Sci Rep 2012;2:571.10.1038/srep00571Search in Google Scholar PubMed PubMed Central

24. Nardelli M, Tedesco L, Bechini A. Cross-lattice behavior of general ACO folding for proteins in the HP model. In: Proceedings of the 28th annual ACM symposium on applied computing, SAC’13, Coimbra, Portugal. New York, NY, USA: ACM, 2013:1320–7.Search in Google Scholar

25. Tsay J-J, Su S-C. An effective evolutionary algorithm for protein folding on 3D FCC HP model by lattice rotation and generalized move sets. Proteome Sci 2013;11:S19.10.1186/1477-5956-11-S1-S19Search in Google Scholar PubMed PubMed Central

26. Liu J, Song B, Liu Z, Huang W, Sun Y, Liu W. Energy-landscape paving for prediction of face-centered-cubic hydrophobic-hydrophilic lattice model proteins. Phys Rev E 2013;88:052704.10.1103/PhysRevE.88.052704Search in Google Scholar PubMed

27. Dotu I, Cebrián M, van Hentenryck P, Clote P. Protein structure prediction with large neighborhood constraint programming search. In: Proc of CP’08, vol. 5202 of LNCS. Heidelberg, Berlin: Springer, 2008:82–96.Search in Google Scholar

28. Dotu I, Cebrián M, van Hentenryck P, Clote P. On lattice protein structure prediction revisited. IEEE/ACM Trans Comput Biol Bioinform 2011;8:1620–32.10.1109/TCBB.2011.41Search in Google Scholar PubMed

29. Dal Palù A, Dovier A, Fogolari F. Constraint logic programming approach to protein structure prediction. BMC Bioinform 2004;5:186.10.1186/1471-2105-5-186Search in Google Scholar PubMed PubMed Central

30. Dal Palù A, Dovier A, Pontelli E. A constraint solver for discrete lattices, its parallelization, and application to protein structure prediction. Softw Pract Exp 2007;37:1405–49.10.1002/spe.810Search in Google Scholar

31. Dal Palù A, Dovier A, Pontelli E. Computing approximate solutions of the protein structure determination problem using global constraints on discrete crystal lattices. J Data Mining Bioinform 2010;4:1–20.10.1504/IJDMB.2010.030964Search in Google Scholar

32. Citrolo AG, Mauri G. A local landscape mapping method for protein structure prediction in the HP model. Nat Comput 2014;13:309–19.10.1007/s11047-014-9427-8Search in Google Scholar

33. Maher B, Albrecht AA, Loomes M, Yang X-S, Steinhfel K. A firefly-inspired method for protein structure prediction in lattice models. Biomolecules 2014;4:56–75.10.3390/biom4010056Search in Google Scholar PubMed PubMed Central

34. Rashid MA, Newton MH, Hoque MT, Shatabda S, Pham D, Sattar A. Spiral search: a hydrophobic-core directed local search for simplified PSP on 3D FCC lattice. BMC Bioinform 2013;14:S16.10.1186/1471-2105-14-S2-S16Search in Google Scholar PubMed PubMed Central

35. Shatabda S, Newton MA, Pham DN, Sattar A. A hybrid local search for simplified protein structure prediction. In: International conference on bioinformatics models, methods and algorithms, 2013:6.10.1186/1471-2105-14-S2-S19Search in Google Scholar

36. Hart WE, Istrail SC. Fast protein folding in the hydrophobic-hydrophilic model within three-eighths of optimal. J Comput Biol 1996;3:53–96.10.1089/cmb.1996.3.53Search in Google Scholar

37. Newman A. A new algorithm for protein folding in the HP model. In: Proceedings of the thirteenth annual ACM-SIAM symposium on discrete algorithms, San Francisco, California. PA, USA: Society for Industrial and Applied Mathematics Philadelphia, 2002.Search in Google Scholar

38. Hart WE, Istrail SC. Lattice and off-lattice side chain models of protein folding: linear time structure prediction better than 86% of optimal. J Comput Biol 1997;4:241–59.10.1089/cmb.1997.4.241Search in Google Scholar

39. Heun V. Approximate protein folding in the HP side chain model on extended cubic lattices. Discrete Appl Math 2003;127:163–77.10.1016/S0166-218X(02)00382-7Search in Google Scholar

40. Hart W, Newman A. Protein structure pre-diction with lattice models. In: Handbook of molecular biology. Chapman & Hall, editors. CRC Computer and Information Science Series. New York: CRC Press, 2006:1–24.Search in Google Scholar

41. Istrail S, Lam F. Combinatorial algorithms for protein folding in lattice models: a survey of mathematical results. Commun Inf Syst 2009;9:303–46.10.4310/CIS.2009.v9.n4.a2Search in Google Scholar

42. Yue K, Dill KA. Forces of tertiary structural organization in globular proteins. Proc Natl Acad Sci USA 1995;92:146–50.10.1073/pnas.92.1.146Search in Google Scholar PubMed PubMed Central

43. Backofen R, Will S. A constraint-based approach to fast and exact structure prediction in three-dimensional protein models. Constraints 2006;11:5–30.10.1007/s10601-006-6848-8Search in Google Scholar

44. Mann M, Smith C, Rabbath M, Edwards M, Will S, Backofen R. CPSP-web-tool: a server for 3D lattice protein studies. Bioinformatics 2009;25:676–7.10.1093/bioinformatics/btp034Search in Google Scholar PubMed PubMed Central

45. Mann M, Will S, Backofen R. CPSP-tools – exact and complete algorithms for high-throughput 3D lattice protein studies. BMC Bioinform 2008;9:230.10.1186/1471-2105-9-230Search in Google Scholar PubMed PubMed Central

46. Backofen R, Will S, Bornberg-Bauer E. Application of constraint programming techniques for structure prediction of lattice proteins with extended alphabets. Bioinformatics 1999;15:234–42.10.1093/bioinformatics/15.3.234Search in Google Scholar PubMed

47. Bornberg-Bauer E. Chain growth algorithms for HP-type lattice proteins. In: Proceedings of RECOMB’97, Santa Fe, New Mexico, USA:ACM, 1997:47–55.10.1145/267521.267528Search in Google Scholar

48. Rashid MA, Newton MH, Hoque MT, Sattar A. Mixing energy models in genetic algorithms for on-lattice protein structure prediction. Biomed Res Int 2013;2013:15.10.1155/2013/924137Search in Google Scholar

49. Mann M, Backofen R, Will S. Equivalence classes of optimal structures in HP protein models including side chains. In: Proceedings of the fifth workshop on constraint based methods for bioinformatics (WCB09), 2009.Search in Google Scholar

50. Mann M. Computational methods for lattice protein models. PhD thesis, Albert-Ludwigs-University Freiburg, 2011. Available at: http://www.freidok.uni-freiburg.de/volltexte/8156/. Accessed on 29 October, 2014.Search in Google Scholar

51. Park B, Levitt M. The complexity and accuracy of discrete state models of protein structure. J Mol Biol 1995;249:493–507.10.1006/jmbi.1995.0311Search in Google Scholar

52. Mann M, Dal Palù A. Lattice model refinement of protein structures. In: Proc of WCB’10, 2010:7, arXiv:1005.1853.Search in Google Scholar

53. Mann M, Saunders R, Smith C, Backofen R, Deane CM. Producing high-accuracy lattice models from protein atomic co-ordinates including side chains. Adv Bioinform 2012;2012:6.10.1155/2012/148045Search in Google Scholar

54. Unger R, Moult J. Finding the lowest free energy conformation of a protein is an NP-hard problem: proof and implications. Bull Math Biol 1993;55:1183–98.10.1016/S0092-8240(05)80169-7Search in Google Scholar

55. Ngo JT, Marks J. Computational complexity of a problem in molecular structure prediction. Protein Eng 1992;5:313–21.10.1093/protein/5.4.313Search in Google Scholar PubMed

56. Perunov N, England JL. Quantitative theory of hydrophobic effect as a driving force of protein structure. Protein Sci 2014;23:387–99.10.1002/pro.2420Search in Google Scholar PubMed PubMed Central

57. Pace C, Shirley B, McNutt M, Gajiwala K. Forces contributing to the conformational stability of proteins. FASEB J 1996;10:75–83.10.1096/fasebj.10.1.8566551Search in Google Scholar PubMed

58. Dill KA, Bromberg S, Yue K, Fiebig KM, Yee DP, Thomas PD, et al. Principles of protein folding – a perspective of simple exact models. Protein Sci 1995;4:561–602.10.1002/pro.5560040401Search in Google Scholar PubMed PubMed Central

59. Li H, Helling R, Tang C, Wingreen N. Emergence of preferred structures in a simple model of protein folding. Science 1996;273:666–9.10.1126/science.273.5275.666Search in Google Scholar PubMed

60. Banavar JR, Cieplak M, Maritan A. Lattice tube model of proteins. Phys Rev Lett 2004;93:238101.10.1103/PhysRevLett.93.238101Search in Google Scholar PubMed

61. Hoque T, Chetty M, Sattar A. Extended HP model for protein structure prediction. J Comput Biol 2009;16:85–103.10.1089/cmb.2008.0082Search in Google Scholar PubMed

62. Miyazawa S, Jernigan RL. Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation. Macromolecules 1985;18:534–52.10.1021/ma00145a039Search in Google Scholar

63. Miyazawa S, Jernigan RL. Residue-residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading. J Mol Biol 1996;256:623–44.10.1006/jmbi.1996.0114Search in Google Scholar PubMed

64. Berrera M, Molinari H, Fogolari F. Amino acid empirical contact energy definitions for fold recognition in the space of contact maps. BMC Bioinform 2003;4:8.10.1186/1471-2105-4-8Search in Google Scholar PubMed PubMed Central

65. Chan HS, Dill KA. Origins of structure in globular proteins. Proc Natl Acad Sci USA 1990;87:6388–92.10.1073/pnas.87.16.6388Search in Google Scholar PubMed PubMed Central

66. Vendruscolo M, Domany E. Pairwise contact potentials are unsuitable for protein folding. J Chem Phys 1998;109:11101–8.10.1063/1.477748Search in Google Scholar

67. Dal Palù A, Dovier A, Pontelli E. A new constraint solver for 3D lattices and its application to the protein folding problem. In: Proc. of logic for programming, artificial intelligence, and reasoning (LPAR’05). Heidelberg, Berlin: Springer, 2005:48–63.Search in Google Scholar

68. Pötzsch S, Scheuermann G, Wolfinger M, Flamm C, Stadler P. Visualization of lattice-based protein folding simulations. In: Proc. of V’06: conference on information visualization, Los Alamitos, CA, USA:IEEE Computer Society, 2006:89–94.Search in Google Scholar

69. Bornberg-Bauer E. Randomness, structural uniqueness, modularity and neutral evolution in sequence space of model proteins. Z Phys Chem 2002;216:139–54.10.1524/zpch.2002.216.2.139Search in Google Scholar

70. Citossi M, Guigliarelli G. Lattice protein models: a computational approach to folding and aggregation phenomena. In: Frontiers of fundamental physics, vol. IV. Netherlands: Springer, 2005:355–8.Search in Google Scholar

71. Huard FP, Deane CM, Wood GR. Modelling sequential protein folding under kinetic control. Bioinformatics 2006;22:e203–10.10.1093/bioinformatics/btl248Search in Google Scholar PubMed

72. Saunders R, Mann M, Deane C. Signatures of co-translational folding. Special issue: Protein folding in vivo. Biotechnol J 2011;6:742–51.10.1002/biot.201000330Search in Google Scholar PubMed

73. Backofen R, Will S. Fast, constraint-based threading of HP-sequences to hydrophobic cores. In: Toby Walsh, editor. Proc. of the 7th international conference on principle and practice of constraint programming (CP’2001), vol. 2239 of LNCS, Paphos, Cyprus. Heidelberg, Berlin, Springer, 2001:494–508.Search in Google Scholar

74. Will S. Exact, constraint-based structure prediction in simple protein models. PhD thesis, Friedrich-Schiller-Universität Jena, 2005. Available at http://www.bioinf.uni-freiburg.de/Publications/. Accessed on 29 October, 2014.Search in Google Scholar

75. Backofen R, Will S. Structure prediction in an HP-type lattice with an extended alphabet. In: Proc. of German conference on bioinformatics (GCB’98), Köln, Germany, 1998.Search in Google Scholar

76. CPSP-home. CPSP-tools: constraint-based protein structure prediction, 2008. Available as an open-source package from http://www.bioinf.uni-freiburg.de/sw/cpsp/. Accessed on 29 October, 2014.Search in Google Scholar

77. CPSP-webtools. CPSP-webtools: constraint-based protein structure prediction webserver, 2009. Available at http://cpsp.informatik.uni-freiburg.de. Accessed on 29 October, 2014.Search in Google Scholar

78. Mann M, Maticzka D, Saunders R, Backofen R. Classifying protein-like sequences in arbitrary lattice protein models using LatPack. Special issue on protein folding: experimental and theoretical approaches. HFSP J 2008;2:396–404.10.2976/1.3027681Search in Google Scholar

79. LatPack-home. LatPack: lattice protein folding package, 2008. Available as an open-source package from http://www.bioinf.uni-freiburg.de/Software/. Accessed on 29 October, 2014.Search in Google Scholar

80. Rossi F, van Beek P, Walsh T. editors. Handbook of constraint programming (foundations of artificial intelligence). New York: Elsevier Science Inc., 2006.Search in Google Scholar

81. Régin J-C. A filtering algorithm for constraints of difference in CSPs. In: Proc. of 12th national conference on AI, Seattle, Washington, USA: American Association for Artificial Intelligence, 1994:362–7.Search in Google Scholar

82. Backofen R, Will S. Excluding symmetries in constraint-based search. Constraints 2002;7:333–49.10.1023/A:1020533821509Search in Google Scholar

83. Backofen R. Optimization techniques for the protein structure prediction problem. Habilitation. Ludwig-Maximilians-Universität München, 2000. Available at: http://www.bioinf.uni-freiburg.de/Publications/. Accessed on 29 October, 2014.Search in Google Scholar

84. Shortle D, Chan HS, Dill KA. Modeling the effects of mutations on the denatured states of proteins. Prot Sci 1992;1:201–15.10.1002/pro.5560010202Search in Google Scholar

85. Backofen R. The protein structure prediction problem: a constraint optimisation approach using a new lower bound. Constraints 2001;6:223–55.10.1023/A:1011485622743Search in Google Scholar

86. Backofen R. An upper bound for number of contacts in the HP-model on the face-centered-cubic lattice (FCC). In: Giancarlo R, Sankoff D, editors. Proceedings of the 11th annual symposium on combinatorial pattern matching (CPM 2000), vol. 1848 of LNCS, Montreal, Canada. Berlin: Springer-Verlag, 2000:277–92.Search in Google Scholar

87. Backofen R. A polynomial time upper bound for the number of contacts in the HP-model on the face-centered-cubic lattice (FCC). J Discr Alg 2004;2:161–206.10.1016/S1570-8667(03)00076-5Search in Google Scholar

88. Backofen R, Will S. Optimally compact finite sphere packings – hydrophobic cores in the FCC. In: Amir A, Landau, GM, editors. Proc. of CPM’01, vol. 2089 of LNCS, Jerusalem, Israel. Berlin: Springer, 2001:257–72.Search in Google Scholar

89. Will S. Constraint-based hydrophobic core construction for protein structure prediction in the face-centered-cubic lattice. In: Altman, Dunker, Hunter, Lauderdale & Klein, editors. Proc. of the Pacific symposium on biocomputing, Kauai, Hawaii. Singapore: World Scientific, 2002:661–72.Search in Google Scholar

90. Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by simulated annealing. Science 1983;220:671–80.10.1126/science.220.4598.671Search in Google Scholar PubMed

91. Černy V. Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Opt Theory Appl 1985;45:41–51.10.1007/BF00940812Search in Google Scholar

92. Böckenhauer H-J, Ullah AZ, Kapsokalivas L, Steinhöfel K. A local move set for protein folding in triangular lattice models. In: Crandall KA, Lagergren J, editors. Proc. of WABI ’08, LNBI. Berlin: Springer, 2008:369–81.Search in Google Scholar

93. Lesh N, Mitzenmacher M, Whitesides S. A complete and effective move set for simplified protein folding. In: Vingron, Martin and Istrail, Sorin and Pevzner, Pavel and Waterman, Michael. Proceedings of the seventh annual international conference on research in computational molecular biology (RECOMB’03), Berlin, Germany:ACM, 2003:188–95.Search in Google Scholar

94. Bornberg-Bauer E, Beaussart F, Kummerfeld S, Teichmann S, Weiner J. The evolution of domain arrangements in proteins and interaction networks. Cell Mol Life Sci 2005;62: 435–45.10.1007/s00018-004-4416-1Search in Google Scholar PubMed

95. Bornberg-Bauer E, Chan HS. Modeling evolutionary landscapes: mutational stability, topology, and superfunnels in sequence space. Proc Natl Acad Sci USA 1999;96:10689–94.10.1073/pnas.96.19.10689Search in Google Scholar PubMed PubMed Central

Received: 2014-8-21
Accepted: 2014-10-17
Published Online: 2014-11-27
Published in Print: 2014-12-19

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