Skip to main content

Advertisement

SpringerLink
Log in

An Algorithm for Simultaneous Backbone Threading and Side-Chain Packing

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

To fully utilize all available information in protein structure prediction, including both backbone and side-chain structures, we present a novel algorithm for solving a generalized threading problem. In this problem, we consider simultaneously backbone threading and side-chain packing during the process of a protein structure prediction. For a given query protein sequence and a template structure, our goal is to find a threading alignment between the query sequence and the template structure, along with a rotamer assignment for each side-chain of the query protein, which optimizes an energy function that combines a backbone threading energy and a side-chain packing energy. This highly computationally challenging problem is solved through first formulating this problem as a graph-based optimization problem. Various graph-theoretic techniques are employed to achieve the computational efficiency to make our algorithm practically useful, which takes advantage of a number of special properties of the graph representing this generalized threading problem. The overall framework of our algorithm is a dynamic programming algorithm implemented on an optimal tree decomposition of the graph representation of our problem. By using various additional heuristic techniques such as the dead-end elimination, we have demonstrated that our algorithm can solve a generalized threading problem within practically acceptable amount of time and space, the first of its kind.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Park, B., Levitt, M.: Energy functions that discriminate X-ray and near native folds from well-constructed decoys. J. Mol. Biol. 258(2), 367–392 (1996)

    Article  Google Scholar 

  2. Ableson, A., Glasgow, J.I.: Crystallographic threading. Proc. Int. Conf. Intell. Syst. Mol. Biol. 2–9 (1999)

  3. Park, B.H., Huang, E.S., Levitt, M.: Factors affecting the ability of energy functions to discriminate correct from incorrect folds. J. Mol. Biol. 266(4), 831–846 (1997)

    Article  Google Scholar 

  4. Ayers, D.J., et al.: Enhanced protein fold recognition using secondary structure information from NMR. Protein Sci. 8(5), 1127–1133 (1999)

    Google Scholar 

  5. Bowie, J.U., Luthy, R., Eisenberg, D.: A method to identify protein sequences that fold into a known three-dimensional structure. Science 253(5016), 164–170 (1991)

    Article  Google Scholar 

  6. Friedberg, I., et al.: The interplay of fold recognition and experimental structure determination in structural genomics. Curr. Opin. Struct. Biol. 14(3), 307–312 (2004)

    Article  MathSciNet  Google Scholar 

  7. Ginalski, K., et al.: Practical lessons from protein structure prediction. Nucleic. Acids Res. 33(6), 1874–1891 (2005)

    Article  Google Scholar 

  8. Jones, D.T., et al.: Successful recognition of protein folds using threading methods biased by sequence similarity and predicted secondary structure. Proteins Suppl. 3, 104–111 (1999)

    Article  Google Scholar 

  9. Jones, D.T.: GenTHREADER: an efficient and reliable protein fold recognition method for genomic sequences. J. Mol. Biol. 287(4), 797–815 (1999)

    Article  Google Scholar 

  10. Karplus, K., Barrett, C., Hughey, R.: Hidden Markov models for detecting remote protein homologies. Bioinformatics 14(10), 846–856 (1998)

    Article  Google Scholar 

  11. Karplus, K., et al.: Predicting protein structure using hidden Markov models. Proteins Suppl. 1, 134–139 (1997)

    Article  Google Scholar 

  12. Yang, A.S., Honig, B.: Sequence to structure alignment in comparative modeling using PrISM. Proteins Suppl. 3, 66–72 (1999)

    Article  Google Scholar 

  13. Petrey, D., et al.: Using multiple structure alignments, fast model building, and energetic analysis in fold recognition and homology modeling. Proteins 53(6), 430–435 (2003)

    Article  Google Scholar 

  14. Skolnick, J., et al.: Ab initio protein structure prediction via a combination of threading, lattice folding, clustering, and structure refinement. Proteins Suppl. 5, 149–156 (2001)

    Article  Google Scholar 

  15. Reva, B.A., et al.: Recognition of protein structure on coarse lattices with residue-residue energy functions. Protein Eng. 10(10), 1123–1130 (1997)

    Article  MathSciNet  Google Scholar 

  16. Reva, B.A., Skolnick, J., Finkelstein, A.V.: Averaging interaction energies over homologs improves protein fold recognition in gapless threading. Proteins 35(3), 353–359 (1999)

    Article  Google Scholar 

  17. Zhang, Y., Arakaki, A.K., Skolnick, J.: TASSER: an automated method for the prediction of protein tertiary structures in CASP6. Proteins 61(7), 91–98 (2005)

    Article  Google Scholar 

  18. Zhang, Y., Skolnick, J.: The protein structure prediction problem could be solved using the current PDB library. Proc. Natl. Acad. Sci. USA 102(4), 1029–1034 (2005)

    Article  Google Scholar 

  19. Xu, Y., Xu, D.: Protein threading using PROSPECT: design and evaluation. Proteins 40(3), 343–354 (2000)

    Article  Google Scholar 

  20. Xu, Y., Xu, D., Uberbacher, E.C.: An efficient computational method for globally optimal threading. J. Comput. Biol. 5(3), 597–614 (1998)

    Google Scholar 

  21. Xu, J., et al.: RAPTOR: optimal protein threading by linear programming. J. Bioinform. Comput. Biol. 1(1), 95–117 (2003)

    Article  Google Scholar 

  22. Xu, J., Xu, Y., Li, M.: Protein threading by linear programming: theoretical analysis and computational results. J. Comb. Optim. 8, 403–418 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Xu, J. et al.: Protein threading by linear programming, Pac. Symp. Biocomput. 264–275 (2003)

  24. Moult, J.: A decade of CASP: progress, bottlenecks and prognosis in protein structure prediction. Curr. Opin. Struct. Biol. 15(3), 285–289 (2005)

    Article  Google Scholar 

  25. Kryshtafovych, A., et al.: Progress over the first decade of CASP experiments. Proteins 61(7), 225–236 (2005)

    Article  Google Scholar 

  26. Moult, J., et al.: Critical assessment of methods of protein structure prediction (CASP)–round 6. Proteins 61(7), 3–7 (2005)

    Article  Google Scholar 

  27. Lathrop, R.H.: The protein threading problem with sequence amino acid interaction preferences is NP-complete. Protein Eng. 7(9), 1059–1068 (1994)

    Article  Google Scholar 

  28. Calland, P.Y.: On the structural complexity of a protein. Protein Eng. 16(2), 79–86 (2003)

    Article  Google Scholar 

  29. Canutescu, A.A., Shelenkov, A.A., Dunbrack, R.L. Jr.: A graph-theory algorithm for rapid protein side-chain prediction. Protein Sci. 12(9), 2001–2014 (2003)

    Article  Google Scholar 

  30. Buchete, N.V., Straub, J.E., Thirumalai, D.: Development of novel statistical potentials for protein fold recognition. Curr. Opin. Struct. Biol. 14(2), 225–232 (2004)

    Article  Google Scholar 

  31. Chen, W.W., Shakhnovich, E.I.: Lessons from the design of a novel atomic potential for protein folding. Protein Sci. 14(7), 1741–1752 (2005)

    Article  Google Scholar 

  32. Shimada, J., Shakhnovich, E.I.: The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation. Proc. Natl. Acad. Sci. USA 99(17), 11175–11180 (2002)

    Article  Google Scholar 

  33. Vendruscolo, M., Najmanovich, R., Domany, E.: Can a pairwise contact potential stabilize native protein folds against decoys obtained by threading? Proteins 38(2), 134–148 (2000)

    Article  Google Scholar 

  34. Crooks, G.E., Wolfe, J., Brenner, S.E.: Measurements of protein sequence-structure correlations. Proteins 57(4), 804–810 (2004)

    Article  Google Scholar 

  35. Buchete, N.V., Straub, J.E., Thirumalai, D.: Orientational potentials extracted from protein structures improve native fold recognition. Protein Sci. 13(4), 862–874 (2004)

    Article  Google Scholar 

  36. Cornell, W.D., et al.: A second generation force-field for the simulation of proteins, nucleic-acids, and organic-molecules. J. Am. Chem. Soc. 117(19), 5179–5197 (1995)

    Article  Google Scholar 

  37. Liu, Z., Dominy, B., Shakhnovich, E.: Structural mining: Self-consistent design on flexible protein-peptide docking and transferable binding affinity potential. J. Am. Chem. Soc. (2004, accepted)

  38. Liu, Z. et al.: Quantitative evaluation of protein-DNA interactions using an optimized knowledge-based potential. Nucleic Acids Res. (2005)

  39. Song, Y. et al.: Efficient algorithms for protein threading via tree decomposition (2007, submitted)

  40. Robertson, N., Seymour, P.D.: Graph Minors 2. Algorithmic aspects of tree-width. J. Algorithms 7(3), 309–322 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  41. Aharoni, R., Herman, G.T., Loebl, M.: Jordan graphs. Graph. Model. Image Process. 58(4), 345–359 (1996)

    Article  Google Scholar 

  42. Bodlaender, H.L.: A linear-time ie algorithm for finding three-decompositions of small treewidth. SIAM J. Comput. 25(6), 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  43. Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a K-tree. SIAM J. Algebr. Discret. Method. 8(2), 277–284 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  44. Arnborg, S., Lagergren, J., Seese, D.: Easy problems for tree-decomposable graphs. J. Algorithms 12(2), 308–340 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  45. Jordan, M.I.: Graphical models. Stat. Sci. 19(1), 140–155 (2004)

    Article  MATH  Google Scholar 

  46. Needleman, S.B., Wunsch, C.D.: A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48(3), 443–453 (1970)

    Article  Google Scholar 

  47. Gotoh, O.: An improved algorithm for matching biological sequences. J. Mol. Biol. 162(3), 705–708 (1982)

    Article  Google Scholar 

  48. Thiele, R., Zimmer, R., Lengauer, T.: Protein threading by recursive dynamic programming. J. Mol. Biol. 290(3), 757–779 (1999)

    Article  Google Scholar 

  49. Dunbrack, R.L. Jr., Karplus, M.: Backbone-dependent rotamer library for proteins. Application to side-chain prediction. J. Mol. Biol. 230(2), 543–574 (1993)

    Article  Google Scholar 

  50. Desmet, J., De Maeyer, M., Lasters, I.: Theoretical and algorithmical optimization of the dead-end elimination theorem. Pac. Symp. Biocomput. 122–133 (1997)

  51. Desmet, J., et al.: The dead-end elimination theorem and its use in protein side-chain positioning. Nature 356(6369), 539–542 (1992)

    Article  Google Scholar 

  52. Goldstein, R.F.: Efficient rotamer elimination applied to protein side-chains and related spin glasses. Biophys. J. 66(5), 1335–1340 (1994)

    Article  Google Scholar 

  53. Xu, J.: Rapid protein side-chain packing via tree decomposition. In: RECOMB 2005 (2005)

  54. Holm, L., Sander, C.: Mapping the protein universe. Science 273(5275), 595–603 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Systems Sciences, Shandong University, Jinan, 250100, China

    Guojun Li

  2. Department of Biochemistry and Molecular Biology, The University of Georgia, Athens, GA, 30602, USA

    Zhijie Liu, Jun-Tao Guo & Ying Xu

Authors
  1. Guojun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhijie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun-Tao Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ying Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, G., Liu, Z., Guo, JT. et al. An Algorithm for Simultaneous Backbone Threading and Side-Chain Packing. Algorithmica 51, 435–450 (2008). https://doi.org/10.1007/s00453-007-9070-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-007-9070-1

Keywords

Search

Navigation