Solving the Protein Threading Problem by Lagrangian Relaxation

  • Stefan Balev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3240)


This paper presents an efficient algorithm for aligning aquery amino-acid sequence to a protein 3D structure template. Solving this problem is one of the main steps of the methods of protein structure prediction by threading. We propose an integer programming model and solve it by branch-and-bound algorithm. The bounds are computed using a Lagrangian dual of the model which turns out to be much easier to solve than its linear programming relaxation. The Lagrangian relaxations are computed using a dynamic programming algorithm. The experimental results show that our algorithm outperforms the commonly used methods. The proposed algorithm is general enough and can be easily plugged in most of the threading tools in order to increase their performance.


protein threading protein structure prediction sequence-structure alignment integer programming dynamic programming Lagrangian relaxation and duality subgradient optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Head-Gordon, T., Wooley, J.C.: Computational challenges in structural and functional genomics. IBM Systems Journal 40, 265–296 (2001)CrossRefGoogle Scholar
  2. 2.
    Lengauer, T.: Computational biology at the beginning of the post-genomic era. In: Wilhelm, R. (ed.) Informatics: 10 Years Back, 10 Years Ahead. LNCS, vol. 2000, pp. 341–355. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Lathrop, R., Rogers Jr., R., Bienkowska, J., Bryant, B., Buturovic, L., Gaitatzes, C., Nambudripad, R., White, J., Smith, T.: Analysis and algorithms for protein sequence-structure alignment. In: Salzberg, S., Searls, D., Kasif, S. (eds.) Computational Methods in Molecular Biology, pp. 227–283. Elsevier Science, Amsterdam (1998)CrossRefGoogle Scholar
  4. 4.
    Lathrop, R., Smith, T.: Global optimum protein threading with gapped alignment and empirical pair potentials. J. Mol. Biol. 255, 641–665 (1996)CrossRefGoogle Scholar
  5. 5.
    Xu, Y., Xu, D., Uberbacher, E.C.: An efficient computational method for globally optimal threading. Journal of Computational Biology 5, 597–614 (1998)CrossRefGoogle Scholar
  6. 6.
    Xu, J., Li, M., Lin, G., Kim, D., Xu, Y.: RAPTOR: optimal protein threading by linear programming. Journal of Bioinformatics and Computational Biology 1, 95–118 (2003)CrossRefGoogle Scholar
  7. 7.
    Andonov, R., Yanev, N.: Solving the protein threading problem in parallel. In: HiCOMB 2003 – Second IEEE International Workshop on High Performance Computational Biology (2003)Google Scholar
  8. 8.
    Andonov, R., Balev, S., Yanev, N.: Protein threading: From mathematical models to parallel implementations. INFORMS Journal on Computing (2004) (to appear)Google Scholar
  9. 9.
    Marin, A., Pothier, J., Zimmermann, K., Gibrat, J.F.: FROST: a filter-based fold recognition method. Proteins 49, 493–509 (2002)CrossRefGoogle Scholar
  10. 10.
    Marin, A., Pothier, J., Zimmermann, K., Gibrat, J.F.: Protein threading statistics: an attempt to assess the significance of a fold assignment to a sequence. In: Tsigelny, I. (ed.) Protein structure prediction: bioinformatic approach, International University Line (2002)Google Scholar
  11. 11.
    Lathrop, R.: The protein threading problem with sequence amino acid interaction preferences is NP-complete. Protein Engineering 7, 1059–1068 (1994)CrossRefGoogle Scholar
  12. 12.
    Akutsu, T., Miyano, S.: On the approximation of protein threading. Theoretical Computer Science 210, 261–275 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, Chichester (1988)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Stefan Balev
    • 1
  1. 1.Laboratoire d’Informatique du HavreUniversité du HavreLe Havre cedexFrance

Personalised recommendations