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Optimization Letters

, Volume 5, Issue 3, pp 421–433 | Cite as

Algorithm engineering for optimal alignment of protein structure distance matrices

  • Inken Wohlers
  • Rumen Andonov
  • Gunnar W. Klau
Original Paper

Abstract

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal dali alignments for the very first time.

Keywords

Protein structure distance matrix alignment Algorithm engineering Integer linear programming Branch-and-cut Preprocessing dali 

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References

  1. 1.
    Althaus E., Caprara A., Lenhof H.P., Reinert K.: Multiple sequence alignment with arbitrary gap costs: computing an optimal solution using polyhedral combinatorics. Bioinformatics 18(Suppl 2), 4–16 (2002)CrossRefGoogle Scholar
  2. 2.
    Andonov R., Malod-Dognin N., Yanev N.: Maximum contact map overlap revisited. J Comput Biol. 18(1), 27–41 (2011)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Andreeva A., Prlić A., Hubbard T.J., Murzin A.G.: SISYPHUS–structural alignments for proteins with non-trivial relationships. Nucleic Acids Res. 35(Database issue), 253–259 (2007)CrossRefGoogle Scholar
  4. 4.
    Berbalk C., Schwaiger C.S., Lackner P.: Accuracy analysis of multiple structure alignments. Protein Sci. 18(10), 2027–2035 (2009)CrossRefGoogle Scholar
  5. 5.
    Caprara A., Carr R., Istrail S., Lancia G., Walenz B.: 1001 optimal PDB structure alignments: integer programming methods for finding the maximum contact map overlap. J. Comput. Biol. 11(1), 27–52 (2004)CrossRefGoogle Scholar
  6. 6.
    Collet, G., Andonov, R., Yanev, N., Gibrat, J.F.: Local protein threading by mixed integer programming. Discret. Appl. Math. (2010 in press)Google Scholar
  7. 7.
    Di Lena P., Fariselli P., Margara L., Vassura M., Casadio R.: Fast overlapping of protein contact maps by alignment of eigenvectors. Bioinformatics 26(18), 2250–2258 (2010)CrossRefGoogle Scholar
  8. 8.
    Hasegawa H., Holm L.: Advances and pitfalls of protein structural alignment. Curr. Opin. Struct. Biol. 19(3), 341–348 (2009)CrossRefGoogle Scholar
  9. 9.
    Havel T., Kuntz I., Crippen G.: The theory and practice of distance geometry. Bull. Math. Biol. 45(5), 665–720 (1983)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Holm, L., Kääriäinen, S., Wilton, C., Plewczynski, D.: Using Dali for structural comparison of proteins. Curr. Protoc. Bioinform. Chapter 5 (2006)Google Scholar
  11. 11.
    Holm L., Sander C.: Protein structure comparison by alignment of distance matrices. J. Mol. Biol. 233(1), 123–138 (1993)CrossRefGoogle Scholar
  12. 12.
    Jain, B.J., Lappe, M.: Joining softassign and dynamic programming for the contact map overlap problem. In: Hochreiter, S., Wagner, R. (eds.) BIRD. Lecture Notes in Computer Science, vol. 4414, pp. 410–423. Springer, UK (2007)Google Scholar
  13. 13.
    Kawabata T., Nishikawa K.: Protein structure comparison using the Markov transition model of evolution. Proteins 41(1), 108–122 (2000)CrossRefGoogle Scholar
  14. 14.
    Kolodny R., Koehl P., Levitt M.: Comprehensive evaluation of protein structure alignment methods: scoring by geometric measures. J. Mol. Biol. 346(4), 1173–1188 (2005)CrossRefGoogle Scholar
  15. 15.
    Lathrop R.H.: The protein threading problem with sequence amino acid interaction preferences is NP-complete. Protein Eng. 7(9), 1059–1068 (1994)CrossRefGoogle Scholar
  16. 16.
    Lenhof H.P., Reinert K., Vingron M.: A polyhedral approach to RNA sequence structure alignment. J. Comput. Biol. 5(3), 517–530 (1998)CrossRefGoogle Scholar
  17. 17.
    Malod-Dognin N., Andonov R., Yanev N.: Maximum cliques in protein structure comparison. In: Festa, P. (ed.) Experimental Algorithms. LNCS, vol. 6049, pp. 106–117. Springer, Berlin (2010)CrossRefGoogle Scholar
  18. 18.
    Marin A., Pothier J., Zimmermann K., Gibrat J.F.: Frost: a filter-based fold recognition method. Proteins 49(4), 493–509 (2002)CrossRefGoogle Scholar
  19. 19.
    Mayr G., Domingues F.S., Lackner P.: Comparative analysis of protein structure alignments. BMC Struct. Biol. 7, 50 (2007)CrossRefGoogle Scholar
  20. 20.
    Pelta D.A., González J.R., Moreno Vega M.: A simple and fast heuristic for protein structure comparison. BMC Bioinform. 9, 161 (2008)CrossRefGoogle Scholar
  21. 21.
    Schrijver A.: Theory of Linear and Integer Programming. Wiley, Chichester (1986)zbMATHGoogle Scholar
  22. 22.
    Taylor W.R., Orengo C.A.: Protein structure alignment. J. Mol. Biol. 208(1), 1–22 (1989)CrossRefGoogle Scholar
  23. 23.
    Wohlers I., Domingues F.S., Klau G.W.: Towards optimal alignment of protein structure distance matrices. Bioinformatics 26(18), 2273–2280 (2010)CrossRefGoogle Scholar
  24. 24.
    Wu D., Wu Z., Yuan Y.: Rigid versus unique determination of protein structures with geometric buildup. Optim. Lett. 2(3), 319–331 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Xie W., Sahinidis N.V.: A reduction-based exact algorithm for the contact map overlap problem. J. Comput. Biol. 14(5), 637–654 (2007)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Life Sciences GroupCWIAmsterdamThe Netherlands
  2. 2.INRIA Rennes, Bretagne Atlantique and University of Rennes 1RennesFrance

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