A Practical Solution for Aligning and Simplifying Pairs of Protein Backbones under the Discrete Fréchet Distance

  • Tim Wylie
  • Jun Luo
  • Binhai Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6784)


Aligning and comparing two polygonal chains in 3D space is an important problem in many areas of research, like in protein structure alignment. A lot of research has been done in the past on this problem, using RMSD as the distance measure. Recently, the discrete Fréchet distance has been applied to align and simplify protein backbones (geometrically, 3D polygonal chains) by Jiang et al., with insightful new results found. On the other hand, as a protein backbone can have as many as 500~600 vertices, even if a pair of chains are nicely aligned, as long as they are not identical, it is still difficult for humans to visualize their similarity and difference. In 2008, a problem called CPS-3F was proposed to simplify a pair of 3D chains simultaneously under the discrete Fréchet distance. However, it is still open whether CPS-3F is NP-complete or not. In this paper, we first present a new practical method to align a pair of protein backbones, improving the previous method by Jiang et al. Finally, we present a greedy-and-backtrack method, using the new alignment method as a subroutine, to handle the CPS-3F problem. We also prove two simple lemmas, giving some evidence to why our new method works well. Some preliminary empirical results using some proteins from the Protein Data Bank (PDB), with comparisons to the previous method, are presented.


Protein Data Bank Protein Backbone Greedy Method Polygonal Chain Protein Structure Comparison 
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.


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  1. 1.
    Alt, H., Behrends, B., Blömer, J.: Approximate matching of polygonal shapes (extended abstract). In: Proceedings of the 7th Annual Symposium on Computational Geometry (SoCG 1991), pp. 186–193 (1991)Google Scholar
  2. 2.
    Alt, H., Godau, M.: Measuring the resemblance of polygonal curves. In: Proceedings of the 8th Annual Symposium on Computational Geometry (SoCG 1992), pp. 102–109 (1992)Google Scholar
  3. 3.
    Alt, H., Godau, M.: Computing the frechet distance between two polygonal curves. Internat. J. Comput. Geom. Appl. 5, 75–91 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Alt, H., Knauer, C., Wenk, C.: Matching polygonal curves with respect to the fréchet distance. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 63–74. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Bereg, S., Jiang, M., Wang, W., Yang, B., Zhu, B.: Simplifying 3D polygonal chains under the discrete Fréchet distance. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 630–641. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Cole, R.: Slowing down sorting networks to obtain faster sorting algorithms. J. ACM 34, 200–208 (1987)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Conte, L., Ailey, B., Hubbard, T., Brenner, S., Murzin, A., Chothia, C.: SCOP: a structural classification of protein database. Nucleic Acids Research 28, 257–259 (2000)CrossRefGoogle Scholar
  8. 8.
    Eiter, T., Mannila, H.: Computing discrete Fréchet distance. Tech. Report CD-TR 94/64, Information Systems Department, Technical University of Vienna (1994)Google Scholar
  9. 9.
    Fréchet, M.: Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Mathematico di Palermo 22, 1–74 (1906)CrossRefzbMATHGoogle Scholar
  10. 10.
    Holm, L., Park, J.: DaliLite workbench for protein structure comparison. Bioinformatics 16, 566–567 (2000)CrossRefGoogle Scholar
  11. 11.
    Holm, L., Sander, C.: Protein structure comparison by alignment of distance matrices. J. Mol. Biol. 233, 123–138 (1993)CrossRefGoogle Scholar
  12. 12.
    Jiang, M., Xu, Y., Zhu, B.: Protein structure-structure alignment with discrete Fréchet distance. J. of Bioinformatics and Computational Biology 6, 51–64 (2008)CrossRefGoogle Scholar
  13. 13.
    Mauzy, C., Hermodson, M.: Structural homology between rbs repressor and ribose binding protein implies functional similarity. Protein Science 1, 843–849 (1992)CrossRefGoogle Scholar
  14. 14.
    Needleman, S., Wunsch, C.: A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48, 443–453 (1970)CrossRefGoogle Scholar
  15. 15.
    Orengo, C., Michie, A., Jones, S., Jones, D., Swindles, M., Thornton, J.: CATH—a hierarchic classification of protein domain structures. Structure 5, 1093–1108 (1997)CrossRefGoogle Scholar
  16. 16.
    Oritz, A., Strauss, C., Olmea, O.: MAMMOTH (matching molecular models obtained from theory): an automated method for model comparison. Protein Science 11, 2606–2621 (2002)CrossRefGoogle Scholar
  17. 17.
    Shindyalov, I., Bourne, P.: Protein structure alignment by incremental combinatorial extension (CE) of the optimal path. Protein Engineering 11, 739–747 (1998)CrossRefGoogle Scholar
  18. 18.
    Shyu, C.-R., Chi, P.-H., Scott, G., Xu, D.: ProteinDBS: a real-time retrieval system for protein structure comparison. Nucleic Acids Research 32, W572–W575 (2004)CrossRefGoogle Scholar
  19. 19.
    Taylor, W., Orengo, C.: Protein structure alignment. J. Mol. Biol. 208, 1–22 (1989)CrossRefGoogle Scholar
  20. 20.
    Wenk, C.: Shape Matching in Higher Dimensions. PhD thesis, Freie Universitaet Berlin (2002)Google Scholar
  21. 21.
    Yang, J.-M., Tung, C.-H.: Protein structure database search and evolutionary classification. Nucleic Acids Research 34, 3646–3659 (2006)CrossRefGoogle Scholar
  22. 22.
    Zhu, B.: Protein local structure alignment under the discrete Fréchet distance. J. Computational Biology 14(10), 1343–1351 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Tim Wylie
    • 1
  • Jun Luo
    • 2
  • Binhai Zhu
    • 1
  1. 1.Department of Computer ScienceMontana State UniversityBozemanUSA
  2. 2.Shenzhen Institutes of Advanced TechnologyChinese Academy of SciencesShenzhenChina

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