Advertisement

RNA Tree Comparisons via Unrooted Unordered Alignments

  • Nimrod Milo
  • Shay Zakov
  • Erez Katzenelson
  • Eitan Bachmat
  • Yefim Dinitz
  • Michal Ziv-Ukelson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7534)

Abstract

We generalize some current approaches for RNA tree alignment, which are traditionally confined to ordered rooted mappings, to also consider unordered unrooted mappings. We define the Homeomorphic Subtree Alignment problem, and present a new algorithm which applies to several modes, including global or local, ordered or unordered, and rooted or unrooted tree alignments. Our algorithm generalizes previous algorithms that either solved the problem in an asymmetric manner, or were restricted to the rooted and/or ordered cases. Focusing here on the most general unrooted unordered case, we show that our algorithm has an O(n T n S min (d T , d S )) time complexity, where n T and n S are the number of nodes and d T and d S are the maximum node degrees in the input trees T and S, respectively. This maintains (and slightly improves) the time complexity of previous, less general algorithms for the problem. Supplemental materials, source code, and web-interface for our tool are found in http://www.cs.bgu.ac.il/~negevcb/FRUUT .

Keywords

Input Tree Hammerhead Ribozyme Bipartite Match Tree Edit Distance Unordered Tree 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andronescu, M., Bereg, V., Hoos, H., Condon, A.: Rna strand: the rna secondary structure and statistical analysis database. BMC Bioinformatics 9, 340 (2008)CrossRefGoogle Scholar
  2. 2.
    Agmon, I., Auerbach, T., Baram, D., Bartels, H., Bashan, A., Berisio, R., Fucini, P., Hansen, H., Harms, J., Kessler, M., et al.: On peptide bond formation, translocation, nascent protein progression and the regulatory properties of ribosomes. European Journal of Biochemistry 270, 2543–2556 (2003)CrossRefGoogle Scholar
  3. 3.
    Hofacker, I., Fontana, W., Stadler, P., Bonhoeffer, L., Tacker, M., Schuster, P.: Fast folding and comparison of RNA secondary structures. Monatshefte fur Chemie/Chemical Monthly 125, 167–188 (1994)CrossRefGoogle Scholar
  4. 4.
    Steffen, P., Voss, B., Rehmsmeier, M., Reeder, J., Giegerich, R.: RNAshapes: an integrated RNA analysis package based on abstract shapes (2006)Google Scholar
  5. 5.
    Hochsmann, M., Toller, T., Giegerich, R., Kurtz, S.: Local similarity in RNA secondary structures. In: Proceedings of the 2003 IEEE Bioinformatics Conference, CSB 2003, pp. 159–168. IEEE (2003)Google Scholar
  6. 6.
    Jiang, T., Lin, G., Ma, B., Zhang, K.: A general edit distance between RNA structures. Journal of Computational Biology 9, 371–388 (2002)CrossRefGoogle Scholar
  7. 7.
    Zhang, K., Wang, L., Ma, B.: Computing Similarity between RNA Structures. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, pp. 281–293. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Bille, P.: A survey on tree edit distance and related problems. Theoretical Computer Science 337, 217–239 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Schirmer, S., Giegerich, R.: Forest Alignment with Affine Gaps and Anchors. In: Giancarlo, R., Manzini, G. (eds.) CPM 2011. LNCS, vol. 6661, pp. 104–117. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Allali, J., Sagot, M.-F.: A Multiple Graph Layers Model with Application to RNA Secondary Structures Comparison. In: Consens, M.P., Navarro, G. (eds.) SPIRE 2005. LNCS, vol. 3772, pp. 348–359. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Blin, G., Denise, A., Dulucq, S., Herrbach, C., Touzet, H.: Alignments of RNA structures. IEEE/ACM Transactions on Computational Biology and Bioinformatics 7, 309–322 (2010)CrossRefGoogle Scholar
  12. 12.
    Jan, E.: Divergent ires elements in invertebrates. Virus Research 119, 16–28 (2006)CrossRefGoogle Scholar
  13. 13.
    Perreault, J., Weinberg, Z., Roth, A., Popescu, O., Chartrand, P., Ferbeyre, G., Breaker, R.: Identification of hammerhead ribozymes in all domains of life reveals novel structural variations. PLoS Computational Biology 7, e1002031 (2011)CrossRefGoogle Scholar
  14. 14.
    Birikh, K., Heaton, P., Eckstein, F.: The structure, function and application of the hammerhead ribozyme. European Journal of Biochemistry 245, 1–16 (1997)CrossRefGoogle Scholar
  15. 15.
    Haas, E., Brown, J.: Evolutionary variation in bacterial RNase P RNAs. Nucleic Acids Research 26, 4093–4099 (1998)CrossRefGoogle Scholar
  16. 16.
    Zhang, K., Jiang, T.: Some MAX SNP-hard results concerning unordered labeled trees. Information Processing Letters 49, 249–254 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Shamir, R., Tsur, D.: Faster subtree isomorphism. J. of Algorithms 33, 267–280 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Chung, M.: O (n2. 5) time algorithms for the subgraph homeomorphism problem on trees. Journal of Algorithms 8, 106–112 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Pinter, R.Y., Rokhlenko, O., Tsur, D., Ziv-Ukelson, M.: Approximate labelled subtree homeomorphism. Journal of Discrete Algorithms 6, 480–496 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Zhang, K.: A constrained edit distance between unordered labeled trees. Algorithmica 15, 205–222 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Kao, M., Lam, T., Sung, W., Ting, H.: Cavity matchings, label compressions, and unrooted evolutionary trees. Arxiv preprint cs/0101031 (2001)Google Scholar
  22. 22.
    Edmonds, J., Karp, R.: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM (JACM) 19, 248–264 (1972)zbMATHCrossRefGoogle Scholar
  23. 23.
    Fredman, M., Tarjan, R.: Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM (JACM) 34, 596–615 (1987)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Gabow, H., Tarjan, R.: Faster scaling algorithms for network problems. SIAM Journal on Computing 18, 1013 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Orlin, J., Ahuja, R.: New scaling algorithms for the assignment and minimum mean cycle problems. Mathematical Programming 54, 41–56 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Zhang, K.: Algorithms for the constrained editing distance between ordered labeled trees and related problems. Pattern Recognition 28, 463–474 (1995)CrossRefGoogle Scholar
  27. 27.
    Maes, M.: On a cyclic string-to-string correction problem. Information Processing Letters 35, 73–78 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Schmidt, J.P.: All highest scoring paths in weighted grid graphs and their application to finding all approximate repeats in strings. SIAM J. of Computing 27, 972–992 (1998)zbMATHCrossRefGoogle Scholar
  29. 29.
    Tiskin, A.: Semi-local string comparison: Algorithmic techniques and applications. Mathematics in Computer Science 1, 571–603 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Hofacker, I.: Vienna RNA secondary structure server. Nucleic Acids Research 31, 3429 (2003)CrossRefGoogle Scholar
  31. 31.
    Pace, N.R., Brown, J.W.: Evolutionary perspective on the structure and function of ribonuclease P, a ribozyme. J. Bacteriol. 177, 1919–1928 (1995)Google Scholar
  32. 32.
    Brown, J.: The ribonuclease p database. Nucleic acids research 27, 314 (1999)CrossRefGoogle Scholar
  33. 33.
    Andronescu, M., Bereg, V., Hoos, H.H., Condon, A.: RNA STRAND: the RNA secondary structure and statistical analysis database. BMC Bioinformatics 9, 340 (2008)CrossRefGoogle Scholar
  34. 34.
    Höchsmann, M.: The tree alignment model: algorithms, implementations and applications for the analysis of RNA secondary structures. PhD thesis, Universitätsbibliothek Bielefeld (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nimrod Milo
    • 1
  • Shay Zakov
    • 2
  • Erez Katzenelson
    • 1
  • Eitan Bachmat
    • 1
  • Yefim Dinitz
    • 1
  • Michal Ziv-Ukelson
    • 1
  1. 1.Dept. of Computer ScienceBen-Gurion University of the NegevIsrael
  2. 2.Dept. of Computer Science and EngineeringUC San DiegoLa JollaUSA

Personalised recommendations