Local Exact Pattern Matching for Non-fixed RNA Structures

  • Mika Amit
  • Rolf Backofen
  • Steffen Heyne
  • Gad M. Landau
  • Mathias Möhl
  • Christina Schmiedl
  • Sebastian Will
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7354)


Detecting local common sequence-structure regions of RNAs is a biologically meaningful problem. By detecting such regions, biologists are able to identify functional similarity between the inspected molecules. We developed dynamic programming algorithms for finding common structure-sequence patterns between two RNAs. The RNAs are given by their sequence and a set of potential base pairs with associated probabilities. In contrast to prior work which matches fixed structures, we support the arc breaking edit operation; this allows to match only a subset of the given base pairs. We present an O(n 3) algorithm for local exact pattern matching between two nested RNAs, and an O(n 3logn) algorithm for one nested RNA and one bounded-unlimited RNA.


Base Pair Time Complexity Maximal Match Edit Operation Tree Edit Distance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Backofen, R., Chen, S., Hermelin, D., Landau, G.M., Roytberg, M.A., Weimann, O., Zhang, K.: Locality and gaps in RNA comparison. Journal of Computational Biology 14, 1074–1087 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Backofen, R., Landau, G.M., Möhl, M., Tsur, D., Weimann, O.: Fast RNA Structure Alignment for Crossing Input Structures. In: Kucherov, G., Ukkonen, E. (eds.) CPM 2009. LNCS, vol. 5577, pp. 236–248. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Bille, P.: A survey on tree edit distance and related problems. Theoretical Computer Science 337, 217–239 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Couzin, J.: Small RNAS make big splash. Science 298(5602), 2296–2297 (2002)CrossRefGoogle Scholar
  5. 5.
    Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An Optimal Decomposition Algorithm for Tree Edit Distance. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 146–157. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Dulucq, S., Touzet, H.: Decomposition algorithms for the tree edit distance problem. J. Discrete Algorithms 3(2-4), 448–471 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Evans, P.A.: Algorithms and Complexity for Annotated Sequence Analysis. PhD thesis, University of Alberta (1999)Google Scholar
  8. 8.
    Jansson, J., Peng, Z.: Algorithms for finding a most similar subforest. Theory Comput. Syst 48(4), 865–887 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Jiang, T., Lin, G., Ma, B., Zhang, K.: The longest common subsequence problem for arc-annotated sequences. J. Discrete Algorithms 2(2), 257–270 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Jiang, T., Wang, L., Zhang, K.: Alignment of trees – an alternative to tree edit. TCS: Theoretical Computer Science 143 (1995)Google Scholar
  11. 11.
    Klein, P.N.: Computing the Edit-Distance between Unrooted Ordered Trees. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 91–102. Springer, Heidelberg (1998)Google Scholar
  12. 12.
    Landau, G.M., Vishkin, U.: Fast parallel and serial approximate string matching. Journal of Algorithms 10, 157–169 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lin, G.H., Chen, Z.Z., Jiang, T., Wen, J.: The longest common subsequence problem for sequences with nested arc annotations. JCSS: Journal of Computer and System Sciences 65(3), 465–480 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Möhl, M., Will, S., Backofen, R.: Lifting Prediction to Alignment of RNA Pseudoknots. In: Batzoglou, S. (ed.) RECOMB 2009. LNCS, vol. 5541, pp. 285–301. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Moore, P.B.: Structural motifs in RNA. Annual Review of Biochemistry 68, 287–300 (1999)CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    Siebert, S., Backofen, R.: A dynamic programming approach for finding common patterns in RNAS. Journal of Computational Biology 14(1), 33–44 (2007)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. Journal of Computer and System Sciences 26(3), 362–391 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Tai, K.C.: The tree-to-tree correction problem. JACM: Journal of the ACM 26(3), 422–433 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM Journal on Computing 18(6), 1245–1262 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mika Amit
    • 1
  • Rolf Backofen
    • 3
    • 4
  • Steffen Heyne
    • 3
  • Gad M. Landau
    • 1
    • 2
  • Mathias Möhl
    • 3
  • Christina Schmiedl
    • 3
  • Sebastian Will
    • 3
    • 5
  1. 1.Department of Computer ScienceUniversity of HaifaHaifaIsrael
  2. 2.Department of Computer Science and EngineeringNYU-PolyBrooklynUSA
  3. 3.Bioinformatics, Institute of Computer ScienceAlbert-Ludwigs-UniversitätFreiburgGermany
  4. 4.Center for Biological Signaling Studies (BIOSS)Albert-Ludwigs-UniversitätFreiburgGermany
  5. 5.CSAIL and Mathematics DepartmentMITCambridgeUSA

Personalised recommendations