Rapid ab initio RNA Folding Including Pseudoknots Via Graph Tree Decomposition

  • Jizhen Zhao
  • Russell L. Malmberg
  • Liming Cai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4175)


The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable computation of the sequence conformation from intriguing nucleotide interactions. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree polynomial time complexity, which is too expensive to use. Heuristic methods may yield time-efficient algorithms but they do not guarantee optimality of the predicted structure. This paper introduces a new and efficient algorithm for the prediction of RNA structure with pseudoknots for which the structure is not restricted. Novel prediction techniques are developed based on graph tree decomposition. In particular, stem overlapping relationships are defined with a graph, in which a specialized maximum independent set (IS) corresponds to the desired optimal structure. Such a graph is tree decomposable; dynamic programming over a tree decomposition of the graph leads to an efficient algorithm. The new algorithm is evaluated on a large number of RNA sequence sets taken from diverse resources. It demonstrates overall sensitivity and specificity that outperforms or is comparable with those of previous optimal and heuristic algorithms yet it requires significantly less time than other optimal algorithms.


Tree Decomposition Hepatitis Delta Virus Tree Width Thermodynamic Energy Dynamic Programming Table 
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.
    Abrahams, J., van den Berg, M., van Batenburg, E., Pleij, C.: Prediction of RNA secondary structure, including pseudoknotting, by computer simulation. Nucleic Acids Res. 18, 3035–3044 (1990)CrossRefGoogle Scholar
  2. 2.
    Bodlaender, H.L.: Classes of graphs with bounded tree-width. Tech. Rep. RUU-CS-86-22, Dept. of Computer Science, Utrecht University, the Netherlands (1986)Google Scholar
  3. 3.
    Bodlaender, H.L.: Dynamic programming algorithms on graphs with bounded tree-width. In: Lepistö, T., Salomaa, A. (eds.) ICALP 1988. LNCS, vol. 317, pp. 105–119. Springer, Heidelberg (1988)Google Scholar
  4. 4.
    Brown, J.: The ribonuclease p database. Nucleic Acids Res. 27, 314 (1999)CrossRefGoogle Scholar
  5. 5.
    Chen, J.-H., Le, S.-Y., Maize, J.V.: Prediction of common secondary structures of RNAs: a genetic algorithm approach. Nucleic Acids Research 28(4), 991–999 (2000)CrossRefGoogle Scholar
  6. 6.
    Dirks, R., Pierce, N.: A partition function algorithm for nucleic acid secondary structure including pseudoknots. J. Comput. Chem. 24, 1664–1677 (2003)CrossRefGoogle Scholar
  7. 7.
    Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.J.: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1998)zbMATHCrossRefGoogle Scholar
  8. 8.
    Eddy, S.R., Durbin, R.: RNA sequence analysis using covariance models. Nucleic Acids Research 22, 2079–2088 (1994)CrossRefGoogle Scholar
  9. 9.
    Giedroc, D., Theimer, C., Nixon, P.: Structure, stability and function of RNA pseudoknots involved in stimulating ribosomal frame shifting. J. of Molecular Biology 298, 167–185 (2000)CrossRefGoogle Scholar
  10. 10.
    Hicks, I.V., Koster, A.M.C.A., Kolotoglu, E.: Branch and tree decomposition techniques for discrete optimization. In: Tutorials in Operations Research: INFORMS – New Orleans 2005 (2005)Google Scholar
  11. 11.
    Ji, Y., Xu, X., Stormo, G.D.: A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences. Bioinformatics 20(10), 1591–1602 (2004)CrossRefGoogle Scholar
  12. 12.
    Ke, A., Zhou, K., Ding, F., Cate, J.H., Doudna, J.A.: A conformational switch controls hepatitis delta virus ribozyme catalysis. Nature 429, 201–205 (2004)CrossRefGoogle Scholar
  13. 13.
    Lyngso, R.B., Pedersen, C.N.S.: RNA pseudoknot prediction in energy-based models. J. of Computational Biology 7(3-4), 409–427 (2000)CrossRefGoogle Scholar
  14. 14.
    Mathews, D.H., Sabina, J., Zuker, M., Pederson, C.N.S.: Expanded sequence dependence of the thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 288, 911–940 (1999)CrossRefGoogle Scholar
  15. 15.
    Nussinov, R., Pieczenik, G., Griggs, J., Kleitman, D.: Algorithms for loop matchings. SIAM J. Applied Mathematics 35, 68–82 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Ren, J., Rastegart, B., Condon, A., Hoos, H.H.: HotKnots: Heuristic prediction of RNA secondary structures including pseudoknots. RNA 11, 1194–1504 (2005)CrossRefGoogle Scholar
  17. 17.
    Rivas, E., Eddy, S.R.: A dynamic programming algorithm for RNA structure prediction including pseudoknots. J. Molecular Biology 285, 2053–2068 (1999)CrossRefGoogle Scholar
  18. 18.
    Robertson, N., Seymour, P.D.: Graph minors ii. algorithmic aspects of tree width. J. Algorithms 7, 309–322 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Ruan, J., Stormo, G.D., Zhang, W.: An iterated loop matching approach to the prediction of RNA secondary structures with pseudoknots. Bioinformatics 20(1), 58–66 (2004)CrossRefGoogle Scholar
  20. 20.
    Serra, M.J., Turner, D.H., Freier, S.M.: Predicting thermodynamic properties of RNA. Meth. Enzymol. 259, 243–261 (1995)Google Scholar
  21. 21.
    Song, Y., Liu, C., Malmberg, R.L., Pan, F., Cai, L.: Tree decomposition based fast search of RNA structures including pseudoknots in genomes. In: Proc. Comput. System Bioinformatics Conf. CSB 2005, pp. 223–234. IEEE Computer Society, Los Alamitos (2005)Google Scholar
  22. 22.
    Sprinzl, M., Horn, C., Brown, M., Ioudovitch, A., Steinberg, S.: Compilation of tRNA sequences and sequences of tRNA genes. Nucleic Acids Res. 26, 148–153 (1998)CrossRefGoogle Scholar
  23. 23.
    Tabaska, J., Cary, R., Gabow, H., Stormo, G.: An RNA folding method capable of identifying pseudoknots and base triples. Bioinformatics 14(8), 691–699 (1998)CrossRefGoogle Scholar
  24. 24.
    van Batenburg, F., Gultyaev, A., Pleij, C., Ng, J., Oliehoek, J.: Pseudobase: a database with RNA pseudoknots. Nucleic Acids Res. 28, 201–204 (2000)CrossRefGoogle Scholar
  25. 25.
    Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9(1), 133–148 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jizhen Zhao
    • 1
  • Russell L. Malmberg
    • 2
  • Liming Cai
    • 1
  1. 1.Department of Computer ScienceUniversity of GeorgiaAthensUSA
  2. 2.Department of Plant BiologyUniversity of GeorgiaAthensUSA

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