Advertisement

Graph Representations and Algorithms in Computational Biology of RNA Secondary Structure

Chapter

Abstract

The analysis of RNA structures is an important problem in computational biology. In this chapter we review various algorithms to predict and compare RNA secondary structures. These algorithms are based on graph theory and use representations of RNA secondary structure as outerplanar graphs and trees.

Keywords

Bioinformatics RNA folding Outerplanar graphs Tree editing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

Funding from the Austrian GEN-AU projects “noncoding RNA” and “Bioinformatics Integration Network” as well as financial support to the CIBIV institute from the Wiener Wissenschafts-, Forschungs- and Technologiefonds (WWTF) is gratefully acknowledged.

References

  1. 1.
    Bartel DP (2004) MicroRNAs: genomics, biogenesis, mechanism, and function. Cell 116(2): 281–297CrossRefGoogle Scholar
  2. 2.
    Bille P (2005) A survey on tree edit distance and related problems. Theor Comput Sci 337 (1–3):217–239MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bunke H (1983) What is the distance between graphs? Bull EATCS 20:35–39Google Scholar
  4. 4.
    Carninci P et al (2005) The transcriptional landscape of the mammalian genome. Science 309(5740):1559–1563CrossRefGoogle Scholar
  5. 5.
    Doudna JA, Cech TR (2002) The chemical repertoire of natural ribozymes. Nature 418(6894):222–228CrossRefGoogle Scholar
  6. 6.
    Dowell RD, Eddy SR (2004) Evaluation of several lightweight stochastic context-free grammars for RNA secondary structure prediction. BMC Bioinformatics 5:71CrossRefGoogle Scholar
  7. 7.
    Eddy SR, Durbin R (1994) RNA sequence analysis using covariance models. Nucleic Acids Res 22(11):2079–2088CrossRefGoogle Scholar
  8. 8.
    Fontana W, Konings DA, Stadler PF, Schuster P (1993) Statistics of RNA secondary structures. Biopolymers 33:1389–1404CrossRefGoogle Scholar
  9. 9.
    Hofacker IL, Fontana W, Stadler PF, Bonhoeffer LS, Tacker M, Schuster P (1994) Fast folding and comparison of RNA secondary structures. Monatsh Chem 125:167–188CrossRefGoogle Scholar
  10. 10.
    Hofacker IL, Schuster P, Stadler PF (1998) Combinatorics of RNA secondary structures. Discrete Appl Math 89:177–207MathSciNetGoogle Scholar
  11. 11.
    Hofacker IL, Stadler PF (2007) RNA secondary structures. In: Lengauer T (ed) Bioinformatics: from genomes to therapies, vol 1. Wiley-VCH, Weinheim, Germany, pp 439–489CrossRefGoogle Scholar
  12. 12.
    Kaden F (1982) Graphmetriken und Distanzgraphen. ZKI-Informationen Akad Wiss DDR 2(82):1–63Google Scholar
  13. 13.
    Klein P (1998) Computing the edit distance between unrooted ordered trees. In: Bilardi G, Italiano GF, Pietracaprina A, Pucci G (eds) Algorithms – ESA ’98, Proceedings of 6th annual European symposium, Venice, Italy, 24–26 August 1998. Lecture Notes in Computer Science, vol 1461. Springer, Heidelberg, pp 91–102Google Scholar
  14. 14.
    Le SY, Nussinov R, Maizel JV (1989) Tree graphs of RNA secondary structures and their comparisons. Comput Biomed Res 22(5):461–473CrossRefGoogle Scholar
  15. 15.
    Mathews DH, Sabina J, Zuker M, Turner H (1999) Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure. J Mol Biol 288:911–940CrossRefGoogle Scholar
  16. 16.
    McCaskill JS (1990) The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29:1105–1119CrossRefGoogle Scholar
  17. 17.
    Nelson DL, Cox MM (2004) Lehninger principles of biochemistry, 4th edn. W.H. Freeman, New YorkGoogle Scholar
  18. 18.
    Nussinov R, Jacobson AB (1980) Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc Natl Acad Sci USA 77(11):6309–6313CrossRefGoogle Scholar
  19. 19.
    Nussinov R, Piecznik G, Griggs JR, Kleitman DJ (1978) Algorithms for loop matching. SIAM J Appl Math 35(1):68–82MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Selkow SM (1977) The tree-to-tree editing problem. Inf Process Lett 6(6):184–186MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Shapiro BA (1988) An algorithm for comparing multiple RNA secondary stuctures. CABIOS 4:387–393Google Scholar
  22. 22.
    Shapiro BA, Zhang K (1990) Comparing multiple RNA secondary structures using tree comparisons. CABIOS 6:309–318Google Scholar
  23. 23.
    Sobik F (1982) Graphmetriken und Klassifikation strukturierter Objekte. ZKI-Informationen Akad Wiss DDR 2(82):63–122Google Scholar
  24. 24.
    Sobik F (1986) Modellierung von Vergleichsprozessen auf der Grundlage von Ähnlichkeitsmaßen für Graphen. ZKI-Informationen Akad Wiss DDR 4:104–144Google Scholar
  25. 25.
    Tai K (1979) The tree-to-tree correction problem. J ACM 26:422–433MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Touchard J (1952) Sur un problème de configurations et sur les fractions continues. Can J Math 4(6894):2–25MATHMathSciNetGoogle Scholar
  27. 27.
    Washietl S et al (2007) Structured RNAs in the ENCODE selected regions of the human genome. Genome Res 17(6):852–864CrossRefGoogle Scholar
  28. 28.
    Washietl S, Hofacker IL, Lukasser M, Hüttenhofer A, Stadler PF (2005) Mapping of conserved RNA secondary structures predicts thousands of functional non-coding RNAs in the human genome. Nat Biotechnol 23:1383–1390CrossRefGoogle Scholar
  29. 29.
    Waterman MS (1978) Secondary structure of single-stranded nucleic acids. Studies on foundations and combinatorics. Advances in Mathematics Supplementary Studies. Academic Press, New York, 1:167–212Google Scholar
  30. 30.
    Waterman MS, Smith TF (1978) RNA secondary structure: a complete mathematical analysis. Math Biosci 42:257–266MATHCrossRefGoogle Scholar
  31. 31.
    Xia T, SantaLucia J, Burkard ME, Kierzek R, Schroeder SJ, Jiao X, Cox C, Turner DH (1998) Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with watson-crick base pairs. Biochemistry 37(42):14719–14735CrossRefGoogle Scholar
  32. 32.
    Yan L (1995) A family of special outerplanar graphs with only one triangle satisfying the cycle basis interpolation property. Discrete Math 143(1–3):293–297MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Yao Z, Weinberg Z, Ruzzo WL (2006) CMfinder – a covariance model based RNA motif finding algorithm. Bioinformatics 22(4):445–452CrossRefGoogle Scholar
  34. 34.
    Zelinka B (1975) On a certain distance between isomorphism classes of graphs. Časopis pro p̆est Mathematiky 100:371–373Google Scholar
  35. 35.
    Zhang K, Shasha D (1989) Simple fast algorithms for the editing distance between trees and related problems. SIAM J Comput 18:1245–1262MATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Zuker M (2003) Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Res 31(13):3406–15CrossRefGoogle Scholar
  37. 37.
    Zuker M, Sankoff D (1984) RNA secondary structures and their prediction. Bull Math Biol 46:591–621MATHGoogle Scholar
  38. 38.
    Zuker M, Stiegler P (1981) Optimal computer folding of larger RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res 9:133–148CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Max F. Perutz LaboratoriesCenter for Integrative Bioinformatics ViennaViennaAustria
  2. 2.University of Vienna, Medical University of Vienna and University of Veterinary MedicineViennaAustria

Personalised recommendations