A Study of Accessible Motifs and RNA Folding Complexity

  • Ydo Wexler
  • Chaya Zilberstein
  • Michal Ziv-Ukelson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3909)

Abstract

mRNA molecules are folded in the cells and therefore many of their substrings may actually be inaccessible to protein and microRNA binding. The need to apply an accessability criterion to the task of genome-wide mRNA motif discovery raises the challenge of overcoming the core O(n3) factor imposed by the time complexity of the currently best known algorithms for RNA secondary structure prediction [24, 25, 43].

We speed up the dynamic programming algorithms that are standard for RNA folding prediction. Our new approach significantly reduces the computations without sacrificing the optimality of the results, yielding an expected time complexity of O(n2ψ(n)), where ψ(n) is shown to be constant on average under standard polymer folding models. Benchmark analysis confirms that in practice the runtime ratio between the previous approach and the new algorithm indeed grows linearly with increasing sequence size.

The fast new RNA folding algorithm is utilized for genome-wide discovery of accessible cis-regulatory motifs in data sets of ribosomal densities and decay rates of S. cerevisiae genes and to the mining of exposed binding sites of tissue-specific microRNAs in A. Thaliana.

Further details, including additional figures and proofs to all lemmas, can be found at: http://www.cs.tau.ac.il/~michaluz/QuadraticRNAFold.pdf

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References

  1. 1.
    Aggarawal, A., Park, J.: Notes on searching in multidimensional monotone arrays. In: Proc. 29th IEEE Symp. on Foundations of Computer Science, pp. 497–512 (1988)Google Scholar
  2. 2.
    Akmaev, V., Kelley, S., Stormo, G.: A phylogenetic approach to RNA structure prediction. Proc. Int. Conf. Intell. Syst. Mol. Biol. 235, 10–17 (1999)Google Scholar
  3. 3.
    Arava, Y., Wang, Y., Storey, J., Liu, C., Brown, P., Herschlag, D.: Genome-wide analysis of mRNA translation profiles in saccharomyces cerevisiae. PNAS 100, 3889–3894 (2003)CrossRefGoogle Scholar
  4. 4.
    Christofferson, R., et al.: Application of computational technologies to ribozyme biotechnology products. J. Molecular Struct (Theochem.) 311, 273 (1994)CrossRefGoogle Scholar
  5. 5.
    Crochemore, M., Landau, G., Schieber, B., Ziv-Ukelson, M.: Re-Use Dynamic Programming for Sequence Alignment:An Algorithmic Toolkit. String Algorithmics. KCL Press (2005)Google Scholar
  6. 6.
    Draper, D.: Themes in RNA-protein recognition. J. Mol. Biol. 293(2), 255–270 (1999)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Eppstein, D., Galil, Z., Giancarlo, R.: Speeding up dynamic programming. In: Proc. 29th IEEE Symp. on Foundations of Computer Science, pp. 488–496 (1988)Google Scholar
  8. 8.
    Fisher, M.: Shape of a self-avoiding walk or polymer chain. JCP 44, 616–622 (1966)CrossRefGoogle Scholar
  9. 9.
    Galil, Z., Giancarlo, R.: Speeding up dynamic programming with applications to molecular biology. Theoretical Computer Science 64, 107–118 (1989)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Giancarlo, R.: Dynamic Programming: Special Cases. In: Apostolico, A., Galil, Z. (eds.) Pattern Matching Algorithms, Oxford University Press, Oxford (1997)Google Scholar
  11. 11.
    Goodwin, E., Okkema, P., Evans, T.C., Kimble, J.: Translational regulation of tra-2 by its 3’ untranslated region controls sexual identity in c. elegans. Cell 75, 329–339 (1993)CrossRefGoogle Scholar
  12. 12.
    Goulden, C.: Methods of Statistical Analysis, 2nd edn. Wiley, New York (1956)Google Scholar
  13. 13.
    Gray, N., Wickens, M.: Annu. Rev. Cell. Dev. Biol. 14, 399–458 (1998)Google Scholar
  14. 14.
    Hofacker, I.L.: Vienna RNA secondary structure server. NAR (13), 3429–3431 (2003)Google Scholar
  15. 15.
    Jayaraman, A., Walton, S.P.: Rational selection and quantitative evaluation of antisense oligonucleotides. Biochim. Biophys. Acta 1520, 105 (2001)Google Scholar
  16. 16.
    Ji, Y., Xu, X., Stormo, G.: Bioinformatics 20, 1591–1602 (2004)Google Scholar
  17. 17.
    Kabakcioglu, A., Stella, A.: A scale-free network hidden in the collapsing polymer. ArXiv Condensed Matter e-prints (September 2004)Google Scholar
  18. 18.
    Kafri, Y., Mukamel, D., Peliti, L.: Why is the dna denaturation transition first order? Physical Review Letters 85, 4988–4991 (2000)CrossRefGoogle Scholar
  19. 19.
    Larmore, L., Schieber, B.: On-line dynamic programming with applications to the prediction of RNA secondary structure. J. Algorithms 12(3), 490–515 (1991)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Liu, T., Bundschuh, R.: Quantification of the differences between quenched and annealed averaging for RNA secondary structures. ArXiv Physics e-prints (April 2005)Google Scholar
  21. 21.
    Llave, C., et al.: Cleavage of scarecrow-like mRNA targets directed by a class of arabidopsis miRNA. Science 297, 2053–2056 (2002)CrossRefGoogle Scholar
  22. 22.
    Lyngsø, R.B., Zuker, M., Pedersen, C.N.S.: An improved algorithm for RNA secondary structure prediction. Technical Report RS-99-15, brics (1999)Google Scholar
  23. 23.
    Mathews, D., et al.: RNA 5, 1458–1469 (1999)Google Scholar
  24. 24.
    Mathews, D., Sabina, J., Zuker, M., Turner, D.: JMB 288, 911 (1999)Google Scholar
  25. 25.
    Nussinov, R., Jacobson, A.: Fast algorithm for predicting the secondary structure of single-stranded RNA. PNAS 77(11), 6309–6313 (1980)CrossRefGoogle Scholar
  26. 26.
    Pavesi, G., et al.: An algorithm for finding conserved secondary structure motifs in unaligned RNA sequences. NAR 32, 3258–3269 (2004)CrossRefGoogle Scholar
  27. 27.
    Robins, et al.: PNAS 102, 4006–4009 (2005)Google Scholar
  28. 28.
    Ross, J.: mRNA stability in mammalian cells. Microbiol Rev. 59(3), 423–450 (1995)Google Scholar
  29. 29.
    Sagot, M.: Spelling approximate or repeated motifs using a suffix tree. LNCS, pp. 111–127. Springer, Heidelberg (1998)Google Scholar
  30. 30.
    Smith, L., et al.: Eur. J. Pharm. Sci. 11, 191 (2000)Google Scholar
  31. 31.
    Tang, G., et al.: Framework for RNA silencing in plants. Genes Dev. 17, 49–63 (2003)CrossRefGoogle Scholar
  32. 32.
    Tinoco, I., et al.: Nature New Biology 246, 40–41 (1973)Google Scholar
  33. 33.
    Vanderzande, C.: Lattice Models of Polymers. Cambridge Lecture Notes in Physics, vol. 11. Cambridge University Press, Cambridge (1998)MATHCrossRefGoogle Scholar
  34. 34.
    Waterman, M., Smith, T.: Rapid dynamic programming algorithms for RNA secondary structure. Adv. Appl. Math. 7, 455–464 (1986)MATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    Welsh, M., Scherberg, N., Gilmore, R., Steiner, D.: Translational control of insulin biosynthesis. Biochem. J. 235, 459–467 (1986)Google Scholar
  36. 36.
    Wilkie, G., Dickson, K., Gray, N.: Regulation of mRNA translation by 5’- and 3’-utr-binding factors. Trends Biochem. Sci. 28, 182–188 (2003)CrossRefGoogle Scholar
  37. 37.
    Yang, E., et al.: Decay rates of human mRNAs: correlation with functional characteristics and sequence attributes. Genome Res. 13, 1863–1872 (2003)CrossRefGoogle Scholar
  38. 38.
    Zilberstein, C., Eskin, E., Yakhini, Z.: Sequence motifs in ranked expression data. In: The First RECOMB Satellite Workshop on Regulatory Genomics (2004)Google Scholar
  39. 39.
    Zilberstein, C., Ziv-Ukelson, M., Pinter, R.Y., Yakhini, Z.: A high-throughput approach for associating microRNAs with their activity conditions. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2005. LNCS (LNBI), vol. 3500, pp. 133–151. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  40. 40.
    Zubiaga, A., Belasco, J., Greenberg, M.: The nonamer uuauuuauu is the key au-rich sequence motif that mediates mRNA degradation. Mol. Cell. Biol. 15, 2219–2230 (1995)Google Scholar
  41. 41.
    Zuker, M.: Computer prediction of RNA structure. Methods Enzymol. 180, 262–288 (1989)CrossRefGoogle Scholar
  42. 42.
    Zuker, M.: NAR (13), 3406–3415 (2003)Google Scholar
  43. 43.
    Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. NAR 9(1), 133–148 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ydo Wexler
    • 1
  • Chaya Zilberstein
    • 1
  • Michal Ziv-Ukelson
    • 2
  1. 1.Dept. of Computer ScienceTechnion – Israel Institute of TechnologyHaifaIsrael
  2. 2.School of Computer ScienceTel-Aviv UniversityTel-AvivIsrael

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