Combinatorial RNA Design: Designability and Structure-Approximating Algorithm

  • Jozef Haleš
  • Ján Maňuch
  • Yann Ponty
  • Ladislav Stacho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9133)

Abstract

In this work, we consider the Combinatorial RNA Design problem, a minimal instance of the RNA design problem in which one must return an RNA sequence that admits a given secondary structure as its unique base pair maximizing structure.

First, we fully characterize designable structures using restricted alphabets. Then, under a classic four-letter alphabet, we provide a complete characterization for designable structures without unpaired bases. When unpaired bases are allowed, we characterize extensive classes of (non-)designable structures, and prove the closure of the set of designable structures under the stutter operation. Membership of a given structure to any of the classes can be tested in \(\varTheta (n)\) time, including the generation of a solution sequence for positive instances. Finally, we consider a structure-approximating version of the problem that allows to extend bands (stems). We provide a \(\varTheta (n)\) algorithm which, given a structure \(S\) avoiding two trivially non-designable motifs, transforms \(S\) into a designable structure by adding at most one base-pair to each of its stems, and returns a solution sequence.

References

  1. 1.
    Aguirre-Hernández, R., Hoos, H.H., Condon, A.: Computational RNA secondary structure design: empirical complexity and improved methods. BMC Bioinform. 8, 34 (2007)CrossRefGoogle Scholar
  2. 2.
    Avihoo, A., Churkin, A., Barash, D.: RNAexinv: an extended inverse RNA folding from shape and physical attributes to sequences. BMC Bioinform. 12(1), 319 (2011)CrossRefGoogle Scholar
  3. 3.
    Busch, A., Backofen, R.: INFO-RNA–a fast approach to inverse RNA folding. Bioinformatics 22(15), 1823–1831 (2006)CrossRefGoogle Scholar
  4. 4.
    Dai, D.C., Tsang, H.H., Wiese, K.C.: RNADesign: local search for RNA secondary structure design. In: IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB) (2009)Google Scholar
  5. 5.
    Esmaili-Taheri, A., Ganjtabesh, M., Mohammad-Noori, M.: Evolutionary solution for the RNA design problem. Bioinformatics 30(9), 1250–1258 (2014)CrossRefGoogle Scholar
  6. 6.
    Frid, Y., Gusfield, D.: A simple, practical and complete \(o(n^3/\log n)\)-time algorithm for RNA folding using the Four-Russians speedup. Algorithms Mol. Biol. 5, 13 (2010)CrossRefGoogle Scholar
  7. 7.
    Garcia-Martin, J.A., Clote, P., Dotu, I.: RNAiFOLD: a constraint programming algorithm for RNA inverse folding and molecular design. J. Bioinform. Comput. Biol. 11(2), 1350001 (2013)CrossRefGoogle Scholar
  8. 8.
    Griffiths-Jones, S., Bateman, A., Marshall, M., Khanna, A., Eddy, S.R.: RFAM: an RNA family database. Nucleic Acids Res. 31(1), 439–441 (2003)CrossRefGoogle Scholar
  9. 9.
    Höner Zu Siederdissen, C., Hammer, S., Abfalter, I., Hofacker, I.L., Flamm, C., Stadler, P.F.: Computational design of RNAs with complex energy landscapes. Biopolymers 99(12), 1124–1136 (2013)Google Scholar
  10. 10.
    Hofacker, I.L., Fontana, W., Stadler, P., Bonhoeffer, L., Tacker, M., Schuster, P.: Fast folding and comparison of RNA secondary structures. Monatshefte für Chemie/Chem. Monthly 125(2), 167–188 (1994)CrossRefGoogle Scholar
  11. 11.
    Levin, A., Lis, M., Ponty, Y., O’Donnell, C.W., Devadas, S., Berger, B., Waldispühl, J.: A global sampling approach to designing and reengineering RNA secondary structures. Nucleic Acids Res. 40(20), 10041–10052 (2012)CrossRefGoogle Scholar
  12. 12.
    Lyngsø, R.B., Anderson, J.W., Sizikova, E., Badugu, A., Hyland, T., Hein, J.: FRNAkenstein: multiple target inverse RNA folding. BMC Bioinform. 13, 260 (2012)CrossRefGoogle Scholar
  13. 13.
    Mathews, D.H., Sabina, J., Zuker, M., Turner, D.H.: Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 288(5), 911–940 (1999)CrossRefGoogle Scholar
  14. 14.
    Nussinov, R., Jacobson, A.: Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc. Natl. Acad. Sci. USA 77, 6903–6913 (1980)CrossRefGoogle Scholar
  15. 15.
    Reinharz, V., Ponty, Y., Waldispühl, J.: A weighted sampling algorithm for the design of RNA sequences with targeted secondary structure and nucleotide distribution. Bioinformatics 29(13), i308–i315 (2013)CrossRefGoogle Scholar
  16. 16.
    Rodrigo, G., Landrain, T.E., Majer, E., Daròs, J.-A., Jaramillo, A.: Full design automation of multi-state RNA devices to program gene expression using energy-based optimization. PLoS Comput. Biol. 9(8), e1003172 (2013)CrossRefGoogle Scholar
  17. 17.
    Schnall-Levin, M., Chindelevitch, L., Berger, B.: Inverting the Viterbi algorithm: an abstract framework for structure design. In: Machine Learning, Proceedings of the Twenty-Fifth International Conference (ICML 2008), Helsinki, Finland, June 5–9, 2008, pp. 904–911 (2008)Google Scholar
  18. 18.
    Takahashi, M.K., Lucks, J.B.: A modular strategy for engineering orthogonal chimeric RNA transcription regulators. Nucleic Acids Res. 41(15), 7577–7588 (2013)CrossRefGoogle Scholar
  19. 19.
    Taneda, A.: MODENA: a multi-objective RNA inverse folding. Adv. Appl. Bioinform. Chem. 4, 1–12 (2011)Google Scholar
  20. 20.
    Turner, D.H., Mathews, D.H.: NNDB: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure. Nucleic Acids Res. 38, D280–D282 (2010). (Database issue)CrossRefGoogle Scholar
  21. 21.
    Wu, S.Y., Lopez-Berestein, G., Calin, G.A., Sood, A.K.: RNAi therapies: drugging the undruggable. Sci. Transl. Med. 6(240), 240ps7 (2014)CrossRefGoogle Scholar
  22. 22.
    Zadeh, J.N., Wolfe, B.R., Pierce, N.A.: Nucleic acid sequence design via efficient ensemble defect optimization. J. Comput. Chem. 32(3), 439–452 (2011)CrossRefGoogle Scholar
  23. 23.
    Zhou, Y., Ponty, Y., Vialette, S., Waldispuhl, J., Zhang, Y., Denise, A.: Flexible RNA design under structure and sequence constraints using formal languages. In: Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics, BCB 2013, pp. 229–238. ACM (2013)Google Scholar
  24. 24.
    Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9, 133–148 (1981)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jozef Haleš
    • 1
  • Ján Maňuch
    • 1
    • 3
  • Yann Ponty
    • 1
    • 2
  • Ladislav Stacho
    • 1
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Pacific Institute for Mathematical SciencesCNRS UMI3069VancouverCanada
  3. 3.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

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