NP-Completeness of the Direct Energy Barrier Problem without Pseudoknots

  • Ján Maňuch
  • Chris Thachuk
  • Ladislav Stacho
  • Anne Condon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5877)

Abstract

Knowledge of energy barriers between pairs of secondary structures for a given DNA or RNA molecule is useful, both in understanding RNA function in biological settings and in design of programmed molecular systems. Current heuristics are not guaranteed to find the exact energy barrier, raising the question whether the energy barrier can be calculated efficiently. In this paper, we study the computational complexity of a simple formulation of the energy barrier problem, in which each base pair contributes an energy of − 1 and only base pairs in the initial and final structures may be used on a folding pathway from initial to final structure. We show that this problem is NP-complete.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Kameda, A., Yamamoto, M., Uejima, H., Hagiya, M., Sakamoto, K., Ohuchi, A.: Hairpin-based state machine and conformational addressing: Design and experiment. Natural Computing 4, 103–126 (2005)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Yurke, B., Turberfield, A.J., Mills, A.J.J., Simmel, F.C., Neumann, J.L.: A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000)CrossRefGoogle Scholar
  3. 3.
    Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314, 1585–1588 (2006)CrossRefGoogle Scholar
  4. 4.
    Simmel, F.C., Dittmer, W.U.: DNA nanodevices. Small 1, 284–299 (2005)CrossRefGoogle Scholar
  5. 5.
    Uejima, H., Hagiya, M.: Secondary structure design of multi-state DNA machines based on sequential structure transitions. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 74–85. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Hagiya, M., Yaegashi, S., Takahashi, K.: Computing with hairpins and secondary structures of DNA. In: Chen, J., Jonoska, N., Rozenberg, G. (eds.) Nanotechnology: Science and Computation. Natural Computing Series, pp. 293–308. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Yin, P., Choi, H., Calvert, C., Pierce, N.: Programming biomolecular self-assembly pathways. Nature 451, 318–322 (2008)CrossRefGoogle Scholar
  8. 8.
    Uejima, H., Hagiya, M.: Analyzing secondary structure transition paths of DNA/RNA molecules. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 86–90. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Chen, S.J., Dill, K.A.: RNA folding energy landscapes. Proc. Nat. Acad. Sci. 97(2), 646–651 (2000)CrossRefGoogle Scholar
  10. 10.
    Russell, R., Zhuang, X., Babcock, H., Millett, I., Doniach, S., Chu, S., Herschlag, D.: Exploring the folding landscape of a structured RNA. Proc. Nat. Acad. Sci. 99, 155–160 (2002)CrossRefGoogle Scholar
  11. 11.
    Shcherbakova, I., Mitra, S., Laederach, A., Brenowitz, M.: Energy barriers, pathways, and dynamics during folding of large, multidomain RNAs. Curr. Opin. Chem. Biol., 655–666 (2008)Google Scholar
  12. 12.
    Treiber, D.K., Williamson, J.R.: Beyond kinetic traps in RNA folding. Curr. Opin. Struc. Biol. 11, 309–314 (2001)CrossRefGoogle Scholar
  13. 13.
    Flamm, C., Fontana, W., Hofacker, I.L., Schuster, P.: RNA folding at elementary step resolution. RNA, 325–338 (2000)Google Scholar
  14. 14.
    Tang, X., Thomas, S., Tapia, L., Giedroc, D.P., Amato, N.M.: Simulating RNA folding kinetics on approximated energy landscapes. J. Mol. Biol. 381, 1055–1067 (2008)CrossRefGoogle Scholar
  15. 15.
    van Batenburg, F.H.D., Gultyaev, A.P., Pleij, C.W.A., Ng, J., Oliehoek, J.: Pseudobase: a database with RNA pseudoknots. Nucl. Acids Res. 28(1), 201–204 (2000)CrossRefGoogle Scholar
  16. 16.
    Wolfinger, M.T.: The energy landscape of RNA folding. Master’s thesis, University Vienna (2001)Google Scholar
  17. 17.
    Flamm, C., Hofacker, I.L., Stadler, P.F., Wolfinger, M.T.: Barrier trees of degenerate landscapes. Zeitschrift für Physikalische Chemie 216, 155–174 (2002)CrossRefGoogle Scholar
  18. 18.
    Morgan, S.R., Higgs, P.G.: Barrier heights between ground states in a model of RNA secondary structure. J. Phys. A: Math. Gen. 31, 3153–3170 (1998)MATHCrossRefGoogle Scholar
  19. 19.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)MATHGoogle Scholar
  20. 20.
    Graham, R., Knuth, D., Patashnik, O.: Concrete Mathematics: a foundation for computer science. Addison-Wesley, Reading (1989)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ján Maňuch
    • 1
  • Chris Thachuk
    • 2
  • Ladislav Stacho
    • 1
  • Anne Condon
    • 2
  1. 1.School of Computing Science and Department of MathematicsSimon Fraser UniversityCanada
  2. 2.Department of Computer ScienceUniversity of British ColumbiaCanada

Personalised recommendations