Advertisement

On the Power of Oritatami Cotranscriptional Folding with Unary Bead Sequence

  • Szilárd Zsolt Fazekas
  • Kohei MaruyamaEmail author
  • Reoto Morita
  • Shinnosuke SekiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)

Abstract

An oritatami system is a novel mathematical model of RNA cotranscriptional folding, which has recently proven extremely significant in information processing in organisms and also controllable artificially in a test tube to construct an artificial structure by folding an RNA sequence. This model has turned out to be Turing universal. One next step is to simplify the Turing universal oritatami system and another is to characterize weaker oritatami systems as we may not need Turing universality for applications. In this paper, we look at oritatami systems that folds a unary sequence, and show that under reasonable assumptions, these systems are not universal.

Notes

Acknowledgements

We thank Yo-Sub Han for his valuable comments on the contents of this paper.

References

  1. 1.
    Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  2. 2.
    Cook, M.: Universality in elementary cellular automata. Complex Syst. 15, 1–40 (2004)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Demaine, E., et al.: Know when to fold ’Em: self-assembly of shapes by folding in oritatami. In: Doty, D., Dietz, H. (eds.) DNA 2018. LNCS, vol. 11145, pp. 19–36. Springer, Cham (2018).  https://doi.org/10.1007/978-3-030-00030-1_2CrossRefGoogle Scholar
  4. 4.
    Elonen, A., et al.: Algorithmic design of 3D wireframes RNA polyhedral. DNA 24 poster (2018)Google Scholar
  5. 5.
    Geary, C.W., Andersen, E.S.: Design principles for single-stranded RNA origami structures. In: Murata, S., Kobayashi, S. (eds.) DNA 2014. LNCS, vol. 8727, pp. 1–19. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-11295-4_1CrossRefGoogle Scholar
  6. 6.
    Geary, C., Meunier, P.E., Schabanel, N., Seki, S.: Programming biomolecules that fold greedily during transcription. In: Proceedings of MFCS 2016, LIPIcs, vol. 58, pp. 43:1–43:14 (2016)Google Scholar
  7. 7.
    Geary, C., Meunier, P.E., Schabanel, N., Seki, S.: Proving the turing universality of oritatami cotranscriptional folding. In: Proceedings of ISAAC 2018 (2018, in press)Google Scholar
  8. 8.
    Geary, C., Rothemund, P.W.K., Andersen, E.S.: A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science 345(6198), 799–804 (2014)CrossRefGoogle Scholar
  9. 9.
    Hales, T.C.: The Jordan curve theorem, formally and informally. Am. Math. Mon. 114(10), 882–894 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Han, D., et al.: Single-stranded DNA and RNA origami. Science 358(6369), 1402 (2017)CrossRefGoogle Scholar
  11. 11.
    Pratchett, T.: Troll Bridge. Pan Books, London (1992)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Engineering ScienceAkita UniversityAkitaJapan
  2. 2.The University of Electro-CommunicationsChofuJapan

Personalised recommendations