Proving the Turing Universality of Oritatami Co-Transcriptional Folding

Authors Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, Shinnosuke Seki



PDF
Thumbnail PDF

File

LIPIcs.ISAAC.2018.23.pdf
  • Filesize: 7.73 MB
  • 13 pages

Document Identifiers

Author Details

Cody Geary
  • California Institute of Technology, Pasadena, CA, USA
Pierre-Étienne Meunier
  • Maynooth University, Ireland
Nicolas Schabanel
  • CNRS, ÉNS de Lyon (LIP, UMR 5668), France and IXXI, U. Lyon, France, http://perso.ens-lyon.fr/nicolas.schabanel/
Shinnosuke Seki
  • Oritatami Lab, University of Electro-Communications, Tokyo, Japan, http://www.sseki.lab.uec.ac.jp/

Cite AsGet BibTex

Cody Geary, Pierre-Étienne Meunier, Nicolas Schabanel, and Shinnosuke Seki. Proving the Turing Universality of Oritatami Co-Transcriptional Folding. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ISAAC.2018.23

Abstract

We study the oritatami model for molecular co-transcriptional folding. In oritatami systems, the transcript (the "molecule") folds as it is synthesized (transcribed), according to a local energy optimisation process, which is similar to how actual biomolecules such as RNA fold into complex shapes and functions as they are transcribed. We prove that there is an oritatami system embedding universal computation in the folding process itself. Our result relies on the development of a generic toolbox, which is easily reusable for future work to design complex functions in oritatami systems. We develop "low-level" tools that allow to easily spread apart the encoding of different "functions" in the transcript, even if they are required to be applied at the same geometrical location in the folding. We build upon these low-level tools, a programming framework with increasing levels of abstraction, from encoding of instructions into the transcript to logical analysis. This framework is similar to the hardware-to-algorithm levels of abstractions in standard algorithm theory. These various levels of abstractions allow to separate the proof of correctness of the global behavior of our system, from the proof of correctness of its implementation. Thanks to this framework, we were able to computerise the proof of correctness of its implementation and produce certificates, in the form of a relatively small number of proof trees, compact and easily readable/checkable by human, while encapsulating huge case enumerations. We believe this particular type of certificates can be generalised to other discrete dynamical systems, where proofs involve large case enumerations as well.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Applied computing → Life and medical sciences
  • Hardware → Biology-related information processing
Keywords
  • Molecular computing
  • Turing universality
  • co-transcriptional folding

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. J. Boyle, G. Robillard, and S. Kim. Sequential folding of transfer RNA. A nuclear magnetic resonance study of successively longer tRNA fragments with a common 5' endA nuclear magnetic resonance study of successively longer tRNA fragments with a common 5' end. J. Mol. Biol., 139:601-625, 1980. Google Scholar
  2. M. Cook. Universality in Elementary Cellular Automata. Complex Systems, 15:1-40, 2004. Google Scholar
  3. E.D. Demaine, J. Hendricks, M. Olsen, M.J. Patitz, T. Rogers N. Schabanel, S. Seki, and H. Thomas. Know When to Fold 'Em: Self-Assembly of Shapes by Folding in Oritatami. In DNA, 2018. To be published. Google Scholar
  4. K. L. Frieda and S. M. Block. Direct observation of cotranscriptional folding in an adenine riboswitch. Science, 338(6105):397-400, 2012. Google Scholar
  5. P. Gács. Reliable cellular automata with self-organization. In FOCS, pages 90-99, 1997. Google Scholar
  6. C. Geary, P.-É. Meunier, N. Schabanel, and S. Seki. Programming Biomolecules that Fold Greedily during Transcription. In MFCS, volume LIPIcs 58, pages 43:1-43:14, 2016. Google Scholar
  7. C. Geary, P-É Meunier, N. Schabanel, and S. Seki. Proving the Turing Universality of Oritatami Co-Transcriptional Folding (Full Text). CoRR, 2018. URL: http://arxiv.org/abs/1508.00510.
  8. C. Geary, P. W. K. Rothemund, and E. S. Andersen. A Single-Stranded Architecture for Cotranscriptional Folding of RNA Nanostructures. Science, 345:799-804, 2014. Google Scholar
  9. Y-S. Han and H. Kim. Ruleset Optimization on Isomorphic Oritatami Systems. In Proc. DNA23, volume LNCS 10467, pages 33-45. Springer, 2017. Google Scholar
  10. Y.-S. Han, H. Kim, M. Ota, and S. Seki. Non-deterministic Seedless Oritatami Systems and Hardness of Testing Their Equivalence. Natural Computing, 17(1):67-79, 2018. Google Scholar
  11. L. Kari, S. Kopecki, P.-É. Meunier, M. J. Patitz, and S. Seki. Binary Pattern Tile Set Synthesis Is NP-hard. In ICALP, volume LNCS 9134, pages 1022-1034, 2015. Google Scholar
  12. Y. Masuda, S. Seki, and Y. Ubukata. Towards the Algorithmic Molecular Self-Assembly of Fractals by Cotranscriptional Folding. In CIAA, volume LNCS 10977, pages 261-273, 2018. Google Scholar
  13. T. Neary. Small universal Turing machines. PhD thesis, NUI, Maynooth, 2008. Google Scholar
  14. N. Ollinger. The quest for small universal cellular automata. In ICALP, volume LNCS 2380, pages 318-329, 2002. Google Scholar
  15. M. Ota and S. Seki. Ruleset Design Problems for Oritatami Systems. Theor. Comput. Sci., 671:26-35, 2017. Google Scholar
  16. D. Woods and T. Neary. On The Time Complexity of 2-tag Systems and Small Universal Turing Machines. In FOCS, pages 439-448, 2006. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail