Abstract
The oritatami system (OS) is a model of computation by cotranscriptional folding, being inspired by the recent experimental succeess of RNA origami to self-assemble an RNA tile cotranscriptionally. The OSs implemented so far, including binary counter and Turing machine simulator, are deterministic, that is, uniquely fold into one conformation, while nondeterminism is intrinsic in biomolecular folding. We introduce nondeterminism to OS (NOS) and propose an NOS that chooses an assignment of Boolean values nondeterministically and evaluates a logical formula on the assignment. This NOS is seedless in the sense that it does not require any initial conformation to begin with like the RNA origami. The NOS allows to prove the co-NP hardness of deciding, given two NOSs, if there exists no conformation that one of them folds into but the other does not.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Borodin, A.: On relating time and space to size and depth. SIAM J. Comput. 6(4), 733–744 (1977)
Frieda, K.L., Block, S.M.: Direct observations of cotranscriptional folding in an adenine riboswitch. Science 338(6105), 397–400 (2012)
Geary, C., Meunier, P., Schabanel, N., Seki, S.: Efficient universal computation by greedy molecular folding (2015). CoRR, abs/1508.00510
Geary, C., Meunier, P., Schabanel, N., Seki, S.: Programming biomolecules that fold greedily during transcription. In: Proceedings of the 41st International Symposium on Mathematical Foundations of Computer Science (2016, to appear)
Geary, C., Rothemund, P.W.K., Andersen, E.S.: A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science 345, 799–804 (2014)
Kleinberg, J., Tardos, É.: Algorithm Design. Addison-Wesley, Reading (2011)
Lai, D., Proctor, J.R., Meyer, I.M.: On the importance of cotranscriptional RNA structure formation. RNA 19, 1461–1473 (2013)
Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: Complexity classes in models of cellular computing with membranes. Nat. Comput. 2(3), 265–285 (2003)
Rivas, E., Eddy, S.R.: A dynamic programming algorithm for RNA structure prediction including pseudoknots. J. Mol. Biol. 285(5), 2053–2068 (1999)
Xayaphoummine, A., Bucher, T., Isambert, H.: Kinefold web server for RNA/DNA folding path and structure prediction including pseudoknots and knots. Nucleic Acids Res. 33, W605–W610 (2005)
Zuker, M.: Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Res. 31(13), 3406–3415 (2003)
Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9(1), 133–148 (1981)
Acknowledgments
We would like to thank the anonymous reviewers for the careful reading of the paper and many valuable suggestions.
Kim was supported by NRF Grant funded by the Korean Government (NRF-2013-Global Ph.D. Fellowship Program). The work of S. S. was supported in part by JST Program to Disseminate Tenure Tracking System, MEXT, Japan, No. 6F36, and by JSPS Grant-in-Aid for Research Activity Start-up No. 15H06212 and for Young Scientists (A) No. 16H05854.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Han, YS., Kim, H., Ota, M., Seki, S. (2016). Nondeterministic Seedless Oritatami Systems and Hardness of Testing Their Equivalence. In: Rondelez, Y., Woods, D. (eds) DNA Computing and Molecular Programming. DNA 2016. Lecture Notes in Computer Science(), vol 9818. Springer, Cham. https://doi.org/10.1007/978-3-319-43994-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-43994-5_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-43993-8
Online ISBN: 978-3-319-43994-5
eBook Packages: Computer ScienceComputer Science (R0)