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Transcript design problem of oritatami systems

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Abstract

RNA cotranscriptional folding refers to the phenomenon in which an RNA transcript folds upon itself while being synthesized out of a gene. Oritatami model is a computation model of this phenomenon, which lets its sequence (transcript) of beads (abstract molecules) fold cotranscriptionally by the interactions between beads according to its ruleset. We study the problem of designing a transcript that folds into the given conformation using the given ruleset, which is called the transcript design problem. We prove that the problem is computationally difficult to solve (NP-hard). Then we design efficient poly-time algorithms with additional restrictions on the oritatami system.

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Notes

  1. For the hardness proof, we use the decision variant of TDP, which determines whether or not such a transcript exists.

  2. This definition does not consider any pair both of whose beads are included in \(C_\sigma \) because such a pair is already inert at the beginning of folding.

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Acknowledgements

Han is supported by the Basic Science Research Program through NRF (2018R1D1A1A09084107) and the International Cooperation Program managed by NRF of Korea (2017K2A9A2A08000270). Kim is partially supported by NIH R01GM109459, and by NSF’s CCF-1526485 and DMS-1800443. Kim is also partially supported by the Southeast Center for Mathematics and Biology, an NSF-Simons Research Center for Mathematics of Complex Biological Systems, under National Science Foundation Grant No. DMS-1764406 and Simons Foundation Grant No. 594594. Seki is supported in part by JST Program to Disseminate Tenure Tracking System, MEXT, Japan, No. 6F36, JSPS Grant-in-Aid for Young Scientists (A) No. 16H05854 and for Challenging Research (Exploratory) No. 18K19779, and JSPS-NRF Bilateral Program No. YB29004.

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Authors and Affiliations

  1. Department of Computer Science, Yonsei University, 50 Yonsei-Ro, Seodaemum-Gu, Seoul, 03722, Republic of Korea

    Yo-Sub Han

  2. Department of Mathematics and Statistics, University of South Florida, 4202 E. Fowler Ave., Tampa, FL, 33620, USA

    Hwee Kim

  3. Department of Computer and Network Engineering, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 1828585, Japan

    Shinnosuke Seki

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  1. Yo-Sub Han
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  2. Hwee Kim
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  3. Shinnosuke Seki
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Correspondence to Hwee Kim.

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Han, YS., Kim, H. & Seki, S. Transcript design problem of oritatami systems. Nat Comput 19, 323–335 (2020). https://doi.org/10.1007/s11047-019-09776-0

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