Document Open Access Logo

Designing 3D RNA Origami Nanostructures with a Minimum Number of Kissing Loops

Authors Antti Elonen , Pekka Orponen

PDF
Thumbnail PDF

File

LIPIcs.DNA.30.4.pdf
  • Filesize: 26.19 MB
  • 12 pages

Document Identifiers

Author Details

Antti Elonen
  • Department of Computer Science, Aalto University, Espoo, Finland
Pekka Orponen
  • Department of Computer Science, Aalto University, Espoo, Finland

Funding

Project "Algorithmic design methods and tools for DNA nanotechnology", Finnish Cultural Foundation (P.O.)

Cite AsGet BibTex

Antti Elonen and Pekka Orponen. Designing 3D RNA Origami Nanostructures with a Minimum Number of Kissing Loops. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DNA.30.4

Abstract

We present a general design technique for rendering any 3D wireframe model, that is any connected graph linearly embedded in 3D space, as an RNA origami nanostructure with a minimum number of kissing loops. The design algorithm, which applies some ideas and methods from topological graph theory, produces renderings that contain at most one kissing-loop pair for many interesting model families, including for instance all fully triangulated wireframes and the wireframes of all Platonic solids. The design method is already implemented and available for use in the design tool DNAforge (https://dnaforge.org).

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • Applied computing → Computational biology
  • Applied computing → Life and medical sciences
Keywords
  • RNA origami
  • wireframe nanostructures
  • polyhedra
  • kissing loops
  • topological graph embeddings
  • self-assembly

Metrics

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

Supplementary Materials

References

  1. Dorothy Buck, Egor Dolzhenko, Nataša Jonoska, Masahico Saito, and Karin Valencia. Genus ranges of 4-regular rigid vertex graphs. Electronic Journal of Combinatorics, 22(3):43, 2015. URL: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p43/pdf.
  2. M. N. Ellingham and Joanna A. Ellis-Monaghan. Bi-eulerian embeddings of graphs and digraphs, 2024. Preprint arXiv:2404.00325, doi: URL: https://doi.org/10.48550/arXiv.2404.00325.
  3. Joanna A Ellis-Monaghan. Transition polynomials, double covers, and biomolecular computing. Congressus Numerantium, 166:181, 2004. Google Scholar
  4. Antti Elonen, Ashwin Karthick Natarajan, Ibuki Kawamata, Lukas Oesinghaus, Abdulmelik Mohammed, Jani Seitsonen, Yuki Suzuki, Friedrich C. Simmel, Anton Kuzyk, and Pekka Orponen. Algorithmic design of 3D wireframe RNA polyhedra. ACS Nano, 16:16608-18816, 2022. doi: URL: https://doi.org/10.1021/acsnano.2c06035.
  5. Antti Elonen and Leon Wimbes. DNAforge. Software, version 1.0.0., swhId: https://archive.softwareheritage.org/swh:1:dir:37818d83c81946377fb47e15688adb686c29d84d;origin=https://github.com/dnaforge/dnaforge;visit=swh:1:snp:06299be61c159fd747fd7f0424eddb486239ade9;anchor=swh:1:rev:d7d8d660f73cfeb3092b12da8c037fa7dafa6836 (visited on 2024-08-29). URL: https://github.com/dnaforge/dnaforge.
  6. Antti Elonen, Leon Wimbes, Abdulmelik Mohammed, and Pekka Orponen. DNAforge: A design tool for nucleic acid wireframe nanostructures. Nucleic Acids Research, 52(W1):W13-W18, 2024. doi: URL: https://doi.org/10.1093/nar/gkae367.
  7. Gašper Fijavž, Tomaž Pisanski, and Jernej Rus. Strong traces model of self-assembly polypeptide structures. MATCH Communications in Mathematical and in Computer Chemistry, 71(1):199-212, 2014. URL: https://match.pmf.kg.ac.rs/electronic_versions/Match71/n1/match71n1_199-212.pdf.
  8. Herbert Fleischner. Eulerian Graphs and Related Topics. Part 1, Volume 1, volume 45 of Annals of Discrete Mathematics. North-Holland Publishing Co., Amsterdam, 1990. Google Scholar
  9. Merrick L. Furst, Jonathan L. Gross, and Lyle A. McGeoch. Finding a maximum-genus graph imbedding. Journal of the ACM (JACM), 35(3):523-534, 1988. doi: URL: https://doi.org/10.1145/44483.44485.
  10. Harold N. Gabow and Matthias Stallmann. Efficient algorithms for graphic matroid intersection and parity. In Automata, Languages and Programming: 12th Colloquium Nafplion, Greece, July 15-19, 1985, pages 210-220. Springer, 1985. URL: https://doi.org/10.1007/BFb0015746.
  11. Cody Geary, Guido Grossi, Ewan K. S. McRae, Paul W. K. Rothemund, and Ebbe S. Andersen. RNA origami design tools enable cotranscriptional folding of kilobase-sized nanoscaffolds. Nature Chemistry, 13(6):549-558, 2021. doi: URL: https://doi.org/10.1038/s41557-021-00679-1.
  12. Cody Geary, Paul W. K. Rothemund, and Ebbe S. Andersen. A single-stranded architecture for cotranscriptional folding of RNA nanostructures. Science, 345(6198):799, 2014. doi: URL: https://doi.org/10.1126/science.1253920.
  13. Jonathan L. Gross, Jay Yellen, and Ping Zhang. Handbook of Graph Theory. CRC Press, 2nd edition, 2013. Google Scholar
  14. Peixuan Guo. The emerging field of RNA nanotechnology. Nature Nanotechnology, 5(12):833-842, December 2010. doi: URL: https://dx.doi.org/10.1038/nnano.2010.231.
  15. Daniel Jasinski, Farzin Haque, Daniel W. Binzel, and Peixuan Guo. Advancement of the emerging field of RNA nanotechnology. ACS Nano, 11(2):1142-1164, 2017. doi: URL: https://doi.org/10.1021/acsnano.6b05737.
  16. Sandi Klavžar and Jernej Rus. Stable traces as a model for self-assembly of polypeptide nanoscale polyhedrons. MATCH Communications in Mathematical and in Computer Chemistry, 70(1):317-330, 2013. URL: https://match.pmf.kg.ac.rs/electronic_versions/Match70/n1/match70n1_317-330.pdf.
  17. David Kuťák, Erik Poppleton, Haichao Miao, Petr Šulc, and Ivan Barišić. Unified Nanotechnology Format: One way to store them all. Molecules, 27(1), 2022. doi: URL: https://doi.org/10.3390/molecules27010063.
  18. John Lee. Introduction to Topological Manifolds. Springer Science & Business Media, 2010. URL: https://doi.org/10.1007/978-1-4419-7940-7.
  19. Di Liu, Cody W. Geary, Gang Chen, Yaming Shao, Mo Li, Chengde Mao, Ebbe S. Andersen, Joseph A. Piccirilli, Paul W. K. Rothemund, and Yossi Weizmann. Branched kissing loops for the construction of diverse RNA homooligomeric nanostructures. Nature Chemistry, 12(3):249-259, 2020. doi: URL: https://doi.org/10.1038/s41557-019-0406-7.
  20. Abdulmelik Mohammed, Nataša Jonoska, and Masahico Saito. The topology of scaffold routings on non-spherical mesh wireframes. In 26th International Conference on DNA Computing and Molecular Programming, pages 1:1-1:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. doi: URL: https://doi.org/10.4230/LIPIcs.DNA.2020.1.
  21. Abdulmelik Mohammed, Pekka Orponen, and Sachith Pai. Algorithmic design of cotranscriptionally folding 2D RNA origami structures. In Unconventional Computation and Natural Computation: 17th International Conference, UCNC 2018, Fontainebleau, France, June 25-29, 2018, pages 159-172. Springer, 2018. doi: URL: https://doi.org/10.1007/978-3-319-92435-9_12.
  22. Molly F. Parsons, Matthew F. Allan, Shanshan Li, Tyson R. Shepherd, Sakul Ratanalert, Kaiming Zhang, Krista M. Pullen, Wah Chiu, Silvi Rouskin, and Mark Bathe. 3D RNA-scaffolded wireframe origami. Nature Communications, 14(1):382, 2023. doi: URL: https://doi.org/10.1038/s41467-023-36156-1.
  23. Erik Poppleton, Joakim Bohlin, Michael Matthies, Shuchi Sharma, Fei Zhang, and Petr Šulc. Design, optimization and analysis of large DNA and RNA nanostructures through interactive visualization, editing and molecular simulation. Nucleic Acids Research, 48(12):e72-e72, 2020. doi: URL: https://doi.org/10.1093/nar/gkaa417.
  24. Ben Roth. Rigid and flexible frameworks. The American Mathematical Monthly, 88(1):6-21, 1981. URL: http://www.jstor.org/stable/2320705.
  25. Matthias Stallmann and Harold N. Gabow. An augmenting path algorithm for the parity problem on linear matroids. In 25th Annual Symposium on Foundations of Computer Science, 1984, pages 217-228. IEEE, 1984. doi: URL: https://doi.org/10.1109/SFCS.1984.715918.
  26. Carsten Thomassen. Bidirectional retracting-free double tracings and upper embeddability of graphs. Journal of Combinatorial Theory, Series B, 50(2):198-207, 1990. doi: URL: https://doi.org/10.1016/0095-8956(90)90074-A.
  27. Rémi Veneziano, Sakul Ratanalert, Kaiming Zhang, Fei Zhang, Hao Yan, Wah Chiu, and Mark Bathe. Designer nanoscale DNA assemblies programmed from the top down. Science, 2016. doi: URL: https://doi.org/10.1126/science.aaf4388.
  28. Martin Škoviera and Roman Nedela. The maximum genus of a graph and doubly eulerian trails. Bollettino dell'Unione Matematica Italiana B, 4 B:541-551, 1990. Google Scholar
  29. Nguyen Huy Xuong. How to determine the maximum genus of a graph. Journal of Combinatorial Theory, Series B, 26(2):217-225, 1979. doi: URL: https://doi.org/10.1016/0095-8956(79)90058-3.
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
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact