Document Open Access Logo

DNA Tile Self-Assembly for 3D-Surfaces: Towards Genus Identification

Authors Florent Becker , Shahrzad Heydarshahi

PDF
Thumbnail PDF

File

LIPIcs.DNA.29.2.pdf
  • Filesize: 2.91 MB
  • 21 pages

Document Identifiers

Author Details

Florent Becker
  • Univ. Orléans, INSA Centre Val de Loire, LIFO EA 4022, F-45067 Orléans, France
Shahrzad Heydarshahi
  • Univ. Orléans, INSA Centre Val de Loire, LIFO EA 4022, F-45067 Orléans, France

Funding

Supported by ANR project SyDySi (ANR JCJC 2019 19-CE48-0007-01).

Cite AsGet BibTex

Florent Becker and Shahrzad Heydarshahi. DNA Tile Self-Assembly for 3D-Surfaces: Towards Genus Identification. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.DNA.29.2

Abstract

We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are flexible, so that the assembly can bind on the edges of the polycube. We are interested in the study of SFTAM self-assemblies on 3D surfaces which are not always embeddable in the Euclidean plane, in order to compare their different behaviors and to compute the topological properties of the host surfaces. We focus on a family of polycubes called order-1 cuboids. Order-0 cuboids are polycubes that have six rectangular faces, and order-1 cuboids are made from two order-0 cuboids by substracting one from the other. Thus, order-1 cuboids can be of genus 0 or of genus 1 (then they contain a tunnel). We are interested in the genus of these structures, and we present a SFTAM tile assembly system that determines the genus of a given order-1 cuboid. The SFTAM tile assembly system which we design, contains a specific set Y of tile types with the following properties. If the assembly is made on a host order-1 cuboid C of genus 0, no tile of Y appears in any producible assembly, but if C has genus 1, every terminal assembly contains at least one tile of Y. Thus, for order-1 cuboids our system is able to distinguish the host surfaces according to their genus, by the tiles used in the assembly. This system is specific to order-1 cuboids but we can expect the techniques we use to be generalizable to other families of shapes.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Tile self-assembly
  • DNA computing
  • Geometric surfaces

Metrics

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

Related Versions

References

  1. Zachary Abel, Nadia Benbernou, Mirela Damian, Erik D Demaine, Martin L Demaine, Robin Flatland, Scott D Kominers, and Robert Schweller. Shape replication through self-assembly and rnase enzymes. In Proceedings of the twenty-first annual ACM-SIAM symposium on discrete algorithms, pages 1045-1064. SIAM, 2010. Google Scholar
  2. Greg Aloupis, Prosenjit K Bose, Sébastien Collette, Erik D Demaine, Martin L Demaine, Karim Douieb, Vida Dujmović, John Iacono, Stefan Langerman, and Pat Morin. Common unfoldings of polyominoes and polycubes. In Computational Geometry, Graphs and Applications: 9th International Conference, CGGA 2010, Dalian, China, November 3-6, 2010, Revised Selected Papers, pages 44-54. Springer, 2011. Google Scholar
  3. Robert D Barish, Rebecca Schulman, Paul WK Rothemund, and Erik Winfree. An information-bearing seed for nucleating algorithmic self-assembly. Proceedings of the National Academy of Sciences, 106(15):6054-6059, 2009. Google Scholar
  4. Matthew Cook, Tristan Stérin, and Damien Woods. Small Tile Sets That Compute While Solving Mazes. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27), volume 205 of Leibniz International Proceedings in Informatics (LIPIcs), pages 8:1–8:20. Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2021. doi:10.4230/LIPIcs.DNA.27.8. Google Scholar
  5. Jérôme Durand-Lose, Jacob Hendricks, Matthew J Patitz, Ian Perkins, and Michael Sharp. Self-assembly of 3-d structures using 2-d folding tiles. Natural Computing, 19:337-355, 2020. Google Scholar
  6. Matthew R Jones, Nadrian C Seeman, and Chad A Mirkin. Programmable materials and the nature of the dna bond. Science, 347(6224):1260901, 2015. Google Scholar
  7. Wenyan Liu, Hong Zhong, Risheng Wang, and Nadrian C Seeman. Crystalline two-dimensional dna-origami arrays. Angewandte Chemie International Edition, 50(1):264-267, 2011. Google Scholar
  8. Kao Ming-Yang and Vijay Ramachandran. Dna self-assembly for constructing 3d boxes. In International Symposium on Algorithms and Computation, pages 429-441. Springer, 2001. Google Scholar
  9. Matthew J Patitz. An introduction to tile-based self-assembly and a survey of recent results. Natural Computing, 13:195-224, 2014. Google Scholar
  10. Paul WK Rothemund. Folding dna to create nanoscale shapes and patterns. Nature, 440(7082):297-302, 2006. Google Scholar
  11. Paul WK Rothemund and Erik Winfree. The program-size complexity of self-assembled squares. In Proceedings of the thirty-second annual ACM symposium on Theory of computing, pages 459-468, 2000. Google Scholar
  12. Ned et al." "Seeman. Dna nanotechnology: Bibliography from ned seeman’s laboratory, 2023. URL: http://seemanlab4.chem.nyu.edu/nanobib.html.
  13. Vyankat A Sontakke and Yohei Yokobayashi. Programmable macroscopic self-assembly of dna-decorated hydrogels. Journal of the American Chemical Society, 144(5):2149-2155, 2022. Google Scholar
  14. Hao Wang. Proving theorems by pattern recognition—ii. Bell system technical journal, 40(1):1-41, 1961. Google Scholar
  15. Erik Winfree. Algorithmic self-assembly of DNA. California Institute of Technology, 1998. Google Scholar
  16. Joseph F Woods, Lucía Gallego, Pauline Pfister, Mounir Maaloum, Andreas Vargas Jentzsch, and Michel Rickhaus. Shape-assisted self-assembly. Nature Communications, 13(1):3681, 2022. Google Scholar
  17. Shuguang Zhang. Fabrication of novel biomaterials through molecular self-assembly. Nature biotechnology, 21(10):1171-1178, 2003. Google Scholar
  18. Rebecca Zhuo, Feng Zhou, Xiaojin He, Ruojie Sha, Nadrian C Seeman, and Paul M Chaikin. Litters of self-replicating origami cross-tiles. Proceedings of the National Academy of Sciences, 116(6):1952-1957, 2019. 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
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact