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

Authors Florent Becker , Shahrzad Heydarshahi



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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

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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

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References

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