License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DNA.2020.1
URN: urn:nbn:de:0030-drops-129540
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12954/
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Mohammed, Abdulmelik ; Jonoska, NataĊĦa ; Saito, Masahico

The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes

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LIPIcs-DNA-2020-1.pdf (0.5 MB)

Abstract

The routing of a DNA-origami scaffold strand is often modelled as an Eulerian circuit of an Eulerian graph in combinatorial models of DNA origami design. The knot type of the scaffold strand dictates the feasibility of an Eulerian circuit to be used as the scaffold route in the design. Motivated by the topology of scaffold routings in 3D DNA origami, we investigate the knottedness of Eulerian circuits on surface-embedded graphs. We show that certain graph embeddings, checkerboard colorable, always admit unknotted Eulerian circuits. On the other hand, we prove that if a graph admits an embedding in a torus that is not checkerboard colorable, then it can be re-embedded so that all its non-intersecting Eulerian circuits are knotted. For surfaces of genus greater than one, we present an infinite family of checkerboard-colorable graph embeddings where there exist knotted Eulerian circuits.

BibTeX - Entry

@InProceedings{mohammed_et_al:LIPIcs:2020:12954,
  author =	{Abdulmelik Mohammed and Nata{\v{s}}a Jonoska and Masahico Saito},
  title =	{{The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Cody Geary and Matthew J. Patitz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12954},
  URN =		{urn:nbn:de:0030-drops-129540},
  doi =		{10.4230/LIPIcs.DNA.2020.1},
  annote =	{Keywords: DNA origami, Scaffold routing, Graphs, Surfaces, Knots, Eulerian circuits}
}

Keywords: DNA origami, Scaffold routing, Graphs, Surfaces, Knots, Eulerian circuits
Collection: 26th International Conference on DNA Computing and Molecular Programming (DNA 26)
Issue Date: 2020
Date of publication: 04.09.2020

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