DNA origami and unknotted A-trails in torus graphs
| Autor: | Ada Morse, David Perry, Jessica Greene, Jo Ellis-Monaghan, Greta Pangborn, William Adkisson, Brenna Smith |
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| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Torus 0102 computer and information sciences 010402 general chemistry Mathematics::Geometric Topology 01 natural sciences 0104 chemical sciences Combinatorics 05C10 57M25 05C45 05C62 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics DNA origami Combinatorics (math.CO) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Journal of Knot Theory and Its Ramifications. 29:2050041 |
| ISSN: | 1793-6527 0218-2165 |
| DOI: | 10.1142/s0218216520500418 |
| Popis: | Motivated by the problem of determining unknotted routes for the scaffolding strand in DNA origami self-assembly, we examine existence and knottedness of A-trails in graphs embedded on the torus. We show that any A-trail in a checkerboard-colorable torus graph is unknotted and characterize the existence of A-trails in checkerboard-colorable torus graphs in terms of pairs of quasitrees in associated embeddings. Surface meshes are frequent targets for DNA nanostructure self-assembly, and so we study both triangular and rectangular torus grids. We show that, aside from one exceptional family, a triangular torus grid contains an A-trail if and only if it has an odd number of vertices, and that such an A-trail is necessarily unknotted. On the other hand, while every rectangular torus grid contains an unknotted A-trail, we also show that any torus knot can be realized as an A-trail in some rectangular grid. Lastly, we use a gluing operation to construct infinite families of triangular and rectangular grids containing unknotted A-trails on surfaces of arbitrary genus. We also give infinite families of triangular grids containing no unknotted A-trail on surfaces of arbitrary nonzero genus. Comment: 23 pages, 20 figures. This version fixes some errors in acknowledgements, typos |
| Databáze: | OpenAIRE |
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