Design tools for reporter strands and DNA origami scaffold strands

Ellis-Monaghan, Joanna A.; Pangborn, Greta; Seeman, Nadrian C.; Blakeley, Sam; Disher, Conor; Falcigno, Mary; Healy, Brianna; Morse, A. Stephen; Singh, Bharti; Westland, Melissa

doi:10.1016/j.tcs.2016.10.007

Cited by 12 publications

(10 citation statements)

References 27 publications

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“…Eulerian tours have previously featured in experimental and theoretical considerations of DNA [3,8,18,25,35] and protein self-assembly [14,21]. Similarly, topological constraints have been implicitly considered in previous works [3,6].…”

Section: Discussionmentioning

confidence: 99%

“…A fundamental topological constraint when employing a circular strand for assembly is that the strand routing must be unknotted. In a recent paper, Ellis-Monaghan et al [8] have shown the scaffold routings of Benson et al [3] can be knotted on highergenus surfaces. In Figure 1, we present another example of a knotted Chinese-postmantour/Eulerian-tour routing on a triangulated torus.…”

Section: Introductionmentioning

confidence: 99%

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Unknotted Strand Routings of Triangulated Meshes

Mohammed

Hajij

2017

Lecture Notes in Computer Science

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In molecular self-assembly such as DNA origami, a circular strand's topological routing determines the feasibility of a design to assemble to a target. In this regard, the Chinese-postman DNA scaffold routings of Benson et al. (2015) only ensure the unknottedness of the scaffold strand for triangulated topological spheres. In this paper, we present a cubic-time 5 3 −approximation algorithm to compute unknotted Chinese-postman scaffold routings on triangulated orientable surfaces of higher genus. Our algorithm guarantees every edge is routed at most twice, hence permitting low-packed designs suitable for physiological conditions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Unknotted Strand Routings of Triangulated Meshes

Mohammed

Hajij

2017

Lecture Notes in Computer Science

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“…Often, an important consideration in determining reporter or scaffolding strand walks is assuring that the result is not knotted. The authors of [7] observed that knotted walks can result from A-trails (non-crossing Eulerian circuits) in toroidal meshes, while [14] characterizes knotted and unknotted A-trails in toroidal meshes and [12] gives an an approximation algorithm for unknotted walks in surface triangulations. In [1] the authors restrict to spheres to assure unknotted routes.…”

Section: A Short Proof That Reporter Strand Walks Existmentioning

confidence: 99%

“…At its most basic level, the design objective for DNA origami assembly of a graph-like structure is a strategy with the scaffolding strand following a single walk that traverses every edge at least once, with any edges that are traversed more than once visited exactly twice, in opposite directions (because DNA strands in a double helix are oppositely directed), and without separating or crossing through at a vertex. See [1,5,7] for further work on routing scaffolding strands.…”

Section: Introductionmentioning

confidence: 99%

Edge-outer graph embedding and the complexity of the DNA reporter strand problem

Ellingham

Ellis-Monaghan

2019

Theoretical Computer Science

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In 2009, Jonoska, Seeman and Wu showed that every graph admits a route for a DNA reporter strand, that is, a closed walk covering every edge either once or twice, in opposite directions if twice, and passing through each vertex in a particular way. This corresponds to showing that every graph has an edge-outer embedding, that is, an orientable embedding with some face that is incident with every edge. In the motivating application, the objective is such a closed walk of minimum length. Here we give a short algorithmic proof of the original existence result, and also prove that finding a shortest length solution is NP-hard, even for 3-connected cubic (3-regular) planar graphs. Independent of the motivating application, this problem opens a new direction in the study of graph embeddings, and we suggest several problems emerging from it.

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“…If the surface is a sphere, as in [5], all A-trails in the target structure are necessarily unknotted, and so may be used as routes for the unknotted scaffolding strand. On higher-genus surfaces such as the torus, this is no longer the case [8].…”

Section: Introductionmentioning

confidence: 99%

DNA Origami and Unknotted A-trails in Torus Graphs

Morse¹,

William²,

Greene³

et al. 2017

Preprint

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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 Atrail 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.

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Design tools for reporter strands and DNA origami scaffold strands

Cited by 12 publications

References 27 publications

Unknotted Strand Routings of Triangulated Meshes

Unknotted Strand Routings of Triangulated Meshes

Edge-outer graph embedding and the complexity of the DNA reporter strand problem

DNA Origami and Unknotted A-trails in Torus Graphs

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