DNA origami and the complexity of Eulerian circuits with turning costs

Ellis-Monaghan, Joanna A.; McDowell, Andrew; Moffatt, Iain; Pangborn, Greta

doi:10.1007/s11047-014-9457-2

Cited by 15 publications

(13 citation statements)

References 31 publications

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“…This approach is equivalent to finding an Eulerian circuit in a graph whose nodes and edges are the vertices and edges of the target geometry. Moreover, this problem is NP-hard [18] and both tools handle this complexity differently. vHelix might introduce duplicated edges to ensure a solution to the problem and runs an efficient systematic search to find an optimal routing.…”

Section: Dna Assembly Conceptsmentioning

confidence: 99%

Multiscale Visualization and Scale-Adaptive Modification of DNA Nanostructures

Miao

Llano

Sorger

et al. 2018

IEEE Trans. Visual. Comput. Graphics

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Abstract-We present an approach to represent DNA nanostructures in varying forms of semantic abstraction, describe ways to smoothly transition between them, and thus create a continuous multiscale visualization and interaction space for applications in DNA nanotechnology. This new way of observing, interacting with, and creating DNA nanostructures enables domain experts to approach their work in any of the semantic abstraction levels, supporting both low-level manipulations and high-level visualization and modifications. Our approach allows them to deal with the increasingly complex DNA objects that they are designing, to improve their features, and to add novel functions in a way that no existing single-scale approach offers today. For this purpose we collaborated with DNA nanotechnology experts to design a set of ten semantic scales. These scales take the DNA's chemical and structural behavior into account and depict it from atoms to the targeted architecture with increasing levels of abstraction. To create coherence between the discrete scales, we seamlessly transition between them in a well-defined manner. We use special encodings to allow experts to estimate the nanoscale object's stability. We also add scale-adaptive interactions that facilitate the intuitive modification of complex structures at multiple scales. We demonstrate the applicability of our approach on an experimental use case. Moreover, feedback from our collaborating domain experts confirmed an increased time efficiency and certainty for analysis and modification tasks on complex DNA structures. Our method thus offers exciting new opportunities with promising applications in medicine and biotechnology.

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Section: Dna Assembly Conceptsmentioning

confidence: 99%

Multiscale Visualization and Scale-Adaptive Modification of DNA Nanostructures

Miao

Llano

Sorger

et al. 2018

IEEE Trans. Visual. Comput. Graphics

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“…Since then, and especially since introduction of the origami technique 2 , DNA nanotechnology has seen astonishing developments and increasingly more complex structures are being produced [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . But even though general approaches for creating DNA origami polygonal meshes and design software are available 14,16,17,[19][20][21] , constraints arising from DNA geometry and sense/antisense pairing still impose important restrictions and necessitate a fair amount of manual adjustment during the design process. Here we present a general method for folding arbitrary polygonal digital meshes in DNA that readily produces structures that would have been very difficult to realize with previous approaches.…”

mentioning

confidence: 99%

DNA rendering of polyhedral meshes at the nanoscale

Benson

Mohammed

Gardell

et al. 2015

Nature

618

604

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It was first suggested 1 more than 30 years ago that Watson-Crick base pairing might be used to rationally design nanoscale structures from nucleic acids. Since then, and especially since introduction of the origami technique 2 , DNA nanotechnology has seen astonishing developments and increasingly more complex structures are being produced [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . But even though general approaches for creating DNA origami polygonal meshes and design software are available 14,16,17,[19][20][21] , constraints arising from DNA geometry and sense/antisense pairing still impose important restrictions and necessitate a fair amount of manual adjustment during the design process. Here we present a general method for folding arbitrary polygonal digital meshes in DNA that readily produces structures that would have been very difficult to realize with previous approaches. This is achieved with a high level of automation of the design process, which uses a routing algorithm based on graph theory and a relaxation simulation to trace scaffold strands through the target structures. Moreover, unlike conventional origami designs built from closed-packed helices, our structures have a more open conformation with one helix per edge and are thus stable in salt conditions commonly used in biological assays.The starting point of the present method is a 3D mesh representing the geometry one wishes to realize at the nanoscale. Focusing only on polyhedral meshes, i.e. meshes which enclose a volume inflatable to a ball, and in contrast to several previous approaches 14,17,19 (see Extended Data Fig. 1) we aim to replace the edges of the mesh by single DNA double helices such that the scaffold strand traverses each of these edges once. This problem is closely related to the Chinese Postman Tour problem 22 in graph theory, which we use to find solutions as doing so by hand would be practically impossible for most meshes. The main principles underpinning our design paradigm are that the technique should allow meshes to be triangulated to optimize structural rigidity; that each edge should be represented by one double helix to enable construction of large structures using as little DNA as possible (though some meshes require two helices to render certain edges as discussed below); and that vertices should be nonBenson et. al, -DNA Rendering of Polyhedral Meshes at the Nanoscale Confidential 2 crossing (i.e. the scaffold should not cross itself in the vertices to ensure non-knotted paths with fewer topological-and kinetic traps during folding, and planar vertex junctions that avoid mesh protrusions due to stacking of crossing helices at each vertex).The overall design scheme is split into four discrete steps: i) Drawing of a 3D polygon mesh in a 3D software, Fig. 1a. ii) Generating an appropriate routing of the long scaffold strand through all the edges of the mesh, Fig. 1b-e. iii) Determining the least strained DNA helix arrangement realizing the 3D mesh, Fig. 1f-i. And iv), Optional fine tuning of the des...

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“…The employed mesh routing is connected to graph theory and a Eulerian circuit pathing problem, where the goal is to systematically find an optimal path through the used network by only crossing each edge of the mesh once. This kind of routing can become very complex (NP-hard) depending on the used mesh size and pathing method, and it usually requires an automated algorithm to do it [59]. Different types of methods have been developed to approach this problem and these are discussed in their dedicated sections: gridiron and simple meshes (3.1.…”

Section: Wireframe Design Principlesmentioning

confidence: 99%

Increasing Complexity in Wireframe DNA Nanostructures

et al. 2020

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Structural DNA nanotechnology has recently gained significant momentum, as diverse design tools for producing custom DNA shapes have become more and more accessible to numerous laboratories worldwide. Most commonly, researchers are employing a scaffolded DNA origami technique by “sculpting” a desired shape from a given lattice composed of packed adjacent DNA helices. Albeit relatively straightforward to implement, this approach contains its own apparent restrictions. First, the designs are limited to certain lattice types. Second, the long scaffold strand that runs through the entire structure has to be manually routed. Third, the technique does not support trouble-free fabrication of hollow single-layer structures that may have more favorable features and properties compared to objects with closely packed helices, especially in biological research such as drug delivery. In this focused review, we discuss the recent development of wireframe DNA nanostructures—methods relying on meshing and rendering DNA—that may overcome these obstacles. In addition, we describe each available technique and the possible shapes that can be generated. Overall, the remarkable evolution in wireframe DNA structure design methods has not only induced an increase in their complexity and thus expanded the prevalent shape space, but also already reached a state at which the whole design process of a chosen shape can be carried out automatically. We believe that by combining cost-effective biotechnological mass production of DNA strands with top-down processes that decrease human input in the design procedure to minimum, this progress will lead us to a new era of DNA nanotechnology with potential applications coming increasingly into view.

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DNA origami and the complexity of Eulerian circuits with turning costs

Cited by 15 publications

References 31 publications

Multiscale Visualization and Scale-Adaptive Modification of DNA Nanostructures

Multiscale Visualization and Scale-Adaptive Modification of DNA Nanostructures

DNA rendering of polyhedral meshes at the nanoscale

Increasing Complexity in Wireframe DNA Nanostructures

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