Abstract
The field of structural DNA nanotechnology aims at the systematic development of self-assembling nanostructures using DNA as the construction material. Research in this area is progressing rapidly, and the controlled, computer-aided design of increasingly complex structures is becoming feasible. One thread of this endeavour is the design and characterisation of self-assembling 3D nanostructures based on wireframe polyhedral models. This article aims to illustrate some of the key developments in this direction, in sufficient detail so that the reader can achieve a general understanding of the main concepts and approaches. The emphasis is on the design principles rather than experimental methodology, and the role of computer science and computational tools is set forth.
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Adapted with permission from Chen and Seeman (1991)
Reprinted with permission from Shih et al. (2004)
Reprinted with permission from Shih et al. (2004)
Reprinted with permission from He et al. (2008)
Reprinted with permission from He et al. (2008)
Adapted with permission from Rothemund (2006b)
Reprinted with permission from Rothemund (2006b)
Reprinted with permission from Douglas et al. (2009)
Reprinted with permission from Iinuma et al. (2014)
Reprinted with permission from Han et al. (2013)
Reprinted with permission from Han et al. (2013)
Adapted with permission from Benson et al. (2015)
Adapted with permission from Benson et al. (2015)
Adapted with permission from Veneziano et al. (2016)
Reprinted with permission from Veneziano et al. (2016)
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We use the standard abbreviations ssDNA = single-stranded DNA, dsDNA = double-stranded DNA.
nt = nucleotide.
An interesting non-origami approach to volume-filling 3D designs, using DNA “bricks”, is presented in (Ke et al. 2012).
In fact, a cube is not an ideal test structure for DNA polyhedral designs, because unless the corner joints are stiff, a wireframe cube is not structurally rigid, i.e. in a rod-hinge model it flexes. A tetrahedron or any other convex polyhedron with only triangular faces would not have this problem (Cromwell 1999, Chapter 6).
It is noted in passing at the end of (Shih et al. 2004) that their design could be simplified further, with some loss of rigidity, by replacing the DX struts by simple duplex struts, and the PX struts by hairpin loops that are first cleaved open by restriction enzymes and then joined by ligation to their partners. One of the reviewers of the present survey also asked if the design could be based on DX-type struts alone. From the strand routing point of view this would seem to be possible, however with the backbone strand crossing itself at some point(s), so that one would need to take care also that the planned routing does not form a knot (cf. Sect. 4.2). The folding of this type of design has most likely not been experimentally tested.
A polyhedron is simplicial if it is homeomorphic (i.e. inflatable to) a sphere. It is trivalent if all vertices have exactly three neighbours.
This specific connection is recognised and summarised in (Rothemund 2006b) with elegant conciseness: “William Shih has observed that single-stranded origami may be used to create arbitrary polygonal networks. To see this, replace helper joins with paranemic cohesion motifs and scaffold joins with Shih’s double-crossover struts in all the diagrams of this section”.
The name A-trail presumably derives from the sharp “A-like” turns the path makes at each vertex.
More precisely, the problem is known to be NP-complete in Eulerian polyhedral graphs (Døvling Andersen and Fleischner 1995), but not in triangulated Eulerian polyhedral graphs. In fact, Fleischner (1990) conjectured that every triangulated Eulerian polyhedral graph has an A-trail, but even under this assumption, no polynomial time algorithm is known for finding such.
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Acknowledgements
Preparing this survey was made possible by a sabbatical leave from Aalto University, and most of it was written during stays at ETH Zürich (host Prof. Roger Wattenhofer), the University of Electro-Communications in Tokyo (host Prof. Shinnosuke Seki) and the Tokyo Institute of Technology (host Prof. Osamu Watanabe). I am very grateful for this opportunity. I also thank the two anonymous reviewers for their constructive and insightful comments.
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Orponen, P. Design methods for 3D wireframe DNA nanostructures. Nat Comput 17, 147–160 (2018). https://doi.org/10.1007/s11047-017-9647-9
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DOI: https://doi.org/10.1007/s11047-017-9647-9