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      In this section, we will present some example of strategies adopted for the creation of polygonal DNA nanostructures. Although the examples in this section precedes what we today call DNA origami, we think it is important to show them both from a historical perspective and for the impact they had on subsequent DNA nanostructure design strategies.

The first example of successful experimental application of structural DNA nanotechnology was the construction of a DNA cube in 1991 [39]. The design comprised 10 ssDNA strands hybridized and ligated together to form the 12 dsDNA edges of a cube (Figure 2.1a). The structure was characterized by gel electrophoresis but as no geometry characterization was possible, the authors could only claim that the structure had the right connectivity.

      An alternative approach to the construction of polyhedral DNA structures was proposed in 2004 by Shih, Quispe, and Joyce [40]. Here, a single, 1.7 kb‐long strand of DNA was used to fold onto itself using only a small number of helper strands. This was achieved using five double‐crossover (DX) struts and seven paranemic‐crossover (PX) struts joined by six 4‐way junctions. The folding occurred in a one‐pot reaction in two stages: first, the DX struts would form between the scaffold and the helper strands, and in a second step the PX struts would form, creating the final octahedron (Figure 2.1c). This approach is somewhat similar to DNA origami (it even included a few short helper oligos) and brings some of the same benefits. First, since the backbone of the structure is a single‐stranded molecule, the stoichiometry of the process is not a concern, as the synthesis consists of a single cooling reaction so it can be completed in one step. In addition, the strand folds into the structure without topological or kinetic traps, so it can, in principle, be mass‐produced by simple DNA cloning. A similar technique with similar advantages was later developed and called “ssDNA origami” [41] and used to created complex 2D DNA structures. RNA structures have also been demonstrated with a similar approach [41, 42].

In 2008, He et al. [43] reported a different approach for the construction of polygonal DNA nanostructures. Building on their previous work on hexagonal 2D arrays [44], they expanded the technique to 3D nanostructures (Figure 2.1b). Their one‐pot self‐assembly process is based on sticky‐ended, three‐armed tiles, which can combine into polyhedral structures. This three‐point‐star motif consists of seven strands: a long, repetitive central strand, three identical medium strands, and three identical short peripheral strands. At the center of each motif, there are three single‐stranded loops, which length can be varied to adjust the tile flexibility. The end of each arm carries two complementary sticky ends, which are four bases long; these allow for the assembly of the tiles. Using these simple basic motifs and rules, He et al. were able to demonstrate the construction of polyhedral structures: a tetrahedron, a dodecahedron, and a truncated icosahedron (a “Buckyball”). These different structures had increasing sizes and number of tiles (3 for the tetrahedron, 20 for the dodecahedron and 60 for the Buckyball); the authors noticed how to an increased size corresponds a decrease in the yield of correctly formed nanostructures. The authors argue that the trend might be attributed to a more difficult assembly process because of the higher number of tiles required and that bigger structures are easier to deform and break.

Figure 2.1 Pre‐origami wireframe DNA structures. (a) Nadrian Seeman’s DNA cube.

      Source: Chen et al. [39] / With permission of Springer Nature.

      (b) Scheme for self‐assembling of three‐armed tiles into polyhedral.

      Source: He et al. [43] / with permission of Springer Nature.

      (c) Folding of a DNA octahedron from a single‐stranded DNA and few helper strands.

      Source: Shih et al. [40] / with permission of Springer Nature.

2.3 Hierarchical DNA Origami Wireframe

      This section will present a series of examples of wireframe DNA origami where the routing of scaffold and staples is used to connect different subsets of monomers.

In a Festschrift paper published in 2006 [45], Paul Rothemund suggested the use of DNA origami to create planar networks out of DNA. Inspired by previous works on DNA tiles [44, 46], Paul Rothemund proposes a multi‐arm motif to create arbitrary polygonal networks. In this article, he lays down the theory for the construction of scaffolded pseudohexagonal networks based on three‐armed DNA tile‐like motifs (called by Rothemund “DNA 3‐stars”) (Figure 2.2a). They would be constituted by scaffold and by three 32‐nucleotide long helper strands. These motifs can be classified in four classes based on the number of breaks in the scaffold strand while it travels around the perimeter of the DNA 3‐star: from a “type‐0,” a single, closed‐loop network, to a “type‐3,” where all the arms are open and can link to other tiles. A polygonal network is created from the combination of these different classes of DNA 3‐stars. When the closed ends of two tiles meet, they are joined by helper strands, a structure called “helper join.” When instead two open ends meet, they are joined by the scaffold strand in a “scaffold join” structure. A simple algorithm can then be used to build molecular designs from the DNA 3‐stars. The molecular designs are arranged in a tree‐like fashion, and Rothemund argues that large 2D and 3D design seemed technically possible, as well as the creation of networks from DNA stars with more than three arms. Although Rothemund’s approach has never been tested in a laboratory, some other recent results come to a similar result from different directions [47, 48].

Figure 2.2 Hierarchical DNA origami wireframe. (a) Schematics for the strategy proposed by Paul Rothemund to create DNA polyhedra.

      Source: Rothemund et al. [45] / with permission of Springer Nature.

      (b) DNA origami icosahedron built by monomers binding.

      Source: Douglas et al. [2] / with permission of Springer Nature.

      (c) Wireframe structures based on DNA origami tripods.

      Source: Linuma et al. [49] / with permission of AAAS.

      (d) Gigadalton‐sized structures from building blocks kept together by shape‐complementarity.

      Source: Wagenbauer et al. [3] / with permission of Springer Nature.

      It was not long after the first report of the DNA origami technique by Paul Rothemund [1] that the technique was expanded to 3D shapes [2]. In this work, among other structures, a 3D wireframe icosahedron is created by the hierarchical assembly of monomers, where the struts are six‐helix‐bundle nanotubes (Figure 2.2b). The icosahedron is built through a two‐stage process. First, a scaffold is folded into one of three double triangles that act as monomers. The three monomers used in this work are built from the same design using the same scaffold and are effectively chemically different, thanks to cyclic permutation of the scaffold sequence. Every monomer displays staple sequences designed to bind to the other two monomers in a controlled fashion. These monomers are then mixed to create an icosahedron with a diameter of around 100 nm.

      One of the first generalized strategies for the multimeric assembly of larger DNA nanostructures was presented by Linuma et al. [49]. In this work, the monomer is a DNA “tripod,” that

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