rel="nofollow" href="#ulink_1250f57a-5540-502a-bfaa-226756226ef4">Figure 2.2c). The tripod inter‐arm angles are controlled by supporting struts and by a vertex helix. Using different kinds of connectors on the different arms of the tripods they were able to control the self‐assembly of these monomers into six different polyhedra. The biggest structure built in this work is a hexagonal prism with an edge length of 100 nm and a diameter of 200 nm. This building technique is, theoretically, capable of creating all trivalent convex polyhedra.
Another interesting approach for the building of multimeric structures was introduced in 2015 by Gerling et al. [50]. Shape‐complementarity and short‐ranged nucleobase stacking bonds were used to stabilize multimeric assemblies. While in this work no polyhedral structures were built, the approach was used shortly after to build gigadalton‐scale structures with controlled sizes [3]. Connecting individual origami building blocks using specifically designed shapes and short‐range interactions, Wagenbuer et al. designed various structures, including impressive 3D polyhedral cages of up to 1.2 gigadaltons and 450 nm in diameter (Figure 2.3d). In this case, they first built a “reactive vertex” from three different building blocks: a triangular brick, a v‐shaped brick, and a connector brick. The reactive vertex is then formed by one central triangular brick, three v‐shaped bricks, and three connector bricks. These reactive vertices are used to create different polyhedral cages (namely, a tetrahedron, a hexahedron, and a dodecahedron) tuning the angles in the v‐shaped bricks. Upon mixing, the cages self‐assembly in a hierarchical and self‐limiting fashion.
2.4 Entire DNA Origami Design
In this section, we will discuss DNA origami designs principles in which the target structure emerges from the routing of the scaffold strand along the edges of a wireframe mesh.
An early example of this type of DNA origami wireframe nanostructure is reported by Smith et al. in 2011 [51]. The authors here designed a DNA origami tetrahedron based on the caDNAno software package (Figure 2.3a). The tetrahedron is composed of six struts that are based on six‐helix bundles, each 227 nucleotides long. These bundles are connected at each of the four vertices to the two neighboring bundles by the circular scaffold, in such a way to minimize possible strains resulting from stretching of the connecting regions. Due to the circular nature of the scaffold, the routing results in half of the struts containing points where scaffold crossovers must be introduced, and only staple strands are stabilizing the sections. As the authors argue in the paper, these junctions can represent a mechanical weak point in the design. Nevertheless, the authors show the folding and characterization of the structures using electron microscopy and super‐resolution DNA PAINT microscopy methods.
Figure 2.3 Entire DNA origami design. (a) DNA origami tetrahedron based on caDNAno design.
Source: Smith et al. [51], Journal of Nucleic Acids / CC BY 3.0.
(b) Schematics for the gridiron structures and examples of 2D and 3D structures.
Source: Han et al. [52] / With permission of AAAS.
(c) Multi‐arms junction schematics and examples of 2D and 3D structures.
Source: Zhang et al. [53] / with permission of Springer Nature.
The first work to describe a scaffold routing different from the traditional based on parallel helices was published in 2015 by Han et al. [52]. In this work, the authors present a global routing of the scaffold through a wireframe mesh (Figure 2.3b). The strategy in this article is to create gridiron‐like DNA structures, where the gridiron unit is formed by four 4‐arm junctions linked together in a double‐layered square. In this square motif, the sides are constituted by antiparallel segments of the scaffold strand connected by staple strands around the perimeters of the square. To allow for the square arrangement of the helices, the Holliday junctions are forced to 90° angle, instead of the natural and relaxed 60° angle. The connection of the gridiron units leads to the formation of a variety of 2D lattices. The simplest scaffold folding connects a series of units in order to fill the first layer; when a corner is reached, the scaffold changes direction and fills the second layer. Returning to the initial position, the scaffold forms a closed loop, producing a structure where the helices in the two layers are oriented perpendicularly to each other. In the paper, a significant variety of modifications to the technique are shown, highlighting its versatility in creating both 2D and 3D structures.
While interesting, this technique was still limited to four 4‐arm junctions. The same research group expanded their method in a more recent paper [53] by Zhang et al. using concepts from graph theory. In the structures presented in this work, the vertices of a mesh are represented by multi‐arm junctions which angle can be controlled (Figure 2.3c). The lines in the mesh are represented by antiparallel DNA crossover tiles of variable lengths. The design process starts with the target pattern, treated as a planar graph, and in the first step all the single lines in the mesh are converted in double lines (representing the antiparallel DNA helices). The second step is to connect and bridge all these lines into a single closed loop, which represents the scaffold routing. To assure the existence of a proper routing, crossovers are placed between the lines, so that the lines in each segment are antiparallel, and the scaffold strand goes through the line only once. At this point, the complementary staple strands are added to create double crossovers (DX), bridging the DNA lines. The angles between arms can be adjusted using poly‐T sequences, which also provide some structural flexibility for the corners to bend correctly. The technique is used in the paper to design complex structures: from simple Platonic tiling, to 2D intricate patterns, including curved planar shapes and almost free hand‐drawn meshes. Additionally, the authors show that the strategy can easily be adapted to create 3D polygonal architectures, simply bridging the scaffold using the equivalent Schlegel diagram as a reference.
In a follow‐up study [54], Hong et al. showed how it is possible to create arbitrary 3D frameworks using layered crossovers, i.e. crossovers that connect different layers of DNA duplexes. All these structures were characterized by transmission electron microscopy (TEM), cryo‐electron microscopy (cryo‐EM), and atomic force microscopy (AFM).
In 2015, Benson et al. [55] presented an approach very different from the ones seen until now. This is a more general top‐down methodology to the design of DNA origami: the scaffold routing is calculated by the software on the user‐defined mesh, without significant user intervention (Figure 2.3a and c). This allows for faster and easier rendering of polyhedral wireframe DNA origami, lowering the entrance barrier to the field. The starting point of the method is a target 3D polyhedral mesh, which is here defined as a triangulated mesh that encloses a volume inflatable to a ball. In contrast with other common approaches, except the gridiron, in this case every edge of the mesh is represented by a single DNA helix. The routing of the scaffold through the triangulated mesh is close to the “Chinese postman tour” problem, a classic graph theory problem. To solve this problem, we chose a routing based on A‐trails, a specific type of Eulerian circuits. While there is no efficient algorithm for finding A‐trails in general graphs, we developed a method of systematic search that was able to find a routing for all the meshes shown in the paper. Once the scaffold routing is completed, the complementary staple strands are added. The next step in the design process is an iterative relaxation of the design using a physical model (Nvidia PhysX), where the helices are represented as rigid rods, connected at the vertices by springs. All these steps are performed by the software package BSCOR (introduced in this work), input of which is a 3D mesh file. The output of the software can be visualized and further modified using