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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 the 3D graphic software Autodesk Maya, running the vHelix plugin (also designed by the same group). In the paper, the folding of six different structures is demonstrated: a “ball” (a subdivided icosahedron), a nicked torus, a helix, a rod, a stickman, a bottle, and a polygonal version of the Stanford bunny. A feature of wireframe polygonal DNA origami highlighted in the paper is the higher resistance to unfolding in low‐salt buffers that are more similar to physiological solutions. Classically, tightly packed DNA origami structures need high concentrations of cations to remain stable, because of the repulsion between the helices. Although alternative approaches have now been proposed to solve this problem [22–24], the possibility of having higher stability without relying on additional modifications is an interesting approach to develop more robust nanostructures for biomedical applications.

In a following paper, we expanded the capabilities of the software packages to 2D meshes [56] by modifying the routing process. We showed the application to the three regular tessellations (hexagon tiling, square tiling, triangular tiling) on a rectangular mesh and four other, less regular structures. The rigidity of the structures appears to be highly dependent on the tessellation used, with the triangular tessellation being the most rigid. According to the authors, these wireframe 2D sheets allow, with the same scaffold usage, to cover an area 70% larger relative to classic DNA origami, and they can be folded in low‐salt buffers.

Compared to the more classical DNA origami designs, these one‐layer, hollow structures are more structurally flexible, making their use less feasible in applications where high rigidity is a desired property. This is addressed in two recent works [57, 58], where both an experimental and a computational approach (through the oxDNA simulation package [18–20]) were used to evaluate and control the flexibility of wireframe DNA nanorods. In the first work, they found out that different factors can be modified to reach the optimal stiffness of a rod nanostructure, with the edge length and the salt concentration apparently the most important. In the second one, an unsupervised software is used to evaluate the stiffness of DNA nanostructures simulated using oxDNA. The software then autonomously modifies the structures by changing the position of internal supports or by adding or removing base pairs. This cycle of modification and simulation is used to create a completely in silico evolution of more rigid DNA structures.

An alternative approach to the design of wireframe DNA origami is the one introduced by Veneziano et al. in 2016 [47] (Figure 2.4b and c). This paper introduced the fully automatic design procedure DAEDALUS (DNA Origami Sequence Design Algorithm for User‐defined Structures) to create arbitrary wireframe DNA origami nanostructures. The authors decided to represent geometries as node‐edge networks, based on the double crossover (DX) motif: each edge thus consists of two duplexes joined by antiparallel double crossovers. The scaffold routing is based on the spanning tree, determined on the Schlegel diagram of a polygon, on which the scaffold crossovers are assigned. Once the scaffold routing is established, the staple strands are assigned using pre‐defined rules, different for vertices and edges. The last step of the process is the modelling of each nucleotide, used to predict the 3D structure of the nanostructures. This design process is used in the work to create 45 different polygonal structures, of which 7 are experimentally characterized using agarose gel electrophoresis, AFM, and cryo‐EM. To realize these structures, Veneziano et al. introduced an asymmetric PCR to produce custom scaffolds of variable length, ranging from 450 nt to over 10 000. The authors also show that these wireframe structures have enhanced stability in physiological buffers.

Figure 2.4 Entire DNA origami design. (a) (I) BSCOR and vHelix design pipeline. (II) Examples of 3D vHelix structures.

Source: Benson et al. [55] / With permission of Springer Nature (III) Examples of 2D vHelix structures.

Source: Benson et al. [56] / With permission of John Wiley & Sons

(b) (I) Daedalus routing workflow.

Source: Veneziano et al. [47] / With permission of AAAS. (II) Perdix routing workflow [59].

(c) Comparison between two octahedrons designed with vHelix (left) and Daedalus (right).

In a following work [59], the same research group introduced an automated procedure to fold any free‐form 2D DNA origami, called PERDIX (Programmed Eulerian Routing for DNA Design using X‐overs). In this paper, the authors change the approach to the scaffold routing, in contrast with previous works [47, 55, 56], using a dual graph approach for the scaffold routing, defined from the starting geometry. Once the scaffold routing is established, the staple strands are determined; the staple strands in the vertices are connected using poly‐T loops to achieve the desired angles. In the end, the structure is converted into an atomic model for visualization and analysis. The versatility and robustness of the method have been shown with the creation of several structures, with arbitrary edge lengths, vertex degree, and vertex angles, imaged by AFM.

In a contemporary work, the group applies the same scaffold routing to 3D objects to render them using 6HB as edges, thus highly enhancing their mechanical stability and resistance against nucleases [60]. The new algorithm, called TALOS (Three‐dimensional, Algorithmically‐generated Library of DNA Origami Shapes), is used to create a library of 240 3D nanostructures. The authors also introduced two different vertices style: a “flat vertex” (FV), with a single‐scaffold crossover between the edges, and a “mitered vertex” (MV), where every duplex in the honeycomb lattice is extended to the neighbor edge in the vertex, creating a three‐way vertex. This further enhances the mechanical stability of these new 3D nanostructures, with variable edge lengths and vertex angles. Like for PERDIX, the length of the edges is arbitrary because the edges do not need to be an integral number of double‐helical turns of B‐form DNA.

Yet another algorithm, called METIS (Mechanically Enhanced and Three‐layered orIgami Structure), has been introduced for the design of 2D wireframe structures with honeycomb edges [61]. This is possible combining the algorithms described above: while PERDIX generated 2D wireframe objects with single‐layer DX edges, METIS generates honeycomb‐based structures stacking three layers and connecting them using the three‐way connection introduced with TALOS. The structures designed using METIS were characterized by AFM, TEM, and molecular dynamics simulations.

All these software packages have been recently united in a single graphical interface called ATHENA [62]. This allows the design of all variety of 2D and 3D nanostructures described in the works before, with DX or 6HB edges; the final structures are then available in PDB format and in JSON format, compatible with caDNAno, for following editing of the nanostructure.