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structures when applied to origami assembly, and the positioning of the origami units can be programmed by using the origami sequence design. The variety of available 2D origami structures can be expanded by introducing predesigned and template‐assisted strategies.

      Seeman and coworkers created a strategy for lattice formation by the self‐assembly of cross‐shaped DNA origami structures [22]. Using the sticky ends of four edges from two different cross‐shaped DNA origamis, a large lattice structure was formed by self‐assembly, generating an array with dimensions of about 2 μm × 3 μm (Figure 1.4c). We examined the formation of a lattice using a lipid bilayer surface to assemble DNA origami structures into large‐sized assemblies. A lipid‐bilayer‐assisted assembly was performed to assemble various DNA origami monomers into 2D lattices (Figure 1.4d) [23]. Due to π–π interaction of the blunt ends of DNA, four edges of a cross‐shaped DNA origami monomer were connected to form a lattice. DNA origami structures were electrostatically adsorbed onto the lipid bilayer surface in the presence of divalent cations. The origami structures were mobile on the lipid bilayer surface and assembled into large 2D lattices in the range of micrometers. We also visualized the dynamic processes including attachment and detachment of monomers and reorganization of lattices using high‐speed AFM (HS‐AFM). Other monomers, including the triangular and hexagonal monomers, were also assembled into packed micrometer‐sized assemblies.

      

Figure 1.4 Programmed self‐assembly of DNA origami. (a) Structure of DNA origami having concavity and a convex connector; the structure is called a “DNA jigsaw piece” for 2D assembly. A 3 × 3 assembly of nine origami tiles and the AFM image of the assembly.

      Source: Rajendran et al. [20]/with permission of American Chemical Society.

      (b) Programmed assembly of multiple DNA origami structures using the assistance of scaffold frames. Target assemblies and their AFM images are shown.

      Source: Zhao et al. [21]/with permission of American Chemical Society.

      (c) Lattice formation by self‐assembly of cross‐shaped DNA origami.

      Source: Liu et al. [22]/with permission of John Wiley & Sons, Inc.

      (d) Surface‐assisted lattice formation on the lipid bilayer.

      Source: Suzuki et al. [23]/Springer Nature/CC BY 4.0.

1.4 Three‐Dimensional DNA Origami Structures

The geometry of double‐helical DNA allows for the design of 3D DNA origami structures by extending the 2D DNA origami system. Two strategies for preparing 3D DNA origami structures have been developed. One is the bundling of dsDNAs, where the relative positioning between adjacent dsDNAs is controlled by crossovers, and the other is the folding of 2D origami domains into 3D structures using interconnection strands. In the former method, developed by Shih and coworkers, the relative positioning of adjacent dsDNAs is geometrically controlled by the crossovers. By arranging the positions of the crossovers, tubular and multilayered structures were constructed (Figure 1.5a) [25]. By increasing or decreasing the number of base pairs between crossovers (in this case, 21 base pairs for two helical turns), the relative positional relationship between adjacent dsDNAs can be controlled. Using a rotational angle of 240° for seven base pairs, three adjacent dsDNAs are placed at a relative angle of ±120° with crossovers every 7 or 14 base pairs. By alternating this relative positioning between adjacent dsDNAs, duplexes form a pleated structure. When adjacent dsDNAs are placed to rotate in one direction, the contiguous duplexes finally form a six‐helix bundled tubular structure. Therefore, when some parts of the pleated structures are turned backward by the introduction of one‐directional rotation of adjacent dsDNAs, the structures fold to become a stacked layer structure (Figure 1.5a). In this case, to stabilize the 3D structures, adjacent layers of dsDNAs are further connected by crossovers of staple strands. Because of the complexity and high density of the introduced crossovers, accurate folding into the target 3D structure requires a long folding time. When the pleated structures were integrated as multilayered structures, the repeating units of the six‐helix bundled tubular structures formed a honeycomb lattice, which was viewed from the axial direction of the double helices. It was also possible to create more complex structures by perpendicularly joining these 3D structures (Figure 1.5b). In addition, a wireframe icosahedron structure was assembled from three double‐triangle monomers made of a six‐helix bundled tubular structure with connections. Importantly, caDNAno software, which is publicly available, has been developed to support the design of these 3D structures [28].

Furthermore, using the layered structures described above, new 3D structures were built by changing the helical twist from the average helical pitch of 10.5 bp/turn to either 10 or 11 bp/turn [29]. When dsDNAs with different helical pitches were bundled together, torque and repulsion between base pairs caused overall structural changes including twisting or 30–180° bending. Using these structures as building blocks, left‐handed or right‐handed helical ribbon structures were prepared. In addition, when angle‐controlled duplex bundles were connected to each other, a six‐tooth gear and a spherical wireframe capsule were created.

Figure 1.5 Design and construction of three‐dimensional DNA origami structures. (a) Scheme for folding the 2D pleated structure into a 3D multilayered structure using staple strands connecting adjacent layers. Sectional views of the positions of the crossovers in the multilayered structure sliced at seven‐base‐pair intervals. (b) Global twisted structures of six‐helix DNA bundles obtained by the selective deletion or insertion of nucleotides to change the helical turns from the normal 10.5 base pairs to 10 or 11 base pairs. TEM images of the polymerized ribbons containing 10.5‐, 10‐, and 11‐base‐pair helical pitches.

      Source: Douglas et al. [25]/with permission of Springer Nature.

      (c) DNA box structure by folding of six DNA origami rectangles using interconnection strands introduced at the edges of rectangles. The DNA box model reconstructed from cryo‐EM images.

      Source: Andersen et al. [26]/with permission of Springer Nature.

      (d) Spherical shells, ellipsoidal shells, and nanoflask DNA origami using combination of curved dsDNAs.

      Source: Han et al. [27]/with permission of American Association for the Advancement of Science.

      Using a different strategy, a DNA box structure was created by folding multiple 2D origami domains with interconnecting strands [26]. Six independent rectangles were sequentially linked and were designed to be folded using interconnection strands in a programmed fashion (Figure 1.5c). Analyses of the assembled structure by AFM, cryo‐electron microscopy, dynamic light scattering, and small‐angle X‐ray scattering indicated that the size was close to the original design. The lid of the box could be opened using a specific DNA strand to release the closing duplex by strand displacement, and the opening event was monitored by fluorescence resonance energy transfer (FRET). Other types of

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