In 1982, Seeman proposed using DNA to construct a 3D periodic network, which is considered to be the origin of “DNA nanotechnology” (a) [
1]. In the early years, DNA branched junctions were selected as basic building blocks for constructing 3D periodic networks, as shown in b. In 1983, Seeman et al. successfully synthesized the four-arm junction structure of DNA [
16]. DNA building blocks are required to have a certain rigidity for assembling into a larger structure, but DNA branched junctions obviously fail to meet this feature. By introducing a crossover between two DNA double helices, Seeman et al. designed the “DNA double-crossover molecule” (DX) with sufficient rigidity to form a larger structure [
17]. In the mathematical theory of tiling, rectangular tiles with programmable interactions, known as Wang tiles, can be tiled into 2D spaces. DX molecules can be arranged in a 2D space imitating a Wang tile, and single-stranded DNA sequences can be extended on both sides of the DX molecule as sticky ends to connect other DX molecules. Reasonably designed sticky ends can assemble DX molecules and DX + J molecules into a 2D array (c) [
6,
18]. The structure of a single DNA tile is relatively simple, consisting of several stoichiometric single oligonucleotide strands. Simple small units are repeatedly arranged to form a large 2D array through the connection of sticky ends. However, this method has relatively low control over the size and shape of the product. Li et al. proposed to restrict the size and shape of DNA tile growth with a prescribed DNA origami frame [
19]. A 2D array consisting of a large number of simple repeating DNA tiles is filled in a hollow origami frame, which have faster growth kinetics when in an origami frame than when there is no frame. The design of DX molecules has been modified to obtain different DNA building blocks, such as paranemic crossover (PX) DNA, topoisomer (JX) DNA, and triple crossover complex. Through the strand displacement reaction, PX and JX can be converted into one another, that is, one end of a DNA strand rotates 180° relative to the other end. Seeman used this conformational change between PX and JX to confirm that a rotary nanomechanical device can be recycled [
20].
Figure 1. Self-assembly based on DNA tiles (
a) Escher’s woodcut depth (
left) and the prototype of DNA nanotechnology inspired by it (
right). Reproduced from [
21]. (
b) A schematic diagram of a two-dimensional (2D) DNA lattice assembled by four-arm holiday junctions connected by sticky ends. Reproduced with permission [
22]. Copyright Materials Research Society, 2017. (
c) A 2D lattice assembled by DNA double-crossover molecule (DX) and DX + J tiles. Reproduced with permission of [
22]. Copyright Materials Research Society, 2017. (
d) The structure of the DNA polyhedron assembled by three-pointed star DNA motifs. Reproduced with permission of [
11]. Copyright Springer Nature, 2008. (
e) DX-based complex DNA tile motif library and its assembly results. (I) 4 × 4 tile. Reproduced with permission of [
9]. Copyright American Association for the Advancement of Science, 2003; (II) three-pointed star. Reproduced with permission of [
23]. Copyright American Chemical Society, 2005; (III) six-pointed star. Reproduced with permission of [
24]. Copyright American Chemical Society, 2006; cop; (IV) DX-based tensegrity triangle. Reproduced with permission of [
25]. Copyright American Chemical Society, 2006; (V) a tensegrity triangle with complete triple symmetry. Reproduced from [
10].
A simple DX structure can be expanded into a high-order DNA motif, which can be assembled into a more complex 2D array, as shown in e. Yan et al. designed a 4 × 4 DNA tile that can self-assemble into uniform-width nanoribbons, 2D nano−grids and ladder-like grids [
10]. These grids can be subsequently used for the periodic arrangement of protein molecules and gold nanoparticles [
26,
27,
28]. In addition, they also confirmed that sophisticated 2D and 3D tessellation patterns can be formed by using three- and four-arm DNA junction tiles with specifically designed arm lengths and inter-tile sticky-end interactions [
29]. Mao et al. designed a series of n-pointed-stars and assembled them into 2D arrays with different topologies [
23,
24,
30,
31,
32]. In addition, five- and six-pointed-stars have been co-crystallized to a 2D array similar to a quasi-crystal arrangement [
33]. By controlling the flexibility and concentration of motifs, a DNA n-pointed-star motif can be assembled into a complex polyhedron framework structure (d) [
11,
31], which can then be used as a nanocage to encapsulate nanoparticles in the frame to form clusters with a specific conformation [
34,
35,
36,
37]. Another complex motif formed by simple DNA tiles is tensegrity triangle. Mao et al. used three four-arm junctions to construct a tensegrity triangle with a double helix on each side [
30] with sticky ends at each vertex, allowing it to self-assemble into one-dimensional (1D) or 2D ordered arrays by selectively using the vertices. Seeman et al. designed a tensegrity triangle composed of DX molecules, and used their assembled 1D and 2D arrays to complete the regular arrangement of gold nanoparticles (e) [
25]. Subsequently, Seeman et al. designed a tensegrity triangle with triple rotational symmetry in sequence [
10]. The structure was assembled with sticky ends to obtain a single crystal with a rhombohedral lattice (e). By adjusting the length of the sides of the tensegrity triangle, single crystals with different lattice parameters were obtained with cavities of different sizes, and the cavities could be used to accommodate guest particles. This work is considered to be a major breakthrough in the field of DNA nanotechnology. Since then, a lot of work has been carried out around the tensegrity triangle, such as controlling the crystal nucleation and growth process [
38], improving the quality and stability of the single crystal [
39,
40], and completing dynamic changes [
41].
The self-assembly product of DNA tiles can be used for the manipulation of nanoparticles. However, due to the limitation of DNA tile assembly products, nanoparticles can only be manipulated on a linear or planar template. The particle spacing and arrangement can be well controlled and, the polyhedral frame assembled by tiles can be used as a nanocage for nanoparticle encapsulation or as a restriction frame template to guide nanoparticle assembly. Thus, clusters of nanoparticles can be obtained, but it is difficult to expand them into a 3D space to form ordered crystals.