Topological Assembly of a Deployable Hoberman Flight Ring from DNA

Abstract

Deployable geometries are 2D or 3D finite structures that preserve their global shapes during expansion and contraction. [1] The structural transformation shows auxetic behaviors, which may be characterized by a negative Poisson's ratio (ν). Such topological behaviors emerge from their unique, intricate geometrical designs. In a Jitterbug transformer, for example, eight rigid equilateral triangles are linked at vertices, and the triangles can rotate around the linkages. [2] This allows deployable reconfigurations between octahedron (one of five Platonic solids) and cuboctahedron (one of thirteen Archimedean solids). By varying the shape and length of elements (regular polygons) in the transformer, multiple variants such as other deployable Platonic and Archimedean solids have been studied mathematically. [3] Another example is the Hoberman sphere, a commercially available, popular toy for kids and a possible choice for sculptures. The Hoberman sphere is also formed by rigid edges with flexible linkages, [4] and can shrink and expand by scissor-like actions at the joints while maintaining the overall spherical shape. In theory, it can be constructed regardless of materials and lengthscale. There is a 6-m-diameter Hoberman sphere from aluminum in the AHHAA Science Center in Tartu, Estonia, while the commercial toys made of plastics are typically ≈10 cm in length. [5] In nature, the shell of cowpea Deployable geometries are finite auxetic structures that preserve their overall shapes during expansion and contraction. The topological behaviors emerge from intricately arranged elements and their connections. Despite the considerable utility of such configurations in nature and in engineering, deployable nanostructures have never been demonstrated. Here a deployable flight ring, a simplified planar structure of Hoberman sphere is shown, using DNA origami. The DNA flight ring consists of topologically assembled six triangles in two layers that can slide against each other, thereby switching between two distinct (open and closed) states. The origami topology is a trefoil knot, and its auxetic reconfiguration results in negative Poisson's ratios. This work shows the feasibility of deployable nanostructures, providing a versatile platform for topological studies and opening new opportunities for bioengineering.

Auxetic Two‐Dimensional Nanostructures from DNA**

“…Mechanics-based guiding principles are developed to prevent curved edges and loose joints.A s abottom-up approach, DNAorigami opens the opportunities for constructing well-defined auxetic unit cells and, with proper scale-up strategies,m acroscopic metamaterials in 2D and 3D.DNA metamaterials could be developed for precision biosensors,filters with variable size-selectivity, [30] and deployable macromolecular topologies. [36]…”

DNA nanostar structures with tunable auxetic properties

“…16 Recently, Li et al bridged this gap in the lengthscale. 17,18 In their studies, nanoscale auxetic units were constructed using DNA origami exploiting sequence complementarity of DNA molecules. DNA self-assembly has been developed as a powerful bottom-up strategy with excellent programmability and precision 19 and demonstrated for complex architectures, [20][21][22][23][24][25] reconfigurable designs, [26][27][28][29] and dynamic processes.…”

DNA Nanostar Structures with Tunable Auxetic Properties

“…16 Recently, Li et al bridged this gap in lengthscale. 17,18 In their studies, nanoscale auxetic units were constructed using DNA origami exploiting sequence complementarity of DNA molecules. DNA self-assembly has been developed as a powerful bottom-up strategy with excellent programmability and precision 19 and demonstrated for complex architectures, [20][21][22][23][24] reconfigurable designs, [25][26][27][28] and dynamics processes.…”