Hybrid RNA:DNA origami, in which a long RNA scaffold strand folds into a target nanostructure via thermal annealing with complementary DNA oligos, has only been explored to a limited extent despite its unique potential for biomedical delivery of mRNA, tertiary structure characterization of long RNAs, and fabrication of artificial ribozymes. Here, we investigate design principles of three-dimensional wireframe RNA-scaffolded origami rendered as polyhedra composed of dual-duplex edges. We computationally design, fabricate, and characterize tetrahedra folded from an EGFP-encoding messenger RNA and de Bruijn sequences, an octahedron folded with M13 transcript RNA, and an octahedron and pentagonal bipyramids folded with 23S ribosomal RNA, demonstrating the ability to make diverse polyhedral shapes with distinct structural and functional RNA scaffolds. We characterize secondary and tertiary structures using dimethyl sulfate mutational profiling and cryo-electron microscopy, revealing insight into both global and local, base-level structures of origami. Our top-down sequence design strategy enables the use of long RNAs as functional scaffolds for complex wireframe origami.
Origami offers an avenue to program three-dimensional shapes via scale-independent and non-destructive fabrication. While such programming has focused on the geometry of a tessellation in a single transient state, here we provide a complete description of folding smooth saddle shapes from concentrically pleated squares. When the offset between square creases of the pattern is uniform, it is known as the pleated hyperbolic paraboloid (hypar) origami. Despite its popularity, much remains unknown about the mechanism that produces such aesthetic shapes. We show that the mathematical limit of the elegant shape folded from concentrically pleated squares, with either uniform or non-uniform (e.g. functionally graded, random) offsets, is invariantly a hyperbolic paraboloid. Using our theoretical model, which connects geometry to mechanics, we prove that a folded hypar origami exhibits bistability between two symmetric configurations. Further, we tessellate the hypar origami and harness its bistability to encode multi-stable metasurfaces with programmable non-Euclidean geometries.
more » « less- NSF-PAR ID:
- 10192572
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract -
more » « less
Abstract Existing Civil Engineering structures have limited capability to adapt their configurations for new functions, non-stationary environments, or future reuse. Although origami principles provide capabilities of dense packaging and reconfiguration, existing origami systems have not achieved deployable metre-scale structures that can support large loads. Here, we established modular and uniformly thick origami-inspired structures that can deploy into metre-scale structures, adapt into different shapes, and carry remarkably large loads. This work first derives general conditions for degree-N origami vertices to be flat foldable, developable, and uniformly thick, and uses these conditions to create the proposed origami-inspired structures. We then show that these origami-inspired structures can utilize high modularity for rapid repair and adaptability of shapes and functions; can harness multi-path folding motions to reconfigure between storage and structural states; and can exploit uniform thickness to carry large loads. We believe concepts of modular and uniformly thick origami-inspired structures will challenge traditional practice in Civil Engineering by enabling large-scale, adaptable, deployable, and load-carrying structures, and offer broader applications in aerospace systems, space habitats, robotics, and more.
-
This paper unites the gauge-theoretic and hyperbolic-geometric perspectives on the asymptotic geometry of the character variety of SL(2, C) representations of a surface group. Specifically, we find an asymptotic correspondence between the analytically defined limiting configuration of a sequence of solutions to the SU(2) self-duality equations on a closed Riemann surface constructed by Mazzeo-Swoboda-Weiß-Witt, and the geometric topological shear-bend parameters of equivariant pleated surfaces in hyperbolic three-space due to Bonahon and Thurston. The geometric link comes from the nonabelian Hodge correspondence and a study of high energy degenerations of harmonic maps. Our result has several applications. We prove: (1) the local invariance of the partial compactification of the moduli space of solutions to the self-duality equations by limiting configurations; (2) a refinement of the harmonic maps characterization of the Morgan-Shalen compactification of the character variety; and (3) a comparison between the family of complex projective structures defined by a quadratic differential and the realizations of the corresponding flat connections as Higgs bundles, as well as a determination of the asymptotic shear-bend cocycle of Thurston’s pleated surface.more » « less
-
more » « less
Abstract Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geometries, and feature many unique and desirable material properties like auxetics, tunable nonlinear stiffness, multistability, and impact absorption. Rich designs in origami offer great freedom to design the performance of such origami materials, and folding offers a unique opportunity to efficiently fabricate these materials at vastly different sizes. Here, recent studies on the different aspects of origami materials—geometric design, mechanics analysis, achieved properties, and fabrication techniques—are highlighted and the challenges ahead discussed. The synergies between these different aspects will continue to mature and flourish this promising field.
-
more » « less
Abstract Several strategies are recently exploited to transform 2D sheets into desired 3D structures. For example, soft materials can be morphed into 3D continuously curved structures by inducing nonhomogeneous strain. On the other hand, rigid materials can be folded, often by origami/kirigami‐inspired approaches (i.e., flat sheets are folded along predesigned crease patterns). Here, for the first time, combining the two strategies, composite sheets are fabricated by embedding rigid origami/kirigami skeleton with creases into heat shrinkable polymer sheets to create novel 3D structures. Upon heating, shrinkage of the polymer sheets is constrained by the origami/kirigami patterns, giving rise to laterally nonuniform strain. As a result, Gaussian curvature of the composite sheets is changed, and flat sheets are transformed into 3D curved structures. A series of 3D structures are folded using this approach, including cones and truncated pyramids with different base shapes. Flat origami loops are folded into step structures. Tessellation of origami loops is transformed into 3D checkerboard pattern.
