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Biology is teeming with intricate molecular structures whose geometries are inextricably linked to their function. A prototypical example is the helical bacterial flagellum, a complex curved crystalline assembly of proteins that the bacterium uses to swim. Because synthetic analogues of these and other curved crystalline assemblies could be valuable platforms for nanotechnologies, including drug delivery and plasmonics, controllable synthesis of variable-curvature structures of diverse material systems, from fullerenes to supramolecular assemblies, has been a long-standing goal. Here, we develop and implement a design strategy to program the self-assembly of a complex spectrum of two-periodic curved crystals with variable periodicity, spatial dimension, and topology, spanning from toroids to achiral serpentine tubules to both left- and right-handed helical tubules. Notably, our design strategy exploits a kirigami-based mapping of a modular class of 2D planar tilings to 3D curved crystals that preserves the periodicity, twofold rotational symmetries, and subunit dimensions by modulating the arrangement of disclination defects. We survey the modular geometry of these curved crystals and infer the addressable interactions required to assemble them from triangular subunits. To demonstrate this design strategy in practice, we program the self-assembly of toroids, helical, and serpentine tubules from DNA origami subunits, deriving the distinct kirigami foldings of a single two-periodic planar tiling. A simulation model of the assembly pathways reveals physical considerations for programming the geometric specificity of the intersubunit angles in the curved crystal required to avoid defect-mediated misassembly.
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Engineering tertiary chirality in helical biopolymers
Tertiary chirality describes the handedness of supramolecular assemblies and relies not only on the primary and secondary structures of the building blocks but also on topological driving forces that have been sparsely characterized. Helical biopolymers, especially DNA, have been extensively investigated as they possess intrinsic chirality that determines the optical, mechanical, and physical properties of the ensuing material. Here, we employ the DNA tensegrity triangle as a model system to locate the tipping points in chirality inversion at the tertiary level by X-ray diffraction. We engineer tensegrity triangle crystals with incremental rotational steps between immobile junctions from 3 to 28 base pairs (bp). We construct a mathematical model that accurately predicts and explains the molecular configurations in both this work and previous studies. Our design framework is extendable to other supramolecular assemblies of helical biopolymers and can be used in the design of chiral nanomaterials, optically active molecules, and mesoporous frameworks, all of which are of interest to physical, biological, and chemical nanoscience.
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- PAR ID:
- 10536558
- Publisher / Repository:
- National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 121
- Issue:
- 19
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1073/pnas.2321992121
