ABSTRACT
The diffraction pattern from the recently reported aperiodic `einstein', or `hat', monohedral tiling [Smith et al. (2023). arXiv:2303.10798v1] has been analyzed. The structure is the hexagonal mta net, a kite tiling, with aperiodic vertex deletions. A large model's diffraction pattern displays a robust sixfold periodicity in plane group p6. A repeating, roughly triangular motif of `diffused intensity' arises between the strongest Bragg peaks. The motif contains high-density regions of discrete `satellite' peaks, rather than continuous `diffuse scattering', breaking mirror symmetry, consistent with the chiral hat tiling.
ABSTRACT
We present a method to fill a container shape with deformable instances of geometric elements selected from a library, creating a 2D artistic composition called an element packing. Each element is represented as a mass-spring system, allowing it to deform to achieve a better fit with its neighbours and the container. We start with an initial placement of small elements and gradually transform them using a physics simulation that trades off between the evenness of the packing and the deformations of the individual elements. Unlike previous work, elements can be given preferred orientations, and we can use shape matching to control the initial placement of elements in tight convex corners. We also explore the creation of tileable packings, and validate our approach using statistical measurements of the distributions of positive and negative space in packings. Our method produces compositions in which the negative space between elements is approximately uniform in width, similar to real-world examples created by artists.
ABSTRACT
Symmetrical protein cages have evolved to fulfil diverse roles in nature, including compartmentalization and cargo delivery1, and have inspired synthetic biologists to create novel protein assemblies via the precise manipulation of protein-protein interfaces. Despite the impressive array of protein cages produced in the laboratory, the design of inducible assemblies remains challenging2,3. Here we demonstrate an ultra-stable artificial protein cage, the assembly and disassembly of which can be controlled by metal coordination at the protein-protein interfaces. The addition of a gold (I)-triphenylphosphine compound to a cysteine-substituted, 11-mer protein ring triggers supramolecular self-assembly, which generates monodisperse cage structures with masses greater than 2 MDa. The geometry of these structures is based on the Archimedean snub cube and is, to our knowledge, unprecedented. Cryo-electron microscopy confirms that the assemblies are held together by 120 S-Aui-S staples between the protein oligomers, and exist in two chiral forms. The cage shows extreme chemical and thermal stability, yet it readily disassembles upon exposure to reducing agents. As well as gold, mercury(II) is also found to enable formation of the protein cage. This work establishes an approach for linking protein components into robust, higher-order structures, and expands the design space available for supramolecular assemblies to include previously unexplored geometries.
Subject(s)
Gold/chemistry , Proteins/chemistry , Cryoelectron Microscopy , Cysteine/chemistry , Mercury/chemistry , Models, Molecular , Proteins/ultrastructureABSTRACT
The assembly of the chiral pentagonal-star-shaped 1,3,5,7,9-pentaphenylcorannulene on a Cu(111) surface has been studied with scanning tunneling microscopy. Two different long-range ordered phases coexist at 60 K, most likely racemic and homochiral phases. The principal motifs emulate a network of meshed gears. One of the observed structures resembles the densest packing of five-fold symmetric stars.
