Equiauxetic Hinged Archimedean Tilings

There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An equiauxetic framework has a unique mechanism of expansion (an equiauxetic mode) where the symmetry forces a Poisson’s ratio of −1. Hinged tilings offer opportunities for the design of auxetic and equiauxetic frameworks in 2D, and generic auxetic behaviour can often be detected using a symmetry extension of the scalar counting rule for mobility of periodic body-bar systems. Hinged frameworks based on Archimedean tilings of the plane are considered here. It is known that the regular hexagonal tiling, {63}, leads to an equiauxetic framework for both single-link and double-link connections between the tiles. For single-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found here to be equiauxetic: these are {3.122}, {4.6.12}, and {4.82}. For double-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found to be equiauxetic: these are {34.6}, {32.4.3.4}, and {3.6.3.6}.

Virus-Based Devices: Prospects for Allopoiesis

The assembly line is a commonly invoked example of allopoiesis, the process whereby a system produces a different system than itself. In this sense, virus production in plants is an instance of bio-enabled bottom-up allopoiesis because the plant host can be regarded as a programmable assembly line for the virus. Reprogramming this assembly line and integrating it into a larger lineup of chemical manipulations has seen a flurry of activity recently, with more sophisticated systems emerging every year. The field of virus nanomaterials now has several subdisciplines that focus on virus shells as assemblers, scaffolds for molecular circuitry, chemical reactors, magnetic and photonic beacons, and therapeutic carriers. A case in point is the work reported by Brillault et al. in this issue of ACS Nano. They show how two types of animal virus coat proteins can be simultaneously expressed and efficiently assembled in plants into a complex virus-like particle of well-defined stoichiometry and composition. Such advances, combined with the promise of scalability and sustainability afforded by plants, paint a bright picture for the future of high-performance virus-based nanomaterials.

How does symmetry impact the flexibility of proteins?

It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures-and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body-bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body-bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains.

Bi-stiffness property of motion structures transformed into square cells

Cellular solids with internal microstructures enable the reduction in some environmental loads because of their lightweight bodies, and deliver unique elastic, electromagnetic and thermal properties. In particular, their large deformability without topological change is one of their most interesting solid properties. In this study, we propose a bar-and-joint framework assembled with a basic unit of motion structure, which has eightfold rotational symmetry (MS-8). The MS-8 is made of tetragons, arranged in a concentric fashion, which are transformed into either one of two different aligned patterns of square cells according to the coordinated rotations of the inside squares. Square cells are extremely anisotropic, which is why the stiffness of the MS-8 changes dramatically in the transformation process. Thus, the MS-8 exhibits bi-stiffness according to the two different motions. Taking advantage of the bi-stiffness property, the possibilities of deformation behaviours for repetitive structures of MS-8s are discussed.

Structure of a Venezuelan equine encephalitis virus assembly intermediate isolated from infected cells

Venezuelan equine encephalitis virus (VEEV) is a prototypical enveloped ssRNA virus of the family Togaviridae. To better understand alphavirus assembly, we analyzed newly formed nucleocapsid particles (termed pre-viral nucleocapsids) isolated from infected cells. These particles were intermediates along the virus assembly pathway, and ultimately bind membrane-associated viral glycoproteins to bud as mature infectious virus. Purified pre-viral nucleocapsids were spherical with a unimodal diameter distribution. The structure of one class of pre-viral nucleocapsids was determined with single particle reconstruction of cryo-electron microscopy images. These studies showed that pre-viral nucleocapsids assembled into an icosahedral structure with a capsid stoichiometry similar to the mature nucleocapsid. However, the individual capsomers were organized significantly differently within the pre-viral and mature nucleocapsids. The pre-viral nucleocapsid structure implies that nucleocapsids are highly plastic and undergo glycoprotein and/or lipid-driven rearrangements during virus self-assembly. This mechanism of self-assembly may be general for other enveloped viruses.

Mobility of ‘ N -loops’: bodies cyclically connected by intersecting revolute hinges

The mobilities of many objects from toys and molecular models to large-scale deployable structures can be understood in terms of N -loops: sets of N bodies, cyclically connected by pairs of intersecting revolute hinges. A symmetry-extended version of the Grübler criterion for counting kinematic degrees of freedom is used to explain and rationalize the observed mobilities of N -loops with small N . Compared with simple counting, the symmetry-based approach gives improved detection and visualization of mechanisms and states of self-stress. It can also give a better account of the differing mobilities of conformers occupying different regions of the phase space, such as the rigid chair and flexible boat forms of cyclohexane.