Related papers: Structures of Spherical Viral Capsids as Quasicrys…
The Caspar-Klug classification of viruses whose protein shell, called viral capsid, exhibits icosahedral symmetry, has recently been extended to incorporate viruses whose capsid proteins are exclusively organised in pentamers. The approach,…
Proteinaceous shells useful for various biomedical applications exhibit a wide range of anomalous structures that are fundamentally different from icosahedral viral capsids described by the Caspar-Klug paradigmatic model. Exploring the…
We apply Landau theory of crystallization to explain and to classify the capsid structures of small viruses with spherical topology and icosahedral symmetry. We develop an explicit method which predicts the positions of centers of mass for…
A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Viral capsids are usually spherical, and for a significant number of viruses exhibit overall…
We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in…
From the analysis of sizes of approximately 130 small icosahedral viruses we find that there is a typical structural capsid protein, having a mean diameter of 5 nm and a mean thickness of 3 nm, with more than two thirds of the analyzed…
A formalism is developed which allows to determine the locations of all local symmetry axes of three-dimensional particles with overall icosahedral symmetry. It relies on the fact that the root system of the non-crystallographic Coxeter…
We present a top-down approach to the study of the dynamics of icosahedral virus capsids, in which each protein is approximated by a point mass. Although this represents a rather crude coarse-graining, we argue that it highlights several…
The protein shells, or capsids, of all sphere-like viruses adopt icosahedral symmetry. In the present paper we propose a statistical thermodynamic model for viral self-assembly. We find that icosahedral symmetry is not expected for viral…
Recent studies reveal that certain viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph theoretical constraints forbid exact realization of icosahedral…
The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral…
We classify all edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are pseudo-double wheels. For this, we characterize these spherical tilings by a quadratic equation for the cosine of an edge-length. By the…
On the example of exceptional families of viruses we i) show the existence of a completely new type of matter organization in nanoparticles, in which the regions with a chiral pentagonal quasicrystalline order of protein positions are…
While small single stranded viral shells encapsidate their genome spontaneously, many large viruses, such as the Herpes virus or Infectious Bursal Disease Virus (IBDV), typically require a template, consisting of either scaffolding proteins…
Recent high resolution structures for viral capsids with 12, 32 and 72 subunits ($T1$, $T3$ and $T7$ viruses) have confirmed theoretical predictions of an icosadeltahedral structure with 12 subunits having five nearest neighbors (pentamers)…
Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can…
Recently, continuum elasticity theory has been applied to explain the shape transition of icosahedral viral capsids - single-protein-thick crystalline shells - from spherical to buckled/faceted as their radius increases through a critical…
The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is…
Quasicrystals are fascinating structures, characterized by strong positional order but lacking the periodicity of a crystal. In colloidal systems, quasicrystals are typically predicted for particles with complex or highly specific…
A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…