Structures of Spherical Viral Capsids as Quasicrystalline Tilings

Spherical viral shells with icosahedral symmetry have been considered as quasicrystalline tilings. Similarly to known Caspar-Klug quasi-equivalence theory, the presented approach also minimizes the number of conformations necessary for the protein molecule bonding with its neighbors in the shell, but is based on different geometrical principles. It is assumed that protein molecule centers are located at vertices of tiles with identical edges, and the number of different tile types is minimal. Idealized coordinates of nonequivalent by symmetry protein positions in six various capsid types are obtained. The approach describes in a uniform way both the structures satisfying the well-known Caspar-Klug geometrical model and the structures contradicting this model.Comment: 8 pages, 2 figures; This version was published in Physics of the Solid State, 2015, Vol. 57, No.4, pp. 810-81

Chiral Quasicrystalline Order and Dodecahedral Geometry in Exceptional Families of Viruses

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 arranged in a structure commensurate with the spherical topology and dodecahedral geometry, ii) generalize the classical theory of quasicrystals (QCs) to explain this organization, and iii) establish the relation between local chiral QC order and nonzero curvature of the dodecahedral capsid faces.Comment: 8 pages, 3 figure

Theory of morphological transformation of viral capsid shell during the maturation process in the HK97 bacteriophage and similar viruses

International audienceWe consider the symmetry and physical origin of collective displacement modes playing a crucial role in the morphological transformation during the maturation of the HK97 bacteriophage and similar viruses. It is shown that the experimentally observed hexamer deformation and pentamer twist in the HK97 procapsid correspond to the simplest irreducible shear strain mode of a spherical shell. We also show that the icosahedral faceting of the bacteriophage capsid shell is driven by the simplest irreducible radial displacement field. The shear field has the rotational icosahedral symmetry group I while the radial field has the full icosahedral symmetry Ih . Thisdifference makes their actions independent. The radial field sign discriminates between the icosahedral and the dodecahedral shapes of the faceted capsid shell, thus making the approach relevant not only for the HK97-like viruses but also for the parvovirus family. In the frame of the Landau-Ginzburg formalism we propose a simple phenomenological model valid for the first reversible step of the HK97 maturation process. The calculated phase diagram illustrates the discontinuous character of the virus shape transformation. The characteristics of the virus shell faceting and expansion obtained in the in vitro and in vivo experiments are related to the decrease in the capsid shell thickness and to the increase of the internal capsid pressure

Chiral quasicrystalline order in an exceptional family of viruses

8 pages, 2 figuresUnderstanding of virus capsid organization and self-assembly mechanisms helps to get an insight into the protein interactions which render virus infectious, but also to advance new methods in nanotechnology which use capsid self-assembly to produce virus-like nanoparticles. As in abiotic nanostructures, the obstacles along this way are related not only to the nanoscopic size of capsids but also to their unconventional topology and symmetry. In the present work on the example of exceptional families of viruses we : i) show the existence of a completely new type of organization, resulting in a chiral pentagonal quasicrystalline order of protein positions in a capsid with spherical topology and dodecahedral geometry; ii) generalize the classical theory of quasicrystals (QC) to explain this organization and demonstrate that a particular non-linear phason strain induces chirality in QC; and iii) establish the relation between chiral order and inhomogeneous buckling strain of the capsid shell