Hidden symmetry of the anomalous bluetongue virus capsid and its role in the infection process.

Clear understanding of the principles that control the arrangement of proteins and their self-assembly into viral shells is very important for the development of antiviral strategies. Here we consider the structural peculiarities and hidden symmetry of the anomalous bluetongue virus (BTV) capsid. Each of its three concentric shells violates the paradigmatic geometrical model of Caspar and Klug, which is otherwise well suited to describe most of the known icosahedral viral shells. As we show, three icosahedral spherical lattices, which are commensurate with each other and possess locally hexagonal (primitive or honeycomb) order, underlie the proteinaceous shells of the BTV capsid. This interpretation of the multishelled envelope allows us to discuss the so-called "symmetry mismatch" between its layers. We also analyze the structural stability of the considered spherical lattices on the basis of the classical theory of spherical packing and relate the proximity of the outer spherical lattice to destabilization with the fact that during infection of the cell VP2 trimers are detached from the surface of the BTV capsid. An electrostatic mechanism that can assist in this detachment is discussed in detail.

Anomalous small viral shells and simplest polyhedra with icosahedral symmetry: the rhombic triacontahedron case.

The development of antiviral strategies requires a clear understanding of the principles that control the protein arrangements in viral shells. Considered here are those capsids that violate the paradigmatic Caspar and Klug (CK) model, and it is shown that the important structural features of such anomalous shells from the Picobirnaviridae, Flaviviridae and Leviviridae families can be revealed by models in the form of spherical icosahedral packings of equivalent rhombic structural units (SUs). These SUs are composed of protein dimers forming the investigated capsids which, as shown here, are based on the rhombic triacontahedron (RT) geometry. How to modify the original CK approach in order to make it compatible with the considered rhombic tessellations of a sphere is also discussed. Analogies between capsids self-assembled from dimers and trimers are demonstrated. This analysis reveals the principles controlling the localization of receptor proteins (which recognize the host cell) on the capsid surface.

Commensurability between protein nanotubes in contractile ejection nanomachines.

Contractile ejection nanomachines being sheath-tube assemblies create an opening in the cell membrane to translocate molecules or ions across it. Here, on the most structurally investigated examples of the bacteriophage T4 tail and pyocin R2, we show that the rearrangement of the sheath structure resulting in its contraction and twist occurs in such a way that the contracted sheath becomes commensurate with the inner tube. This fact dictates the previously unknown simple geometrical relationship between the nanotube symmetries. Using the Frank and van der Merwe classical theory of commensurability, we study an interaction between two protein nanotubes forming such nanomachines and obtain an expression for the corresponding energy, which depends on the tube structures and their mutual arrangement. The appearance of commensurability between the contracted sheath and the inner tube decreases both the interaction energy and the total energy of the system. It improves the nanomachine efficiency, since the energy gain obtained increases the torque of the inner tube piercing the cell membrane.

Static and dynamic hidden symmetries of icosahedral viral capsids.

Viral shells self-assemble from identical proteins, which tend to form equivalent environments in the resulting assembly. However, in icosahedral capsids containing more than 60 proteins, they are enforced to occupy not only the symmetrically equivalent locations but also the quasi-equivalent ones. Due to this important fact, static and dynamic symmetries of viral shells can include additional hidden components. Here, developing the Caspar and Klug ideas concerning the quasi-equivalence of protein environments, we derive the simplest hexagonal tilings, that in principle could correspond to the local protein order in viral shells, and apply the resulting theory to nucleocytoplasmic large dsDNA viruses. In addition, analyzing the dynamic symmetry of the P22 viral shell, we demonstrate that the collective critical modes responsible for the protein reorganization during the procapsid maturation are approximately equivalent to the normal modes of the isotropic spherical membrane with O(3) symmetry. Furthermore, we establish the relationship between the dynamic symmetry of the P22 procapsid and the protein arrangement regularities that appear only in the mature capsid.