Static and dynamic hidden symmetries of icosahedral viral capsids

Abstract

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.

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

“…In this article, developing the previous work (Twarock, 2004(Twarock, , 2005Konevtsova et al, 2012Konevtsova et al, , 2017Raguram et al, 2017;Rochal et al, 2016Rochal et al, , 2017 further, we show that some small anomalous icosahedral capsids are based on the rhombic triacontahedron (RT) geometry. Considering these capsids, we discuss the protein tilings covering the RT surface and obtain a relation between them and icosahedral SLs.…”

“…This work continues our series of publications (Konevtsova et al, 2012Rochal et al, 2016Rochal et al, , 2017 devoted to the principles of protein arrangement in anomalous (i.e. violating the CK model; Caspar & Klug, 1962) viral capsids with icosahedral symmetry.…”

“…It is easy to note that the set of all edges of any honeycomb SL coincides with the set of all short diagonals of the dual rhombic SL. As was discussed by Rochal et al (2017), the honeycomb lattice is deduced from the PHL due to multiplication of its primitive unit cell by 3. Therefore, any triangular SL with its T factor a multiple of 3 can generate both the honeycomb SL and the rhombic one dual to it.…”

pH-induced morphological changes of proteinaceous viral shells

“…Moreover, the asphericity in the γ → 0 limit does not possess an icosahedral but rather a dodecahedral character, and the shell radii lying on the 5-fold axes are smaller than those lying on the 3-fold ones (see also the discussion of dodecahedral viral shells in ref. 34 ).

Figure 3Asphericity as a function of the FvK number for several icosahedral shells. The curves labeled 1–4 correspond to shells with the number of triangles equal to N = 60, 180, 420, and 2160, respectively.

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Breaking Symmetry in Viral Icosahedral Capsids as Seen through the Lenses of X-ray Crystallography and Cryo-Electron Microscopy

“…The principles governing assembly of icosahedral capsids are well understood and have been reviewed in detail [ 1 , 2 , 3 , 4 , 5 , 6 ]. A true icosahedral shell displays a combination of 5-fold, 3-fold, and 2-fold symmetry axes, which results in 60-fold redundancy.…”