μ (the number of subunits per turn). The pitch of the helix, P, is given by the formula P = ρ × μ. (B) Tobacco mosaic virus. (Left) A cryo-EM reconstruction at <5-Å resolution of a 70-nm segment of this particle. Each helical turn contains 16.3 protein molecules. Reprinted from Sachse J et al. 2007. J Mol Biol 371:812–835, with permission. Courtesy of N. Grigorieff, Leibniz-Institut für Alterforschung, Jena, Germany. (Right) The regular interaction of the (+) strand RNA genome with coat protein subunits is illustrated in the model based on an X-ray diffraction structure. Data from Namba K et al. 1989. J Mol Biol 208:307–325. (C) Vesicular stomatitis virus. Representative averages of cryo-EM images of the central trunk, conical tip, and flat base of this bullet-shaped virus particle are shown at the left. The trunk and tip were analyzed and reconstructed separately to form the montage model shown on the right, with N and M proteins in green and blue, respectively, and the membrane in purple and pink. The N protein packages the (−) strand RNA genome in a left-handed helix. The crystal structure of N determined in an N-RNA complex (Fig. 4.7) fits unambiguously with the cryo-EM density of trunk N subunits. The turns of the N protein helix are not closely associated with one another, a property that accounts for the unwinding of the nucleoprotein in the absence of M (see text), which forms an outer, left-handed helix. At the tip, N molecules interact in the absence of RNA. In the trunk, the N helix contains 37.5 subunits per turn. Comparison of N-N interactions in such a turn and in rings of 10 N molecules (Fig 4.7), as well as the results of mutational analysis, are consistent with formation of rings containing increasing numbers of N molecules from the tip via different modes of N-N interaction induced by association with long genomic RNA. Once a second turn of the N-RNA is stacked on the first, the M protein can bind to add rigidity. Reprinted from Ge P et al. 2010. Science 327:689–693, with permission. Courtesy of Z.H. Zhou, University of California, Los Angeles.
Figure 4.7 Structure of a ribonucleoprotein-like complex of vesicular stomatitis virus. Shown is the structure of a decamer of the N protein bound to RNA, determined by X-ray crystallography, with alternating monomers in the ring colored red and blue and the RNA ribose-phosphate backbone depicted as a green tube. To allow visualization of the RNA, the C-terminal domain of the monomer at the top center is not shown. The decamer was isolated by dissociation of the viral P protein from RNA-bound oligomers formed when the N and P proteins were synthesized in Escherichia coli. Although considerably smaller than N-RNA rings in the virus particles, this structure revealed how N protein molecules interact with the RNA genome and with one another. For example, the N-terminal extension and the extended loop in the C-terminal lobe contribute to the extensive interactions among neighboring N monomers. Adapted from Green TJ et al. 2006. Science 313:357–360, with permission. Courtesy of M. Luo, University of Alabama at Birmingham.
Figure 4.8 Structure of an influenza A virus ribonucleoprotein. (A) (Left) Ribonucleoproteins (RNPs) were isolated from purified influenza A virus particles and examined by scanning transmission EM tomography. Shown is a single RNP segment, with the NP loops indicated by arrowheads: most RNPs have the viral RNA polymerase bound at the end opposite the NP loop. Scale bar, 50 nm. Adapted from Sugita Y et al. 2013. J Virol 87:12879–12884. Courtesy of Y. Kawoaka, University of Tokyo, Japan. (Right) Central and terminal regions of purified RNPs were analyzed separately following cryo-EM. This procedure was adopted to overcome the heterogeneity in length of individual RNPs and their flexibility. Class averaging of images of straight segments of central regions and three-dimensional reconstruction revealed that the RNA-binding NP protein forms a double helix closed by a loop at one end. The likely localization of the (−) strand genome RNA (yellow ribbon) was deduced from the surface electrostatic potential (left, with positive and negative charge shown in blue and red, respectively) and the positions of substitutions that impair binding of NP to RNA (blue in the model on the right). Reprinted from Arranz R et al. 2012. Science 338:1634–1637, with permission. Courtesy of J. Martin-Benito, Centro Nacional de Biotecnologia, Madrid, Spain. (B) Non-uniform association of (–) strand RNA segments with the NP double helix is illustrated schematically, with the NP strands of opposite polarity shown in pale and dark tan; the RNA polymerase subunits at the other end in green, pink, and yellow; and the RNA shown in green. This mode of association, in which G-rich sequences in each RNA genome segment are more tightly bound, was deduced from high-throughput sequencing of RNA fragments bound to RNPs isolated by immunoprecipitation following UV cross-linking of influenza A virus particles and limited RNase digestion of viral lysates. Adapted from Lee N et al. 2017. Nucleic Acids Res 45:8968–8977, with permission.
Capsids with Icosahedral Symmetry
General Principles
Icosahedral symmetry. Platonic solids are symmetrical forms in which each face is the same regular polygon and the same number of faces meet at each vertex. An icosahedron contains the largest number of faces (20), and 12 vertices related by two-, three-, and fivefold axes of rotational symmetry (Fig. 4.9A). In a few cases, virus particles can be readily seen to be icosahedral (e.g., see Fig. 4.16A and 4.26). However, most closed capsids look spherical, and they often possess prominent surface features or viral glycoproteins in the envelope that do not conform to the underlying icosahedral symmetry of the capsid shell. Nevertheless, the symmetry with which the structural units interact is that of an icosahedron.
Figure 4.9 Icosahedral packing in simple structures. (A) An icosahedron, which comprises 20 equilateral triangular faces characterized by positions of five-, three-, and twofold rotational symmetry. The three views at the bottom illustrate these positions. (B and C) A comma represents a single protein molecule, and axes of rotational symmetry are indicated as in panel A. In the simplest case, T = 1 (B), the protein molecule forms the structural unit, and each of the 60 molecules is related to its neighbors by the two-, three-, and fivefold rotational axes that define a structure with icosahedral symmetry. In such a simple icosahedral structure, the interactions of all molecules with their neighbors are identical. In the T = 3 structure (C) with 180 identical protein subunits, there are three modes of packing of a subunit (shown in orange, yellow, and purple): a trimer (outlined in blue) is now the asymmetric unit, which, when replicated according to 60-fold icosahedral symmetry, generates the complete structure. The orange subunits are present in pentamers, formed by tail-to-tail interactions, and interact in rings of three (head to head) with purple and yellow subunits, and in pairs (head to head) with a purple or a yellow subunit. The purple and yellow subunits are arranged in rings of six molecules (by tail-to-tail interactions) that alternate in the particle. Despite these packing differences, the bonding interactions in which each subunit engages are similar, that is, quasiequivalent: for example, all engage in tail-to-tail and head-to-head interactions. Adapted from Harrison SC. 1984. Trends Biochem Sci 9:345–351, with permission.
In solid geometry, each of the 20 faces of an icosahedron is an equilateral triangle, and five such triangles interact at each of the 12 vertices (Fig. 4.9A). In the simplest protein shells, a trimer of
