Role of the scaffolding protein in P22 procapsid size determination suggested by T = 4 and T = 7 procapsid structures.

Assembly of bacteriophage P22 procapsids requires the participation of approximately 300 molecules of scaffolding protein in addition to the 420 coat protein subunits. In the absence of the scaffolding, the P22 coat protein can assemble both wild-type-size and smaller size closed capsids. Both sizes of procapsid assembled in the absence of the scaffolding protein have been studied by electron cryomicroscopy. These structural studies show that the larger capsids have T = 7 icosahedral lattices and appear the same as wild-type procapsids. The smaller capsids possess T = 4 icosahedral symmetry. The two procapsids consist of very similar penton and hexon clusters, except for an increased curvature present in the T = 4 hexon. In particular, the pronounced skewing of the hexons is conserved in both sizes of capsid. The T = 7 procapsid has a local non-icosahedral twofold axis in the center of the hexon and thus contains four unique quasi-equivalent coat protein conformations that are the same as those in the T = 4 procapsid. Models of how the scaffolding protein may direct these four coat subunit types into a T = 7 rather than a T = 4 procapsid are presented.     

3D domain swapping modulates the stability of members of an icosahedral virus group

BACKGROUND: Rice yellow mottle virus (RYMV) is a major pathogen that dramatically reduces rice production in many African countries. RYMV belongs to the genus sobemovirus, one group of plant viruses with icosahedral capsids and single-stranded, positive-sense RNA genomes. RESULTS: The structure of RYMV was determined and refined to 2.8 A resolution by X-ray crystallography. The capsid contains 180 copies of the coat protein subunit arranged with T = 3 icosahedral symmetry. Each subunit adopts a jelly-roll beta sandwich fold. The RYMV capsid structure is similar to those of other sobemoviruses. When compared with these viruses, however, the betaA arm of the RYMV C subunit, which is a molecular switch that regulates quasi-equivalent subunit interactions, is swapped with the 2-fold-related betaA arm to a similar, noncovalent bonding environment. This exchange of identical structural elements across a symmetry axis is categorized as 3D domain swapping and produces long-range interactions throughout the icosahedral surface lattice. Biochemical analysis supports the notion that 3D domain swapping increases the stability of RYMV. CONCLUSIONS: The quasi-equivalent interactions between the RYMV proteins are regulated by the N-terminal ordered residues of the betaA arm, which functions as a molecular switch. Comparative analysis suggests that this molecular switch can also modulate the stability of the viral capsids.     

A novel method to map and compare protein-protein interactions in spherical viral capsids

Viral capsids are composed of multiple copies of one or a few chemically distinct capsid proteins and are mostly stabilized by inter subunit protein-protein interactions. There have been efforts to identify and analyze these protein-protein interactions, in terms of their extent and similarity, between the subunit interfaces related by quasi- and icosahedral symmetry. Here, we describe a new method to map quaternary interactions in spherical virus capsids onto polar angle space with respect to the icosahedral symmetry axes using azimuthal orthographic diagrams. This approach enables one to map the nonredundant interactions in a spherical virus capsid, irrespective of its size or triangulation number (T), onto the reference icosahedral asymmetric unit space. The resultant diagrams represent characteristic fingerprints of quaternary interactions of the respective capsids. Hence, they can be used as road maps of the protein-protein interactions to visualize the distribution and the density of the interactions. In addition, unlike the previous studies, the fingerprints of different capsids, when represented in a matrix form, can be compared with one another to quantitatively evaluate the similarity (S-score) in the subunit environments and the associated protein-protein interactions. The S-score selectively distinguishes the similarity, or lack of it, in the locations of the quaternary interactions as opposed to other well-known structural similarity metrics (e.g., RMSD, TM-score). Application of this method on a subset of T = 1 and T = 3 capsids suggests that S-score values range between 1 and 0.6 for capsids that belong to the same virus family/genus; 0.6-0.3 for capsids from different families with the same T-number and similar subunit fold; and <0.3 for comparisons of the dissimilar capsids that display different quaternary architectures (T-numbers). Finally, the sequence conserved interface residues within a virus family, whose spatial locations were also conserved have been hypothesized as the essential residues for self-assembly of the member virus capsids.     

Three-dimensional structure of baculovirus-expressed Norwalk virus capsids.

The three-dimensional structure of the baculovirus-expressed Norwalk virus capsid has been determined to a resolution of 2.2 nm using electron cryomicroscopy and computer image processing techniques. The empty capsid, 38.0 nm in diameter, exhibits T = 3 icosahedral symmetry and is composed of 90 dimers of the capsid protein. The striking features of the capsid structure are arch-like capsomeres, at the local and strict 2-fold axes, formed by dimers of the capsid protein and large hollows at the icosahedral 5- and 3-fold axes. Despite its distinctive architecture, the Norwalk virus capsid has several similarities with the structures of T = 3 single-stranded RNA (ssRNA) viruses. The structure of the protein subunit appears to be modular with three distinct domains: the distal globular domain (P2) that appears bilobed, a central stem domain (P1), and a lower shell domain (S). The distal domains of the 2-fold related subunits interact with each other to form the top of the arch. The lower domains of the adjacent subunits associate tightly to form a continuous shell between the radii of 11.0 and 15.0 nm. No significant mass density is observed below the radius of 11.0 mm. It is suspected that the hinge peptide in the adjoining region between the central domain and the shell domain may facilitate the subunits adapting to various quasi-equivalent environments. Architectural similarities between the Norwalk virus capsid and the other ssRNA viruses have suggested a possible domain organization along the primary sequence of the Norwalk virus capsid protein. It is suggested that the N-terminal 250 residues constitute the lower shell domain (S) with an eight-strand beta-barrel structure and that the C-terminal residues beyond 250 constitute the protruding (P1+P2) domains. A lack of an N-terminal basic region and the ability of the Norwalk virus capsid protein to form empty T = 3 shells suggest that the assembly pathway and the RNA packing mechanisms may be different from those proposed for tomato bushy stunt virus and southern bean mosaic virus but similar to that in tymoviruses and comoviruses.     

Extent of protein-protein interactions and quasi-equivalence in viral capsids

Viral capsids are composed of multiple copies of one or a few gene products that self-assemble on their own or in the presence of the viral genome and/or auxiliary proteins into closed shells (capsids). We have analyzed 75 high-resolution virus capsid structures by calculating the average fraction of the solvent-accessible surface area of the coat protein subunits buried in the viral capsids. This fraction ranges from 0 to 1 and represents a normalized protein-protein interaction (PPI) index and is a measure of the extent of protein-protein interactions. The PPI indices were used to compare the extent of association of subunits among different capsids. We further examined the variation of the PPI indices as a function of the molecular weight of the coat protein subunit and the capsid diameter. Our results suggest that the PPI indices in T=1 and pseudo-T=3 capsids vary linearly with the molecular weight of the subunit and capsid size. This is in contrast to quasi-equivalent capsids with T>or=3, where the extent of protein-protein interactions is relatively independent of the subunit and capsid sizes. The striking outcome of this analysis is the distinctive clustering of the "T=2" capsids, which are distinguished by higher subunit molecular weights and a much lower degree of protein-protein interactions. Furthermore, the calculated residual (R(sym)) of the fraction buried surface areas of the structurally unique subunits in capsids with T>1 was used to calculate the quasi-equivalence of different subunit environments.     

Refined structure of southern bean mosaic virus at 2.9 A resolution

The T = 3 capsid of southern bean mosaic virus is analyzed in detail. The beta-sheets of the beta-barrel folding motif that form the subunits show a high degree of twist, generated by several beta-bulges. Only 34 water molecules were identified in association with the three quasi-equivalent subunits, most of them on the external viral surface. Subunit contacts related by quasi-3-fold axes are similar, are dominated by polar interactions and have almost identical calcium binding sites. There is no metal ion on the quasi-3-fold axis, as previously reported. Subunits related by quasi-2-fold and icosahedral 2-fold axes have different contacts but nevertheless display almost identical interactions between the antiparallel helices alpha A. A dipole-dipole type interaction between these helices may produce an energetically stable hinge that allows two types of dimers in a T = 3 assembly. The temperature factor distribution, the hydrogen-bonding pattern, and the contacts across the icosahedral 2-fold axes suggest that one of the dimer types is present in the intact virion and probably also in solution; the other is produced only during capsid assembly. Interactions along the 5-fold axes are mainly polar and possibly form an ion channel. The beta-sheet structures of the three subunits can be superimposed with considerable precision. Significant relative distortions between quasi-equivalent subunits occur mainly in helices and loops. The two dimeric forms and the subunit distortions are the consequence of the non-equivalent subunit environments in the capsid.     

A dissection of the protein-protein interfaces in icosahedral virus capsids

We selected 49 icosahedral virus capsids whose crystal structures are reported in the Protein Data Bank. They belong to the T=1, T=3, pseudo T=3 and other lattice types. We identified in them 779 unique interfaces between pairs of subunits, all repeated by icosahedral symmetry. We analyzed the geometric and physical chemical properties of these interfaces and compared with interfaces in protein-protein complexes and homodimeric proteins, and with crystal packing contacts. The capsids contain one to 16 subunits implicated in three to 66 unique interfaces. Each subunit loses 40-60% of its accessible surface in contacts with an average of 8.5 neighbors. Many of the interfaces are very large with a buried surface area (BSA) that can exceed 10,000 A(2), yet 39% are small with a BSA<800 A(2) comparable to crystal packing contacts. Pairwise capsid interfaces overlap, so that one-third of the residues are part of more than one interface. Those with a BSA>800 A(2) resemble homodimer interfaces in their chemical composition. Relative to the protein surface, they are non-polar, enriched in aliphatic residues and depleted of charged residues, but not of neutral polar residues. They contain one H-bond per about 200 A(2) BSA. Small capsid interfaces (BSA<800 A(2)) are only slightly more polar. They have a similar amino acid composition, but they bury fewer atoms and contain fewer H-bonds for their size. Geometric parameters that estimate the quality of the atomic packing suggest that the small capsid interfaces are loosely packed like crystal packing contacts, whereas the larger interfaces are close-packed as in protein-protein complexes and homodimers. We discuss implications of these findings on the mechanism of capsid assembly, assuming that the larger interfaces form first to yield stable oligomeric species (capsomeres), and that medium-size interfaces allow the stepwise addition of capsomeres to build larger intermediates.     

Structures of T=1 and T=3 particles of cucumber necrosis virus: evidence of internal scaffolding

Cucumber necrosis virus (CNV) is a member of the genus Tombusvirus, of which tomato bushy stunt virus (TBSV) is the type member. The capsid protein for this group of viruses is composed of three major domains: the R domain, which interacts with the RNA genome: the S domain, which forms the tight capsid shell: and the protruding P domain, which extends approximately 40 Angstrom from the surface. Here, we present the cryo-transmission electron microscopy structures of both the T=1 and T=3 capsids to a resolution of approximately 12 Angstrom. The T=3 capsid is essentially identical with that of TBSV, and the T=1 particles are well described by the A subunit pentons from TBSV. Perhaps most notable is the fact that the T=3 particles have an articulated internal structure with two major internal shells, while the internal core of the T=1 particle is essentially disordered. These internal shells of the T=3 capsid agree extremely well in both dimension and character with published neutron-scattering results. This structure, combined with mutagenesis results in the accompanying article, suggests that the R domain forms an internal icosahedral scaffold that may play a role in T=3 capsid assembly. In addition, the N-terminal region has been shown to be involved in chloroplast targeting. Therefore, this region apparently has remarkably diverse functions that may be distributed unevenly among the quasi-equivalent A, B, and C subunits.     

Three-dimensional structure of the inner core of rice dwarf virus

Rice dwarf virus (RDV) is a double-shelled icosahedral virus.Using electron cryomicroscopy and computer reconstruction techniques, we have determined a 3.3 nm resolution three-dimensional (3D) structure of the inner shell capsid without the outer shell and viral RNA. The results show that the inner shell is a thin, densely packed, smooth structure, which provides a scaffold for the full virus. A total of 120 copies of the major inner shell capsid protein P3 forms 60 dimers arranged in a T=1 icosahedral lattice. A close examination on the subunit packing of the T=1 inner core P3 with that of the T=13l outer shell P8 indicated that P8 trimers connect with P3 through completely non-equivalent, yet highly specific, intermolecular interactions.     

Three-dimensional structure of the inner core of rice dwarf virus

Rice dwarf virus (RDV) is a double-shelled icosahedral virus. Using electron cryomicro-scopy and computer reconstruction techniques, we have determined a 3.3 nm resolution three-dimensional (3D) structure of the inner shell capsid without the outer shell and viral RNA. The results show that the inner shell is a thin, densely packed, smooth structure, which provides a scaffold for the full virus. A total of 120 copies of the major inner shell capsid protein P3 forms 60 dimers arranged in a T=1 icosahedral lattice. A close examination on the subunit packing of the T=1 inner core P3 with that of the T=13/ outer shell P8 indicated that P8 trimers connect with P3 through completely non-equivalent, yet highly specific, intermolecular interactions.     

A micromolar pool of antigenically distinct precursors is required to initiate cooperative assembly of hepatitis B virus capsids in Xenopus oocytes.

Assembly of hepatitis B virus capsid-like (core) particles occurs efficiently in a variety of heterologous systems via aggregation of approximately 180 molecules of a single 21.5-kDa core protein (p21.5), resulting in an icosahedral capsid structure with T = 3 symmetry. Recent studies on the assembly of hepatitis B virus core particles in Xenopus oocytes suggested that dimers of p21.5 represent the major building block from which capsids are generated. Here we determined the concentration dependence of this assembly process. By injecting serially diluted synthetic p21.5 mRNA into Xenopus oocytes, we expressed different levels of intracellular p21.5 and monitored the production of p21.5 dimers and capsids by radiolabeling and immunoprecipitation, by radioimmunoassay, or by quantitative enzyme-linked immunosorbent assay analysis. The data revealed that (i) p21.5 dimers and capsids are antigenically distinct, (ii) capsid assembly is a highly cooperative and concentration-dependent process, and (iii) p21.5 must accumulate to a signature concentration of approximately 0.7 to 0.8 microM before capsid assembly initiates. This assembly process is strikingly similar to the assembly of RNA bacteriophage R17 as defined by in vitro studies.     

C terminus of infectious bursal disease virus major capsid protein VP2 is involved in definition of the T number for capsid assembly

Infectious bursal disease virus (IBDV), a member of the Birnaviridae family, is a double-stranded RNA virus. The IBDV capsid is formed by two major structural proteins, VP2 and VP3, which assemble to form a T=13 markedly nonspherical capsid. During viral infection, VP2 is initially synthesized as a precursor, called VPX, whose C end is proteolytically processed to the mature form during capsid assembly. We have computed three-dimensional maps of IBDV capsid and virus-like particles built up by VP2 alone by using electron cryomicroscopy and image-processing techniques. The IBDV single-shelled capsid is characterized by the presence of 260 protruding trimers on the outer surface. Five classes of trimers can be distinguished according to their different local environments. When VP2 is expressed alone in insect cells, dodecahedral particles form spontaneously; these may be assembled into larger, fragile icosahedral capsids built up by 12 dodecahedral capsids. Each dodecahedral capsid is an empty T=1 shell composed of 20 trimeric clusters of VP2. Structural comparison between IBDV capsids and capsids consisting of VP2 alone allowed the determination of the major capsid protein locations and the interactions between them. Whereas VP2 forms the outer protruding trimers, VP3 is found as trimers on the inner surface and may be responsible for stabilizing functions. Since elimination of the C-terminal region of VPX is correlated with the assembly of T=1 capsids, this domain might be involved (either alone or in cooperation with VP3) in the induction of different conformations of VP2 during capsid morphogenesis.     

Prediction of stability changes upon mutation in an icosahedral capsid

Identifying the contributions to thermodynamic stability of capsids is of fundamental and practical importance. Here we use simulation to assess how mutations affect the stability of lumazine synthase from the hyperthermophile Aquifex aeolicus, a T = 1 icosahedral capsid; in the simulations the icosahedral symmetry of the capsid is preserved by simulating a single pentamer and imposing crystal symmetry, in effect simulating an infinite cubic lattice of icosahedral capsids. The stability is assessed by estimating the free energy of association using an empirical method previously proposed to identify biological units in crystal structures. We investigate the effect on capsid formation of seven mutations, for which it has been experimentally assessed whether they disrupt capsid formation or not. With one exception, our approach predicts the effect of the mutations on the capsid stability. The method allows the identification of interaction networks, which drive capsid assembly, and highlights the plasticity of the interfaces between subunits in the capsid. Proteins 2015; 83:1733–1741. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc     

The role of subunit hinges and molecular "switches" in the control of viral capsid polymorphism

The coat protein (CP) of cowpea chlorotic mottle virus assembles exclusively into a T=3 capsid in vivo and, under proper conditions, in vitro. The N-terminal domain of CP has been implicated in proper assembly and was viewed as a required switch for mediating hexamer and pentamer formation in T=3 assembly. We observed that a mutant CP lacking most of the N-terminal domain, NDelta34, assembles, in vitro, into statistically predictable numbers of: native-like T=3 capsids of 90 dimers; "T=2" capsids of 60 dimers; T=1 capsids of 30 dimers. We generated cryo-EM image reconstructions of each form and built pseudo-atomic models based on the subunits from the crystal structure of plant-derived T=3 virus allowing a detailed comparison of stabilizing interactions in the three assemblies. The statistical nature of the distribution of assembly products and the observed structures indicates that the N-terminus of CP is not a switch that is required to form the proper ratio of hexamers and pentamers for T=3 assembly; rather, it biases the direction of assembly to T=3 particles from the possibilities available to NDelta34 through flexible dimer hinges and variations in subunit contacts. Our results are consistent with a pentamer of dimers (PODs) nucleating assembly in all cases but subunit dimers can be added with different trajectories that favor specific T=3 or T=1 global particle geometries. Formation of the "T=2" particles appears to be fundamentally different in that they not only nucleate with PODs, but assembly propagates by the addition of mostly, if not exclusively PODs generating an entirely new subunit interface in the process. These results show that capsid geometry is flexible and may readily adapt to new requirements as the virus evolves.     

Crystal structure of tobacco necrosis virus at 2.25 A resolution

The crystal structure of tobacco necrosis virus (TNV) has been determined by real-space averaging with 5-fold non-crystallographic symmetry, and refined to R=25.3 % for diffraction data to 2.25 A resolution. A total of 180 subunits form a T=3 virus shell with a diameter of about 280 A and a small protrusion at the 5-fold axis. In 276 amino acid residues, the respective amino terminal 86, 87 and 56 residues of the A, B and C subunits are disordered. No density for the RNA was found. The subunits have a "jelly roll" beta-barrel structure, as have the structures of the subunits of other spherical viruses. The tertiary and quaternary structures of TNV are, in particular, similar to those of southern bean mosaic virus, although they are classified in different groups. Invisible residues 1 to 56 with a high level of basic residues are considered to be located inside the particle. Sequence comparison of the coat proteins of several TNV strains showed that the sequences of the disordered segment diverge considerably as compared with those of the ordered segment, consistent with a small tertiary structural constraint being imposed on the N-terminal segment. Basic residues are localized on the subunit interfaces or inner surface of the capsid. Positive charges of the basic residues facing the interior, as well as those of the N-terminal segment, may neutralize the negative charge of the RNA inside. Five calcium ions per icosahedral asymmetric unit are located at the subunit interfaces; three are close to the exterior surface, the other two away from it. The environments of the first three are similar, and those of the other two sites are similar. These calcium ions are assumed to be responsible for the stabilization/transition of the quaternary structure of the shell. Three peptide segments ordered only in the C subunits are clustered around each 3-fold (quasi-6-fold) axis forming a beta-annulus, and may lead to quasi-equivalent interactions for the organization of the T=3 shell.     

Mechanical disassembly of single virus particles reveals kinetic intermediates predicted by theory

New experimental approaches are required to detect the elusive transient intermediates predicted by simulations of virus assembly or disassembly. Here, an atomic force microscope (AFM) was used to mechanically induce partial disassembly of single icosahedral T=1 capsids and virions of the minute virus of mice. The kinetic intermediates formed were imaged by AFM. The results revealed that induced disassembly of single minute-virus-of-mice particles is frequently initiated by loss of one of the 20 equivalent capsomers (trimers of capsid protein subunits) leading to a stable, nearly complete particle that does not readily lose further capsomers. With lower frequency, a fairly stable, three-fourths-complete capsid lacking one pentamer of capsomers and a free, stable pentamer were obtained. The intermediates most frequently identified (capsids missing one capsomer, capsids missing one pentamer of capsomers, and free pentamers of capsomers) had been predicted in theoretical studies of reversible capsid assembly based on thermodynamic-kinetic models, molecular dynamics, or oligomerization energies. We conclude that mechanical manipulation and imaging of simple virus particles by AFM can be used to experimentally identify kinetic intermediates predicted by simulations of assembly or disassembly.     

The three-dimensional structure of frozen-hydrated Nudaurelia capensis β Virus, a T = 4 insect Virus

The three-dimensional structure of Nudaurelia capensis beta virus (N beta V) was reconstructed to 3.2-nm resolution from images of frozen-hydrated virions. The distinctly icosahedral capsid (approximately 40-nm diameter) contains 240 copies of a single 61-kDa protein subunit arranged with T = 4 lattice symmetry. The outer surface of unstained virions compares remarkably well with that previously observed in negatively stained specimens. Inspection of the density map, volume estimates, and model building experiments indicate that each subunit consists of two distinct domains. The large domain (approximately 40 kDa) has a cylindrical shape, approximately 4-nm diameter by approximately 4-nm high, and associates with two large domains of neighboring subunits to form a Y-shaped trimeric aggregate in the outer capsid surface. Four trimers make up each of the 20 planar faces of the capsid. Small domains (approximately 21 kDa) presumably associate at lower radii (approximately 13-16.5 nm) to form a contiguous, non-spherical shell. A T = 4 model, constructed from 80 trimers of the common beta-barrel core motif (approximately 20 kDa) found in many of the smaller T = 3 and pseudo T = 3 viruses, fits the dimensions and features seen in the N beta V reconstruction, suggesting that the contiguous shell of N beta V may be formed by intersubunit contacts between small domains having that motif. The small (approximately 1800 kDa), ssRNA genome is loosely packed inside the capsid with a low average density.     

Residue conservation in viral capsid assembly

To evaluate the evolutionary constraints placed on viral proteins by the structure and assembly of the capsid, we calculate Shannon entropies in the aligned sequences of 45 polypeptide chains in 32 icosahedral viruses, and relate these entropies to the residue location in the three-dimensional structure of the capsids. Three categories of residues have entropies lower than the chain average implying that they are better conserved than average: residues that are buried within a subunit (the protein core), residues that contain atoms buried at an interface between subunits (the interface core), and residues that contribute to several such interfaces. The interface core is also conserved in homomeric proteins and in transient protein-protein complexes, which have only one interface whereas capsids have many. In capsids, the subunit interfaces implicate most of the polypeptide chain: on average, 66% of the capsid residues are at an interface, 34% at more than one, and 47% at the interface core. Nevertheless, we observe that the degree of residue conservation can vary widely between interfaces within a capsid and between regions within an interface. The interfaces and regions of interfaces that show a low sequence variability are likely to play major roles in the self-assembly of the capsid, with implications on its mechanism that we discuss taking adeno-associated virus as an example.     

RNA-protein interactions in some small plant viruses

The structure of the three quasi-equivalent protein subunits A, B and C of the spherical, T = 3 southern bean mosaic virus (SBMV) have been carefully built in accordance with a refined electron density map of the complete virus. The lower electron density in the RNA portion of the map could not be explicitly interpreted in terms of a preferred RNA structure on which some icosahedral symmetry might have been imposed. However, the extremely basic nature of the interior surface of the coat protein must be associated with the binding and organization of the RNA. Comparison with the small spherical, T = 1 satellite tobacco necrosis virus (STNV; Liljas et al., J. Mol. Biol. 159, 93-108, 1982) and the T = 1 aggregate of alfalfa mosaic virus (AMV) protein (Fukuyama et al., J. Mol. Biol. 150, 33-41, 1981) showed similar results. The pattern of basic residues on the SBMV coat protein surface facing the RNA is able to dock a 9 base pair double-helical A-RNA structure with surprising accuracy. The basic residues are each associated with a different phosphate and the protein can make interactions with five bases in the minor groove. This may be one of a small number of ways in which the RNA interacts with SBMV coat protein. The self-assembly of SBMV has been studied in relation to the presence of the 63 basic amino-terminal coat protein sequence, pH, Ca2+ and Mg2+ ions and RNA. These results have led to a two-state model where the "relaxed" dimers initially self-assemble into 10-mer caps which nucleate the assembly of T = 1 or T = 3 capsids depending on the charge state of the carboxyl group clusters in the subunit contact region. The two-state condition of dimers in a viral coat protein extends the range of structures originally envisaged by Caspar and Klug (Cold Spring Harbor Symp. Quant. Biol. 27, 1-24, 1962).