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Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfill predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3 – 4 Å resolution. This review summarizes technical developments, both in instrumentation and in computation, that have led to the new structures, which advance our understanding of virus assembly and cell entry.
Most cellular activities are outcomes of interactions among many components, including proteins, nucleic acids and lipids. Electron cryo-microscopy of isolated macromolecular complexes ("single particle cryo-EM") can now visualize icosahedral viruses at near-atomic resolution (Table 1, [1–9]), and it should soon achieve similar resolution with less symmetrical particles. In a seminal review 15 years ago, Henderson predicted the success of single-particle techniques in visualizing detail at 3 – 4 Å resolution , and Glaeser extended the analysis a few years later . A major step towards this goal was visualization of the hepatitis B icosahedral capsid at sub-nanometer resolution [12,13], allowing for the first time the identification of a protein fold using single-particle cryo-EM. Reconstructions at sub-nanometer resolution of particles with lower symmetry followed, and it is now possible to obtain reconstructions of ribosomes at about 5 Å resolution .
The leading role of icosahedral viruses in achieving near-atomic resolution is due primarily to: (i) their high symmetry, which effectively increases the size of the data set 60-fold, or more if quasi-equivalent subunits can be averaged; (ii) their large molecular mass, producing strong image contrast and hence more accurate alignments and reconstructions; and (iii) their rigidity and uniformity, ensuring near-perfect superposition of structural features in three-dimensional (3D) reconstructions. In this review, we consider technological improvements made over the last decade that have enabled the recent successes, explain some of the remaining challenges and discuss some of the resulting functional conclusions about the organization of non-enveloped virions.
Inelastic scattering of high-energy electrons by the sample leads to radiolysis of macromolecules and of the embedding medium, usually vitrified water. The extent of radiation damage depends on the electron dose and sample temperature and beam energy, thus limiting the useful dose for imaging to 5 – 10 e−/Å2 at liquid nitrogen temperature when using 100 kV electrons [10,15]. The doses used for the near-atomic resolution reconstructions listed in Table 1 range between 15 and 30 e−/Å2 which is a bit higher due to the smaller scattering cross-sections at the higher voltage used (300 kV). The dose limitation imposes a lower molecular mass limit of 20 to 50 kDa for molecules that can be detected and aligned in an image [10,11], well below the typical mass of an icosahedral virus (see Table 1). The products of radiolysis require more space than the original molecules, leading to buildup of internal pressure in the sample and ultimately to breakdown (“bubbling”) of the sample matrix . The pressure increase and bubbling cause movement in the exposed area of the sample and blurring in the image, thereby attenuating or eliminating the signal at higher resolution . A recent study suggests that decreasing the rate of radiolysis by using an electron beam with lower intensity can reduce pressure buildup and bubbling . Inelastic scattering also leads to ejection of electrons from the sample and buildup of positive charge that can act as a weak “lens”, again shifting the image and causing blurring .
While the dose limitation represents a fundamental limit of the technique, sample movement and charging can be minimized by using more rigid and conductive sample support films (for example, TiSi , doped silicon carbide ). The performance of these new support films at near-atomic resolution remains to be evaluated. Virus sample is usually prepared using perforated support films in which the vitrified sample is imaged in ice over the holes. It is generally recognized that charging can be reduced by using an objective aperture  and by including a small amount of the support film in the illuminated sample area at the edge of a hole, which acts as a drain for the evolving charge. Machined grids (Quantifoil™ , C-Flat™ ) provide reproducible hole sizes and allow symmetrical imaging conditions, in which a centered beam includes the rim of the circular hole. Machined grids also help produce a more uniform ice thickness, which can then be optimized by adjusting the vitrification procedure. Circular holes and optimized ice thickness have led to higher average image quality and thus to higher resolution in 3D reconstructions of icosahedral viruses and other samples. The spot-scan technique  in which only a small sample area is exposed at a time can also reduce beam-induced sample movement in single-particle EM but it is predominantly used in two-dimensional crystallography.
Cooling the sample at liquid helium temperature has been discussed as a way to prolong the molecular integrity of the sample under the high-energy electron beam [23,24] and may generate superior results for 2D crystals. Most recent high-resolution virus structures were calculated from data recorded at liquid nitrogen temperature, however (see Table 1), as increased charging and reduced image contrast at liquid helium temperature annul the advantage gained by the increased dose tolerance of single particles [25,26].
New sample stages for cryo-microscopy have been introduced during the last ten years to improve cooling and mechanical stability. The new stages include top-entry designs (for example, JEOL JEM3000SFF) as well as specially designed side-entry stages (for example, FEI Polara and FEI Titan Krios), all of which use detachable sample cartridges that afford better vacuum, insulation from the environment and temperature stability. The FEI Titan Krios also features a symmetrical lens design to allow operation with a constant total lens current to keep the heat generation constant. Furthermore, most modern microscopes allow remote operation, to eliminate instabilities caused by the presence of a human operator. The FEI Titan Krios offers additional protection against environmental changes with a box housing the microscope. While the new stage designs and environmental protection are clear improvements over older designs, several of the recent near-atomic resolution structures were obtained with traditional side-entry stages and electron microscopes that were available a decade ago (see Table 1). The older designs are therefore still a competitive and cost-effective alternative to the much more expensive latest-generation instruments.
The data for all reconstructions listed in Table 1, except CPV, were collected on photographic film. Film has a higher detective quantum efficiency (DQE) and larger number of pixels per frame compared with the scintillator-based electronic detectors in general use today . A new generation of solid state detectors is emerging, based on direct detection of the high-energy electrons [27,28]. Future improvements to these detectors will include back-thinning and a single-electron counting mode, in which incident electron positions can be detected with sub-pixel accuracy. These detectors will represent a substantial improvement over photographic film with respect to DQE, speed and effective number of pixels per frame. They will therefore have an important role in high-resolution cryo-EM of macromolecular assemblies, either by reducing the number of images required to reach a certain resolution or by extending the attainable resolution.
A fundamental improvement in image quality is also anticipated with the introduction of phase plates [29–32], which boost low-resolution contrast. This enhancement will be especially important for work on particles of lower molecular mass but may still help in the accurate alignment of large virus particles (see below).
The single-particle technique gains its greatest advantage over x-ray crystallography by not requiring crystals. While molecules in a crystal have fixed orientations, imposed by crystal contacts, the orientation and x,y position of each single particle in an image must be determined separately. Errors in these parameters, in particular in the Euler angles specifying the view of a particle, probably pose one of the most severe limitations in attainable resolution for single-particle work . The angular alignment error of rotavirus DLPs was estimated to be about 0.2° which attenuates the signal at the periphery of this 700-Å particle by roughly 70% . The accuracy with which alignment parameters can be determined depends primarily on the signal strength associated with each particle, especially at low resolution where the benefit of a phase plate is expected to be greatest. The alignment accuracy can be improved by introducing appropriate resolution-dependent weighting of the data  and parameter restraints . The use of symmetry-adapted functions can also help in determining more accurate particle angles and shifts [35,36]. Another promising approach is the use of maximum likelihood functions in estimating 3D reconstructions , as this approach should be more noise-tolerant and should increase the radius of convergence in a refinement . The significantly higher computational cost of this approach has so far prevented its application to reconstructions at near-atomic resolution.
Even the most accurate particle alignment cannot overcome limitations introduced by molecular flexibility and disorder within a particle. This restriction applies also to icosahedral viruses, which are generally extremely regular and rigid assemblies, when internal disorder limits the attainable resolution, just as in x-ray crystallography. Depending on the nature of the disorder, introducing additional parameters or image classes can separate particles into more homogeneous subsets, each of which can (in principle) yield a higher resolution reconstruction. The development of methods dealing with particle heterogeneity represents one of the most important current research topics in the field. The separation of damaged or distorted particles and particle images affected by beam-induced movement and other imperfections from intact particles and high-quality images can be made more easily for large assemblies such as icosahedral viruses than for smaller particles due to their strong image contrast .
Cryo-EM images are affected by small variations in magnification  and corruption by the contrast transfer function (CTF) of the microscope. While the former did not require special accommodation in image processing procedures to reach near-atomic resolution, the latter must be corrected to retrieve the high-resolution signal. The oscillating behavior of the CTF depends on the image defocus and produces so-called Thon rings  in the image power spectrum. The Thon ring pattern can be used to determine the CTF by fitting a calculated ring pattern. Inaccuracies in the determined defocus were estimated between 100 Å and 1000 Å, depending on the presence of carbon support film in the images . These inaccuracies lead to phase errors in the corrected data and affect the signal at high resolution more strongly than at low resolution. For example, an average defocus error of 300 Å will lead to about 60% signal loss in a reconstruction at 4 Å resolution . Because virus particles produce strong image contrast, it is possible to refine the defocus per particle using restraints, leading to a modest resolution improvement .
Additional phase error comes from beam tilt [42,43]. Careful alignment of the microscope can eliminate beam tilt, but unless the C3 lens of the microscope is freely adjustable, as in the FEI Titan Krios and JEOL JEM3200FSC, it is hard to obtain a strictly parallel beam. A small amount of variable tilt will therefore remain (axial coma ). In this case, the beam tilt will be a function of the position within the image, and a computational procedure will be needed to retrieve corrected phases. Beam tilt is routinely determined and corrected for in 2D crystallography by minimizing the phase difference between an image and a reference . Although beam tilt correction has been implemented in the software package Frealign  which was used for some of the reconstructions listed in Table 1, it has not been attempted for any of the published near-atomic resolution virus structures because its measurement is less accurate for single particles than for 2D crystal due to the weaker signal. As beam tilt does not change significantly from image to image, it should be possible to measure it for an entire data set of large single particles such as viruses, using an appropriate reference to maximize the average correlation coefficient with all aligned particles in the data set.
Ewald sphere curvature (limited depth of focus) also introduces phase errors, which are expected to reach about 60° at 3.3 Å for a 700 Å particle imaged at 300 kV . A correction procedure for the Ewald sphere curvature  was applied in the reconstruction of BPV , leading to a small improvement in the map. This result suggests that Ewald sphere curvature is not limiting at the resolution levels reported in Table 1. The icosahedral particle symmetry implies that many of the asymmetric units within the particle will be imaged close to the average defocus determined for the entire particle; for these asymmetric units the phase error will be small and Ewald sphere curvature will not be a major resolution-limiting factor.
Contrast transfer is also affected by the limited coherence of the electron beam. To avoid resolution loss, focal pairs can be recorded with a close-to-focus image containing strong high-resolution signal, and a far-from-focus image containing strong low-resolution signal needed for reliable particle alignment (for example, see [3,13]). The brightness of modern field emission guns generates highly coherent electron beams, while keeping exposure times within one to two seconds. Therefore, focal pairs for large icosahedral particles are no longer required, and the procedure was not used in any of the recent cryo-EM studies, except for the work on CPV (see Table 1).
The performance of computer hardware, including capacity of in-core memory and speed of program execution, has restricted achievable resolution at all stages since the first icosahedral reconstructions in 1970 from 6 particles of negatively stained TBSV (to 28 Å resolution) and two of human wart virus (to 60 Å) . The resolution of early virus reconstructions from cryo-EM was limited by the pixel size. For example, the HepB capsid reconstructions published in 1997 [12,13] used a pixel size of about 2.5 Å, imposing a limit of 6 – 7 Å on the reconstruction, when the typical signal loss due to interpolation is taken into account. The reconstructions listed in Table 1 were all done with pixel sizes of 1.3 Å or smaller. Limiting computing resources also affected the pioneering reconstruction algorithms developed for icosahedral viruses, which used symmetry-adapted Fourier-Bessel synthesis to reduce the determination of the 3D Fourier transform of the virus to a set of one-dimensional problems that could be solved using standard matrix inversion techniques . This simplification limited the accuracy of the least-squares solution found for each matrix inversion. Contemporary computing hardware has enabled the development of more powerful algorithms that calculate least-squares solutions of the inversion problem using spherical harmonics [35,36,50]. These new algorithms have been implemented in the software packages RIco [36,50] and IMIRS [35,51], used for some of the reconstructions listed in Table 1. Other reconstructions in Table 1 were calculated using EMAN  and Frealign , which employ a more general algorithm commonly referred to as direct Fourier inversion .
The resolution of a 3D reconstruction is less objectively determined than in x-ray crystallography, where "resolution" has come to mean the highest spatial frequency contributing in a meaningful way to the map or to the refinement. A resolution cutoff is important, however, not only for reporting a reasonable assessment of detail in 3D-reconstruction density maps, but also for avoiding oversharpening when amplitude scaling is used to restore high-resolution features. Scaling is generally accomplished by using reference data from x-ray solution scattering profiles  or by determining an effective B-factor and figure-of-merit .
Different resolution criteria are in use, but each can be somewhat unreliable. The values listed in Table 1 are those provided in the respective publications. In all cases, the Fourier Shell Correlation (FSC ) was calculated, but in some the resolution was determined at FSC = 0.5 and in others, at FSC = 0.143. The former cutoff was introduced ad hoc , while the latter was proposed to adjust the FSC resolution criterion to relate more closely to figure-of-merit criteria used in x-ray crystallography . In each case, using the other resolution criterion will lead to an unrealistic estimate as judged by the detail seen in the maps. For example, a resolution of 4.5 Å was reported for the reconstruction of bacteriophage epsilon15  at FSC = 0.5. The FSC curve published for this structure shows that FSC = 0.143 at a resolution of about 3.3 Å, an estimate inconsistent with the lack of clear density for many of the side chains. Conversely, a resolution of 3.3 Å was reported for the VP1 protein of aquareovirus  at FSC = 0.143; the estimate would have been only 3.8 Å at FSC = 0.5, incompatible with the distinctive density for many VP1 side chains.
A possible source of these inconsistencies lies in the alignment algorithms. The use of a correlation coefficient can lead to amplification of noise in 3D reconstructions and a strong bias towards higher values in the FSC, depending on the weighting of the data and the resolution limits used for the alignment [34,56]. In reconstructions affected by a bias in the FSC, it may then be necessary to compensate by reporting the resolution at FSC = 0.5. The software package Frealign reduces noise bias by using a weighted correlation coefficient  and parameter restraints , and FSC=0.143 appears to provide a reliable estimate for the resulting maps. In several cases listed in Table 1, the resolution of the reconstruction extends beyond the visibility of Thon rings in power spectra calculated from image fields of the viruses [2,3,6,8], showing that useful signal can be obtained beyond detectable Thon rings, contrary to earlier suggestions .
The head-protein subunits of a large class of dsDNA bacteriophages have a folded structure first recognized in crystallographic analyses of the HK97 phage head and its assembly precursors . Unlike the largely α-helical HepB capsid protein, which could be traced correctly at about 7 Å resolution [12,13], the phage-head subunit is largely β-sheet, for which strands are resolved only if the resolution extends beyond 5 Å. One of the first group of higher-resolution cryo-EM reconstructions showed that the bacteriophage epsilon15 head subunit is a member of the HK97 class . This conclusion derived from a chain trace based on automatic assignment of secondary structural elements, and it may therefore not have exact sequence assignments in some parts of the fit. Local averaging within the T-7 icosahedral asymmetric unit, as in the work on bovine papillomavirus (BPV: see below ), and direct visual model building, as in most of the other efforts reviewed here, might enable a number of adjustments. A subsequent study by the same group of the T7-like cyanophage, P-SSP7, at 4.6 Å resolution showed, as expected, conservation of the same subunit design .
These viruses have segmented RNA genomes, packaged into a shell formed by 120 subunits of an "inner shell protein" (ISP). The ISPs are homologous in all cases described here . The "inner capsid particle" (ICP) based on this shell also contains an RNA-dependent RNA polymerase, a capping activity, and in some cases an additional set of stabilizing subunits. The capping enzymes (guanylyl transferase and methylases) are part of a single polypeptide chain, which may be on the outer surface of the ICP ("turreted" ICPs) or within its shell ("non-turreted" ICPs).
The rotavirus ICP is known as a "double layered particle" (DLP), because a complete layer of a protein known as VP6 surrounds the ISP layer, forming a T=13 icosahedral lattice. DLP structures have been determined both by cryo-EM at 3.8 Å nominal resolution  and by x-ray crystallography at about the same resolution . Fig. 1 shows a comparison of the density maps, filtered to 4.2Å resolution. The cryo-EM density is roughly equivalent to the 2Fo-Fc x-ray map, even though the latter has been calculated with phases from a refined model.
One or both of the outer-layer proteins (VP7 and VP4) can be added back to the DLP -- a step known as recoating . A cryo-EM structure of the DLP recoated with VP7 (4.2 Å resolution) shows that a VP7 trimer caps each VP6 trimer in the T=13 intermediate layer, through contacts mediated largely by a 25-residue, N-terminal arm, which is not ordered in VP7 crystals . The polypeptide chain of the N-terminal arm of VP7 was traced unambiguously, with a glycan at position 65 as a particularly prominent landmark. In the complete rotavirus triple-layered particle (TLP), nearly half of the VP4 polypeptide chain was traced de novo in a 4.2 Å resolution cryo-EM map . By excising density from the final three-dimensional reconstruction and inserting it into a suitable P1 unit cell, "structure factors" were obtained and used as targets in standard x-ray crystallographic refinement procedures, with strong constraints to compensate for limited resolution.
The layer of 120 ISP subunits in turreted reovirus ICPs is stabilized by a set of "clamp" subunits . Cytoplasmic polyhedrosis virus (CPV) does not require an additional outer layer to penetrate. A model, published in 2008, was the first example of a complete de novo chain trace from a cryo-EM reconstruction with clear evidence of amino-acid residue positions from side-chain density . Homology of the ISP with the corresponding proteins of orthoreoviruses and orbiviruses, for which crystal structures had been determined previously [61,62], added confidence to the interpretation.
Surrounding the turreted ICP of orthoreoviruses is an outer protein layer based on a T=13 icosahedral lattice, through which the ICP turrets project at each fivefold . The assembly unit is a threefold symmetric, outer-layer heterohexamer . Proteolytic removal of one of the two subunits (a "chaperone") primes the other (a "penetration protein") to mediate ICP penetration into a host cell. Autolytic cleavage of the penetration protein liberates a pore-forming, myristoylated, N-terminal peptide. Reconstruction of an aquareovirus particle, protease treated to remove the outer-layer chaperone, generating a so-called "infectious subviral particle" (ISVP), confirmed earlier conclusions about the autolytic cleavage derived from a crystal structure of the othroreovirus penetration-protein:chaperone heterohexamer  and a ~6 Å resolution reconstruction of the virion . The aquareovirus ISVP density map was of sufficient clarity to allow building of a full atomic model, which also showed the myristoyl groups inserted into long, hydrophobic pockets.
The papillomavirus capsid is a shell of 72 pentamers (protein L1), which surrounds a closed circular DNA genome coiled into about 25 nucleosomes. BPV has been, until recently, the only full virion that could be prepared in quantities sufficient even for cryo-EM. A reconstruction of BPV at about 3.8Å resolution  has permitted fitting and refinement of a complete model for the L1 shell, using a crystal structure of the HPV16 L1 pentamer as a homology template for the framework of the subunit . Projecting loops and N- and C-terminal arms were build de novo. The framework and loops have identical structures on all subunits, allowing further local averaging of the initial icosahedral reconstruction. This sixfold "non-capsid symmetry" (ncs) averaging greatly facilitated model building. An earlier effort to fit a much lower resolution (~ 13 Å) BPV reconstruction had misconnected one part of the C-terminal arm . The full BPV atomic model was refined against calculated structure factors, as described above for parts of the rotavirus TLP. Weights for the refinement (Hendrickson-Lattman coefficients) were assigned in shells, based on the Fourier shell correlation . This calculation is effectively a real-space refinement carried out indirectly in reciprocal space. That is, there is no iterative improvement of the unmeasured parameters of the reconstruction (Euler angles, etc., for each image), unlike the phase improvement that accompanies cycles of refinement and rebuilding in x-ray crystallography. Whether some combination of model density with the reconstruction used to build the model could be used as a reference for further improvement of image parameters, leading to a better map for extending or adjusting the model, is an important open question.
Adenoviruses have a striking icosahedral shape and a complex molecular design. A recently published 3D reconstruction of adenovirus type 5  is a tour de force of cryo-EM, as it allows assignment of density (with amino-acid residue resolution in most places) not only to the polypeptide chains of the principal outer-shell subunits (the so-called "hexon" and "penton"), but also to the set of "minor" proteins that cement the capsid together (Fig. 2). A recurring architectural feature of most non-enveloped virus particles is the interlacing of extended "arms" (N-terminal, C-terminal, or both), which hold the principal subunits together in a way that can adapt to various symmetry environments . The size of the adenovirus genome allows it to encode a set of separate cement proteins that are, in effect, detached arms. These proteins switch the characteristics of the subunit interface at which they are found, leading to accurate assembly of a complex shell.
The first image reconstructions of icosahedral viruses, derived from images of negatively stained particles, were published 40 years ago . Reconstructions of icosahedral viruses at near-atomic resolution published during the past two years show that in favorable cases, atomic models can be derived from cryo-EM images [1–9], yielding valuable new information about virus assembly. Advances in EM instrumentation, in computational algorithms, and in available computing power have all contributed. The large size and high symmetry of icosahedral viruses have made them particularly favorable objects for analysis by high-resolution cryo-EM. On-going developments in both instrumentation and computation should extend the range of structures that can be studied in this way to smaller and less symmetrical particles and to image fields containing particles in more than one conformational state.
The authors are grateful to David DeRosier and Alexis Rohou for comments and careful reading of the manuscript. Supported by NIH Grant P01 GM-62580. The authors are Investigators in the Howard Hughes Medical Institute.
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