Ewald sphere correction for single-particle electron microscopy

Ghostbuster: A phase retrieval diffraction tomography algorithm for cryo-EM

Ewald sphere curvature correction, which extends beyond the projection approximation, stretches the shallow depth of field in cryo-EM reconstructions of thick particles. Here we show that even for previously assumed thin particles, reconstruction artifacts which we refer to as ghosts can appear. By retrieving the lost phases of the electron exitwaves and accounting for the first Born approximation scattering within the particle, we show that these ghosts can be effectively eliminated. Our simulations demonstrate how such ghostbusting can improve reconstructions as compared to existing state-of-the-art software. Like ptychographic cryo-EM, our Ghostbuster algorithm uses phase retrieval to improve reconstructions, but unlike the former, we do not need to modify the existing data acquisition pipelines.

Structure determination by cryoEM at 100 keV

Electron cryomicroscopy can, in principle, determine the structures of most biological molecules but is currently limited by access, specimen preparation difficulties, and cost. We describe a purpose-built instrument operating at 100 keV-including advances in electron optics, detection, and processing-that makes structure determination fast and simple at a fraction of current costs. The instrument attains its theoretical performance limits, allowing atomic resolution imaging of gold test specimens and biological molecular structure determination in hours. We demonstrate its capabilities by determining the structures of eleven different specimens, ranging in size from 140 kDa to 2 MDa, using a fraction of the data normally required. CryoEM with a microscope designed specifically for high-efficiency, on-the-spot imaging of biological molecules will expand structural biology to a wide range of previously intractable problems.

Virus structures revealed by advanced cryoelectron microscopy methods

Before the resolution revolution, cryoelectron microscopy (cryo-EM) single-particle analysis (SPA) already achieved resolutions beyond 4 Å for certain icosahedral viruses, enabling ab initio atomic model building of these viruses. As the only samples that achieved such high resolution at that time, cryo-EM method development was closely intertwined with the improvement of reconstructions of symmetrical viruses. Viral morphology exhibits significant diversity, ranging from small to large, uniform to non-uniform, and from containing single symmetry to multiple symmetries. Furthermore, viruses undergo conformational changes during their life cycle. Several methods, such as asymmetric reconstruction, Ewald sphere correction, cryoelectron tomography (cryo-ET), and sub-tomogram averaging (STA), have been developed and applied to determine virus structures in vivo and in vitro. This review outlines current advanced cryo-EM methods for high-resolution structure determination of viruses and summarizes accomplishments obtained with these approaches. Moreover, persisting challenges in comprehending virus structures are discussed and we propose potential solutions.

CryoEM single particle reconstruction with a complex-valued particle stack

Single particle reconstruction (SPR) in cryoEM is an image processing task with an elaborate hierarchy that starts with many very noisy multi-frame images. Efficient representation of the intermediary image structures is critical for keeping the calculations manageable. One such intermediary structure is called a particle stack and contains cut-out images of particles in square boxes of predefined size. The micrograph that is the source of the boxed images is usually corrected for motion between frames prior to particle stack creation. However, the contrast transfer function (CTF) or its Fourier Transform point spread function (PSF) are not considered at this step. Historically, the particle stack was intended for large particles and for a tighter PSF, which is characteristic of lower resolution data. The field now performs analyses of smaller particles and to higher resolution, and these conditions result in a broader PSF that requires larger padding and slower calculations to integrate information for each particle. Consequently, the approach to handling structures such as the particle stack should be reexamined to optimize data processing. Here we propose to use as a source image for the particle stack a complex-valued image, in which CTF correction is implicitly applied as a real component of the image. We can achieve it by applying an initial CTF correction to the entire micrograph first and perform box cutouts as a subsequent step. The final CTF correction that we refine and apply later has a very narrow PSF, and so cutting out particles from micrographs that were approximately corrected for CTF does not require extended buffering, i.e. the boxes during the analysis only have to be large enough to encompass the particle. The Fourier Transform of an exit-wave reconstruction creates an image that has complex values. This is a complex value image considered in real space, opposed to standard SPR data processing where complex numbers appear only in Fourier space. This extension of the micrograph concept provides multiple advantages because the particle box size can be small and calculations crucial for high resolution reconstruction such as Ewald sphere correction, aberration refinement, and particle-specific defocus refinement can be performed on the small box data.

Cryo-electron Microscopy of Protein Cages

Protein cages are one of the most widely studied objects in the field of cryogenic electron microscopy-encompassing natural and synthetic constructs, from enzymes assisting protein folding such as chaperonin to virus capsids. Tremendous diversity of morphology and function is demonstrated by the structure and role of proteins, some of which are nearly ubiquitous, while others are present in few organisms. Protein cages are often highly symmetrical, which helps improve the resolution obtained by cryo-electron microscopy (cryo-EM). Cryo-EM is the study of vitrified samples using an electron probe to image the subject. A sample is rapidly frozen in a thin layer on a porous grid, attempting to keep the sample as close to a native state as possible. This grid is kept at cryogenic temperatures throughout imaging in an electron microscope. Once image acquisition is complete, a variety of software packages may be employed to carry out analysis and reconstruction of three-dimensional structures from the two-dimensional micrograph images. Cryo-EM can be used on samples that are too large or too heterogeneous to be amenable to other structural biology techniques like NMR or X-ray crystallography. In recent years, advances in both hardware and software have provided significant improvements to the results obtained using cryo-EM, recently demonstrating true atomic resolution from vitrified aqueous samples. Here, we review these advances in cryo-EM, especially in that of protein cages, and introduce several tips for situations we have experienced.

The Ewald sphere/focus gradient does not limit the resolution of cryoEM reconstructions

In our quest to solve biomolecular structures to higher resolutions in cryoEM, care must be taken to deal with all aspects of image formation in the electron microscope. One of these is the Ewald sphere/focus gradient that derives from the scattering geometry in the microscope and its implications for recovering high resolution and handedness information. While several methods to deal with it has been proposed and implemented, there are still questions as to the correct approach. At the high acceleration voltages used for cryoEM, the traditional projection approximation that ignores the Ewald sphere breaks down around 2-3 Å and with large particles. This is likely not crucial for most biologically interesting molecules, but is required to understand detail about catalytic events, molecular orbitals, orientation of bound water molecules, etc. Through simulation I show that integration along the Ewald spheres in frequency space during reconstruction, the "simple insertion method" is adequate to reach resolutions to the Nyquist frequency. Both theory and simulations indicate that the handedness information encoded in such phases is irretrievably lost in the formation of real space images. The conclusion is that correct reconstruction along the Ewald spheres avoids the limitations of the projection approximation.

Molecular architecture of the Chikungunya virus replication complex

To better understand how positive-strand (+) RNA viruses assemble membrane-associated replication complexes (RCs) to synthesize, process, and transport viral RNA in virus-infected cells, we determined both the high-resolution structure of the core RNA replicase of chikungunya virus and the native RC architecture in its cellular context at subnanometer resolution, using in vitro reconstitution and in situ electron cryotomography, respectively. Within the core RNA replicase, the viral polymerase nsP4, which is in complex with nsP2 helicase-protease, sits in the central pore of the membrane-anchored nsP1 RNA-capping ring. The addition of a large cytoplasmic ring next to the C terminus of nsP1 forms the holo-RNA-RC as observed at the neck of spherules formed in virus-infected cells. These results represent a major conceptual advance in elucidating the molecular mechanisms of RNA virus replication and the principles underlying the molecular architecture of RCs, likely to be shared with many pathogenic (+) RNA viruses.

Cryomicroscopy in situ: what is the smallest molecule that can be directly identified without labels in a cell?

Electron cryomicroscopy (cryoEM) has made great strides in the last decade, such that the atomic structure of most biological macromolecules can, at least in principle, be determined. Major technological advances - in electron imaging hardware, data analysis software, and cryogenic specimen preparation technology - continue at pace and contribute to the exponential growth in the number of atomic structures determined by cryoEM. It is now conceivable that within the next decade we will have structures for hundreds of thousands of unique protein and nucleic acid molecular complexes. But the answers to many important questions in biology would become obvious if we could identify these structures precisely inside cells with quantifiable error. In the context of an abundance of known structures, it is appropriate to consider the current state of electron cryomicroscopy for frozen specimens prepared directly from cells, and try to answer to the question of the title, both now and in the foreseeable future.

Cryo-EM of Helical Polymers

While the application of cryogenic electron microscopy (cryo-EM) to helical polymers in biology has a long history, due to the huge number of helical macromolecular assemblies in viruses, bacteria, archaea, and eukaryotes, the use of cryo-EM to study synthetic soft matter noncovalent polymers has been much more limited. This has mainly been due to the lack of familiarity with cryo-EM in the materials science and chemistry communities, in contrast to the fact that cryo-EM was developed as a biological technique. Nevertheless, the relatively few structures of self-assembled peptide nanotubes and ribbons solved at near-atomic resolution by cryo-EM have demonstrated that cryo-EM should be the method of choice for a structural analysis of synthetic helical filaments. In addition, cryo-EM has also demonstrated that the self-assembly of soft matter polymers has enormous potential for polymorphism, something that may be obscured by techniques such as scattering and spectroscopy. These cryo-EM structures have revealed how far we currently are from being able to predict the structure of these polymers due to their chaotic self-assembly behavior.

Cryo-electron Microscopy of Adeno-associated Virus

Adeno-associated virus (AAV) has a single-stranded DNA genome encapsidated in a small icosahedrally symmetric protein shell with 60 subunits. AAV is the leading delivery vector in emerging gene therapy treatments for inherited disorders, so its structure and molecular interactions with human hosts are of intense interest. A wide array of electron microscopic approaches have been used to visualize the virus and its complexes, depending on the scientific question, technology available, and amenability of the sample. Approaches range from subvolume tomographic analyses of complexes with large and flexible host proteins to detailed analysis of atomic interactions within the virus and with small ligands at resolutions as high as 1.6 Å. Analyses have led to the reclassification of glycan receptors as attachment factors, to structures with a new-found receptor protein, to identification of the epitopes of antibodies, and a new understanding of possible neutralization mechanisms. AAV is now well-enough characterized that it has also become a model system for EM methods development. Heralding a new era, cryo-EM is now also being deployed as an analytic tool in the process development and production quality control of high value pharmaceutical biologics, namely AAV vectors.

A Method for High-Resolution Three-Dimensional Reconstruction with Ewald Sphere Curvature Correction from Transmission Electron Images

A method for three-dimensional reconstruction of objects from defocused images collected at multiple illumination directions in high-resolution transmission electron microscopy is presented. The method effectively corrects for the Ewald sphere curvature by taking into account the in-particle propagation of the electron beam. Numerical simulations demonstrate that the proposed method is capable of accurately reconstructing biological molecules or nanoparticles from high-resolution defocused images under conditions achievable in single-particle electron cryo-microscopy or electron tomography with realistic radiation doses, non-trivial aberrations, multiple scattering, and other experimentally relevant factors. The physics of the method is based on the well-known Diffraction Tomography formalism, but with the phase-retrieval step modified to include a conjugation of the phase (i.e., multiplication of the phase by a negative constant). At each illumination direction, numerically backpropagating the beam with the conjugated phase produces maximum contrast at the location of individual atoms in the molecule or nanoparticle. The resultant algorithm, Conjugated Holographic Reconstruction, can potentially be incorporated into established software tools for single-particle analysis, such as, for example, RELION or FREALIGN, in place of the conventional contrast transfer function correction procedure, in order to account for the Ewald sphere curvature and improve the spatial resolution of the three-dimensional reconstruction.

An electron counting algorithm improves imaging of proteins with low-acceleration-voltage cryo-electron microscope

Relative to the 300-kV accelerating field, electrons accelerated under lower voltages are potentially scattered more strongly. Lowering the accelerate voltage has been suggested to enhance the signal-to-noise ratio (SNR) of cryo-electron microscopy (cryo-EM) images of small-molecular-weight proteins (<100 kD). However, the detection efficient of current Direct Detection Devices (DDDs) and temporal coherence of cryo-EM decrease at lower voltage, leading to loss of SNR. Here, we present an electron counting algorithm to improve the detection of low-energy electrons. The counting algorithm increased the SNR of 120-kV and 200-kV cryo-EM image from a Falcon III camera by 8%, 20% at half the Nyquist frequency and 21%, 80% at Nyquist frequency, respectively, resulting in a considerable improvement in resolution of 3D reconstructions. Our results indicate that with further improved temporal coherence and a dedicated designed camera, a 120-kV cryo-electron microscope has potential to match the 300-kV microscope at imaging small proteins.

Assembly mechanism of the pleomorphic immature poxvirus scaffold

In Vaccinia virus (VACV), the prototype poxvirus, scaffold protein D13 forms a honeycomb-like lattice on the viral membrane that results in formation of the pleomorphic immature virion (IV). The structure of D13 is similar to those of major capsid proteins that readily form icosahedral capsids in nucleocytoplasmic large DNA viruses (NCLDVs). However, the detailed assembly mechanism of the nonicosahedral poxvirus scaffold has never been understood. Here we show the cryo-EM structures of the D13 trimer and scaffold intermediates produced in vitro. The structures reveal that the displacement of the short N-terminal α-helix is critical for initiation of D13 self-assembly. The continuous curvature of the IV is mediated by electrostatic interactions that induce torsion between trimers. The assembly mechanism explains the semiordered capsid-like arrangement of D13 that is distinct from icosahedral NCLDVs. Our structures explain how a single protein can self-assemble into different capsid morphologies and represent a local exception to the universal Caspar-Klug theory of quasi-equivalence.

Immature poxviruses are characterized by nonicosahedral semiordered protein scaffolds critical for morphogenesis. Here, the authors use cryo-EM structures of Vaccinia virus D13 scaffold intermediates to explain their assembly mechanism.

Acid-stable capsid structure of Helicobacter pylori bacteriophage KHP30 by single-particle cryoelectron microscopy

The acid-stable capsid structures of Helicobacter pylori phages KHP30 and KHP40 are solved at 2.7 and 3.0 Å resolutions by cryoelectron microscopy, respectively. The capsids have icosahedral T = 9 symmetry and consist of each 540 copies of 2 structural proteins, a major capsid protein, and a cement protein. The major capsid proteins form 12 pentagonal capsomeres occupying icosahedral vertexes and 80 hexagonal capsomeres located at icosahedral faces and edges. The major capsid protein has a unique protruding loop extending to the neighboring subunit that stabilizes hexagonal capsomeres. Furthermore, the capsid is decorated with trimeric cement proteins with a jelly roll motif. The cement protein trimer sits on the quasi-three-fold axis formed by three major capsid protein capsomeres, thereby enhancing the particle stability by connecting these capsomeres. Sequence and structure comparisons between the related Helicobacter pylori phages suggest a possible mechanism of phage adaptation to the human gastric environment.

Adeno-Associated Virus (AAV-DJ)-Cryo-EM Structure at 1.56 Å Resolution

Adeno-associated virus is the leading viral vector for gene therapy. AAV-DJ is a recombinant variant developed for tropism to the liver. The AAV-DJ structure has been determined to 1.56 Å resolution through cryo-electron microscopy (cryo-EM). Only apoferritin is reported in preprints at 1.6 Å or higher resolution, and AAV-DJ nearly matches the highest resolutions ever attained through X-ray diffraction of virus crystals. However, cryo-EM has the advantage that most of the hydrogens are clear, improving the accuracy of atomic refinement, and removing ambiguity in hydrogen bond identification. Outside of secondary structures where hydrogen bonding was predictable a priori, the networks of hydrogen bonds coming from direct observation of hydrogens and acceptor atoms are quite different from those inferred even at 2.8 Å resolution. The implications for understanding viral assembly mean that cryo-EM will likely become the favored approach for high resolution structural virology.

Near-atomic-scale observation of grain boundaries in a layer-stacked two-dimensional polymer

Two-dimensional (2D) polymers hold great promise in the rational materials design tailored for next-generation applications. However, little is known about the grain boundaries in 2D polymers, not to mention their formation mechanisms and potential influences on the material's functionalities. Using aberration-corrected high-resolution transmission electron microscopy, we present a direct observation of the grain boundaries in a layer-stacked 2D polyimine with a resolution of 2.3 Å, shedding light on their formation mechanisms. We found that the polyimine growth followed a "birth-and-spread" mechanism. Antiphase boundaries implemented a self-correction to the missing-linker and missing-node defects, and tilt boundaries were formed via grain coalescence. Notably, we identified grain boundary reconstructions featuring closed rings at tilt boundaries. Quantum mechanical calculations revealed that boundary reconstruction is energetically allowed and can be generalized into different 2D polymer systems. We envisage that these results may open up the opportunity for future investigations on defect-property correlations in 2D polymers.

TEM bright field imaging of thick specimens: nodes in Thon ring patterns

The thickness of an object will, at some point, exceed the depth of field of a transmission electron microscope; the value at which this occurs, depends on the resolution and the wavelength considered. An image is then no longer a true projection of the 3D structure. This effect will be expressed in the power spectrum. Here, we first demonstrate this phenomenon experimentally, using carbon foils of different thicknesses and working at 40, 60, 80 and 300 kV. Since we determined the thicknesses of the foils by tomography, we are also able to confirm experimentally that in the case of a thick object, the Thon ring pattern can be described as the sum of the power spectra originating from thin, independently scattering slices. Thus, a sinc function envelope is observed that attenuates the Thon rings' amplitudes, yielding "nodes" in the pattern at which the amplitudes are zero. These nodes move to lower spatial frequencies with decreasing acceleration voltages and increasing thicknesses. Conversely, the object thickness can be directly derived from node positions at a particular acceleration voltage. We validate our approach by applying it to frozen-hydrated bacteria with experimentally determined thicknesses. Our model will contribute to more reliably determining the defocus to be used with contrast transfer function correction for thicker objects and at lower acceleration voltages.

A potential difference for single-particle cryo-EM

Nydenova et al. [(2019), IUCrJ, 6, 1086-1098] determine structures of frozen-hydrated protein and nucleic acid assemblies using 100 keV electrons, and describe characteristics of electron microscopes designed to exploit advantages of a lower operating voltage for single-particle cryo-EM.

Structures of enveloped virions determined by cryogenic electron microscopy and tomography

Enveloped viruses enclose their genomes inside a lipid bilayer which is decorated by membrane proteins that mediate virus entry. These viruses display a wide range of sizes, morphologies and symmetries. Spherical viruses are often isometric and their envelope proteins follow icosahedral symmetry. Filamentous and pleomorphic viruses lack such global symmetry but their surface proteins may display locally ordered assemblies. Determining the structures of enveloped viruses, including the envelope proteins and their protein-protein interactions on the viral surface, is of paramount importance. These structures can reveal how the virions are assembled and released by budding from the infected host cell, how the progeny virions infect new cells by membrane fusion, and how antibodies bind surface epitopes to block infection. In this chapter, we discuss the uses of cryogenic electron microscopy (cryo-EM) in elucidating structures of enveloped virions. Starting from a detailed outline of data collection and processing strategies, we highlight how cryo-EM has been successfully utilized to provide unique insights into enveloped virus entry, assembly, and neutralization.

Interpretation of medium resolution cryoEM maps of multi-protein complexes

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CryoEM maps at medium (3.5–6 Å) resolution can be challenging to interpret.

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Integration of multiple methods can inform cryoEM studies.

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Mass spectrometry and biochemistry facilitate map interpretation and model building.

Electron cryo-microscopy (cryoEM) is used to determine structures of biological molecules, including multi-protein complexes. Maps at better than 3.0 Å resolution are relatively straightforward to interpret since atomic models of proteins and nucleic acids can be built directly. Still, these resolutions are often difficult to achieve, and map quality frequently varies within a structure. This results in data that are challenging to interpret, especially when crystal structures or suitable homology models are not available. Recent advances in mass spectrometry techniques, computational methods and model building tools facilitate subunit/domain fitting into maps, elucidation of protein contacts, and de novo generation of atomic models. Here, we review techniques for map interpretation and provide examples from recent studies of multi-protein complexes.

The Plasticity of Molecular Interactions Governs Bacterial Microcompartment Shell Assembly

Bacterial microcompartments (BMCs) are composed of an enzymatic core encapsulated by a selectively permeable protein shell that enhances catalytic efficiency. Many pathogenic bacteria derive competitive advantages from their BMC-based catabolism, implicating BMCs as drug targets. BMC shells are of interest for bioengineering due to their diverse and selective permeability properties and because they self-assemble. A complete understanding of shell composition and organization is a prerequisite for biotechnological applications. Here, we report the cryoelectron microscopy structure of a BMC shell at 3.0-Å resolution, using an image-processing strategy that allowed us to determine the previously uncharacterized structural details of the interactions formed by the BMC-T^S and BMC-T^D shell subunits in the context of the assembled shell. We found unexpected structural plasticity among these interactions, resulting in distinct shell populations assembled from varying numbers of the BMC-T^S and BMC-T^D subunits. We discuss the implications of these findings on shell assembly and function.

How Good Can Single-Particle Cryo-EM Become? What Remains Before It Approaches Its Physical Limits?

Impressive though the achievements of single-particle cryo-electron microscopy are today, a substantial gap still remains between what is currently accomplished and what is theoretically possible. As is reviewed here, twofold or more improvements are possible as regards (a) the detective quantum efficiency of cameras at high resolution, (b) converting phase modulations to intensity modulations in the image, and (c) recovering the full amount of high-resolution signal in the presence of beam-induced motion of the specimen. In addition, potential for improvement is reviewed for other topics such as optimal choice of electron energy, use of aberration correctors, and quantum metrology. With the help of such improvements, it does not seem to be too much to imagine that determining the structural basis for every aspect of catalytic control, signaling, and regulation, in any type of cell of interest, could easily be accelerated fivefold or more.

Capabilities of the Falcon III detector for single-particle structure determination

Direct electron detectors are an essential asset for the resolution revolution in electron cryo microscopy of biological objects. The direct detectors provide two modes of data acquisition; the counting mode in which single electrons are counted, and the integrating mode in which the signal that arises from the incident electrons is integrated. While counting mode leads to far higher detective quantum efficiency at all spatial frequencies, the integrating mode enables faster data acquisition at higher exposure rates. For optimal throughput at best possible resolution it is important to understand when the better performance in counting mode becomes essential for solving a structure and when the lower detective quantum efficiency in integrating mode can be compensated by increasing the number of particles in the data set. Here, we provide a case study of the Falcon III camera, which has counting mode capability at exposure rates of <0.9 e^-/Px² and integrating mode capability at exposure rates above 10 e^-/Px². We found that counting mode gives better resolution for medium sized complexes such as the β-galactosidase (465 kDa) (2.2 Å, 97% of Nyquist vs. 2.4 Å, 89% of Nyquist) with data sets of similar size. However, for larger particles such as Hepatitis B virus capsid like particles (4.8 MDa) we did not find any resolution gain in counting mode.

New tools for automated high-resolution cryo-EM structure determination in RELION-3

Here, we describe the third major release of RELION. CPU-based vector acceleration has been added in addition to GPU support, which provides flexibility in use of resources and avoids memory limitations. Reference-free autopicking with Laplacian-of-Gaussian filtering and execution of jobs from python allows non-interactive processing during acquisition, including 2D-classification, de novo model generation and 3D-classification. Per-particle refinement of CTF parameters and correction of estimated beam tilt provides higher resolution reconstructions when particles are at different heights in the ice, and/or coma-free alignment has not been optimal. Ewald sphere curvature correction improves resolution for large particles. We illustrate these developments with publicly available data sets: together with a Bayesian approach to beam-induced motion correction it leads to resolution improvements of 0.2–0.7 Å compared to previous RELION versions.

Sub-2 Å Ewald curvature corrected structure of an AAV2 capsid variant

Single-particle cryogenic electron microscopy (cryo-EM) provides a powerful methodology for structural biologists, but the resolutions typically attained with experimentally determined structures have lagged behind microscope capabilities. Here, we exploit several technical advances to improve resolution, including per-particle contrast transfer function (CTF) refinement and correction for Ewald sphere curvature. The latter is demonstrated with several experimental samples and should become more standard as resolutions increase or at lower microscope accelerating voltages. The combined application of the described methods to micrographs recorded on a Titan Krios enables structure determination at ~1.86-Å resolution of an adeno-associated virus serotype 2 variant (AAV2), an important gene-delivery vehicle. The resulting structural details provide an improved model for understanding the biology of AAV that will guide future vector development for gene therapy.

Single-particle cryo-EM is a powerful method for macromolecular structure determination. Here the authors demonstrate that Ewald sphere curvature correction, sub-Angstrom pixilation and per-particle CTF refinement can improve map quality and resolution and present the 1.86 Å cryo-EM structure of an adeno-associated virus serotype 2 variant.

Pushing the resolution limit by correcting the Ewald sphere effect in single-particle Cryo-EM reconstructions

The Ewald sphere effect is generally neglected when using the Central Projection Theorem for cryo electron microscopy single-particle reconstructions. This can reduce the resolution of a reconstruction. Here we estimate the attainable resolution and report a “block-based” reconstruction method for extending the resolution limit. We find the Ewald sphere effect limits the resolution of large objects, especially large viruses. After processing two real datasets of large viruses, we show that our procedure can extend the resolution for both datasets and can accommodate the flexibility associated with large protein complexes.

Conventional reconstruction methods used in cryo-EM single particle analysis do not take the depth of field effect into account. Here the authors present a block-based reconstruction method to deal with the depth of field effect and show that this approach can improve the resolution of cryo-EM virus structures.

Ewald sphere correction using a single side-band image processing algorithm

Curvature of the Ewald sphere limits the resolution at which Fourier components in an image can be approximated as corresponding to a projection of the object. Since the radius of the Ewald sphere is inversely proportional to the wavelength of the imaging electrons, this normally imposes a limit on the thickness of specimen for which images can be easily interpreted to a particular resolution. Here we present a computational method for precisely correcting for the curvature of the Ewald sphere using defocused images that delocalise the high-resolution Fourier components from the primary image. By correcting for each approximately Friedel-symmetry-related sideband separately using two distinct complex transforms that effectively move the displaced Fourier components back to where they belong in the structure, we can determine the amplitude and phase of each of the Fourier components separately. This precisely accounts for the effect of Ewald sphere curvature over a bandwidth defined by the defocus and the size of the particle being imaged. We demonstrate this processing algorithm using: 1. simulated images of a particle with only a single, high-resolution Fourier component, and 2. experimental images of gold nanoparticles embedded in ice. Processing micrographs with this algorithm will allow higher resolution imaging of thicker specimens at lower energies without any image degradation or blurring due to errors made by the assumption of a flat Ewald sphere. Although the procedure will work best on images recorded with higher defocus settings than used normally, it should still improve 3D single-particle structure determination using images recorded at any defocus and any electron energy. Finally, since the Ewald sphere curvature is in a known direction in the third dimension which is parallel to the direction of view, this algorithm automatically determines the absolute hand of the specimen without the need for pairs of images with a known tilt angle difference.

Atomic cryo-EM structures of viruses

During the development of single particle cryo-EM in past five decades, icosahedral viruses have led the resolution progress owing to their large mass and high symmetry. Many technical advances in cryo-EM were first established with viruses. Since reaching ∼4Å resolution in 2008, it has become a relatively routine task to solve the atomic structure of isolated viruses. The future of structural virology will be increasingly focused on remaining challenges including solving structures of jumbo viruses, intermediate functional states during assembly, maturation, and infection, and in situ structures. Recent demonstrations of near-atomic resolution structure with electron tomography and sub-tomogram averaging opens a new direction for high resolution studies of pleomorphic viruses and the pleomorphic states of icosahedral viruses that have defied past efforts using the single particle cryo-EM approach.

Estimating the effect of finite depth of field in single-particle cryo-EM

The extent to which the resolution varies within a three-dimensional (3-D) reconstruction, when the diameter of an object is large, is investigated computationally. Numerical simulation is used to model ideal three-dimensional point-spread functions at different radial positions within an object. It is shown that reconstructed density maps are affected less than might have been expected when particles are larger than the depth of field. This favorable outcome is attributed mainly to the fact that a point which lies outside the depth of field relative to the center, for some orientations of the object, will also lie within the depth of field for other orientations. We find, as a result, that the diameter of a particle can be as much as four times the depth of field (as defined by a 90° phase-error criterion) before curvature of the Ewald sphere becomes a limiting factor in determining the resolution that can be achieved.

Frealign: An Exploratory Tool for Single-Particle Cryo-EM

Frealign is a software tool designed to process electron microscope images of single molecules and complexes to obtain reconstructions at the highest possible resolution. It provides a number of refinement parameters and options that allow users to tune their refinement to achieve specific goals, such as masking to classify selected regions within a particle, control over the refinement of specific alignment parameters to accommodate various data collection schemes, refinement of pseudosymmetric particles, and generation of initial maps. This chapter provides a general overview of Frealign functions and a more detailed guide to using Frealign in typical scenarios.

How good can cryo-EM become?

The suddenness with which single-particle cryo-electron microscopy (cryo-EM) has emerged as a method for determining high-resolution structures of biological macromolecules invites the questions, how much better can this technology get, and how fast is that likely to happen? Though we can rightly celebrate the maturation of cryo-EM as a high-resolution structure-determination tool, I believe there still are many developments to look forward to.

Transmission electron microscopy and the molecular structure of icosahedral viruses

The field of structural virology developed in parallel with methodological advances in X-ray crystallography and cryo-electron microscopy. At the end of the 1970s, crystallography yielded the first high resolution structure of an icosahedral virus, the T=3 tomato bushy stunt virus at 2.9Å. It took longer to reach near-atomic resolution in three-dimensional virus maps derived from electron microscopy data, but this was finally achieved, with the solution of complex icosahedral capsids such as the T=25 human adenovirus at ∼3.5Å. Both techniques now work hand-in-hand to determine those aspects of virus assembly and biology that remain unclear. This review examines the trajectory followed by EM imaging techniques in showing the molecular structure of icosahedral viruses, from the first two-dimensional negative staining images of capsids to the latest sophisticated techniques that provide high resolution three-dimensional data, or snapshots of the conformational changes necessary to complete the infectious cycle.

Single particle cryo-electron microscopy and 3-D reconstruction of viruses

With fast progresses in instrumentation, image processing algorithms, and computational resources, single particle electron cryo-microscopy (cryo-EM) 3-D reconstruction of icosahedral viruses has now reached near-atomic resolutions (3-4 Å). With comparable resolutions and more predictable outcomes, cryo-EM is now considered a preferred method over X-ray crystallography for determination of atomic structure of icosahedral viruses. At near-atomic resolutions, all-atom models or backbone models can be reliably built that allow residue level understanding of viral assembly and conformational changes among different stages of viral life cycle. With the developments of asymmetric reconstruction, it is now possible to visualize the complete structure of a complex virus with not only its icosahedral shell but also its multiple non-icosahedral structural features. In this chapter, we will describe single particle cryo-EM experimental and computational procedures for both near-atomic resolution reconstruction of icosahedral viruses and asymmetric reconstruction of viruses with both icosahedral and non-icosahedral structure components. Procedures for rigorous validation of the reconstructions and resolution evaluations using truly independent de novo initial models and refinements are also introduced.

Single particle electron microscopy

Single particle electron microscopy is a versatile technique for the structural analysis of protein complexes in near-native conditions. While tremendous progress has been made during the past few decades in techniques for specimen preparation, imaging, and image analysis, the field is still in development. In the context of this volume on electron crystallography, the following chapter gives practical guidelines on how to begin single particle EM studies, including preparing specimens, selecting imaging conditions, and choosing which of the many approaches to image analysis are appropriate for a specific sample.

Limiting factors in atomic resolution cryo electron microscopy: no simple tricks

To bring cryo electron microscopy (cryoEM) of large biological complexes to atomic resolution, several factors--in both cryoEM image acquisition and 3D reconstruction--that may be neglected at low resolution become significantly limiting. Here we present thorough analyses of four limiting factors: (a) electron-beam tilt, (b) inaccurate determination of defocus values, (c) focus gradient through particles, and (d) particularly for large particles, dynamic (multiple) scattering of electrons. We also propose strategies to cope with these factors: (a) the divergence and direction tilt components of electron-beam tilt could be reduced by maintaining parallel illumination and by using a coma-free alignment procedure, respectively. Moreover, the effect of all beam tilt components, including spiral tilt, could be eliminated by use of a spherical aberration corrector. (b) More accurate measurement of defocus value could be obtained by imaging areas adjacent to the target area at high electron dose and by measuring the image shift induced by tilting the electron beam. (c) Each known Fourier coefficient in the Fourier transform of a cryoEM image is the sum of two Fourier coefficients of the 3D structure, one on each of two curved 'characteristic surfaces' in 3D Fourier space. We describe a simple model-based iterative method that could recover these two Fourier coefficients on the two characteristic surfaces. (d) The effect of dynamic scattering could be corrected by deconvolution of a transfer function. These analyses and our proposed strategies offer useful guidance for future experimental designs targeting atomic resolution cryoEM reconstruction.

Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy

Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfil predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3-4Å 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.

Atomic resolution cryo electron microscopy of macromolecular complexes

Single-particle cryo electron microscopy (cryoEM) is a technique for determining three-dimensional (3D) structures from projection images of molecular complexes preserved in their "native," noncrystalline state. Recently, atomic or near-atomic resolution structures of several viruses and protein assemblies have been determined by single-particle cryoEM, allowing ab initio atomic model building by following the amino acid side chains or nucleic acid bases identifiable in their cryoEM density maps. In particular, these cryoEM structures have revealed extended arms contributing to molecular interactions that are otherwise not resolved by the conventional structural method of X-ray crystallography at similar resolutions. High-resolution cryoEM requires careful consideration of a number of factors, including proper sample preparation to ensure structural homogeneity, optimal configuration of electron imaging conditions to record high-resolution cryoEM images, accurate determination of image parameters to correct image distortions, efficient refinement and computation to reconstruct a 3D density map, and finally appropriate choice of modeling tools to construct atomic models for functional interpretation. This progress illustrates the power of cryoEM and ushers it into the arsenal of structural biology, alongside conventional techniques of X-ray crystallography and NMR, as a major tool (and sometimes the preferred one) for the studies of molecular interactions in supramolecular assemblies or machines.

Fully three-dimensional defocus-gradient corrected backprojection in cryoelectron microscopy

Recognizing that the microscope depth of field is a significant resolution-limiting factor in 3D cryoelectron microscopy, Jensen and Kornberg proposed a concept they called defocus-gradient corrected backprojection (DGCBP) and illustrated by computer simulations that DGCBP can effectively eliminate the depth of field limitation. They did not provide a mathematical justification for their concept. Our paper provides this, by showing (in the idealized case of noiseless data being available for all projection directions) that the reconstructions obtained based on DGCBP from data produced with distance-dependent blurring are essentially the same as what is obtained by a classical method of reconstruction of a 3D object from its line integrals. The approach is general enough to be applicable for correcting for any distance-dependent blurring during projection data collection. We present a new implementation of the DGCBP concept, one that closely follows the mathematics of its justifications, and illustrate it using mathematically described phantoms and their reconstructions from finitely many distance-dependently blurred projections.

Subunit interactions in bovine papillomavirus

Papillomaviruses, members of a group of dsDNA viruses associated with epithelial growths and tumors, have compact capsids assembled from 72 pentamers of the protein L1. We have determined the structure of bovine papillomavirus by electron cryomicrosopy (cryoEM), at approximately 3.6 A resolution. The density map, obtained from single-particle analysis of approximately 4,000 particle images, shows the trace of the L1 polypeptide chain and reveals how the N- and C-terminal "arms" of a subunit (extensions from its beta-jelly-roll core) associate with a neighboring pentamer. Critical contacts come from the C-terminal arm, which loops out from the core of the subunit, forms contacts (including a disulfide) with two subunits in a neighboring pentamer, and reinserts into the pentamer from which it emanates. This trace corrects one feature of an earlier model. We discuss implications of the structure for virion assembly and for pathways of infectious viral entry. We suggest that it should be possible to obtain image reconstructions of comparable resolution from cryoEM images of asymmetric particles. From the work on papillomavirus described here, we estimate that such a reconstruction will require about 1.5 million images to achieve the same number of averaged asymmetric units; structural variability will increase this number substantially.

Fundamentals of three-dimensional reconstruction from projections

Three-dimensional (3D) reconstruction of an object mass density from the set of its 2D line projections lies at a core of both single-particle reconstruction technique and electron tomography. Both techniques utilize electron microscope to collect a set of projections of either multiple objects representing in principle the same macromolecular complex in an isolated form, or a subcellular structure isolated in situ. Therefore, the goal of macromolecular electron microscopy is to invert the projection transformation to recover the distribution of the mass density of the original object. The problem is interesting in that in its discrete form it is ill-posed and not invertible. Various algorithms have been proposed to cope with the practical difficulties of this inversion problem and their differ widely in terms of their robustness with respect to noise in the data, completeness of the collected projection dataset, errors in projections orientation parameters, abilities to efficiently handle large datasets, and other obstacles typically encountered in molecular electron microscopy. Here, we review the theoretical foundations of 3D reconstruction from line projections followed by an overview of reconstruction algorithms routinely used in practice of electron microscopy.

Correcting for the ewald sphere in high-resolution single-particle reconstructions

To avoid the challenges of crystallization and the size limitations of NMR, it has long been hoped that single-particle cryo-electron microscopy (cryo-EM) would eventually yield atomically interpretable reconstructions. For the most favorable class of specimens (large icosahedral viruses), one of the key obstacles is curvature of the Ewald sphere, which leads to a breakdown of the Projection Theorem used by conventional three-dimensional (3D) reconstruction programs. Here, we review the basic problem and our implementation of the "paraboloid" reconstruction method, which overcomes the limitation by averaging information from images recorded from different points of view.

Towards atomic resolution structural determination by single-particle cryo-electron microscopy

Recent advances in cryo-electron microscopy and single-particle reconstruction (collectively referred to as 'cryoEM') have made it possible to determine the three-dimensional (3D) structures of several macromolecular complexes at near-atomic resolution ( approximately 3.8-4.5A). These achievements were accomplished by overcoming the challenges in sample handling, instrumentation, image processing, and model building. At near-atomic resolution, many detailed structural features can be resolved, such as the turns and deep grooves of helices, strand separation in beta sheets, and densities for loops and bulky amino acid side chains. Such structural data of the cytoplasmic polyhedrosis virus (CPV), the Epsilon 15 bacteriophage and the GroEL complex have provided valuable constraints for atomic model building using integrative tools, thus significantly enhancing the value of the cryoEM structures. The CPV structure revealed a drastic conformational change from a helix to a beta hairpin associated with RNA packaging and replication, coupling of RNA processing and release, and the long sought-after polyhedrin-binding domain. These latest advances in single-particle cryoEM provide exciting opportunities for the 3D structural determination of viruses and macromolecular complexes that are either too large or too heterogeneous to be investigated by conventional X-ray crystallography or nuclear magnetic resonance (NMR) methods.

FREALIGN: high-resolution refinement of single particle structures

The refinement of three-dimensional reconstructions and correction for the contrast transfer function of the microscope are important steps in the determination of macromolecular structures by single particle electron microscopy. The algorithms implemented in the computer program FREALIGN are optimized to perform these tasks efficiently. A general overview and details on how to use FREALIGN are provided. The program is free and available for download on the author's web page.