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

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.

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.

A novel capsid protein network allows the characteristic internal membrane structure of Marseilleviridae giant viruses

Marseilleviridae is a family of giant viruses, showing a characteristic internal membrane with extrusions underneath the icosahedral vertices. However, such large objects, with a maximum diameter of 250 nm are technically difficult to examine at sub-nanometre resolution by cryo-electron microscopy. Here, we tested the utility of 1 MV high-voltage cryo-EM (cryo-HVEM) for single particle structural analysis (SPA) of giant viruses using tokyovirus, a species of Marseilleviridae, and revealed the capsid structure at 7.7 Å resolution. The capsid enclosing the viral DNA consisted primarily of four layers: (1) major capsid proteins (MCPs) and penton proteins, (2) minor capsid proteins (mCPs), (3) scaffold protein components (ScPCs), and (4) internal membrane. The mCPs showed a novel capsid lattice consisting of eight protein components. ScPCs connecting the icosahedral vertices supported the formation of the membrane extrusions, and possibly act like tape measure proteins reported in other giant viruses. The density on top of the MCP trimer was suggested to include glycoproteins. This is the first attempt at cryo-HVEM SPA. We found the primary limitations to be the lack of automated data acquisition and software support for collection and processing and thus achievable resolution. However, the results pave the way for using cryo-HVEM for structural analysis of larger biological specimens.

Unified fast reconstruction algorithm for conventional, phase-contrast, and diffraction tomography

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based, phase-contrast, or diffraction imaging using x rays, electrons, and other forms of penetrating radiation or matter waves. Both the phase retrieval (also known as contrast transfer function correction) and the effect of Ewald sphere curvature (in the cases with a shallow depth of field and significant in-object diffraction) are incorporated in the proposed algorithm and can be taken into account. Multiple scattering is not treated explicitly but can be mitigated as a result of angular averaging that constitutes an essential feature of the method. The corresponding numerical algorithm is based on three-dimensional gridding which allows for fast computational implementation, including a straightforward parallelization. The algorithm can be used with any scanning geometry involving plane-wave illumination. A software code implementing the proposed algorithm has been developed, tested on simulated and experimental image data, and made publicly available.

Emerging Themes in CryoEM─Single Particle Analysis Image Processing

Cryo-electron microscopy (CryoEM) has become a vital technique in structural biology. It is an interdisciplinary field that takes advantage of advances in biochemistry, physics, and image processing, among other disciplines. Innovations in these three basic pillars have contributed to the boosting of CryoEM in the past decade. This work reviews the main contributions in image processing to the current reconstruction workflow of single particle analysis (SPA) by CryoEM. Our review emphasizes the time evolution of the algorithms across the different steps of the workflow differentiating between two groups of approaches: analytical methods and deep learning algorithms. We present an analysis of the current state of the art. Finally, we discuss the emerging problems and challenges still to be addressed in the evolution of CryoEM image processing methods in SPA.

Method for virtual optical sectioning and tomography utilizing shallow depth of field

A method is proposed for high-resolution, three-dimensional reconstruction of internal structures of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle, provided that the depth of field is smaller than the thickness of the sample. The physical optics basis for the method is elucidated, and the reconstruction algorithm is presented in detail. A simulated example demonstrates an application of the method to three-dimensional electron transmission imaging of a nanoparticle under realistic radiation dose and spatial resolution constraints. It is envisaged that the method can be applicable in high-resolution transmission electron microscopy, soft x-ray microscopy, ultrasound imaging, and other areas.

Cryo-Electron Microscopy of the Giant Viruses

High resolution study of the giant viruses presents one of the latest challenges in cryo-electron microscopy of viruses. Too small for light microscopy, but too large for easy study at high resolution by electron microscopy, they range in size from ~0.2-2 μm, from high symmetry icosahedral viruses such as Paramecium burseria Chlorella virus 1 to asymmetric forms like Tupanvirus or Pithovirus. To attain high resolution, two strategies exist to study these large viruses by cryo-EM: firstly, increasing the acceleration voltage of the electron microscope to improve sample penetration and overcome the limitations imposed by electro-optical physics at lower voltages, and secondly the method of "block-based reconstruction" pioneered by Michael G. Rossmann and his collaborators, which resolves the latter limitation through an elegant leveraging of high symmetry, but cannot overcome sample penetration limitations. In addition, more recent advances in both computational capacity and image processing also yield assistance in studying the giant viruses. Especially, the inclusion of Ewald sphere correction can provide large improvements in attainable resolutions for 300 kV electron microscopes. Despite this, the study of giant viruses remains a significant challenge.

Single-Particle Cryo-EM of Membrane Proteins in Lipid Nanodiscs

Single-particle cryo-electron microscopy has become an indispensable technique in structural biology. In particular when studying membrane proteins, it allows the use of membrane-mimicking tools, which can be crucial for a comprehensive understanding of the structure-function relationship of the protein in its native environment. In this chapter we focus on the application of nanodiscs and use our recent studies on the TMEM16 family as an example.

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.

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

Electron cryomicroscopy (cryoEM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize macromolecular complexes such as ribosomes, viruses, and ion channels. Determination of structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryoEM a scientific rebirth. As a result of these technological advances image processing and analysis have yielded molecular structures at atomic resolution. Nevertheless there continue to be challenges in image processing, and in this article we will touch on the most essential in order to derive an accurate three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. We will then highlight new approaches for each image processing subproblem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking.

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.