Fourier Amplitude Decay of Electron Cryomicroscopic Images of Single Particles and Effects on Structure Determination

A basic introduction to single particles cryo-electron microscopy

<abstract> <p>In the last years, cryogenic-electron microscopy (cryo-EM) underwent the most impressive improvement compared to other techniques used in structural biology, such as X-ray crystallography and NMR. Electron microscopy was invented nearly one century ago but, up to the beginning of the last decades, the 3D maps produced through this technique were poorly detailed, justifying the term “blobbology” to appeal to cryo-EM. Recently, thanks to a new generation of microscopes and detectors, more efficient algorithms, and easier access to computational power, single particles cryo-EM can routinely produce 3D structures at resolutions comparable to those obtained with X-ray crystallography. However, unlike X-ray crystallography, which needs crystallized proteins, cryo-EM exploits purified samples in solution, allowing the study of proteins and protein complexes that are hard or even impossible to crystallize. For these reasons, single-particle cryo-EM is often the first choice of structural biologists today. Nevertheless, before starting a cryo-EM experiment, many drawbacks and limitations must be considered. Moreover, in practice, the process between the purified sample and the final structure could be trickier than initially expected. Based on these observations, this review aims to offer an overview of the principal technical aspects and setups to be considered while planning and performing a cryo-EM experiment.</p> </abstract>

Non-uniformity of projection distributions attenuates resolution in Cryo-EM

Virtually all single-particle cryo-EM experiments currently suffer from specimen adherence to the air-water interface, leading to a non-uniform distribution in the set of projection views. Whereas it is well accepted that uniform projection distributions can lead to high-resolution reconstructions, non-uniform (anisotropic) distributions can negatively affect map quality, elongate structural features, and in some cases, prohibit interpretation altogether. Although some consequences of non-uniform sampling have been described qualitatively, we know little about how sampling quantitatively affects resolution in cryo-EM. Here, we show how inhomogeneity in any projection distribution scheme attenuates the global Fourier Shell Correlation (FSC) in relation to the number of particles and a single geometrical parameter, which we term the sampling compensation factor (SCF). The reciprocal of the SCF is defined as the average over Fourier shells of the reciprocal of the per-particle sampling and normalized to unity for uniform distributions. The SCF therefore ranges from one to zero, with values close to the latter implying large regions of poorly sampled or completely missing data in Fourier space. Using two synthetic test cases, influenza hemagglutinin and human apoferritin, we demonstrate how any amount of sampling inhomogeneity always attenuates the FSC compared to a uniform distribution. We advocate quantitative evaluation of the SCF criterion to approximate the effect of non-uniform sampling on resolution within experimental single-particle cryo-EM reconstructions.

Single-particle cryoEM analysis at near-atomic resolution from several thousand asymmetric subunits

A single-particle cryoEM reconstruction of the large ribosomal subunit from Saccharomyces cerevisiae was obtained from a dataset of ∼75,000 particles. The gold-standard and frequency-limited approaches to single-particle refinement were each independently used to determine orientation parameters for the final reconstruction. Both approaches showed similar resolution curves and nominal resolution values for the 60S dataset, estimated at 2.9 Å. The amount of over-fitting present during frequency-limited refinement was quantitatively analyzed using the high-resolution phase-randomization test, and the results showed no apparent over-fitting. The number of asymmetric subunits required to reach specific resolutions was subsequently analyzed by refining subsets of the data in an ab initio manner. With our data collection and processing strategies, sub-nanometer resolution was obtained with ∼200 asymmetric subunits (or, equivalently for the ribosomal subunit, particles). Resolutions of 5.6 Å, 4.5 Å, and 3.8 Å were reached with ∼1000, ∼1600, and ∼5000 asymmetric subunits, respectively. At these resolutions, one would expect to detect alpha-helical pitch, separation of beta-strands, and separation of Cα atoms, respectively. Using this map, together with strategies for ab initio model building and model refinement, we built a region of the ribosomal protein eL6, which was missing in previous models of the yeast ribosome. The relevance for more routine high-resolution structure determination is discussed.

Visualization and quality assessment of the contrast transfer function estimation

The contrast transfer function (CTF) describes an undesirable distortion of image data from a transmission electron microscope. Many users of full-featured processing packages are often new to electron microscopy and are unfamiliar with the CTF concept. Here we present a common graphical output to clearly demonstrate the CTF fit quality independent of estimation software. Separately, many software programs exist to estimate the four CTF parameters, but their results are difficult to compare across multiple runs and it is all but impossible to select the best parameters to use for further processing. A new measurement is presented based on the correlation falloff of the calculated CTF oscillations against the normalized oscillating signal of the data, called the CTF resolution. It was devised to provide a robust numerical quality metric of every CTF estimation for high-throughput screening of micrographs and to select the best parameters for each micrograph. These new CTF visualizations and quantitative measures will help users better assess the quality of their CTF parameters and provide a mechanism to choose the best CTF tool for their data.

Mechanistic insights into the recycling machine of the SNARE complex

Evolutionarily conserved SNARE (soluble N-ethylmaleimide sensitive factor attachment protein receptors) proteins form a complex that drives membrane fusion in eukaryotes. The ATPase NSF (N-ethylmaleimide sensitive factor), together with SNAPs (soluble NSF attachment protein), disassembles the SNARE complex into its protein components, making individual SNAREs available for subsequent rounds of fusion. Here we report structures of ATP- and ADP-bound NSF, and the NSF/SNAP/SNARE (20S) supercomplex determined by single-particle electron cryomicroscopy at near-atomic to sub-nanometre resolution without imposing symmetry. Large, potentially force-generating, conformational differences exist between ATP- and ADP-bound NSF. The 20S supercomplex exhibits broken symmetry, transitioning from six-fold symmetry of the NSF ATPase domains to pseudo four-fold symmetry of the SNARE complex. SNAPs interact with the SNARE complex with an opposite structural twist, suggesting an unwinding mechanism. The interfaces between NSF, SNAPs, and SNAREs exhibit characteristic electrostatic patterns, suggesting how one NSF/SNAP species can act on many different SNARE complexes.

An atomic model of brome mosaic virus using direct electron detection and real-space optimization

Advances in electron cryo-microscopy have enabled structure determination of macromolecules at near-atomic resolution. However, structure determination, even using de novo methods, remains susceptible to model bias and overfitting. Here we describe a complete workflow for data acquisition, image processing, all-atom modelling and validation of brome mosaic virus, an RNA virus. Data were collected with a direct electron detector in integrating mode and an exposure beyond the traditional radiation damage limit. The final density map has a resolution of 3.8 Å as assessed by two independent data sets and maps. We used the map to derive an all-atom model with a newly implemented real-space optimization protocol. The validity of the model was verified by its match with the density map and a previous model from X-ray crystallography, as well as the internal consistency of models from independent maps. This study demonstrates a practical approach to obtain a rigorously validated atomic resolution electron cryo-microscopy structure.

Recent developments in cryo-electron microscopy have enabled structure determination of large protein complexes at almost atomic resolution. Wang et al. combine some of these technologies into an effective workflow, and demonstrate the protocol by solving the atomic structure of an icosahedral RNA virus.

CTER-rapid estimation of CTF parameters with error assessment

In structural electron microscopy, the accurate estimation of the Contrast Transfer Function (CTF) parameters, particularly defocus and astigmatism, is of utmost importance for both initial evaluation of micrograph quality and for subsequent structure determination. Due to increases in the rate of data collection on modern microscopes equipped with new generation cameras, it is also important that the CTF estimation can be done rapidly and with minimal user intervention. Finally, in order to minimize the necessity for manual screening of the micrographs by a user it is necessary to provide an assessment of the errors of fitted parameters values. In this work we introduce CTER, a CTF parameters estimation method distinguished by its computational efficiency. The efficiency of the method makes it suitable for high-throughput EM data collection, and enables the use of a statistical resampling technique, bootstrap, that yields standard deviations of estimated defocus and astigmatism amplitude and angle, thus facilitating the automation of the process of screening out inferior micrograph data. Furthermore, CTER also outputs the spatial frequency limit imposed by reciprocal space aliasing of the discrete form of the CTF and the finite window size. We demonstrate the efficiency and accuracy of CTER using a data set collected on a 300kV Tecnai Polara (FEI) using the K2 Summit DED camera in super-resolution counting mode. Using CTER we obtained a structure of the 80S ribosome whose large subunit had a resolution of 4.03Å without, and 3.85Å with, inclusion of astigmatism parameters.

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.

ResLog plots as an empirical metric of the quality of cryo-EM reconstructions

Compared to the field of X-ray crystallography, the field of single particle three-dimensional electron microscopy has few reliable metrics for assessing the quality of 3D reconstructions. New metrics are needed that can determine whether a given 3D reconstruction accurately reflects the structure of the particles from which it was derived or instead depicts a plausible though incorrect structure due to coarse misalignment of particles. Here an empirical procedure is presented for differentiating between a reconstruction with well-aligned particles and a reconstruction with grossly misclassified particles. For a given dataset, 3D reconstructions are computed from subsets of particles with decreasing numbers of particles contributing to the reconstruction. A plot of inverse resolution vs. the logarithm of the number of particles (a "ResLog" plot) provides metrics for the reliability of the reconstruction and the overall quality of the dataset and processing. Specifically, the y-intercept of a regression line provides a measure of the relative accuracy of the particle alignment and classification, and the slope is an indicator of the overall data quality including the imaging conditions and processing steps. ResLog plots can also be used to optimize conditions for data collection and reconstruction parameters. Although resolution estimates can vary by method of calculation, ResLog-derived parameters are consistent whether calculated by Fourier shell correlation or Fourier neighbor correlation, or a new coordinate-based metric that serves as a yardstick for structures where atomic coordinates are available. ResLog plots could become part of a standard set of parameters to be included in 3D reconstruction reports.

Critical importance of the correction of contrast transfer function for transmission electron microscopy-mediated structural biology

Background

Transmission electron microscopy (TEM) is an excellent tool for studying detailed biological structures. High-resolution structure determination is now routinely performed using advanced sample preparation techniques and image processing software. In particular, correction for contrast transfer function (CTF) is crucial for extracting high-resolution information from TEM image that is convoluted by imperfect imaging condition. Accurate determination of defocus, one of the major elements constituting the CTF, is mandatory for CTF correction.

Findings

To investigate the effect of correct estimation of image defocus and subsequent CTF correction, we tested arbitrary CTF imposition onto the images of two-dimensional crystals of Rous sarcoma virus capsid protein. The morphology of the crystal in calculated projection maps from incorrect CTF imposition was utterly distorted in comparison to an appropriately CTF-corrected image.

Conclusion

This result demonstrates critical importance of CTF correction for producing true representation of the specimen at high resolution.

Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM

In recent work with large high symmetry viruses, single particle electron cryomicroscopy (cryoEM) has reached the milestone of determining near atomic resolution structures by allowing direct fitting of atomic models into experimental density maps. However, achieving this goal with smaller particles of lower symmetry remains extraordinarily challenging. Using a newly developed single electron counting detector, we confirm that electron beam induced motion significantly degrades resolution and, importantly, show how the combination of rapid readout and nearly noiseless electron counting allow image blurring to be corrected to subpixel accuracy. Thus, intrinsic image information can be restored to high resolution (Thon rings visible to ~3 Å). Using this approach we determined a 3.3 Å resolution structure of a ~700 kDa protein with D7 symmetry showing clear side chain density. Our method greatly enhances image quality and data acquisition efficiency - key bottlenecks in applying near atomic resolution cryoEM to a broad range of protein samples.

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.

Atomic modeling of cryo-electron microscopy reconstructions--joint refinement of model and imaging parameters

When refining the fit of component atomic structures into electron microscopic reconstructions, use of a resolution-dependent atomic density function makes it possible to jointly optimize the atomic model and imaging parameters of the microscope. Atomic density is calculated by one-dimensional Fourier transform of atomic form factors convoluted with a microscope envelope correction and a low-pass filter, allowing refinement of imaging parameters such as resolution, by optimizing the agreement of calculated and experimental maps. A similar approach allows refinement of atomic displacement parameters, providing indications of molecular flexibility even at low resolution. A modest improvement in atomic coordinates is possible following optimization of these additional parameters. Methods have been implemented in a Python program that can be used in stand-alone mode for rigid-group refinement, or embedded in other optimizers for flexible refinement with stereochemical restraints. The approach is demonstrated with refinements of virus and chaperonin structures at resolutions of 9 through 4.5 Å, representing regimes where rigid-group and fully flexible parameterizations are appropriate. Through comparisons to known crystal structures, flexible fitting by RSRef is shown to be an improvement relative to other methods and to generate models with all-atom rms accuracies of 1.5-2.5 Å at resolutions of 4.5-6 Å.

A graph theory method for determination of cryo-EM image focuses

Accurate determination of micrograph focuses is essential for averaging multiple images to reach high-resolution 3-D reconstructions in electron cryo-microscopy (cryo-EM). Current methods use iterative fitting of focus-dependent simulated power spectra to the power spectra of experimental images, with the fitting performed independently for different images. Here we have developed a novel graph theory based method in which the rotational average focus and individual angular sector focuses of all images are determined simultaneously in closed form using the least square solution of overdetermined linear equations. The new method was shown to be fast, accurate, and robust in tests with large datasets of experimental low dose cryo-EM images. Its integration with three classic power spectra fitting methods also allows cross validation of the results by these vastly different methods. The new integrated focus determination method will improve reliability of automated focus determination for large-scale data processing that is increasingly common in the cryo-EM field.

Structure and size determination of bacteriophage P2 and P4 procapsids: function of size responsiveness mutations

Bacteriophage P4 is dependent on structural proteins supplied by a helper phage, P2, to assemble infectious virions. Bacteriophage P2 normally forms an icosahedral capsid with T=7 symmetry from the gpN capsid protein, the gpO scaffolding protein and the gpQ portal protein. In the presence of P4, however, the same structural proteins are assembled into a smaller capsid with T=4 symmetry. This size determination is effected by the P4-encoded protein Sid, which forms an external scaffold around the small P4 procapsids. Size responsiveness (sir) mutants in gpN fail to assemble small capsids even in the presence of Sid. We have produced large and small procapsids by co-expression of gpN with gpO and Sid, respectively, and applied cryo-electron microscopy and three-dimensional reconstruction methods to visualize these procapsids. gpN has an HK97-like fold and interacts with Sid in an exposed loop where the sir mutations are clustered. The T=7 lattice of P2 has dextro handedness, unlike the laevo lattices of other phages with this fold observed so far.

Fabs enable single particle cryoEM studies of small proteins

In spite of its recent achievements, the technique of single particle electron cryomicroscopy (cryoEM) has not been widely used to study proteins smaller than 100 kDa, although it is a highly desirable application of this technique. One fundamental limitation is that images of small proteins embedded in vitreous ice do not contain adequate features for accurate image alignment. We describe a general strategy to overcome this limitation by selecting a fragment antigen binding (Fab) to form a stable and rigid complex with a target protein, thus providing a defined feature for accurate image alignment. Using this approach, we determined a three-dimensional structure of an ∼65 kDa protein by single particle cryoEM. Because Fabs can be readily generated against a wide range of proteins by phage display, this approach is generally applicable to study many small proteins by single particle cryoEM.

Reconstructing virus structures from nanometer to near-atomic resolutions with cryo-electron microscopy and tomography

The past few decades have seen tremendous advances in single-particle electron -cryo-microscopy (cryo-EM). The field has matured to the point that near-atomic resolution density maps can be generated for icosahedral viruses without the need for crystallization. In parallel, substantial progress has been made in determining the structures of nonicosahedrally arranged proteins in viruses by employing either single-particle cryo-EM or cryo-electron tomography (cryo-ET). Implicit in this course have been the availability of a new generation of electron cryo-microscopes and the development of the computational tools that are essential for generating these maps and models. This methodology has enabled structural biologists to analyze structures in increasing detail for virus particles that are in different morphogenetic states. Furthermore, electron imaging of frozen, hydrated cells, in the process of being infected by viruses, has also opened up a new avenue for studying virus structures "in situ". Here we present the common techniques used to acquire and process cryo-EM and cryo-ET data and discuss their implications for structural virology both now and in the future.

1.16 Cryo-Electron Microscopy and Tomography of Virus Particles

Human infectious disease is classified into five etiologies: bacterial, viral, parasitic, fungal, and prion. Viral infections are unique in that they recruit human cellular machinery to replicate themselves and spread infection. The number of viruses causing human disease is vast, and viruses can be broadly categorized by their structures. Many viruses, such as influenza, appear to be amorphous particles, whereas others, such as herpes simplex virus, rhinovirus, dengue virus, and adenovirus, have roughly symmetric structural components. Icosahedral viruses have been a target of electron microscopists for years, and they were some of the first objects to be reconstructed three-dimensionally from electron micrographs. The ease with which highly purified and conformationally uniform virus samples can be produced makes them an ideal target structural studies. Apart from their biological significance, these virus samples have played a pivotal role in the development of new methodologies in the field of molecular biology as well as in cryo-electron microscopy and cryo-electron tomography.

Defocus estimation from stroboscopic cryo-electron microscopy data

Defocus estimation is an important step for improving the resolution of single particle reconstructions. It can be troublesome to estimate the defocus from low-dose cryo-electron microscopy (cryo-EM) data, particularly if there is not sufficient contrast present in the Fourier transform of the micrograph. Most existing approaches estimate the defocus from the presence of Thon rings within the power spectrum, employing image enhancement techniques to highlight these rings. In this paper, an approach to estimating the defocus from a stroboscopic image series is described. The image series is used to obtain two statistical metrics: figure of merit (FOM) and Q-factor. These metrics have been used to estimate the defoci from low-dose stroboscopic cryo-EM data consisting of a variable number of images.

Practical performance evaluation of a 10k × 10k CCD for electron cryo-microscopy

Electron cryo-microscopy (cryo-EM) images are commonly collected using either charge-coupled devices (CCD) or photographic film. Both film and the current generation of 16 megapixel (4k × 4k) CCD cameras have yielded high-resolution structures. Yet, despite the many advantages of CCD cameras, more than two times as many structures of biological macromolecules have been published in recent years using photographic film. The continued preference to film, especially for subnanometer-resolution structures, may be partially influenced by the finer sampling and larger effective specimen imaging area offered by film. Large format digital cameras may finally allow them to overtake film as the preferred detector for cryo-EM. We have evaluated a 111-megapixel (10k × 10k) CCD camera with a 9 μm pixel size. The spectral signal-to-noise ratios of low dose images of carbon film indicate that this detector is capable of providing signal up to at least 2/5 Nyquist frequency potentially retrievable for 3D reconstructions of biological specimens, resulting in more than double the effective specimen imaging area of existing 4k × 4k CCD cameras. We verified our estimates using frozen-hydrated ε15 bacteriophage as a biological test specimen with previously determined structure, yielding a ∼7 Å resolution single particle reconstruction from only 80 CCD frames. Finally, we explored the limits of current CCD technology by comparing the performance of this detector to various CCD cameras used for recording data yielding subnanometer resolution cryo-EM structures submitted to the electron microscopy data bank (http://www.emdatabank.org/).

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.

Zernike phase contrast cryo-electron microscopy and tomography for structure determination at nanometer and subnanometer resolutions

Zernike phase contrast cryo-electron microscopy (ZPC-cryoEM) is an emerging technique that is capable of producing higher image contrast than conventional cryoEM. By combining this technique with advanced image processing methods, we achieved subnanometer resolution for two biological specimens: 2D bacteriorhodopsin crystal and epsilon15 bacteriophage. For an asymmetric reconstruction of epsilon15 bacteriophage, ZPC-cryoEM can reduce the required amount of data by a factor of approximately 3, compared with conventional cryoEM. The reconstruction was carried out to 13 A resolution without the need to correct the contrast transfer function. New structural features at the portal vertex of the epsilon15 bacteriophage are revealed in this reconstruction. Using ZPC cryo-electron tomography (ZPC-cryoET), a similar level of data reduction and higher resolution structures of epsilon15 bacteriophage can be obtained relative to conventional cryoET. These results show quantitatively the benefits of ZPC-cryoEM and ZPC-cryoET for structural determinations of macromolecular machines at nanometer and subnanometer resolutions.

Cryo-EM of macromolecular assemblies at near-atomic resolution

With single-particle electron cryomicroscopy (cryo-EM), it is possible to visualize large, macromolecular assemblies in near-native states. Although subnanometer resolutions have been routinely achieved for many specimens, state of the art cryo-EM has pushed to near-atomic (3.3-4.6 Å) resolutions. At these resolutions, it is now possible to construct reliable atomic models directly from the cryo-EM density map. In this study, we describe our recently developed protocols for performing the three-dimensional reconstruction and modeling of Mm-cpn, a group II chaperonin, determined to 4.3 Å resolution. This protocol, utilizing the software tools EMAN, Gorgon and Coot, can be adapted for use with nearly all specimens imaged with cryo-EM that target beyond 5 Å resolution. Additionally, the feature recognition and computational modeling tools can be applied to any near-atomic resolution density maps, including those from X-ray crystallography.

Zernike phase plate cryoelectron microscopy facilitates single particle analysis of unstained asymmetric protein complexes

Single particle reconstruction from cryoelectron microscopy images, though emerging as a powerful means in structural biology, is faced with challenges as applied to asymmetric proteins smaller than megadaltons due to low contrast. Zernike phase plate can improve the contrast by restoring the microscope contrast transfer function. Here, by exploiting simulated Zernike and conventional defocused cryoelectron microscope images with noise characteristics comparable to those of experimental data, we quantified the efficiencies of the steps in single particle analysis of ice-embedded RNA polymerase II (500 kDa), transferrin receptor complex (290 kDa), and T7 RNA polymerase lysozyme (100 kDa). Our results show Zernike phase plate imaging is more effective as to particle identification and also sorting of orientations, conformations, and compositions. Moreover, our analysis on image alignment indicates that Zernike phase plate can, in principle, reduce the number of particles required to attain near atomic resolution by 10-100 fold for proteins between 100 kDa and 500 kDa.

Resolution measures in molecular electron microscopy

Resolution measures in molecular electron microscopy provide means to evaluate quality of macromolecular structures computed from sets of their two-dimensional (2D) line projections. When the amount of detail in the computed density map is low there are no external standards by which the resolution of the result can be judged. Instead, resolution measures in molecular electron microscopy evaluate consistency of the results in reciprocal space and present it as a one-dimensional (1D) function of the modulus of spatial frequency. Here we provide description of standard resolution measures commonly used in electron microscopy. We point out that the organizing principle is the relationship between these measures and the spectral signal-to-noise ratio (SSNR) of the computed density map. Within this framework it becomes straightforward to describe the connection between the outcome of resolution evaluations and the quality of electron microscopy maps, in particular, the optimum filtration, in the Wiener sense, of the computed map. We also provide a discussion of practical difficulties of evaluation of resolution in electron microscopy, particularly in terms of its sensitivity to data processing operations used during structure determination process in single particle analysis and in electron tomography (ET).

Multiparticle cryo-EM of ribosomes

As the resolution of cryo-EM reconstructions has improved to the subnanometer range, conformational and compositional heterogeneity have become increasing problems in cryo-EM, limiting the resolution of reconstructions. Since further purification is not feasible, the presence of several conformational states of ribosomal complexes in thermodynamic equilibrium requires methods for separating these states in silico. We describe a procedure for generating subnanometer resolution cryo-EM structures from large sets of projection images of ribosomal complexes. The incremental K-means-like method of unsupervised 3D sorting discussed here allows separation of classes in the dataset by exploiting intrinsic divisions in the data. The classification procedure is described in detail and its effectiveness is illustrated using current examples from our work. Through a good separation of conformational modes, higher resolution reconstructions can be calculated. This increases information gained from single states, while exploiting the coexistence of multiple states to gather comprehensive mechanistic insight into biological processes like ribosomal translocation.

Single particle analysis at high resolution

Electron cryomicroscopy (cryo-EM) and single particle analysis is emerging as a powerful technique for determining the 3D structure of large biomolecules and biomolecular assemblies in close to their native solution environment. Over the last decade, this technology has improved, first to sub-nanometer resolution, and more recently beyond 0.5 nm resolution. Achieving sub-nanometer resolution is now readily approachable on mid-range microscopes with straightforward data processing, so long as the target specimen meets some basic requirements. Achieving resolutions beyond 0.5 nm currently requires a high-end microscope and careful data acquisition and processing, with much more stringent specimen requirements. This chapter will review and discuss the methodologies for determining high-resolution cryo-EM structures of nonvirus particles to sub-nanometer resolution and beyond, with a particular focus on the reconstruction strategy implemented in the EMAN software suite.

3-D structures of macromolecules using single-particle analysis in EMAN

Single-particle reconstruction is a methodology whereby transmission electron microscopy (TEM) is used to record images of individual monodisperse molecules or macromolecular assemblies, then sets of images of individual particles are computationally combined to produce a 3-D volumetric reconstruction. Ideally the TEM specimen will be prepared in vitreous ice (electron cryomicroscopy), but negative stain preparations may be used for lower resolution work. This technique has been demonstrated to produce structures at resolutions as high as ∼ 4 A, though this is not yet typical. The reconstruction process is quite computationally intensive, and several software packages are available for this task. EMAN is one of the easier to master software suites for single-particle analysis. This protocol explains how to perform an initial low-resolution reconstruction using EMAN.

Image restoration in cryo-electron microscopy

Image restoration techniques are used to obtain, given experimental measurements, the best possible approximation of the original object within the limits imposed by instrumental conditions and noise level in the data. In molecular electron microscopy (EM), we are mainly interested in linear methods that preserve the respective relationships between mass densities within the restored map. Here, we describe the methodology of image restoration in structural EM, and more specifically, we will focus on the problem of the optimum recovery of Fourier amplitudes given electron microscope data collected under various defocus settings. We discuss in detail two classes of commonly used linear methods, the first of which consists of methods based on pseudoinverse restoration, and which is further subdivided into mean-square error, chi-square error, and constrained based restorations, where the methods in the latter two subclasses explicitly incorporates non-white distribution of noise in the data. The second class of methods is based on the Wiener filtration approach. We show that the Wiener filter-based methodology can be used to obtain a solution to the problem of amplitude correction (or "sharpening") of the EM map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparative interpretation. Finally, we present a semiheuristic Wiener filter-based solution to the problem of image restoration given sets of heterogeneous solutions. We conclude the chapter with a discussion of image restoration protocols implemented in commonly used single particle software packages.

Characterization of antibiotic peptide pores using cryo-EM and comparison to neutron scattering

Magainin, a 23-residue antibiotic peptide, interacts directly with the lipid bilayer leading to cell lysis in a strongly concentration-dependent fashion. Utilizing cryo-electron microscopy, we have directly observed magainin interacting with synthetic DMPC/DMPG membranes. Visual examination shows that visibly unperturbed vesicles are often found adjacent to vesicles that are lysed or porous, demonstrating that magainin disruption is a highly stochastic process. Quantitatively, power spectra of large numbers of porous vesicles can be averaged together to produce the equivalent of an electron scattering curve, which can be related to theory, simulation, and published neutron scattering experiments. We demonstrate that magainin-induced pores in lipid vesicles have a mean diameter of approximately 80 A, compatible with earlier reported results in multilayer stacks. In addition to establishing a connection between experiments in multilayer stacks and vesicles, this also demonstrates that computed power spectra from windowed-out regions of cryo-EM images can be compared to neutron scattering data in a meaningful way, even though the pores of interest cannot yet be individually identified in images. Cryo-EM offers direct imaging of systems in configurations closely related to in vivo conditions, whereas neutron scattering has a greater variety of mechanisms for specific contrast variation via D2O and deuterated lipids. Combined, the two mechanisms support each other, and provide a clearer picture of such 'soft' systems than either could provide alone.

Evaluation of imaging plates as recording medium for images of negatively stained single particles and electron diffraction patterns of two-dimensional crystals

We evaluated imaging plates (IPs) and the DITABIS Micron scanner for their use in recording images of negatively stained single-particle specimens and electron diffraction patterns of two-dimensional crystals. We first established the optimal imaging and read-out conditions for images of negatively stained single-particle specimens using the signal-to-noise ratio of the images as the evaluation criterion. We found that images were best recorded on IPs at a magnification of 67,000x, read out with a gain setting of 20,000 and a laser power setting of 30% with subsequent binning over 2 x 2 pixels. Our results show that for images of negatively stained specimens, for which the resolution is limited to approximately 20 A, IPs are a good alternative to EM film. We also compared IPs with a 2K x 2K Gatan charge-coupled device (CCD) camera for their use in recording electron diffraction patterns of sugar-embedded two-dimensional crystals. Diffraction patterns of aquaporin-0 recorded on IPs and with the CCD camera showed reflections beyond 3 A and had similar R(Friedel) as well as R(merge) values. IPs can thus be used to collect diffraction patterns, but CCD cameras are more convenient and remain the best option for recording electron diffraction patterns.

The advent of near-atomic resolution in single-particle electron microscopy

Single-particle electron microscopy (EM) can provide structural information for a large variety of biological molecules, ranging from small proteins to large macromolecular assemblies, without the need to produce crystals. The year 2008 has become a landmark year for single-particle EM as for the first time density maps have been produced at a resolution that made it possible to trace protein backbones or even to build atomic models. In this review, we highlight some of the recent successes achieved by single-particle EM and describe the individual steps involved in producing a density map by this technique. We also discuss some of the remaining challenges and areas, in which further advances would have a great impact on the results that can be achieved by single-particle EM.

Error analysis in the determination of the electron microscopical contrast transfer function parameters from experimental power Spectra

BACKGROUND

The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.

RESULTS

In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.

CONCLUSION

We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Visualization of bacteriophage T3 capsids with DNA incompletely packaged in vivo

The tightly packaged double-stranded DNA (dsDNA) genome in the mature particles of many tailed bacteriophages has been shown to form multiple concentric rings when reconstructed from cryo-electron micrographs. However, recent single-particle DNA packaging force measurements have suggested that incompletely packaged DNA (ipDNA) is less ordered when it is shorter than approximately 25% of the full genome length. The study presented here initially achieves both the isolation and the ipDNA length-based fractionation of ipDNA-containing T3 phage capsids (ipDNA-capsids) produced by DNA packaging in vivo; some ipDNA has quantized lengths, as judged by high-resolution gel electrophoresis of expelled DNA. This is the first isolation of such particles among the tailed dsDNA bacteriophages. The ipDNA-capsids are a minor component (containing approximately 10(-4) of packaged DNA in all particles) and are initially detected by nondenaturing gel electrophoresis after partial purification by buoyant density centrifugation. The primary contaminants are aggregates of phage particles and empty capsids. This study then investigates ipDNA conformations by the first cryo-electron microscopy of ipDNA-capsids produced in vivo. The 3-D structures of DNA-free capsids, ipDNA-capsids with various lengths of ipDNA, and mature bacteriophage are reconstructed, which reveals the typical T=7l icosahedral shell of many tailed dsDNA bacteriophages. Though the icosahedral shell structures of these capsids are indistinguishable at the current resolution for the protein shell (approximately 15 A), the conformations of the DNA inside the shell are drastically different. T3 ipDNA-capsids with 10.6 kb or shorter dsDNA (<28% of total genome) have an ipDNA conformation indistinguishable from random. However, T3 ipDNA-capsids with 22 kb DNA (58% of total genome) form a single DNA ring next to the inner surface of the capsid shell. In contrast, dsDNA fully packaged (38.2 kb) in mature T3 phage particles forms multiple concentric rings such as those seen in other tailed dsDNA bacteriophages. The distance between the icosahedral shell and the outermost DNA ring decreases in the mature, fully packaged phage structure. These results suggest that, in the early stage of DNA packaging, the dsDNA genome is randomly distributed inside the capsid, not preferentially packaged against the inner surface of the capsid shell, and that the multiple concentric dsDNA rings seen later are the results of pressure-driven close-packing.

Structural insights into P-glycoprotein (ABCB1) by small angle X-ray scattering and electron crystallography

P-glycoprotein (ABCB1) is an ATP-binding cassette protein that is associated with the acquisition of multi-drug resistance in cancer and the failure of chemotherapy in humans. Structural insights into this protein are described using a combination of small angle X-ray scattering data and cryo-electron crystallography data. We have compared the structures with bacterial homologues, and discuss the development of homology models for P-glycoprotein based on the bacterial Sav1866 structure.

De novo backbone trace of GroEL from single particle electron cryomicroscopy

In this work, we employ single-particle electron cryo-microscopy (cryo-EM) to reconstruct GroEL to approximately 4 A resolution with both D7 and C7 symmetry. Using a newly developed skeletonization algorithm and secondary structure element identification in combination with sequence-based secondary structure prediction, we demonstrate that it is possible to achieve a de novo Calpha trace directly from a cryo-EM reconstruction. The topology of our backbone trace is completely accurate, though subtle alterations illustrate significant differences from existing crystal structures. In the map with C7 symmetry, the seven monomers in each ring are identical; however, the subunits have a subtly different structure in each ring, particularly in the equatorial domain. These differences include an asymmetric salt bridge, density in the nucleotide-binding pocket of only one ring, and small shifts in alpha helix positions. This asymmetric conformation is different from previous asymmetric structures, including GroES-bound GroEL, and may represent a "primed state" in the chaperonin pathway.

Sindbis virus conformational changes induced by a neutralizing anti-E1 monoclonal antibody

A rare Sindbis virus anti-E1 neutralizing monoclonal antibody, Sin-33, was investigated to determine the mechanism of in vitro neutralization. A cryoelectron microscopic reconstruction of Sindbis virus (SVHR) neutralized with FAb from Sin-33 (FAb-33) revealed conformational changes on the surface of the virion at a resolution of 24 A. FAb-33 was found to bind E1 in less than 1:1 molar ratios, as shown by the absence of FAb density in the reconstruction and stoichiometric measurements using radiolabeled FAb-33, which determined that about 60 molecules of FAb-33 bound to the 240 possible sites in a single virus particle. FAb-33-neutralized virus particles became sensitive to digestion by endoproteinase Glu-C, providing further evidence of antibody-induced structural changes within the virus particle. The treatment of FAb-33-neutralized or Sin-33-neutralized SVHR with low pH did not induce the conformational rearrangements required for virus membrane-cell membrane fusion. Exposure to low pH, however, increased the amount of Sin-33 or FAb-33 that bound to the virus particles, indicating the exposure of additional epitopes. The neutralization of SVHR infection by FAb-33 or Sin-33 did not prevent the association of virus with host cells. These data are in agreement with the results of previous studies that demonstrated that specific antibodies can inactivate the infectious state of a metastable virus in vitro by the induction of conformational changes to produce an inactive structure. A model is proposed which postulates that the induction of conformational changes in the infectious state of a metastable enveloped virus may be a general mechanism of antibody inactivation of virus infectivity.

Achievable resolution from images of biological specimens acquired from a 4k x 4k CCD camera in a 300-kV electron cryomicroscope

Bacteriorhodopsin and epsilon 15 bacteriophage were used as biological test specimens to evaluate the potential structural resolution with images captured from a 4k x 4k charge-coupled device (CCD) camera in a 300-kV electron cryomicroscope. The phase residuals computed from the bacteriorhodopsin CCD images taken at 84,000x effective magnification averaged 15.7 degrees out to 5.8-A resolution relative to Henderson's published values. Using a single-particle reconstruction technique, we obtained an 8.2-A icosahedral structure of epsilon 15 bacteriophage with the CCD images collected at an effective magnification of 56,000x. These results demonstrate that it is feasible to retrieve biological structures to a resolution close to 2/3 of the Nyquist frequency from the CCD images recorded in a 300-kV electron cryomicroscope at a moderately high but practically acceptable microscope magnification.

Backbone structure of the infectious epsilon15 virus capsid revealed by electron cryomicroscopy

A half-century after the determination of the first three-dimensional crystal structure of a protein, more than 40,000 structures ranging from single polypeptides to large assemblies have been reported. The challenge for crystallographers, however, remains the growing of a diffracting crystal. Here we report the 4.5-A resolution structure of a 22-MDa macromolecular assembly, the capsid of the infectious epsilon15 (epsilon15) particle, by single-particle electron cryomicroscopy. From this density map we constructed a complete backbone trace of its major capsid protein, gene product 7 (gp7). The structure reveals a similar protein architecture to that of other tailed double-stranded DNA viruses, even in the absence of detectable sequence similarity. However, the connectivity of the secondary structure elements (topology) in gp7 is unique. Protruding densities are observed around the two-fold axes that cannot be accounted for by gp7. A subsequent proteomic analysis of the whole virus identifies these densities as gp10, a 12-kDa protein. Its structure, location and high binding affinity to the capsid indicate that the gp10 dimer functions as a molecular staple between neighbouring capsomeres to ensure the particle's stability. Beyond epsilon15, this method potentially offers a new approach for modelling the backbone conformations of the protein subunits in other macromolecular assemblies at near-native solution states.

Modular software platform for low-dose electron microscopy and tomography

Transmission electron microscopy imaging protocols required by structural scientists vary widely and can be laborious without tailor-made applications. We present here the jeol automated microscopy expert system (james) api integrator, a programming library for computer control of transmission electron microscopy operations and equipment. james has been implemented on JEOL microscopes with Gatan CCDs but is designed to be modular so it can be adapted to run on different microscopes and detectors. We have used the james api integrator to develop two applications for low-dose digital imaging: james imaging application and the mr t tomographic imaging application. Both applications have been widely used within our NCRR-supported Center for routine data collection and are now made available for public download.

Fast, robust, and accurate determination of transmission electron microscopy contrast transfer function

Transmission electron microscopy, as most imaging devices, introduces optical aberrations that in the case of thin specimens are usually modeled in Fourier space by the so-called contrast transfer function (CTF). Accurate determination of the CTF is crucial for its posterior correction. Furthermore, the CTF estimation must be fast and robust if high-throughput three-dimensional electron microscopy (3DEM) studies are to be carried out. In this paper we present a robust algorithm that fits a theoretical CTF model to the power spectrum density (PSD) measured on a specific micrograph or micrograph area. Our algorithm is capable of estimating the envelope of the CTF which is absolutely needed for the correction of the CTF amplitude changes.

Gold nanoparticle-protein arrays improve resolution for cryo-electron microscopy

Cryo-electron microscopy single particle analysis shows limited resolution due to poor alignment precision of noisy images taken under low electron exposure. Certain advantages can be obtained by assembling proteins into two-dimensional (2D) arrays since protein particles are locked into repetitive orientation, thus improving alignment precision. We present a labeling method to prepare protein 2D arrays using gold nanoparticles (NPs) interconnecting genetic tag sites on proteins. As an example, mycobacterium tuberculosis 20S proteasomes tagged with 6x-histidine were assembled into 2D arrays using 3.9-nm Au NPs functionalized with nickel-nitrilotriacetic acid. The averaged top-view images from the array particles showed higher resolution (by 6-8A) compared to analysis of single particles. The correct 7-fold symmetry was also evident by using array particles whereas it was not clear by analysis of a comparable number of single particles. The applicability of this labeling method for three-dimensional reconstruction of biological macromolecules is discussed.

Averaging tens to hundreds of icosahedral particle images to resolve protein secondary structure elements using a Multi-Path Simulated Annealing optimization algorithm

Accurately determining a cryoEM particle's alignment parameters is crucial to high resolution single particle 3-D reconstruction. We developed Multi-Path Simulated Annealing, a Monte-Carlo type of optimization algorithm, for globally aligning the center and orientation of a particle simultaneously. A consistency criterion was developed to ensure the alignment parameters are correct and to remove some bad particles from a large pool of images of icosahedral particles. Without using any a priori model, this procedure is able to reconstruct a structure from a random initial model. Combining the procedure above with a new empirical double threshold particle selection method, we are able to pick tens of best quality particles to reconstruct a subnanometer resolution map from scratch. Using the best 62 particles of rice dwarf virus, the reconstruction reached 9.6A resolution at which four helices of the P3A subunit of RDV are resolved. Furthermore, with the 284 best particles, the reconstruction is improved to 7.9A resolution, and 21 of 22 helices and six of seven beta sheets are resolved.

3D electron microscopy of biological nanomachines: principles and applications

Transmission electron microscopy is a powerful technique for studying the three-dimensional (3D) structure of a wide range of biological specimens. Knowledge of this structure is crucial for fully understanding complex relationships among macromolecular complexes and organelles in living cells. In this paper, we present the principles and main application domains of 3D transmission electron microscopy in structural biology. Moreover, we survey current developments needed in this field, and discuss the close relationship of 3D transmission electron microscopy with other experimental techniques aimed at obtaining structural and dynamical information from the scale of whole living cells to atomic structure of macromolecular complexes.

Characterization of Vibrio cholerae O1 ElTor typing phage S5

S5 (ATCC No. 51352-B2), a Vibrio cholerae O1 ElTor typing phage was characterized. The growth characteristics and inactivation kinetics (thermal, UV and pH) of this lytic phage were investigated. Phage morphology was examined by electron microscopy and was classified as belonging to the family Podoviridae. The S5 phage genome is shown to be a linear double-stranded 39-kb-long DNA as determined by electron microscopy and restriction digestion. Partial denaturation maps were constructed and were used to show that the DNA is non-permuted and terminally redundant. The replication origin of this T7-like phage was visualized by electron microscopy. The polarity of packaging of S5 DNA in the phage head was determined. SDS-PAGE of phage S5 shows two major structural polypeptides of 50 and 42 kDa. A 3D structure of the phage head was reconstructed at a resolution of 37 A using Cryo-EM and a single-particle reconstruction technique.