Zernike phase contrast cryo-electron tomography of whole bacterial cells

Cryo-electron tomography (cryo-ET) provides three-dimensional (3D) structural information of bacteria preserved in a native, frozen-hydrated state. The typical low contrast of tilt-series images, a result of both the need for a low electron dose and the use of conventional defocus phase-contrast imaging, is a challenge for high-quality tomograms. We show that Zernike phase-contrast imaging allows the electron dose to be reduced. This limits movement of gold fiducials during the tilt series, which leads to better alignment and a higher-resolution reconstruction. Contrast is also enhanced, improving visibility of weak features. The reduced electron dose also means that more images at more tilt angles could be recorded, further increasing resolution.     

Analysis of symmetry and three-dimensional reconstruction of thin gp32*I crystals.

Thin, multilayered crystals of gp32*I were analyzed by negative stain electron microscopy and image processing. Images of untilted crystals exhibited different projection symmetries and structural motifs. Systematic analysis of these images categorized the projections into four types. Areas producing the type 1 projection were reconstructed in three-dimensions from four tilt series containing 111 images. The three-dimensional data has excellent p121 plane group symmetry and reveals that the gp32*I molecule contains two large domains linked together by a small domain. Computer simulations utilizing projection data suggested that the type 2 and 3 projections arise from superposition of type 1 projections related by a 21 screw axis along the projection axis. The three-dimensional reconstruction was utilized in a final simulation that explained the occurrence of the fourth type of projection. This work provides a firm foundation for future high-resolution analysis of the crystal by electron cryomicroscopy.     

Determination of three-dimensional imaging properties of a light microscope system. Partial confocal behavior in epifluorescence microscopy.

We have determined the three-dimensional image-forming properties of an epifluorescence microscope for use in obtaining very high resolution three-dimensional images of biological structures by image processing methods. Three-dimensional microscopic data is collected as a series of two-dimensional images recorded at different focal planes. Each of these images contains not only in-focus information from the region around the focal plane, but also out-of-focus contributions from the remainder of the specimen. Once the imaging properties of the microscope system are characterized, powerful image processing methods can be utilized to remove the out-of-focus information and to correct for image distortions. Although theoretical calculations for the behavior of an aberration-free microscope system are available, the properties of real lenses under the conditions used for biological observation are often far from an ideal. For this reason, we have directly determined the image-forming properties of an epifluorescence microscope under conditions relevant to biological observations. Through-focus series of a point object (fluorescently-coated microspheres) were recorded on a charge-coupled device image detector. From these images, the three-dimensional point spread function and its Fourier transform, the optical transfer function, were derived. There were significant differences between the experimental results and the theoretical models which have important implications for image processing. The discrepancies can be explained by imperfections of the microscope system, nonideal observation conditions, and partial confocal effects found to occur with epifluorescence illumination. Understanding the optical behavior of the microscope system has indicated how to optimize specimen preparation, data collection, and processing protocols to obtain significantly improved images.     

Tilt-pair analysis of images from a range of different specimens in single-particle electron cryomicroscopy

The comparison of a pair of electron microscope images recorded at different specimen tilt angles provides a powerful approach for evaluating the quality of images, image-processing procedures, or three-dimensional structures. Here, we analyze tilt-pair images recorded from a range of specimens with different symmetries and molecular masses and show how the analysis can produce valuable information not easily obtained otherwise. We show that the accuracy of orientation determination of individual single particles depends on molecular mass, as expected theoretically since the information in each particle image increases with molecular mass. The angular uncertainty is less than 1° for particles of high molecular mass (∼ 50 MDa), several degrees for particles in the range 1-5 MDa, and tens of degrees for particles below 1 MDa. Orientational uncertainty may be the major contributor to the effective temperature factor (B-factor) describing contrast loss and therefore the maximum resolution of a structure determination. We also made two unexpected observations. Single particles that are known to be flexible showed a wider spread in orientation accuracy, and the orientations of the largest particles examined changed by several degrees during typical low-dose exposures. Smaller particles presumably also reorient during the exposure; hence, specimen movement is a second major factor that limits resolution. Tilt pairs thus enable assessment of orientation accuracy, map quality, specimen motion, and conformational heterogeneity. A convincing tilt-pair parameter plot, where 60% of the particles show a single cluster around the expected tilt axis and tilt angle, provides confidence in a structure determined using electron cryomicroscopy.     

Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy

A computational procedure is described for assigning the absolute hand of the structure of a protein or assembly determined by single-particle electron microscopy. The procedure requires a pair of micrographs of the same particle field recorded at two tilt angles of a single tilt-axis specimen holder together with the three-dimensional map whose hand is being determined. For orientations determined from particles on one micrograph using the map, the agreement (average phase residual) between particle images on the second micrograph and map projections is determined for all possible choices of tilt angle and axis. Whether the agreement is better at the known tilt angle and axis of the microscope or its inverse indicates whether the map is of correct or incorrect hand. An increased discrimination of correct from incorrect hand (free hand difference), as well as accurate identification of the known values for the tilt angle and axis, can be used as targets for rapidly optimizing the search or refinement procedures used to determine particle orientations. Optimized refinement reduces the tendency for the model to match noise in a single image, thus improving the accuracy of the orientation determination and therefore the quality of the resulting map. The hand determination and refinement optimization procedure is applied to image pairs of the dihydrolipoyl acetyltransferase (E2) catalytic core of the pyruvate dehydrogenase complex from Bacillus stearothermophilus taken by low-dose electron cryomicroscopy. Structure factor amplitudes of a three-dimensional map of the E2 catalytic core obtained by averaging untilted images of 3667 icosahedral particles are compared to a scattering reference using a Guinier plot. A noise-dependent structure factor weight is derived and used in conjunction with a temperature factor (B=-1000A(2)) to restore high-resolution contrast without amplifying noise and to visualize molecular features to 8.7A resolution, according to a new objective criterion for resolution assessment proposed here.     

Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L(2,3) edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell's nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Focal pair merging for contrast enhancement of single particles

A common technique in transmission electron microscopy is the collection of a focal pair, in which the first, close to focus image contains higher resolution information at lower contrast, and the second, far from focus image has high contrast but less reliable high-resolution information. Typically these second micrographs are used for purposes of particle selection, orientation estimate or micrograph evaluation. We introduce a technique for merging the information from both images, including signal to noise ratio weighting, contrast transfer function correction, and optional Weiner filtration. This produces a composite image with reduced contrast transfer function artifacts and optimized contrast. This technique is useful in numerous cases where low-contrast images are produced, such as small particles, proteins solubilized in detergent or projects with high-resolution goals when the first image is taken very close to focus.     

Reprint of "Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)" [J. Struct. Biol. 160 (2007) 35-48

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L_2,3 edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell’s nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Tomographic subvolume alignment and subvolume classification applied to myosin V and SIV envelope spikes

Electron tomography is a technique for three-dimensional reconstruction, that is widely used for imaging macromolecules, macromolecular assemblies or whole cells. Combined with cryo-electron microscopy, it is capable of visualizing structural detail in a state close to in vivo conditions in the cell. In electron tomography, micrographs are taken while tilting the specimen to different angles about a fixed axis. Due to mechanical constraints, the angular tilt range is limited. As a consequence, the reconstruction of a 3D image is missing data, which for a single axis tilt series is called the “missing wedge”, a region in reciprocal space where Fourier coefficients cannot be obtained experimentally. Tomographic data is analyzed by extracting subvolumes from the raw tomograms, by alignment of the extracted subvolumes, multivariate data analysis, classification, and class-averaging, which results in an increased signal-to-noise ratio and substantial data reduction. Subvolume analysis is a valuable tool to discriminate heterogeneous populations of macromolecules, or conformations of a macromolecule or macromolecular assembly as well as to characterize interactions between macromolecules. However, this analysis is hampered by the lack of data in the original tomograms caused by the missing wedge. Here, we report enhancements of our subvolume processing protocols in which the problem of the missing data in reciprocal space is addressed by using constrained correlation and weighted averaging in reciprocal space. These procedures are applied to the analysis of myosin V and simian immunodeficiency virus (SIV) envelope spikes. We also investigate the effect of the missing wedge on image classification and establish limits of reliability by model calculations with generated phantoms.     

Accurate determination of local defocus and specimen tilt in electron microscopy

Accurate knowledge of defocus and tilt parameters is essential for the determination of three-dimensional protein structures at high resolution using electron microscopy. We present two computer programs, CTFFIND3 and CTFTILT, which determine defocus parameters from images of untilted specimens, as well as defocus and tilt parameters from images of tilted specimens, respectively. Both programs use a simple algorithm that fits the amplitude modulations visible in a power spectrum with a calculated contrast transfer function (CTF). The background present in the power spectrum is calculated using a low-pass filter. The background is then subtracted from the original power spectrum, allowing the fitting of only the oscillatory component of the CTF. CTFTILT determines specimen tilt parameters by measuring the defocus at a series of locations on the image while constraining them to a single plane. We tested the algorithm on images of two-dimensional crystals by comparing the results with those obtained using crystallographic methods. The images also contained contrast from carbon support film that added to the visibility of the CTF oscillations. The tests suggest that the fitting procedure is able to determine the image defocus with an error of about 10nm, whereas tilt axis and tilt angle are determined with an error of about 2 degrees and 1 degrees, respectively. Further tests were performed on images of single protein particles embedded in ice that were recorded from untilted or slightly tilted specimens. The visibility of the CTF oscillations from these images was reduced due to the lack of a carbon support film. Nevertheless, the test results suggest that the fitting procedure is able to determine image defocus and tilt angle with errors of about 100 nm and 6 degrees, respectively.     

Tilted specimen in the electron microscope: A simple specimen holder and the calculation of tilt angles for crystalline specimens

A simple specimen holder is described for a Siemens electron microscope which will allow the specimen grid to be set at inclinations up to 75° to the electron beam in any azimuthal direction. This device is suitable for measuring tilted images for the three-dimensional reconstruction of crystalline specimens. A method is also described for calculating the tilt angles for such crystalline specimens by comparing the unit cell dimensions in tilted and untilted images.     

7A projection map of the S-layer protein sbpA obtained with trehalose-embedded monolayer crystals

Two-dimensional crystallization on lipid monolayers is a versatile tool to obtain structural information of proteins by electron microscopy. An inherent problem with this approach is to prepare samples in a way that preserves the crystalline order of the protein array and produces specimens that are sufficiently flat for high-resolution data collection at high tilt angles. As a test specimen to optimize the preparation of lipid monolayer crystals for electron microscopy imaging, we used the S-layer protein sbpA, a protein with potential for designing arrays of both biological and inorganic materials with engineered properties for a variety of nanotechnology applications. Sugar embedding is currently considered the best method to prepare two-dimensional crystals of membrane proteins reconstituted into lipid bilayers. We found that using a loop to transfer lipid monolayer crystals to an electron microscopy grid followed by embedding in trehalose and quick-freezing in liquid ethane also yielded the highest resolution images for sbpA lipid monolayer crystals. Using images of specimens prepared in this way we could calculate a projection map of sbpA at 7A resolution, one of the highest resolution projection structures obtained with lipid monolayer crystals to date.     

A Strategy for Electron Tomographic Data Collection and Crystallographic Reconstruction of Biological Bundles

Structures of highly ordered biological bundles have unique features which call for special experimental and computational methods in electron cryomicroscopy. They can be considered as three-dimensional quasi-crystals and reconstructed using a crystallographic approach. However, they are neither “infinitely” large with respect to the borders of the bundle, nor are they a single unit cell in thickness along the viewing direction. Also, because of their shape, bundles do not generally have a preferred azimuthal orientation, which poses challenges for orientation estimation and refinement. We developed a strategy for recording and processing electron cryomicroscopic images that differs from classical two-dimensional crystalline reconstruction techniques. These developments allowed us to merge data from tomographic tilt series of ice-embedded acrosomal bundles. The goal is to determine accurately amplitudes and phases at the diffraction maxima in terms ofhklindices, and compute a three-dimensional map from the diffraction data.     

A procedure to deposit fiducial markers on vitreous cryo-sections for cellular tomography

We describe a novel approach for the accurate alignment of images in electron tomography of vitreous cryo-sections. Quantum dots, suspended in organic solvents at cryo-temperatures, are applied directly onto the sections and are subsequently used as fiducial markers to align the tilt series. Data collection can be performed from different regions of the vitreous sections, even when the sections touch the grid only at a few places. We present high-resolution tomograms of some organelles in cryo-sections of human skin cells using this method. The average error in image alignment was about 1nm and the resolution was estimated to be 5-7nm. Thus, the use of section-attached quantum dots as fiducial markers in electron tomography of vitreous cryo-sections facilitates high-resolution in situ 3D imaging of organelles and macromolecular complexes in their native hydrated state.     

Improved specimen reconstruction by Hilbert phase contrast tomography

The low signal-to-noise ratio (SNR) in images of unstained specimens recorded with conventional defocus phase contrast makes it difficult to interpret 3D volumes obtained by electron tomography (ET). The high defocus applied for conventional tilt series generates some phase contrast but leads to an incomplete transfer of object information. For tomography of biological weak-phase objects, optimal image contrast and subsequently an optimized SNR are essential for the reconstruction of details such as macromolecular assemblies at molecular resolution. The problem of low contrast can be partially solved by applying a Hilbert phase plate positioned in the back focal plane (BFP) of the objective lens while recording images in Gaussian focus. Images recorded with the Hilbert phase plate provide optimized positive phase contrast at low spatial frequencies, and the contrast transfer in principle extends to the information limit of the microscope. The antisymmetric Hilbert phase contrast (HPC) can be numerically converted into isotropic contrast, which is equivalent to the contrast obtained by a Zernike phase plate. Thus, in-focus HPC provides optimal structure factor information without limiting effects of the transfer function. In this article, we present the first electron tomograms of biological specimens reconstructed from Hilbert phase plate image series. We outline the technical implementation of the phase plate and demonstrate that the technique is routinely applicable for tomography. A comparison between conventional defocus tomograms and in-focus HPC volumes shows an enhanced SNR and an improved specimen visibility for in-focus Hilbert tomography.     

7 Å projection map of the S-layer protein sbpA obtained with trehalose-embedded monolayer crystals

Two-dimensional crystallization on lipid monolayers is a versatile tool to obtain structural information of proteins by electron microscopy. An inherent problem with this approach is to prepare samples in a way that preserves the crystalline order of the protein array and produces specimens that are sufficiently flat for high-resolution data collection at high tilt angles. As a test specimen to optimize the preparation of lipid monolayer crystals for electron microscopy imaging, we used the S-layer protein sbpA, a protein with potential for designing arrays of both biological and inorganic materials with engineered properties for a variety of nanotechnology applications. Sugar embedding is currently considered the best method to prepare two-dimensional crystals of membrane proteins reconstituted into lipid bilayers. We found that using a loop to transfer lipid monolayer crystals to an electron microscopy grid followed by embedding in trehalose and quick-freezing in liquid ethane also yielded the highest resolution images for sbpA lipid monolayer crystals. Using images of specimens prepared in this way we could calculate a projection map of sbpA at 7 Å resolution, one of the highest resolution projection structures obtained with lipid monolayer crystals to date.     

Correlation of topographic surface and volume data from three-dimensional electron microscopy

Three-dimensional(3D) reconstructions from tilt series in an electron microscope show in general an anisotropic resolution due to an instrumentally limited tilt angle. As a consequence, the information in the z direction is blurred, thus making it difficult to detect the boundary of the reconstructed structures. In contrast, high-resolution topography data from microscopic surface techniques provide exactly complementary information. The combination of topographic surface and volume data leads to a better understanding of the 3D structure. The new correlation procedure presented determines both the height scaling of the topographic surface and the relative position of surface and volume data, thus allowing information to be combined. Experimental data for crystalline T4 bacteriophage polyheads were used to test the new method. Three-dimensional volume data were reconstructed from a negatively stained tilt series. Topographic data for both surfaces were obtained by surface relief reconstruction of electron micrographs of freeze-dried and unidirectionally metal-shadowed polyheads. The combined visualization of volume data with the scaled and aligned surface data shows that the correlation technique yields meaningful results. The reported correlation method may be applied to surface data obtained by any microscopic technique yielding topographic data.     

Parakeet: a digital twin software pipeline to assess the impact of experimental parameters on tomographic reconstructions for cryo-electron tomography

In cryo-electron tomography (cryo-ET) of biological samples, the quality of tomographic reconstructions can vary depending on the transmission electron microscope (TEM) instrument and data acquisition parameters. In this paper, we present Parakeet, a ‘digital twin’ software pipeline for the assessment of the impact of various TEM experiment parameters on the quality of three-dimensional tomographic reconstructions. The Parakeet digital twin is a digital model that can be used to optimize the performance and utilization of a physical instrument to enable in silico optimization of sample geometries, data acquisition schemes and instrument parameters. The digital twin performs virtual sample generation, TEM image simulation, and tilt series reconstruction and analysis within a convenient software framework. As well as being able to produce physically realistic simulated cryo-ET datasets to aid the development of tomographic reconstruction and subtomogram averaging programs, Parakeet aims to enable convenient assessment of the effects of different microscope parameters and data acquisition parameters on reconstruction quality. To illustrate the use of the software, we present the example of a quantitative analysis of missing wedge artefacts on simulated planar and cylindrical biological samples and discuss how data collection parameters can be modified for cylindrical samples where a full 180° tilt range might be measured.     

Angle determination for side views in single particle electron microscopy

In order to build a first model in single particle electron microscopy the relative angular orientation of each image of a protein complex must be determined. These orientations can be described by three Eulerian angles. Images of complexes that present the same view can be aligned in two-dimensions and averaged in order to increase their signal-to-noise ratio. Based on these averaged images, several standard approaches exist for determining Euler angles for randomly oriented projection images. The common lines and angular reconstitution methods work well for particles with symmetry while the random conical tilting and related orthogonal tilt reconstruction methods work in most cases but require the acquisition of tilt pairs of images. For the situation where views of particles can be identified that are rotations about a single axis parallel to the grid, an alternative algorithm to determine the orientations of class averages without the need to acquire tilt pairs can be applied. This type of view of a complex is usually called a side view. This paper describes the detailed workings and characterization of an algorithm, named rotational analysis, which uses real-space fiducial markers derived from the averages themselves to determine the Euler angles for side views. We demonstrate how this algorithm works in practice by applying it to a data set of images of affinity-purified bovine mitochondrial ATP synthase.     

Fragment-based phase extension for three-dimensional structure determination of membrane proteins by electron crystallography

In electron crystallography, membrane protein structure is determined from two-dimensional crystals where the protein is embedded in a membrane. Once large and well-ordered 2D crystals are grown, one of the bottlenecks in electron crystallography is the collection of image data to directly provide experimental phases to high resolution. Here, we describe an approach to bypass this bottleneck, eliminating the need for high-resolution imaging. We use the strengths of electron crystallography in rapidly obtaining accurate experimental phase information from low-resolution images and accurate high-resolution amplitude information from electron diffraction. The low-resolution experimental phases were used for the placement of α helix fragments and extended to high resolution using phases from the fragments. Phases were further improved by density modifications followed by fragment expansion and structure refinement against the high-resolution diffraction data. Using this approach, structures of three membrane proteins were determined rapidly and accurately to atomic resolution without high-resolution image data.