CTF determination and correction for low dose tomographic tilt series

The resolution of cryo-electron tomography can be limited by the first zero of the microscope’s contrast transfer function (CTF). To achieve higher resolution, it is critical to determine the CTF and correct its phase inversions. However, the extremely low signal-to-noise ratio (SNR) and the defocus gradient in the projections of tilted specimens make this process challenging. Two programs, CTFPLOTTER and CTFPHASEFLIP, have been developed to address these issues. CTFPLOTTER obtains a 1D power spectrum by periodogram averaging and rotational averaging and it estimates the noise background with a novel approach, which uses images taken with no specimen. The background-subtracted 1D power spectra from image regions at different defocus values are then shifted to align their first zeros and averaged together. This averaging improves the SNR sufficiently that it becomes possible to determine the defocus for subsets of the tilt series rather than just the entire series. CTFPHASEFLIP corrects images line-by-line by inverting phases appropriately in thin strips of the image at nearly constant defocus. CTF correction by these methods is shown to improve the resolution of aligned, averaged particles extracted from tomograms. However, some restoration of Fourier amplitudes at high frequencies is important for seeing the benefits from CTF correction.     

goCTF: Geometrically optimized CTF determination for single-particle cryo-EM

Preferred particle orientation represents a recurring problem in single-particle cryogenic electron microcopy (cryo-EM). A specimen-independent approach through tilting has been attempted to increase particle orientation coverage, thus minimizing anisotropic three-dimensional (3D) reconstruction. However, focus gradient is a critical issue hindering tilt applications from being a general practice in single-particle cryo-EM. The present study describes a newly developed geometrically optimized approach, goCTF, to reliably determine the global focus gradient. A novel strategy of determining contrast transfer function (CTF) parameters from a sector of the signal preserved power spectrum is applied to increase reliability. Subsequently, per-particle based local focus refinement is conducted in an iterative manner to further improve the defocus accuracy. Novel diagnosis methods using a standard deviation defocus plot and goodness of fit heatmap have also been proposed to evaluate CTF fitting quality prior to 3D refinement. In a benchmark study, goCTF processed a published single-particle cryo-EM dataset for influenza hemagglutinin trimer collected at a 40-degree specimen tilt. The resulting 3D reconstruction map was improved from 4.1?Å to 3.7?Å resolution. The goCTF program is built on the open-source code of CTFFIND4, which adopts a consistent user interface for ease of use.     

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

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

Assessing the benefits of focal pair cryo-electron tomography

Cryo electron tomography provides nanometer-scale information on biological matter preserved in a close-to native state. The resolution of tomograms and structures resolved by sub-tomogram averaging is typically limited by the contrast transfer function of the electron microscope, which is especially critical for thick samples. Here, we report a method to increase the attainable resolution by recording tomographic 'focal pairs', which are pairs of tilt series of the same object acquired in complementary defocus conditions. Low defocus imaging provides high resolution at low contrast, while high defocus imaging yields high contrast at the price of limited resolution. Quantitative assessment of the quality of lipid bilayer reconstructions in the resulting tomograms demonstrates stable resolution preservation beyond 3 nm for cells thicker than 500 nm. Further, in computational simulations on synthetic datasets we show the applicability of the method to sub-tomogram averaging, demonstrating its potential for achieving higher resolution.     

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.     

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.     

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.     

TomoAlign: A novel approach to correcting sample motion and 3D CTF in CryoET

TomoAlign is a software package that integrates tools to mitigate two important resolution limiting factors in cryoET, namely the beam-induced sample motion and the contrast transfer function (CTF) of the microscope. The package is especially focused on cryoET of thick specimens where fiducial markers are required for accurate tilt-series alignment and sample motion estimation. TomoAlign models the beam-induced sample motion undergone during the tilt-series acquisition. The motion models are used to produce motion-corrected subtilt-series centered on the particles of interest. In addition, the defocus of each particle at each tilt image is determined and can be corrected, resulting in motion-corrected and CTF-corrected subtilt-series from which the subtomograms can be computed. Alternatively, the CTF information can be passed on so that CTF correction can be carried out entirely within external packages like Relion. TomoAlign serves as a versatile tool that can streamline the cryoET workflow from initial alignment of tilt-series to final subtomogram averaging during in situ structure determination.     

Three-Dimensional Reconstruction with Contrast Transfer Function Correction from Energy-Filtered Cryoelectron Micrographs: Procedure and Application to the 70SEscherichia coliRibosome

Cryoelectron microscopy provides the means of studying macromolecules in their native state. However, the contrast transfer function (CTF) makes the images and the three-dimensional (3D) maps derived from them difficult to interpret. We developed methods to determine the CTF from experimental data and to obtain a CTF-corrected 3D reconstruction. The CTF correction and 3D reconstruction accomplished in one step make it easy to combine different defocus data sets and decrease the error accumulation in the computation. These methods were applied to energy-filtered images of the 70SEscherichia coliribosome, resulting in a distortion-free 3D map of the ribosome at 1/24.5 Å⁻¹resolution, as determined by the differential phase residual resolution criterion.     

Practical Image Restoration of Thick Biological Specimens Using Multiple Focus Levels in Transmission Electron Microscopy

Three-dimensional electron tomographic studies of thick specimens such as cellular organelles or supramolecular structures require accurate interpretations of transmission electron micrograph intensities. In addition to microscope lens aberrations, thick specimen imaging is complicated by additional distortions resulting from multiple elastic and inelastic scattering. Extensive analysis of the mechanism of image formation using electron energy-loss spectroscopy and imaging as well as exit wavefront reconstruction demonstrated that multiple scattering does not contribute to the coherent component of the exit wave (Hanet al.,1996, 1995). Although exit wavefront restored images showed enhanced contrast and resolution, that technique, which requires the collection of more than 30 images at different focus levels, is not practical for routine data collection in 3D electron tomography, where usually over 100 projection views are required for each reconstruction. Using a 0.7-μm-thick specimen imaged at 200 keV, the accuracy of reconstructions using small numbers of defocused images and a simple linear filter (Schiske, 1968) was assessed by comparison to the complete exit wave restoration. We demonstrate that only four optimal focus levels are required to effectively restore the coherent component (deviation 5.1%). By contrast, the optimal single image (zero defocus) shows a 25.5% deviation to the exit wave restoration. Two pairs of under- and over-defocus images should be taken: one pair at quite high defocus (>10 μm) to differentiate the coherent (single elastic scattering) from the incoherent (multiple elastic and inelastic scattering) components, and the second pair to optimize information content at the highest desired resolution (e.g., 5 μm for (2.5 nm)⁻¹resolution). We also propose a new interpretation of the restored amplitude and phase components where the specimen mass-density is proportional to the logarithm of the amplitude component and linearly related to the phase component. This approach should greatly facilitate the collection of high resolution tomographic data from thick samples.     

Local refinement: an attempt to correct for shrinkage and distortion in electron tomography

A critical problem in electron tomography is the deformation of the specimen due to radiation, or "shrinkage," which interferes with image alignment and thereby limits resolution. Here, we describe a general strategy for refining preliminary reconstructions which allows the damage due to the shrinkage of plastic-embedded thin sectioned specimens (50-80 nm) to be corrected. The basic steps of the strategy involve: (a) the partition of the preliminary reconstruction into sub-volumes; (b) the extraction of corresponding sub-areas for each sub-volume from the micrographs of the tilt series; (c) the re-projection of each sub-volume according to the orientation parameters; and (d) the refinement of these parameters by correlating each sub-area to the corresponding computed projection. We tested the strategy by refining chemical synapses reconstructed from series imaged with conical, double and single tilt geometries. The results gathered with local refinement were evaluated by visually inspecting the structure of biological membranes in the maps. In an effort to quantify these improvements, we studied the refined maps using correlation criteria and mapped the corrections applied to the orientation parameters in each sub-volume of the reconstruction. Simulation experiments complemented the data gathered by correlation analysis. Based on these criteria, we concluded that local refinement significantly improves the overall quality of the reconstructions of chemical synapses calculated from series imaged with conical and double tilt geometries.     

Fast rotational matching of single-particle images

The presence of noise and absence of contrast in electron micrographs lead to a reduced resolution of the final 3D reconstruction, due to the inherent limitations of single-particle image alignment. The fast rotational matching (FRM) algorithm was introduced recently for an accurate alignment of 2D images under such challenging conditions. Here, we implemented this algorithm for the first time in a standard 3D reconstruction package used in electron microscopy. This allowed us to carry out exhaustive tests of the robustness and reliability in iterative orientation determination, classification, and 3D reconstruction on simulated and experimental image data. A classification test on GroEL chaperonin images demonstrates that FRM assigns up to 13% more images to their correct reference orientation, compared to the classical self-correlation function method. Moreover, at sub-nanometer resolution, GroEL and rice dwarf virus reconstructions exhibit a remarkable resolution gain of 10-20% that is attributed to the novel image alignment kernel.     

Dual-Axis Tomography: An Approach with Alignment Methods That Preserve Resolution

Tomographic reconstructions of biological specimens are now routinely being generated in our high voltage electron microscope by tilting the specimen around two orthogonal axes. Separate tomograms are computed from each tilt series. The two tomograms are aligned to each other with general 3-D linear transformations that can correct for distortions between the two tomograms, thus preserving the inherent resolution of the reconstruction throughout its volume. The 3-D Fourier transforms of the two tomograms are then selectively combined to achieve a single tomogram. Unlike a single-axis tomogram, a dual-axis tomogram shows good resolution for extended features at any orientation in the plane of the specimen; it also has improved resolution in the depth of the specimen. Calculations indicate that the improvements available from double tilting and from tilting to higher angles are largely additive. Actual and model data were used to assess whether varying the increment between tilted views in proportion to the cosine of the tilt angle would allow a reduction in the number of pictures required to achieve a given resolution of reconstruction. Analysis by Fourier sector correlation indicated that the variable tilt increment improved the reconstruction in some respects but degraded it in others. A varying tilt increment thus does not give an unqualified improvement, at least when using back-projection algorithms for the reconstruction.     

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.     

A binary segmentation approach for boxing ribosome particles in cryo EM micrographs

Three-dimensional reconstruction of ribosome particles from electron micrographs requires selection of many single-particle images. Roughly 100,000 particles are required to achieve approximately 10 A resolution. Manual selection of particles, by visual observation of the micrographs on a computer screen, is recognized as a bottleneck in automated single-particle reconstruction. This paper describes an efficient approach for automated boxing of ribosome particles in micrographs. Use of a fast, anisotropic non-linear reaction-diffusion method to pre-process micrographs and rank-leveling to enhance the contrast between particles and the background, followed by binary and morphological segmentation constitute the core of this technique. Modifying the shape of the particles to facilitate segmentation of individual particles within clusters and boxing the isolated particles is successfully attempted. Tests on a limited number of micrographs have shown that over 80% success is achieved in automatic particle picking.     

Scaling structure factor amplitudes in electron cryomicroscopy using X-Ray solution scattering

The structure factors derived from electron cryomicroscopic images are modified by the contrast transfer function of the microscope's objective lens and other influences. The phases of the structure factors can be corrected in a straightforward way when the positions of the contrast transfer function rings are determined. However, corrected amplitudes are also essential to yield an accurate distribution of mass in the reconstruction. The correct scale factors for the amplitudes are difficult to evaluate for data that are merged from many different micrographs. We opt to use X-ray solution scattering intensity from a concentrated suspension of the specimen to correct the amplitudes of the spherically averaged structure factors. When this approach is applied to the three-dimensional image data of ice-embedded acrosomal bundles, the core of a filament in a three-dimensional reconstruction of the acrosomal bundle becomes denser and matches more closely the outer density ascribed to scruin.     

Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only two-thirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized.     

Comparison of the decameric structure of peroxiredoxin-II by transmission electron microscopy and X-ray crystallography.

The decameric human erythrocyte protein torin is identical to the thiol-specific antioxidant protein-II (TSA-II), also termed peroxiredoxin-II (Prx-II). Single particle analysis from electron micrographs of Prx-II molecules homogeneously orientated across holes in the presence of a thin film of ammonium molybdate and trehalose has facilitated the production of a >/=20 A 3-D reconstruction by angular reconstitution that emphasises the D5 symmetry of the ring-like decamer. The X-ray structure for Prx-II was fitted into the transmission electron microscopic reconstruction by molecular replacement. The surface-rendered transmission electron microscopy (TEM) reconstruction correlates well with the solvent-excluded surface of the X-ray structure of the Prx-II molecule. This provides confirmation that transmission electron microscopy of negatively stained specimens, despite limited resolution, has the potential to reveal a valid representation of surface features of protein molecules. 2-D crystallisation of the Prx-II protein on mica as part of a TEM study resulted in the formation of a p2 crystal form with parallel linear arrays of stacked rings. This latter 2-D form correlates well with that observed from the 2.7 A X-ray structure of Prx-II solved from a new orthorhombic 3-D crystal form.     

Difference imaging of adenovirus: bridging the resolution gap between X-ray crystallography and electron microscopy.

While X-ray crystallography provides atomic resolution structures of proteins and small viruses, electron microscopy provides complementary structural information on the organization of larger assemblies at lower resolution. A novel combination of these two techniques has bridged this resolution gap and revealed the various structural components forming the capsid of human type 2 adenovirus. An image reconstruction of the intact virus, derived from cryo-electron micrographs, was deconvolved with an approximate contrast transfer function to mitigate microscope distortions. A model capsid was calculated from 240 copies of the crystallographic structure of the major capsid protein and filtered to the correct resolution. Subtraction of the calculated capsid from the corrected reconstruction gave a three-dimensional difference map revealing the minor proteins that stabilize the virion. Elongated density penetrating the hexon capsid at the facet edges was ascribed to polypeptide IIIa, a component required for virion assembly. Density on the inner surface of the capsid, connecting the ring of peripentonal hexons, was assigned as polypeptide VI, a component that binds DNA. Identification of the regions of hexon that contact the penton base suggests a structural mechanism for previously proposed events during cell entry.     

Maximum-Entropy Three-Dimensional Reconstruction with Deconvolution of the Contrast Transfer Function: A Test Application with Adenovirus

We have developed an objective, quantitative, and general algorithm to improve the fidelity of three-dimensional reconstructions made from electron micrographs while at the same time filtering much of the noise present in the recorded data. The new technique is called constrained maximum entropy tomography (COMET). The essence of the method is that it will produce the most featureless reconstruction that fits the projection data within their observational accuracy. In particular, the COMET procedure will minimise the detrimental effects of errors in the measured data and deconvolute the effects of the contrast transfer function. An objective test has been performed using COMET on a conventional image reconstruction obtained from cryo-electron micrographs of adenovirus. The density for hexon, the major coat protein of the virus, which is known to high resolution from X-ray crystallography, provided a known high-resolution control. The COMET reconstruction is in considerably better agreement with the crystallographic electron density than the original reconstruction, throughout the entire resolution range.