Cryo-EM density maps adjustment for subtraction,consensus and sharpening

Electron cryomicroscopy (cryo-EM) has emerged as a powerful structural biology instrument to solve near-atomic three-dimensional structures. Despite the fast growth in the number of density maps generated from cryo-EM data, comparison tools among these reconstructions are still lacking. Current proposals to compare cryo-EM data derived volumes perform map subtraction based on adjustment of each volume grey level to the same scale. We present here a more sophisticated way of adjusting the volumes before comparing, which implies adjustment of grey level scale and spectrum energy, but keeping phases intact inside a mask and imposing the results to be strictly positive. The adjustment that we propose leaves the volumes in the same numeric frame, allowing to perform operations among the adjusted volumes in a more reliable way. This adjustment can be a preliminary step for several applications such as comparison through subtraction, map sharpening, or combination of volumes through a consensus that selects the best resolved parts of each input map. Our development might also be used as a sharpening method using an atomic model as a reference. We illustrate the applicability of this algorithm with the reconstructions derived of several experimental examples. This algorithm is implemented in Xmipp software package and its applications are user-friendly accessible through the cryo-EM image processing framework Scipion.     

Developing a denoising filter for electron microscopy and tomography data in the cloud

The low radiation conditions and the predominantly phase-object image formation of cryo-electron microscopy (cryo-EM) result in extremely high noise levels and low contrast in the recorded micrographs. The process of single particle or tomographic 3D reconstruction does not completely eliminate this noise and is even capable of introducing new sources of noise during alignment or when correcting for instrument parameters. The recently developed Digital Paths Supervised Variance (DPSV) denoising filter uses local variance information to control regional noise in a robust and adaptive manner. The performance of the DPSV filter was evaluated in this review qualitatively and quantitatively using simulated and experimental data from cryo-EM and tomography in two and three dimensions. We also assessed the benefit of filtering experimental reconstructions for visualization purposes and for enhancing the accuracy of feature detection. The DPSV filter eliminates high-frequency noise artifacts (density gaps), which would normally preclude the accurate segmentation of tomography reconstructions or the detection of alpha-helices in single-particle reconstructions. This collaborative software development project was carried out entirely by virtual interactions among the authors using publicly available development and file sharing tools.     

Helical structure of unidirectionally shadowed metal replicas of cyanide hydratase from Gloeocercospora sorghi

The helical filaments of the cyanide hydratase from Gloeocercospora sorghi have been reconstructed in three dimensions from freeze dried, unidirectionally shadowed specimens using iterative real-space helical reconstruction. The average power spectrum of all selected images has three clear reflections on different layer lines. The reconstruction is complicated by the fact that three possible indexing schemes are possible and reconstructions using the starting symmetries based on each of these indexing schemes converge on three-dimensional volumes which appear plausible. Because only one side is visible in shadowed specimens, it is necessary to examine the phases from a single filament by cryo-electron microscopy in order to make an unequivocal assignment of the symmetry. Because of the novel nature of the reconstruction method used here, conventional cryo-EM methods were also used to determine a second reconstruction, allowing us to make comparisons between the two. The filament is shown to have a left-handed one-start helix with D(1) symmetry, 5.46 dimers per turn and a pitch of 7.15nm. The reconstruction suggests the presence of an interaction across the groove not previously seen in nitrilase helical fibres.     

Three-dimensional spectral signal-to-noise ratio for a class of reconstruction algorithms

A three-dimensional (3D) version of the spectral signal-to-noise ratio (SSNR)-based resolution measure is introduced. The measure is defined for a class of 3D reconstruction algorithms that use interpolation in Fourier space. The statistical properties of the SSNR are discussed and related to the properties of another resolution measure, the Fourier shell correlation (FSC). The new measure was tested on 3D structures calculated from a simulated set of quasi-evenly spaced 2D projections using a nearest-neighbor interpolation and a gridding algorithm. In the latter case, the results agree very well with the FSC-based estimate, with the exception of very high SSNR values. The main applicability of the 3D SSNR is tomography, where due to the small number of projections collected, FSC cannot be used. The new measure was applied to three sets of tomographic data. It was demonstrated that the measure is sufficiently sensitive to yield theoretically expected results. Therefore, the 3D SSNR opens up the possibility of evaluating the quality of tomographic reconstructions in an objective manner. The 3D distribution of SSNR is of major interest in single-particle analysis. It is shown that the new measure can be used to evaluate the anisotropy of 3D reconstructions. The distribution of SSNR is characterized by three anisotropy indices derived from principal axes of the 3D inertia covariance matrix of the SSNR. These indices are used to construct a 3D Fourier filter which, when applied to a 3D reconstruction of a macromolecule, maximizes the SNR in real space and minimizes real-space artifacts caused by uneven distribution of 2D projections.     

Loop L5 Assumes Three Distinct Orientations during the ATPase Cycle of the Mitotic Kinesin Eg5: A TRANSIENT AND TIME-RESOLVED FLUORESCENCE STUDY*

Members of the kinesin superfamily of molecular motors differ in several key structural domains, which probably allows these molecular motors to serve the different physiologies required of them. One of the most variable of these is a stem-loop motif referred to as L5. This loop is longest in the mitotic kinesin Eg5, and previous structural studies have shown that it can assume different conformations in different nucleotide states. However, enzymatic domains often consist of a mixture of conformations whose distribution shifts in response to substrate binding or product release, and this information is not available from the “static” images that structural studies provide. We have addressed this issue in the case of Eg5 by attaching a fluorescent probe to L5 and examining its fluorescence, using both steady state and time-resolved methods. This reveals that L5 assumes an equilibrium mixture of three orientations that differ in their local environment and segmental mobility. Combining these studies with transient state kinetics demonstrates that there is a major shift in this distribution during transitions that interconvert weak and strong microtubule binding states. Finally, in conjunction with previous cryo-EM reconstructions of Eg5·microtubule complexes, these fluorescence studies suggest a model in which L5 regulates both nucleotide and microtubule binding through a set of reversible interactions with helix α3. We propose that these features facilitate the production of sustained opposing force by Eg5, which underlies its role in supporting formation of a bipolar spindle in mitosis.     

How to correct relative voxel scale factors for calculations of vector-difference Fourier maps in cryo-EM

The atomic coordinates derived from cryo-electron microscopy (cryo-EM) maps can be inaccurate when the voxel scaling factors are not properly calibrated. Here, we describe a method for correcting relative voxel scaling factors between pairs of cryo-EM maps for the same or similar structures that are expanded or contracted relative to each other. We find that the correction of scaling factors reduces the amplitude differences of Fourier-inverted structure factors from voxel-rescaled maps by up to 20–30%, as shown by two cryo-EM maps of the SARS-CoV-2 spike protein measured at pH 4.0 and pH 8.0. This allows for the calculation of the difference map after properly scaling, revealing differences between the two structures for individual amino acid residues. Unexpectedly, the analysis uncovers two previously overlooked differences of amino acid residues in structures and their local structural changes. Furthermore, we demonstrate the method as applied to two cryo-EM maps of monomeric apo-photosystem II from the cyanobacteria Synechocystis sp. PCC 6803 and Thermosynechococcus elongatus. The resulting difference maps reveal many changes in the peripheral transmembrane PsbX subunit between the two species.     

Exploring high-resolution cryo-ET and subtomogram averaging capabilities of contemporary DEDs

The potential of energy filtering and direct electron detection for cryo-electron microscopy (cryo-EM) has been well documented. Here, we assess the performance of recently introduced hardware for cryo-electron tomography (cryo-ET) and subtomogram averaging (STA), an increasingly popular structural determination method for complex 3D specimens. We acquired cryo-ET datasets of EIAV virus-like particles (VLPs) on two contemporary cryo-EM systems equipped with different energy filters and direct electron detectors (DED), specifically a Krios G4, equipped with a cold field emission gun (CFEG), Thermo Fisher Scientific Selectris X energy filter, and a Falcon 4 DED; and a Krios G3i, with a Schottky field emission gun (XFEG), a Gatan Bioquantum energy filter, and a K3 DED. We performed constrained cross-correlation-based STA on equally sized datasets acquired on the respective systems. The resulting EIAV CA hexamer reconstructions show that both systems perform comparably in the 4–6 Å resolution range based on Fourier-Shell correlation (FSC). In addition, by employing a recently introduced multiparticle refinement approach, we obtained a reconstruction of the EIAV CA hexamer at 2.9 Å. Our results demonstrate the potential of the new generation of energy filters and DEDs for STA, and the effects of using different processing pipelines on their STA outcomes.     

Practical considerations for using K3 cameras in CDS mode for high-resolution and high-throughput single particle cryo-EM

Detector technology plays a pivotal role in high-resolution and high-throughput cryo-EM structure determination. Compared with the first-generation, single-electron counting direct detection camera (Gatan K2), the latest K3 camera is faster, larger, and now offers a correlated-double sampling mode (CDS). Importantly this results in a higher DQE and improved throughput compared to its predecessor. In this study, we focused on optimizing camera data collection parameters for daily use within a cryo-EM facility and explored the balance between throughput and resolution. In total, eight data sets of murine heavy-chain apoferritin were collected at different dose rates and magnifications, using 9-hole image shift data collection strategies. The performance of the camera was characterized by the quality of the resultant 3D reconstructions. Our results demonstrated that the Gatan K3 operating in CDS mode outperformed standard (nonCDS) mode in terms of reconstruction resolution in all tested conditions with 8 electrons per pixel per second being the optimal dose rate. At low magnification (64kx) we were able to achieve reconstruction resolutions of 149% of the physical Nyquist limit (1.8 Å with a 1.346 Å physical pixel size). Low magnification allows more particles to be collected per image, aiding analysis of heterogeneous samples requiring large data sets. At moderate magnification (105kx, 0.834 Å physical pixel size) we achieved a resolution of 1.65 Å within 8-h of data collection, a condition optimal for achieving high-resolution on well behaved samples. Our results also show that for an optimal sample like apoferritin, one can achieve better than 2.5 Å resolution with 5 min of data collection. Together, our studies validate the most efficient ways of imaging protein complexes using the K3 direct detector and will greatly benefit the cryo-EM community.     

Cryo-EM image alignment: From pair-wise to joint with deep unsupervised difference learning

Cryo-electron microscopy (cryo-EM) single-particle analysis is a revolutionary imaging technique to resolve and visualize biomacromolecules. Image alignment in cryo-EM is an important and basic step to improve the precision of the image distance calculation. However, it is a very challenging task due to high noise and low signal-to-noise ratio. Therefore, we propose a new deep unsupervised difference learning (UDL) strategy with novel pseudo-label guided learning network architecture and apply it to pair-wise image alignment in cryo-EM. The training framework is fully unsupervised. Furthermore, a variant of UDL called joint UDL (JUDL), is also proposed, which is capable of utilizing the similarity information of the whole dataset and thus further increase the alignment precision. Assessments on both real-world and synthetic cryo-EM single-particle image datasets suggest the new unsupervised joint alignment method can achieve more accurate alignment results. Our method is highly efficient by taking advantages of GPU devices. The source code of our methods is publicly available at “http://www.csbio.sjtu.edu.cn/bioinf/JointUDL/” for academic use.     

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.     

Rapid increase of near atomic resolution virus capsid structures determined by cryo-electron microscopy

The recent technological advances in electron microscopes, detectors, as well as image processing and reconstruction software have brought single particle cryo-electron microscopy (cryo-EM) into prominence for determining structures of bio-molecules at near atomic resolution. This has been particularly true for virus capsids, ribosomes, and other large assemblies, which have been the ideal specimens for structural studies by cryo-EM approaches. An analysis of time series metadata of virus structures on the methods of structure determination, resolution of the structures, and size of the virus particles revealed a rapid increase in the virus structures determined by cryo-EM at near atomic resolution since 2010. In addition, the data highlight the median resolution (～3.0?Å) and size (～310.0?Å in diameter) of the virus particles determined by X-ray crystallography while no such limits exist for cryo-EM structures, which have a median diameter of 508?Å. Notably, cryo-EM virus structures in the last four years have a median resolution of 3.9?Å. Taken together with minimal sample requirements, not needing diffraction quality crystals, and being able to achieve similar resolutions of the crystal structures makes cryo-EM the method of choice for current and future virus capsid structure determinations.     

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.     

Revisiting the structure of Alvinella pompejana hemoglobin at 20A resolution by cryoelectron microscopy

The hemoglobin of the polychaete worm Alvinella pompejana was reconstructed at 20A resolution from frozen-hydrated samples observed by electron microscopy according to the random conical tilt series method. This three-dimensional reconstruction was mirror-inverted with respect to a previous volume published by de Haas et al. in 1996. In order to explain this handedness discrepancy, various 3D reconstructions using different reference volumes were carried out showing that the choice of the first volume was the keystone during the refinement process. The 3D reconstruction volume of A. pompejana Hb presented structural features characteristic of annelid Hbs with two hexagonal layers each comprising six hollow globular subassemblies and a complex of non-heme linker chains. Moreover, the eclipsed conformation of the two hexagonal layers and a HGS architecture similar to that described for Arenicola marina Hb led to the conclusion that A. pompejana Hb belonged to the architectural type II according to the definition of Jouan et al. (2001). A comparison between this cryo-EM volume and X-ray crystallography density maps of Lumbricus terrestris type-I Hb (Royer et al., 2000) showed that the triple stranded coiled coil structures of linker chains were different. Based on this observation, a model was proposed to explain the eclipsed conformation of the two hexagonal layers of type-II Hbs.     

Robust filtering and particle picking in micrograph images towards 3D reconstruction of purified proteins with cryo-electron microscopy

In order to make a high resolution model of macromolecular structures from cryo-electron microscope (cryo-EM) raw images one has to be precise at every processing step from particle picking to 3D image reconstruction. In this paper we propose a collection of novel methods for filtering cryo-EM images and for automatic picking of particles. These methods have been developed for two cases: (1) when particles can be identified and (2) when particle are not distinguishable. The advantages of these methods are demonstrated in standard purified protein samples and to generalize them we do not use any ad hoc presumption of the geometry of the particle projections. We have also suggested a filtering method to increase the signal-to-noise (S/N) ratio which has proved to be useful for other levels of reconstruction, i.e., finding orientations and 3D model reconstruction.     

Structural Characterization of the Bacteriophage T7 Tail Machinery

Most bacterial viruses need a specialized machinery, called “tail,” to inject their genomes inside the bacterial cytoplasm without disrupting the cellular integrity. Bacteriophage T7 is a well characterized member of the Podoviridae family infecting Escherichia coli, and it has a short noncontractile tail that assembles sequentially on the viral head after DNA packaging. The T7 tail is a complex of around 2.7 MDa composed of at least four proteins as follows: the connector (gene product 8, gp8), the tail tubular proteins gp11 and gp12, and the fibers (gp17). Using cryo-electron microscopy and single particle image reconstruction techniques, we have determined the precise topology of the tail proteins by comparing the structure of the T7 tail extracted from viruses and a complex formed by recombinant gp8, gp11, and gp12 proteins. Furthermore, the order of assembly of the structural components within the complex was deduced from interaction assays with cloned and purified tail proteins. The existence of common folds among similar tail proteins allowed us to obtain pseudo-atomic threaded models of gp8 (connector) and gp11 (gatekeeper) proteins, which were docked into the corresponding cryo-EM volumes of the tail complex. This pseudo-atomic model of the connector-gatekeeper interaction revealed the existence of a common molecular architecture among viruses belonging to the three tailed bacteriophage families, strongly suggesting that a common molecular mechanism has been favored during evolution to coordinate the transition between DNA packaging and tail assembly.     

Cryo-electron microscope image denoising based on the geodesic distance

Background

To perform a three-dimensional (3-D) reconstruction of electron cryomicroscopy (cryo-EM) images of viruses, it is necessary to determine the similarity of image blocks of the two-dimensional (2-D) projections of the virus. The projections containing high resolution information are typically very noisy. Instead of the traditional Euler metric, this paper proposes a new method, based on the geodesic metric, to measure the similarity of blocks.

Results

Our method is a 2-D image denoising approach. A data set of 2243 cytoplasmic polyhedrosis virus (CPV) capsid particle images in different orientations was used to test the proposed method. Relative to Block-matching and three-dimensional filtering (BM3D), Stein’s unbiased risk estimator (SURE), Bayes shrink and K-means singular value decomposition (K-SVD), the experimental results show that the proposed method can achieve a peak signal-to-noise ratio (PSNR) of 45.65. The method can remove the noise from the cryo-EM image and improve the accuracy of particle picking.

Conclusions

The main contribution of the proposed model is to apply the geodesic distance to measure the similarity of image blocks. We conclude that manifold learning methods can effectively eliminate the noise of the cryo-EM image and improve the accuracy of particle picking.

     

Revelation of an enigmatic signaling machinery—First insights into the mammalian TRPC architecture

Canonical TRP channels (TRPCs) are a particularly enigmatic family of signaling molecules with multimodal sensing features, being involved in a wide range of biological functions. Until very recently, the main hurdle towards comprehensive mechanistic understanding of TRPC signaling has been the lack of structural information. This has changed early this year by several reports on TRPC architectures resolved by single particle cryo-EM analysis. These studies confirmed recently elaborated concepts on TRPC structure-function relations, and unveiled unanticipated features and complexity in the TRPC sensing machinery.     

Automated most-probable loss tomography of thick selectively stained biological specimens with quantitative measurement of resolution improvement

We describe the technique and application of energy filtering, automated most-probable loss (MPL) tomography to intermediate voltage electron microscopy (IVEM). We show that for thick, selectively stained biological specimens, this method produces a dramatic increase in resolution of the projections and the computed volumes versus standard unfiltered transmission electron microscopy (TEM) methods. This improvement in resolution is attributed to the reduction of chromatic aberration, which results from the large percentage of inelastic electron-scattering events for thick specimens. These improvements are particularly evident at the large tilt angles required to improve tomographic resolution in the z-direction. This method effectively increases the usable thickness of selectively stained samples that can be imaged at a given accelerating voltage by dramatically improving resolution versus unfiltered TEM and increasing signal-to-noise versus zero-loss imaging, thereby expanding the utility of the IVEM to deliver information from within specimens up to 3 microm thick.     

The resolution dependence of optimal exposures in liquid nitrogen temperature electron cryomicroscopy of catalase crystals

Electron beam damage is the fundamental limit to resolution in electron cryomicroscopy (cryo-EM) of frozen, hydrated specimens. Radiation damage increases with the number of electrons used to obtain an image and affects information at higher spatial frequencies before low-resolution information. For the experimentalist, a balance exists between electron exposures sufficient to obtain a useful signal-to-noise ratio (SNR) in images and exposures that limit the damage to structural features. In single particle cryo-EM this balance is particularly delicate: low-resolution features must be imaged with a sufficient SNR to allow image alignment so that high-resolution features recorded below the noise level can be recovered by averaging independent images. By measuring the fading of Fourier components from images obtained at 200 kV of thin crystals of catalase embedded in ice, we have determined the electron exposures that will maximize the SNR at resolutions between 86 and 2.9 Å. These data allow for a rational choice of exposure for single particle cryo-EM. For example, for 20 Å resolution, the SNR is maximized at ～20 e^?/Ų, whereas for 3 Å resolution, it is maximized at ～10 e^?/Ų. We illustrate the effects of exposure in single particle cryo-EM with data collected at ～12–15 and ～24–30 e^?/Ų.     

A measure for the angle between projections based on the extent of correlation between corresponding central sections

A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.