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.     

Unsupervised classification of single particles by cluster tracking in multi-dimensional space

In cryo-electron microscopy (cryo-EM) single-particle reconstruction, the heterogeneity of two-dimensional projection image data resulting from the co-existence of different conformational or ligand binding states of a macromolecular complex remains a major obstacle as it impairs the validity of reconstructed density maps and limits the progress toward higher resolution. Classification of cryo-EM data according to the different conformations is difficult because of the coexistence of multiple orientations in a single dataset. Here, we present an unsupervised classification method, termed cluster tracking, which utilizes the continuity in multi-dimensional space induced by angular adjacency of projections in large datasets. In a proof of concept, the testing of cluster tracking on simulated projection data, which were generated from multiple conformations and orientations of an existing volume, produced clusters that are consistent with the conformational identity of the data. The application of the method to experimental cryo-EM projection data is found to result in a partition similar to the one generated by supervised classification.     

A dose-rate effect in single-particle electron microscopy

A low beam intensity, low electron dose imaging method has been developed for single-particle electron cryo-microscopy (cryo-EM). Experiments indicate that the new technique can reduce beam-induced specimen movement and secondary radiolytic effects, such as "bubbling". The improvement in image quality, especially for multiple-exposure data collection, will help single-particle cryo-EM to reach higher resolution.     

In silico reconstitution of DNA replication. Lessons from single-molecule imaging and cryo-tomography applied to single-particle cryo-EM

DNA replication has been reconstituted in vitro with yeast proteins, and the minimal system requires the coordinated assembly of 16 distinct replication factors, consisting of 42 polypeptides. To understand the molecular interplay between these factors at the single residue level, new structural biology tools are being developed. Inspired by advances in single-molecule fluorescence imaging and cryo-tomography, novel single-particle cryo-EM experiments have been used to characterise the structural mechanism for the loading of the replicative helicase. Here, we discuss how in silico reconstitution of single-particle cryo-EM data can help describe dynamic systems that are difficult to approach with conventional three-dimensional classification tools.     

A new cryo-EM single-particle ab initio reconstruction method visualizes secondary structure elements in an ATP-fueled AAA+ motor

The generation of ab initio three-dimensional (3D) models is a bottleneck in the studies of large macromolecular assemblies by single-particle cryo-electron microscopy. We describe here a novel method, in which established methods for two-dimensional image processing are combined with newly developed programs for joint rotational 3D alignment of a large number of class averages (RAD) and calculation of 3D volumes from aligned projections (VolRec). We demonstrate the power of the method by reconstructing an ∼ 660-kDa ATP-fueled AAA+ motor to 7.5 Å resolution, with secondary structure elements identified throughout the structure. We propose the method as a generally applicable automated strategy to obtain 3D reconstructions from unstained single particles imaged in vitreous ice.     

Deep generative modeling for volume reconstruction in cryo-electron microscopy

Advances in cryo-electron microscopy (cryo-EM) for high-resolution imaging of biomolecules in solution have provided new challenges and opportunities for algorithm development for 3D reconstruction. Next-generation volume reconstruction algorithms that combine generative modelling with end-to-end unsupervised deep learning techniques have shown promise, but many technical and theoretical hurdles remain, especially when applied to experimental cryo-EM images. In light of the proliferation of such methods, we propose here a critical review of recent advances in the field of deep generative modelling for cryo-EM reconstruction. The present review aims to (i) provide a unified statistical framework using terminology familiar to machine learning researchers with no specific background in cryo-EM, (ii) review the current methods in this framework, and (iii) outline outstanding bottlenecks and avenues for improvements in the field.     

High-resolution structure of phosphoketolase from Bifidobacterium longum determined by cryo-EM single-particle analysis

In bifidobacteria, phosphoketolase (PKT) plays a key role in the central hexose fermentation pathway called “bifid shunt.” The three-dimensional structure of PKT from Bifidobacterium longum with co-enzyme thiamine diphosphate (ThDpp) was determined at 2.1 Å resolution by cryo-EM single-particle analysis using 196,147 particles to build up the structural model of a PKT octamer related by D₄ symmetry. Although the cryo-EM structure of PKT was almost identical to the X-ray crystal structure previously determined at 2.2 Å resolution, several interesting structural features were observed in the cryo-EM structure. Because this structure was solved at relatively high resolution, it was observed that several amino acid residues adopt multiple conformations. Among them, Q546–D547–H548–N549 (the QN-loop) demonstrate the largest structural change, which seems to be related to the enzymatic function of PKT. The QN-loop is at the entrance to the substrate binding pocket. The minor conformer of the QN-loop is similar to the conformation of the QN-loop in the crystal structure. The major conformer is located further from ThDpp than the minor conformer. Interestingly, the major conformer in the cryo-EM structure of PKT resembles the corresponding loop structure of substrate-bound Escherichia coli transketolase. That is, the minor and major conformers may correspond to “closed” and “open” states for substrate access, respectively. Moreover, because of the high-resolution analysis, many water molecules were observed in the cryo-EM structure of PKT. Structural features of the water molecules in the cryo-EM structure are discussed and compared with water molecules observed in the crystal structure.     

New method for global alignment of 2 DNA sequences by the tree data structure

We introduce a new approach to investigate problem of DNA sequence alignment. The method consists of three parts: (i) simple alignment algorithm, (ii) extension algorithm for largest common substring, (iii) graphical simple alignment tree (GSA tree). The approach firstly obtains a graphical representation of scores of DNA sequences by the scoring equation R₀*R−S₀*S−T₀*(a+bk). Then a GSA tree is constructed to facilitate solving the problem for global alignment of 2 DNA sequences. Finally we give several practical examples to illustrate the utility and practicality of the approach.     

An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent (“spectral”) signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.     

CryoRes: Local Resolution Estimation of Cryo-EM Density Maps by Deep Learning

Recent progress in cryo-EM research has ignited a revolution in biological macromolecule structure determination. Resolution is an essential parameter for quality assessment of a cryo-EM density map, and it is known that resolution varies in different regions of a map. Currently available methods for local resolution estimation require manual adjustment of parameters and in some cases necessitate acquisition or de novo generation of so-called “half maps”. Here, we developed CryoRes, a deep-learning algorithm to estimate local resolution directly from a single final cryo-EM density map, specifically by learning resolution-aware patterns of density map voxels through supervised training on a large dataset comprising 1,174 experimental cryo-EM density maps. CryoRes significantly outperforms all of the state-of-the-art competing resolution estimation methods, achieving an average RMSE of 2.26 Å for local resolution estimation relative to the currently most reliable FSC-based method blocres, yet requiring only the single final map as input. Further, CryoRes is able to generate a molecular mask for each map, with accuracy 12.12% higher than the masks generated by ResMap. CryoRes is ultra-fast, fully automatic, parameter-free, applicable to cryo-EM subtomogram data, and freely available at https://cryores.zhanglab.net.     

Single-particle cryo-EM reveals conformational variability of the oligomeric VCC β-barrel pore in a lipid bilayer

Vibrio cholerae cytolysin (VCC) is a water-soluble, membrane-damaging, pore-forming toxin (PFT) secreted by pathogenic V. cholerae, which causes eukaryotic cell death by altering the plasma membrane permeability. VCC self-assembles on the cell surface and undergoes a dramatic conformational change from prepore to heptameric pore structure. Over the past few years, several high-resolution structures of detergent-solubilized PFTs have been characterized. However, high-resolution structural characterization of small β-PFTs in a lipid environment is still rare. Therefore, we used single-particle cryo-EM to characterize the structure of the VCC oligomer in large unilamellar vesicles, which is the first atomic-resolution cryo-EM structure of VCC. From our study, we were able to provide the first documented visualization of the rim domain amino acid residues of VCC interacting with lipid membrane. Furthermore, cryo-EM characterization of lipid bilayer–embedded VCC suggests interesting conformational variabilities, especially in the transmembrane channel, which could have a potential impact on the pore architecture and assist us in understanding the pore formation mechanism.     

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.     

A Maximum-Likelihood Approach to Single-Particle Image Refinement

The alignment of single-particle images fails at low signal-to-noise ratios and small particle sizes, because noise produces false peaks in the cross-correlation function used for alignment. A maximum-likelihood approach to the two-dimensional alignment problem is described which allows the underlying structure to be estimated from large data sets of very noisy images. Instead of finding the optimum alignment for each image, the algorithm forms a weighted sum over all possible in-plane rotations and translations of the image. The weighting factors, which are the probabilities of the image transformations, are computed as the exponential of a cross-correlation function. Simulated data sets were constructed and processed by the algorithm. The results demonstrate a greatly reduced sensitivity to the choice of a starting reference, and the ability to recover structures from large data sets having very low signal-to-noise ratios.     

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.

     

Direct electron detection yields cryo-EM reconstructions at resolutions beyond 3/4 Nyquist frequency

One limitation in electron cryo-microscopy (cryo-EM) is the inability to recover high-resolution signal from the image-recording media at the full-resolution limit of the transmission electron microscope. Direct electron detection using CMOS-based sensors for digitally recording images has the potential to alleviate this shortcoming. Here, we report a practical performance evaluation of a Direct Detection Device (DDD®) for biological cryo-EM at two different microscope voltages: 200 and 300 kV. Our DDD images of amorphous and graphitized carbon show strong per-pixel contrast with image resolution near the theoretical sampling limit of the data. Single-particle reconstructions of two frozen-hydrated bacteriophages, P22 and ε15, establish that the DDD is capable of recording usable signal for 3D reconstructions at about 4/5 of the Nyquist frequency, which is a vast improvement over the performance of conventional imaging media. We anticipate the unparalleled performance of this digital recording device will dramatically benefit cryo-EM for routine tomographic and single-particle structural determination of biological specimens.     

Fitting low-resolution cryo-EM maps of proteins using constrained geometric simulations

Recent experimental advances in producing density maps from cryo-electron microscopy (cryo-EM) have challenged theorists to develop improved techniques to provide structural models that are consistent with the data and that preserve all the local stereochemistry associated with the biomolecule. We develop a new technique that maintains the local geometry and chemistry at each stage of the fitting procedure. A geometric simulation is used to drive the structure from some appropriate starting point (a nearby experimental structure or a modeled structure) toward the experimental density, via a set of small incremental motions. Structural motifs such as α-helices can be held rigid during the fitting procedure as the starting structure is brought into alignment with the experimental density. After validating this procedure on simulated data for adenylate kinase and lactoferrin, we show how cryo-EM data for two different GroEL structures can be fit using a starting x-ray crystal structure. We show that by incorporating the correct local stereochemistry in the modeling, structures can be obtained with effective resolution that is significantly higher than might be expected from the nominal cryo-EM resolution.     

Bacillus aryabhattai FACU: A promising bacterial strain capable of manipulate the glyphosate herbicide residues

Glyphosate is a commonly used organophosphate herbicide that has an adverse impact on humans, mammals and soil microbial ecosystems. The redundant utilize of glyphosate to control weed growth cause the pollution of the soil environment by this chemical. The discharge of glyphosate in the agricultural drainage can also cause serious environmental damage and water pollution problems. Therefore, it is important to develop methods for enhancing glyphosate degradation in the soil through bioremediation. In this study, thirty bacterial isolates were selected from an agro-industrial zone located in Sadat City of Monufia Governorate, Egypt. The isolates were able to grow in LB medium supplemented with 7.2 mg/ml glyphosate. Ten isolates only had the ability to grow in a medium containing different concentrations of glyphosate (50, 100, 150, 200 and 250 mg/ml). The FACU3 bacterial isolate showed the highest CFU in the different concentrations of glyphosate. The FACU3 isolate was Gram-positive, spore-forming and rod-shape bacteria. Based on API 50 CHB/E medium kit, biochemical properties and 16S rRNA gene sequencing, the FACU3 isolate was identified as Bacillus aryabhattai. Different bioinformatics tools, including multiple sequence alignment (MSA), basic local alignment search tool (BLAST) and primer alignment, were used to design specific primers for goxB gene amplification and isolation. The goxB gene encodes FAD-dependent glyphosate oxidase enzyme that responsible for biodegradation process. The selected primers were successfully used to amplify the goxB gene from Bacillus aryabhattai FACU3. The results indicated that the Bacillus aryabhattai FACU3 can be utilized in glyphosate-contaminated environments for bioremediation. According to our knowledge, this is the first time to isolate of FAD-dependent glyphosate oxidase (goxB) gene from Bacillus aryabhattai.     

Engineering cell alignment in vitro

Cell alignment plays a critical role in various cell behaviors including cytoskeleton reorganization, membrane protein relocation, nucleus gene expression, and ECM remodeling. Cell alignment is also known to exert significant effects on tissue regeneration (e.g., neuron) and modulate mechanical properties of tissues including skeleton, cardiac muscle and tendon. Therefore, it is essential to engineer cell alignment in vitro for biomechanics, cell biology, tissue engineering and regenerative medicine applications. With advances in nano- and micro-scale technologies, a variety of approaches have been developed to engineer cell alignment in vitro, including mechanical loading, topographical patterning, and surface chemical treatment. In this review, we first present alignments of various cell types and their functionality in different tissues in vivo including muscle and nerve tissues. Then, we provide an overview of recent approaches for engineering cell alignment in vitro. Finally, concluding remarks and perspectives are addressed for future improvement of engineering cell alignment.     

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.     

Structural Identification of Individual Helical Amyloid Filaments by Integration of Cryo-Electron Microscopy-Derived Maps in Comparative Morphometric Atomic Force Microscopy Image Analysis

The presence of amyloid fibrils is a hallmark of more than 50 human disorders, including neurodegenerative diseases and systemic amyloidoses. A key unresolved challenge in understanding the involvement of amyloid in disease is to explain the relationship between individual structural polymorphs of amyloid fibrils, in potentially mixed populations, and the specific pathologies with which they are associated. Although cryo-electron microscopy (cryo-EM) and solid-state nuclear magnetic resonance (ssNMR) spectroscopy methods have been successfully employed in recent years to determine the structures of amyloid fibrils with high resolution detail, they rely on ensemble averaging of fibril structures in the entire sample or significant subpopulations. Here, we report a method for structural identification of individual fibril structures imaged by atomic force microscopy (AFM) by integration of high-resolution maps of amyloid fibrils determined by cryo-EM in comparative AFM image analysis. This approach was demonstrated using the hitherto structurally unresolved amyloid fibrils formed in vitro from a fragment of tau (297–391), termed ‘dGAE’. Our approach established unequivocally that dGAE amyloid fibrils bear no structural relationship to heparin-induced tau fibrils formed in vitro. Furthermore, our comparative analysis resulted in the prediction that dGAE fibrils are structurally closely related to the paired helical filaments (PHFs) isolated from Alzheimer’s disease (AD) brain tissue characterised by cryo-EM. These results show the utility of individual particle structural analysis using AFM, provide a workflow of how cryo-EM data can be incorporated into AFM image analysis and facilitate an integrated structural analysis of amyloid polymorphism.