Three-dimensional reconstruction of single particles embedded in ice

Non-uniform Fourier transform based image classification in single-particle Cryo-EM

In the single-particle Cryo-EM projection image classification, it is a common practice to apply the Fourier transform to the images and extract rotation-invariant features in the frequency domain. However, this process involves interpolation, which can reduce the accuracy of the results. In contrast, the non-uniform Fourier transform provides more direct and accurate computation of rotation-invariant features without the need for interpolation in the computation process. Leveraging the capabilities of the non-uniform discrete Fourier transform (NUDFT), we have developed an algorithm for the rotation-invariant classification. To highlight its potential and applicability in the field of single-particle Cryo-EM, we conducted a direct comparison with the traditional Fourier transform and other methods, demonstrating the superior performance of the NUDFT.

The myth of high-resolution liquid phase biological electron microscopy

Cryo-electron microscopy (cryo-EM) has transformed structural biology over the past 12 years, with it now being routine rather than exceptional to reach a near-atomic level of resolution for proteins and macromolecular complexes. Samples are immobilized by vitrification and this sample can be maintained at liquid nitrogen temperatures in the vacuum of the electron microscope with negligible sublimation. Due to the low electron doses needed to avoid radiation damage, averaging over tens of thousands to hundreds of thousands of particle images is used to achieve a high signal-to-noise ratio. An alternative approach has been proposed where samples are at room temperature in the liquid state, maintained in the vacuum of the electron microscope by thin film enclosures that are relatively transparent to electrons while preventing evaporation of the liquid. A paper has argued that using this liquid-phase approach, higher resolution (3.2 Å) can be achieved than using cryo-EM (3.4 Å) when imaging and reconstructing adeno-associated virus particles. I show here that these assertions are untrue, and that basic principles in mathematics and physics would need to be violated to achieve the stated resolution in the liquid state. Thus, high resolution liquid phase EM of macromolecules remains science fiction.

Overcoming resolution attenuation during tilted cryo-EM data collection

Structural biology efforts using cryogenic electron microscopy are frequently stifled by specimens adopting "preferred orientations" on grids, leading to anisotropic map resolution and impeding structure determination. Tilting the specimen stage during data collection is a generalizable solution but has historically led to substantial resolution attenuation. Here, we develop updated data collection and image processing workflows and demonstrate, using multiple specimens, that resolution attenuation is negligible or significantly reduced across tilt angles. Reconstructions with and without the stage tilted as high as 60° are virtually indistinguishable. These strategies allowed the reconstruction to 3 Å resolution of a bacterial RNA polymerase with preferred orientation, containing an unnatural nucleotide for studying novel base pair recognition. Furthermore, we present a quantitative framework that allows cryo-EM practitioners to define an optimal tilt angle during data acquisition. These results reinforce the utility of employing stage tilt for data collection and provide quantitative metrics to obtain isotropic maps.

Overcoming Resolution Attenuation During Tilted Cryo-EM Data Collection

Structural biology efforts using cryogenic electron microscopy are frequently stifled by specimens adopting "preferred orientations" on grids, leading to anisotropic map resolution and impeding structure determination. Tilting the specimen stage during data collection is a generalizable solution but has historically led to substantial resolution attenuation. Here, we develop updated data collection and image processing workflows and demonstrate, using multiple specimens, that resolution attenuation is negligible or significantly reduced across tilt angles. Reconstructions with and without the stage tilted as high as 60° are virtually indistinguishable. These strategies allowed the reconstruction to 3 Å resolution of a bacterial RNA polymerase with preferred orientation. Furthermore, we present a quantitative framework that allows cryo-EM practitioners to define an optimal tilt angle for dataset acquisition. These data reinforce the utility of employing stage tilt for data collection and provide quantitative metrics to obtain isotropic maps.

Unsupervised Cryo-EM Images Denoising and Clustering Based on Deep Convolutional Autoencoder and K-Means+

Cryo-electron microscopy (cryo-EM) is a widely used structural determination technique. Because of the extremely low signal-to-noise ratio (SNR) of images captured by cryo-EM, clustering single-particle cryo-EM images with high accuracy is challenging. To address this, we proposed an iterative denoising and clustering method based on a deep convolutional variational autoencoder and K-means++. The proposed method contains two modules: a denoising ResNet variational autoencoder (DRVAE), and Balance size K-means++ (BSK-means++). First, the DRVAE is trained in a fully unsupervised manner to initialize the neural network and obtain preliminary denoised images. Second, BSK-means++ is built for clustering denoised images, and images closer to class centers are divided into reliable samples. Third, the training of DRVAE is continued, while the class-average images are used as pseudo supervision of reliable samples to reserve more detailed information of denoised images. Finally, the second and third steps mentioned above can be performed jointly and iteratively until convergence occurs. The experimental results showed that the proposed method can generate reliable class average images and achieve better clustering accuracy and normalized mutual information than current methods. This study confirmed that DRVAE with BSK-means++ could achieve a good denoise performance on single-particle cryo-EM images, which can help researchers obtain information such as symmetry and heterogeneity of the target particles. In addition, the proposed method avoids the extreme imbalance of class size, which improves the reliability of the clustering result.

Machine Learning for Structure Determination in Single-Particle Cryo-Electron Microscopy: A Systematic Review

Recently, single-particle cryo-electron microscopy (cryo-EM) has become an indispensable method for determining macromolecular structures at high resolution to deeply explore the relevant molecular mechanism. Its recent breakthrough is mainly because of the rapid advances in hardware and image processing algorithms, especially machine learning. As an essential support of single-particle cryo-EM, machine learning has powered many aspects of structure determination and greatly promoted its development. In this article, we provide a systematic review of the applications of machine learning in this field. Our review begins with a brief introduction of single-particle cryo-EM, followed by the specific tasks and challenges of its image processing. Then, focusing on the workflow of structure determination, we describe relevant machine learning algorithms and applications at different steps, including particle picking, 2-D clustering, 3-D reconstruction, and other steps. As different tasks exhibit distinct characteristics, we introduce the evaluation metrics for each task and summarize their dynamics of technology development. Finally, we discuss the open issues and potential trends in this promising field.

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.

Fast Cryo-EM Image Alignment Algorithm Using Power Spectrum Features

Cryo-electron microscopy (cryo-EM) single-particle image analysis is a powerful technique to resolve structures of biomacromolecules, while the challenge is that the cryo-EM image is of a low signal-to-noise ratio. For both two-dimensional image analysis and three-dimensional density map analysis, image alignment is an important step to improve the precision of the image distance calculation. In this paper, we introduce a new algorithm for performing two-dimensional pairwise alignment for cryo-EM particle images, which is based on the Fourier transform and power spectrum analysis. Compared to the existing heuristic iterative alignment methods, our method utilizes the signal distribution and signal feature on images' power spectrum to directly compute the alignment parameters. It does not require iterative computations and is robust against the cryo-EM image noise. Both theoretical analysis and experimental results suggest that our power-spectrum-feature-based alignment method is highly computational-efficient and is capable of offering effective alignment results. This new alignment algorithm is publicly available at: www.csbio.sjtu.edu.cn/bioinf/EMAF/for academic use.

Centering Noisy Images with Application to Cryo-EM

We target the problem of estimating the center of mass of objects in noisy two-dimensional images. We assume that the noise dominates the image, and thus many standard approaches are vulnerable to estimation errors, e.g., the direct computation of the center of mass and the geometric median which is a robust alternative to the center of mass. In this paper, we define a novel surrogate function to the center of mass. We present a mathematical and numerical analysis of our method and show that it outperforms existing methods for estimating the center of mass of an object in various realistic scenarios. As a case study, we apply our centering method to data from single-particle cryo-electron microscopy (cryo-EM), where the goal is to reconstruct the three-dimensional structure of macromolecules. We show how to apply our approach for a better translational alignment of molecule images picked from experimental data. In this way, we facilitate the succeeding steps of reconstruction and streamline the entire cryo-EM pipeline, saving computational time and supporting resolution enhancement.

DeepAlign, a 3D alignment method based on regionalized deep learning for Cryo-EM

Cryo Electron Microscopy (Cryo-EM) is currently one of the main tools to reveal the structural information of biological specimens at high resolution. Despite the great development of the techniques involved to solve the biological structures with Cryo-EM in the last years, the reconstructed 3D maps can present lower resolution due to errors committed while processing the information acquired by the microscope. One of the main problems comes from the 3D alignment step, which is an error-prone part of the reconstruction workflow due to the very low signal-to-noise ratio (SNR) common in Cryo-EM imaging. In fact, as we will show in this work, it is not unusual to find a disagreement in the alignment parameters in approximately 20-40% of the processed images, when outputs of different alignment algorithms are compared. In this work, we present a novel method to align sets of single particle images in the 3D space, called DeepAlign. Our proposal is based on deep learning networks that have been successfully used in plenty of problems in image classification. Specifically, we propose to design several deep neural networks on a regionalized basis to classify the particle images in sub-regions and, then, make a refinement of the 3D alignment parameters only inside that sub-region. We show that this method results in accurately aligned images, improving the Fourier shell correlation (FSC) resolution obtained with other state-of-the-art methods while decreasing computational time.

DRPnet: automated particle picking in cryo-electron micrographs using deep regression

BACKGROUND

Identification and selection of protein particles in cryo-electron micrographs is an important step in single particle analysis. In this study, we developed a deep learning-based particle picking network to automatically detect particle centers from cryoEM micrographs. This is a challenging task due to the nature of cryoEM data, having low signal-to-noise ratios with variable particle sizes, shapes, distributions, grayscale variations as well as other undesirable artifacts.

RESULTS

We propose a double convolutional neural network (CNN) cascade for automated detection of particles in cryo-electron micrographs. This approach, entitled Deep Regression Picker Network or "DRPnet", is simple but very effective in recognizing different particle sizes, shapes, distributions and grayscale patterns corresponding to 2D views of 3D particles. Particles are detected by the first network, a fully convolutional regression network (FCRN), which maps the particle image to a continuous distance map that acts like a probability density function of particle centers. Particles identified by FCRN are further refined to reduce false particle detections by the second classification CNN. DRPnet's first CNN pretrained with only a single cryoEM dataset can be used to detect particles from different datasets without retraining. Compared to RELION template-based autopicking, DRPnet results in better particle picking performance with drastically reduced user interactions and processing time. DRPnet also outperforms the state-of-the-art particle picking networks in terms of the supervised detection evaluation metrics recall, precision, and F-measure. To further highlight quality of the picked particle sets, we compute and present additional performance metrics assessing the resulting 3D reconstructions such as number of 2D class averages, efficiency/angular coverage, Rosenthal-Henderson plots and local/global 3D reconstruction resolution.

CONCLUSION

DRPnet shows greatly improved time-savings to generate an initial particle dataset compared to manual picking, followed by template-based autopicking. Compared to other networks, DRPnet has equivalent or better performance. DRPnet excels on cryoEM datasets that have low contrast or clumped particles. Evaluating other performance metrics, DRPnet is useful for higher resolution 3D reconstructions with decreased particle numbers or unknown symmetry, detecting particles with better angular orientation coverage.

Negative-Stain Electron Microscopy Reveals Dramatic Structural Rearrangements in Ni-Fe-S-Dependent Carbon Monoxide Dehydrogenase/Acetyl-CoA Synthase

The Ni-Fe-S-containing A-cluster of acetyl-coenzyme A (CoA) synthase (ACS) assembles acetyl-CoA from carbon monoxide (CO), a methyl group (CH3+), and CoA. To accomplish this feat, ACS must bind CoA and interact with two other proteins that contribute the CO and CH3+, respectively: CO dehydrogenase (CODH) and corrinoid Fe-S protein (CFeSP). Previous structural data show that, in the model acetogen Moorella thermoacetica, domain 1 of ACS binds to CODH such that a 70-Å-long internal channel is created that allows CO to travel from CODH to the A-cluster. The A-cluster is largely buried and is inaccessible to CFeSP for methylation. Here we use electron microscopy to capture multiple snapshots of ACS that reveal previously uncharacterized domain motion, forming extended and hyperextended structural states. In these structural states, the A-cluster is accessible for methylation by CFeSP.

Pre-pro is a fast pre-processor for single-particle cryo-EM by enhancing 2D classification

2D classification plays a pivotal role in analyzing single particle cryo-electron microscopy images. Here, we introduce a simple and loss-less pre-processor that incorporates a fast dimension-reduction (2SDR) de-noiser to enhance 2D classification. By implementing this 2SDR pre-processor prior to a representative classification algorithm like RELION and ISAC, we compare the performances with and without the pre-processor. Tests on multiple cryo-EM experimental datasets show the pre-processor can make classification faster, improve yield of good particles and increase the number of class-average images to generate better initial models. Testing on the nanodisc-embedded TRPV1 dataset with high heterogeneity using a 3D reconstruction workflow with an initial model from class-average images highlights the pre-processor improves the final resolution to 2.82 Å, close to 0.9 Nyquist. Those findings and analyses suggest the 2SDR pre-processor, of minimal cost, is widely applicable for boosting 2D classification, while its generalization to accommodate neural network de-noisers is envisioned.

A Review of Experimentally Informed Micromechanical Modeling of Nanoporous Metals: From Structural Descriptors to Predictive Structure-Property Relationships

Nanoporous metals made by dealloying take the form of macroscopic (mm- or cm-sized) porous bodies with a solid fraction of around 30%. The material exhibits a network structure of "ligaments" with an average ligament diameter that can be adjusted between 5 and 500 nm. Current research explores the use of nanoporous metals as functional materials with respect to electrochemical conversion and storage, bioanalytical and biomedical applications, and actuation and sensing. The mechanical behavior of the network structure provides the scope for fundamental research, particularly because of the high complexity originating from the randomness of the structure and the challenges arising from the nanosized ligaments, which can be accessed through an experiment only indirectly via the testing of the macroscopic properties. The strength of nanoscale ligaments increases systematically with decreasing size, and owing to the high surface-to-volume ratio their elastic and plastic properties can be additionally tuned by applying an electric potential. Therefore, nanoporous metals offer themselves as suitable model systems for exploring the structure-property relationships of complex interconnected microstructures as well as the basic mechanisms of the chemo-electro-mechanical coupling at interfaces. The micromechanical modeling of nanoporous metals is a rapidly growing field that strongly benefits from developments in computational methods, high-performance computing, and visualization techniques; it also benefits at the same time through advances in characterization techniques, including nanotomography, 3D image processing, and algorithms for geometrical and topological analysis. The review article collects articles on the structural characterization and micromechanical modeling of nanoporous metals and discusses the acquired understanding in the context of advancements in the experimental discipline. The concluding remarks are given in the form of a summary and an outline of future perspectives.

Preparation of Proteins and Macromolecular Assemblies for Cryo-electron Microscopy

Cryo-electron microscopy has become popular as the penultimate step on the road to structure determination for many proteins and macromolecular assemblies. The process of obtaining high-resolution images of a purified biomolecular complex in an electron microscope often follows a long, and in many cases exhaustive screening process in which many iterative rounds of protein purification are employed and the sample preparation procedure progressively re-evaluated in order to improve the distribution of particles visualized under the electron microscope, and thus maximize the opportunity for high-resolution structure determination. Typically, negative stain electron microscopy is employed to obtain a preliminary assessment of the sample quality, followed by cryo-EM which first requires the identification of optimal vitrification conditions. The original methods for frozen-hydrated specimen preparation developed over 40 years ago still enjoy widespread use today, although recent developments have set the scene for a future where more systematic and high-throughput approaches to the preparation of vitrified biomolecular complexes may be routinely employed. Here we summarize current approaches and ongoing innovations for the preparation of frozen-hydrated single particle specimens for cryo-EM, highlighting some of the commonly encountered problems and approaches that may help overcome these.

Full-length human cytomegalovirus terminase pUL89 adopts a two-domain structure specific for DNA packaging

A key step in replication of human cytomegalovirus (HCMV) in the host cell is the generation and packaging of unit-length genomes into preformed capsids. The enzymes involved in this process are the terminases. The HCMV terminase complex consists of two terminase subunits, the ATPase pUL56 and the nuclease pUL89. A potential third component pUL51 has been proposed. Even though the terminase subunit pUL89 has been shown to be essential for DNA packaging and interaction with pUL56, it is not known how pUL89 mechanistically achieves sequence-specific DNA binding and nicking. To identify essential domains and invariant amino acids vis-a-vis nuclease activity and DNA binding, alanine substitutions of predicted motifs were analyzed. The analyses indicated that aspartate 463 is an invariant amino acid for the nuclease activity, while argine 544 is an invariant aa for DNA binding. Structural analysis of recombinant protein using electron microscopy in conjunction with single particle analysis revealed a curvilinear monomer with two distinct domains connected by a thinner hinge-like region that agrees well with the predicted structure. These results allow us to model how the terminase subunit pUL89’s structure may mediate its function.

HCMV is a member of the herpesvirus family and represents a major human pathogen causing severe disease in newborns and immunocompromised patients for which the development of new non-nucleosidic antiviral agents are highly important. This manuscript focuses on DNA packaging, which is a target for development of new antivirals. The terminase subunit pUL89 is involved in this process. The paper presents the identification of DNA binding and nuclease motifs with invariant amino acids and highlights its first 3-D surface structure at approx. 3 nm resolution. At this resolution, the calculated 3-D surface structure matches well with the predicted structure. In conjunction with earlier studies it was possible to define structure-function relationships for the HCMV terminase subunit pUL89.

Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction

Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data.

Robustness of signal detection in cryo-electron microscopy via a bi-objective-function approach

Background

The detection of weak signals and selection of single particles from low-contrast micrographs of frozen hydrated biomolecules by cryo-electron microscopy (cryo-EM) represents a major practical bottleneck in cryo-EM data analysis. Template-based particle picking by an objective function using fast local correlation (FLC) allows computational extraction of a large number of candidate particles from micrographs. Another independent objective function based on maximum likelihood estimates (MLE) can be used to align the images and verify the presence of a signal in the selected particles. Despite the widespread applications of the two objective functions, an optimal combination of their utilities has not been exploited. Here we propose a bi-objective function (BOF) approach that combines both FLC and MLE and explore the potential advantages and limitations of BOF in signal detection from cryo-EM data.

Results

The robustness of the BOF strategy in particle selection and verification was systematically examined with both simulated and experimental cryo-EM data. We investigated how the performance of the BOF approach is quantitatively affected by the signal-to-noise ratio (SNR) of cryo-EM data and by the choice of initialization for FLC and MLE. We quantitatively pinpointed the critical SNR (~ 0.005), at which the BOF approach starts losing its ability to select and verify particles reliably. We found that the use of a Gaussian model to initialize the MLE suppresses the adverse effects of reference dependency in the FLC function used for template-matching.

Conclusion

The BOF approach, which combines two distinct objective functions, provides a sensitive way to verify particles for downstream cryo-EM structure analysis. Importantly, reference dependency of the FLC does not necessarily transfer to the MLE, enabling the robust detection of weak signals. Our insights into the numerical behavior of the BOF approach can be used to improve automation efficiency in the cryo-EM data processing pipeline for high-resolution structural determination.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2714-8) contains supplementary material, which is available to authorized users.

Clustering cryo-EM images of helical protein polymers for helical reconstructions

Helical protein polymers are often dynamic and complex assemblies, with many conformations and flexible domains possible within the helical assembly. During cryo-electron microscopy reconstruction, classification of the image data into homogeneous subsets is a critical step for achieving high resolution, resolving different conformations and elucidating functional mechanisms. Hence, methods aimed at improving the homogeneity of these datasets are becoming increasingly important. In this paper, we introduce a new algorithm that uses results from 2D image classification to sort 2D classes into groups of similar helical polymers. We show that our approach is able to distinguish helical polymers that differ in conformation, composition, and helical symmetry. Our results on test and experimental cases - actin filaments and amyloid fibrils - illustrate how our approach can be useful to improve the homogeneity of a data set. This method is exclusively applicable to helical polymers and other limitations are discussed.

Single-Particle Reconstruction of Biological Molecules-Story in a Sample (Nobel Lecture)

Pictures tell a thousand words: The development of single-particle cryo-electron microscopy set the stage for high-resolution structure determination of biological molecules. In his Nobel lecture, J. Frank describes the ground-breaking discoveries that have enabled the development of cryo-EM. The method has taken biochemistry into a new era.

Use of Cryo-EM to Study the Structure of Chemoreceptor Arrays In Vivo

Cryo-electron microscopy (cryo-EM) allows the imaging of intact macromolecular complexes in the context of whole cells. The biological samples for cryo-EM are kept in a near-native state by flash freezing, without the need for any additional sample preparation or fixation steps. Since transmission electron microscopy only generates 2D projections of the samples, the specimen has to be tilted in order to recover its 3D structural information. This is done by collecting images of the sample with various tilt angles in respect to the electron beam. The acquired tilt series can then be computationally back-projected. This technique is called electron cryotomography (ECT), and has been instrumental in unraveling the architecture of chemoreceptor arrays. Here we describe the method of visualizing in vivo bacterial chemoreceptor arrays in three main steps: immobilization of bacterial cells on EM grids by plunge-freezing; 2D image acquisition in tilt series; and 3D tomogram reconstruction.

MAHALANOBIS DISTANCE FOR CLASS AVERAGING OF CRYO-EM IMAGES

Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions. One of the main challenges in cryo-EM is the typically low signal to noise ratio (SNR) of the acquired images. 2D classification of images, followed by class averaging, improves the SNR of the resulting averages, and is used for selecting particles from micrographs and for inspecting the particle images. We introduce a new affinity measure, akin to the Mahalanobis distance, to compare cryo-EM images belonging to different defocus groups. The new similarity measure is employed to detect similar images, thereby leading to an improved algorithm for class averaging. We evaluate the performance of the proposed class averaging procedure on synthetic datasets, obtaining state of the art classification.

A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET).

Single-particle cryo-EM using alignment by classification (ABC): the structure of Lumbricus terrestris haemoglobin

Single-particle cryogenic electron microscopy (cryo-EM) can now yield near-atomic resolution structures of biological complexes. However, the reference-based alignment algorithms commonly used in cryo-EM suffer from reference bias, limiting their applicability (also known as the 'Einstein from random noise' problem). Low-dose cryo-EM therefore requires robust and objective approaches to reveal the structural information contained in the extremely noisy data, especially when dealing with small structures. A reference-free pipeline is presented for obtaining near-atomic resolution three-dimensional reconstructions from heterogeneous ('four-dimensional') cryo-EM data sets. The methodologies integrated in this pipeline include a posteriori camera correction, movie-based full-data-set contrast transfer function determination, movie-alignment algorithms, (Fourier-space) multivariate statistical data compression and unsupervised classification, 'random-startup' three-dimensional reconstructions, four-dimensional structural refinements and Fourier shell correlation criteria for evaluating anisotropic resolution. The procedures exclusively use information emerging from the data set itself, without external 'starting models'. Euler-angle assignments are performed by angular reconstitution rather than by the inherently slower projection-matching approaches. The comprehensive 'ABC-4D' pipeline is based on the two-dimensional reference-free 'alignment by classification' (ABC) approach, where similar images in similar orientations are grouped by unsupervised classification. Some fundamental differences between X-ray crystallography versus single-particle cryo-EM data collection and data processing are discussed. The structure of the giant haemoglobin from Lumbricus terrestris at a global resolution of ∼3.8 Å is presented as an example of the use of the ABC-4D procedure.

Massively parallel unsupervised single-particle cryo-EM data clustering via statistical manifold learning

Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM) data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the assessment of structural heterogeneity. However, traditional algorithms for unsupervised classification, such as K-means clustering and maximum likelihood optimization, may classify images into wrong classes with decreasing signal-to-noise-ratio (SNR) in the image data, yet demand increased computational costs. Overcoming these limitations requires further development of clustering algorithms for high-performance cryo-EM data processing. Here we introduce an unsupervised single-particle clustering algorithm derived from a statistical manifold learning framework called generative topographic mapping (GTM). We show that unsupervised GTM clustering improves classification accuracy by about 40% in the absence of input references for data with lower SNRs. Applications to several experimental datasets suggest that our algorithm can detect subtle structural differences among classes via a hierarchical clustering strategy. After code optimization over a high-performance computing (HPC) environment, our software implementation was able to generate thousands of reference-free class averages within hours in a massively parallel fashion, which allows a significant improvement on ab initio 3D reconstruction and assists in the computational purification of homogeneous datasets for high-resolution visualization.

Single-protein detection in crowded molecular environments in cryo-EM images

We present an approach to study macromolecular assemblies by detecting component proteins' characteristic high-resolution projection patterns, calculated from their known 3D structures, in single electron cryo-micrographs. Our method detects single apoferritin molecules in vitreous ice with high specificity and determines their orientation and location precisely. Simulations show that high spatial-frequency information and-in the presence of protein background-a whitening filter are essential for optimal detection, in particular for images taken far from focus. Experimentally, we could detect small viral RNA polymerase molecules, distributed randomly among binding locations, inside rotavirus particles. Based on the currently attainable image quality, we estimate a threshold for detection that is 150 kDa in ice and 300 kDa in 100 nm thick samples of dense biological material.

A Fast and Effective Microfluidic Spraying-Plunging Method for High-Resolution Single-Particle Cryo-EM

We describe a spraying-plunging method for preparing cryoelectron microscopy (cryo-EM) grids with vitreous ice of controllable, highly consistent thickness using a microfluidic device. The new polydimethylsiloxane (PDMS)-based sprayer was tested with apoferritin. We demonstrate that the structure can be solved to high resolution with this method of sample preparation. Besides replacing the conventional pipetting-blotting-plunging method, one of many potential applications of the new sprayer is in time-resolved cryo-EM, as part of a PDMS-based microfluidic reaction channel to study short-lived intermediates on the timescale of 10-1,000 ms.

Cross-Validation of Data Compatibility Between Small Angle X-ray Scattering and Cryo-Electron Microscopy

Cryo-electron microscopy (EM) and small angle X-ray scattering (SAXS) are two different data acquisition modalities often used to glean information about the structure of large biomolecular complexes in their native states. A SAXS experiment is generally considered fast and easy but unveils the structure at very low resolution, whereas a cryo-EM experiment needs more extensive preparation and postacquisition computation to yield a three-dimensional (3D) density map at higher resolution. In certain applications, we may need to verify whether the data acquired in the SAXS and cryo-EM experiments correspond to the same structure (e.g., before reconstructing the 3D density map in EM). In this article, a simple and fast method is proposed to verify the compatibility of the SAXS and EM experimental data. The method is based on averaging the two-dimensional correlation of EM images and the Abel transform of the SAXS data. Orientational preferences are known to exist in cryo-EM experiments, and we also consider these effects on our method. The results are verified on simulations of conformational states of large biomolecular complexes.

Unsupervised Cryo-EM Data Clustering through Adaptively Constrained K-Means Algorithm

In single-particle cryo-electron microscopy (cryo-EM), K-means clustering algorithm is widely used in unsupervised 2D classification of projection images of biological macromolecules. 3D ab initio reconstruction requires accurate unsupervised classification in order to separate molecular projections of distinct orientations. Due to background noise in single-particle images and uncertainty of molecular orientations, traditional K-means clustering algorithm may classify images into wrong classes and produce classes with a large variation in membership. Overcoming these limitations requires further development on clustering algorithms for cryo-EM data analysis. We propose a novel unsupervised data clustering method building upon the traditional K-means algorithm. By introducing an adaptive constraint term in the objective function, our algorithm not only avoids a large variation in class sizes but also produces more accurate data clustering. Applications of this approach to both simulated and experimental cryo-EM data demonstrate that our algorithm is a significantly improved alterative to the traditional K-means algorithm in single-particle cryo-EM analysis.

Design of a molecular support for cryo-EM structure determination

Despite the recent rapid progress in cryo-electron microscopy (cryo-EM), there still exist ample opportunities for improvement in sample preparation. Macromolecular complexes may disassociate or adopt nonrandom orientations against the extended air-water interface that exists for a short time before the sample is frozen. We designed a hollow support structure using 3D DNA origami to protect complexes from the detrimental effects of cryo-EM sample preparation. For a first proof-of-principle, we concentrated on the transcription factor p53, which binds to specific DNA sequences on double-stranded DNA. The support structures spontaneously form monolayers of preoriented particles in a thin film of water, and offer advantages in particle picking and sorting. By controlling the position of the binding sequence on a single helix that spans the hollow support structure, we also sought to control the orientation of individual p53 complexes. Although the latter did not yet yield the desired results, the support structures did provide partial information about the relative orientations of individual p53 complexes. We used this information to calculate a tomographic 3D reconstruction, and refined this structure to a final resolution of ∼15 Å. This structure settles an ongoing debate about the symmetry of the p53 tetramer bound to DNA.

Structure and specificity of the RNA-guided endonuclease Cas9 during DNA interrogation, target binding and cleavage

CRISPR-associated endonuclease Cas9 cuts DNA at variable target sites designated by a Cas9-bound RNA molecule. Cas9's ability to be directed by single 'guide RNA' molecules to target nearly any sequence has been recently exploited for a number of emerging biological and medical applications. Therefore, understanding the nature of Cas9's off-target activity is of paramount importance for its practical use. Using atomic force microscopy (AFM), we directly resolve individual Cas9 and nuclease-inactive dCas9 proteins as they bind along engineered DNA substrates. High-resolution imaging allows us to determine their relative propensities to bind with different guide RNA variants to targeted or off-target sequences. Mapping the structural properties of Cas9 and dCas9 to their respective binding sites reveals a progressive conformational transformation at DNA sites with increasing sequence similarity to its target. With kinetic Monte Carlo (KMC) simulations, these results provide evidence of a 'conformational gating' mechanism driven by the interactions between the guide RNA and the 14th-17th nucleotide region of the targeted DNA, the stabilities of which we find correlate significantly with reported off-target cleavage rates. KMC simulations also reveal potential methodologies to engineer guide RNA sequences with improved specificity by considering the invasion of guide RNAs into targeted DNA duplex.

Immunogenic Display of Purified Chemically Cross-Linked HIV-1 Spikes

HIV-1 envelope glycoprotein (Env) spikes are prime vaccine candidates, at least in principle, but suffer from instability, molecular heterogeneity and a low copy number on virions. We anticipated that chemical cross-linking of HIV-1 would allow purification and molecular characterization of trimeric Env spikes, as well as high copy number immunization. Broadly neutralizing antibodies bound tightly to all major quaternary epitopes on cross-linked spikes. Covalent cross-linking of the trimer also stabilized broadly neutralizing epitopes, although surprisingly some individual epitopes were still somewhat sensitive to heat or reducing agent. Immunodepletion using non-neutralizing antibodies to gp120 and gp41 was an effective method for removing non-native-like Env. Cross-linked spikes, purified via an engineered C-terminal tag, were shown by negative stain EM to have well-ordered, trilobed structure. An immunization was performed comparing a boost with Env spikes on virions to spikes cross-linked and captured onto nanoparticles, each following a gp160 DNA prime. Although differences in neutralization did not reach statistical significance, cross-linked Env spikes elicited a more diverse and sporadically neutralizing antibody response against Tier 1b and 2 isolates when displayed on nanoparticles, despite attenuated binding titers to gp120 and V3 crown peptides. Our study demonstrates display of cross-linked trimeric Env spikes on nanoparticles, while showing a level of control over antigenicity, purity and density of virion-associated Env, which may have relevance for Env based vaccine strategies for HIV-1.

IMPORTANCE

The envelope spike (Env) is the target of HIV-1 neutralizing antibodies, which a successful vaccine will need to elicit. However, native Env on virions is innately labile, as well as heterogeneously and sparsely displayed. We therefore stabilized Env spikes using a chemical cross-linker and removed non-native Env by immunodepletion with non-neutralizing antibodies. Fixed native spikes were recognized by all classes of known broadly neutralizing antibodies but not by non-neutralizing antibodies and displayed on nanoparticles in high copy number. An immunization experiment in rabbits revealed that cross-linking Env reduced its overall immunogenicity; however, high-copy display on nanoparticles enabled boosting of antibodies that sporadically neutralized some relatively resistant HIV-1 isolates, albeit at a low titer. This study describes the purification of stable and antigenically correct Env spikes from virions that can be used as immunogens.

Cryogenic electron microscopy and single-particle analysis

About 20 years ago, the first three-dimensional (3D) reconstructions at subnanometer (<10-Å) resolution of an icosahedral virus assembly were obtained by cryogenic electron microscopy (cryo-EM) and single-particle analysis. Since then, thousands of structures have been determined to resolutions ranging from 30 Å to near atomic (<4 Å). Almost overnight, the recent development of direct electron detectors and the attendant improvement in analysis software have advanced the technology considerably. Near-atomic-resolution reconstructions can now be obtained, not only for megadalton macromolecular complexes or highly symmetrical assemblies but also for proteins of only a few hundred kilodaltons. We discuss the developments that led to this breakthrough in high-resolution structure determination by cryo-EM and point to challenges that lie ahead.

A tilt-pair based method for assigning the projection directions of randomly oriented single-particle molecules

In this article, we describe an improved method to assign the projection angle for averaged images using tilt-pair images for three-dimensional reconstructions from randomly oriented single-particle molecular images. Our study addressed the so-called 'initial volume problem' in the single-particle reconstruction, which involves estimation of projection angles of the particle images. The projected images of the particles in different tilt observations were mixed and averaged for the characteristic views. After the ranking of these group average images in terms of reliable tilt angle information, mutual tilt angles between images are assigned from the constituent tilt-pair information. Then, multiples of the conical tilt series are made and merged to construct a network graph of the particle images in terms of projection angles, which are optimized for the three-dimensional reconstruction. We developed the method with images of a synthetic object and applied it to a single-particle image data set of the purified deacetylase from archaea. With the introduction of low-angle tilt observations to minimize unfavorable imaging conditions due to tilting, the results demonstrated reasonable reconstruction models without imposing symmetry to the structure. This method also guides its users to discriminate particle images of different conformational state of the molecule.

Structural plasticity of helical nanotubes based on coiled-coil assemblies

Numerous instances can be seen in evolution in which protein quaternary structures have diverged while the sequences of the building blocks have remained fairly conserved. However, the path through which such divergence has taken place is usually not known. We have designed two synthetic 29-residue α-helical peptides, based on the coiled-coil structural motif, that spontaneously self-assemble into helical nanotubes in vitro. Using electron cryomicroscopy with a newly available direct electron detection capability, we can achieve near-atomic resolution of these thin structures. We show how conservative changes of only one or two amino acids result in dramatic changes in quaternary structure, in which the assemblies can be switched between two very different forms. This system provides a framework for understanding how small sequence changes in evolution can translate into very large changes in supramolecular structure, a phenomenon that may have significant implications for the de novo design of synthetic peptide assemblies.

New simulated annealing approach considering helix bending applied to determine the 8.8Å structure of 15-protofilament microtubules

The helix is an important motif in biological architectures. The helical structures of nanoscale proteins are principally determined by three-dimensional (3D) reconstruction from electron micrographs. However, bending or distortion of flexible helices and the low contrast of the images recorded by cryo-electron microscopy, prevent the analysis from reaching high resolution. We have developed a novel helical reconstruction method that overcomes these issues, and present the processing of microtubule images to demonstrate its application. Cropping long helical structures into small square pieces allows bending or distortion of the helices to be accounted for. The initial image-frames are automatically positioned assuming perfect helical symmetry. A simulated annealing (SA)-based algorithm is then used to adjust the framing. This is guided by the contrast of 2D averages, which serve as an accuracy index. After the initial 3D reconstruction, the position and orientation of each average image is iteratively adjusted to give the best match between the input average and the reprojection from the reconstruction. Finally, reconstructions from images recorded at different defocus values, are aligned and averaged to compensate the contrast transfer modulation and improve the resolution. The method successfully determined the structure of a 15-protofilament microtubule. The 8.8Å resolution (7.8Å using the 0.143 FSC criterion) attained allows differences between the α- and β- tubulins to be discerned in the absence of a molecular landmark such as microtubule-associated proteins, for the first time by electron microscopy. The SA-based method is applicable to other helical protein complexes and in general to helical structures.

Serial block face scanning electron microscopy for the study of cardiac muscle ultrastructure at nanoscale resolutions

Electron microscopy techniques have made a significant contribution towards understanding muscle physiology since the 1950s. Subsequent advances in hardware and software have led to major breakthroughs in terms of image resolution as well as the ability to generate three-dimensional (3D) data essential for linking structure to function and dysfunction. In this methodological review we consider the application of a relatively new technique, serial block face scanning electron microscopy (SBF-SEM), for the study of cardiac muscle morphology. Employing SBF-SEM we have generated 3D data for cardiac myocytes within the myocardium with a voxel size of ~15 nm in the X-Y plane and 50 nm in the Z-direction. We describe how SBF-SEM can be used in conjunction with selective staining techniques to reveal the 3D cellular organisation and the relationship between the t-tubule (t-t) and sarcoplasmic reticulum (SR) networks. These methods describe how SBF-SEM can be used to provide qualitative data to investigate the organisation of the dyad, a specialised calcium microdomain formed between the t-ts and the junctional portion of the SR (jSR). We further describe how image analysis methods may be applied to interrogate the 3D volumes to provide quantitative data such as the volume of the cell occupied by the t-t and SR membranes and the volumes and surface area of jSR patches. We consider the strengths and weaknesses of the SBF-SEM technique, pitfalls in sample preparation together with tips and methods for image analysis. By providing a 'big picture' view at high resolutions, in comparison to conventional confocal microscopy, SBF-SEM represents a paradigm shift for imaging cellular networks in their native environment.

Initial bridges between two ribosomal subunits are formed within 9.4 milliseconds, as studied by time-resolved cryo-EM

Association of the two ribosomal subunits during the process of translation initiation is a crucial step of protein synthesis. The two subunits (30S and 50S) of the bacterial 70S ribosome are held together by 12 dynamic bridges involving RNA-RNA, RNA-protein, and protein-protein interactions. The process of bridge formation, such as whether all these bridges are formed simultaneously or in a sequential order, is poorly understood. To understand such processes, we have developed and implemented a class of microfluidic devices that mix two components to completion within 0.4 ms and spray the mixture in the form of microdroplets onto an electron microscopy grid, yielding a minimum reaction time of 9.4 ms before cryofixation. Using these devices, we have obtained cryo-EM data corresponding to reaction times of 9.4 and 43 ms and have determined 3D structures of ribosomal subunit association intermediates. Molecular analyses of the cryo-EM maps reveal that eight intersubunit bridges (bridges B1a, B1b, B2a, B2b, B3, B7a, B7b, and B8) form within 9.4 ms, whereas the remaining four bridges (bridges B2c, B4, B5, and B6) take longer than 43 ms to form, suggesting that bridges are formed in a stepwise fashion. Our approach can be used to characterize sequences of various dynamic functional events on complex macromolecular assemblies such as ribosomes.