Definition and estimation of resolution in single-particle reconstructions

A kinetic model for solving a combination optimization problem in ab-initio Cryo-EM 3D reconstruction

Cryo-Electron Microscopy (cryo-EM) is a widely used and effective method for determining the three-dimensional (3D) structure of biological molecules. For ab-initio Cryo-EM 3D reconstruction using single particle analysis (SPA), estimating the projection direction of the projection image is a crucial step. However, the existing SPA methods based on common lines are sensitive to noise. The error in common line detection will lead to a poor estimation of the projection directions and thus may greatly affect the final reconstruction results. To improve the reconstruction results, multiple candidate common lines are estimated for each pair of projection images. The key problem then becomes a combination optimization problem of selecting consistent common lines from multiple candidates. To solve the problem efficiently, a physics-inspired method based on a kinetic model is proposed in this work. More specifically, hypothetical attractive forces between each pair of candidate common lines are used to calculate a hypothetical torque exerted on each projection image in the 3D reconstruction space, and the rotation under the hypothetical torque is used to optimize the projection direction estimation of the projection image. This way, the consistent common lines along with the projection directions can be found directly without enumeration of all the combinations of the multiple candidate common lines. Compared with the traditional methods, the proposed method is shown to be able to produce more accurate 3D reconstruction results from high noise projection images. Besides the practical value, the proposed method also serves as a good reference for solving similar combinatorial optimization problems.

A robust normalized local filter to estimate compositional heterogeneity directly from cryo-EM maps

Cryo electron microscopy (cryo-EM) is used by biological research to visualize biomolecular complexes in 3D, but the heterogeneity of cryo-EM reconstructions is not easily estimated. Current processing paradigms nevertheless exert great effort to reduce flexibility and heterogeneity to improve the quality of the reconstruction. Clustering algorithms are typically employed to identify populations of data with reduced variability, but lack assessment of remaining heterogeneity. Here we develope a fast and simple algorithm based on spatial filtering to estimate the heterogeneity of a reconstruction. In the absence of flexibility, this estimate approximates macromolecular component occupancy. We show that our implementation can derive reasonable input parameters, that composition heterogeneity can be estimated based on contrast loss, and that the reconstruction can be modified accordingly to emulate altered constituent occupancy. This stands to benefit conventionally employed maximum-likelihood classification methods, whereas we here limit considerations to cryo-EM map interpretation, quantification, and particle-image signal subtraction.

Local heterogeneity analysis of crystallographic and cryo-EM maps using shell-approximation

In X-ray crystallography and cryo-EM, experimental maps can be heterogeneous, showing different level of details in different regions. In this work we interpret heterogeneity in terms of two parameters, assigned individually for each atom, combining the conventional atomic displacement parameter with the resolution of the atomic image in the map. We propose a local real-space procedure to estimate the values of these heterogeneity parameters, assuming that a fragment of the density map and atomic positions are given. The procedure is based on an analytic representation of the atomic image, as a function of the inhomogeneity parameters and atomic coordinates. In this article, we report the results of the tests both with maps simulated and those derived from experimental data. For simulated maps containing regions with different resolutions, the method determines the local map resolution around the atomic centers and the values of the displacement parameter with reasonable accuracy. For experimental maps, obtained as a Fourier synthesis of a given global resolution, estimated values of the local resolution are close to the global one, and the values of the estimated displacement parameters are close to the respective values of the closest atoms in the refined model. Shown successful applications of the proposed method to experimental crystallographic and cryo-EM maps can be seen as a practical proof of method.

Cryoelectron microscopic structure of the nucleoprotein-RNA complex of the European filovirus, Lloviu virus

Lloviu virus (LLOV) is a novel filovirus detected in Schreiber's bats in Europe. The isolation of the infectious LLOV from bats has raised public health concerns. However, the virological and molecular characteristics of LLOV remain largely unknown. The nucleoprotein (NP) of LLOV encapsidates the viral genomic RNA to form a helical NP-RNA complex, which acts as a scaffold for nucleocapsid formation and de novo viral RNA synthesis. In this study, using single-particle cryoelectron microscopy, we determined two structures of the LLOV NP-RNA helical complex, comprising a full-length and a C-terminally truncated NP. The two helical structures were identical, demonstrating that the N-terminal region determines the helical arrangement of the NP. The LLOV NP-RNA protomers displayed a structure similar to that in the Ebola and Marburg virus, but the spatial arrangements in the helix differed. Structure-based mutational analysis identified amino acids involved in the helical assembly and viral RNA synthesis. These structures advance our understanding of the filovirus nucleocapsid formation and provide a structural basis for the development of antifiloviral therapeutics.

Skopi: a simulation package for diffractive imaging of noncrystalline biomolecules

X-ray free-electron lasers (XFELs) have the ability to produce ultra-bright femtosecond X-ray pulses for coherent diffraction imaging of biomolecules. While the development of methods and algorithms for macromolecular crystallography is now mature, XFEL experiments involving aerosolized or solvated biomolecular samples offer new challenges in terms of both experimental design and data processing. Skopi is a simulation package that can generate single-hit diffraction images for reconstruction algorithms, multi-hit diffraction images of aggregated particles for training machine learning classifiers using labeled data, diffraction images of randomly distributed particles for fluctuation X-ray scattering algorithms, and diffraction images of reference and target particles for holographic reconstruction algorithms. Skopi is a resource to aid feasibility studies and advance the development of algorithms for noncrystalline experiments at XFEL facilities.

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.

Entropy-regularized deconvolution of cellular cryotransmission electron tomograms

Cellular cryo-electron tomography suffers from severely compromised Z resolution due to the missing wedges of information not collected during the acquisition of tilt series. This paper shows that application of entropy-regularized deconvolution to transmission electron tomography substantially fills in this missing information, allowing for improved Z resolution and better interpretation of cellular structures.

Cryo-electron tomography (cryo-ET) allows for the high-resolution visualization of biological macromolecules. However, the technique is limited by a low signal-to-noise ratio (SNR) and variance in contrast at different frequencies, as well as reduced Z resolution. Here, we applied entropy-regularized deconvolution (ER-DC) to cryo-ET data generated from transmission electron microscopy (TEM) and reconstructed using weighted back projection (WBP). We applied deconvolution to several in situ cryo-ET datasets and assessed the results by Fourier analysis and subtomogram analysis (STA).

End-to-end robust joint unsupervised image alignment and clustering

Computing dense pixel-to-pixel image correspondences is a fundamental task of computer vision. Often, the objective is to align image pairs from the same semantic category for manipulation or segmentation purposes. Despite achieving superior performance, existing deep learning alignment methods cannot cluster images; consequently, clustering and pairing images needed to be a separate laborious and expensive step. Given a dataset with diverse semantic categories, we propose a multi-task model, Jim-Net, that can directly learn to cluster and align images without any pixel-level or image-level annotations. We design a pair-matching alignment unsupervised training algorithm that selectively matches and aligns image pairs from the clustering branch. Our unsupervised Jim-Net achieves comparable accuracy with state-of-the-art supervised methods on benchmark 2D image alignment dataset PF-PASCAL. Specifically, we apply Jim-Net to cryo-electron tomography, a revolutionary 3D microscopy imaging technique of native subcellular structures. After extensive evaluation on seven datasets, we demonstrate that Jim-Net enables systematic discovery and recovery of representative macromolecular structures in situ, which is essential for revealing molecular mechanisms underlying cellular functions. To our knowledge, Jim-Net is the first end-to-end model that can simultaneously align and cluster images, which significantly improves the performance as compared to performing each task alone.

Cryo-EM and antisense targeting of the 28-kDa frameshift stimulation element from the SARS-CoV-2 RNA genome

Drug discovery campaigns against COVID-19 are beginning to target the SARS-CoV-2 RNA genome. The highly conserved frameshift stimulation element (FSE), required for balanced expression of viral proteins, is a particularly attractive SARS-CoV-2 RNA target. Here we present a 6.9 Å resolution cryo-EM structure of the FSE (88 nucleotides, ~28 kDa), validated through an RNA nanostructure tagging method. The tertiary structure presents a topologically complex fold in which the 5' end is threaded through a ring formed inside a three-stem pseudoknot. Guided by this structure, we develop antisense oligonucleotides that impair FSE function in frameshifting assays and knock down SARS-CoV-2 virus replication in A549-ACE2 cells at 100 nM concentration.

Fast X-ray Nanotomography with Sub-10 nm Resolution as a Powerful Imaging Tool for Nanotechnology and Energy Storage Applications

In the last decade, transmission X-ray microscopes (TXMs) have come into operation in most of the synchrotrons worldwide. They have proven to be outstanding tools for non-invasive ex and in situ 3D characterization of materials at the nanoscale across varying range of scientific applications. However, their spatial resolution has not improved in many years, while newly developed functional materials and microdevices with enhanced performances exhibit nanostructures always finer. Here, optomechanical breakthroughs leading to fast 3D tomographic acquisitions (85 min) with sub-10 nm spatial resolution, narrowing the gap between X-ray and electron microscopy, are reported. These new achievements are first validated with 3D characterizations of nanolithography objects corresponding to ultrahigh-aspect-ratio hard X-ray zone plates. Then, this powerful technique is used to investigate the morphology and conformality of nanometer-thick film electrodes synthesized by atomic layer deposition and magnetron sputtering deposition methods on 3D silicon scaffolds for electrochemical energy storage applications.

Local computational methods to improve the interpretability and analysis of cryo-EM maps

Cryo-electron microscopy (cryo-EM) maps usually show heterogeneous distributions of B-factors and electron density occupancies and are typically B-factor sharpened to improve their contrast and interpretability at high-resolutions. However, 'over-sharpening' due to the application of a single global B-factor can distort processed maps causing connected densities to appear broken and disconnected. This issue limits the interpretability of cryo-EM maps, i.e. ab initio modelling. In this work, we propose 1) approaches to enhance high-resolution features of cryo-EM maps, while preventing map distortions and 2) methods to obtain local B-factors and electron density occupancy maps. These algorithms have as common link the use of the spiral phase transformation and are called LocSpiral, LocBSharpen, LocBFactor and LocOccupancy. Our results, which include improved maps of recent SARS-CoV-2 structures, show that our methods can improve the interpretability and analysis of obtained reconstructions.

An encryption-decryption framework to validating single-particle imaging

We propose an encryption-decryption framework for validating diffraction intensity volumes reconstructed using single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) when the ground truth volume is absent. This conceptual framework exploits each reconstructed volumes' ability to decipher latent variables (e.g. orientations) of unseen sentinel diffraction patterns. Using this framework, we quantify novel measures of orientation disconcurrence, inconsistency, and disagreement between the decryptions by two independently reconstructed volumes. We also study how these measures can be used to define data sufficiency and its relation to spatial resolution, and the practical consequences of focusing XFEL pulses to smaller foci. This conceptual framework overcomes critical ambiguities in using Fourier Shell Correlation (FSC) as a validation measure for SPI. Finally, we show how this encryption-decryption framework naturally leads to an information-theoretic reformulation of the resolving power of XFEL-SPI, which we hope will lead to principled frameworks for experiment and instrument design.

A basic introduction to single particles cryo-electron microscopy

<abstract> <p>In the last years, cryogenic-electron microscopy (cryo-EM) underwent the most impressive improvement compared to other techniques used in structural biology, such as X-ray crystallography and NMR. Electron microscopy was invented nearly one century ago but, up to the beginning of the last decades, the 3D maps produced through this technique were poorly detailed, justifying the term “blobbology” to appeal to cryo-EM. Recently, thanks to a new generation of microscopes and detectors, more efficient algorithms, and easier access to computational power, single particles cryo-EM can routinely produce 3D structures at resolutions comparable to those obtained with X-ray crystallography. However, unlike X-ray crystallography, which needs crystallized proteins, cryo-EM exploits purified samples in solution, allowing the study of proteins and protein complexes that are hard or even impossible to crystallize. For these reasons, single-particle cryo-EM is often the first choice of structural biologists today. Nevertheless, before starting a cryo-EM experiment, many drawbacks and limitations must be considered. Moreover, in practice, the process between the purified sample and the final structure could be trickier than initially expected. Based on these observations, this review aims to offer an overview of the principal technical aspects and setups to be considered while planning and performing a cryo-EM experiment.</p> </abstract>

Structural Heterogeneity in Single Particle Imaging Using X-ray Lasers

One of the challenges facing single particle imaging with ultrafast X-ray pulses is the structural heterogeneity of the sample to be imaged. For the method to succeed with weakly scattering samples, the diffracted images from a large number of individual proteins need to be averaged. The more the individual proteins differ in structure, the lower the achievable resolution in the final reconstructed image. We use molecular dynamics to simulate two globular proteins in vacuum, fully desolvated as well as with two different solvation layers, at various temperatures. We calculate the diffraction patterns based on the simulations and evaluate the noise in the averaged patterns arising from the structural differences and the surrounding water. Our simulations show that the presence of a minimal water coverage with an average 3 Å thickness will stabilize the protein, reducing the noise associated with structural heterogeneity, whereas additional water will generate more background noise.

Mitigating local over-fitting during single particle reconstruction with SIDESPLITTER

Single particle analysis has become a key structural biology technique. Experimental images are extremely noisy, and during iterative refinement it is possible to stably incorporate noise into the reconstruction. Such "over-fitting" can lead to misinterpretation of the structure and flawed biological results. Several strategies are routinely used to prevent over-fitting, the most common being independent refinement of two sides of a split dataset. In this study, we show that over-fitting remains an issue within regions of low local signal-to-noise, despite independent refinement of half datasets. We propose a modification of the refinement process through the application of a local signal-to-noise filter: SIDESPLITTER. We show that our approach can reduce over-fitting for both idealised and experimental data while maintaining independence between the two sides of a split refinement. SIDESPLITTER refinement leads to improved density, and can also lead to improvement of the final resolution in extreme cases where datasets are prone to severe over-fitting, such as small membrane proteins.

Cryo-electron Microscopy and Exploratory Antisense Targeting of the 28-kDa Frameshift Stimulation Element from the SARS-CoV-2 RNA Genome

Drug discovery campaigns against Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) are beginning to target the viral RNA genome ^{1, 2} . The frameshift stimulation element (FSE) of the SARS-CoV-2 genome is required for balanced expression of essential viral proteins and is highly conserved, making it a potential candidate for antiviral targeting by small molecules and oligonucleotides ^3-6 . To aid global efforts focusing on SARS-CoV-2 frameshifting, we report exploratory results from frameshifting and cellular replication experiments with locked nucleic acid (LNA) antisense oligonucleotides (ASOs), which support the FSE as a therapeutic target but highlight difficulties in achieving strong inactivation. To understand current limitations, we applied cryogenic electron microscopy (cryo-EM) and the Ribosolve ⁷ pipeline to determine a three-dimensional structure of the SARS-CoV-2 FSE, validated through an RNA nanostructure tagging method. This is the smallest macromolecule (88 nt; 28 kDa) resolved by single-particle cryo-EM at subnanometer resolution to date. The tertiary structure model, defined to an estimated accuracy of 5.9 Å, presents a topologically complex fold in which the 5' end threads through a ring formed inside a three-stem pseudoknot. Our results suggest an updated model for SARS-CoV-2 frameshifting as well as binding sites that may be targeted by next generation ASOs and small molecules.

Simulation-Based Methods for Model Building and Refinement in Cryoelectron Microscopy

Advances in cryoelectron microscopy (cryo-EM) have revolutionized the structural investigation of large macromolecular assemblies. In this review, we first provide a broad overview of modeling methods used for flexible fitting of molecular models into cryo-EM density maps. We give special attention to approaches rooted in molecular simulations-atomistic molecular dynamics and Monte Carlo. Concise descriptions of the methods are given along with discussion of their advantages, limitations, and most popular alternatives. We also describe recent extensions of the widely used molecular dynamics flexible fitting (MDFF) method and discuss how different model-building techniques could be incorporated into new hybrid modeling schemes and simulation workflows. Finally, we provide two illustrative examples of model-building and refinement strategies employing MDFF, cascade MDFF, and RosettaCM. These examples come from recent cryo-EM studies that elucidated transcription preinitiation complexes and shed light on the functional roles of these assemblies in gene expression and gene regulation.

A simulated annealing approach for resolution guided homogeneous cryo-electron microscopy image selection

BACKGROUND

Cryo-electron microscopy (Cryo-EM) and tomography (Cryo-ET) have emerged as important imaging techniques for studying structures of macromolecular complexes. In 3D reconstruction of large macromolecular complexes, many 2D projection images of macromolecular complex particles are usually acquired with low signal-to-noise ratio. Therefore, it is meaningful to select multiple images containing the same structure with identical orientation. The selected images are averaged to produce a higher-quality representation of the underlying structure with improved resolution. Existing approaches of selecting such images have limited accuracy and speed.

METHODS

We propose a simulated annealing-based algorithm (SA) to pick the homogeneous image set with best average. Its performance is compared with two baseline methods based on both 2D and 3D datasets. When tested on simulated and experimental 3D Cryo-ET images of Ribosome complex, SA sometimes stopped at a local optimal solution. Restarting is applied to settle this difficulty and significantly improved the performance of SA on 3D datasets.

RESULTS

Experimented on simulated and experimental 2D Cryo-EM images of Ribosome complex datasets respectively with SNR = 10 and SNR = 0.5, our method achieved better accuracy in terms of F-measure, resolution score, and time cost than two baseline methods. Additionally, SA shows its superiority when the proportion of homogeneous images decreases.

CONCLUSIONS

SA is introduced for homogeneous image selection to realize higher accuracy with faster processing speed. Experiments on both simulated and real 2D Cryo-EM and 3D Cryo-ET images demonstrated that SA achieved expressively better performance. This approach serves as an important step for improving the resolution of structural recovery of macromolecular complexes captured by Cryo-EM and Cryo-ET.

Adversarial domain adaptation for cross data source macromolecule in situ structural classification in cellular electron cryo-tomograms

MOTIVATION

Since 2017, an increasing amount of attention has been paid to the supervised deep learning-based macromolecule in situ structural classification (i.e. subtomogram classification) in cellular electron cryo-tomography (CECT) due to the substantially higher scalability of deep learning. However, the success of such supervised approach relies heavily on the availability of large amounts of labeled training data. For CECT, creating valid training data from the same data source as prediction data is usually laborious and computationally intensive. It would be beneficial to have training data from a separate data source where the annotation is readily available or can be performed in a high-throughput fashion. However, the cross data source prediction is often biased due to the different image intensity distributions (a.k.a. domain shift).

RESULTS

We adapt a deep learning-based adversarial domain adaptation (3D-ADA) method to timely address the domain shift problem in CECT data analysis. 3D-ADA first uses a source domain feature extractor to extract discriminative features from the training data as the input to a classifier. Then it adversarially trains a target domain feature extractor to reduce the distribution differences of the extracted features between training and prediction data. As a result, the same classifier can be directly applied to the prediction data. We tested 3D-ADA on both experimental and realistically simulated subtomogram datasets under different imaging conditions. 3D-ADA stably improved the cross data source prediction, as well as outperformed two popular domain adaptation methods. Furthermore, we demonstrate that 3D-ADA can improve cross data source recovery of novel macromolecular structures.

AVAILABILITY AND IMPLEMENTATION

https://github.com/xulabs/projects.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Deep Learning for Validating and Estimating Resolution of Cryo-Electron Microscopy Density Maps †

Cryo-electron microscopy (cryo-EM) is becoming the imaging method of choice for determining protein structures. Many atomic structures have been resolved based on an exponentially growing number of published three-dimensional (3D) high resolution cryo-EM density maps. However, the resolution value claimed for the reconstructed 3D density map has been the topic of scientific debate for many years. The Fourier Shell Correlation (FSC) is the currently accepted cryo-EM resolution measure, but it can be subjective, manipulated, and has its own limitations. In this study, we first propose supervised deep learning methods to extract representative 3D features at high, medium and low resolutions from simulated protein density maps and build classification models that objectively validate resolutions of experimental 3D cryo-EM maps. Specifically, we build classification models based on dense artificial neural network (DNN) and 3D convolutional neural network (3D CNN) architectures. The trained models can classify a given 3D cryo-EM density map into one of three resolution levels: high, medium, low. The preliminary DNN and 3D CNN models achieved 92.73% accuracy and 99.75% accuracy on simulated test maps, respectively. Applying the DNN and 3D CNN models to thirty experimental cryo-EM maps achieved an agreement of 60.0% and 56.7%, respectively, with the author published resolution value of the density maps. We further augment these previous techniques and present preliminary results of a 3D U-Net model for local resolution classification. The model was trained to perform voxel-wise classification of 3D cryo-EM density maps into one of ten resolution classes, instead of a single global resolution value. The U-Net model achieved 88.3% and 94.7% accuracy when evaluated on experimental maps with local resolutions determined by MonoRes and ResMap methods, respectively. Our results suggest deep learning can potentially improve the resolution evaluation process of experimental cryo-EM maps.

De Novo Structural Pattern Mining in Cellular Electron Cryotomograms

Electron cryotomography enables 3D visualization of cells in a near-native state at molecular resolution. The produced cellular tomograms contain detailed information about a plethora of macromolecular complexes, their structures, abundances, and specific spatial locations in the cell. However, extracting this information in a systematic way is very challenging, and current methods usually rely on individual templates of known structures. Here, we propose a framework called "Multi-Pattern Pursuit" for de novo discovery of different complexes from highly heterogeneous sets of particles extracted from entire cellular tomograms without using information of known structures. These initially detected structures can then serve as input for more targeted refinement efforts. Our tests on simulated and experimental tomograms show that our automated method is a promising tool for supporting large-scale template-free visual proteomics analysis.

Single-particle reconstruction statistics: a diagnostic tool in solving biomolecular structures by cryo-EM

In single-particle analysis (SPA), the aim is to obtain a 3D reconstruction of a biological molecule from 2D electron micrographs to the highest level of detail or resolution as possible. Current practice is to collect large volumes of data, hoping to reach high-resolution maps through sheer numbers. However, adding more particles from a specific data set eventually leads to diminishing improvements in resolution. Understanding what these resolution limits are and how to deal with them are important in optimization and automation of SPA. This study revisits the theory of 3D reconstruction and demonstrates how the associated statistics can provide a diagnostic tool to improve SPA. Small numbers of images already give sufficient information on micrograph quality and the amount of data required to reach high resolution. Such feedback allows the microscopist to improve sample-preparation and imaging parameters before committing to extensive data collection. Once a larger data set is available, a B factor can be determined describing the suppression of the signal owing to one or more causes, such as specimen movement, radiation damage, alignment inaccuracy and structural variation. Insight into the causes of signal suppression can then guide the user to consider appropriate actions to obtain better reconstructions.

A Local Agreement Filtering Algorithm for Transmission EM Reconstructions

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We propose an algorithm, LAFTER, that recovers features with more signal than noise from half maps.

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LAFTER is shown to recover features over a wide range of FSCs and local signal-to-noise ratios.

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We suggest effective local noise suppression be evaluated by comparing the filter-sum xFSC to C_ref.

We present LAFTER, an algorithm for de-noising single particle reconstructions from cryo-EM.

Single particle analysis entails the reconstruction of high-resolution volumes from tens of thousands of particle images with low individual signal-to-noise. Imperfections in this process result in substantial variations in the local signal-to-noise ratio within the resulting reconstruction, complicating the interpretation of molecular structure. An effective local de-noising filter could therefore improve interpretability and maximise the amount of useful information obtained from cryo-EM maps.

LAFTER is a local de-noising algorithm based on a pair of serial real-space filters. It compares independent half-set reconstructions to identify and retain shared features that have power greater than the noise. It is capable of recovering features across a wide range of signal-to-noise ratios, and we demonstrate recovery of the strongest features at Fourier shell correlation (FSC) values as low as 0.144 over a 256³-voxel cube. A fast and computationally efficient implementation of LAFTER is freely available.

We also propose a new way to evaluate the effectiveness of real-space filters for noise suppression, based on the correspondence between two FSC curves: 1) the FSC between the filtered and unfiltered volumes, and 2) C_ref, the FSC between the unfiltered volume and a hypothetical noiseless volume, which can readily be estimated from the FSC between two half-set reconstructions.

Multi-task Learning for Macromolecule Classification, Segmentation and Coarse Structural Recovery in Cryo-Tomography

Cellular Electron Cryo-Tomography (CECT) is a powerful 3D imaging tool for studying the native structure and organization of macromolecules inside single cells. For systematic recognition and recovery of macromolecular structures captured by CECT, methods for several important tasks such as subtomogram classification and semantic segmentation have been developed. However, the recognition and recovery of macromolecular structures are still very difficult due to high molecular structural diversity, crowding molecular environment, and the imaging limitations of CECT. In this paper, we propose a novel multi-task 3D convolutional neural network model for simultaneous classification, segmentation, and coarse structural recovery of macromolecules of interest in subtomograms. In our model, the learned image features of one task are shared and thereby mutually reinforce the learning of other tasks. Evaluated on realistically simulated and experimental CECT data, our multi-task learning model outperformed all single-task learning methods for classification and segmentation. In addition, we demonstrate that our model can generalize to discover, segment and recover novel structures that do not exist in the training data.

New tools for the analysis and validation of cryo-EM maps and atomic models

Recent advances in the field of electron cryomicroscopy (cryo-EM) have resulted in a rapidly increasing number of atomic models of biomacromolecules that have been solved using this technique and deposited in the Protein Data Bank and the Electron Microscopy Data Bank. Similar to macromolecular crystallography, validation tools for these models and maps are required. While some of these validation tools may be borrowed from crystallography, new methods specifically designed for cryo-EM validation are required. Here, new computational methods and tools implemented in PHENIX are discussed, including d99 to estimate resolution, phenix.auto_sharpen to improve maps and phenix.mtriage to analyze cryo-EM maps. It is suggested that cryo-EM half-maps and masks should be deposited to facilitate the evaluation and validation of cryo-EM-derived atomic models and maps. The application of these tools to deposited cryo-EM atomic models and maps is also presented.

Deep learning-based subdivision approach for large scale macromolecules structure recovery from electron cryo tomograms

Motivation

Cellular Electron CryoTomography (CECT) enables 3D visualization of cellular organization at near-native state and in sub-molecular resolution, making it a powerful tool for analyzing structures of macromolecular complexes and their spatial organizations inside single cells. However, high degree of structural complexity together with practical imaging limitations makes the systematic de novo discovery of structures within cells challenging. It would likely require averaging and classifying millions of subtomograms potentially containing hundreds of highly heterogeneous structural classes. Although it is no longer difficult to acquire CECT data containing such amount of subtomograms due to advances in data acquisition automation, existing computational approaches have very limited scalability or discrimination ability, making them incapable of processing such amount of data.

Results

To complement existing approaches, in this article we propose a new approach for subdividing subtomograms into smaller but relatively homogeneous subsets. The structures in these subsets can then be separately recovered using existing computation intensive methods. Our approach is based on supervised structural feature extraction using deep learning, in combination with unsupervised clustering and reference-free classification. Our experiments show that, compared with existing unsupervised rotation invariant feature and pose-normalization based approaches, our new approach achieves significant improvements in both discrimination ability and scalability. More importantly, our new approach is able to discover new structural classes and recover structures that do not exist in training data.

Availability and Implementation

Source code freely available at http://www.cs.cmu.edu/∼mxu1/software.

Supplementary information

Supplementary data are available at Bioinformatics online.

Validating Resolution Revolution

Recent advances in instrumentation and image-processing software have resulted in a resolution revolution in cryo-electron microscopy (cryo-EM) and a surge in the popularity of this technique. However, despite technical progress and hundreds of structures determined so far, development of standards assessing the agreement between the cryo-EM map and the respective model has fallen behind. Here we establish a validation procedure evaluating this agreement and applied it to a set of 565 cryo-EM structures. Analysis of the results revealed that three-quarters of the validated structures exhibit moderate or low agreement between the map and the corresponding model, mostly due to limited structural features possessed by these maps. Model re-refinement significantly improved the agreement for only one-fifth of the structures, reaffirming the necessity to re-evaluate map resolution. The presented procedure provides an approach to re-estimate the resolution of cryo-EM map areas interpreted by the model.

X-rays in the Cryo-Electron Microscopy Era: Structural Biology's Dynamic Future

Over the past several years, single-particle cryo-electron microscopy (cryo-EM) has emerged as a leading method for elucidating macromolecular structures at near-atomic resolution, rivaling even the established technique of X-ray crystallography. Cryo-EM is now able to probe proteins as small as hemoglobin (64 kDa) while avoiding the crystallization bottleneck entirely. The remarkable success of cryo-EM has called into question the continuing relevance of X-ray methods, particularly crystallography. To say that the future of structural biology is either cryo-EM or crystallography, however, would be misguided. Crystallography remains better suited to yield precise atomic coordinates of macromolecules under a few hundred kilodaltons in size, while the ability to probe larger, potentially more disordered assemblies is a distinct advantage of cryo-EM. Likewise, crystallography is better equipped to provide high-resolution dynamic information as a function of time, temperature, pressure, and other perturbations, whereas cryo-EM offers increasing insight into conformational and energy landscapes, particularly as algorithms to deconvolute conformational heterogeneity become more advanced. Ultimately, the future of both techniques depends on how their individual strengths are utilized to tackle questions at the frontiers of structural biology. Structure determination is just one piece of a much larger puzzle: a central challenge of modern structural biology is to relate structural information to biological function. In this perspective, we share insight from several leaders in the field and examine the unique and complementary ways in which X-ray methods and cryo-EM can shape the future of structural biology.

Dawning of a new era in TRP channel structural biology by cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) permits the determination of atomic protein structures by averaging large numbers of individual projection images recorded at cryogenic temperatures-a method termed single-particle analysis. The cryo-preservation traps proteins within a thin glass-like ice layer, making literally a freeze image of proteins in solution. Projections of randomly adopted orientations are merged to reconstruct a 3D density map. While atomic resolution for highly symmetric viruses was achieved already in 2009, the development of new sensitive and fast electron detectors has enabled cryo-EM for smaller and asymmetrical proteins including fragile membrane proteins. As one of the most important structural biology methods at present, cryo-EM was awarded in October 2017 with the Nobel Prize in Chemistry. The molecular understanding of Transient-Receptor-Potential (TRP) channels has been boosted tremendously by cryo-EM single-particle analysis. Several near-atomic and atomic structures gave important mechanistic insights, e.g., into ion permeation and selectivity, gating, as well as into the activation of this enigmatic and medically important membrane protein family by various chemical and physical stimuli. Lastly, these structures have set the starting point for the rational design of TRP channel-targeted therapeutics to counteract life-threatening channelopathies. Here, we attempt a brief introduction to the method, review the latest advances in cryo-EM structure determination of TRP channels, and discuss molecular insights into the channel function based on the wealth of TRP channel cryo-EM structures.

Hollow Cone Electron Imaging for Single Particle 3D Reconstruction of Proteins

The main bottlenecks for high-resolution biological imaging in electron microscopy are radiation sensitivity and low contrast. The phase contrast at low spatial frequencies can be enhanced by using a large defocus but this strongly reduces the resolution. Recently, phase plates have been developed to enhance the contrast at small defocus but electrical charging remains a problem. Single particle cryo-electron microscopy is mostly used to minimize the radiation damage and to enhance the resolution of the 3D reconstructions but it requires averaging images of a massive number of individual particles. Here we present a new route to achieve the same goals by hollow cone dark field imaging using thermal diffuse scattered electrons giving about a 4 times contrast increase as compared to bright field imaging. We demonstrate the 3D reconstruction of a stained GroEL particle can yield about 13.5 Å resolution but using a strongly reduced number of images.

Resolution and Probabilistic Models of Components in CryoEM Maps of Mature P22 Bacteriophage

CryoEM continues to produce density maps of larger and more complex assemblies with multiple protein components of mixed symmetries. Resolution is not always uniform throughout a cryoEM map, and it can be useful to estimate the resolution in specific molecular components of a large assembly. In this study, we present procedures to 1) estimate the resolution in subcomponents by gold-standard Fourier shell correlation (FSC); 2) validate modeling procedures, particularly at medium resolutions, which can include loop modeling and flexible fitting; and 3) build probabilistic models that combine high-accuracy priors (such as crystallographic structures) with medium-resolution cryoEM densities. As an example, we apply these methods to new cryoEM maps of the mature bacteriophage P22, reconstructed without imposing icosahedral symmetry. Resolution estimates based on gold-standard FSC show the highest resolution in the coat region (7.6 Å), whereas other components are at slightly lower resolutions: portal (9.2 Å), hub (8.5 Å), tailspike (10.9 Å), and needle (10.5 Å). These differences are indicative of inherent structural heterogeneity and/or reconstruction accuracy in different subcomponents of the map. Probabilistic models for these subcomponents provide new insights, to our knowledge, and structural information when taking into account uncertainty given the limitations of the observed density.

Electron Microscopy and Image Processing: Essential Tools for Structural Analysis of Macromolecules

Macromolecular electron microscopy typically depicts the structures of macromolecular complexes ranging from ∼200 kDa to hundreds of MDa. The amount of specimen required, a few micrograms, is typically 100 to 1000 times less than needed for X-ray crystallography or nuclear magnetic resonance spectroscopy. Micrographs of frozen-hydrated (cryogenic) specimens portray native structures, but the original images are noisy. Computational averaging reduces noise, and three-dimensional reconstructions are calculated by combining different views of free-standing particles ("single-particle analysis"). Electron crystallography is used to characterize two-dimensional arrays of membrane proteins and very small three-dimensional crystals. Under favorable circumstances, near-atomic resolutions are achieved. For structures at somewhat lower resolution, pseudo-atomic models are obtained by fitting high-resolution components into the density. Time-resolved experiments describe dynamic processes. Electron tomography allows reconstruction of pleiomorphic complexes and subcellular structures and modeling of macromolecules in their cellular context. Significant information is also obtained from metal-coated and dehydrated specimens.

A method for estimating spatial resolution of real image in the Fourier domain

Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high-angle diffraction in reciprocal space. In electron microscopy, correlation in the Fourier domain is used for estimating the resolution. In this paper, we report a method for estimating the spatial resolution of real images from a logarithmic intensity plot in the Fourier domain. The logarithmic intensity plots of test images indicated that the full width at half maximum of a Gaussian point spread function can be estimated from the images. The spatial resolution of imaging X-ray microtomography using Fresnel zone-plate optics was also estimated with this method. A cross section of a test object visualized with the imaging microtomography indicated that square-wave patterns up to 120-nm pitch were resolved. The logarithmic intensity plot was calculated from a tomographic cross section of brain tissue. The full width at half maximum of the point spread function estimated from the plot coincided with the resolution determined from the test object. These results indicated that the logarithmic intensity plot in the Fourier domain provides an alternative measure of the spatial resolution without explicitly defining a noise criterion.

Membrane protein structures without crystals, by single particle electron cryomicroscopy

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Electron microscopy of membrane proteins as single particles.

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Membrane protein structures without crystals.

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Direct electron detectors have high signal to noise.

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Medium to high-resolution structures of molecules between 0.13 and 2 MDa.

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Sub-tomogram averaging to study membrane proteins in situ.

It is an exciting period in membrane protein structural biology with a number of medically important protein structures determined at a rapid pace. However, two major hurdles still remain in the structural biology of membrane proteins. One is the inability to obtain large amounts of protein for crystallization and the other is the failure to get well-diffracting crystals. With single particle electron cryomicroscopy, both these problems can be overcome and high-resolution structures of membrane proteins and other labile protein complexes can be obtained with very little protein and without the need for crystals. In this review, I highlight recent advances in electron microscopy, detectors and software, which have allowed determination of medium to high-resolution structures of membrane proteins and complexes that have been difficult to study by other structural biological techniques.

The influence of frame alignment with dose compensation on the quality of single particle reconstructions

As direct electron detection devices in cryo-electron microscopy become ubiquitous, the field is now ripe for new developments in image analysis techniques that take advantage of their increased SNR coupled with their high-throughput frame collection abilities. In approaching atomic resolution of native-like biomolecules, the accurate extraction of structural locations and orientations of side-chains from frames depends not only on the electron dose that a sample receives but also on the ability to accurately estimate the CTF. Here we use a new 2.8Å resolution structure of a recombinant gene therapy virus, AAV-DJ with Arixtra, imaged on an FEI Titan Krios with a DE-20 direct electron detector to probe new metrics including relative side-chain density and ResLog analysis for optimizing the compensation of electron beam damage and to characterize the factors that are limiting the resolution of the reconstruction. The influence of dose compensation on the accuracy of CTF estimation and particle classifiability are also presented. We show that rigorous dose compensation allows for better particle classifiability and greater recovery of structural information from negatively charged, electron-sensitive side-chains, resulting in a more accurate macromolecular model.

Resolution improvement by 3D particle averaging in localization microscopy

Inspired by recent developments in localization microscopy that applied averaging of identical particles in 2D for increasing the resolution even further, we discuss considerations for alignment (registration) methods for particles in general and for 3D in particular. We detail that traditional techniques for particle registration from cryo electron microscopy based on cross-correlation are not suitable, as the underlying image formation process is fundamentally different. We argue that only localizations, i.e. a set of coordinates with associated uncertainties, are recorded and not a continuous intensity distribution. We present a method that owes to this fact and that is inspired by the field of statistical pattern recognition. In particular we suggest to use an adapted version of the Bhattacharyya distance as a merit function for registration. We evaluate the method in simulations and demonstrate it on three-dimensional super-resolution data of Alexa 647 labelled to the Nup133 protein in the nuclear pore complex of Hela cells. From the simulations we find suggestions that for successful registration the localization uncertainty must be smaller than the distance between labeling sites on a particle. These suggestions are supported by theoretical considerations concerning the attainable resolution in localization microscopy and its scaling behavior as a function of labeling density and localization precision.

Validation of 3D EM Reconstructions: The Phantom in the Noise

Validation is a necessity to trust the structures solved by electron microscopy by single particle techniques. The impressive achievements in single particle reconstruction fuel its expansion beyond a small community of image processing experts. This poses the risk of inappropriate data processing with dubious results. Nowhere is it more clearly illustrated than in the recovery of a reference density map from pure noise aligned to that map—a phantom in the noise. Appropriate use of existing validating methods such as resolution-limited alignment and the processing of independent data sets (“gold standard”) avoid this pitfall. However, these methods can be undermined by biases introduced in various subtle ways. How can we test that a map is a coherent structure present in the images selected from the micrographs? In stead of viewing the phantom emerging from noise as a cautionary tale, it should be used as a defining baseline. Any map is always recoverable from noise images, provided a sufficient number of images are aligned and used in reconstruction. However, with smaller numbers of images, the expected coherence in the real particle images should yield better reconstructions than equivalent numbers of noise or background images, even without masking or imposing resolution limits as potential biases. The validation test proposed is therefore a simple alignment of a limited number of micrograph and noise images against the final reconstruction as reference, demonstrating that the micrograph images yield a better reconstruction. I examine synthetic cases to relate the resolution of a reconstruction to the alignment error as a function of the signal-to-noise ratio. I also administered the test to real cases of publicly available data. Adopting such a test can aid the microscopist in assessing the usefulness of the micrographs taken before committing to lengthy processing with questionable outcomes.

Autonomous reconstruction and segmentation of tomographic data

A Bayesian approach to reconstruction and segmentation of tomographic data is outlined and further detailed for the case of absorption tomography. The algorithm allows the quantification of reconstruction errors and segmentation confidence. Calculation results for various experimental settings (number of projections, incident dose, different materials) are shown and discussed.

Quantifying the local resolution of cryo-EM density maps

We propose a definition of local resolution for three-dimensional electron cryo-microscopy (cryo-EM) density maps that uses local sinusoidal features. Our algorithm has no free parameters and is applicable to other imaging modalities, including tomography. By evaluating the local resolution of single-particle reconstructions and subtomogram averages for four example data sets, we report variable resolution across a 4- to 40-Å range.

ResLog plots as an empirical metric of the quality of cryo-EM reconstructions

Compared to the field of X-ray crystallography, the field of single particle three-dimensional electron microscopy has few reliable metrics for assessing the quality of 3D reconstructions. New metrics are needed that can determine whether a given 3D reconstruction accurately reflects the structure of the particles from which it was derived or instead depicts a plausible though incorrect structure due to coarse misalignment of particles. Here an empirical procedure is presented for differentiating between a reconstruction with well-aligned particles and a reconstruction with grossly misclassified particles. For a given dataset, 3D reconstructions are computed from subsets of particles with decreasing numbers of particles contributing to the reconstruction. A plot of inverse resolution vs. the logarithm of the number of particles (a "ResLog" plot) provides metrics for the reliability of the reconstruction and the overall quality of the dataset and processing. Specifically, the y-intercept of a regression line provides a measure of the relative accuracy of the particle alignment and classification, and the slope is an indicator of the overall data quality including the imaging conditions and processing steps. ResLog plots can also be used to optimize conditions for data collection and reconstruction parameters. Although resolution estimates can vary by method of calculation, ResLog-derived parameters are consistent whether calculated by Fourier shell correlation or Fourier neighbor correlation, or a new coordinate-based metric that serves as a yardstick for structures where atomic coordinates are available. ResLog plots could become part of a standard set of parameters to be included in 3D reconstruction reports.

One number does not fit all: mapping local variations in resolution in cryo-EM reconstructions

The resolution of density maps from single particle analysis is usually measured in terms of the highest spatial frequency to which consistent information has been obtained. This calculation represents an average over the entire reconstructed volume. In practice, however, substantial local variations in resolution may occur, either from intrinsic properties of the specimen or for technical reasons such as a non-isotropic distribution of viewing orientations. To address this issue, we propose the use of a space-frequency representation, the short-space Fourier transform, to assess the quality of a density map, voxel-by-voxel, i.e. by local resolution mapping. In this approach, the experimental volume is divided into small subvolumes and the resolution determined for each of them. It is illustrated in applications both to model data and to experimental density maps. Regions with lower-than-average resolution may be mobile components or ones with incomplete occupancy or result from multiple conformational states. To improve the interpretability of reconstructions, we propose an adaptive filtering approach that reconciles the resolution to which individual features are calculated with the results of the local resolution map.

High-resolution noise substitution to measure overfitting and validate resolution in 3D structure determination by single particle electron cryomicroscopy

Three-dimensional (3D) structure determination by single particle electron cryomicroscopy (cryoEM) involves the calculation of an initial 3D model, followed by extensive iterative improvement of the orientation determination of the individual particle images and the resulting 3D map. Because there is much more noise than signal at high resolution in the images, this creates the possibility of noise reinforcement in the 3D map, which can give a false impression of the resolution attained. The balance between signal and noise in the final map at its limiting resolution depends on the image processing procedure and is not easily predicted. There is a growing awareness in the cryoEM community of how to avoid such over-fitting and over-estimation of resolution. Equally, there has been a reluctance to use the two principal methods of avoidance because they give lower resolution estimates, which some people believe are too pessimistic. Here we describe a simple test that is compatible with any image processing protocol. The test allows measurement of the amount of signal and the amount of noise from overfitting that is present in the final 3D map. We have applied the method to two different sets of cryoEM images of the enzyme beta-galactosidase using several image processing packages. Our procedure involves substituting the Fourier components of the initial particle image stack beyond a chosen resolution by either the Fourier components from an adjacent area of background, or by simple randomisation of the phases of the particle structure factors. This substituted noise thus has the same spectral power distribution as the original data. Comparison of the Fourier Shell Correlation (FSC) plots from the 3D map obtained using the experimental data with that from the same data with high-resolution noise (HR-noise) substituted allows an unambiguous measurement of the amount of overfitting and an accompanying resolution assessment. A simple formula can be used to calculate an unbiased FSC from the two curves, even when a substantial amount of overfitting is present. The approach is software independent. The user is therefore completely free to use any established method or novel combination of methods, provided the HR-noise test is carried out in parallel. Applying this procedure to cryoEM images of beta-galactosidase shows how overfitting varies greatly depending on the procedure, but in the best case shows no overfitting and a resolution of ~6 Å. (382 words)

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A new method to validate 3D cryoEM maps of biological structures is described.

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High-resolution noise substitution is a tool to measure the amount of overfitting of noise in single particle cryoEM.

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A reliable, unbiased resolution estimation can be obtained even when some overfitting is present.

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Structure of beta-galactosidase at ~6 Å resolution is determined by cryoEM.

Fourier ring correlation as a resolution criterion for super-resolution microscopy

Optical nanoscopy techniques using localization based image reconstruction, also termed super-resolution microscopy (SRM), have become a standard tool to bypass the diffraction limit in fluorescence light microscopy. The localization precision measured for the detected fluorophores is commonly used to describe the maximal attainable resolution. However, this measure takes not all experimental factors, which impact onto the finally achieved resolution, into account. Several other methods to measure the resolution of super-resolved images were previously suggested, typically relying on intrinsic standards, such as molecular rulers, or on a priori knowledge about the specimen, e.g. its spatial frequency content. Here we show that Fourier ring correlation provides an easy-to-use, laboratory consistent standard for measuring the resolution of SRM images. We provide a freely available software tool that combines resolution measurement with image reconstruction.

Subunit organization of the membrane-bound HIV-1 envelope glycoprotein trimer

The trimeric human immunodeficiency virus type 1 (HIV-1) envelope glycoprotein (Env) spike is a molecular machine that mediates virus entry into host cells and is the sole target for virus-neutralizing antibodies. The mature Env spike results from cleavage of a trimeric glycoprotein precursor, gp160, into three gp120 and three gp41 subunits. Here, we describe an ~11-Å cryo-EM structure of the trimeric HIV-1 Env precursor in its unliganded state. The three gp120 and three gp41 subunits form a cage-like structure with an interior void surrounding the trimer axis. Interprotomer contacts are limited to the gp41 transmembrane region, the torus-like gp41 ectodomain and a trimer-association domain of gp120 composed of the V1, V2 and V3 variable regions. The cage-like architecture, which is unique among characterized viral envelope proteins, restricts antibody access, reflecting requirements imposed by HIV-1 persistence in the host.

1.16 Cryo-Electron Microscopy and Tomography of Virus Particles

Human infectious disease is classified into five etiologies: bacterial, viral, parasitic, fungal, and prion. Viral infections are unique in that they recruit human cellular machinery to replicate themselves and spread infection. The number of viruses causing human disease is vast, and viruses can be broadly categorized by their structures. Many viruses, such as influenza, appear to be amorphous particles, whereas others, such as herpes simplex virus, rhinovirus, dengue virus, and adenovirus, have roughly symmetric structural components. Icosahedral viruses have been a target of electron microscopists for years, and they were some of the first objects to be reconstructed three-dimensionally from electron micrographs. The ease with which highly purified and conformationally uniform virus samples can be produced makes them an ideal target structural studies. Apart from their biological significance, these virus samples have played a pivotal role in the development of new methodologies in the field of molecular biology as well as in cryo-electron microscopy and cryo-electron tomography.

Radiation damage in single-particle cryo-electron microscopy: effects of dose and dose rate

Radiation damage is an important resolution limiting factor both in macromolecular X-ray crystallography and cryo-electron microscopy. Systematic studies in macromolecular X-ray crystallography greatly benefited from the use of dose, expressed as energy deposited per mass unit, which is derived from parameters including incident flux, beam energy, beam size, sample composition and sample size. In here, the use of dose is reintroduced for electron microscopy, accounting for the electron energy, incident flux and measured sample thickness and composition. Knowledge of the amount of energy deposited allowed us to compare doses with experimental limits in macromolecular X-ray crystallography, to obtain an upper estimate of radical concentrations that build up in the vitreous sample, and to translate heat-transfer simulations carried out for macromolecular X-ray crystallography to cryo-electron microscopy. Stroboscopic exposure series of 50-250 images were collected for different incident flux densities and integration times from Lumbricus terrestris extracellular hemoglobin. The images within each series were computationally aligned and analyzed with similarity metrics such as Fourier ring correlation, Fourier ring phase residual and figure of merit. Prior to gas bubble formation, the images become linearly brighter with dose, at a rate of approximately 0.1% per 10 MGy. The gradual decomposition of a vitrified hemoglobin sample could be visualized at a series of doses up to 5500 MGy, by which dose the sample was sublimed. Comparison of equal-dose series collected with different incident flux densities showed a dose-rate effect favoring lower flux densities. Heat simulations predict that sample heating will only become an issue for very large dose rates (50 e(-)Å(-2) s(-1) or higher) combined with poor thermal contact between the grid and cryo-holder. Secondary radiolytic effects are likely to play a role in dose-rate effects. Stroboscopic data collection combined with an improved understanding of the effects of dose and dose rate will aid single-particle cryo-electron microscopists to have better control of the outcome of their experiments.