Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization

Automated model-free analysis of cryo-EM volume ensembles with SIREn

Cryogenic electron microscopy (cryo-EM) has the potential to capture snapshots of proteins in motion and generate hypotheses linking conformational states to biological function. This potential has been increasingly realized by the advent of machine learning models that allow 100s-1,000s of 3D density maps to be generated from a single dataset. How to identify distinct structural states within these volume ensembles and quantify their relative occupancies remain open questions. Here, we present an approach to inferring variable regions directly from a volume ensemble based on the statistical co-occupancy of voxels, as well as a 3D convolutional neural network that predicts binarization thresholds for volumes in an unbiased and automated manner. We show that these tools recapitulate known heterogeneity in a variety of simulated and real cryo-EM datasets and highlight how integrating these tools with existing data processing pipelines enables improved particle curation.

How Cryo-EM Revolutionized the Field of Bioenergetics

Ten years ago, the term "resolution revolution" was used for the first time to describe how cryogenic electron microscopy (cryo-EM) marked the beginning of a new era in the field of structural biology, enabling the investigation of previously unsolvable protein targets. The success of cryo-EM was recognized with the 2017 Chemistry Nobel Prize and has become a widely used method for the structural characterization of biological macromolecules, quickly catching up to x-ray crystallography. Bioenergetics is the division of biochemistry that studies the mechanisms of energy conversion in living organisms, strongly focused on the molecular machines (enzymes) that carry out these processes in cells. As bioenergetic enzymes can be arranged in complexes characterized by conformational heterogeneity/flexibility, they represent challenging targets for structural investigation by crystallography. Over the last decade, cryo-EM has therefore become a powerful tool to investigate the structure and function of bioenergetic complexes; here, we provide an overview of the main achievements enabled by the technique. We first summarize the features of cryo-EM and compare them to x-ray crystallography, and then, we present the exciting discoveries brought about by cryo-EM, particularly but not exclusively focusing on the oxidative phosphorylation system, which is a crucial energy-converting mechanism in humans.

Improvement in positional accuracy of neural-network predicted hydration sites of proteins by incorporating atomic details of water-protein interactions and site-searching algorithm

Visualization of hydration structures over the entire protein surface is necessary to understand why the aqueous environment is essential for protein folding and functions. However, it is still difficult for experiments. Recently, we developed a convolutional neural network (CNN) to predict the probability distribution of hydration water molecules over protein surfaces and in protein cavities. The deep network was optimized using solely the distribution patterns of protein atoms surrounding each hydration water molecule in high-resolution X-ray crystal structures and successfully provided probability distributions of hydration water molecules. Despite the effectiveness of the probability distribution, the positional differences of the predicted positions obtained from the local maxima as predicted sites remained inadequate in reproducing the hydration sites in the crystal structure models. In this work, we modified the deep network by subdividing atomic classes based on the electronic properties of atoms composing amino acids. In addition, the exclusion volumes of each protein atom and hydration water molecule were taken to predict the hydration sites from the probability distribution. These information on chemical properties of atoms leads to an improvement in positional prediction accuracy. We selected the best CNN from 47 CNNs constructed by systematically varying the number of channels and layers of neural networks. Here, we report the improvements in prediction accuracy by the reorganized CNN together with the details in the architecture, training data, and peak search algorithm.

CryoSTAR: leveraging structural priors and constraints for cryo-EM heterogeneous reconstruction

Resolving conformational heterogeneity in cryogenic electron microscopy datasets remains an important challenge in structural biology. Previous methods have often been restricted to working exclusively on volumetric densities, neglecting the potential of incorporating any preexisting structural knowledge as prior or constraints. Here we present cryoSTAR, which harnesses atomic model information as structural regularization to elucidate such heterogeneity. Our method uniquely outputs both coarse-grained models and density maps, showcasing the molecular conformational changes at different levels. Validated against four diverse experimental datasets, spanning large complexes, a membrane protein and a small single-chain protein, our results consistently demonstrate an efficient and effective solution to conformational heterogeneity with minimal human bias. By integrating atomic model insights with cryogenic electron microscopy data, cryoSTAR represents a meaningful step forward, paving the way for a deeper understanding of dynamic biological processes.

Bayesian reweighting of biomolecular structural ensembles using heterogeneous cryo-EM maps with the cryoENsemble method

Cryogenic electron microscopy (cryo-EM) has emerged as a powerful method for the determination of structures of complex biological molecules. The accurate characterisation of the dynamics of such systems, however, remains a challenge. To address this problem, we introduce cryoENsemble, a method that applies Bayesian reweighting to conformational ensembles derived from molecular dynamics simulations to improve their agreement with cryo-EM data, thus enabling the extraction of dynamics information. We illustrate the use of cryoENsemble to determine the dynamics of the ribosome-bound state of the co-translational chaperone trigger factor (TF). We also show that cryoENsemble can assist with the interpretation of low-resolution, noisy or unaccounted regions of cryo-EM maps. Notably, we are able to link an unaccounted part of the cryo-EM map to the presence of another protein (methionine aminopeptidase, or MetAP), rather than to the dynamics of TF, and model its TF-bound state. Based on these results, we anticipate that cryoENsemble will find use for challenging heterogeneous cryo-EM maps for biomolecular systems encompassing dynamic components.

Conventional Electron Microscopy, Cryogenic Electron Microscopy, and Cryogenic Electron Tomography of Viruses

Electron microscopy (EM) techniques have been crucial for understanding the structure of biological specimens such as cells, tissues and macromolecular assemblies. Viruses and related viral assemblies are ideal targets for structural studies that help to define essential biological functions. Whereas conventional EM methods use chemical fixation, dehydration, and staining of the specimens, cryogenic electron microscopy (cryo-EM) preserves the native hydrated state. Combined with image processing and three-dimensional reconstruction techniques, cryo-EM provides three-dimensional maps of these macromolecular complexes from projection images, at atomic or near-atomic resolutions. Cryo-EM is also a major technique in structural biology for dynamic studies of functional complexes, which are often unstable, flexible, scarce, or transient in their native environments. State-of-the-art techniques in structural virology now extend beyond purified symmetric capsids and focus on the asymmetric elements such as the packaged genome and minor structural proteins that were previously missed. As a tool, cryo-EM also complements high-resolution techniques such as X-ray diffraction and NMR spectroscopy; these synergistic hybrid approaches provide important new information. Three-dimensional cryogenic electron tomography (cryo-ET), a variation of cryo-EM, goes further, and allows the study of pleomorphic and complex viruses not only in their physiological state but also in their natural environment in the cell, thereby bridging structural studies at the molecular and cellular levels. Cryo-EM and cryo-ET have been applied successfully in basic research, shedding light on fundamental aspects of virus biology and providing insights into threatening viruses, including SARS-CoV-2, responsible for the COVID-19 pandemic.

Insights into protein structure using cryogenic light microscopy

Fluorescence microscopy has witnessed many clever innovations in the last two decades, leading to new methods such as structured illumination and super-resolution microscopies. The attainable resolution in biological samples is, however, ultimately limited by residual motion within the sample or in the microscope setup. Thus, such experiments are typically performed on chemically fixed samples. Cryogenic light microscopy (Cryo-LM) has been investigated as an alternative, drawing on various preservation techniques developed for cryogenic electron microscopy (Cryo-EM). Moreover, this approach offers a powerful platform for correlative microscopy. Another key advantage of Cryo-LM is the strong reduction in photobleaching at low temperatures, facilitating the collection of orders of magnitude more photons from a single fluorophore. This results in much higher localization precision, leading to Angstrom resolution. In this review, we discuss the general development and progress of Cryo-LM with an emphasis on its application in harnessing structural information on proteins and protein complexes.

MDSPACE and MDTOMO Software for Extracting Continuous Conformational Landscapes from Datasets of Single Particle Images and Subtomograms Based on Molecular Dynamics Simulations: Latest Developments in ContinuousFlex Software Package

Cryo electron microscopy (cryo-EM) instrumentation allows obtaining 3D reconstruction of the structure of biomolecular complexes in vitro (purified complexes studied by single particle analysis) and in situ (complexes studied in cells by cryo electron tomography). Standard cryo-EM approaches allow high-resolution reconstruction of only a few conformational states of a molecular complex, as they rely on data classification into a given number of classes to increase the resolution of the reconstruction from the most populated classes while discarding all other classes. Such discrete classification approaches result in a partial picture of the full conformational variability of the complex, due to continuous conformational transitions with many, uncountable intermediate states. In this article, we present the software with a user-friendly graphical interface for running two recently introduced methods, namely, MDSPACE and MDTOMO, to obtain continuous conformational landscapes of biomolecules by analyzing in vitro and in situ cryo-EM data (single particle images and subtomograms) based on molecular dynamics simulations of an available atomic model of one of the conformations. The MDSPACE and MDTOMO software is part of the open-source ContinuousFlex software package (starting from version 3.4.2 of ContinuousFlex), which can be run as a plugin of the Scipion software package (version 3.1 and later), broadly used in the cryo-EM field.

Focused classifications and refinements in high-resolution single particle cryo-EM analysis

Recent advances in cryo electron microscopy (cryo-EM) and image processing provide new opportunities to analyse drug targets at high resolution. However, structural heterogeneity limits resolution in many practical cases, hence restricting the level at which structural details can be analysed and drug design be performed. As structural disorder is not spread throughout the entire structure of a given macromolecular complex but instead is found in certain regions that move with respect to others and covering molecular scales from domain conformational changes up to the level of side chain conformations in ligand binding pockets, it is possible to focus the attention on those regions and the associated relative movements. Here we show how the usage of focused classifications and refinements provide insights into global conformational arrangements, exemplified on the human ribosome and on the cannabinoid G protein coupled receptor (GPCR), and how they can improve the local map resolution from an essentially disordered region to the 3-4 Å and finally to the 2 Å resolution range. A systematic analysis with variable spherical masks during focused refinement is presented showing that the choice of an optimal mask size helps refining to high resolution. This study covers several practical approaches on 4 examples illustrating how important mask size & shape and including neighbouring structural elements are for a focused analysis of a macromolecular complex. Such methods will be crucial for cryo-EM structure-based drug design of various medical targets and are applicable to single particle cryo-EM and electron tomography data.

Detecting continuous structural heterogeneity in single-molecule localization microscopy data

Fusion of multiple chemically identical complexes, so-called particles, in localization microscopy, can improve the signal-to-noise ratio and overcome under-labeling. To this end, structural homogeneity of the data must be assumed. Biological heterogeneity, however, could be present in the data originating from distinct conformational variations or (continuous) variations in particle shapes. We present a prior-knowledge-free method for detecting continuous structural variations with localization microscopy. Detecting this heterogeneity leads to more faithful fusions and reconstructions of the localization microscopy data as their heterogeneity is taken into account. In experimental datasets, we show the continuous variation of the height of DNA origami tetrahedrons imaged with 3D PAINT and of the radius of Nuclear Pore Complexes imaged in 2D with STORM. In simulation, we study the impact on the heterogeneity detection pipeline of Degree Of Labeling and of structural variations in the form of two independent modes.

Advances in computational approaches to structure determination of alphaviruses and flaviviruses using cryo-electron microscopy

Advancements in the field of cryo-electron microscopy (cryo-EM) have greatly contributed to our current understanding of virus structures and life cycles. In this review, we discuss the application of single particle cryo-electron microscopy (EM) for the structure elucidation of small enveloped icosahedral viruses, namely, alpha- and flaviviruses. We focus on technical advances in cryo-EM data collection, image processing, three-dimensional reconstruction, and refinement strategies for obtaining high-resolution structures of these viruses. Each of these developments enabled new insights into the alpha- and flavivirus architecture, leading to a better understanding of their biology, pathogenesis, immune response, immunogen design, and therapeutic development.

3DFlex: determining structure and motion of flexible proteins from cryo-EM

Modeling flexible macromolecules is one of the foremost challenges in single-particle cryogenic-electron microscopy (cryo-EM), with the potential to illuminate fundamental questions in structural biology. We introduce Three-Dimensional Flexible Refinement (3DFlex), a motion-based neural network model for continuous molecular heterogeneity for cryo-EM data. 3DFlex exploits knowledge that conformational variability of a protein is often the result of physical processes that transport density over space and tend to preserve local geometry. From two-dimensional image data, 3DFlex enables the determination of high-resolution 3D density, and provides an explicit model of a flexible protein's motion over its conformational landscape. Experimentally, for large molecular machines (tri-snRNP spliceosome complex, translocating ribosome) and small flexible proteins (TRPV1 ion channel, αVβ8 integrin, SARS-CoV-2 spike), 3DFlex learns nonrigid molecular motions while resolving details of moving secondary structure elements. 3DFlex can improve 3D density resolution beyond the limits of existing methods because particle images contribute coherent signal over the conformational landscape.

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.

Methods for Cryo-EM Single Particle Reconstruction of Macromolecules Having Continuous Heterogeneity

Macromolecules change their shape (conformation) in the process of carrying out their functions. The imaging by cryo-electron microscopy of rapidly-frozen, individual copies of macromolecules (single particles) is a powerful and general approach to understanding the motions and energy landscapes of macromolecules. Widely-used computational methods already allow the recovery of a few distinct conformations from heterogeneous single-particle samples, but the treatment of complex forms of heterogeneity such as the continuum of possible transitory states and flexible regions remains largely an open problem. In recent years there has been a surge of new approaches for treating the more general problem of continuous heterogeneity. This paper surveys the current state of the art in this area.

Computational Methods Toward Unbiased Pattern Mining and Structure Determination in Cryo-Electron Tomography Data

Cryo-electron tomography can uniquely probe the native cellular environment for macromolecular structures. Tomograms feature complex data with densities of diverse, densely crowded macromolecular complexes, low signal-to-noise, and artifacts such as the missing wedge effect. Post-processing of this data generally involves isolating regions or particles of interest from tomograms, organizing them into related groups, and rendering final structures through subtomogram averaging. Template-matching and reference-based structure determination are popular analysis methods but are vulnerable to biases and can often require significant user input. Most importantly, these approaches cannot identify novel complexes that reside within the imaged cellular environment. To reliably extract and resolve structures of interest, efficient and unbiased approaches are therefore of great value. This review highlights notable computational software and discusses how they contribute to making automated structural pattern discovery a possibility. Perspectives emphasizing the importance of features for user-friendliness and accessibility are also presented.

High-resolution cryo-EM performance comparison of two latest-generation cryo electron microscopes on the human ribosome

Recent technological advances in cryo electron microscopy (cryo-EM) have led to new opportunities in the structural biology field. Here we benchmark the performance of two 300 kV latest-generation cryo electron microscopes, Titan Krios G4 from Thermofisher Scientific and CRYO ARM 300 from Jeol, with regards to achieving high resolution single particle reconstructions on a real case sample. We compare potentially limiting factors such as drift rates, astigmatism & coma aberrations and performance during image processing and show that both microscopes, while comprising rather different technical setups & parameter settings and equipped with different types of energy filters & cameras, achieve a resolution of around 2 Å on the human ribosome, a non-symmetric object which constitutes a key drug target. Astigmatism correction, CTF refinement and correction of higher order aberrations through refinement in separate optics groups helped to account for astigmatism/coma caused by beam tilting during multi-spot and multi-hole acquisition in neighbouring holes without stage movement. The obtained maps resolve Mg²⁺ ions, water molecules, inhibitors and side-chains including chemical modifications. The fact that both instruments can resolve such detailed features will greatly facilitate understanding molecular mechanisms of various targets and helps in cryo-EM structure based drug design. The methods and analysis tools used here will be useful also to characterize existing instruments and optimize data acquisition settings and are applicable broadly to other drug targets in structural biology.

Prediction of hydrophilic and hydrophobic hydration structure of protein by neural network optimized using experimental data

The hydration structures of proteins, which are necessary for their folding, stability, and functions, were visualized using X-ray and neutron crystallography and transmission electron microscopy. However, complete visualization of hydration structures over the entire protein surface remains difficult. To compensate for this incompleteness, we developed a three-dimensional convolutional neural network to predict the probability distribution of hydration water molecules on the hydrophilic and hydrophobic surfaces, and in the cavities of proteins. The neural network was optimized using the distribution patterns of protein atoms around the hydration water molecules identified in the high-resolution X-ray crystal structures. We examined the feasibility of the neural network using water sites in the protein crystal structures that were not included in the datasets. The predicted distribution covered most of the experimentally identified hydration sites, with local maxima appearing in their vicinity. This computational approach will help to highlight the relevance of hydration structures to the biological functions and dynamics of proteins.

MDSPACE: Extracting Continuous Conformational Landscapes from Cryo-EM Single Particle Datasets Using 3D-to-2D Flexible Fitting based on Molecular Dynamics Simulation

This article presents an original approach for extracting atomic-resolution landscapes of continuous conformational variability of biomolecular complexes from cryo electron microscopy (cryo-EM) single particle images. This approach is based on a new 3D-to-2D flexible fitting method, which uses molecular dynamics (MD) simulation and is embedded in an iterative conformational-landscape refinement scheme. This new approach is referred to as MDSPACE, which stands for Molecular Dynamics simulation for Single Particle Analysis of Continuous Conformational hEterogeneity. The article describes the MDSPACE approach and shows its performance using synthetic and experimental datasets.

Exploring the Structural Variability of Dynamic Biological Complexes by Single-Particle Cryo-Electron Microscopy

Biological macromolecules and assemblies precisely rearrange their atomic 3D structures to execute cellular functions. Understanding the mechanisms by which these molecular machines operate requires insight into the ensemble of structural states they occupy during the functional cycle. Single-particle cryo-electron microscopy (cryo-EM) has become the preferred method to provide near-atomic resolution, structural information about dynamic biological macromolecules elusive to other structure determination methods. Recent advances in cryo-EM methodology have allowed structural biologists not only to probe the structural intermediates of biochemical reactions, but also to resolve different compositional and conformational states present within the same dataset. This article reviews newly developed sample preparation and single-particle analysis (SPA) techniques for high-resolution structure determination of intrinsically dynamic and heterogeneous samples, shedding light upon the intricate mechanisms employed by molecular machines and helping to guide drug discovery efforts.

CryoEM of endogenous mammalian V-ATPase interacting with the TLDc protein mEAK-7

V-ATPases are rotary proton pumps that serve as signaling hubs with numerous protein binding partners. CryoEM with exhaustive focused classification allowed detection of endogenous proteins associated with porcine kidney V-ATPase. An extra C subunit was found in ∼3% of complexes, whereas ∼1.6% of complexes bound mEAK-7, a protein with proposed roles in dauer formation in nematodes and mTOR signaling in mammals. High-resolution cryoEM of porcine kidney V-ATPase with recombinant mEAK-7 showed that mEAK-7's TLDc domain interacts with V-ATPase's stator, whereas its C-terminal α helix binds V-ATPase's rotor. This crosslink would be expected to inhibit rotary catalysis. However, unlike the yeast TLDc protein Oxr1p, exogenous mEAK-7 does not inhibit V-ATPase and mEAK-7 overexpression in cells does not alter lysosomal or phagosomal pH. Instead, cryoEM suggests that the mEAK-7:V-ATPase interaction is disrupted by ATP-induced rotation of the rotor. Comparison of Oxr1p and mEAK-7 binding explains this difference. These results show that V-ATPase binding by TLDc domain proteins can lead to effects ranging from strong inhibition to formation of labile interactions that are sensitive to the enzyme's activity.

Emerging Themes in CryoEM─Single Particle Analysis Image Processing

Cryo-electron microscopy (CryoEM) has become a vital technique in structural biology. It is an interdisciplinary field that takes advantage of advances in biochemistry, physics, and image processing, among other disciplines. Innovations in these three basic pillars have contributed to the boosting of CryoEM in the past decade. This work reviews the main contributions in image processing to the current reconstruction workflow of single particle analysis (SPA) by CryoEM. Our review emphasizes the time evolution of the algorithms across the different steps of the workflow differentiating between two groups of approaches: analytical methods and deep learning algorithms. We present an analysis of the current state of the art. Finally, we discuss the emerging problems and challenges still to be addressed in the evolution of CryoEM image processing methods in SPA.

DeepHEMNMA: ResNet-based hybrid analysis of continuous conformational heterogeneity in cryo-EM single particle images

Single-particle cryo-electron microscopy (cryo-EM) is a technique for biomolecular structure reconstruction from vitrified samples containing many copies of a biomolecular complex (known as single particles) at random unknown 3D orientations and positions. Cryo-EM allows reconstructing multiple conformations of the complexes from images of the same sample, which usually requires many rounds of 2D and 3D classifications to disentangle and interpret the combined conformational, orientational, and translational heterogeneity. The elucidation of different conformations is the key to understand molecular mechanisms behind the biological functions of the complexes and the key to novel drug discovery. Continuous conformational heterogeneity, due to gradual conformational transitions giving raise to many intermediate conformational states of the complexes, is both an obstacle for high-resolution 3D reconstruction of the conformational states and an opportunity to obtain information about multiple coexisting conformational states at once. HEMNMA method, specifically developed for analyzing continuous conformational heterogeneity in cryo-EM, determines the conformation, orientation, and position of the complex in each single particle image by image analysis using normal modes (the motion directions simulated for a given atomic structure or EM map), which in turn allows determining the full conformational space of the complex but at the price of high computational cost. In this article, we present a new method, referred to as DeepHEMNMA, which speeds up HEMNMA by combining it with a residual neural network (ResNet) based deep learning approach. The performance of DeepHEMNMA is shown using synthetic and experimental single particle images.

Visualizing Conformational Space of Functional Biomolecular Complexes by Deep Manifold Learning

The cellular functions are executed by biological macromolecular complexes in nonequilibrium dynamic processes, which exhibit a vast diversity of conformational states. Solving the conformational continuum of important biomolecular complexes at the atomic level is essential to understanding their functional mechanisms and guiding structure-based drug discovery. Here, we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions that approximately visualize the conformational space of biomolecular complexes of interest. AlphaCryo4D integrates 3D deep residual learning with manifold embedding of pseudo-energy landscapes, which simultaneously improves 3D classification accuracy and reconstruction resolution via an energy-based particle-voting algorithm. In blind assessments using simulated heterogeneous datasets, AlphaCryo4D achieved 3D classification accuracy three times those of alternative methods and reconstructed continuous conformational changes of a 130-kDa protein at sub-3 Å resolution. By applying this approach to analyze several experimental datasets of the proteasome, ribosome and spliceosome, we demonstrate its potential generality in exploring hidden conformational space or transient states of macromolecular complexes that remain hitherto invisible. Integration of this approach with time-resolved cryo-EM further allows visualization of conformational continuum in a nonequilibrium regime at the atomic level, thus potentially enabling therapeutic discovery against highly dynamic biomolecular targets.

Structures of the human CST-Polα-primase complex bound to telomere templates

The mammalian DNA polymerase-α-primase (Polα-primase) complex is essential for DNA metabolism, providing the de novo RNA-DNA primer for several DNA replication pathways^1-4 such as lagging-strand synthesis and telomere C-strand fill-in. The physical mechanism underlying how Polα-primase, alone or in partnership with accessory proteins, performs its complicated multistep primer synthesis function is unknown. Here we show that CST, a single-stranded DNA-binding accessory protein complex for Polα-primase, physically organizes the enzyme for efficient primer synthesis. Cryogenic electron microscopy structures of the CST-Polα-primase preinitiation complex (PIC) bound to various types of telomere overhang reveal that template-bound CST partitions the DNA and RNA catalytic centres of Polα-primase into two separate domains and effectively arranges them in RNA-DNA synthesis order. The architecture of the PIC provides a single solution for the multiple structural requirements for the synthesis of RNA-DNA primers by Polα-primase. Several insights into the template-binding specificity of CST, template requirement for assembly of the CST-Polα-primase PIC and activation are also revealed in this study.

CryoEM Reveals the Complexity and Diversity of ATP Synthases

During respiration, adenosine triphosphate (ATP) synthases harness the electrochemical proton motive force (PMF) generated by the electron transport chain (ETC) to synthesize ATP. These macromolecular machines operate by a remarkable rotary catalytic mechanism that couples transmembrane proton translocation to rotation of a rotor subcomplex, and rotation to ATP synthesis. Initially, x-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, and cross-linking were the only ways to gain insights into the three-dimensional (3D) structures of ATP synthases and, in particular, provided ground-breaking insights into the soluble parts of the complex that explained the catalytic mechanism by which rotation is coupled to ATP synthesis. In contrast, early electron microscopy was limited to studying the overall shape of the assembly. However, advances in electron cryomicroscopy (cryoEM) have allowed determination of high-resolution structures, including the membrane regions of ATP synthases. These studies revealed the high-resolution structures of the remaining ATP synthase subunits and showed how these subunits work together in the intact macromolecular machine. CryoEM continues to uncover the diversity of ATP synthase structures across species and has begun to show how ATP synthases can be targeted by therapies to treat human diseases.

Deciphering a hexameric protein complex with Angstrom optical resolution

Cryogenic optical localization in three dimensions (COLD) was recently shown to resolve up to four binding sites on a single protein. However, because COLD relies on intensity fluctuations that result from the blinking behavior of fluorophores, it is limited to cases where individual emitters show different brightness. This significantly lowers the measurement yield. To extend the number of resolved sites as well as the measurement yield, we employ partial labeling and combine it with polarization encoding in order to identify single fluorophores during their stochastic blinking. We then use a particle classification scheme to identify and resolve heterogenous subsets and combine them to reconstruct the three-dimensional arrangement of large molecular complexes. We showcase this method (polarCOLD) by resolving the trimer arrangement of proliferating cell nuclear antigen (PCNA) and six different sites of the hexamer protein Caseinolytic Peptidase B (ClpB) of Thermus thermophilus in its quaternary structure, both with Angstrom resolution. The combination of polarCOLD and single-particle cryogenic electron microscopy (cryoEM) promises to provide crucial insight into intrinsic heterogeneities of biomolecular structures. Furthermore, our approach is fully compatible with fluorescent protein labeling and can, thus, be used in a wide range of studies in cell and membrane biology.

Probing Structural Perturbation of Biomolecules by Extracting Cryo-EM Data Heterogeneity

Single-particle cryogenic electron microscopy (cryo-EM) has become an indispensable tool to probe high-resolution structural detail of biomolecules. It enables direct visualization of the biomolecules and opens a possibility for averaging molecular images to reconstruct a three-dimensional Coulomb potential density map. Newly developed algorithms for data analysis allow for the extraction of structural heterogeneity from a massive and low signal-to-noise-ratio (SNR) cryo-EM dataset, expanding our understanding of multiple conformational states, or further implications in dynamics, of the target biomolecule. This review provides an overview that briefly describes the workflow of single-particle cryo-EM, including imaging and data processing, and new methods developed for analyzing the data heterogeneity to understand the structural variability of biomolecules.

Cryogenic electron microscopy approaches that combine images and tilt series

Cryogenic electron microscopy can be widely applied to biological specimens from the molecular to the cellular scale. In single-particle analysis, 3D structures may be obtained in high resolution by averaging 2D images of single particles in random orientations. For pleomorphic specimens, structures may be obtained by recording the tilt series of a single example of the specimen and calculating tomograms. Where many copies of a single structure such as a protein or nucleic acid assembly are present within the tomogram, averaging of the sub-volumes (subtomogram averaging) has been successfully applied. The choice of data collection method for any given specimen may depend on the structural question of interest and is determined by the radiation sensitivity of the specimen. Here, we survey some recent developments on the use of hybrid methods for recording and analysing data from radiation-sensitive biological specimens. These include single-particle reconstruction from 2D images where additional views are recorded at a single tilt angle of the specimen and methods where image tilt series, initially used for tomogram reconstruction, are processed as individual single-particle images. There is a continuum of approaches now available to maximize structural information obtained from the specimen.

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 Bayesian approach to single-particle electron cryo-tomography in RELION-4.0

We present a new approach for macromolecular structure determination from multiple particles in electron cryo-tomography (cryo-ET) data sets. Whereas existing subtomogram averaging approaches are based on 3D data models, we propose to optimise a regularised likelihood target that approximates a function of the 2D experimental images. In addition, analogous to Bayesian polishing and contrast transfer function (CTF) refinement in single-particle analysis, we describe the approaches that exploit the increased signal-to-noise ratio in the averaged structure to optimise tilt-series alignments, beam-induced motions of the particles throughout the tilt-series acquisition, defoci of the individual particles, as well as higher-order optical aberrations of the microscope. Implementation of our approaches in the open-source software package RELION aims to facilitate their general use, particularly for those researchers who are already familiar with its single-particle analysis tools. We illustrate for three applications that our approaches allow structure determination from cryo-ET data to resolutions sufficient for de novo atomic modelling.

Cryo-EM Analyses Permit Visualization of Structural Polymorphism of Biological Macromolecules

The functions of biological macromolecules are often associated with conformational malleability of the structures. This phenomenon of chemically identical molecules with different structures is coined structural polymorphism. Conventionally, structural polymorphism is observed directly by structural determination at the density map level from X-ray crystal diffraction. Although crystallography approach can report the conformation of a macromolecule with the position of each atom accurately defined in it, the exploration of structural polymorphism and interpreting biological function in terms of crystal structures is largely constrained by the crystal packing. An alternative approach to studying the macromolecule of interest in solution is thus desirable. With the advancement of instrumentation and computational methods for image analysis and reconstruction, cryo-electron microscope (cryo-EM) has been transformed to be able to produce “in solution” structures of macromolecules routinely with resolutions comparable to crystallography but without the need of crystals. Since the sample preparation of single-particle cryo-EM allows for all forms co-existing in solution to be simultaneously frozen, the image data contain rich information as to structural polymorphism. The ensemble of structure information can be subsequently disentangled through three-dimensional (3D) classification analyses. In this review, we highlight important examples of protein structural polymorphism in relation to allostery, subunit cooperativity and function plasticity recently revealed by cryo-EM analyses, and review recent developments in 3D classification algorithms including neural network/deep learning approaches that would enable cryo-EM analyese in this regard. Finally, we brief the frontier of cryo-EM structure determination of RNA molecules where resolving the structural polymorphism is at dawn.

Structural features of nucleosomes in interphase and metaphase chromosomes

Structural heterogeneity of nucleosomes in functional chromosomes is unknown. Here, we devise the template-, reference- and selection-free (TRSF) cryo-EM pipeline to simultaneously reconstruct cryo-EM structures of protein complexes from interphase or metaphase chromosomes. The reconstructed interphase and metaphase nucleosome structures are on average indistinguishable from canonical nucleosome structures, despite DNA sequence heterogeneity, cell-cycle-specific posttranslational modifications, and interacting proteins. Nucleosome structures determined by a decoy-classifying method and structure variability analyses reveal the nucleosome structural variations in linker DNA, histone tails, and nucleosome core particle configurations, suggesting that the opening of linker DNA, which is correlated with H2A C-terminal tail positioning, is suppressed in chromosomes. High-resolution (3.4-3.5 Å) nucleosome structures indicate DNA-sequence-independent stabilization of superhelical locations ±0-1 and ±3.5-4.5. The linker histone H1.8 preferentially binds to metaphase chromatin, from which chromatosome cryo-EM structures with H1.8 at the on-dyad position are reconstituted. This study presents the structural characteristics of nucleosomes in chromosomes.

Deep learning-based mixed-dimensional Gaussian mixture model for characterizing variability in cryo-EM

Structural flexibility and/or dynamic interactions with other molecules is a critical aspect of protein function. CryoEM provides direct visualization of individual macromolecules sampling different conformational and compositional states. While numerous methods are available for computational classification of discrete states, characterization of continuous conformational changes or large numbers of discrete state without human supervision remains challenging. Here we present e2gmm, a machine learning algorithm to determine a conformational landscape for proteins or complexes using a 3-D Gaussian mixture model mapped onto 2-D particle images in known orientations. Using a deep neural network architecture, e2gmm can automatically resolve the structural heterogeneity within the protein complex and map particles onto a small latent space describing conformational and compositional changes. This system presents a more intuitive and flexible representation than other manifold methods currently in use. We demonstrate this method on both simulated data as well as three biological systems, to explore compositional and conformational changes at a range of scales. The software is distributed as part of EMAN2.

An Overview of Microcrystal Electron Diffraction (MicroED)

The bedrock of drug discovery and a key tool for understanding cellular function and drug mechanisms of action is the structure determination of chemical compounds, peptides, and proteins. The development of new structure characterization tools, particularly those that fill critical gaps in existing methods, presents important steps forward for structural biology and drug discovery. The emergence of microcrystal electron diffraction (MicroED) expands the application of cryo-electron microscopy to include samples ranging from small molecules and membrane proteins to even large protein complexes using crystals that are one-billionth the size of those required for X-ray crystallography. This review outlines the conception, achievements, and exciting future trajectories for MicroED, an important addition to the existing biophysical toolkit.

Bayesian Random Tomography of Particle Systems

Random tomography is a common problem in imaging science and refers to the task of reconstructing a three-dimensional volume from two-dimensional projection images acquired in unknown random directions. We present a Bayesian approach to random tomography. At the center of our approach is a meshless representation of the unknown volume as a mixture of spherical Gaussians. Each Gaussian can be interpreted as a particle such that the unknown volume is represented by a particle cloud. The particle representation allows us to speed up the computation of projection images and to represent a large variety of structures accurately and efficiently. We develop Markov chain Monte Carlo algorithms to infer the particle positions as well as the unknown orientations. Posterior sampling is challenging due to the high dimensionality and multimodality of the posterior distribution. We tackle these challenges by using Hamiltonian Monte Carlo and a global rotational sampling strategy. We test the approach on various simulated and real datasets.

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.

State-dependent sequential allostery exhibited by chaperonin TRiC/CCT revealed by network analysis of Cryo-EM maps

The eukaryotic chaperonin TRiC/CCT plays a major role in assisting the folding of many proteins through an ATP-driven allosteric cycle. Recent structures elucidated by cryo-electron microscopy provide a broad view of the conformations visited at various stages of the chaperonin cycle, including a sequential activation of its subunits in response to nucleotide binding. But we lack a thorough mechanistic understanding of the structure-based dynamics and communication properties that underlie the TRiC/CCT machinery. In this study, we present a computational methodology based on elastic network models adapted to cryo-EM density maps to gain a deeper understanding of the structure-encoded allosteric dynamics of this hexadecameric machine. We have analysed several structures of the chaperonin resolved in different states toward mapping its conformational landscape. Our study indicates that the overall architecture intrinsically favours cooperative movements that comply with the structural variabilities observed in experiments. Furthermore, the individual subunits CCT1-CCT8 exhibit state-dependent sequential events at different states of the allosteric cycle. For example, in the ATP-bound state, subunits CCT5 and CCT4 selectively initiate the lid closure motions favoured by the overall architecture; whereas in the apo form of the heteromer, the subunit CCT7 exhibits the highest predisposition to structural change. The changes then propagate through parallel fluxes of allosteric signals to neighbours on both rings. The predicted state-dependent mechanisms of sequential activation provide new insights into TRiC/CCT intra- and inter-ring signal transduction events.

Improve the Resolution and Parallel Performance of the Three-Dimensional Refine Algorithm in RELION Using CUDA and MPI

In cryo-electron microscopy, RELION is a powerful tool for high-resolution reconstruction. Due to the complicated imaging procedure and the heterogeneity of particles, some of the selected particle images offer more disturbing information than others. However, in the current RELION, all these particle images are treated equally. In our work, we extend RELION's model with one scalar parameter to score the contribution of a particle depending on the error between the experimental particle and the corresponding reprojection. This scores down weight potentially poor particles, hence accelerating the convergence. Besides, by now there is no sophisticated memory management system for RELION, fragmentation on GPU will increase with iterations, eventually crashing the program. In our work, we designed the stack-based memory management system to guarantee the stability of RELION and to optimize the memory usage condition. Also, to reduce memory usage, we developed a customized compressed data structure for the memory-demanding weight array. In addition, to speed up the GPU version of RELION, we proposed two highly efficient parallel algorithms for weight calculation algorithm and weight selection algorithm. Experiments show that compared with RELION, the optimized three-dimensional refine algorithm can speed up the converge procedure, the memory system can avoid memory fragmentation, and a better speed-up ratio can be obtained.

3D variability analysis: Resolving continuous flexibility and discrete heterogeneity from single particle cryo-EM

Single particle cryo-EM excels in determining static structures of protein molecules, but existing 3D reconstruction methods have been ineffective in modelling flexible proteins. We introduce 3D variability analysis (3DVA), an algorithm that fits a linear subspace model of conformational change to cryo-EM data at high resolution. 3DVA enables the resolution and visualization of detailed molecular motions of both large and small proteins, revealing new biological insight from single particle cryo-EM data. Experimental results demonstrate the ability of 3DVA to resolve multiple flexible motions of α-helices in the sub-50 kDa transmembrane domain of a GPCR complex, bending modes of a sodium ion channel, five types of symmetric and symmetry-breaking flexibility in a proteasome, large motions in a spliceosome complex, and discrete conformational states of a ribosome assembly. 3DVA is implemented in the cryoSPARC software package.

Preparing Better Samples for Cryo-Electron Microscopy: Biochemical Challenges Do Not End with Isolation and Purification

The preparation of extremely thin samples, which are required for high-resolution electron microscopy, poses extreme risk of damaging biological macromolecules due to interactions with the air-water interface. Although the rapid increase in the number of published structures initially gave little indication that this was a problem, the search for methods that substantially mitigate this hazard is now intensifying. The two main approaches under investigation are (a) immobilizing particles onto structure-friendly support films and (b) reducing the length of time during which such interactions may occur. While there is little possibility of outrunning diffusion to the interface, intentional passivation of the interface may slow the process of adsorption and denaturation. In addition, growing attention is being given to gaining more effective control of the thickness of the sample prior to vitrification.

ENRICH: A fast method to improve the quality of flexible macromolecular reconstructions

Cryo-electron microscopy using single particle analysis requires the computational averaging of thousands of projection images captured from identical macromolecules. However, macromolecules usually present some degree of flexibility showing different conformations. Computational approaches are then required to classify heterogeneous single particle images into homogeneous sets corresponding to different structural states. Nonetheless, sometimes the attainable resolution of reconstructions obtained from these smaller homogeneous sets is compromised because of reduced number of particles or lack of images at certain macromolecular orientations. In these situations, the current solution to improve map resolution is returning to the electron microscope and collect more data. In this work, we present a fast approach to partially overcome this limitation for heterogeneous data sets. Our method is based on deforming and then moving particles between different conformations using an optical flow approach. Particles are then merged into a unique conformation obtaining reconstructions with improved resolution, contrast and signal-to-noise ratio. We present experimental results that show clear improvements in the quality of obtained 3D maps, however, there are also limits to this approach, i.e., the method is restricted to small deformations and cannot determine local patterns of flexibility of small elements, such as secondary structures, which we discuss in the manuscript.

Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination

Three-dimensional reconstruction of the electron-scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularization approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge that it exploits compares unfavorably with the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, a regularization framework for cryo-EM structure determination is presented that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. This neural network is inserted into the iterative cryo-EM structure-determination process through an approach that is inspired by regularization by denoising. It is shown that the new regularization approach yields better reconstructions than the current state of the art for simulated data, and options to extend this work for application to experimental cryo-EM data are discussed.

Single Particle Analysis for High-Resolution 2D Electron Crystallography

Electron crystallography has been used for decades to determine three-dimensional structures of membrane proteins embedded in a lipid bilayer. However, high-resolution information could only be retrieved from samples where the 2D crystals were well ordered and perfectly flat. This is rarely the case in practice. We implemented in the FOCUS package a module to export transmission electron microscopy images of 2D crystals for 3D reconstruction by single particle algorithms. This approach allows for correcting local distortions of the 2D crystals, yielding much higher resolution reconstructions than otherwise expected from the observable diffraction spots. In addition, the single particle framework enables classification of heterogeneous structures coexisting within the 2D crystals. We provide here a detailed guide on single particle analysis of 2D crystal data based on the FOCUS and FREALIGN packages.

CryoEM of bacterial secretion systems: A primer for microbiologists

"CryoEM" has come of age, enabling considerable structural insights into many facets of molecular biology. Here, we present a primer for microbiologists to understand the capabilities and limitations of two complementary cryoEM techniques for studying bacterial secretion systems. The first, single particle analysis, determines the structures of purified protein complexes to resolutions sufficient for molecular modeling, while the second, electron cryotomography and subtomogram averaging, tends to determine more modest resolution structures of protein complexes in intact cells. We illustrate these abilities with examples of insights provided into how secretion systems work by cryoEM, with a focus on type III secretion systems.

Assessment of Force Field Accuracy Using Cryogenic Electron Microscopy Data of Hyper-thermostable Glutamate Dehydrogenase

Molecular dynamics (MD) simulations in biophysically relevant time scales of microseconds is a powerful tool for studying biomolecular processes, but results often display force field dependency. Therefore, assessment of force field accuracy using experimental data of biomolecules in solution is essential for simulation studies. Here, we propose the use of structural models obtained via cryo-electron microscopy (cryoEM), which provides biomolecular structures in vitreous ice mimicking the environment in solution. The accuracy of the AMBER (ff99SB-ILDN-NMR, ff14SB, ff15ipq, and ff15FB) and CHARMM (CHARMM22 and CHARMM36m) force fields was assessed by comparing their MD trajectories with the cryoEM data of thermostable hexameric glutamate dehydrogenase (GDH), which included a cryoEM map at a resolution of approximately 3 Å and structure models of subunits reflecting metastable conformations in domain motion occurring in GDH. In the assessment, we validated the force fields with respect to the reproducibility and stability of secondary structures and intersubunit interactions in the cryoEM data. Furthermore, we evaluated the force fields regarding the reproducibility of the energy landscape in the domain motion expected from the cryoEM data. As a result, among the six force fields, ff15FB and ff99SB-ILDN-NMR displayed good agreement with the experiment. The present study demonstrated the advantages of the high-resolution cryoEM map and suggested the optimal force field to reproduce experimentally observed protein structures.

Continuous flexibility analysis of SARS-CoV-2 spike prefusion structures

Using a new consensus-based image-processing approach together with principal component analysis, the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state have been analysed. These studies revealed concerted motions involving the receptor-binding domain (RBD), N-terminal domain, and subdomains 1 and 2 around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. It is shown that in this data set there are not well defined, stable spike conformations, but virtually a continuum of states. An ensemble map was obtained with minimum bias, from which the extremes of the change along the direction of maximal variance were modeled by flexible fitting. The results provide a warning of the potential image-processing classification instability of these complicated data sets, which has a direct impact on the interpretability of the results.

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.

Continuous flexibility analysis of SARS-CoV-2 Spike prefusion structures

With the help of novel processing workflows and algorithms, we have obtained a better understanding of the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state. We have re-analyzed previous cryo-EM data combining 3D clustering approaches with ways to explore a continuous flexibility space based on 3D Principal Component Analysis. These advanced analyses revealed a concerted motion involving the receptor-binding domain (RBD), N-terminal domain (NTD), and subdomain 1 and 2 (SD1 & SD2) around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. We show that in this dataset there are not well-defined, stable, spike conformations, but virtually a continuum of states moving in a concerted fashion. We obtained an improved resolution ensemble map with minimum bias, from which we model by flexible fitting the extremes of the change along the direction of maximal variance. Moreover, a high-resolution structure of a recently described biochemically stabilized form of the spike is shown to greatly reduce the dynamics observed for the wild-type spike. Our results provide new detailed avenues to potentially restrain the spike dynamics for structure-based drug and vaccine design and at the same time give a warning of the potential image processing classification instability of these complicated datasets, having a direct impact on the interpretability of the results.

Computational Methods for Single-Particle Electron Cryomicroscopy

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the three-dimensional molecular structure needs to be determined from many noisy two-dimensional tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications.