Image restoration in cryo-electron microscopy

Ghostbuster: A phase retrieval diffraction tomography algorithm for cryo-EM

Ewald sphere curvature correction, which extends beyond the projection approximation, stretches the shallow depth of field in cryo-EM reconstructions of thick particles. Here we show that even for previously assumed thin particles, reconstruction artifacts which we refer to as ghosts can appear. By retrieving the lost phases of the electron exitwaves and accounting for the first Born approximation scattering within the particle, we show that these ghosts can be effectively eliminated. Our simulations demonstrate how such ghostbusting can improve reconstructions as compared to existing state-of-the-art software. Like ptychographic cryo-EM, our Ghostbuster algorithm uses phase retrieval to improve reconstructions, but unlike the former, we do not need to modify the existing data acquisition pipelines.

Improved Denoising of Cryo-Electron Microscopy Micrographs with Simulation-Aware Pretraining

Cryo-electron microscopy (cryo-EM) has emerged as a potent technique for determining the structure and functionality of biological macromolecules. However, limited by the physical imaging conditions, such as low electron beam dose, micrographs in cryo-EM typically contend with an extremely low signal-to-noise ratio (SNR), impeding the efficiency and efficacy of subsequent analyses. Therefore, there is a growing demand for an efficient denoising algorithm designed for cryo-EM micrographs, aiming to enhance the quality of macromolecular analysis. However, owing to the absence of a comprehensive and well-defined dataset with ground truth images, supervised image denoising methods exhibit limited generalization when applied to experimental micrographs. To tackle this challenge, we introduce a simulation-aware image denoising (SaID) pretrained model designed to enhance the SNR of cryo-EM micrographs where the training is solely based on an accurately simulated dataset. First, we propose a parameter calibration algorithm for simulated dataset generation, aiming to align simulation parameters with those of experimental micrographs. Second, leveraging the accurately simulated dataset, we propose to train a deep general denoising model that can well generalize to real experimental cryo-EM micrographs. Comprehensive experimental results demonstrate that our pretrained denoising model achieves excellent denoising performance on experimental cryo-EM micrographs, significantly streamlining downstream analysis.

Rational Design of Drugs Targeting G-Protein-Coupled Receptors: A Structural Biology Perspective

G protein-coupled receptors (GPCRs) play a key role in the transduction of extracellular signals to cells and regulation of many biological processes, which makes these membrane proteins one of the most important targets for pharmacological agents. A significant increase in the number of resolved atomic structures of GPCRs has opened the possibility of developing pharmaceuticals targeting these receptors via structure-based drug design (SBDD). SBDD employs information on the structure of receptor-ligand complexes to search for selective ligands without the need for an extensive high-throughput experimental ligand screening and can significantly expand the chemical space for ligand search. In this review, we describe the process of deciphering GPCR structures using X-ray diffraction analysis and cryoelectron microscopy as an important stage in the rational design of drugs targeting this receptor class. Our main goal was to present modern developments and key features of experimental methods used in SBDD of GPCR-targeting agents to a wide range of specialists.

Joint micrograph denoising and protein localization in cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) is an imaging technique that allows the visualization of proteins and macromolecular complexes at near-atomic resolution. The low electron doses used to prevent radiation damage to the biological samples result in images where the power of noise is 100 times stronger than that of the signal. Accurate identification of proteins from these low signal-to-noise ratio (SNR) images is a critical task, as the detected positions serve as inputs for the downstream 3D structure determination process. Current methods either fail to identify all true positives or result in many false positives, especially when analyzing images from smaller-sized proteins that exhibit extremely low contrast, or require manual labeling that can take days to complete. Acknowledging the fact that accurate protein identification is dependent upon the visual interpretability of micrographs, we propose a framework that can perform denoising and detection in a joint manner and enable particle localization under extremely low SNR conditions using self-supervised denoising and particle identification from sparsely annotated data. We validate our approach on three challenging single-particle cryo-EM datasets and projection images from one cryo-electron tomography dataset with extremely low SNR, showing that it outperforms existing state-of-the-art methods used for cryo-EM image analysis by a significant margin. We also evaluate the performance of our algorithm under decreasing SNR conditions and show that our method is more robust to noise than competing methods.

Self Fourier shell correlation: properties and application to cryo-ET

The Fourier shell correlation (FSC) is a measure of the similarity between two signals computed over corresponding shells in the frequency domain and has broad applications in microscopy. In structural biology, the FSC is ubiquitous in methods for validation, resolution determination, and signal enhancement. Computing the FSC usually requires two independent measurements of the same underlying signal, which can be limiting for some applications. Here, we analyze and extend on an approach to estimate the FSC from a single measurement. In particular, we derive the necessary conditions required to estimate the FSC from downsampled versions of a single noisy measurement. These conditions reveal additional corrections which we implement to increase the applicability of the method. We then illustrate two applications of our approach, first as an estimate of the global resolution from a single 3-D structure and second as a data-driven method for denoising tomographic reconstructions in electron cryo-tomography. These results provide general guidelines for computing the FSC from a single measurement and suggest new applications of the FSC in microscopy.

Self Fourier shell correlation: properties and application to cryo-ET

The Fourier shell correlation (FSC) is a measure of the similarity between two signals computed over corresponding shells in the frequency domain and has broad applications in microscopy. In structural biology, the FSC is ubiquitous in methods for validation, resolution determination, and signal enhancement. Computing the FSC usually requires two independent measurements of the same underlying signal, which can be limiting for some applications. Here, we analyze and extend on an approach proposed by Koho et al. [1] to estimate the FSC from a single measurement. In particular, we derive the necessary conditions required to estimate the FSC from downsampled versions of a single noisy measurement. These conditions reveal additional corrections which we implement to increase the applicability of the method. We then illustrate two applications of our approach, first as an estimate of the global resolution from a single 3-D structure and second as a data-driven method for denoising tomographic reconstructions in electron cryo-tomography. These results provide general guidelines for computing the FSC from a single measurement and suggest new applications of the FSC in microscopy.

Visualizing lipid membrane structure with cryo-EM: past, present, and future

The development of electron cryomicroscopy (cryo-EM) has evolved immensely in the last several decades and is now well-established in the analysis of protein structure both in isolation and in their cellular context. This review focuses on the history and application of cryo-EM to the analysis of membrane architecture. Parallels between the levels of organization of protein structure are useful in organizing the discussion of the unique parameters that influence membrane structure and function. Importantly, the timescales of lipid motion in bilayers with respect to the timescales of sample vitrification is discussed and reveals what types of membrane structure can be reliably extracted in cryo-EM images of vitrified samples. Appreciating these limitations, a review of the application of cryo-EM to examine the lateral organization of ordered and disordered domains in reconstituted and biologically derived membranes is provided. Finally, a brief outlook for further development and application of cryo-EM to the analysis of membrane architecture is provided.

OUP accepted manuscript

Motivation

Cryo-electron microscopy (cryo-EM) is a widely used technology for ultrastructure determination, which constructs the 3D structures of protein and macromolecular complex from a set of 2D micrographs. However, limited by the electron beam dose, the micrographs in cryo-EM generally suffer from the extremely low signal-to-noise ratio (SNR), which hampers the efficiency and effectiveness of downstream analysis. Especially, the noise in cryo-EM is not simple additive or multiplicative noise whose statistical characteristics are quite different from the ones in natural image, extremely shackling the performance of conventional denoising methods.

Results

Here, we introduce the Noise-Transfer2Clean (NT2C), a denoising deep neural network (DNN) for cryo-EM to enhance image contrast and restore specimen signal, whose main idea is to improve the denoising performance by correctly learning the noise distribution of cryo-EM images and transferring the statistical nature of noise into the denoiser. Especially, to cope with the complex noise model in cryo-EM, we design a contrast-guided noise and signal re-weighted algorithm to achieve clean-noisy data synthesis and data augmentation, making our method authentically achieve signal restoration based on noise’s true properties. Our work verifies the feasibility of denoising based on mining the complex cryo-EM noise patterns directly from the noise patches. Comprehensive experimental results on simulated datasets and real datasets show that NT2C achieved a notable improvement in image denoising, especially in background noise removal, compared with the commonly used methods. Moreover, a case study on the real dataset demonstrates that NT2C can greatly alleviate the obstacles caused by the SNR to particle picking and simplify the identifying of particles.

Availabilityand implementation

The code is available at https://github.com/Lihongjia-ict/NoiseTransfer2Clean/.

Supplementary information

Supplementary data are available at Bioinformatics online.

[Progress in filters for denoising cryo-electron microscopy images]

Cryo-electron microscopy (cryo-EM) imaging has the unique potential to bridge the gap between cellular and molecular biology. Therefore, cryo-EM three-dimensional (3D) reconstruction has been rapidly developed in recent several years and applied widely in life science research to reveal the structures of large macromolecular assemblies and cellular complexes, which is critical to understanding their functions at all scales. Although the technical breakthrough in recent years, for example, the introduction of the direct detection device (DDD) camera and the development of cryo-EM software tools, made the three cryo-EM pioneers share the 2017 Nobel Prize, several bottleneck problems still exist that hamper the further increase of the resolution of single-particle reconstruction and hold back the application of in situ subnanometer structure determination by cryo-tomography. Radiation damage is still the key limiting factor in cryo-EM. In order to minimize the radiation damage and preserve as much resolution as possible, the imaging conditions of a low dose and weak contrast make cryo-EM images extremely noisy with very low signal-to-noise ratios (SNR), generally about 0.1. The high noise will obscure the fine details in cryo-EM images or reconstructed maps. Thus, a method to reduce the level of noise and improve the resolution has become an important issue. In this paper, we systematically reviewed and compared some robust filters in the cryo-EM field of two aspects, single-particle analysis (SPA) and cryo-electron tomography (cryo-ET), and especially studied their applications, such as, 3D reconstruction, visualization, structural analysis, and interpretation. Conventional approaches to noise reduction in cryo-EM imaging include the use of Gaussian, median, and bilateral filters, among other means. A Gaussian filter selects an appropriate filter kernel to conduct spatial convolution with a noisy image. Although noise with larger standard deviations in cryo-EM images can be suppressed and satisfactory performance is achieved in certain cases, this filter also blurs the images and over-smooths small-scale image features. This is especially detrimental when precise quantitative information needs to be extracted. Unlike a Gaussian filter, a median filter is based on the order statistics of the image and selects the median intensity in a window of the adjacent pixels to denoise the image. Although this filter is robust to outliers, it suffers from aliasing problems that possibly result in incorrect information for cryo-EM structure interpretation. A bilateral filter is a nonlinear filter that performs spatial weighted averaging and is more selective in the pixels allowing to contribute to the weighted sum, excluding the high frequency noise from the smoothing process. Thus, this filter can be used to smooth out noise while maintaining the edge details, which is similar to an anisotropic diffusion filter, and distinct from a Gaussian filter but its utility will be limited when the SNR of a cryo-EM image is very low. Generally, spatial filtering methods have the disadvantage of losing image resolution when reducing noise. A wavelet transform can exploit the wavelet's natural ability to separate a signal from noise at multiple image scales to allow for joint resolution in both the spatial and frequency domains, and thus has the potential to outperform existing methods. The modified wavelet shrinkage filter we developed can offer a remarkable improvement in image quality with a good compromise between detail preservation and noise smoothing. We expect that our review study on different filters can provide benefits to cryo-EM applications and the interpretation of biological structures.

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.

Topaz-Denoise: general deep denoising models for cryoEM and cryoET

Cryo-electron microscopy (cryoEM) is becoming the preferred method for resolving protein structures. Low signal-to-noise ratio (SNR) in cryoEM images reduces the confidence and throughput of structure determination during several steps of data processing, resulting in impediments such as missing particle orientations. Denoising cryoEM images can not only improve downstream analysis but also accelerate the time-consuming data collection process by allowing lower electron dose micrographs to be used for analysis. Here, we present Topaz-Denoise, a deep learning method for reliably and rapidly increasing the SNR of cryoEM images and cryoET tomograms. By training on a dataset composed of thousands of micrographs collected across a wide range of imaging conditions, we are able to learn models capturing the complexity of the cryoEM image formation process. The general model we present is able to denoise new datasets without additional training. Denoising with this model improves micrograph interpretability and allows us to solve 3D single particle structures of clustered protocadherin, an elongated particle with previously elusive views. We then show that low dose collection, enabled by Topaz-Denoise, improves downstream analysis in addition to reducing data collection time. We also present a general 3D denoising model for cryoET. Topaz-Denoise and pre-trained general models are now included in Topaz. We expect that Topaz-Denoise will be of broad utility to the cryoEM community for improving micrograph and tomogram interpretability and accelerating analysis.

Present and Emerging Methodologies in Cryo-EM Single-Particle Analysis

Over the past decade, technical and methodological improvements in cryogenic electron microscopy (cryo-EM) single-particle analysis have enabled routine high-resolution structural analyses of biological macromolecules, resulting in a flood of new molecular insights into protracted biological questions. However, despite the tremendous progress and success of the field in recent years, opportunities for improvement remain in various aspects of the cryo-EM single-particle analysis workflow (e.g., sample preparation, image acquisition and processing, and structure validation). Here, we review recent advances that have contributed to the principal methods in cryo-EM and identify persisting challenges and bottlenecks that will require further methodological and hardware development.

Investigating eukaryotic cells with cryo-ET

The interior of eukaryotic cells is mysterious. How do the large communities of macromolecular machines interact with each other? How do the structures and positions of these nanoscopic entities respond to new stimuli? Questions like these can now be answered with the help of a method called electron cryotomography (cryo-ET). Cryo-ET will ultimately reveal the inner workings of a cell at the protein, secondary structure, and perhaps even side-chain levels. Combined with genetic or pharmacological perturbation, cryo-ET will allow us to answer previously unimaginable questions, such as how structure, biochemistry, and forces are related in situ. Because it bridges structural biology and cell biology, cryo-ET is indispensable for structural cell biology-the study of the 3-D macromolecular structure of cells. Here we discuss some of the key ideas, strategies, auxiliary techniques, and innovations that an aspiring structural cell biologist will consider when planning to ask bold questions.

Low-energy in-line electron holographic imaging of vitreous ice-embedded small biomolecules using a modified scanning electron microscope

Cryo-electron microscopy (cryo-EM) has become the method of choice in the field of structural biology, owing to its unique ability to deduce structures of vitreous ice-embedded, hydrated biomolecules over a wide range of structural resolutions. As cryo-transmission electron microscopes (cryo-TEM) become increasingly specialised for high, near-atomic resolution studies, operational complexity and associated costs serve as significant barriers to widespread usability and adoptability. To facilitate the expansion and accessibility of the cryo-EM method, an efficient, user-friendly means of imaging vitreous ice-embedded biomolecules has been called for. In this study, we present a solution to this issue by integrating cryo-EM capabilities into a commercial scanning electron microscope (SEM). Utilising the principle of low-energy in-line electron holography, our newly developed hybrid microscope permits low-to-moderate resolution imaging of vitreous ice-embedded biomolecules without the need for any form of sample staining or chemical fixation. Operating at 20 kV, the microscope takes advantage of the ease-of-use of SEM-based imaging and phase contrast imaging of low-energy electron holography. This study represents the first reported successful application of low-energy in-line electron holographic imaging to vitreous ice-embedded small biomolecules, the effectiveness of which is demonstrated here with three morphologically distinct specimens.

A complete data processing workflow for cryo-ET and subtomogram averaging

Electron cryotomography (CryoET) is currently the only method capable of visualizing cells in 3D at nanometer resolutions. While modern instruments produce massive amounts of tomography data containing extremely rich structural information, the data processing is very labor intensive and results are often limited by the skills of the personnel rather than the data. We present an integrated workflow that covers the entire tomography data processing pipeline, from automated tilt series alignment to subnanometer resolution subtomogram averaging. Resolution enhancement is made possible through the use of per-particle per-tilt CTF correction and alignment. The workflow greatly reduces human effort and increases throughput and is capable of determining protein structures at state-of-the-art resolutions for both purified macromolecules and cells.

Non-uniformity of projection distributions attenuates resolution in Cryo-EM

Virtually all single-particle cryo-EM experiments currently suffer from specimen adherence to the air-water interface, leading to a non-uniform distribution in the set of projection views. Whereas it is well accepted that uniform projection distributions can lead to high-resolution reconstructions, non-uniform (anisotropic) distributions can negatively affect map quality, elongate structural features, and in some cases, prohibit interpretation altogether. Although some consequences of non-uniform sampling have been described qualitatively, we know little about how sampling quantitatively affects resolution in cryo-EM. Here, we show how inhomogeneity in any projection distribution scheme attenuates the global Fourier Shell Correlation (FSC) in relation to the number of particles and a single geometrical parameter, which we term the sampling compensation factor (SCF). The reciprocal of the SCF is defined as the average over Fourier shells of the reciprocal of the per-particle sampling and normalized to unity for uniform distributions. The SCF therefore ranges from one to zero, with values close to the latter implying large regions of poorly sampled or completely missing data in Fourier space. Using two synthetic test cases, influenza hemagglutinin and human apoferritin, we demonstrate how any amount of sampling inhomogeneity always attenuates the FSC compared to a uniform distribution. We advocate quantitative evaluation of the SCF criterion to approximate the effect of non-uniform sampling on resolution within experimental single-particle cryo-EM reconstructions.

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.

Single-molecule 3D imaging of human plasma intermediate-density lipoproteins reveals a polyhedral structure

Intermediate-density lipoproteins (IDLs), the remnants of very-low-density lipoproteins via lipolysis, are rich in cholesteryl ester and are associated with cardiovascular disease. Despite pharmacological interest in IDLs, their three-dimensional (3D) structure is still undetermined due to their variation in size, composition, and dynamic structure. To explore the 3D structure of IDLs, we reconstructed 3D density maps from individual IDL particles using cryo-electron microscopy (cryo-EM) and individual-particle electron tomography (IPET, without averaging from different molecules). 3D reconstructions of IDLs revealed an unexpected polyhedral structure that deviates from the generally assumed spherical shape model (Frias et al., 2007; Olson, 1998; Shen et al., 1977). The polyhedral-shaped IDL contains a high-density shell formed by flat surfaces that are similar to those of very-low-density lipoproteins but have sharper dihedral angles between nearby surfaces. These flat surfaces would be less hydrophobic than the curved surface of mature spherical high-density lipoprotein (HDL), leading to a lower binding affinity of IDL to hydrophobic proteins (such as cholesteryl ester transfer protein) than HDL. This is the first visualization of the IDL 3D structure, which could provide fundamental clues for delineating the role of IDL in lipid metabolism and cardiovascular disease.

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

Electron cryomicroscopy (cryoEM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize macromolecular complexes such as ribosomes, viruses, and ion channels. Determination of structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryoEM a scientific rebirth. As a result of these technological advances image processing and analysis have yielded molecular structures at atomic resolution. Nevertheless there continue to be challenges in image processing, and in this article we will touch on the most essential in order to derive an accurate three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. We will then highlight new approaches for each image processing subproblem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking.

Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the three-dimensional (3D) electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy two-dimensional images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For n images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O ( n N 4 + κ N 6 log N ) , where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in six dimensions. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed nonconsistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.

Likelihood-based structural analysis of electron microscopy images

Likelihood-based analysis of single-particle electron microscopy images has contributed much to the recent improvements in resolution. By treating particle orientations and classes probabilistically, uncertainties in the reconstruction process are explicitly accounted for, and the risk of bias towards the initial model is diminished. As a result, the quality and reliability of the reconstructions have greatly improved at manageable computational cost. Likelihood-based analysis of electron microscopy images also offers a route to direct coordinate refinement for dynamic systems, as an alternative to 3D density reconstruction. Here, we review recent developments in the algorithms used for reconstructions of high-resolution maps, and in the integrative framework of combining likelihood methods with simulations to address conformational variability in cryo-electron microscopy.

Defocus and magnification dependent variation of TEM image astigmatism

Daily alignment of the microscope is a prerequisite to reaching optimal lens conditions for high resolution imaging in cryo-EM. In this study, we have investigated how image astigmatism varies with the imaging conditions (e.g. defocus, magnification). We have found that the large change of defocus/magnification between visual correction of astigmatism and subsequent data collection tasks, or during data collection, will inevitably result in undesirable astigmatism in the final images. The dependence of astigmatism on the imaging conditions varies significantly from time to time, so that it cannot be reliably compensated by pre-calibration of the microscope. Based on these findings, we recommend that the same magnification and the median defocus of the intended defocus range for final data collection are used in the objective lens astigmatism correction task during microscope alignment and in the focus mode of the iterative low-dose imaging. It is also desirable to develop a fast, accurate method that can perform dynamic correction of the astigmatism for different intended defocuses during automated imaging. Our findings also suggest that the slope of astigmatism changes caused by varying defocuses can be used as a convenient measurement of objective lens rotation symmetry and potentially an acceptance test of new electron microscopes.

Single-particle cryo-EM-Improved ab initio 3D reconstruction with SIMPLE/PRIME

Cryogenic electron microscopy (cryo-EM) and single-particle analysis now enables the determination of high-resolution structures of macromolecular assemblies that have resisted X-ray crystallography and other approaches. We developed the SIMPLE open-source image-processing suite for analysing cryo-EM images of single-particles. A core component of SIMPLE is the probabilistic PRIME algorithm for identifying clusters of images in 2D and determine relative orientations of single-particle projections in 3D. Here, we extend our previous work on PRIME and introduce new stochastic optimization algorithms that improve the robustness of the approach. Our refined method for identification of homogeneous subsets of images in accurate register substantially improves the resolution of the cluster centers and of the ab initio 3D reconstructions derived from them. We now obtain maps with a resolution better than 10 Å by exclusively processing cluster centers. Excellent parallel code performance on over-the-counter laptops and CPU workstations is demonstrated.

Factor Analysis for Spectral Estimation

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model where a signal is given by a random linear combination of fixed, yet unknown, stochastic sources. Given multiple such signals, we estimate the subspace spanned by the power spectra of these fixed sources. Projecting individual power spectrum estimates onto this subspace increases estimation accuracy. We provide accuracy guarantees for this method and demonstrate it on simulated and experimental data from cryo-electron microscopy.

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

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

Processing of Structurally Heterogeneous Cryo-EM Data in RELION

This chapter describes algorithmic advances in the RELION software, and how these are used in high-resolution cryo-electron microscopy (cryo-EM) structure determination. Since the presence of projections of different three-dimensional structures in the dataset probably represents the biggest challenge in cryo-EM data processing, special emphasis is placed on how to deal with structurally heterogeneous datasets. As such, this chapter aims to be of practical help to those who wish to use RELION in their cryo-EM structure determination efforts.

A Stochastic Hill Climbing Approach for Simultaneous 2D Alignment and Clustering of Cryogenic Electron Microscopy Images

A critical step in the analysis of novel cryogenic electron microscopy (cryo-EM) single-particle datasets is the identification of homogeneous subsets of images. Methods for solving this problem are important for data quality assessment, ab initio 3D reconstruction, and analysis of population diversity due to the heterogeneous nature of macromolecules. Here we formulate a stochastic algorithm for identification of homogeneous subsets of images. The purpose of the method is to generate improved 2D class averages that can be used to produce a reliable 3D starting model in a rapid and unbiased fashion. We show that our method overcomes inherent limitations of widely used clustering approaches and proceed to test the approach on six publicly available experimental cryo-EM datasets. We conclude that, in each instance, ab initio 3D reconstructions of quality suitable for initialization of high-resolution refinement are produced from the cluster centers.

Denoising of high-resolution single-particle electron-microscopy density maps by their approximation using three-dimensional Gaussian functions

Cryo-electron microscopy (cryo-EM) of frozen-hydrated preparations of isolated macromolecular complexes is the method of choice to obtain the structure of complexes that cannot be easily studied by other experimental methods due to their flexibility or large size. An increasing number of macromolecular structures are currently being obtained at subnanometer resolution but the interpretation of structural details in such EM-derived maps is often difficult because of noise at these high-frequency signal components that reduces their contrast. In this paper, we show that the method for EM density-map approximation using Gaussian functions can be used for denoising of single-particle EM maps of high (typically subnanometer) resolution. We show its denoising performance using simulated and experimental EM density maps of several complexes.

Generalized single-particle cryo-EM--a historical perspective

This is a brief account of the earlier history of single-particle cryo-EM of biological molecules lacking internal symmetry, which goes back to the mid-seventies. The emphasis of this review is on the mathematical concepts and computational approaches. It is written as the field experiences a turning point in the wake of the introduction of digital cameras capable of single electron counting, and near-atomic resolution can be reached even for smaller molecules.

Single-particle cryo-electron microscopy of macromolecular complexes

Recent technological breakthroughs in image acquisition have enabled single-particle cryo-electron microscopy (cryo-EM) to achieve near-atomic resolution structural information for biological complexes. The improvements in image quality coupled with powerful computational methods for sorting distinct particle populations now also allow the determination of compositional and conformational ensembles, thereby providing key insights into macromolecular function. However, the inherent instability and dynamic nature of biological assemblies remain a tremendous challenge that often requires tailored approaches for successful implementation of the methodology. Here, we briefly describe the fundamentals of single-particle cryo-EM with an emphasis on covering the breadth of techniques and approaches, including low- and high-resolution methods, aiming to illustrate specific steps that are crucial for obtaining structural information by this method.

A primer to single-particle cryo-electron microscopy

Cryo-electron microscopy (cryo-EM) of single-particle specimens is used to determine the structure of proteins and macromolecular complexes without the need for crystals. Recent advances in detector technology and software algorithms now allow images of unprecedented quality to be recorded and structures to be determined at near-atomic resolution. However, compared with X-ray crystallography, cryo-EM is a young technique with distinct challenges. This primer explains the different steps and considerations involved in structure determination by single-particle cryo-EM to provide an overview for scientists wishing to understand more about this technique and the interpretation of data obtained with it, as well as a starting guide for new practitioners.

Cryogenic electron microscopy and single-particle analysis

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

CTER-rapid estimation of CTF parameters with error assessment

In structural electron microscopy, the accurate estimation of the Contrast Transfer Function (CTF) parameters, particularly defocus and astigmatism, is of utmost importance for both initial evaluation of micrograph quality and for subsequent structure determination. Due to increases in the rate of data collection on modern microscopes equipped with new generation cameras, it is also important that the CTF estimation can be done rapidly and with minimal user intervention. Finally, in order to minimize the necessity for manual screening of the micrographs by a user it is necessary to provide an assessment of the errors of fitted parameters values. In this work we introduce CTER, a CTF parameters estimation method distinguished by its computational efficiency. The efficiency of the method makes it suitable for high-throughput EM data collection, and enables the use of a statistical resampling technique, bootstrap, that yields standard deviations of estimated defocus and astigmatism amplitude and angle, thus facilitating the automation of the process of screening out inferior micrograph data. Furthermore, CTER also outputs the spatial frequency limit imposed by reciprocal space aliasing of the discrete form of the CTF and the finite window size. We demonstrate the efficiency and accuracy of CTER using a data set collected on a 300kV Tecnai Polara (FEI) using the K2 Summit DED camera in super-resolution counting mode. Using CTER we obtained a structure of the 80S ribosome whose large subunit had a resolution of 4.03Å without, and 3.85Å with, inclusion of astigmatism parameters.

Bayesian analysis of individual electron microscopy images: towards structures of dynamic and heterogeneous biomolecular assemblies

We develop a method to extract structural information from electron microscopy (EM) images of dynamic and heterogeneous molecular assemblies. To overcome the challenge of disorder in the imaged structures, we analyze each image individually, avoiding information loss through clustering or averaging. The Bayesian inference of EM (BioEM) method uses a likelihood-based probabilistic measure to quantify the consistency between each EM image and given structural models. The likelihood function accounts for uncertainties in the molecular position and orientation, variations in the relative intensities and noise in the experimental images. The BioEM formalism is physically intuitive and mathematically simple. We show that for experimental GroEL images, BioEM correctly identifies structures according to the functional state. The top-ranked structure is the corresponding X-ray crystal structure, followed by an EM structure generated previously from a superset of the EM images used here. To analyze EM images of highly flexible molecules, we propose an ensemble refinement procedure, and validate it with synthetic EM maps of the ESCRT-I-II supercomplex. Both the size of the ensemble and its structural members are identified correctly. BioEM offers an alternative to 3D-reconstruction methods, extracting accurate population distributions for highly flexible structures and their assemblies. We discuss limitations of the method, and possible applications beyond ensemble refinement, including the cross-validation and unbiased post-assessment of model structures, and the structural characterization of systems where traditional approaches fail. Overall, our results suggest that the BioEM framework can be used to analyze EM images of both ordered and disordered molecular systems.

Outcome of the first electron microscopy validation task force meeting

This Meeting Review describes the proceedings and conclusions from the inaugural meeting of the Electron Microscopy Validation Task Force organized by the Unified Data Resource for 3DEM (http://www.emdatabank.org) and held at Rutgers University in New Brunswick, NJ on September 28 and 29, 2010. At the workshop, a group of scientists involved in collecting electron microscopy data, using the data to determine three-dimensional electron microscopy (3DEM) density maps, and building molecular models into the maps explored how to assess maps, models, and other data that are deposited into the Electron Microscopy Data Bank and Protein Data Bank public data archives. The specific recommendations resulting from the workshop aim to increase the impact of 3DEM in biology and medicine.

Electron tomography of cells

The electron microscope has contributed deep insights into biological structure since its invention nearly 80 years ago. Advances in instrumentation and methodology in recent decades have now enabled electron tomography to become the highest resolution three-dimensional (3D) imaging technique available for unique objects such as cells. Cells can be imaged either plastic-embedded or frozen-hydrated. Then the series of projection images are aligned and back-projected to generate a 3D reconstruction or 'tomogram'. Here, we review how electron tomography has begun to reveal the molecular organization of cells and how the existing and upcoming technologies promise even greater insights into structural cell biology.

A Bayesian view on cryo-EM structure determination

Three-dimensional (3D) structure determination by single-particle analysis of cryo-electron microscopy (cryo-EM) images requires many parameters to be determined from extremely noisy data. This makes the method prone to overfitting, that is, when structures describe noise rather than signal, in particular near their resolution limit where noise levels are highest. Cryo-EM structures are typically filtered using ad hoc procedures to prevent overfitting, but the tuning of arbitrary parameters may lead to subjectivity in the results. I describe a Bayesian interpretation of cryo-EM structure determination, where smoothness in the reconstructed density is imposed through a Gaussian prior in the Fourier domain. The statistical framework dictates how data and prior knowledge should be combined, so that the optimal 3D linear filter is obtained without the need for arbitrariness and objective resolution estimates may be obtained. Application to experimental data indicates that the statistical approach yields more reliable structures than existing methods and is capable of detecting smaller classes in data sets that contain multiple different structures.