Algorithmic robustness to preferred orientations in single particle analysis by CryoEM

Correction of preferred orientation-induced distortion in cryo-electron microscopy maps

Reconstruction maps of cryo-electron microscopy (cryo-EM) exhibit distortion when the cryo-EM dataset is incomplete, usually caused by unevenly distributed orientations. Prior efforts had been attempted to address this preferred orientation problem using tilt-collection strategy and modifications to grids or to air-water interfaces. However, these approaches often require time-consuming experiments, and the effect was always protein dependent. Here, we developed a procedure containing removing misaligned particles and an iterative reconstruction method based on signal-to-noise ratio of Fourier component to correct this distortion by recovering missing data using a purely computational algorithm. This procedure called signal-to-noise ratio iterative reconstruction method (SIRM) was applied on incomplete datasets of various proteins to fix distortion in cryo-EM maps and to a more isotropic resolution. In addition, SIRM provides a better reference map for further reconstruction refinements, resulting in an improved alignment, which ultimately improves map quality and benefits model building.

Factors affecting macromolecule orientations in thin films formed in cryo-EM

The formation of a vitrified thin film embedded with randomly oriented macromolecules is an essential prerequisite for cryogenic sample electron microscopy. Most commonly, this is achieved using the plunge-freeze method first described nearly 40 years ago. Although this is a robust method, the behaviour of different macromolecules shows great variation upon freezing and often needs to be optimized to obtain an isotropic, high-resolution reconstruction. For a macromolecule in such a film, the probability of encountering the air-water interface in the time between blotting and freezing and adopting preferred orientations is very high. 3D reconstruction using preferentially oriented particles often leads to anisotropic and uninterpretable maps. Currently, there are no general solutions to this prevalent issue, but several approaches largely focusing on sample preparation with the use of additives and novel grid modifications have been attempted. In this study, the effect of physical and chemical factors on the orientations of macromolecules was investigated through an analysis of selected well studied macromolecules, and important parameters that determine the behaviour of proteins on cryo-EM grids were revealed. These insights highlight the nature of the interactions that cause preferred orientations and can be utilized to systematically address orientation bias for any given macromolecule and to provide a framework to design small-molecule additives to enhance sample stability and behaviour.

Program VUE: analysing distributions of cryo-EM projections using uniform spherical grids

Three-dimensional cryo electron microscopy reconstructions are obtained by extracting information from a large number of projections of the object. These projections correspond to different 'views' or 'orientations', i.e. directions in which these projections show the reconstructed object. Uneven distribution of these views and the presence of dominating preferred orientations may distort the reconstructed spatial images. This work describes the program VUE (views on uniform grids for cryo electron microscopy), designed to study such distributions. Its algorithms, based on uniform virtual grids on a sphere, allow an easy calculation and accurate quantitative analysis of the frequency distribution of the views. The key computational element is the Lambert azimuthal equal-area projection of a spherical uniform grid onto a disc. This projection keeps the surface area constant and represents the frequency distribution with no visual bias. Since it has multiple tunable parameters, the program is easily adaptable to individual needs, and to the features of a particular project or of the figure to be produced. It can help identify problems related to an uneven distribution of views. Optionally, it can modify the list of projections, distributing the views more uniformly. The program can also be used as a teaching tool.

Missing Wedge Completion via Unsupervised Learning with Coordinate Networks

Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3-20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.

Missing Wedge Completion via Unsupervised Learning with Coordinate Networks

Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3 - 20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.

Cryo-EM Map Anisotropy Can Be Attenuated by Map Post-Processing and a New Method for Its Estimation

One of the most important challenges in cryogenic electron microscopy (cryo-EM) is the substantial number of samples that exhibit preferred orientations, which leads to an uneven coverage of the projection sphere. As a result, the overall quality of the reconstructed maps can be severely affected, as manifested by the presence of anisotropy in the map resolution. Several methods have been proposed to measure the directional resolution of maps in tandem with experimental protocols to address the problem of preferential orientations in cryo-EM. Following these works, in this manuscript we identified one potential limitation that may affect most of the existing methods and we proposed an alternative approach to evaluate the presence of preferential orientations in cryo-EM reconstructions. In addition, we also showed that some of the most recently proposed cryo-EM map post-processing algorithms can attenuate map anisotropy, thus offering alternative visualization opportunities for cases affected by moderate levels of preferential orientations.

Cryo-EM of a heterogeneous biochemical fraction elucidates multiple protein complexes from a multicellular thermophilic eukaryote

Biomolecular complexes and their interactions govern cellular structure and function. Understanding their architecture is a prerequisite for dissecting the cell's inner workings, but their higher-order assembly is often transient and challenging for structural analysis. Here, we performed cryo-EM on a single, highly heterogeneous biochemical fraction derived from Chaetomium thermophilum cell extracts to visualize the biomolecular content of the multicellular eukaryote. After cryo-EM single-particle image processing, results showed that a simultaneous three-dimensional structural characterization of multiple chemically diverse biomacromolecules is feasible. Namely, the thermophilic, eukaryotic complexes of (a) ATP citrate-lyase, (b) Hsp90, (c) 20S proteasome, (d) Hsp60 and (e) UDP-glucose pyrophosphorylase were characterized. In total, all five complexes have been structurally dissected in a thermophilic eukaryote in a total imaged sample area of 190.64 μm2, and two, in particular, 20S proteasome and Hsp60, exhibit side-chain resolution features. The C. thermophilum Hsp60 near-atomic model was resolved at 3.46 Å (FSC = 0.143) and shows a hinge-like conformational change of its equatorial domain, highly similar to the one previously shown for its bacterial orthologue, GroEL. This work demonstrates that cryo-EM of cell extracts will greatly accelerate the structural analysis of cellular complexes and provide unprecedented opportunities to annotate architectures of biomolecules in a holistic approach.

Overview of Membrane Protein Sample Preparation for Single-Particle Cryo-Electron Microscopy Analysis

Single-particle cryo-electron microscopy (cryo-EM SPA) has recently emerged as an exceptionally well-suited technique for determining the structure of membrane proteins (MPs). Indeed, in recent years, huge increase in the number of MPs solved via cryo-EM SPA at a resolution better than 3.0 Å in the Protein Data Bank (PDB) has been observed. However, sample preparation remains a significant challenge in the field. Here, we evaluated the MPs solved using cryo-EM SPA deposited in the PDB in the last two years at a resolution below 3.0 Å. The most critical parameters for sample preparation are as follows: (i) the surfactant used for protein extraction from the membrane, (ii) the surfactant, amphiphiles, nanodiscs or other molecules present in the vitrification step, (iii) the vitrification method employed, and (iv) the type of grids used. The aim is not to provide a definitive answer on the optimal sample conditions for cryo-EM SPA of MPs but rather assess the current trends in the MP structural biology community towards obtaining high-resolution cryo-EM structures.

New measures of anisotropy of cryo-EM maps

We propose two new measures of resolution anisotropy for cryogenic electron microscopy maps: Fourier shell occupancy (FSO), and the Bingham test (BT). FSO varies from 1 to 0, with 1 representing perfect isotropy, and lower values indicating increasing anisotropy. The threshold FSO = 0.5 occurs at Fourier shell correlation resolution. BT is a hypothesis test that complements the FSO to ensure the existence of anisotropy. FSO and BT allow visualization of resolution anisotropy. We illustrate their use with different experimental cryogenic electron microscopy maps.

An Unsupervised Classification Algorithm for Heterogeneous Cryo-EM Projection Images Based on Autoencoders

Heterogeneous three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is an important but very challenging technique for recovering the conformational heterogeneity of flexible biological macromolecules such as proteins in different functional states. Heterogeneous projection image classification is a feasible solution to solve the structural heterogeneity problem in single-particle cryo-EM. The majority of heterogeneous projection image classification methods are developed using supervised learning technology or require a large amount of a priori knowledge, such as the orientations or common lines of the projection images, which leads to certain limitations in their practical applications. In this paper, an unsupervised heterogeneous cryo-EM projection image classification algorithm based on autoencoders is proposed, which only needs to know the number of heterogeneous 3D structures in the dataset and does not require any labeling information of the projection images or other a priori knowledge. A simple autoencoder with multi-layer perceptrons trained in iterative mode and a complex autoencoder with residual networks trained in one-pass learning mode are implemented to convert heterogeneous projection images into latent variables. The extracted high-dimensional features are reduced to two dimensions using the uniform manifold approximation and projection dimensionality reduction algorithm, and then clustered using the spectral clustering algorithm. The proposed algorithm is applied to two heterogeneous cryo-EM datasets for heterogeneous 3D reconstruction. Experimental results show that the proposed algorithm can effectively extract category features of heterogeneous projection images and achieve high classification and reconstruction accuracy, indicating that the proposed algorithm is effective for heterogeneous 3D reconstruction in single-particle cryo-EM.

Higher resolution in cryo-EM by the combination of macromolecular prior knowledge and image-processing tools

Single-particle cryo-electron microscopy has become a powerful technique for the 3D structure determination of biological molecules. The last decade has seen an astonishing development of both hardware and software, and an exponential growth of new structures obtained at medium-high resolution. However, the knowledge accumulated in this field over the years has hardly been utilized as feedback in the reconstruction of new structures. In this context, this article explores the use of the deep-learning approach deepEMhancer as a regularizer in the RELION refinement process. deepEMhancer introduces prior information derived from macromolecular structures, and contributes to noise reduction and signal enhancement, as well as a higher degree of isotropy. These features have a direct effect on image alignment and reduction of overfitting during iterative refinement. The advantages of this combination are demonstrated for several membrane proteins, for which it is especially useful because of their high disorder and flexibility.

Structure Insights Into Photosystem I Octamer From Cyanobacteria

The diversity of photosystem oligomers is essential to understanding how photosynthetic organisms adapt to light conditions. Due to its structural and physiological significance, the assembly of the PSI supercomplex has been of great interest recently in terms of both chloroplast and cyanobacteria. In this study, two novel photosystem I supercomplexes were isolated for the first time from the low light incubated culture of filamentous cyanobacterium Anabaena sp. PCC 7120. These complexes were defined as PSI hexamers and octamers through biochemical and biophysical characterization. Their 77K emission spectra indicated that the red forms of chlorophylls seemed not to be affected during oligomerization. By cryo-EM single-particle analysis, a near-atomic (7.0 Å) resolution structure of a PSI octamer was resolved, and the molecular assemblies of a stable PSI octamer were revealed.

IceBreaker: Software for high-resolution single-particle cryo-EM with non-uniform ice

Despite the abundance of available software tools, optimal particle selection is still a vital issue in single-particle cryoelectron microscopy (cryo-EM). Regardless of the method used, most pickers struggle when ice thickness varies on a micrograph. IceBreaker allows users to estimate the relative ice gradient and flatten it by equalizing the local contrast. It allows the differentiation of particles from the background and improves overall particle picking performance. Furthermore, we introduce an additional parameter corresponding to local ice thickness for each particle. Particles with a defined ice thickness can be grouped and filtered based on this parameter during processing. These functionalities are especially valuable for on-the-fly processing to automatically pick as many particles as possible from each micrograph and to select optimal regions for data collection. Finally, estimated ice gradient distributions can be stored separately and used to inspect the quality of prepared samples.

3D reconstruction from cryo-EM projection images using two spherical embeddings

Single-particle analysis (SPA) in cryo-electron microscopy has become a powerful tool for determining and studying the macromolecular structure at an atomic level. However, since the SPA problem is a non-convex optimization problem with enormous search space and there is high level of noise in the input images, the existing methods may produce biased or even wrong final models. In this work, to deal with the problem, consistent constraints from the input data are explored in an embedding space, a 3D spherical surface. More specifically, the orientation of a projection image is represented by two intersection points of the normal vector and the local X-axis vector of the projection image on the unit spherical surface. To determine the orientations of the projection images, the global consistency constraints of the relative orientations of all the projection images are satisfied by two spherical embeddings which estimate the normal vectors and the local X-axis vectors of the projection images respectively. Compared to the traditional methods, the proposed method is shown to be able to rectify the initial computation errors and produce a more accurate estimation of the projection angles, which results in a better final model reconstruction from the noisy image data.

A 3D reconstruction method using two spherical embeddings to resolve projection angles of the cryo-EM images is shown to improve the initial model reconstruction for single-particle analysis.

On bias, variance, overfitting, gold standard and consensus in single-particle analysis by cryo-electron microscopy

Cryo-electron microscopy (cryoEM) has become a well established technique to elucidate the 3D structures of biological macromolecules. Projection images from thousands of macromolecules that are assumed to be structurally identical are combined into a single 3D map representing the Coulomb potential of the macromolecule under study. This article discusses possible caveats along the image-processing path and how to avoid them to obtain a reliable 3D structure. Some of these problems are very well known in the community. These may be referred to as sample-related (such as specimen denaturation at interfaces or non-uniform projection geometry leading to underrepresented projection directions). The rest are related to the algorithms used. While some have been discussed in depth in the literature, such as the use of an incorrect initial volume, others have received much less attention. However, they are fundamental in any data-analysis approach. Chiefly among them, instabilities in estimating many of the key parameters that are required for a correct 3D reconstruction that occur all along the processing workflow are referred to, which may significantly affect the reliability of the whole process. In the field, the term overfitting has been coined to refer to some particular kinds of artifacts. It is argued that overfitting is a statistical bias in key parameter-estimation steps in the 3D reconstruction process, including intrinsic algorithmic bias. It is also shown that common tools (Fourier shell correlation) and strategies (gold standard) that are normally used to detect or prevent overfitting do not fully protect against it. Alternatively, it is proposed that detecting the bias that leads to overfitting is much easier when addressed at the level of parameter estimation, rather than detecting it once the particle images have been combined into a 3D map. Comparing the results from multiple algorithms (or at least, independent executions of the same algorithm) can detect parameter bias. These multiple executions could then be averaged to give a lower variance estimate of the underlying parameters.

Heterogeneous cryo-EM projection image classification using a two-stage spectral clustering based on novel distance measures

Single-particle cryo-electron microscopy (cryo-EM) has become one of the mainstream technologies in the field of structural biology to determine the three-dimensional (3D) structures of biological macromolecules. Heterogeneous cryo-EM projection image classification is an effective way to discover conformational heterogeneity of biological macromolecules in different functional states. However, due to the low signal-to-noise ratio of the projection images, the classification of heterogeneous cryo-EM projection images is a very challenging task. In this paper, two novel distance measures between projection images integrating the reliability of common lines, pixel intensity and class averages are designed, and then a two-stage spectral clustering algorithm based on the two distance measures is proposed for heterogeneous cryo-EM projection image classification. In the first stage, the novel distance measure integrating common lines and pixel intensities of projection images is used to obtain preliminary classification results through spectral clustering. In the second stage, another novel distance measure integrating the first novel distance measure and class averages generated from each group of projection images is used to obtain the final classification results through spectral clustering. The proposed two-stage spectral clustering algorithm is applied on a simulated and a real cryo-EM dataset for heterogeneous reconstruction. Results show that the two novel distance measures can be used to improve the classification performance of spectral clustering, and using the proposed two-stage spectral clustering algorithm can achieve higher classification and reconstruction accuracy than using RELION and XMIPP.

Cryo-EM structure of a tetrameric photosystem I from Chroococcidiopsis TS-821, a thermophilic, unicellular, non-heterocyst-forming cyanobacterium

Photosystem I (PSI) is one of two photosystems involved in oxygenic photosynthesis. PSI of cyanobacteria exists in monomeric, trimeric, and tetrameric forms, in contrast to the strictly monomeric form of PSI in plants and algae. The tetrameric organization raises questions about its structural, physiological, and evolutionary significance. Here we report the ∼3.72 Å resolution cryo-electron microscopy structure of tetrameric PSI from the thermophilic, unicellular cyanobacterium Chroococcidiopsis sp. TS-821. The structure resolves 44 subunits and 448 cofactor molecules. We conclude that the tetramer is arranged via two different interfaces resulting from a dimer-of-dimers organization. The localization of chlorophyll molecules permits an excitation energy pathway within and between adjacent monomers. Bioinformatics analysis reveals conserved regions in the PsaL subunit that correlate with the oligomeric state. Tetrameric PSI may function as a key evolutionary step between the trimeric and monomeric forms of PSI organization in photosynthetic organisms.

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.

Advances in Xmipp for Cryo-Electron Microscopy: From Xmipp to Scipion

Xmipp is an open-source software package consisting of multiple programs for processing data originating from electron microscopy and electron tomography, designed and managed by the Biocomputing Unit of the Spanish National Center for Biotechnology, although with contributions from many other developers over the world. During its 25 years of existence, Xmipp underwent multiple changes and updates. While there were many publications related to new programs and functionality added to Xmipp, there is no single publication on the Xmipp as a package since 2013. In this article, we give an overview of the changes and new work since 2013, describe technologies and techniques used during the development, and take a peek at the future of the package.