A review of resolution measures and related aspects in 3D Electron Microscopy

Utilizing the scale-invariant feature transform algorithm to align distance matrices facilitates systematic protein structure comparison

MOTIVATION

Protein structure comparison is pivotal for deriving homological relationships, elucidating protein functions, and understanding evolutionary developments. The burgeoning field of in-silico protein structure prediction now yields billions of models with near-experimental accuracy, necessitating sophisticated tools for discerning structural similarities among proteins, particularly when sequence similarity is limited.

RESULTS

In this article, we have developed the align distance matrix with scale (ADAMS) pipeline, which synergizes the distance matrix alignment method with the scale-invariant feature transform algorithm, streamlining protein structure comparison on a proteomic scale. Utilizing a computer vision-centric strategy for contrasting disparate distance matrices, ADAMS adeptly alleviates challenges associated with proteins characterized by a high degree of structural flexibility. Our findings indicate that ADAMS achieves a level of performance and accuracy on par with Foldseek, while maintaining similar speed. Crucially, ADAMS overcomes certain limitations of Foldseek in handling structurally flexible proteins, establishing it as an efficacious tool for in-depth protein structure analysis with heightened accuracy.

AVAILABILITY

ADAMS can be download and used as a python package from Python Package Index (PyPI): adams · PyPI. Source code and other materials are available from young55775/ADAMS-developing (github.com). An online server is available: Bseek Search Server (cryonet.ai).

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.

CryoRes: Local Resolution Estimation of Cryo-EM Density Maps by Deep Learning

Recent progress in cryo-EM research has ignited a revolution in biological macromolecule structure determination. Resolution is an essential parameter for quality assessment of a cryo-EM density map, and it is known that resolution varies in different regions of a map. Currently available methods for local resolution estimation require manual adjustment of parameters and in some cases necessitate acquisition or de novo generation of so-called "half maps". Here, we developed CryoRes, a deep-learning algorithm to estimate local resolution directly from a single final cryo-EM density map, specifically by learning resolution-aware patterns of density map voxels through supervised training on a large dataset comprising 1,174 experimental cryo-EM density maps. CryoRes significantly outperforms all of the state-of-the-art competing resolution estimation methods, achieving an average RMSE of 2.26 Å for local resolution estimation relative to the currently most reliable FSC-based method blocres, yet requiring only the single final map as input. Further, CryoRes is able to generate a molecular mask for each map, with accuracy 12.12% higher than the masks generated by ResMap. CryoRes is ultra-fast, fully automatic, parameter-free, applicable to cryo-EM subtomogram data, and freely available at https://cryores.zhanglab.net.

Image processing tools for the validation of CryoEM maps

The number of maps deposited in public databases (Electron Microscopy Data Bank, EMDB) determined by cryo-electron microscopy has quickly grown in recent years. With this rapid growth, it is critical to guarantee their quality. So far, map validation has primarily focused on the agreement between maps and models. From the image processing perspective, the validation has been mostly restricted to using two half-maps and the measurement of their internal consistency. In this article, we suggest that map validation can be taken much further from the point of view of image processing if 2D classes, particles, angles, coordinates, defoci, and micrographs are also provided. We present a progressive validation scheme that qualifies a result validation status from 0 to 5 and offers three optional qualifiers (A, W, and O) that can be added. The simplest validation state is 0, while the most complete would be 5AWO. This scheme has been implemented in a website https://biocomp.cnb.csic.es/EMValidationService/ to which reconstructed maps and their ESI can be uploaded.

Towards routine 3D characterization of intact mesoscale samples by multi-scale and multimodal scanning X-ray tomography

Non-invasive multi-scale and multimodal 3D characterization of heterogeneous or hierarchically structured intact mesoscale samples is of paramount importance in tackling challenging scientific problems. Scanning hard X-ray tomography techniques providing simultaneous complementary 3D information are ideally suited to such studies. However, the implementation of a robust on-site workflow remains the bottleneck for the widespread application of these powerful multimodal tomography methods. In this paper, we describe the development and implementation of such a robust, holistic workflow, including semi-automatic data reconstruction. Due to its flexibility, our approach is especially well suited for on-the-fly tuning of the experiments to study features of interest progressively at different length scales. To demonstrate the performance of the method, we studied, across multiple length scales, the elemental abundances and morphology of two complex biological systems, Arabidopsis plant seeds and mouse renal papilla samples. The proposed approach opens the way towards routine multimodal 3D characterization of intact samples by providing relevant information from pertinent sample regions in a wide range of scientific fields such as biology, geology, and material sciences.

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.

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

Single-particle analysis (SPA) by cryo-electron microscopy comprises the estimation of many parameters along its image-processing pipeline. Overfitting observed in SPA is normally due to misestimated parameters, and the only way to identify these is by comparing the estimates of multiple algorithms or, at least, multiple executions of the same algorithm.

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.

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.

Image Processing in Cryo-Electron Microscopy of Single Particles: The Power of Combining Methods

Cryo-electron microscopy has established as a mature structural biology technique to elucidate the three-dimensional structure of biological macromolecules. The Coulomb potential of the sample is imaged by an electron beam, and fast semi-conductor detectors produce movies of the sample under study. These movies have to be further processed by a whole pipeline of image-processing algorithms that produce the final structure of the macromolecule. In this chapter, we illustrate this whole processing pipeline putting in value the strength of "meta algorithms," which are the combination of several algorithms, each one with different mathematical rationale, in order to distinguish correctly from incorrectly estimated parameters. We show how this strategy leads to superior performance of the whole pipeline as well as more confident assessments about the reconstructed structures. The "meta algorithms" strategy is common to many fields and, in particular, it has provided excellent results in bioinformatics. We illustrate this combination using the workflow engine, Scipion.

Evaluating Local and Directional Resolution of Cryo-EM Density Maps

A systematic and quantitative evaluation of cryo-EM maps is necessary to judge their quality and to capture all possible sources of error. A single value for global resolution is insufficient to accurately describe the quality of a reconstructed density. We describe the estimation and evaluation of two additional resolution measures, local and directional resolution, using methods based on the Fourier shell correlation (FSC). We apply the protocol to samples that encompass different types of pathologies a user is expected to encounter and provide analyses on how to interpret the output files and resulting maps. Implementation of these tools will facilitate density interpretation and can guide the user in adapting their experiments to improve the quality of cryo-EM maps, and by extension atomic models.

Validation tests for cryo-EM maps using an independent particle set

Cryo-electron microscopy (cryo-EM) has revolutionized structural biology by providing 3D density maps of biomolecules at near-atomic resolution. However, map validation is still an open issue. Despite several efforts from the community, it is possible to overfit 3D maps to noisy data. Here, we develop a novel methodology that uses a small independent particle set (not used during the 3D refinement) to validate the maps. The main idea is to monitor how the map probability evolves over the control set during the 3D refinement. The method is complementary to the gold-standard procedure, which generates two reconstructions at each iteration. We low-pass filter the two reconstructions for different frequency cutoffs, and we calculate the probability of each filtered map given the control set. For high-quality maps, the probability should increase as a function of the frequency cutoff and the refinement iteration. We also compute the similarity between the densities of probability distributions of the two reconstructions. As higher frequencies are included, the distributions become more dissimilar. We optimized the BioEM package to perform these calculations, and tested it over systems ranging from quality data to pure noise. Our results show that with our methodology, it possible to discriminate datasets that are constructed from noise particles. We conclude that validation against a control particle set provides a powerful tool to assess the quality of cryo-EM maps.

Tools for visualizing and analyzing Fourier space sampling in Cryo-EM

A complete understanding of how an orientation distribution contributes to a cryo-EM reconstruction remains lacking. It is necessary to begin critically assessing the set of views to gain an understanding of its effect on experimental reconstructions. Toward that end, we recently suggested that the type of orientation distribution may alter resolution measures in a systematic manner. We introduced the sampling compensation factor (SCF), which incorporates how the collection geometry might change the spectral signal-to-noise ratio (SSNR), irrespective of the other experimental aspects. We show here that knowledge of the sampling restricted to spherical surfaces of sufficiently large radii in Fourier space is equivalent to knowledge of the set of projection views. Moreover, the SCF geometrical factor may be calculated from one such surface. To aid cryo-EM practitioners, we developed a graphical user interface (GUI) tool that evaluates experimental orientation distributions. The GUI returns plots of projection directions, sampling constrained to the surface of a sphere, the SCF value, the fraction of the empty region of Fourier space, and a histogram of the sampling values over the points on a sphere. Finally, a fixed tilt angle may be incorporated to determine how tilting the grid during collection may improve the distribution of views and Fourier space sampling. We advocate this simple conception of sampling and the use of such tools as a complement to the distribution of views to capture the different aspects of the effect of projection directions on cryo-EM reconstructions.

Local resolution estimates of cryoEM reconstructions

The field of cryoEM has quickly advanced in last years with the new biochemical, technological, methodological and computational developments. It has allowed significant progresses in Structural Biology, typically reaching quasi-atomic resolutions in the reconstructed maps. However, this rapid advance has also generated new questions relevant to resolution estimates. The global resolution metrics and their criteria have been deeply discussed in the last decade, but despite that, it remains as an important issue in the field. Recently, the introduction of local resolution measurements has changed how cryoEM reconstructions are interpreted, providing information about the existence of heterogeneity, flexibility, and angular assignment errors, and using it as a tool to aid in modeling. In this review we revisit the concept of local resolution and the different algorithms in the current state of the art. However, the concept of local resolution is not uniquely defined, and each implementation measures different features. This may lead to inappropriate interpretation of local resolution maps. Hence, a set of good practices is provided in this review to avoid misleading and over-interpretation of the reconstructions.

Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities

In recent years, an abundance of new molecular structures have been elucidated using cryo-electron microscopy (cryo-EM), largely due to advances in hardware technology and data processing techniques. Owing to these new exciting developments, cryo-EM was selected by Nature Methods as Method of the Year 2015, and the Nobel Prize in Chemistry 2017 was awarded to three pioneers in the field. The main goal of this article is to introduce the challenging and exciting computational tasks involved in reconstructing 3-D molecular structures by cryo-EM. Determining molecular structures requires a wide range of computational tools in a variety of fields, including signal processing, estimation and detection theory, high-dimensional statistics, convex and non-convex optimization, spectral algorithms, dimensionality reduction, and machine learning. The tools from these fields must be adapted to work under exceptionally challenging conditions, including extreme noise levels, the presence of missing data, and massively large datasets as large as several Terabytes. In addition, we present two statistical models: multi-reference alignment and multi-target detection, that abstract away much of the intricacies of cryo-EM, while retaining some of its essential features. Based on these abstractions, we discuss some recent intriguing results in the mathematical theory of cryo-EM, and delineate relations with group theory, invariant theory, and information theory.

Need for Cross-Validation of Single Particle Cryo-EM

Cross-validation is used to determine the validity of a model on unseen data by assessing if the model is overfitted to noise. It is widely used in many fields, from artificial intelligence to structural biology in X-ray crystallography and nuclear magnetic resonance. Although there are concerns of map overfitting in cryo-electron microscopy (cryo-EM), cross-validation is rarely used. The problem is that establishing a performance metric of the maps over unseen data (given by 2D-projection images) is difficult due to the low signal-to-noise ratios in the individual particles. Here, I present recent advances for cryo-EM map reconstruction. I highlight that the gold-standard procedure can fail to detect map overfitting in certain cases, showing the necessity of assessing the map quality on unbiased data. Finally, I describe the challenges and advantages of developing a robust cross-validation methodology for cryo-EM.

Measuring local-directional resolution and local anisotropy in cryo-EM maps

The introduction of local resolution has enormously helped the understanding of cryo-EM maps. Still, for any given pixel it is a global, aggregated value, that makes impossible the individual analysis of the contribution of the different projection directions. We introduce MonoDir, a fully automatic, parameter-free method that, starting only from the final cryo-EM map, decomposes local resolution into the different projection directions, providing a detailed level of analysis of the final map. Many applications of directional local resolution are possible, and we concentrate here on map quality and validation.

It is important to analyse the local resolution of cryo-EM maps. Here the authors present MonoDir, a fully automatic and parameter free method for the directional local resolution analysis of cryo-EM maps that requires only the final map as input and they also propose indicators for assessing map quality.

Measurement of local resolution in electron tomography

Resolution (global and local) is one of the most reported metrics of quality measurement in Single Particle Analysis (SPA). However, in electron tomography, the situation is different and its computation is not straightforward. Typically, resolution estimation is global and, therefore, reduces the assessment of a whole tomogram to a single number. However, it is known that tomogram quality is spatially variant. Still, up to our knowledge, a method to estimate local quality metrics in tomography is lacking. This work introduces MonoTomo, a method developed to estimate locally in a tomogram the highest reliable frequency component, expressed as a form of local resolution. The fundamentals lie in a local analysis of the density map via monogenic signals, which, in analogy to MonoRes, allows for local estimations. Results with experimental data show that the local resolution range that MonoTomo casts agrees with reported resolution values for experimental data sets, with the advantage of providing a local estimation. A range of applications of MonoTomo are suggested for further exploration.

DeepRes: a new deep-learning- and aspect-based local resolution method for electron-microscopy maps

In this article, a method is presented to estimate a new local quality measure for 3D cryoEM maps that adopts the form of a 'local resolution' type of information. The algorithm (DeepRes) is based on deep-learning 3D feature detection. DeepRes is fully automatic and parameter-free, and avoids the issues of most current methods, such as their insensitivity to enhancements owing to B-factor sharpening (unless the 3D mask is changed), among others, which is an issue that has been virtually neglected in the cryoEM field until now. In this way, DeepRes can be applied to any map, detecting subtle changes in local quality after applying enhancement processes such as isotropic filters or substantially more complex procedures, such as model-based local sharpening, non-model-based methods or denoising, that may be very difficult to follow using current methods. It performs as a human observer expects. The comparison with traditional local resolution indicators is also addressed.

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.

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.

Assessing the quality of single particle reconstructions by atomic model building

The 2015/2016 Map Challenge challenged cryo-EM practitioners to process a series of publicly available cryo-EM datasets. As part of the challenge, metrics needed to be developed to assess and compare the quality of the different map submissions. The most common metric for assessing maps is determining the resolution by Fourier shell correlation (FSC), but there are well known instances where the resolution can be misleading. In this manuscript, we present a new approach for assessing the quality of a map by determining the map "modelability" rather than on resolution. We used the automated map tracing and modeling algorithms in Rosetta to generate populations of models, and then compared the populations between different map entries by the Rosetta score, RMSD to a reference model provided by the map challenge, and by pair-wise RMSDs between different models in the population. These metrics were used to determine statistically significant rankings for the map challengers for each dataset. The rankings revealed inconsistencies between the resolution by FSC, emphasized the importance of the interplay between number of particles contributing to a map and map quality, and revealed the importance of software familiarity on single particle reconstruction results. However, because multiple variables changed between map entries, it was challenging to derive best practices from the map challenge results.

The first single particle analysis Map Challenge: A summary of the assessments

The recent successes of cryo-electron microscopy fostered great expectation of solving many new and previously recalcitrant biomolecular structures. However, it also brings with it the danger of compromising the validity of the outcomes if not done properly. The Map Challenge is a first step in assessing the state of the art and to shape future developments in data processing. The organizers presented seven cases for single particle reconstruction, and 27 members of the community responded with 66 submissions. Seven groups analyzed these submissions, resulting in several assessment reports, summarized here. We devised a range of analyses to evaluate the submitted maps, including visual impressions, Fourier shell correlation, pairwise similarity and interpretation through modeling. Unfortunately, we did not find strong trends. We ascribe this to the complexity of the challenge, dealing with multiple cases, software packages and processing approaches. This puts the user in the spotlight, where his/her choices becomes the determinant of map quality. The future focus should therefore be on promulgating best practices and encapsulating these in the software. Such practices include adherence to validation principles, most notably the processing of independent sets, proper resolution-limited alignment, appropriate masking and map sharpening. We consider the Map Challenge to be a highly valuable exercise that should be repeated frequently or on an ongoing basis.

3D high resolution imaging for microelectronics: A multi-technique survey on copper pillars

In microelectronics, recently developed 3D integration offers the possibility to stack the dice or wafers vertically instead of putting their different parts next to one another, in order to save space. As this method becomes of greater interest, the need for 3D imaging techniques becomes higher. We here report a study about different 3D characterization techniques applied to copper pillars, which are used to stack different dice together. Destructive techniques such as FIB/SEM, FIB/FIB, and PFIB/PFIB slice and view protocols have been assessed, as well as non-destructive ones, such as laboratory-based and synchrotron-based computed tomographies. A comparison of those techniques in the specific case of copper pillars is given, taking into account the constraints linked to the microelectronics industry, mainly concerning resolution and sample throughput. Laboratory-based imaging techniques are shown to be relevant in the case of punctual analyses, while synchrotron based tomographies offer highly resolved volumes for larger batches of samples.

MonoRes: Automatic and Accurate Estimation of Local Resolution for Electron Microscopy Maps

Since the beginning of electron microscopy, resolution has been a critical parameter. In this article, we propose a fully automatic, accurate method for determining the local resolution of a 3D map (MonoRes). The foundation of this algorithm is an extension of the concept of analytic signal, termed monogenic signal. The map is filtered at different frequencies and the amplitude of the monogenic signal is calculated, after which a criterion is applied to determine the resolution at each voxel. MonoRes is fully automatic without compulsory user parameters, with great accuracy in all tests, and is computationally more rapid than existing methods in the field. In addition, MonoRes offers the option of local filtering of the original map based on the calculated local resolution.

Scipion web tools: Easy to use cryo-EM image processing over the web

Macromolecular structural determination by Electron Microscopy under cryogenic conditions is revolutionizing the field of structural biology, interesting a large community of potential users. Still, the path from raw images to density maps is complex, and sophisticated image processing suites are required in this process, often demanding the installation and understanding of different software packages. Here, we present Scipion Web Tools, a web-based set of tools/workflows derived from the Scipion image processing framework, specially tailored to nonexpert users in need of very precise answers at several key stages of the structural elucidation process.