Normalizing projection images: a study of image normalizing procedures for single particle three-dimensional electron microscopy

Cryo-EM phase-plate images reveal unexpected levels of apparent specimen damage

Apoferritin (apoF) is commonly used as a test specimen in single-particle electron cryo-microscopy (cryo-EM), since it consistently produces density maps that go to 3 Å resolution or higher. When we imaged apoF with a laser phase plate (LPP), however, we observed more severe particle-to-particle variation in the images than we had previously thought to exist. Similarly, we found that images of ribulose bisphosphate carboxylase/oxygenase (rubisco) also exhibited a much greater amount of heterogeneity than expected. By comparison to simulations of images, we verified that the heterogeneity is not explained by the known features of the LPP, shot noise, or differences in particle orientation. We also demonstrate that our specimens are comparable to those previously used in the literature, based on using the final-reconstruction resolution as the metric for evaluation. All of this leads us to the hypothesis that the heterogeneity is due to damage that has occurred either during purification of the specimen or during preparation of the grids. It is not, however, our goal to explain the causes of heterogeneity; rather, we report that using the LPP has made the apparent damage too obvious to be ignored. In hindsight, similar heterogeneity can be seen in images of apoF and the 20S proteasome which others had recorded with a Volta phase plate. We therefore conclude that the increased contrast of phase-plate images (at low spatial frequencies) should also make it possible to visualize, on a single-particle basis, various forms of biologically functional heterogeneity in structure that had previously gone unnoticed.

Ab-initio contrast estimation and denoising of cryo-EM images

BACKGROUND AND OBJECTIVE

The contrast of cryo-EM images varies from one to another, primarily due to the uneven thickness of the ice layer. This contrast variation can affect the quality of 2-D class averaging, 3-D ab-initio modeling, and 3-D heterogeneity analysis. Contrast estimation is currently performed during 3-D iterative refinement. As a result, the estimates are not available at the earlier computational stages of class averaging and ab-initio modeling. This paper aims to solve the contrast estimation problem directly from the picked particle images in the ab-initio stage, without estimating the 3-D volume, image rotations, or class averages.

METHODS

The key observation underlying our analysis is that the 2-D covariance matrix of the raw images is related to the covariance of the underlying clean images, the noise variance, and the contrast variability between images. We show that the contrast variability can be derived from the 2-D covariance matrix and we apply the existing Covariance Wiener Filtering (CWF) framework to estimate it. We also demonstrate a modification of CWF to estimate the contrast of individual images.

RESULTS

Our method improves the contrast estimation by a large margin, compared to the previous CWF method. Its estimation accuracy is often comparable to that of an oracle that knows the ground truth covariance of the clean images. The more accurate contrast estimation also improves the quality of image restoration as demonstrated in both synthetic and experimental datasets.

CONCLUSIONS

This paper proposes an effective method for contrast estimation directly from noisy images without using any 3-D volume information. It enables contrast correction in the earlier stage of single particle analysis, and may improve the accuracy of downstream processing.

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.

Automatic local resolution-based sharpening of cryo-EM maps

MOTIVATION

Recent technological advances and computational developments have allowed the reconstruction of Cryo-Electron Microscopy (cryo-EM) maps at near-atomic resolution. On a typical workflow and once the cryo-EM map has been calculated, a sharpening process is usually performed to enhance map visualization, a step that has proven very important in the key task of structural modeling. However, sharpening approaches, in general, neglects the local quality of the map, which is clearly suboptimal.

RESULTS

Here, a new method for local sharpening of cryo-EM density maps is proposed. The algorithm, named LocalDeblur, is based on a local resolution-guided Wiener restoration approach of the original map. The method is fully automatic and, from the user point of view, virtually parameter-free, without requiring either a starting model or introducing any additional structure factor correction or boosting. Results clearly show a significant impact on map interpretability, greatly helping modeling. In particular, this local sharpening approach is especially suitable for maps that present a broad resolution range, as is often the case for membrane proteins or macromolecules with high flexibility, all of them otherwise very suitable and interesting specimens for cryo-EM. To our knowledge, and leaving out the use of local filters, it represents the first application of local resolution in cryo-EM sharpening.

AVAILABILITY AND IMPLEMENTATION

The source code (LocalDeblur) can be found at https://github.com/I2PC/xmipp and can be run using Scipion (http://scipion.cnb.csic.es) (release numbers greater than or equal 1.2.1).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Fast multiscale reconstruction for Cryo-EM

We present a multiscale reconstruction framework for single-particle analysis (SPA). The representation of three-dimensional (3D) objects with scaled basis functions permits the reconstruction of volumes at any desired scale in the real-space. This multiscale approach generates interesting opportunities in SPA for the stabilization of the initial volume problem or the 3D iterative refinement procedure. In particular, we show that reconstructions performed at coarse scale are more robust to angular errors and permit gains in computational speed. A key component of the proposed iterative scheme is its fast implementation. The costly step of reconstruction, which was previously hindering the use of advanced iterative methods in SPA, is formulated as a discrete convolution with a cost that does not depend on the number of projection directions. The inclusion of the contrast transfer function inside the imaging matrix is also done at no extra computational cost. By permitting full 3D regularization, the framework is by itself a robust alternative to direct methods for performing reconstruction in adverse imaging conditions (e.g., heavy noise, large angular misassignments, low number of projections). We present reconstructions obtained at different scales from a dataset of the 2015/2016 EMDataBank Map Challenge. The algorithm has been implemented in the Scipion package.

A Survey of the Use of Iterative Reconstruction Algorithms in Electron Microscopy

One of the key steps in Electron Microscopy is the tomographic reconstruction of a three-dimensional (3D) map of the specimen being studied from a set of two-dimensional (2D) projections acquired at the microscope. This tomographic reconstruction may be performed with different reconstruction algorithms that can be grouped into several large families: direct Fourier inversion methods, back-projection methods, Radon methods, or iterative algorithms. In this review, we focus on the latter family of algorithms, explaining the mathematical rationale behind the different algorithms in this family as they have been introduced in the field of Electron Microscopy. We cover their use in Single Particle Analysis (SPA) as well as in Electron Tomography (ET).

Foil-hole and data image quality assessment in 3DEM: Towards high-throughput image acquisition in the electron microscope

Automatic or semiautomatic data collection approaches on a transmission electron microscope (TEM) for Single Particle Analysis, capable of acquiring large datasets composed of only high quality images, are of great importance to obtain 3D density maps with the highest resolution possible. Typically, this task is performed by an experienced microscopist, who manually decides to keep or discard images according to subjective criteria. Therefore, this methodology is slow, intensive in human work and subjective. In this work, we propose a method to automatically or semiautomatically perform this image selection task. The approach is based on some simple, fast and effective image quality descriptors, which can be computed during acquisition, to characterize foil-hole and data images. The proposed approach has been used to evaluate the quality of different datasets consisting of foil-hole and data images obtained with a FEI Titan Krios electron microscope. The results show that the proposed method is very effective evaluating the quality of foil-hole and data images, as well as predicting the quality of the data images from the foil-hole images.

Single-Particle Cryo-EM and 3D Reconstruction of Hybrid Nanoparticles with Electron-Dense Components

Single-particle cryo-electron microscopy (cryo-EM), accompanied with 3D reconstruction, is a broadly applicable tool for the structural characterization of macromolecules and nanoparticles. Recently, the cryo-EM field has pushed the limits of this technique to higher resolutions and samples of smaller molecular mass, however, some samples still present hurdles to this technique. Hybrid particles with electron-dense components, which have been studied using single-particle cryo-EM yet with limited success in 3D reconstruction due to the interference caused by electron-dense elements, constitute one group of such challenging samples. To process such hybrid particles, a masking method is developed in this work to adaptively remove pixels arising from electron-dense portions in individual projection images while maintaining maximal biomass signals for subsequent 2D alignment, 3D reconstruction, and iterative refinements. As demonstrated by the success in 3D reconstruction of an octahedron DNA/gold hybrid particle, which has been previously published without a 3D reconstruction, the devised strategy that combines adaptive masking and standard single-particle 3D reconstruction approach has overcome the hurdle of electron-dense elements interference, and is generally applicable to cryo-EM structural characterization of most, if not all, hybrid nanomaterials with electron-dense components.

Efficient estimation of three-dimensional covariance and its application in the analysis of heterogeneous samples in cryo-electron microscopy

Single-particle cryogenic electron microscopy (cryo-EM) is a powerful tool for the study of macromolecular structures at high resolution. Classification allows multiple structural states to be extracted and reconstructed from the same sample. One classification approach is via the covariance matrix, which captures the correlation between every pair of voxels. Earlier approaches employ computing-intensive resampling and estimate only the eigenvectors of the matrix, which are then used in a separate fast classification step. We propose an iterative scheme to explicitly estimate the covariance matrix in its entirety. In our approach, the flexibility in choosing the solution domain allows us to examine a part of the molecule in greater detail. Three-dimensional covariance maps obtained in this way from experimental data (cryo-EM images of the eukaryotic pre-initiation complex) prove to be in excellent agreement with conclusions derived by using traditional approaches, revealing in addition the interdependencies of ligand bindings and structural changes.

Semi-automated selection of cryo-EM particles in RELION-1.3

The selection of particles suitable for high-resolution cryo-EM structure determination from noisy micrographs may represent a tedious and time-consuming step. Here, a semi-automated particle selection procedure is presented that has been implemented within the open-source software RELION. At the heart of the procedure lies a fully CTF-corrected template-based picking algorithm, which is supplemented by a fast sorting algorithm and reference-free 2D class averaging to remove false positives. With only limited user-interaction, the proposed procedure yields results that are comparable to manual particle selection. Together with an improved graphical user interface, these developments further contribute to turning RELION from a stand-alone refinement program into a convenient image processing pipeline for the entire single-particle approach.

Detection of late intermediates in virus capsid assembly by charge detection mass spectrometry

The assembly of hundreds of identical proteins into an icosahedral virus capsid is a remarkable feat of molecular engineering. How this occurs is poorly understood. Key intermediates have been anticipated at the end of the assembly reaction, but it has not been possible to detect them. In this work we have used charge detection mass spectrometry to identify trapped intermediates from late in the assembly of the hepatitis B virus T = 4 capsid, a complex of 120 protein dimers. Prominent intermediates are found with 104/105, 110/111, and 117/118 dimers. Cryo-EM observations indicate the intermediates are incomplete capsids and, hence, on the assembly pathway. On the basis of their stability and kinetic accessibility we have proposed plausible structures. The prominent trapped intermediate with 104 dimers is attributed to an icosahedron missing two neighboring facets, the 111-dimer species is assigned to an icosahedron missing a single facet, and the intermediate with 117 dimers is assigned to a capsid missing a ring of three dimers in the center of a facet.

Structure of the dengue virus glycoprotein non-structural protein 1 by electron microscopy and single-particle analysis

The flavivirus non-structural protein 1 (NS1) is a glycoprotein that is secreted as a soluble hexameric complex during the course of natural infection. Growing evidence indicates that this secreted form of NS1 (sNS1) plays a significant role in immune evasion and modulation during infection. Attempts to determine the crystal structure of NS1 have been unsuccessful to date and relatively little is known about the macromolecular organization of the sNS1 hexamer. Here, we have applied single-particle analysis to images of baculovirus-derived recombinant dengue 2 virus NS1 obtained by electron microscopy to determine its 3D structure to a resolution of 23 Å. This structure reveals a barrel-like organization of the three dimeric units that comprise the hexamer and provides further insights into the overall organization of oligomeric sNS1.

Classification of structural heterogeneity by maximum-likelihood methods

With the advent of computationally feasible approaches to maximum-likelihood (ML) image processing for cryo-electron microscopy, these methods have proven particularly useful in the classification of structurally heterogeneous single-particle data. A growing number of experimental studies have applied these algorithms to study macromolecular complexes with a wide range of structural variability, including nonstoichiometric complex formation, large conformational changes, and combinations of both. This chapter aims to share the practical experience that has been gained from the application of these novel approaches. Current insights on how to prepare the data and how to perform two- or three-dimensional classifications are discussed together with the aspects related to high-performance computing. Thereby, this chapter will hopefully be of practical use for those microscopists wishing to apply ML methods in their own investigations.

Introducing robustness to maximum-likelihood refinement of electron-microscopy data

An expectation-maximization algorithm for maximum-likelihood refinement of electron-microscopy images is presented that is based on fitting mixtures of multivariate t-distributions. The novel algorithm has intrinsic characteristics for providing robustness against atypical observations in the data, which is illustrated using an experimental test set with artificially generated outliers. Tests on experimental data revealed only minor differences in two-dimensional classifications, while three-dimensional classification with the new algorithm gave stronger elongation factor G density in the corresponding class of a structurally heterogeneous ribosome data set than the conventional algorithm for Gaussian mixtures.

Maximum likelihood refinement of electron microscopy data with normalization errors

Commonly employed data models for maximum likelihood refinement of electron microscopy images behave poorly in the presence of normalization errors. Small variations in background mean or signal brightness are relatively common in cryo-electron microscopy data, and varying signal-to-noise ratios or artifacts in the images interfere with standard normalization procedures. In this paper, a statistical data model that accounts for normalization errors is presented, and a corresponding algorithm for maximum likelihood classification of structurally heterogeneous projection data is derived. The extended data model has general relevance, since similar algorithms may be derived for other maximum likelihood approaches in the field. The potentials of this approach are illustrated for two structurally heterogeneous data sets: 70S E.coli ribosomes and human RNA polymerase II complexes. In both cases, maximum likelihood classification based on the conventional data model failed, whereas the new approach was capable of revealing previously unobserved conformations.

3D morphology of the human hepatic ferritin mineral core: new evidence for a subunit structure revealed by single particle analysis of HAADF-STEM images

Ferritin, the major iron storage protein, has dual functions; it sequesters redox activity of intracellular iron and facilitates iron turn-over. Here we present high angle annular dark field (HAADF) images from individual hepatic ferritin cores within tissue sections, these images were obtained using spherical aberration corrected scanning transmission electron microscopy (STEM) under controlled electron fluence. HAADF images of the cores suggest a cubic morphology and a polycrystalline (ferrihydrite) subunit structure that is not evident in equivalent bright field images. By calibrating contrast levels in the HAADF images using quantitative electron energy loss spectroscopy, we have estimated the absolute iron content in any one core, and produced a three dimensional reconstruction of the average core morphology. The core is composed of up to eight subunits, consistent with the eight channels in the protein shell that deliver iron to the central cavity. We find no evidence of a crystallographic orientation relationship between core subunits. Our results confirm that the ferritin protein shell acts as a template for core morphology and within the core, small (approximately 2 nm), surface-disordered ferrihydrite subunits connect to leave a low density centre and a high surface area that would allow rapid turn-over of iron in biological systems.

Volumetric restrictions in single particle 3DEM reconstruction

3D electron microsscopy aims at the reconstruction of density volumes corresponding to the electrostatic potential distribution of macro-molecules. There are many factors limiting the resolution achievable when this technique is applied to biological macromolecules: microscope imperfections, molecule flexibility, lack of projections from certain directions, unknown angular distribution, noise, etc. In this communication we explore the quality gain in the reconstruction by including a priori knowledge such as particle symmetry, occupied volume, known surface relief, density nonnegativity and similarity to a known volume in order to improve the quality of the reconstruction. If the reconstruction is represented as a series expansion, such constraints can be expressed by set of equations that the expansion coefficients must satisfy. In this work, these equation sets are specified and combined in a novel way with the ART + blobs reconstruction algorithm. The effect of each one on the reconstruction of a realistic phantom is explored. Finally, the application of these restrictions to 3D reconstructions from experimental data are studied.

TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy

BACKGROUND

Transmission electron tomography is an increasingly common three-dimensional electron microscopy approach that can provide new insights into the structure of subcellular components. Transmission electron tomography fills the gap between high resolution structural methods (X-ray diffraction or nuclear magnetic resonance) and optical microscopy. We developed new software for transmission electron tomography, TomoJ. TomoJ is a plug-in for the now standard image analysis and processing software for optical microscopy, ImageJ.

RESULTS

TomoJ provides a user-friendly interface for alignment, reconstruction, and combination of multiple tomographic volumes and includes the most recent algorithms for volume reconstructions used in three-dimensional electron microscopy (the algebraic reconstruction technique and simultaneous iterative reconstruction technique) as well as the commonly used approach of weighted back-projection.

CONCLUSION

The software presented in this work is specifically designed for electron tomography. It has been written in Java as a plug-in for ImageJ and is distributed as freeware.

3D electron microscopy of biological nanomachines: principles and applications

Transmission electron microscopy is a powerful technique for studying the three-dimensional (3D) structure of a wide range of biological specimens. Knowledge of this structure is crucial for fully understanding complex relationships among macromolecular complexes and organelles in living cells. In this paper, we present the principles and main application domains of 3D transmission electron microscopy in structural biology. Moreover, we survey current developments needed in this field, and discuss the close relationship of 3D transmission electron microscopy with other experimental techniques aimed at obtaining structural and dynamical information from the scale of whole living cells to atomic structure of macromolecular complexes.

Elastic registration of biological images using vector-spline regularization

We present an elastic registration algorithm for the alignment of biological images. Our method combines and extends some of the best techniques available in the context of medical imaging. We express the deformation field as a B-spline model, which allows us to deal with a rich variety of deformations. We solve the registration problem by minimizing a pixelwise mean-square distance measure between the target image and the warped source. The problem is further constrained by way of a vector-spline regularization which provides some control over two independent quantities that are intrinsic to the deformation: its divergence, and its curl. Our algorithm is also able to handle soft landmark constraints, which is particularly useful when parts of the images contain very little information or when its repartition is uneven. We provide an optimal analytical solution in the case when only landmarks and smoothness considerations are taken into account. We have applied our approach to perform the elastic registration of images such as electrophoretic gels and fly embryos. The validation of the results by experts has been favorable in all cases.