3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs)

An image processing pipeline for electron cryo-tomography in RELION-5

Electron tomography of frozen, hydrated samples allows structure determination of macromolecular complexes that are embedded in complex environments. Provided that the target complexes may be localised in noisy, three-dimensional tomographic reconstructions, averaging images of multiple instances of these molecules can lead to structures with sufficient resolution for de novo atomic modelling. Although many research groups have contributed image processing tools for these tasks, a lack of standardisation and interoperability represents a barrier for newcomers to the field. Here, we present an image processing pipeline for electron tomography data in RELION-5, with functionality ranging from the import of unprocessed movies to the automated building of atomic models in the final maps. Our explicit definition of metadata items that describe the steps of our pipeline has been designed for interoperability with other software tools and provides a framework for further standardisation.

Analysis of 3D pathology samples using weakly supervised AI

Human tissue, which is inherently three-dimensional (3D), is traditionally examined through standard-of-care histopathology as limited two-dimensional (2D) cross-sections that can insufficiently represent the tissue due to sampling bias. To holistically characterize histomorphology, 3D imaging modalities have been developed, but clinical translation is hampered by complex manual evaluation and lack of computational platforms to distill clinical insights from large, high-resolution datasets. We present TriPath, a deep-learning platform for processing tissue volumes and efficiently predicting clinical outcomes based on 3D morphological features. Recurrence risk-stratification models were trained on prostate cancer specimens imaged with open-top light-sheet microscopy or microcomputed tomography. By comprehensively capturing 3D morphologies, 3D volume-based prognostication achieves superior performance to traditional 2D slice-based approaches, including clinical/histopathological baselines from six certified genitourinary pathologists. Incorporating greater tissue volume improves prognostic performance and mitigates risk prediction variability from sampling bias, further emphasizing the value of capturing larger extents of heterogeneous morphology.

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.

Pixel-driven computation of parallel and fan-beam projections of a digital image based on pixel-representation using a new formula

BACKGROUND

The computation of the projections of a digital image - modelled as a superposition of square pixels - is essential in several algorithms in computed tomography, and also in many machine vision applications. Projections of digital images are computed through the ray-driven approach. Current pixel-driven methods, though simpler, involve interpolation kernels in the projection-domain - not based on the exact Radon transform (RT) of a square.

METHODS

A new analytical formula - for the line-integral of the unit pixel - simpler than that published previously, is derived. The formula allows easy, pixel-driven computation of the RT of a digital image based on the pixel model i.e., Riemann-sum approximation to the line integral. The method naturally allows pixel-driven backprojection, based on the same (pixel) model. The approach is extended to computing projections over divergent (fan-) beams, and its application as a generalized version of the traditional Hough transform, is discussed.

RESULTS

The Radon transform of the unit-pixel match that of a digital square image. The RT, of a mathematical phantom consisting of a superposition of elliptical disks, compares well with that based on analytical formula. A comparative study with the pixel driven approach with interpolation in the projection-domain, and its important variant, is included. The fan-beam projections of the square image and the phantom are presented. The applicability of the RT in estimating the Hough transform over precise lines, is shown.

CONCLUSION

The new formula, a simplified version of that of Deans, is useful in pixel-driven computation of parallel and fan-beam projections based on Riemann-sum approximation, which is exact in the case of the common pixel-based image model. Pixel-driven approach is amenable to parallel, and also region-of-interest computation. The method is useful in CT as well as machine vision applications.

Method for fast lipid reconstruction and removal processing in 1 H MRSI of the brain

PURPOSE

To develop a new rapid spatial filtering method for lipid removal, fast lipid reconstruction and removal processing (FLIP), which selectively isolates and removes interfering lipid signals from outside the brain in a full-FOV 2D MRSI and whole-brain 3D echo planar spectroscopic imaging (EPSI).

THEORY AND METHODS

FLIP uses regularized least-squares regression based on spatial prior information from MRI to selectively remove lipid signals originating from the scalp and measure the brain metabolite signals with minimum cross contamination. FLIP is a noniterative approach, thus allowing a rapid processing speed, and uses only spatial information without any spectral priors. The performance of FLIP was compared with the Papoulis-Gerchberg algorithm (PGA), Hankel singular value decomposition (HSVD), and fast image reconstruction with L2 regularization (L2).

RESULTS

FLIP in both 2D and 3D MRSI resulted in consistent metabolite quantification in a greater number of voxels with less concentration variation than other algorithms, demonstrating effective and robust lipid-removal performance. The percentage of voxels that met quality criteria with FLIP, PGA, HSVD, and L2 processing were 90%, 57%, 29%, and 42% in 2D MRSI, and 80%, 75%, 76%, and 74% in 3D EPSI, respectively. The quantification results of full-FOV MRSI using FLIP were comparable to those of volume-localized MRSI, while allowing significantly increased spatial coverage. FLIP performed the fastest in 2D MRSI.

CONCLUSION

FLIP is a new lipid-removal algorithm that promises fast and effective lipid removal with improved volume coverage in MRSI.

Computational Methods for Single-Particle Electron Cryomicroscopy

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

Cryo-Electron microscopy for the study of self-assembled poly(ionic liquid) nanoparticles and protein supramolecular structures

Cryo-electron microscopy (cryo-EM) is a powerful structure determination technique that is well-suited to the study of protein and polymer self-assembly in solution. In contrast to conventional transmission electron microscopy (TEM) sample preparation, which often times involves drying and staining, the frozen-hydrated sample preparation allows the specimens to be kept and imaged in a state closest to their native one. Here, we give a short overview of the basic principles of Cryo-EM and review our results on applying it to the study of different protein and polymer self-assembled nanostructures. More specifically, we show how we have applied cryo-electron tomography (cryo-ET) to visualize the internal morphology of self-assembled poly(ionic liquid) nanoparticles and cryo-EM single particle analysis (SPA) to determine the three-dimensional (3D) structures of artificial protein microtubules.

MBIR: A cryo-ET 3D reconstruction method that effectively minimizes missing wedge artifacts and restores missing information

Cryo-Electron Tomography (cryo-ET) has become an essential technique in revealing cellular and macromolecular assembly structures in their native states. However, due to radiation damage and the limited tilt range, cryo-ET suffers from low contrast and missing wedge artifacts, which limits the tomograms to low resolution and hinders further biological interpretation. In this study, we applied the Model-Based Iterative Reconstruction (MBIR) method to obtain tomographic 3D reconstructions of experimental cryo-ET datasets and demonstrated the advantages of MBIR in contrast improvement, missing wedge artifacts reduction, missing information restoration, and subtomogram averaging compared with other reconstruction approaches. Considering the outstanding reconstruction quality, MBIR has a great potential in the determination of high resolution biological structures with cryo-ET.

Investigation of Morphological Features of Autophagy During Plant Programmed Cell Death

The investigation of autophagy particularly when observed during programmed cell death (PCD) is strongly based on the morphological features recorded with transmission electron microscope (TEM). Here we describe methods to induce and to inhibit autophagy in plants. Also some tips for obtaining better preservation of biological membranes, crucial for the investigation of autophagy, are provided together with information about plant autophagic mutants, use of antibodies and methods for 3D reconstruction of large membrane-bound objects that are commonly formed during autophagic processes leading to PCD in plants.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

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).

AuTom: A novel automatic platform for electron tomography reconstruction

We have developed a software package towards automatic electron tomography (ET): Automatic Tomography (AuTom). The presented package has the following characteristics: accurate alignment modules for marker-free datasets containing substantial biological structures; fully automatic alignment modules for datasets with fiducial markers; wide coverage of reconstruction methods including a new iterative method based on the compressed-sensing theory that suppresses the "missing wedge" effect; and multi-platform acceleration solutions that support faster iterative algebraic reconstruction. AuTom aims to achieve fully automatic alignment and reconstruction for electron tomography and has already been successful for a variety of datasets. AuTom also offers user-friendly interface and auxiliary designs for file management and workflow management, in which fiducial marker-based datasets and marker-free datasets are addressed with totally different subprocesses. With all of these features, AuTom can serve as a convenient and effective tool for processing in electron tomography.

The advent of structural biology in situ by single particle cryo-electron tomography

Single particle tomography (SPT), also known as subtomogram averaging, is a powerful technique uniquely poised to address questions in structural biology that are not amenable to more traditional approaches like X-ray crystallography, nuclear magnetic resonance, and conventional cryoEM single particle analysis. Owing to its potential for in situ structural biology at subnanometer resolution, SPT has been gaining enormous momentum in the last five years and is becoming a prominent, widely used technique. This method can be applied to unambiguously determine the structures of macromolecular complexes that exhibit compositional and conformational heterogeneity, both in vitro and in situ. Here we review the development of SPT, highlighting its applications and identifying areas of ongoing development.

Spherically symmetric volume elements as basis functions for image reconstructions in computed laminography

BACKGROUND

Laminography is a tomographic technique that allows three-dimensional imaging of flat, elongated objects that stretch beyond the extent of a reconstruction volume. Laminography datasets can be reconstructed using iterative algorithms based on the Kaczmarz method.

OBJECTIVE

The goal of this study is to develop a reconstruction algorithm that provides superior reconstruction quality for a challenging class of problems.

METHODS

Images are represented in computer memory using coefficients over basis functions, typically piecewise constant functions (voxels). By replacing voxels with spherically symmetric volume elements (blobs) based on generalized Kaiser-Bessel window functions, we obtained an adapted version of the algebraic reconstruction technique.

RESULTS

Band-limiting properties of blob functions are beneficial particular in the case of noisy projections and if only a limited number of projections is available. In this case, using blob basis functions improved the full-width-at-half-maximum resolution from 10.2±1.0 to 9.9±0.9 (p value = 2.3·10-4). For the same dataset, the signal-to-noise ratio improved from 16.1 to 31.0. The increased computational demand per iteration is compensated for by a faster convergence rate, such that the overall performance is approximately identical for blobs and voxels.

CONCLUSIONS

Despite the higher complexity, tomographic reconstruction from computed laminography data should be implemented using blob basis functions, especially if noisy data is expected.

Cryo-Electron Tomography and Subtomogram Averaging

Cryo-electron tomography (cryo-ET) allows 3D volumes to be reconstructed from a set of 2D projection images of a tilted biological sample. It allows densities to be resolved in 3D that would otherwise overlap in 2D projection images. Cryo-ET can be applied to resolve structural features in complex native environments, such as within the cell. Analogous to single-particle reconstruction in cryo-electron microscopy, structures present in multiple copies within tomograms can be extracted, aligned, and averaged, thus increasing the signal-to-noise ratio and resolution. This reconstruction approach, termed subtomogram averaging, can be used to determine protein structures in situ. It can also be applied to facilitate more conventional 2D image analysis approaches. In this chapter, we provide an introduction to cryo-ET and subtomogram averaging. We describe the overall workflow, including tomographic data collection, preprocessing, tomogram reconstruction, subtomogram alignment and averaging, classification, and postprocessing. We consider theoretical issues and practical considerations for each step in the workflow, along with descriptions of recent methodological advances and remaining limitations.

Bayesian inference of initial models in cryo-electron microscopy using pseudo-atoms

Single-particle cryo-electron microscopy is widely used to study the structure of macromolecular assemblies. Tens of thousands of noisy two-dimensional images of the macromolecular assembly viewed from different directions are used to infer its three-dimensional structure. The first step is to estimate a low-resolution initial model and initial image orientations. This is a challenging global optimization problem with many unknowns, including an unknown orientation for each two-dimensional image. Obtaining a good initial model is crucial for the success of the subsequent refinement step. We introduce a probabilistic algorithm for estimating an initial model. The algorithm is fast, has very few algorithmic parameters, and yields information about the precision of estimated model parameters in addition to the parameters themselves. Our algorithm uses a pseudo-atomic model to represent the low-resolution three-dimensional structure, with isotropic Gaussian components as moveable pseudo-atoms. This leads to a significant reduction in the number of parameters needed to represent the three-dimensional structure, and a simplified way of computing two-dimensional projections. It also contributes to the speed of the algorithm. We combine the estimation of the unknown three-dimensional structure and image orientations in a Bayesian framework. This ensures that there are very few parameters to set, and specifies how to combine different types of prior information about the structure with the given data in a systematic way. To estimate the model parameters we use Markov chain Monte Carlo sampling. The advantage is that instead of just obtaining point estimates of model parameters, we obtain an ensemble of models revealing the precision of the estimated parameters. We demonstrate the algorithm on both simulated and real data.

Blob parameter selection for image representation

A technique for optimizing parameters for image representation using blob basis functions is presented and demonstrated. The exact choice of the basis functions significantly influences the quality of the image representation. It has been previously established that using spherically symmetric volume elements (blobs) as basis functions, instead of the more traditional voxels, yields superior representations of real objects, provided that the parameters that occur in the definition of the family of blobs are appropriately tuned. The technique presented in this paper makes use of an extra degree of freedom, which has been previously ignored, in the blob parameter space. The efficacy of the resulting parameters is illustrated.

Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series

Combined tilt- and focal series scanning transmission electron microscopy is a recently developed method to obtain nanoscale three-dimensional (3D) information of thin specimens. In this study, we formulate the forward projection in this acquisition scheme as a linear operator and prove that it is a generalization of the Ray transform for parallel illumination. We analytically derive the corresponding backprojection operator as the adjoint of the forward projection. We further demonstrate that the matched backprojection operator drastically improves the convergence rate of iterative 3D reconstruction compared to the case where a backprojection based on heuristic weighting is used. In addition, we show that the 3D reconstruction is of better quality.

Combined scanning transmission electron microscopy tilt- and focal series

In this study, a combined tilt- and focal series is proposed as a new recording scheme for high-angle annular dark-field scanning transmission electron microscopy (STEM) tomography. Three-dimensional (3D) data were acquired by mechanically tilting the specimen, and recording a through-focal series at each tilt direction. The sample was a whole-mount macrophage cell with embedded gold nanoparticles. The tilt-focal algebraic reconstruction technique (TF-ART) is introduced as a new algorithm to reconstruct tomograms from such combined tilt- and focal series. The feasibility of TF-ART was demonstrated by 3D reconstruction of the experimental 3D data. The results were compared with a conventional STEM tilt series of a similar sample. The combined tilt- and focal series led to smaller "missing wedge" artifacts, and a higher axial resolution than obtained for the STEM tilt series, thus improving on one of the main issues of tilt series-based electron tomography.

Morphology of influenza B/Lee/40 determined by cryo-electron microscopy

Cryo-electron microscopy projection image analysis and tomography is used to describe the overall architecture of influenza B/Lee/40. Algebraic reconstruction techniques with utilization of volume elements (blobs) are employed to reconstruct tomograms of this pleomorphic virus and distinguish viral surface spikes. The purpose of this research is to examine the architecture of influenza type B virions by cryo-electron tomography and projection image analysis. The aims are to explore the degree of ribonucleoprotein disorder in irregular shaped virions; and to quantify the number and distribution of glycoprotein surface spikes (hemagglutinin and neuraminidase) on influenza B. Projection image analysis of virion morphology shows that the majority (∼83%) of virions are spherical with an average diameter of 134±19 nm. The aspherical virions are larger (average diameter = 155±47 nm), exhibit disruption of the ribonucleoproteins, and show a partial loss of surface protein spikes. A count of glycoprotein spikes indicates that a typical 130 nm diameter type B virion contains ∼460 surface spikes. Configuration of the ribonucleoproteins and surface glycoprotein spikes are visualized in tomogram reconstructions and EM densities visualize extensions of the spikes into the matrix. The importance of the viral matrix in organization of virus structure through interaction with the ribonucleoproteins and the anchoring of the glycoprotein spikes to the matrix is demonstrated.

Iterative reconstruction of cryo-electron tomograms using nonuniform fast Fourier transforms

Algorithms for three-dimensional (3D) reconstruction of objects based on their projections are essential in various biological and medical imaging modalities. In cryo-electron tomography (CET) a major challenge for reconstruction is the limited range of projection angles, which manifests itself as a "missing wedge" of data in Fourier space making the reconstruction problem ill-posed. Here, we apply an iterative reconstruction method that makes use of nonuniform fast Fourier transform (NUFFT) to the reconstruction of cryo-electron tomograms. According to several measures the reconstructions are superior to those obtained using conventional methods, most notably weighted backprojection. Most importantly, we show that it is possible to fill in partially the unsampled region in Fourier space with meaningful information without making assumptions about the data or applying prior knowledge. As a consequence, particles of known structure can be localized with higher confidence in cryotomograms and subtomogram averaging yields higher resolution densities.

Orientation Determination of Cryo-EM Images Using Least Unsquared Deviations

A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines-based methods estimate the orientations without additional geometric information. However, such methods fail when the detection rate of common-lines is too low due to the high level of noise in the images. An approximation to the least squares global self-consistency error was obtained in [A. Singer and Y. Shkolnisky, SIAM J. Imaging Sci., 4 (2011), pp. 543-572] using convex relaxation by semidefinite programming. In this paper we introduce a more robust global self-consistency error and show that the corresponding optimization problem can be solved via semidefinite relaxation. In order to prevent artificial clustering of the estimated viewing directions, we further introduce a spectral norm term that is added as a constraint or as a regularization term to the relaxed minimization problem. The resulting problems are solved using either the alternating direction method of multipliers or an iteratively reweighted least squares procedure. Numerical experiments with both simulated and real images demonstrate that the proposed methods significantly reduce the orientation estimation error when the detection rate of common-lines is low.

Image formation modeling in cryo-electron microscopy

Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimen's scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvent's dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson-Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.

A Bayesian adaptive basis algorithm for single particle reconstruction

Traditional single particle reconstruction methods use either the Fourier or the delta function basis to represent the particle density map. This paper proposes a more flexible algorithm that adaptively chooses the basis based on the data. Because the basis adapts to the data, the reconstruction resolution and signal-to-noise ratio (SNR) is improved compared to a reconstruction with a fixed basis. Moreover, the algorithm automatically masks the particle, thereby separating it from the background. This eliminates the need for ad hoc filtering or masking in the refinement loop. The algorithm is formulated in a Bayesian maximum-a-posteriori framework and uses an efficient optimization algorithm for the maximization. Evaluations using simulated and actual cryogenic electron microscopy data show resolution and SNR improvements as well as the effective masking of particle from background.

Visualizing and quantifying cell phenotype using soft X-ray tomography

Soft X-ray tomography (SXT) is an imaging technique capable of characterizing and quantifying the structural phenotype of cells. In particular, SXT is used to visualize the internal architecture of fully hydrated, intact eukaryotic and prokaryotic cells at high spatial resolution (50 nm or better). Image contrast in SXT is derived from the biochemical composition of the cell, and obtained without the need to use potentially damaging contrast-enhancing agents, such as heavy metals. The cells are simply cryopreserved prior to imaging, and are therefore imaged in a near-native state. As a complement to structural imaging by SXT, the same specimen can now be imaged by correlated cryo-light microscopy. By combining data from these two modalities specific molecules can be localized directly within the framework of a high-resolution, three-dimensional reconstruction of the cell. This combination of data types allows sophisticated analyses to be carried out on the impact of environmental and/or genetic factors on cell phenotypes.

Reconstructing virus structures from nanometer to near-atomic resolutions with cryo-electron microscopy and tomography

The past few decades have seen tremendous advances in single-particle electron -cryo-microscopy (cryo-EM). The field has matured to the point that near-atomic resolution density maps can be generated for icosahedral viruses without the need for crystallization. In parallel, substantial progress has been made in determining the structures of nonicosahedrally arranged proteins in viruses by employing either single-particle cryo-EM or cryo-electron tomography (cryo-ET). Implicit in this course have been the availability of a new generation of electron cryo-microscopes and the development of the computational tools that are essential for generating these maps and models. This methodology has enabled structural biologists to analyze structures in increasing detail for virus particles that are in different morphogenetic states. Furthermore, electron imaging of frozen, hydrated cells, in the process of being infected by viruses, has also opened up a new avenue for studying virus structures "in situ". Here we present the common techniques used to acquire and process cryo-EM and cryo-ET data and discuss their implications for structural virology both now and in the future.

Single-particle reconstruction using L(2)-gradient flow

In this paper, we present an iterative algorithm for reconstructing a three-dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy functional consisting of a fidelity term and a regularization term, an L(2)-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Our method compares favorably with those of the weighted back projection, Fourier method, algebraic reconstruction technique and simultaneous iterative reconstruction technique.

Simulation of transmission electron microscope images of biological specimens

We present a new approach to simulate electron cryo-microscope images of biological specimens. The framework for simulation consists of two parts; the first is a phantom generator that generates a model of a specimen suitable for simulation, the second is a transmission electron microscope simulator. The phantom generator calculates the scattering potential of an atomic structure in aqueous buffer and allows the user to define the distribution of molecules in the simulated image. The simulator includes a well defined electron-specimen interaction model based on the scalar Schrödinger equation, the contrast transfer function for optics, and a noise model that includes shot noise as well as detector noise including detector blurring. To enable optimal performance, the simulation framework also includes a calibration protocol for setting simulation parameters. To test the accuracy of the new framework for simulation, we compare simulated images to experimental images recorded of the Tobacco Mosaic Virus (TMV) in vitreous ice. The simulated and experimental images show good agreement with respect to contrast variations depending on dose and defocus. Furthermore, random fluctuations present in experimental and simulated images exhibit similar statistical properties. The simulator has been designed to provide a platform for development of new instrumentation and image processing procedures in single particle electron microscopy, two-dimensional crystallography and electron tomography with well documented protocols and an open source code into which new improvements and extensions are easily incorporated.

Electric-Potential Reconstructions of Single Particles Using L-Gradient Flows

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy functional consisting of a fidelity term and a regularization term, a L(2)-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

An introduction to maximum-likelihood methods in cryo-EM

The maximum-likelihood method provides a powerful approach to many problems in cryo-electron microscopy (cryo-EM) image processing. This contribution aims to provide an accessible introduction to the underlying theory and reviews existing applications in the field. In addition, current developments to reduce computational costs and to improve the statistical description of cryo-EM images are discussed. Combined with the increasing power of modern computers and yet unexplored possibilities provided by theory, these developments are expected to turn the statistical approach into an essential image-processing tool for the electron microscopist.

Fundamentals of three-dimensional reconstruction from projections

Three-dimensional (3D) reconstruction of an object mass density from the set of its 2D line projections lies at a core of both single-particle reconstruction technique and electron tomography. Both techniques utilize electron microscope to collect a set of projections of either multiple objects representing in principle the same macromolecular complex in an isolated form, or a subcellular structure isolated in situ. Therefore, the goal of macromolecular electron microscopy is to invert the projection transformation to recover the distribution of the mass density of the original object. The problem is interesting in that in its discrete form it is ill-posed and not invertible. Various algorithms have been proposed to cope with the practical difficulties of this inversion problem and their differ widely in terms of their robustness with respect to noise in the data, completeness of the collected projection dataset, errors in projections orientation parameters, abilities to efficiently handle large datasets, and other obstacles typically encountered in molecular electron microscopy. Here, we review the theoretical foundations of 3D reconstruction from line projections followed by an overview of reconstruction algorithms routinely used in practice of electron microscopy.

Electron lambda-tomography

Filtered back-projection and weighted back-projection have long been the methods of choice within the electron microscopy community for reconstructing the structure of macromolecular assemblies from electron tomography data. Here, we describe electron lambda-tomography, a reconstruction method that enjoys the benefits of the above mentioned methods, namely speed and ease of implementation, but also addresses some of their shortcomings. In particular, compared to these standard methods, electron lambda-tomography is less sensitive to artifacts that come from structures outside the region that is being reconstructed, and it can sharpen boundaries.

Molecular cryo-electron tomography of vitreous tissue sections: current challenges

Electron tomography of vitreous tissue sections (tissue TOVIS) allows the study of the three-dimensional structure of molecular complexes in a near-native cellular context. Its usage is, however, limited by an unfortunate combination of noisy and incomplete data, by a technically demanding sample preparation procedure, and by a disposition for specimen degradation during data collection. Here we outline some major challenges as experienced from the application of TOVIS to human skin. We further consider a number of practical measures as well as theoretical approaches for its future development.

Insights into the molecular architecture of the 26S proteasome

Cryo-electron microscopy in conjunction with advanced image analysis was used to analyze the structure of the 26S proteasome and to elucidate its variable features. We have been able to outline the boundaries of the ATPase module in the "base" part of the regulatory complex that can vary in its position and orientation relative to the 20S core particle. This variation is consistent with the "wobbling" model that was previously proposed to explain the role of the regulatory complex in opening the gate in the alpha-rings of the core particle. In addition, a variable mass near the mouth of the ATPase ring has been identified as Rpn10, a multiubiquitin receptor, by correlating the electron microscopy data with quantitative mass spectrometry.

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.

Curiel D, Marabini R, Dmitriev IP. Localization of the N-terminus of minor coat protein IIIa in the adenovirus capsid

Minor coat protein IIIa is conserved in all adenoviruses (Ads) and is required for correct viral assembly, but its precise function in capsid organization is unknown. The latest Ad capsid model proposes that IIIa is located underneath the vertex region. To obtain experimental evidence on the location of IIIa and to further define its role, we engineered the IIIa gene to encode heterologous N-terminal peptide extensions. Recombinant Ad variants with IIIa encoding six-histidine (6His) tag, 6His, and FLAG peptides, or with 6His linked to FLAG with a (Gly(4)Ser)(3) linker were rescued and analyzed for virus yield, capsid incorporation of heterologous peptides, and capsid stability. Longer extensions could not be rescued. Western blot analysis confirmed that the modified IIIa proteins were expressed in infected cells and incorporated into virions. In the Ad encoding the 6His-linker-FLAG-IIIa gene, the 6His tag was present in light particles, but not in mature virions. Immunoelectron microscopy of this virus showed that the FLAG epitope is not accessible to antibodies on the viral particles. Three-dimensional electron microscopy and difference mapping located the IIIa N-terminal extension beneath the vertex complex, wedged at the interface between the penton base and peripentonal hexons, therefore supporting the latest proposed model. The position of the IIIa N-terminus and its low tolerance for modification provide new clues for understanding the role of this minor coat protein in Ad capsid assembly and disassembly.

Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only two-thirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized.

Quantitative 3-D imaging of eukaryotic cells using soft X-ray tomography

Imaging has long been one of the principal techniques used in biological and biomedical research. Indeed, the field of cell biology grew out of the first electron microscopy images of organelles in a cell. Since this landmark event, much work has been carried out to image and classify the organelles in eukaryotic cells using electron microscopy. Fluorescently labeled organelles can now be tracked in live cells, and recently, powerful light microscope techniques have pushed the limit of optical resolution to image single molecules. In this paper, we describe the use of soft X-ray tomography, a new tool for quantitative imaging of organelle structure and distribution in whole, fully hydrated eukaryotic Schizosaccharomyces pombe cells. In addition to imaging intact cells, soft X-ray tomography has the advantage of not requiring the use of any staining or fixation protocols--cells are simply transferred from their growth environment to a sample holder and immediately cryofixed. In this way the cells can be imaged in a near native state. Soft X-ray tomography is also capable of imaging relatively large numbers of cells in a short period of time, and is therefore a technique that has the potential to produce information on organelle morphology from statistically significant numbers of cells.

Computational resources for cryo-electron tomography in Bsoft

The Bsoft package [Heymann, J.B., Belnap, D.M., 2007. Bsoft: image processing and molecular modeling for electron microscopy. J. Struct. Biol. 157, 3-18] has been enhanced by adding utilities for processing electron tomographic (ET) data; in particular, cryo-ET data characterized by low contrast and high noise. To handle the high computational load efficiently, a workflow was developed, based on the database-like parameter handling in Bsoft, aimed at minimizing user interaction and facilitating automation. To the same end, scripting elements distribute the processing among multiple processors on the same or different computers. The resolution of a tomogram depends on the precision of projection alignment, which is usually based on pinpointing fiducial markers (electron-dense gold particles). Alignment requires accurate specification of the tilt axis, and our protocol includes a procedure for determining it to adequate accuracy. Refinement of projection alignment provides information that allows assessment of its precision, as well as projection quality control. We implemented a reciprocal space algorithm that affords an alternative to back-projection or real space algorithms for calculating tomograms. Resources are also included that allow resolution assessment by cross-validation (NLOO2D); denoising and interpretation; and the extraction, mutual alignment, and averaging of tomographic sub-volumes.