Three-Dimensional Reconstruction from Reduced Sets of Very Noisy Images Acquired Following a Single-Axis Tilt Schema: Application of a New Three-Dimensional Reconstruction Algorithm and Objective Comparison with Weighted Backprojection

In this work we propose a reconstruction algorithm (ART with blobs) that has not been previously used in electron Tomography and we compare it with the standard method in the field (weighted back projection, WBP). We assume that only a limited set of very noisy images, collected around a single axis tilt, is available; which is a typical situation in Electron Tomography. In general, the reconstruction problem is underdetermined (due to the limited number of projections) and the data are inconsistent (due to the high level of noise). The evaluation of the results is performed in a rigorous way by a task-oriented approach which makes use of numerical observers. ART with blobs outperforms WBP for a number of key tasks. Results are presented both for simplified line integral data and for realistic simulations of macromolecular structures embedded in amorphous ice.     

Spectral signal-to-noise ratio and resolution assessment of 3D reconstructions

Measuring the quality of three-dimensional (3D) reconstructed biological macromolecules by transmission electron microscopy is still an open problem. In this article, we extend the applicability of the spectral signal-to-noise ratio (SSNR) to the evaluation of 3D volumes reconstructed with any reconstruction algorithm. The basis of the method is to measure the consistency between the data and a corresponding set of reprojections computed for the reconstructed 3D map. The idiosyncrasies of the reconstruction algorithm are taken explicitly into account by performing a noise-only reconstruction. This results in the definition of a 3D SSNR which provides an objective indicator of the quality of the 3D reconstruction. Furthermore, the information to build the SSNR can be used to produce a volumetric SSNR (VSSNR). Our method overcomes the need to divide the data set in two. It also provides a direct measure of the performance of the reconstruction algorithm itself; this latter information is typically not available with the standard resolution methods which are primarily focused on reproducibility alone.     

电子显微三维重构技术发展与前沿

本文对电子显微三维重构技术(也称电镜三维重构,electron microscopy 3D reconstruction)进行简要介绍,并在此基础上对该技术当前研究的发展和前沿进行综述,包括高分辨率电镜三维重构、仪器设备性能突破、自动化数据收集和处理、高性能计算技术应用、二/三维图像处理技术的发展和创新、基于三维重构图的模型计算等方面,最后对电子显微三维重构技术的未来进行了展望。     

Single particle reconstruction of membrane proteins: A tool for understanding the 3D structure of disease-related macromolecules

Membrane proteins play important roles in cell functions such as neurotransmission, muscle contraction, and hormone secretion, but their structures are mostly undetermined. Several techniques have been developed to elucidate the structure of macromolecules; X-ray or electron crystallography, nuclear magnetic resonance spectroscopy, and high-resolution electron microscopy. Electron microscopy-based single particle reconstruction, a computer-aided structure determination method, reconstructs a three-dimensional (3D) structure from projections of monodispersed protein. A large number of particle images are picked up from EM films, aligned and classified to generate two-dimensional (2D) averages, and, using the Euler angle of each 2D average, reconstructed into a 3D structure. This method is challenging due to the necessity for close collaboration between classical biochemistry and innovative information technology, including parallel computing. However, recent progress in electron microscopy, mathematical algorithms, and computational ability has greatly increased the subjects that are considered to be primarily addressable using single particle reconstruction. Membrane proteins are one of these targets to which the single particle reconstruction is successfully applied for understanding of their structures. In this paper, we will introduce recently reconstructed channel-related proteins and discuss the applicability of this technique in understanding molecular structures and their roles in pathology.     

Zebrafish Cardiac Muscle Thick Filaments: Isolation Technique and Three-Dimensional Structure

To understand how mutations in thick filament proteins such as cardiac myosin binding protein-C or titin, cause familial hypertrophic cardiomyopathies, it is important to determine the structure of the cardiac thick filament. Techniques for the genetic manipulation of the zebrafish are well established and it has become a major model for the study of the cardiovascular system. Our goal is to develop zebrafish as an alternative system to the mammalian heart model for the study of the structure of the cardiac thick filaments and the proteins that form it. We have successfully isolated thick filaments from zebrafish cardiac muscle, using a procedure similar to those for mammalian heart, and analyzed their structure by negative-staining and electron microscopy. The isolated filaments appear well ordered with the characteristic 42.9 nm quasi-helical repeat of the myosin heads expected from x-ray diffraction. We have performed single particle image analysis on the collected electron microscopy images for the C-zone region of these filaments and obtained a three-dimensional reconstruction at 3.5 nm resolution. This reconstruction reveals structure similar to the mammalian thick filament, and demonstrates that zebrafish may provide a useful model for the study of the changes in the cardiac thick filament associated with disease processes.     

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 L²-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.     

Zebrafish Cardiac Muscle Thick Filaments: Isolation Technique and Three-Dimensional Structure

To understand how mutations in thick filament proteins such as cardiac myosin binding protein-C or titin, cause familial hypertrophic cardiomyopathies, it is important to determine the structure of the cardiac thick filament. Techniques for the genetic manipulation of the zebrafish are well established and it has become a major model for the study of the cardiovascular system. Our goal is to develop zebrafish as an alternative system to the mammalian heart model for the study of the structure of the cardiac thick filaments and the proteins that form it. We have successfully isolated thick filaments from zebrafish cardiac muscle, using a procedure similar to those for mammalian heart, and analyzed their structure by negative-staining and electron microscopy. The isolated filaments appear well ordered with the characteristic 42.9 nm quasi-helical repeat of the myosin heads expected from x-ray diffraction. We have performed single particle image analysis on the collected electron microscopy images for the C-zone region of these filaments and obtained a three-dimensional reconstruction at 3.5 nm resolution. This reconstruction reveals structure similar to the mammalian thick filament, and demonstrates that zebrafish may provide a useful model for the study of the changes in the cardiac thick filament associated with disease processes.     

A fast reconstruction algorithm for electron microscope tomography

We have implemented a Fast Fourier Summation algorithm for tomographic reconstruction of three-dimensional biological data sets obtained via transmission electron microscopy. We designed the fast algorithm to reproduce results obtained by the direct summation algorithm (also known as filtered or R-weighted backprojection). For two-dimensional images, the new algorithm scales as O(N(theta)M log M)+O(MN log N) operations, where N(theta) is the number of projection angles and M x N is the size of the reconstructed image. Three-dimensional reconstructions are constructed from sequences of two-dimensional reconstructions. We demonstrate the algorithm on real data sets. For typical sizes of data sets, the new algorithm is 1.5-2.5 times faster than using direct summation in the space domain. The speed advantage is even greater as the size of the data sets grows. The new algorithm allows us to use higher order spline interpolation of the data without additional computational cost. The algorithm has been incorporated into a commonly used package for tomographic reconstruction.     

The effect of overabundant projection directions on 3D reconstruction algorithms

The experimental process of collecting images from macromolecules in an electron microscope is such that it does not allow for prior specification of the angular distribution of the projection images. As a consequence, an uneven distribution of projection directions may occur. Concerns have been raised recently about the behavior of 3D reconstruction algorithms for the case of unevenly distributed projections. It has been illustrated on experimental data that in the case of a heavily uneven distribution of projection directions some algorithms tend to elongate the reconstructed volumes along the overloaded direction so much as to make a quantitative biological analysis impossible. In answer to these concerns we have developed a strategy for quantitative comparison and optimization of 3D reconstruction algorithms. We apply this strategy to quantitatively analyze algebraic reconstruction techniques (ART) with blobs, simultaneous iterative reconstruction techniques (SIRT) with voxels, and weighted backprojection (WBP). We show that the elongation artifacts that had been previously reported can be strongly reduced. With our specific choices for the free parameters of the three algorithms, WBP reconstructions tend to be inferior to those obtained with either SIRT or ART and the results obtained with ART are comparable to those with SIRT, but at a very small fraction of the computational cost of SIRT.     

Three-dimensional structure of unstained, frozen-hydrated extended tails of bacteriophage T4

Unsupported, unstained frozen-hydrated extended tails of bacteriophage T4 have been studied by cryo-electron microscopy. Their three-dimensional structure has been reconstructed after correlation and averaging of the information from different particles. While the reconstructions of hydrated tails show all the features found by conventional electron microscopy, they are characterized by an open structure. Individual subunits constituting the axial repeat cannot be outlined unambiguously, as the density connectivity is sensitive to the phase-contrast transfer function effects. In order to minimize these effects, we found that the best data set for three-dimensional reconstruction is composed of layer-lines corrected for the phase-contrast transfer function and an uncorrected equator.     

ART: mathematics and applications. A report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques

Some properties of the algebraic reconstruction techniques (ART) for reconstructing objects from their projections (e.g. electron micrographs) are discussed. Some generalizations of previously published ART algorithms are given. In particular, ART is extended to handle weighted projection data. An early conjecture about ART is proved for one of the algorithms: it converges to the most uniform solution of the constraint equations provided by the projection data. Other convergence properties of the ART algorithms are discussed and proved. Some new ART algorithms are described. These are believed to converge to optimal reconstructions consistent with the projection data. The importance of choosing the correct ray widths in case of real projection data is demonstrated, and a method for calculating correct ray widths is given. A method is proposed for estimating the optimal number of iterations in a reconstruction. The performance of ART on real data is demonstrated both in the absence of and in the presence of noise.     

Electron crystallographic methods for investigating gap junction structure

Gap junctions are clusters of closely packed intercellular membrane channels embedded in the plasma membranes of two adjoining cells. The central pore of the membrane channels serves as a conduit between cell cytoplasms for molecules less than 1000 Da in size. Advances in the purification of gap junctions and electron cryocrystallography and computer reconstruction techniques have produced new insights into the intercellular channel structure. Methods are described here for the purification of gap junction membranes, biochemical treatments to produce hemichannel layers ("split junctions"), assessment of the purity of gap junction preparations, electron cryomicroscopy, image processing and reconstruction, three-dimensional visualization, and interpretation. The critical step in electron crystallographic structure determination remains the isolation of crystalline material in sufficient and pure quantities for recording of electron microscope images. Along with sodium dodecyl sulfate-polyacrylamide gel electrophoresis and Western blotting, the quality of gap junction purification is assessed using electron microscopy of negatively stained preparations. Electron microscopy is also used to assess the crystallinity of the purified gap junctions and split junctions. Electron cryocrystallography is a powerful technique for high-resolution structural characterization. Image processing is used to combine and enhance two-dimensional images. Electron crystallographic analysis is used to generate a three-dimensional structure from a set of electron micrographs. This three-dimensional information is extracted from a set of images recorded after tilting the specimen in the electron microscope stage and recombined using Fourier analysis techniques analogous to those used in X-ray crystallography. Computer modeling of the three-dimensional gap junction structures is a useful tool for analyzing hemichannel docking.     

Three-dimensional structure of bovine NADH:ubiquinone oxidoreductase of the mitochondrial respiratory chain

We have studied the structure of bovine heart mitochondrial NADH:ubiquinone (Q) oxidoreductase (EC 1.6.99.3) by image analysis of electron micrographs. A three-dimensional reconstruction was calculated from a tilt-series of a two-dimensional crystal of the molecule. Our interpretation of the position of the molecule in the unit cell of the crystal is supported by additional (low-resolution) analysis of images of single molecules. The three-dimensional reconstruction was calculated with the aid of an iterative real-space reconstruction algorithm. The various projections used as input to the algorithm were obtained by averaging the images of the tilted crystal through a Fourier-space peak-filtering procedure. The reconstructed unit cell measures 15.2 X 15.2 nm in the plane of the two-dimensional crystal and has a height of 10-11 nm. The unit cell contains one molecule consisting of four large subunits. At the present resolution of about 1.3 nm in the untilted projection, these four monomers are seen as two dimers related by a two-fold axis. Two views of the single particles have been recognized; they are the top and side view of the building block of the crystal. After computer image alignment and correspondence analysis, clusters of similar particles have been averaged. In the averages an uneven stain distribution is seen around the molecules, which may result from preferential staining of hydrophilic parts of the molecule. The molecular mass of the whole molecule was determined from scanning transmission electron microscopy measurements as (1.6 +/- 0.2) X 10(6) daltons.     

Low-resolution density maps from atomic models: how stepping "back" can be a step "forward"

Atomic-resolution structures have had a tremendous impact on modern biological science. Much useful information also has been gleaned by merging and correlating atomic-resolution structural details with lower-resolution (15-40 A), three-dimensional (3D) reconstructions computed from images recorded with cryo-transmission electron microscopy (cryoTEM) procedures. One way to merge these structures involves reducing the resolution of an atomic model to a level comparable to a cryoTEM reconstruction. A low-resolution density map can be derived from an atomic-resolution structure by retrieving a set of atomic coordinates editing the coordinate file, computing structure factors from the model coordinates, and computing the inverse Fourier transform of the structure factors. This method is a useful tool for structural studies primarily in combination with 3D cryoTEM reconstructions. It has been used to assess the quality of 3D reconstructions, to determine corrections for the phase-contrast transfer function of the transmission electron microscope, to calibrate the dimensions and handedness of 3D reconstructions, to produce difference maps, to model features in macromolecules or macromolecular complexes, and to generate models to initiate model-based determination of particle orientation and origin parameters for 3D reconstruction.     

Biosensors and molecular imaging

The increase in the understanding of the physical and functional properties of the biological material, from the cellular level down to single molecules, owes its success to the development of suitable high-sensitivity platforms to image the biomaterial and analyze its response to specific stimuli. Imaging has indeed reached molecular capabilities, thanks to optical or magnetic markers [1], to the atomic force microscopy (AFM) in surface reconstruction [2], and is nearing success in three-dimensional (3-D) reconstruction thanks to X-ray holography [3].     

Progress in applying the high-voltage electron microscope to biomedical research

This review attempts a physical definition of the technical problems and achievements in applying the high-voltage electron microscope (HVEM) to biological and medical research. It is hoped that the review will summarize for biologists, funding agencies, and institutions the achievements of the HVEM, its future prospects, and the main problem areas that still need to be explored. At present it is not known whether future HVEMs will favor the fixed beam or the scanning transmission electron microscopy (STEM) mode. The STEM mode offers reduced radiation damage as a result of more efficient electron detection and ease of manipulation of the collected signals by separating the elastic and inelastic signals. Energy filtration to remove the inelastic signal provides a means to enhance the contrast and improve the resolution for thick specimens. Several prototype STEM-mode HVEMs are now under development and it is expected that, in a few years, comparisons of fixed beam and STEM modes will be possible. The review discusses several HVEM instrument features that remain poorly developed. In the area of image recording a photographic emulsion has been designed to give optimized performance at an acceleration voltage of 1 MV. However, this remains unavailable commercially. Conversion of the HVEM electron image to a usable light image by phosphors etc., involves some difficulties, making it difficult to obtain good performance from TV systems. Since the HVEM is particularly useful for three-dimensional imaging, the further development of improved goniometers for stereo viewing and image reconstruction is important. The large volume available in the objective specimen volume and the increased penetration at high acceleration voltages make the HVEM particularly suitable for the application of environmental chambers in the microscopy and electron diffraction of thick wet specimens. An improved signal-to-noise ratio improves the prospects for elemental analysis at high acceleration voltages. When carefully carried out, improved resolution can be obtained in dark-field over that obtainable at 100 kV. Dark-field provides the easiest way to obtain high contrast on weakly stained or unstained objects. Its further improvement requires the use of specially thick and shaped beam stops and apertures that are not penetrated by the 1 MV beam. Recent HVEM studies of whole cells and microorganisms are reviewed. These studies already show that the former thin-section approach led to some incorrect ideas about the shape of some organelles and their three-dimensional relationships. This new information is proving important in helping to establish the function of fibrillar and membranous components of the cell. The most important limitation in examining thick sections is the large depth of field that causes excessive overlap of in-focus structures in stereo views of thick sections. In a few cases special specific heavy metal stains have been developed to overcome this problem, but an optical solution would be more generally applicable. Attempts are now being made to unscramble overlapped detail by applying the image reconstruction techniques of tomography and holography. It is concluded that even with existing techniques, the HVEM examination of thick sections provides a very useful improvement in sampling statistics and in three-dimensional imaging of cell structures over that obtainable by examining thin sections at a lower acceleration voltage (100 kV). Randomized author sequence.     

Projected structure of the pore-forming OmpC protein from Escherichia coli outer membrane.

A single-projection structure analysis of a bacterial outer membrane protein, OmpC, has been carried out by electron microscopy of frozen hydrated specimens. Two distinct crystal polymorphs have been observed in the frozen-hydrated samples, and projection structures of both forms have been obtained to a resolution of 13.5 A. Preliminary examination of negatively stained samples revealed the expected, trimeric appearance of pores in the OmpC specimens. Electron microscopy of unstained, frozen-hydrated OmpC reveals the trimeric pore structure with equal clarity. In addition, the overall molecular envelope of the protein is readily discerned, and a major lipid-containing domain can also be seen. Because of the small coherent patch size, mosaic disorder, and unpredictable polymorphism of the presently available specimens, three-dimensional reconstruction of frozen-hydrated OmpC has not been carried out.     

Three-dimensional structure of the large ribosomal subunit from Escherichia coli.

The three-dimensional structure of the large (50S) ribosomal subunit from Escherichia coli has been determined from electron micrographs of negatively stained specimens. A new method of three-dimensional reconstruction was used which combines many images of individual subunits recorded at a single high tilt angle. A prominent feature of the reconstruction is a large groove on the side of the subunit that interacts with the small ribosomal subunit. This feature is probably of functional significance as it includes the regions where the peptidyl transferase site and the binding locations of the elongation factors have been mapped previously by immunoelectron microscopy.     

Classification of single-projection reconstructions for cryo-electron microscopy data of icosahedral viruses

We present a novel strategy for classification of heterogeneous electron microscopy data of icosahedral virus particles. The effectiveness of the procedure, which is based on classification of single-projection reconstructions (SPRs), is first investigated using simulated data. Of several reconstruction approaches examined, best results were obtained with algebraic reconstruction techniques (ART) when providing prior information about the reconstruction in the form of a starting volume. The results presented indicate that SPR-classification is sufficiently sensitive to classify assemblies with differences of only a few percent of the total mass. The usefulness of this procedure is illustrated by application to a heterogeneous cryo-electron microscopy dataset of adenovirus mutant dl313, lacking minor coat protein IX. These data were successfully divided into two distinct classes, in agreement with gel analysis and immuno-electron microscopy results. The classes yielded a wildtype-like reconstruction and a reconstruction representing the polypeptide IX-deficient dl313 virion. As the largest difference between these volumes is found at the location previously assigned to the external portion of minor coat protein polypeptide IIIa, questions arise concerning the current adenovirus model.     

XMIPP: a new generation of an open-source image processing package for electron microscopy

X-windows based microscopy image processing package (Xmipp) is a specialized suit of image processing programs, primarily aimed at obtaining the 3D reconstruction of biological specimens from large sets of projection images acquired by transmission electron microscopy. This public-domain software package was introduced to the electron microscopy field eight years ago, and since then it has changed drastically. New methodologies for the analysis of single-particle projection images have been added to classification, contrast transfer function correction, angular assignment, 3D reconstruction, reconstruction of crystals, etc. In addition, the package has been extended with functionalities for 2D crystal and electron tomography data. Furthermore, its current implementation in C++, with a highly modular design of well-documented data structures and functions, offers a convenient environment for the development of novel algorithms. In this paper, we present a general overview of a new generation of Xmipp that has been re-engineered to maximize flexibility and modularity, potentially facilitating its integration in future standardization efforts in the field. Moreover, by focusing on those developments that distinguish Xmipp from other packages available, we illustrate its added value to the electron microscopy community.