The Laplacian of Gaussian and arbitrary z-crossings approach applied to automated single particle reconstruction

The automation of single particle selection and tomographic segmentation of asymmetric particles and objects is facilitated by continuing improvement of methods based on the detection of pixel discontinuity. Here, we present the new arbitrary z-crossings approach which can be employed to enhance the accuracy of edge detection algorithms that are based on the second derivative. This is demonstrated using the Laplacian of Gaussian (LoG) filter. In its normal implementation the LoG filter uses a z value of zero to define edge contours. In contrast, the arbitrary z-crossings approach allows the user to adjust z, which causes the subsequently generated contours to tend towards lighter or darker image objects, depending on the sign of z. This functionality has been coupled with an additional feature: the ability to use the major and minor axes of bounding contours to hone automated object selection. In combination, these features significantly enhance the accuracy of particle selection and the speed of tomographic segmentation. Both features have been incorporated into the software package Swarm(PS) in which parameters are automatically adjusted based on user defined target selection.     

SPRING – An image processing package for single-particle based helical reconstruction from electron cryomicrographs

Helical reconstruction from electron cryomicrographs has become a routine technique for macromolecular structure determination of helical assemblies since the first days of Fourier-based three-dimensional image reconstruction. In the past decade, the single-particle technique has had an important impact on the advancement of helical reconstruction. Here, we present the software package SPRING that combines Fourier based symmetry analysis and real-space helical processing into a single workflow. One of the most time-consuming steps in helical reconstruction is the determination of the initial symmetry parameters. First, we propose a class-based helical reconstruction approach that enables the simultaneous exploration and evaluation of many symmetry combinations at low resolution. Second, multiple symmetry solutions can be further assessed and refined by single-particle based helical reconstruction using the correlation of simulated and experimental power spectra. Finally, the 3D structure can be determined to high resolution. In order to validate the procedure, we use the reference specimen Tobacco Mosaic Virus (TMV). After refinement of the helical symmetry, a total of 50,000 asymmetric units from two micrographs are sufficient to reconstruct a subnanometer 3D structure of TMV at 6.4 Å resolution. Furthermore, we introduce the individual programs of the software and discuss enhancements of the helical reconstruction workflow. Thanks to its user-friendly interface and documentation, SPRING can be utilized by the novice as well as the expert user. In addition to the study of well-ordered helical structures, the development of a streamlined workflow for single-particle based helical reconstruction opens new possibilities to analyze specimens that are heterogeneous in symmetries.     

Single particle analysis of filamentous and highly elongated macromolecular assemblies

The application of single particle techniques to the three-dimensional analysis of electron microscope images of elongated or filamentous macromolecular assemblies is evaluated, taking as an example the muscle thin filament. Although the thin filament contains local helical symmetry, because of the inherent variable twist along it, the helical coherence does not extend for large enough distances to allow the symmetry to be used for full reconstruction of the tropomyosin/troponin repeat along the filament. The muscle thin filament therefore represents a general case of a filamentous object in that it is not possible to exploit symmetry in a full analysis. Due to the nature of the imaging process in the electron microscope, only projections of the thin filament around its long axis are available without tilting the grid. Crucially, projection images around a single axis do not provide enough information to assign Euler angles ab initio using current methods. Tests with a model thin filament structure indicated that an out-of-plane tilt of approximately 20 degrees was needed for ab initio angular assignment of sufficient accuracy to calculate a 3D structure to a resolution of approximately 25 A. If no out-of-plane views are available, an alternative approach is to use a prior 3D model as a reference for the initial angle assignment. Tests with the thin filament model indicated that reasonably accurate angular assignment can be made using a reference containing actin, but lacking the regulatory proteins tropomyosin and troponin. We also found that an adaptation of the exact filtered back projection method is required to allow the correct weighting of projection images in which the particle has a very large axial ratio. This adaptation resulted in significant improvements in the reconstruction.     

Robust filtering and particle picking in micrograph images towards 3D reconstruction of purified proteins with cryo-electron microscopy

In order to make a high resolution model of macromolecular structures from cryo-electron microscope (cryo-EM) raw images one has to be precise at every processing step from particle picking to 3D image reconstruction. In this paper we propose a collection of novel methods for filtering cryo-EM images and for automatic picking of particles. These methods have been developed for two cases: (1) when particles can be identified and (2) when particle are not distinguishable. The advantages of these methods are demonstrated in standard purified protein samples and to generalize them we do not use any ad hoc presumption of the geometry of the particle projections. We have also suggested a filtering method to increase the signal-to-noise (S/N) ratio which has proved to be useful for other levels of reconstruction, i.e., finding orientations and 3D model reconstruction.     

IMIRS: a high-resolution 3D reconstruction package integrated with a relational image database

Recent advances in electron cryomicroscopy instrumentation and single particle reconstruction have created opportunities for high-throughput and high-resolution three-dimensional (3D) structure determination of macromolecular complexes. However, it has become impractical and inefficient to rely on conventional text file data management and command-line programs to organize and process the increasing numbers of image data required in high-resolution studies. Here, we present a distributed relational database for managing complex datasets and its integration into our high-resolution software package IMIRS (Image Management and Icosahedral Reconstruction System). IMIRS consists of a complete set of modular programs for icosahedral reconstruction organized under a graphical user interface and provides options for user-friendly, step-by-step data processing as well as automatic reconstruction. We show that the integration of data management with processing in IMIRS automates the tedious tasks of data management, enables data coherence, and facilitates information sharing in a distributed computer and user environment without significantly increasing the time of program execution. We demonstrate the applicability of IMIRS in icosahedral reconstruction toward high resolution by using it to obtain an 8-A 3D structure of an intermediate-sized dsRNA virus.     

Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction

Cryo-electron microscopy (cryo-EM), combined with image processing, is an increasingly powerful tool for structure determination of macromolecular protein complexes and assemblies. In fact, single particle electron microscopy¹ and two-dimensional (2D) electron crystallography² have become relatively routine methodologies and a large number of structures have been solved using these methods. At the same time, image processing and three-dimensional (3D) reconstruction of helical objects has rapidly developed, especially, the iterative helical real-space reconstruction (IHRSR) method³, which uses single particle analysis tools in conjunction with helical symmetry. Many biological entities function in filamentous or helical forms, including actin filaments⁴, microtubules⁵, amyloid fibers⁶, tobacco mosaic viruses⁷, and bacteria flagella⁸, and, because a 3D density map of a helical entity can be attained from a single projection image, compared to the many images required for 3D reconstruction of a non-helical object, with the IHRSR method, structural analysis of such flexible and disordered helical assemblies is now attainable.In this video article, we provide detailed protocols for obtaining a 3D density map of a helical protein assembly (HIV-1 capsid⁹ is our example), including protocols for cryo-EM specimen preparation, low dose data collection by cryo-EM, indexing of helical diffraction patterns, and image processing and 3D reconstruction using IHRSR. Compared to other techniques, cryo-EM offers optimal specimen preservation under near native conditions. Samples are embedded in a thin layer of vitreous ice, by rapid freezing, and imaged in electron microscopes at liquid nitrogen temperature, under low dose conditions to minimize the radiation damage. Sample images are obtained under near native conditions at the expense of low signal and low contrast in the recorded micrographs. Fortunately, the process of helical reconstruction has largely been automated, with the exception of indexing the helical diffraction pattern. Here, we describe an approach to index helical structure and determine helical symmetries (helical parameters) from digitized micrographs, an essential step for 3D helical reconstruction. Briefly, we obtain an initial 3D density map by applying the IHRSR method. This initial map is then iteratively refined by introducing constraints for the alignment parameters of each segment, thus controlling their degrees of freedom. Further improvement is achieved by correcting for the contrast transfer function (CTF) of the electron microscope (amplitude and phase correction) and by optimizing the helical symmetry of the assembly.     

Single particle 3D reconstruction for 2D crystal images of membrane proteins

In cases where ultra-flat cryo-preparations of well-ordered two-dimensional (2D) crystals are available, electron crystallography is a powerful method for the determination of the high-resolution structures of membrane and soluble proteins. However, crystal unbending and Fourier-filtering methods in electron crystallography three-dimensional (3D) image processing are generally limited in their performance for 2D crystals that are badly ordered or non-flat. Here we present a single particle image processing approach, which is implemented as an extension of the 2D crystallographic pipeline realized in the 2dx software package, for the determination of high-resolution 3D structures of membrane proteins. The algorithm presented, addresses the low single-to-noise ratio (SNR) of 2D crystal images by exploiting neighborhood correlation between adjacent proteins in the 2D crystal. Compared with conventional single particle processing for randomly oriented particles, the computational costs are greatly reduced due to the crystal-induced limited search space, which allows a much finer search space compared to classical single particle processing. To reduce the considerable computational costs, our software features a hybrid parallelization scheme for multi-CPU clusters and computer with high-end graphic processing units (GPUs). We successfully apply the new refinement method to the structure of the potassium channel MloK1. The calculated 3D reconstruction shows more structural details and contains less noise than the map obtained by conventional Fourier-filtering based processing of the same 2D crystal images.     

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing techniques. We propose the use of wavelets to match the experimental projections with those obtained from a reference 3D model. The wavelet decomposition of the projection images provides a framework for a multiscale matching algorithm in which speed and robustness to noise are gained. Furthermore, this multiresolution approach is combined with a novel orientation selection strategy. Results obtained from computer simulations as well as experimental data encourage the use of this approach.     

Automatic particle selection from electron micrographs using machine learning techniques

The 3D reconstruction of biological specimens using Electron Microscopy is currently capable of achieving subnanometer resolution. Unfortunately, this goal requires gathering tens of thousands of projection images that are frequently selected manually from micrographs. In this paper we introduce a new automatic particle selection that learns from the user which particles are of interest. The training phase is semi-supervised so that the user can correct the algorithm during picking and specifically identify incorrectly picked particles. By treating such errors specially, the algorithm attempts to minimize the number of false positives. We show that our algorithm is able to produce datasets with fewer wrongly selected particles than previously reported methods. Another advantage is that we avoid the need for an initial reference volume from which to generate picking projections by instead learning which particles to pick from the user. This package has been made publicly available in the open-source package Xmipp.     

Orientation determination by wavelets matching for 3D reconstruction of very noisy electron microscopic virus images

Background  

In order to perform a 3D reconstruction of electron microscopic images of viruses, it is necessary to determine the orientation (Euler angels) of the 2D projections of the virus. The projections containing high resolution information are usually very noisy. This paper proposes a new method, based on weighted-projection matching in wavelet space for virus orientation determination. In order to speed the retrieval of the best match between projections from a model and real virus particle, a hierarchical correlation matching method is also proposed.     

EMAN: semiautomated software for high-resolution single-particle reconstructions

We present EMAN (Electron Micrograph ANalysis), a software package for performing semiautomated single-particle reconstructions from transmission electron micrographs. The goal of this project is to provide software capable of performing single-particle reconstructions beyond 10 A as such high-resolution data become available. A complete single-particle reconstruction algorithm is implemented. Options are available to generate an initial model for particles with no symmetry, a single axis of rotational symmetry, or icosahedral symmetry. Model refinement is an iterative process, which utilizes classification by model-based projection matching. CTF (contrast transfer function) parameters are determined using a new paradigm in which data from multiple micrographs are fit simultaneously. Amplitude and phase CTF correction is then performed automatically as part of the refinement loop. A graphical user interface is provided, so even those with little image processing experience will be able to begin performing reconstructions. Advanced users can directly use the lower level shell commands and even expand the package utilizing EMAN's extensive image-processing library. The package was written from scratch in C++ and is provided free of charge on our Web site. We present an overview of the package as well as several conformance tests with simulated data.     

A fully automatic 3D reconstruction method using simulated annealing enables accurate posterioric angular assignment of protein projections

Single-particle analysis is a structure determining method using electron microscopic (EM) images, which does not require protein crystal. In this method, projections are picked up and used to reconstruct a three-dimensional (3D) structure. When the conical tilting method is not available, the particle images are usually classified and averaged to improve the signal-to-noise ratio. The Euler angles of these average images must be posteriorically assigned to create a primary 3D model. We developed a new, fully automatic unsupervised Euler angle assignment method, which does not require an initial 3D reference and which is applicable to asymmetric molecules. In this method, the Euler angle of each average image is initially set randomly and then automatically corrected in relation to those of the other averages by iterated optimizations using the Simulated Annealing (SA) algorithm. At each iteration, the 3D structure is reconstructed based on the current Euler angles and reprojected back in the average-input directions. A modified cross-correlation between each reprojection and its corresponding original average is then calculated. The correlations are summed as a total 3D echo-correlation score to evaluate the Euler angles at this iteration. Then, one of the projections is selected, its Euler angle is changed randomly, and the score is also calculated. Based on the score change, judgment of whether to accept or reject the new angle is made using the SA algorithm, which is introduced to overcome the local minimums. After a certain number of iterations of this process, the angles of all averages converge so as to create a reliable primary 3D model. This echo-correlated 3D reconstruction with simulated annealing also has potential for wide application to general 3D reconstruction from various types of 2D images.     

Cryo-electron microscope image denoising based on the geodesic distance

Background

To perform a three-dimensional (3-D) reconstruction of electron cryomicroscopy (cryo-EM) images of viruses, it is necessary to determine the similarity of image blocks of the two-dimensional (2-D) projections of the virus. The projections containing high resolution information are typically very noisy. Instead of the traditional Euler metric, this paper proposes a new method, based on the geodesic metric, to measure the similarity of blocks.

Results

Our method is a 2-D image denoising approach. A data set of 2243 cytoplasmic polyhedrosis virus (CPV) capsid particle images in different orientations was used to test the proposed method. Relative to Block-matching and three-dimensional filtering (BM3D), Stein’s unbiased risk estimator (SURE), Bayes shrink and K-means singular value decomposition (K-SVD), the experimental results show that the proposed method can achieve a peak signal-to-noise ratio (PSNR) of 45.65. The method can remove the noise from the cryo-EM image and improve the accuracy of particle picking.

Conclusions

The main contribution of the proposed model is to apply the geodesic distance to measure the similarity of image blocks. We conclude that manifold learning methods can effectively eliminate the noise of the cryo-EM image and improve the accuracy of particle picking.

     

A statistical approach to computer processing of cryo-electron microscope images: virion classification and 3-D reconstruction

The scattering density of the virus is represented as a truncated weighted sum of orthonormal basis functions in spherical coordinates, where the angular dependence of each basis function has icosahedral symmetry. A statistical model of the image formation process is proposed and the maximum likelihood estimation method computed by an expectation-maximization algorithm is used to estimate the weights in the sum and thereby compute a 3-D reconstruction of the virus particle. If multiple types of virus particle are represented in the boxed images then multiple 3-D reconstructions are computed simultaneously without first requiring that the type of particle shown in each boxed image be determined. Examples of the procedure are described for viruses with known structure: (1). 3-D reconstruction of Flockhouse Virus from experimental images, (2). 3-D reconstruction of the capsid of Nudaurelia Omega Capensis Virus from synthetic images, and (3). 3-D reconstruction of both the capsid and the procapsid of Nudaurelia Omega Capensis Virus from a mixture of unclassified synthetic images.     

A measure for the angle between projections based on the extent of correlation between corresponding central sections

A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.     

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.     

SCA: symmetry-based center assignment of 2D projections of symmetric 3D objects

A method for finding the center of cryo-EM images which correspond to the projections of a symmetric 3D structure, based on mathematical properties of symmetry adapted functions and the Fourier-Bessel transform, is presented. It is a model independent one-step procedure with no parameters to be chosen by the user. The proposed method is tested in one synthetic tetrahedral case with different noise levels and in two real cases with D7 and icosahedral symmetries.     

TMaCS: A hybrid template matching and classification system for partially-automated particle selection

Selection of particle images from electron micrographs presents a bottleneck in determining the structures of macromolecular assemblies by single particle electron cryomicroscopy (cryo-EM). The problem is particularly important when an experimentalist wants to improve the resolution of a 3D map by increasing by tens or hundreds of thousands of images the size of the dataset used for calculating the map. Although several existing methods for automatic particle image selection work well for large protein complexes that produce high-contrast images, it is well known in the cryo-EM community that small complexes that give low-contrast images are often refractory to existing automated particle image selection schemes. Here we develop a method for partially-automated particle image selection when an initial 3D map of the protein under investigation is already available. Candidate particle images are selected from micrographs by template matching with template images derived from projections of the existing 3D map. The candidate particle images are then used to train a support vector machine, which classifies the candidates as particle images or non-particle images. In a final step in the analysis, the selected particle images are subjected to projection matching against the initial 3D map, with the correlation coefficient between the particle image and the best matching map projection used to assess the reliability of the particle image. We show that this approach is able to rapidly select particle images from micrographs of a rotary ATPase, a type of membrane protein complex involved in many aspects of biology.