Markov random field based automatic image alignment for electron tomography

We present a method for automatic full-precision alignment of the images in a tomographic tilt series. Full-precision automatic alignment of cryo electron microscopy images has remained a difficult challenge to date, due to the limited electron dose and low image contrast. These facts lead to poor signal to noise ratio (SNR) in the images, which causes automatic feature trackers to generate errors, even with high contrast gold particles as fiducial features. To enable fully automatic alignment for full-precision reconstructions, we frame the problem probabilistically as finding the most likely particle tracks given a set of noisy images, using contextual information to make the solution more robust to the noise in each image. To solve this maximum likelihood problem, we use Markov Random Fields (MRF) to establish the correspondence of features in alignment and robust optimization for projection model estimation. The resulting algorithm, called Robust Alignment and Projection Estimation for Tomographic Reconstruction, or RAPTOR, has not needed any manual intervention for the difficult datasets we have tried, and has provided sub-pixel alignment that is as good as the manual approach by an expert user. We are able to automatically map complete and partial marker trajectories and thus obtain highly accurate image alignment. Our method has been applied to challenging cryo electron tomographic datasets with low SNR from intact bacterial cells, as well as several plastic section and X-ray datasets.     

Applications of a bilateral denoising filter in biological electron microscopy

Due to the sensitivity of biological sample to the radiation damage, the low dose imaging conditions used for electron microscopy result in extremely noisy images. The processes of digitization, image alignment, and 3D reconstruction also introduce additional sources of noise in the final 3D structure. In this paper, we investigate the effectiveness of a bilateral denoising filter in various biological electron microscopy applications. In contrast to the conventional low pass filters, which inevitably smooth out both noise and structural features simultaneously, we found that bilateral filter holds a distinct advantage in being capable of effectively suppressing noise without blurring the high resolution details. In as much, we have applied this technique to individual micrographs, entire 3D reconstructions, segmented proteins, and tomographic reconstructions.     

Maximum-Entropy Three-Dimensional Reconstruction with Deconvolution of the Contrast Transfer Function: A Test Application with Adenovirus

We have developed an objective, quantitative, and general algorithm to improve the fidelity of three-dimensional reconstructions made from electron micrographs while at the same time filtering much of the noise present in the recorded data. The new technique is called constrained maximum entropy tomography (COMET). The essence of the method is that it will produce the most featureless reconstruction that fits the projection data within their observational accuracy. In particular, the COMET procedure will minimise the detrimental effects of errors in the measured data and deconvolute the effects of the contrast transfer function. An objective test has been performed using COMET on a conventional image reconstruction obtained from cryo-electron micrographs of adenovirus. The density for hexon, the major coat protein of the virus, which is known to high resolution from X-ray crystallography, provided a known high-resolution control. The COMET reconstruction is in considerably better agreement with the crystallographic electron density than the original reconstruction, throughout the entire resolution range.     

Developing a denoising filter for electron microscopy and tomography data in the cloud

The low radiation conditions and the predominantly phase-object image formation of cryo-electron microscopy (cryo-EM) result in extremely high noise levels and low contrast in the recorded micrographs. The process of single particle or tomographic 3D reconstruction does not completely eliminate this noise and is even capable of introducing new sources of noise during alignment or when correcting for instrument parameters. The recently developed Digital Paths Supervised Variance (DPSV) denoising filter uses local variance information to control regional noise in a robust and adaptive manner. The performance of the DPSV filter was evaluated in this review qualitatively and quantitatively using simulated and experimental data from cryo-EM and tomography in two and three dimensions. We also assessed the benefit of filtering experimental reconstructions for visualization purposes and for enhancing the accuracy of feature detection. The DPSV filter eliminates high-frequency noise artifacts (density gaps), which would normally preclude the accurate segmentation of tomography reconstructions or the detection of alpha-helices in single-particle reconstructions. This collaborative software development project was carried out entirely by virtual interactions among the authors using publicly available development and file sharing tools.     

The reconstruction of structure from electron micrographs of randomly oriented particles

A new method for enhancing and reconstructing the three dimensional structure of randomly oriented particles from their electron micrographs is developed. The method requires as an input many pictures of randomly oriented identical particles. The analysis is based on the calculation and accumulation of the spatial correlation of the densities on the electron micrographs, from which the spherical harmonic coefficients of the structure can be found. The process of enhancement of the spatial correlation and the averaging out of background noise enables reconstructions by use of pictures with low signal-to-noise ratio. The theory is presented and implemented in a computer program package. Simulated electron micrographs of ellipses, rods and a model of hexameric glutamate dehydrogenase are analyzed to demonstrate reconstructions using the computer programs.     

Divalent ion-dependent swelling of tomato bushy stunt virus: a multi-approach study

Time-resolved small-angle X-ray and neutron scattering (SAXS and SANS) in solution were used to study the swelling reaction of TBSV upon chelation of its constituent calcium at mildly basic pH. SAXS intensities comprise contribution from the protein capsid and the RNA moiety, while neutron scattering, recorded in 72% D2O, is essentially due to the protein capsid. Cryo-electron micrographs of compact and swollen virus were used to produce 3D reconstructions of the initial and final conformations of the virus at a resolution of 13 A and 19 A, respectively. While compact particles appear to be very homogeneous in size, solutions of swollen particles exhibit some size heterogeneity. A procedure has been developed to compute the SAXS pattern from the 3D reconstruction for comparison with experimental data. Cryo-electron microscopy thereby provides an invaluable starting (and ending) point for the analysis of the time-resolved swelling process using the scattering data.     

Model-based particle picking for cryo-electron microscopy

We describe an algorithm for finding particle images in cryo-EM micrographs. The algorithm starts from a crude 3D map of the target particle, computed from a relatively small number of manually picked images, and then projects the map in many different directions to give synthetic 2D templates. The templates are clustered and averaged and then cross-correlated with the micrographs. A probabilistic model of the imaging process then scores cross-correlation peaks to produce the final picks. We give quantitative results on two quite different target particles: keyhole limpet hemocyanin and p97 AAA ATPase. On these particles our automatic particle picker shows human performance level, as measured by the Fourier shell correlations of 3D reconstructions.     

Fast rotational matching of single-particle images

The presence of noise and absence of contrast in electron micrographs lead to a reduced resolution of the final 3D reconstruction, due to the inherent limitations of single-particle image alignment. The fast rotational matching (FRM) algorithm was introduced recently for an accurate alignment of 2D images under such challenging conditions. Here, we implemented this algorithm for the first time in a standard 3D reconstruction package used in electron microscopy. This allowed us to carry out exhaustive tests of the robustness and reliability in iterative orientation determination, classification, and 3D reconstruction on simulated and experimental image data. A classification test on GroEL chaperonin images demonstrates that FRM assigns up to 13% more images to their correct reference orientation, compared to the classical self-correlation function method. Moreover, at sub-nanometer resolution, GroEL and rice dwarf virus reconstructions exhibit a remarkable resolution gain of 10-20% that is attributed to the novel image alignment kernel.     

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 binary segmentation approach for boxing ribosome particles in cryo EM micrographs

Three-dimensional reconstruction of ribosome particles from electron micrographs requires selection of many single-particle images. Roughly 100,000 particles are required to achieve approximately 10 A resolution. Manual selection of particles, by visual observation of the micrographs on a computer screen, is recognized as a bottleneck in automated single-particle reconstruction. This paper describes an efficient approach for automated boxing of ribosome particles in micrographs. Use of a fast, anisotropic non-linear reaction-diffusion method to pre-process micrographs and rank-leveling to enhance the contrast between particles and the background, followed by binary and morphological segmentation constitute the core of this technique. Modifying the shape of the particles to facilitate segmentation of individual particles within clusters and boxing the isolated particles is successfully attempted. Tests on a limited number of micrographs have shown that over 80% success is achieved in automatic particle picking.     

A symmetry mismatch at the site of RNA packaging in the polymerase complex of dsRNA bacteriophage phi6

The polymerase complex of the enveloped double-stranded RNA (dsRNA) bacteriophage phi6 fulfils a similar function to those of other dsRNA viruses such as Reoviridae. The phi6 complex comprises protein P1, which forms the shell, and proteins P2, P4 and P7, which are involved in RNA synthesis and packaging. Icosahedral reconstructions from cryo-electron micrographs of recombinant polymerase particles revealed a clear dodecahedral shell and weaker satellites. Difference imaging demonstrated that these weak satellites were the sites of P4 and P2 within the complex. The structure determined by icosahedral reconstruction was used as an initial model in an iterative reconstruction technique to examine the departures from icosahedral symmetry. This approach showed that P4 and P2 contribute to structures at the 5-fold positions of the icosahedral P1 shell which lack 5-fold symmetry and appear in variable orientations. Reconstruction of isolated recombinant P4 showed that it was a hexamer with a size and shape matching the satellite. Symmetry mismatch between the satellites and the shell could play a role in RNA packaging akin to that of the portal vertex of dsDNA phages in DNA packaging. This is the first example of dsRNA virus in which the structure of the polymerase complex has been determined without the assumption of icosahedral symmetry. Our result with phi6 illustrates the symmetry mismatch which may occur at the sites of RNA packaging in other dsRNA viruses such as members of the Reoviridae.     

A novel three-dimensional variant of the watershed transform for segmentation of electron density maps

Electron density maps at moderate resolution are often difficult to interpret due to the lack of recognizable features. This is especially true for electron tomograms that suffer in addition to the resolution limitation from low signal-to-noise ratios. Reliable segmentation of such maps into smaller, manageable units can greatly facilitate interpretation. Here, we present a segmentation approach targeting three-dimensional electron density maps derived by electron microscopy. The approach consists of a novel three-dimensional variant of the immersion-based watershed algorithm. We tested the algorithm on calculated data and applied it to a wide variety of electron density maps ranging from reconstructions of single macromolecules to tomograms of subcellular structures. The results indicate that the algorithm is reliable, efficient, accurate, and applicable to a wide variety of biological problems.     

Detecting particles in cryo-EM micrographs using learned features

A new learning-based approach is presented for particle detection in cryo-electron micrographs using the Adaboost learning algorithm. The approach builds directly on the successful detectors developed for the domain of face detection. It is a discriminative algorithm which learns important features of the particle's appearance using a set of training examples of the particles and a set of images that do not contain particles. The algorithm is fast (10 s on a 1.3 GHz Pentium M processor), is generic, and is not limited to any particular shape or size of the particle to be detected. The method has been evaluated on a publicly available dataset of 82 cryoEM images of keyhole lympet hemocyanin (KLH). From 998 automatically extracted particle images, the 3-D structure of KLH has been reconstructed at a resolution of 23.2 A which is the same resolution as obtained using particles manually selected by a trained user.     

Focus gradient correction applied to tilt series image data used in electron tomography

The resolution in 3D reconstructions from tilt series is limited to the information below the first zero of the contrast transfer function unless the signal is corrected computationally. The restoration is usually based on the assumption of a linear space-invariant system and a linear relationship between object mass density and observed image contrast. The space-invariant model is no longer valid when applied to tilted micrographs because the defocus varies in a direction perpendicular to the tilt axis and with it the shape of the associated point spread function. In this paper, a method is presented for determining the defocus gradient in thin specimens such as sections and 2D crystals, and for restoration of the images subsequently used for 3D reconstruction. The alignment procedure for 3D reconstruction includes area matching and tilt geometry refinement. A map with limited resolution computed from uncorrected micrographs is compared to a volume computed from corrected micrographs with extended resolution.     

Serial section scanning electron microscopy (S3EM) on silicon wafers for ultra-structural volume imaging of cells and tissues

High resolution, three-dimensional (3D) representations of cellular ultrastructure are essential for structure function studies in all areas of cell biology. While limited subcellular volumes have been routinely examined using serial section transmission electron microscopy (ssTEM), complete ultrastructural reconstructions of large volumes, entire cells or even tissue are difficult to achieve using ssTEM. Here, we introduce a novel approach combining serial sectioning of tissue with scanning electron microscopy (SEM) using a conductive silicon wafer as a support. Ribbons containing hundreds of 35 nm thick sections can be generated and imaged on the wafer at a lateral pixel resolution of 3.7 nm by recording the backscattered electrons with the in-lens detector of the SEM. The resulting electron micrographs are qualitatively comparable to those obtained by conventional TEM. S(3)EM images of the same region of interest in consecutive sections can be used for 3D reconstructions of large structures. We demonstrate the potential of this approach by reconstructing a 31.7 μm(3) volume of a calyx of Held presynaptic terminal. The approach introduced here, Serial Section SEM (S(3)EM), for the first time provides the possibility to obtain 3D ultrastructure of large volumes with high resolution and to selectively and repetitively home in on structures of interest. S(3)EM accelerates process duration, is amenable to full automation and can be implemented with standard instrumentation.     

Molecular structure determination by electron microscopy of unstained crystalline specimens.

The projected structures of two unstained periodic biological specimens, the purple membrane and catalase, have been determined by electron microscopy to resolutions of 7 Å and 9 Å, respectively. Glucose was used to facilitate their in vacuo preservation and extremely low electron doses were applied to avoid their destruction.The information on which the projections are based was extracted from defocussed bright-field micrographs and electron diffraction patterns. Fourier analysis of the micrograph data provided the phases of the Fourier components of the structures; measurement of the electron diffraction patterns provided the amplitudes.Large regions of the micrographs (3000 to 10,000 unit cells) were required for each analysis because of the inherently low image contrast (<1%) and the statistical noise due to the low electron dose.Our methods appear to be limited in resolution only by the performance of the microscope at the unusually low magnifications which were necessary. Resolutions close to 3 Å should ultimately be possible.     

Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers

We have used conical tomography to study the structure of integral proteins in their phospholipid bilayer environments. Complete conical series were collected from replicas of the water channel aquaporin-0 (AQP0), a 6.6 nm side tetramer with a molecular weight of approximately 120 kDa that was purified and reconstituted in liposomes. The replicas were tilted at 38 degrees , 50 degrees or 55 degrees and rotated by 2.5 degrees , 4 degrees , or 5 degrees increments until completing 360 degrees turns. The elliptical paths of between 6 and 12 freeze-fracture particles aligned the images to a common coordinate system. Using the weighted back projection algorithm, small volumes of the replicas were independently reconstructed to reconstitute the field. Using the Fourier Shell Correlation computed from reconstructions of even and odd projections of the series, we estimated a resolution of 2-3 nm, a value that was close to the thickness of the replica (approximately 1.5 nm). The 3D reconstructions exhibited isotropic resolution along the x-y plane, which simplified the analysis of particles oriented randomly in the membrane plane. In contrast to reconstructions from single particles imaged using random conical tilt [J. Mol. Biol. 325 (2003) 210], the reconstructions using conical tomography allowed the size and shape of individual particles representing the AQP0 channel to be identified without averaging or imposing symmetry. In conclusion, the reconstruction of freeze-fracture replicas with electron tomography has provided a novel experimental approach for the study of integral proteins inserted in phospholipid bilayers.     

Toward understanding the structure and interactions of microtubules and motor proteins

To obtain an overall three-dimensional picture of the interaction between microtubules and the motor proteins of the kinesin family it will be necessary to take account of both atomic resolution structures obtained by X-ray crystallography and medium resolution reconstructions obtained by electron cryomicroscopy. We examine the problems associated with obtaining the required structural information from electron micrographs of vitreous ice-embedded microtubules decorated with motor domains. We find that the minus-end directed motor, ncd, decorates microtubules with an 80 Å periodicity as for kinesin. Our theoretical analysis and experiments with ncd illustrate the difficulty in determining unambiguously the surface lattice organization by diffraction analysis of micrographs. 3D reconstructions of decorated microtubules are required to accurately locate the motor domains. Helical diffraction theory is not usually applicable because microtubules are cylindrical structures that rarely have complete helical symmetry. We propose using a back-projection method based on the long pitch helices formed by individual protofilaments. Model reconstructions show that this approach is feasible. © 1995 Wiley-Liss, Inc.     

Automatic particle pickup method using a neural network has high accuracy by applying an initial weight derived from eigenimages: a new reference free method for single-particle analysis

The single-particle analysis is a structure-determining method for electron microscope (EM) images which does not require crystal. In this method, the projections are picked up and averaged by the images of similar Euler angles to improve the signal to noise ratio, and then create a 3-D reconstruction. The selection of a large number of particles from the cryo-EM micrographs is a pre-requisite for obtaining a high resolution. To pickup a low-contrast cryo-EM protein image, we have recently found that a three-layer pyramidal-type neural network is successful in detecting such a faint image, which had been difficult to detect by other methods. The connection weights between the input and hidden layers, which work as a matching filter, have revealed that they reflect characters of the particle projections in the training data. The images stored in terms of the connection weights were complex, more similar to the eigenimages which are created by the principal component analysis of the learning images rather than to the averages of the particle projections. When we set the initial learning weights according to the eigenimages in advance, the learning period was able to be shortened to less than half the time of the NN whose initial weights had been set randomly. Further, the pickup accuracy increased from 90 to 98%, and a combination of the matching filters were found to work as an integrated matching filter there. The integrated filters were amazingly similar to averaged projections and can be used directly as references for further two-dimensional averaging. Therefore, this research also presents a brand-new reference-free method for single-particle analysis.