An ab initio algorithm for low-resolution 3-D reconstructions from cryoelectron microscopy images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

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.     

From high symmetry to high resolution in biological electron microscopy: a commentary on Crowther (1971) ‘Procedures for three-dimensional reconstruction of spherical viruses by Fourier synthesis from electron micrographs’

Elucidation of the structure of biological macromolecules and larger assemblies has been essential to understanding the roles they play in living processes. Methods for three-dimensional structure determination of biological assemblies from images recorded in the electron microscope were therefore a key development. In his paper published in Philosophical Transactions B in 1971, Crowther described new computational procedures applied to the first three-dimensional reconstruction of an icosahedral virus from images of virus particles preserved in negative stain. The method for determining the relative orientation of randomly oriented particles and combining their images for reconstruction exploited the high symmetry of the virus particle. Computational methods for image analysis have since been extended to include biological assemblies without symmetry. Further experimental advances, combined with image analysis, have led to the method of cryomicroscopy, which is now used by structural biologists to study the structure and dynamics of biological machines and assemblies in atomic detail. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.     

Chemical conjugation of heterologous proteins on the surface of Cowpea mosaic virus

Genetic economy leads to symmetric distributions of chemically identical subunits in icosaherdal and helical viruses. Modification of the subunit genes of a variety of viruses has permitted the display of polypeptides on both the infectious virions and virus particles made in expression systems. Icosahedral chimeric particles of this type often display novel properties resulting in high local concentrations of the insert. Here we report an extension of this concept in which entire proteins were chemically cross-linked to lysine and cysteine residues genetically engineered on the coat protein of icosahedral Cowpea mosaic virus particles. Three exogenous proteins, the LRR domain of internalin B, the T4 lysozyme, and the Intron 8 gene product of the of the HER2 tyrosine kinase receptor were derivatized with appropriate bifunctional cross-linkers and conjugated to the virus capsid. Characterization of these particles demonstrated that (1) virtually 100% occupancy of the 60 sites was achieved; (2) biological activity (either enzyme or binding specificity) of the attached protein was preserved; (3) in one case (LRR-internalin B) the attached protein conformed with the icosahedral symmetry to the extent that a reconstruction of the derivatized particles displayed added density with a shape consistent with the X-ray structure of the attached protein. Strategies demonstrated here allow virus particle targeting to specific cell types and the use of an icosahedral virus as a platform for structure determination of small proteins at moderate resolution.     

Solution x-ray scattering-based estimation of electron cryomicroscopy imaging parameters for reconstruction of virus particles

Structure factor amplitudes and phases can be computed directly from electron cryomicroscopy images. Inherent aberrations of the electromagnetic lenses and other instrumental factors affect the structure factors, however, resulting in decreased accuracy in the determined three-dimensional reconstruction. In contrast, solution x-ray scattering provides absolute and accurate measurement of spherically averaged structure factor amplitudes of particles in solution but does not provide information on the phases. In the present study, we explore the merits of using solution x-ray scattering data to estimate the imaging parameters necessary to make corrections to the structure factor amplitudes derived from electron cryomicroscopic images of icosahedral virus particles. Using 400-kV spot-scan images of the bacteriophage P22 procapsid, we have calculated an amplitude contrast of 8.0 +/- 5.2%. The amplitude decay parameter has been estimated to be 523 +/- 188 A2 with image noise compensation and 44 +/- 66 A2 without it. These results can also be used to estimate the minimum number of virus particles needed for reconstruction at different resolutions.     

An automatic particle pickup method using a neural network applicable to low-contrast electron micrographs

Three-dimensional reconstruction from electron micrographs requires the selection of many single-particle projection images; more than 10 000 are generally required to obtain 5- to 10-A structural resolution. Consequently, various automatic detection algorithms have been developed and successfully applied to large symmetric protein complexes. This paper presents a new automated particle recognition and pickup procedure based on the three-layer neural network that has a large application range than other automated procedures. Its use for both faint and noisy electron micrographs is demonstrated. The method requires only 200 selected particles as learning data and is able to detect images of proteins as small as 200 kDa.     

Cryoelectron-microscopy image reconstruction of symmetry mismatches in bacteriophage phi29

A method has been developed for three-dimensional image reconstruction of symmetry-mismatched components in tailed phages. Although the method described here addresses the specific case where differing symmetry axes are coincident, the method is more generally applicable, for instance, to the reconstruction of images of viral particles that deviate from icosahedral symmetry. Particles are initially oriented according to their dominant symmetry, thus reducing the search space for determining the orientation of the less dominant, symmetry-mismatched component. This procedure produced an improved reconstruction of the sixfold-symmetric tail assembly that is attached to the fivefold-symmetric prolate head of phi29, demonstrating that this method is capable of detecting and reconstructing an object that included a symmetry mismatch. A reconstruction of phi29 prohead particles using the methods described here establishes that the pRNA molecule has fivefold symmetry when attached to the prohead, consistent with its proposed role as a component of the stator in the phi29 DNA packaging motor.     

Averaging tens to hundreds of icosahedral particle images to resolve protein secondary structure elements using a Multi-Path Simulated Annealing optimization algorithm

Accurately determining a cryoEM particle's alignment parameters is crucial to high resolution single particle 3-D reconstruction. We developed Multi-Path Simulated Annealing, a Monte-Carlo type of optimization algorithm, for globally aligning the center and orientation of a particle simultaneously. A consistency criterion was developed to ensure the alignment parameters are correct and to remove some bad particles from a large pool of images of icosahedral particles. Without using any a priori model, this procedure is able to reconstruct a structure from a random initial model. Combining the procedure above with a new empirical double threshold particle selection method, we are able to pick tens of best quality particles to reconstruct a subnanometer resolution map from scratch. Using the best 62 particles of rice dwarf virus, the reconstruction reached 9.6A resolution at which four helices of the P3A subunit of RDV are resolved. Furthermore, with the 284 best particles, the reconstruction is improved to 7.9A resolution, and 21 of 22 helices and six of seven beta sheets are resolved.     

Wavelets filtering for classification of very noisy electron microscopic single particles images- application on structure determination of VP5-VP19C recombinant

Background

Images of frozen hydrated [vitrified] virus particles were taken close-to-focus in an electron microscope containing structural signals at high spatial frequencies. These images had very low contrast due to the high levels of noise present in the image. The low contrast made particle selection, classification and orientation determination very difficult. The final purpose of the classification is to improve the signal-to-noise ratio of the particle representing the class, which is usually the average. In this paper, the proposed method is based on wavelet filtering and multi-resolution processing for the classification and reconstruction of this very noisy data. A multivariate statistical analysis (MSA) is used for this classification.

Results

The MSA classification method is noise dependant. A set of 2600 projections from a 3D map of a herpes simplex virus -to which noise was added- was classified by MSA. The classification shows the power of wavelet filtering in enhancing the quality of class averages (used in 3D reconstruction) compared to Fourier band pass filtering. A 3D reconstruction of a recombinant virus (VP5-VP19C) is presented as an application of multi-resolution processing for classification and reconstruction.

Conclusion

The wavelet filtering and multi-resolution processing method proposed in this paper offers a new way for processing very noisy images obtained from electron cryo-microscopes. The multi-resolution and filtering improves the speed and accuracy of classification, which is vital for the 3D reconstruction of biological objects. The VP5-VP19C recombinant virus reconstruction presented here is an example, which demonstrates the power of this method. Without this processing, it is not possible to get the correct 3D map of this virus.

     

Electron Tomography of Single Ice-Embedded Macromolecules: Three-Dimensional Alignment and Classification

From 3-D reconstructions of automatically recorded tilt series of ice-embedded macromolecules, several hundred 3-D images of single particles can be extracted. Here we describe correlation-based techniques to align the particles with respect to translation and orientation in 3-D and the calculation of an averaged reconstruction after application of the correct weighting function to the particle projections. Multivariate statistical analysis and classification are applied to the set of three-dimensionally reconstructed particles to investigate interimage variations on the 3-D level.     

Measurement of protein size in concentrated solutions by small angle X‐ray scattering

By simulations on the distance distribution function (DDF) derived from small angle X‐ray scattering (SAXS) theoretical data of a dense monodisperse system, we found a quantitative mathematical correlation between the apparent size of a spherically symmetric (or nearly spherically symmetric) homogenous particle and the concentration of the solution. SAXS experiments on protein solutions of human hemoglobin and horse myoglobin validated the correlation. This gives a new method to determine, from the SAXS DDF, the size of spherically symmetric (or nearly spherically symmetric) particles of a dense monodisperse system, specifically for protein solutions with interference effects.     

Two-dimensional versus three-dimensional morphometry of monogenoidean sclerites

A new method of three-dimensional (3-D) analysis of sclerotised structures of monogenoids was performed by processing z-series images using 3D-Doctor. Z-series were obtained from Gomori's trichrome-stained specimens of marine and freshwater monogenoids under laser scanning confocal fluorescence microscopy. Measurements obtained from 3-D images were then compared with those from 2-D images taken from both flattened and unflattened specimens. Data comparison demonstrated that 3-D morphometry allowed avoidance of over-estimation due to deformation and the reduction of errors associated with different spatial orientations. Moreover, study of 3-D images permitted observation of morphological details that are not detectable in 2-D representations.     

Structural analysis of viral nucleocapsids by subtraction of partial projections

The nucleocapsid of flavivirus particles does not have a recognizable capsid structure when using icosahedral averaging for cryo-electron microscopy structure determinations. The apparent absence of a definitive capsid structure could be due to a lack of synchronization of the symmetry elements of the external glycoprotein layer with those of the core or because the nucleocapsid does not have the same structure within each particle. A technique has been developed to determine the structure of the capsid, and possibly also of the genome, for icosahedral viruses, such as flaviviruses, using cryo-electron microscopy. The method is applicable not only to the analyses of viral cores, but also to the missing structure of multi-component complexes due to symmetry mismatches. The density contributed by external glycoprotein and membrane layers, derived from previously determined three-dimensional icosahedrally averaged reconstructions, was subtracted from the raw images of the virus particles. The resultant difference images were then used for a three-dimensional reconstruction. After appropriate test data sets were constructed and tested, the procedure was applied to examine the nucleocapsids of flaviviruses, which showed that there is no distinct protein density surrounding the genome. Furthermore, there was no evidence of any icosahedral symmetry within the nucleocapsid core.     

Small heat-shock protein structures reveal a continuum from symmetric to variable assemblies

The small heat-shock proteins (sHSPs) form a diverse family of proteins that are produced in all organisms. They function as chaperone-like proteins in that they bind unfolded polypeptides and prevent uncontrolled protein aggregation. Here, we present parallel cryo-electron microscopy studies of five different sHSP assemblies: Methanococcus jannaschii HSP16.5, human alphaB-crystallin, human HSP27, bovine native alpha-crystallin, and the complex of alphaB-crystallin and unfolded alpha-lactalbumin. Gel-filtration chromatography indicated that HSP16.5 is the most monodisperse, while HSP27 and the alpha-crystallin assemblies are more polydisperse. Particle images revealed a similar trend showing mostly regular and symmetric assemblies for HSP16.5 particles and the most irregular assemblies with a wide range of diameters for HSP27. A symmetry test on the particle images indicated stronger octahedral symmetry for HSP16.5 than for HSP27 or the alpha-crystallin assemblies. A single particle reconstruction of HSP16.5, based on 5772 particle images with imposed octahedral symmetry, resulted in a structure that closely matched the crystal structure. In addition, the cryo-EM reconstruction revealed internal density presumably corresponding to the flexible 32 N-terminal residues that were not observed in the crystal structure. The N termini were found to partially fill the central cavity making it unlikely that HSP16.5 sequesters denatured proteins in the cavity. A reconstruction calculated without imposed symmetry confirmed the presence of at least loose octahedral symmetry for HSP16.5 in contrast to the other sHSPs examined, which displayed no clear overall symmetry. Asymmetric reconstructions for the alpha-crystallin assemblies, with an additional mass selection step during image processing, resulted in lower resolution structures. We interpret the alpha-crystallin reconstructions to be average representations of variable assemblies and suggest that the resolutions achieved indicate the degree of variability. Quaternary structural information derived from cryo-electron microscopy is related to recent EPR studies of the alpha-crystallin domain fold and dimer interface of alphaA-crystallin.     

Auto-accumulation method using simulated annealing enables fully automatic particle pickup completely free from a matching template or learning data

Single-particle analysis is a 3-D structure determining method using electron microscopy (EM). In this method, a large number of projections is required to create 3-D reconstruction. In order to enable completely automatic pickup without a matching template or a training data set, we established a brand-new method in which the frames to pickup particles are randomly shifted and rotated over the electron micrograph and, using the total average image of the framed images as an index, each frame reaches a particle. In this process, shifts are selected to increase the contrast of the average. By iterated shifts and further selection of the shifts, the frames are induced to shift so as to surround particles. In this algorithm, hundreds of frames are initially distributed randomly over the electron micrograph in which multi-particle images are dispersed. Starting with these frames, one of them is selected and shifted randomly, and acceptance or non-acceptance of its new position is judged using the simulated annealing (SA) method in which the contrast score of the total average image is adopted as an index. After iteration of this process, the position of each frame converges so as to surround a particle and the framed images are picked up. This method is the first unsupervised fully automatic particle picking method which is applicable to EM of various kinds of proteins, especially to low-contrasted cryo-EM protein images.     

The bacteriophage phi 29 head-tail connector shows 13-fold symmetry in both hexagonally packed arrays and as single particles.

The symmetry of the phi 29 head-tail connector is controversial: several studies of two-dimensional arrays of the connector have found a 12-fold symmetry, while a recent study of isolated particles has found a 13-fold symmetry. To investigate whether a polymorphism of the structure might explain these different results, electron microscopy and image analysis were used to study both isolated connectors and particles in hexagonally packed arrays. The hexagonally packed arrays have a P1 symmetry, and the connectors displayed 13 subunits both in the arrays and as isolated single particles. While we do not observe a polymorphism between connectors in two-dimensional arrays and as isolated particles, data show that the connectors can exist with either 12 or 13 subunits. A three-dimensional reconstruction of our 13-fold connector was generated by combining an averaged side-view projection with the known symmetry. The structure of rosettes of the connectors formed in the presence of phi 29 prohead RNA (pRNA) was also examined. These rosettes contain five connectors arranged about a single connector in the center, and this arrangement may reflect an essential role of the pRNA in mediating a symmetry mismatch between either a 12- or 13-fold symmetric connector and a putative fivefold symmetric prohead portal vertex into which the connector fits.     

Three-dimensional structure of the Chinese Sacbrood bee virus

The RNA of Chinese Sacbrood Bee Virus (CSBV) was purified and used as template to obtain a 1096 bp cDNA fragment by RT-PCR amplification. This DNA fragment was cloned into pGEM-T Easy Vector for sequencing. Analyses of the sequenced CSBV RNA fragment revealed a nucleotide sequence homology of 87.6% and a deduced amino-acid sequence homology of 94.6% with that of the Sacbrood Virus (SBV), indicating that CSBV is a different but highly homologous virus of SBV. The three-dimensional (3D) structure of CSBV was determined at 2.5 nm resolution by using electron cryo-microscopy (cryoEM) and computer reconstruction methods. The 3-D structure showed that the capsid has aT = 1 (orP = 3) icosahedral capsid shell with a smooth surface. There were 12 pentons at its icosahedral vertices (5-fold axes) and 132 holes penetrating the shell. The 3-D structure also revealed densities corresponding to the CSBV genome, suggesting icosahedrally-ordered RNA organization, a novel feature not previously reported for any picornaviruses.     

Post-imaging fiducial markers aid in the orientation determination of complexes with mixed or unknown symmetry

During the entry process many icosahedral viruses must adopt a lower-order symmetry or incur a symmetry mismatch to release their genome through a single site. A membrane model system in which poliovirus was bound to receptor-decorated liposomes was used to pioneer techniques that studied the break in the symmetry of the initial attachment complex by cryo-electron microscopy. Novel methods involving a fiducial marker for the membrane contact point were developed to objectively determine the symmetry of this complex and provide a starting model to initiate a bootstrap orientation refinement. Here we analyze how errors in the subjective assignment of this position affect the determination of symmetry, and the accuracy of calculating Euler angles for each raw image. In this study we have optimized the method and applied it to study the membrane-attachment complex of Semliki Forest virus (SFV), a model system for enveloped virus fusion. The resulting reconstruction of the SFV-membrane complex with a fiducial provides the first experimental evidence that this pre-fusion cell entry intermediate approaches the membrane along the viral 5-fold axis. The analysis reported here, and its subsequent application to enveloped virus fusion, indicate that this is a robust tool for solving the structures of mixed-symmetry complexes.     

A Deep Learning-based correction to EPID dosimetry for attenuation and scatter in the Unity MR-Linac system

PurposeEPID dosimetry in the Unity MR-Linac system allows for reconstruction of absolute dose distributions within the patient geometry. Dose reconstruction is accurate for the parts of the beam arriving at the EPID through the MRI central unattenuated region, free of gradient coils, resulting in a maximum field size of ~10 × 22 cm² at isocentre. The purpose of this study is to develop a Deep Learning-based method to improve the accuracy of 2D EPID reconstructed dose distributions outside this central region, accounting for the effects of the extra attenuation and scatter.MethodsA U-Net was trained to correct EPID dose images calculated at the isocenter inside a cylindrical phantom using the corresponding TPS dose images as ground truth for training. The model was evaluated using a 5-fold cross validation procedure. The clinical validity of the U-Net corrected dose images (the so-called DEEPID dose images) was assessed with in vivo verification data of 45 large rectum IMRT fields. The sensitivity of DEEPID to leaf bank position errors (±1.5 mm) and ±5% MU delivery errors was also tested.ResultsCompared to the TPS, in vivo 2D DEEPID dose images showed an average γ-pass rate of 90.2% (72.6%–99.4%) outside the central unattenuated region. Without DEEPID correction, this number was 44.5% (4.0%–78.4%). DEEPID correctly detected the introduced delivery errors.ConclusionsDEEPID allows for accurate dose reconstruction using the entire EPID image, thus enabling dosimetric verification for field sizes up to ~19 × 22 cm² at isocentre. The method can be used to detect clinically relevant errors.     

Molecular Packing in Virus Crystals: Geometry, Chemistry, and Biology

An automated procedure was developed to determine the geometrical and chemical interactions of crystalline virus particles using the crystal parameters, particle position, orientation, and atomic coordinates for an icosahedral asymmetric unit. Two applications of the program are reported: (1) An analysis of a novelpseudo-rhombohedral (R32) symmetry present in the monoclinic crystal lattices of both Nodamura Virus (NOV) and Coxsackie virus B3 (CVB3). The study shows that in both cases the interactions between particles is substantially increased by minor deviations from exact R32 symmetry and that only particles with the proper ratio of dimensions along twofold and fivefold symmetry axes (such as southern bean mosaic virus) can achieve comparable buried surface area in the true R32 space group. (2) An attempt was made to correlate biological function with remarkably conserved interparticle contact regions found in different crystal forms of three members of the nodavirus family, NOV, Flock House Virus (FHV), and Black Beetle Virus (BBV). Mutational evidence implicates the quasi-threefold region on the viral surface in receptor binding in nodaviruses and this region is dominant in particle contacts in all three virus crystals. Examination of particle contacts in numerous crystal structures of viruses in the picornavirus superfamily showed that portions of the capsid surface known to interact with a receptor or serve as an epitope for monoclonal antibodies frequently stabilize crystal contacts.