Affine extensions of the icosahedral group with applications to the three-dimensional organisation of simple viruses

Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognised that icosahedral symmetry is crucial for the structural organisation of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, information on their tertiary structures and the organisation of the viral genome within the capsid are inaccessible. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to describe those aspects of the three-dimensional structure of simple viruses. This approach complements Caspar-Klug theory and provides details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.      

In vivo virus structures: simultaneous classification, resolution enhancement, and noise reduction in whole-cell electron tomography

Hutchinson-Gilford progeria syndrome (HGPS) is a premature aging syndrome caused by the expression and accumulation of a mutant form of lamin A, Δ50 lamin A. As a component of the cell's nucleoskeleton, lamin A plays an important role in the mechanical stabilization of the nuclear envelope and in other nuclear functions. It is largely unknown how the characteristic 50 amino acid deletion affects the conformation of the mostly intrinsically disordered tail domain of lamin A. Here we perform replica exchange molecular dynamics simulations of the tail domain and determine an ensemble of semi-stable structures. Based on these structures we show that the ZMPSTE 24 cleavage site on the precursor form of the lamin A tail domain orients itself in such a way as to facilitate cleavage during the maturation process. We confirm our simulated structures by comparing the thermodynamic properties of the ensemble structures to in vitro stability measurements. Using this combination of experimental and computational techniques, we compare the size, heterogeneity of size, thermodynamic stability of the Ig-fold, as well as the mechanisms of force-induced denaturation. Our data shows that the Δ50 lamin A tail domain is more compact and displays less heterogeneity than the mature lamin A tail domain. Altogether these results suggest that the altered structure and stability of the tail domain can explain changed protein-protein and protein-DNA interactions and may represent an etiology of the disease. Also, this study provides the first molecular structure(s) of the lamin A tail domain, which is confirmed by thermodynamic tests in experiment.     

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.     

Three-dimensional reconstruction of bovine brain V-ATPase by cryo-electron microscopy and single particle analysis

Bovine V-ATPase from brain clathrin-coated vesicles was investigated by cryo-electron microscopy and single particle analysis. Our studies revealed great flexibility of the central linker region connecting V₁ and V₀. As a consequence, the two sub-complexes were processed separately and the resulting volumes were merged computationally. We present the first three-dimensional (3D) map of a V-ATPase obtained from cryo-electron micrographs. The overall resolution was estimated 34 Å by Fourier shell correlation (0.5 cutoff). Our 3D reconstruction shows a large peripheral stalk and a smaller, isolated peripheral density, suggesting a second, less well-resolved peripheral connection. The 3D map reveals new features of the large peripheral stator and of the collar-like density attached to the membrane domain. Our analyses of the membrane domain indicate the presence of six proteolipid subunits. In addition, we could localize the V₀ subunit a flanking the large peripheral stalk.     

Automated three-dimensional reconstruction of keyhole limpet hemocyanin type 1

We have reconstructed a three-dimensional map of keyhole limpet hemocyanin isoform 1 (KLH1), using our automated data collection software, Leginon, integrated with particle selection algorithms, and the SPIDER reconstruction package. KLH1, a 7.9 MDa macromolecule, is an extracellular respiratory pigment composed of two asymmetric decamers, and presents an overall D(5) point-group symmetry. The reconstruction is in agreement with previous data published on molluscan hemocyanins. The reconstructed map (11.3A resolution, 3sigma criterion) was used to fit an available X-ray crystallography structure of Octopus dofleini Odg, solved at 2.3A [J. Mol. Biol. 278 (4) (1998) 855], with satisfactory results. The results validate the approach of automating the cryoEM process and demonstrate that the quality of the images acquired and the particles selected is comparable to those obtained using manual methods. Several problems remain to be solved however before these results can be generalized.     

Symmetry embedding in the reconstruction of macromolecular assemblies via the discrete Radon transform

In this paper we discuss the embedding of symmetry information in an algorithm for three-dimensional reconstruction, which is based on the discrete Radon transform. The original algorithm was designed for randomly oriented and in principal asymmetric particles. The expanded version presented here covers all symmetry point groups which can be exhibited by macromolecular protein assemblies. The orientations of all symmetry equivalent projections, based on the orientation of an experimental projection, are obtained using global group operators. Further, an improved interpolation scheme for the recovery of the three-dimensional discrete Radon transform has been designed for greater computational efficiency. The algorithm has been tested on phantom structures as well as on real data, a virus structure possessing icosahedral symmetry.     

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.     

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.     

Cryoelectron microscopy reveals new features in the three-dimensional structure of phosphorylase kinase

Phosphorylase kinase (PhK), a regulatory enzyme in the cascade activation of glycogenolysis, is a 1.3-MDa hexadecameric complex, (alphabetagammadelta)(4). PhK comprises two arched octameric (alphabetagammadelta)(2) lobes that are oriented back-to-back with overall D(2) symmetry and connected by small bridges. These interlobal bridges, arguably the most questionable structural component of PhK, are one of several structural features that potentially are artifactually generated or altered by conventional sample preparation techniques for electron microscopy (EM). To minimize such artifacts, we have solved by cryoEM the first three-dimensional (3D) structure of nonactivated PhK from images of frozen hydrated molecules of the kinase. Minimal dose electron micrographs of PhK in vitreous ice revealed particles in a multitude of orientations. A simple model was used to orient the individual images for 3D reconstruction, followed by multiple rounds of refinement. Three-dimensional reconstruction of nonactivated PhK from approximately 5000 particles revealed a bridged, bilobal molecule with a resolution estimated by Fourier shell correlation analysis at 25 A. This new structure suggests that several prominent features observed in the structure of PhK derived from negatively stained particles arise as artifacts of specimen preparation. In comparison to the structure from negative staining, the cryoEM structure shows three important differences: (1) a dihedral angle between the two lobes of approximately 90 degrees instead of 68 degrees, (2) a compact rather than extended structure for the lobes, and (3) the presence of four, rather than two, connecting bridges, which provides the first direct evidence for these components as authentic elements of the kinase solution structure.     

Automation of random conical tilt and orthogonal tilt data collection using feature-based correlation

Visualization by electron microscopy has provided many insights into the composition, quaternary structure, and mechanism of macromolecular assemblies. By preserving samples in stain or vitreous ice it is possible to image them as discrete particles, and from these images generate three-dimensional structures. This ‘single-particle’ approach suffers from two major shortcomings; it requires an initial model to reconstitute 2D data into a 3D volume, and it often fails when faced with conformational variability. Random conical tilt (RCT) and orthogonal tilt (OTR) are methods developed to overcome these problems, but the data collection required, particularly for vitreous ice specimens, is difficult and tedious. In this paper, we present an automated approach to RCT/OTR data collection that removes the burden of manual collection and offers higher quality and throughput than is otherwise possible. We show example datasets collected under stain and cryo conditions and provide statistics related to the efficiency and robustness of the process. Furthermore, we describe the new algorithms that make this method possible, which include new calibrations, improved targeting and feature-based tracking.     

A strategy for determining the orientations of refractory particles for reconstruction from cryo-electron micrographs with particular reference to round, smooth-surfaced, icosahedral viruses

Cryo-electron microscopy and three-dimensional image reconstruction are powerful tools for analyzing icosahedral virus capsids at resolutions that now extend below 1 nm. However, the validity of such density maps depends critically on correct identification of the viewing geometry of each particle in the data set. In some cases-for example, round capsids with low surface relief-it is difficult to identify orientations by conventional application of the two most widely used approaches-"common lines" and model-based iterative refinement. We describe here a strategy for determining the orientations of such refractory specimens. The key step is to determine reliable orientations for a base set of particles. For each particle, a list of candidate orientations is generated by common lines: correct orientations are then identified by computing a single-particle reconstruction for each candidate and then systematically matching their reprojections with the original images by visual criteria and cross-correlation analysis. This base set yields a first-generation reconstruction that is fed into the model-based procedure. This strategy has led to the structural determination of two viruses that, in our hands, resisted solution by other means.     

The orthogonal tilt reconstruction method: an approach to generating single-class volumes with no missing cone for ab initio reconstruction of asymmetric particles

Generating reliable initial models is a critical step in the reconstruction of asymmetric single-particles by 3D electron microscopy. This is particularly difficult to do if heterogeneity is present in the sample. The Random Conical Tilt (RCT) method, arguably the most robust presently to accomplish this task, requires significant user intervention to solve the "missing cone" problem. We present here a novel approach, termed the orthogonal tilt reconstruction method, that eliminates the missing cone altogether, making it possible for single-class volumes to be used directly as initial references in refinement without further processing. The method involves collecting data at +45 degrees and -45 degrees tilts and only requires that particles adopt a relatively large number of orientations on the grid. One tilted data set is used for alignment and classification and the other set--which provides views orthogonal to those in the first--is used for reconstruction, resulting in the absence of a missing cone. We have tested this method with synthetic data and compared its performance to that of the RCT method. We also propose a way of increasing the level of homogeneity in individual 2D classes (and volumes) in a heterogeneous data set and identifying the most homogeneous volumes.     

玉米冠层的数学描述与三维重建研究

采用Lang提出的原理开发了空间坐标仪。利用该仪器测定玉米冠层的空间坐标,以此提出了应用一般二次方程描述玉米叶曲线和叶形的数学方法,方程的系数由最小二乘回归方法得到,其中叶曲线系数由叶片主脉坐标决定,叶形系数由沿叶长方向叶宽测定值决定。从而使应用较少参数描述真实的玉米群体结构成为可能。另外,还实现了玉米冠层的计算机三维重建,为农业生态系统研究提供了新的手段。     

Fluorescence correlation spectroscopy as a sensitive and useful tool for revealing potential overlaps between the epitopes of monoclonal antibodies on viral particles

Although the enzyme-linked immunosorbent assay (ELISA) is well established for quantitating epitopes on inactivated virions used as vaccines, it is less suited for detecting potential overlaps between the epitopes recognized by different antibodies raised against the virions. We used fluorescent correlation spectroscopy (FCS) to detect the potential overlaps between 3 monoclonal antibodies (mAbs 4B7-1H8-2E10, 1E3-3G4, 4H8-3A12-2D3) selected for their ability to specifically recognize poliovirus type 3. Competition of the Alexa488-labeled mAbs with non-labeled mAbs revealed that mAbs 4B7-1H8-2E10 and 4H8-3A12-2D3 compete strongly for their binding sites on the virions, suggesting an important overlap of their epitopes. This was confirmed by the cryo-electron microscopy (cryo EM) structure of the poliovirus type 3 complexed with the corresponding antigen-binding fragments (Fabs) of the mAbs, which revealed that Fabs 4B7-1H8-2E10 and 4H8-3A12-2D3 epitopes share common amino acids. In contrast, a less efficient competition between mAb 1E3-3G4 and mAb 4H8-3A12-2D3 was observed by FCS, and there was no competition between mAbs 1E3-3G4 and 4B7-1H8-2E10. The Fab 1E3-3G4 epitope was found by cryoEM to be close to but distinct from the epitopes of both Fabs 4H8-3A12-2D3 and 4B7-1H8-2E10. Therefore, the FCS data additionally suggest that mAbs 4H8-3A12-2D3 and 4B7-1H8-2E10 bind in a different orientation to their epitopes, so that only the former sterically clashes with the mAb 1E3-3G4 bound to its epitope. Our results demonstrate that FCS can be a highly sensitive and useful tool for assessing the potential overlap of mAbs on viral particles.     

Maurer's cleft organization in the cytoplasm of plasmodium falciparum-infected erythrocytes: new insights from three-dimensional reconstruction of serial ultrathin sections

Maurer's clefts are single-membrane-limited structures in the cytoplasm of erythrocytes infected with the human malarial parasite Plasmodium falciparum. The currently accepted model suggests that Maurer's clefts act as an intermediate compartment in protein transport processes from the parasite across the cytoplasm of the host cell to the erythrocyte surface, by receiving and delivering protein cargo packed in vesicles. This model is mainly based on two observations. Firstly, single-section electron micrographs have shown, within the cytoplasm of infected erythrocytes, stacks of long slender membranes in close vicinity to round membrane profiles considered to be vesicles. Secondly, proteins that are transported from the parasite to the erythrocyte surface as well as proteins facilitating the budding of vesicles have been found in association with Maurer's clefts. Verification of this model would be greatly assisted by a better understanding of the morphology, dimensions and origin of the Maurer's clefts. Here, we have generated and analyzed three-dimensional reconstructions of serial ultrathin sections covering segments of P. falciparum-infected erythrocytes of more than 1 microm thickness. Our results indicate that Maurer's clefts are heterogeneous in structure and size. We have found Maurer's clefts consisting of a single disk-shaped cisternae localized beneath the plasma membrane. In other examples, Maurer' clefts formed an extended membranous network that bridged most of the distance between the parasite and the plasma membrane of the host erythrocyte. Maurer's cleft membrane networks were composed of both branched membrane tubules and stacked disk-shaped membrane cisternae that eventually formed whorls. Maurer's clefts were visible in other cells as a loose membrane reticulum composed of scattered tubular and disk-shaped membrane profiles. We have not seen clearly discernable isolated vesicles in the analyzed erythrocyte segments suggesting that the current view of how proteins are transported within the Plasmodium-infected erythrocyte may need reconsideration.     

Classification, assessment and trophic reconstruction of Danish lakes using chironomids

1. Surface-sediment assemblages of subfossil chironomid head capsules from fifty-four primarily shallow and nutrient-rich Danish lakes were analysed using multivariate numerical techniques. The species data, comprising forty-one chironomid taxa, were compared to environmental monitoring data in order to establish a relationship between chironomid faunal composition and lake trophic state.
2. The subfossil assemblages were compared to the chironomid bathymetric distributions along transects from four lakes. Correspondence analysis and similarity coefficients showed that the subfossil assemblages, sampled in the lake centre, reflect the chironomid communities in the littoral at a depth of 2–7 m.
3. Two-way indicator species analysis (TWINSPAN) was used to classify the Danish lakes into five groups defined by trophic state, lake depth and pH. Eighteen chironomid taxa showed significant differences in abundance among the five groups. Canonical correspondence analysis (CCA) showed the chlorophyll a concentration ([Chl a ]) and Secchi depth to be the variables best correlated to the faunal data, and fourteen taxa were significantly correlated to [Chl a ].
4. The strong correlation between chironomid data and the ln-transformed ([Chl a ]) was used to create a weighted averaging (WA) model to infer lake trophic state. Several models were tested by cross validation (leave-one-out jack-knifing), and a simple WA model using inverse de-shrinking had a RMSEP_jack of 0.65 (ln units) and a r ²_jack of 0.67.
5. The results can be used in the assessment and reconstruction of lake trophic state for long-term monitoring and palaeoecological investigations of shallow, temperate lakes in the mesotrophic to hypertrophic nutrient range.     

Ultrastructural characterization and three-dimensional reconstruction of isolated maize (Zea mays L.) egg cell protoplasts

Summary Isolated egg cell protoplasts ofZea mays L., inbred line A 188, have been studied at the transmission electron microscope level. Their preparation for electron microscopy has been performed by embedding in ultra-low gelling agarose as a preliminary step. Five isolated egg cell protoplasts were serially ultrathin sectioned and studied in detail. One of these protoplasts was reconstructed in three dimensions to provide additional information on its structure. After enzymatic digestion and microdissection, isolated egg cells are true, highly vacuolized protoplasts. The structure of their organelles agrees with in situ observations, indicating an ultrastructural intactness after isolation: the mitochondria are polymorphic, form reticulate networks, and have well developed cristae; the plastids contain starch grains; and the spherical nucleus is euchromatic. As in situ, the organelles of the isolated egg cell protoplasts are aggregated near the nucleus. The complete picture provided by this work should serve as a comparative base for studies on in vitro fertilization products.     

Classification and Reconstruction of a Heterogeneous Set of Electron Microscopic Images: A Case Study of GroEL–Substrate Complexes

Image analysis methods were used to separate images of a large macromolecular complex, the chaperonin GroEL, in a preparation in which it is partially liganded to a nonnative protein substrate, glutamine synthetase. The relatively small difference (6%) in size between the chaperonin in its free and complexed forms, and the absence of gross changes in overall conformation, made separation of the two types of particles challenging. Different approaches were evaluated and used for alignment and classification of images, both in two common projections and in three dimensions, yielding 2D averages and a 3D reconstruction. The results of 3D analysis describe the conformational changes effected by binding of this particular protein substrate and demonstrate the utility of 2D analysis as an indicator of structural change in this system.     

Helical reconstruction of Salmonella and Shigella needle filaments attached to type 3 basal bodies

Gram-negative pathogens evolved a syringe-like nanomachine, termed type 3 secretion system, to deliver protein effectors into the cytoplasm of host cells. An essential component of this system is a long helical needle filament that protrudes from the bacterial surface and connects the cytoplasms of the bacterium and the eukaryotic cell. Previous structural research was predominantly focused on reconstituted type 3 needle filaments, which lacked the biological context. In this work we introduce a facile procedure to obtain high-resolution cryo-EM structure of needle filaments attached to the basal body of type 3 secretion systems. We validate our approach by solving the structure of Salmonella PrgI filament and demonstrate its utility by obtaining the first high-resolution cryo-EM reconstruction of Shigella MxiH filament. Our work paves the way to systematic structural characterization of attached type 3 needle filaments in the context of mutagenesis studies, protein structural evolution and drug development.     

Electron microscopy and three-dimensional reconstruction of native thin filaments reveal species-specific differences in regulatory strand densities

Throughout the animal kingdom striated muscle contraction is regulated by the thin filament troponin-tropomyosin complex. Homologous regulatory components are shared among vertebrate and arthropod muscles; however, unique protein extensions and/or components characterize the latter. The Troponin T (TnT) isoforms of Drosophila indirect flight and tarantula femur muscle for example contain distinct C-terminal extensions and are ∼20% larger overall than their vertebrate counterpart. Using electron microscopy and three-dimensional helical reconstruction of native Drosophila, tarantula and frog muscle thin filaments we have identified species-specific differences in tropomyosin regulatory strand densities. The strands on the arthropod thin filaments were significantly larger in diameter than those from vertebrates, although not significantly different from each other. These findings reflect differences in the regulatory troponin-tropomyosin complex, which are likely due to the larger TnT molecules aligning and extending along much of the tropomyosin strands’ length. Such an arrangement potentially alters the physical properties of the regulatory strands and may help establish contractile characteristics unique to certain arthropod muscles.