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

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

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.     

Difference imaging of adenovirus: bridging the resolution gap between X-ray crystallography and electron microscopy.

While X-ray crystallography provides atomic resolution structures of proteins and small viruses, electron microscopy provides complementary structural information on the organization of larger assemblies at lower resolution. A novel combination of these two techniques has bridged this resolution gap and revealed the various structural components forming the capsid of human type 2 adenovirus. An image reconstruction of the intact virus, derived from cryo-electron micrographs, was deconvolved with an approximate contrast transfer function to mitigate microscope distortions. A model capsid was calculated from 240 copies of the crystallographic structure of the major capsid protein and filtered to the correct resolution. Subtraction of the calculated capsid from the corrected reconstruction gave a three-dimensional difference map revealing the minor proteins that stabilize the virion. Elongated density penetrating the hexon capsid at the facet edges was ascribed to polypeptide IIIa, a component required for virion assembly. Density on the inner surface of the capsid, connecting the ring of peripentonal hexons, was assigned as polypeptide VI, a component that binds DNA. Identification of the regions of hexon that contact the penton base suggests a structural mechanism for previously proposed events during cell entry.     

A Strategy for Electron Tomographic Data Collection and Crystallographic Reconstruction of Biological Bundles

Structures of highly ordered biological bundles have unique features which call for special experimental and computational methods in electron cryomicroscopy. They can be considered as three-dimensional quasi-crystals and reconstructed using a crystallographic approach. However, they are neither “infinitely” large with respect to the borders of the bundle, nor are they a single unit cell in thickness along the viewing direction. Also, because of their shape, bundles do not generally have a preferred azimuthal orientation, which poses challenges for orientation estimation and refinement. We developed a strategy for recording and processing electron cryomicroscopic images that differs from classical two-dimensional crystalline reconstruction techniques. These developments allowed us to merge data from tomographic tilt series of ice-embedded acrosomal bundles. The goal is to determine accurately amplitudes and phases at the diffraction maxima in terms ofhklindices, and compute a three-dimensional map from the diffraction data.     

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.     

Structural studies of tropomyosin by cryoelectron microscopy and x-ray diffraction.

A comparison has been made between cryoelectron microscope images and the x-ray structure of one projection of the Bailey tropomyosin crystal. The computed transforms of the electron micrographs extend to a resolution of approximately 18 A compared with the reflections from x-ray crystallography which extend to 15 A. After correction of the images for lattice distortions and the contrast transfer function, the structure factors were constrained to the plane group (pmg) symmetry of this projection. Amplitude and phase data for five images were compared with the corresponding view from the three-dimensional x-ray diffraction data (Phillips, G.N., Jr., J.P. Fillers, and C. Cohen. 1986. J. Mol. Biol. 192: 111-131). The average R factor between the electron microscopy and x-ray amplitudes was 15%, with an amplitude-weighted mean phase difference of 4.8 degrees. The density maps derived from cryoelectron microscopy contain structural features similar to those from x-ray diffraction: these include the width and run of the filaments and their woven appearance at the crossover regions. Preliminary images obtained from frozen-hydrated tropomyosin/troponin cocrystals suggest that this approach may provide structural details not readily obtainable from x-ray diffraction studies.     

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.     

Three-dimensional structure of a single filament in the Limulus acrosomal bundle: scruin binds to homologous helix-loop-beta motifs in actin

Frozen, hydrated acrosomal bundles from Limulus sperm were imaged with a 400 kV electron cryomicroscope. Segments of this long bundle can be studied as a P1 crystal with a unit cell containing an acrosomal filament with 28 actin and 28 scruin molecules in 13 helical turns. A novel computational procedure was developed to extract single columns of superimposed acrosomal filaments from the distinctive crystallographic view. Helical reconstruction was used to generate a three-dimensional structure of this computationally isolated acrosomal filament. The scruin molecule is organized into two domains which contact two actin subunits in different strands of the same actin filament. A correlation of Holmes' actin filament model to the density in our acrosomal filament map shows that actin subdomains 1, 2, and 3 match the model density closely. However, actin subdomain 4 matches rather poorly, suggesting that interactions with scruin may have altered actin conformation. Scruin makes extensive interactions with helix-loop-beta motifs in subdomain 3 of one actin subunit and in subdomain 1 of a consecutive actin subunit along the genetic filament helix. These two actin subdomains are structurally homologous and are closely spaced along the actin filament. Our model suggests that scruin, which is derived from a tandemly duplicated gene, has evolved to bind structurally homologous but non-identical positions across two consecutive actin subunits.     

Cross-correlation and merging of crystallographic reflections derived from cryoelectron micrographs of 3D crystals: application to the Limulus acrosomal bundle

A method is described for merging in reciprocal space of electron microscopic data from three-dimensional crystals of the acrosomal bundle. Permutation of indices was required to find the proper alignment of data from different bundles. The method utilizes a statistical evaluation of the significance of the cross-correlation results to indicate the proper order for merging. The three-dimensional (3D) merging is a reference-free operation that does not depend on choosing a "zero-tilt" user-defined starting point. Results from the merging are given and the merged 3D data to 9.5A resolution is evaluated for coherence. General issues such as statistical significance of cross-correlation function peaks, symmetry evaluation, and phase coherence as a function of amplitude are discussed.     

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.     

Three-dimensional structure of the truncated core of the Saccharomyces cerevisiae pyruvate dehydrogenase complex determined from negative stain and cryoelectron microscopy images.

Dihydrolipoamide acyltransferase (E2), a catalytic and structural component of the three functional classes of multienzyme complexes that catalyze the oxidative decarboxylation of alpha-keto acids, forms the central core to which the other components are attached. We have imaged by negative stain and cryoelectron microscopy the truncated dihydrolipoamide acetyltransferase core (60 subunits; M(r) = 2.7 x 10(6)) of the Saccharomyces cerevisiae pyruvate dehydrogenase complex. Using icosahedral particle reconstruction techniques, we determined its structure to 25 A resolution. Although the model derived from the negative stain reconstruction was approximately 20% smaller than the model derived from the frozen-hydrated data, when corrected for the effects of the electron microscope contrast transfer functions, the reconstructions showed excellent correspondence. The pentagonal dodecahedron-shaped macromolecule has a maximum diameter, as measured along the 3-fold axis, of approximately 226 A (frozen-hydrated value), and 12 large openings (approximately 63 A in diameter) on the 5-fold axes that lead into a large solvent-accessible cavity (approximately 76-140 A diameter). The 20 vertices consist of cone-shaped trimers, each with a flattened base on the outside of the structure and an apex directed toward the center. The trimers are interconnected by 20 A thick "bridges" on the 2-fold axes. These studies also show that the highest resolution features apparent in the frozen-hydrated reconstruction are revealed in a filtered reconstruction of the stained molecule.     

Three-Dimensional Reconstruction with Contrast Transfer Function Correction from Energy-Filtered Cryoelectron Micrographs: Procedure and Application to the 70SEscherichia coliRibosome

Cryoelectron microscopy provides the means of studying macromolecules in their native state. However, the contrast transfer function (CTF) makes the images and the three-dimensional (3D) maps derived from them difficult to interpret. We developed methods to determine the CTF from experimental data and to obtain a CTF-corrected 3D reconstruction. The CTF correction and 3D reconstruction accomplished in one step make it easy to combine different defocus data sets and decrease the error accumulation in the computation. These methods were applied to energy-filtered images of the 70SEscherichia coliribosome, resulting in a distortion-free 3D map of the ribosome at 1/24.5 Å⁻¹resolution, as determined by the differential phase residual resolution criterion.     

染色体三维结构重建方法研究

染色体三维结构重构问题是近年生物领域中基因组学的热点研究问题,是以二维交互频率数据为基础来预测其三维空间结构。最新相关实验表明染色质的三维空间结构对于基因表达、调控等方面都具有重要意义。而Hi-c数据能利用染色质交互信息形成二维接触矩阵重构出染色体三维结构。本综述以染色体三维结构重建方法为研究对象,通过对染色体三维结构重建方法进行比较分析,综述了目前基于Hi-c数据在染色体三维结构重建中的经典方法,系统介绍了染色体三维结构重建技术的发展脉络,以促进染色体三维结构重建的进一步研究。     

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

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

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.     

Low-Resolution Density Maps from Atomic Models: How Stepping “Back” Can Be a Step “Forward”

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

Three-dimensional velocity field reconstruction

The problem of inter-slice magnetic resonance (MR) image reconstruction is encountered often in medical imaging applications, in such scenarios, there is a need to approximate information not captured in contiguously acquired MR images due to hardware sampling limitations. In the context of velocity field reconstruction, these data are required for visualization and computational analyses of flow fields to be effective. To provide more complete velocity information, a method has been developed for the reconstruction of flow fields based on adaptive control grid interpolation (ACGI). In this study, data for reconstruction were acquired via MRJ from in vitro models of surgically corrected pediatric cardiac vasculatures. Reconstructed velocity fields showed strong qualitative agreement with those obtained via other acquisition techniques. Quantitatively reconstruction was shown to produce data of comparable quality to accepted velocity data acquisition methods. Results indicate that ACGI-based velocity field reconstruction is capable of producing information suitable for a variety of applications demanding three-dimensional in vivo velocity data.     

The relative merits of direct morphometry of reconstructions of whole cells, and statistical morphometry by stereology of random sections of cells.

Stereology, or the derivation of quantitative, three-dimensional (3-D) data about cells by statistical analysis of the structures of random sections, is widely used in cytology and pathology. However, there are situations where this approach is inadequate, and only an analysis of a homogeneous population of whole cells will give the required results. This involved 3-D reconstruction from physical or optical sections, or tomography or photogrammetry of whole-cell mounts. Use of stereo views of individual sections or projections adds considerably to the information available for both contouring and reconstruction. Recent image-processing advances in clinical radiography have shown, for the first time, that rapid, high-resolution digitization and contrast enhancement enable nearly all structural details to be routinely extracted from the micrographs and adequately portrayed. Three-D whole-cell reconstructions provide the digital data for many kinds of morphometric measurements on both whole cells and their individual organelles and membranes. Rapid fixation or freezing allows improved quantitative structure/function correlations of organelles with disturbances in cell metabolism or gene expression.     

The relative merits of direct morphometry of reconstructions of whole cells,and statistical morphometry by stereology of random sections of cells

Stereology, or the derivation of quantitative, three-dimensional (3-D) data about cells by statistical analysis of the structures of random sections, is widely used in cytology and pathology. However, there are situations where this approach is inadequate, and only an analysis of a homogeneous population of whole cells will give the required results. This involved 3-D reconstruction from physical or optical sections, or tomography or photogrammetry of whole-cell mounts. Use of stereo views of individual sections or projections adds considerably to the information available for both contouring and reconstruction. Recent image-processing advances in clinical radiography have shown, for the first time, that rapid, high-resolution digitization and contrast enhancement enable nearly all structural details to be routinely extracted from the micrographs and adequately portrayed. Three-D whole-cell reconstructions provide the digital data for many kinds of morphometric measurements on both whole cells and their individual organelles and membranes. Rapid fixation or freezing allows improved quantitative structure/function correlations of organelles with disturbances in cell metabolism or gene expression.     

Projected structure of unstained, frozen-hydrated T-layer of Bacillus brevis.

This paper presents the projected structure of the T-layer of Bacillus brevis, obtained from electron microscopic studies of the unstained protein layer in the frozen-hydrated state. Computer image processing is used to correct for the effects of the contrast transfer function, and to increase the signal-to-noise ratio by lattice averaging. The results obtained show a good agreement with those previously obtained using negatively stained specimens. It is shown that the contrast of T-layer embedded in ice can be approximated to pure phase contrast.