Compensation of Missing Wedge Effects with Sequential Statistical Reconstruction in Electron Tomography

Electron tomography (ET) of biological samples is used to study the organization and the structure of the whole cell and subcellular complexes in great detail. However, projections cannot be acquired over full tilt angle range with biological samples in electron microscopy. ET image reconstruction can be considered an ill-posed problem because of this missing information. This results in artifacts, seen as the loss of three-dimensional (3D) resolution in the reconstructed images. The goal of this study was to achieve isotropic resolution with a statistical reconstruction method, sequential maximum a posteriori expectation maximization (sMAP-EM), using no prior morphological knowledge about the specimen. The missing wedge effects on sMAP-EM were examined with a synthetic cell phantom to assess the effects of noise. An experimental dataset of a multivesicular body was evaluated with a number of gold particles. An ellipsoid fitting based method was developed to realize the quantitative measures elongation and contrast in an automated, objective, and reliable way. The method statistically evaluates the sub-volumes containing gold particles randomly located in various parts of the whole volume, thus giving information about the robustness of the volume reconstruction. The quantitative results were also compared with reconstructions made with widely-used weighted backprojection and simultaneous iterative reconstruction technique methods. The results showed that the proposed sMAP-EM method significantly suppresses the effects of the missing information producing isotropic resolution. Furthermore, this method improves the contrast ratio, enhancing the applicability of further automatic and semi-automatic analysis. These improvements in ET reconstruction by sMAP-EM enable analysis of subcellular structures with higher three-dimensional resolution and contrast than conventional methods.     

Single particle macromolecular structure determination via electron microscopy

Three-dimensional structure determination of macromolecules and macromolecular complexes is an integral part of understanding biological functions. For large protein and macromolecular complexes structure determination is often performed using electron cryomicroscopy where projection images of individual macromolecular complexes are combined to produce a three-dimensional reconstruction. Single particle methods have been devised to perform this structure determination for macromolecular complexes with little or no underlying symmetry. These computational methods generally involve an iterative process of aligning unique views of the macromolecular images followed by determination of the angular components that define those views. In this review, this structure determination process is described with the aim of clarifying a seemingly complex structural method.     

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.     

Electron tomography of amplified nanogold immunolabelling: Improvement of quality based on alignment of projections with sinograms and use of post-reconstruction deconvolution

Electron tomography of immunolabelled proteins identified with amplified nanogold particles imaged by Scanning and Transmission Electron Microscopy within thick sections is a powerful method to investigate the three-dimensional organization of complex cellular machineries. In order to increase the overall quality of the reconstructed cube, we have developed two methods that improve the tomographic reconstruction process. We first performed a very precise alignment of the projections before reconstruction with a technique using sinograms. After reconstruction, we propose to compute image restoration by calculating the Point Spread Function of the projection/back-projection system and to use it to deblur the reconstructed cubes. Improvement in the quality of the reconstructed cubes is demonstrated on images of nucleolar proteins tagged with EGFP and immunolabelled with nanogold particles.     

Finite element simulation of skeletal muscular structures obtained from images of histological serial sections

In this study, we present a method for the three-dimensional reconstruction of objects obtained from histological serial sections (exemplified by those of a pennate striated skeletal muscle) and its application to the finite element method. A hyperelastic material model is used for modeling biological soft tissue. The reconstruction process relies on the direct construction of a volumetric mesh using an octree approach which leads to a stable finite element method. Stability can be expressed in the spectral matrix condition number. To visualize stress patterns within the underlying anatomy the simulation results are projected onto images of the histological scenario.     

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.     

冷冻电镜单颗粒三维重构密度掩模的自动生成方法研究

冷冻电镜单颗粒三维重构技术是用来解析生物大分子三维结构的常用方法.然而目前在单颗粒三维重构过程中,溶剂平滑操作还存在一定缺陷:没有一款主流的单颗粒三维重构程序能够自动寻找掩模(mask)三维密度图,使得三维重构过程难免受到噪音统计学模型计算偏差的干扰.为解决这一问题,本研究借鉴X射线晶体学中解析优化相位所广泛采用的溶剂平滑方法,采用高斯滤波、坎尼边缘检测、最小误差阈值处理等方法处理重构所得三维密度图,优化溶剂平滑操作,发展在单颗粒三维重构过程中自动寻找mask三维密度图的方法.运用三维密度图傅里叶壳层相关系数(fourier shell correlation,FSC)曲线图、模拟颗粒数据重构角度误差散点图等指标评估此方法的效果.结果表明,自动寻找mask密度图的方法能够较好地找到涵盖分子结构信号区域的mask密度图,较为明显提高三维重构所得密度图分辨率.     

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。     

The "third" dimension in craniofacial surgery

A new method for reconstruction of a three-dimensional surface from a sequence of high-resolution axial CT scans has been developed. This algorithm is realized as a set of computer programs that can operate on commercially available CT scanners or evaluation consoles. The program is both efficient and easy to implement. No operator intervention is required. The images produced simulate photographs of the skull. Frontal, lateral, oblique, bird's eye, worm's eye, and rear views are generated. As with photographs and conventional radiographs, each of these projections uniquely displays specific anatomic details. This method of osseous surface reconstruction is now routinely applied to all patients evaluated for major craniofacial reconstruction at our institution. The images are useful in defining aberrant anatomy, planning surgical procedures, and evaluating the results of such operations. This method replaces an inexact concept in the surgeon's imagination with a three-dimensional image of the craniofacial skeleton.     

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.     

Three-dimensional computed tomography of the mummy Wenuhotep

Computed tomography allows cross-sectional imaging of anthropological as well as clinical subjects. Recently, technical innovations have made three-dimensional reconstruction of these images feasible. We performed two-dimensional and three-dimensional computed tomography of a Late Period Egyptian mummy to reexamine findings seen on previous radiographic studies and to evaluate the usefulness of these techniques in paleopathology. Two-dimensional images provided excellent anatomic detail. There was graphic depiction of the mummification process that corroborated information previously obtained from Egyptological studies. Three-dimensional reconstruction provided images of facial features as if the mummy had been unwrapped. Three-dimensional computed tomography is a useful method of nondestructively evaluating paleopathological remains, and it may yield information not obtainable by any other means.     

Volume interpolation of CT images from tree trunks

Computerized tomography as a non-destructive scanning method to analyze wood structures has become an important technique in tree research. The possibility to reconstruct three-dimensional volumes based on a number of slices of two-dimensional data from CT scans is strongly dependent on the number of measured slices. Radial basis function methods can be successfully used to interpolate CT images with the aim of obtaining a satisfactory reconstruction of tree trunks. In contrast to standard interpolation techniques, our method takes into account that wood structures differ more in the radial than in the longitudinal direction. Therefore we obtain better interpolation results for wood structures.     

Ab initio random model method facilitates 3D reconstruction of icosahedral particles

Model-based, three-dimensional (3D) image reconstruction procedures require a starting model to initiate data analysis. We have designed an ab initio method, which we call the random model (RM) method, that automatically generates models to initiate structural analysis of icosahedral viruses imaged by cryo-electron microscopy. The robustness of the RM procedure was demonstrated on experimental sets of images for five representative viruses. The RM method also provides a straightforward way to generate unbiased starting models to derive independent 3D reconstructions and obtain a more reliable assessment of resolution. The fundamental scheme embodied in the RM method should be relatively easy to integrate into other icosahedral software packages.     

Helical structure of unidirectionally shadowed metal replicas of cyanide hydratase from Gloeocercospora sorghi

The helical filaments of the cyanide hydratase from Gloeocercospora sorghi have been reconstructed in three dimensions from freeze dried, unidirectionally shadowed specimens using iterative real-space helical reconstruction. The average power spectrum of all selected images has three clear reflections on different layer lines. The reconstruction is complicated by the fact that three possible indexing schemes are possible and reconstructions using the starting symmetries based on each of these indexing schemes converge on three-dimensional volumes which appear plausible. Because only one side is visible in shadowed specimens, it is necessary to examine the phases from a single filament by cryo-electron microscopy in order to make an unequivocal assignment of the symmetry. Because of the novel nature of the reconstruction method used here, conventional cryo-EM methods were also used to determine a second reconstruction, allowing us to make comparisons between the two. The filament is shown to have a left-handed one-start helix with D(1) symmetry, 5.46 dimers per turn and a pitch of 7.15nm. The reconstruction suggests the presence of an interaction across the groove not previously seen in nitrilase helical fibres.     

Scaling structure factor amplitudes in electron cryomicroscopy using X-Ray solution scattering

The structure factors derived from electron cryomicroscopic images are modified by the contrast transfer function of the microscope's objective lens and other influences. The phases of the structure factors can be corrected in a straightforward way when the positions of the contrast transfer function rings are determined. However, corrected amplitudes are also essential to yield an accurate distribution of mass in the reconstruction. The correct scale factors for the amplitudes are difficult to evaluate for data that are merged from many different micrographs. We opt to use X-ray solution scattering intensity from a concentrated suspension of the specimen to correct the amplitudes of the spherically averaged structure factors. When this approach is applied to the three-dimensional image data of ice-embedded acrosomal bundles, the core of a filament in a three-dimensional reconstruction of the acrosomal bundle becomes denser and matches more closely the outer density ascribed to scruin.     

Tracking of Ball and Players in Beach Volleyball Videos

This paper presents methods for the determination of players'' positions and contact time points by tracking the players and the ball in beach volleyball videos. Two player tracking methods are compared, a classical particle filter and a rigid grid integral histogram tracker. Due to mutual occlusion of the players and the camera perspective, results are best for the front players, with 74,6% and 82,6% of correctly tracked frames for the particle method and the integral histogram method, respectively. Results suggest an improved robustness against player confusion between different particle sets when tracking with a rigid grid approach. Faster processing and less player confusions make this method superior to the classical particle filter. Two different ball tracking methods are used that detect ball candidates from movement difference images using a background subtraction algorithm. Ball trajectories are estimated and interpolated from parabolic flight equations. The tracking accuracy of the ball is 54,2% for the trajectory growth method and 42,1% for the Hough line detection method. Tracking results of over 90% from the literature could not be confirmed. Ball contact frames were estimated from parabolic trajectory intersection, resulting in 48,9% of correctly estimated ball contact points.     

Electron Tomography of Large, Multicomponent Biological Structures

Electron tomography is an extremely useful method for deriving three-dimensional structure from electron microscope images. The application of this technique to the reconstruction of large, complex structures such as mitochondria is described in conjunction with several tools for segmentation, measurement, classification, and visualization. In addition, the use of massively parallel computers to perform the tomographic reconstruction efficiently using R-weighted backprojection or iterative techniques is described.     

A simple method for in vivo measurement of implant rod three-dimensional geometry during scoliosis surgery

Scoliosis is defined as a spinal pathology characterized as a three-dimensional deformity of the spine combined with vertebral rotation. Treatment for severe scoliosis is achieved when the scoliotic spine is surgically corrected and fixed using implanted rods and screws. Several studies performed biomechanical modeling and corrective forces measurements of scoliosis correction. These studies were able to predict the clinical outcome and measured the corrective forces acting on screws, however, they were not able to measure the intraoperative three-dimensional geometry of the spinal rod. In effect, the results of biomechanical modeling might not be so realistic and the corrective forces during the surgical correction procedure were intra-operatively difficult to measure. Projective geometry has been shown to be successful in the reconstruction of a three-dimensional structure using a series of images obtained from different views. In this study, we propose a new method to measure the three-dimensional geometry of an implant rod using two cameras. The reconstruction method requires only a few parameters, the included angle θ between the two cameras, the actual length of the rod in mm, and the location of points for curve fitting. The implant rod utilized in spine surgery was used to evaluate the accuracy of the current method. The three-dimensional geometry of the rod was measured from the image obtained by a scanner and compared to the proposed method using two cameras. The mean error in the reconstruction measurements ranged from 0.32 to 0.45 mm. The method presented here demonstrated the possibility of intra-operatively measuring the three-dimensional geometry of spinal rod. The proposed method could be used in surgical procedures to better understand the biomechanics of scoliosis correction through real-time measurement of three-dimensional implant rod geometry in vivo.     

Separating distinct structures of multiple macromolecular assemblies from cryo-EM projections

Single particle analysis for structure determination in cryo-electron microscopy is traditionally applied to samples purified to near homogeneity as current reconstruction algorithms are not designed to handle heterogeneous mixtures of structures from many distinct macromolecular complexes. We extend on long established methods and demonstrate that relating two-dimensional projection images by their common lines in a graphical framework is sufficient for partitioning distinct protein and multiprotein complexes within the same data set. The feasibility of this approach is first demonstrated on a large set of synthetic reprojections from 35 unique macromolecular structures spanning a mass range of hundreds to thousands of kilodaltons. We then apply our algorithm on cryo-EM data collected from a mixture of five protein complexes and use existing methods to solve multiple three-dimensional structures ab initio. Incorporating methods to sort single particle cryo-EM data from extremely heterogeneous mixtures will alleviate the need for stringent purification and pave the way toward investigation of samples containing many unique structures.     

Morphology and structure of lipoproteins revealed by an optimized negative-staining protocol of electron microscopy

Plasma lipoprotein levels are predictors of risk for coronary artery disease. Lipoprotein structure-function relationships provide important clues that help identify the role of lipoproteins in cardiovascular disease. The compositional and conformational heterogeneity of lipoproteins are major barriers to the identification of their structures, as discovered using traditional approaches. Although electron microscopy (EM) is an alternative approach, conventional negative staining (NS) produces rouleau artifacts. In a previous study of apolipoprotein (apo)E4-containing reconstituted HDL (rHDL) particles, we optimized the NS method in a way that eliminated rouleaux. Here we report that phosphotungstic acid at high buffer salt concentrations plays a key role in rouleau formation. We also validate our protocol for analyzing the major plasma lipoprotein classes HDL, LDL, IDL, and VLDL, as well as homogeneously prepared apoA-I-containing rHDL. High-contrast EM images revealed morphology and detailed structures of lipoproteins, especially apoA-I-containing rHDL, that are amenable to three-dimensional reconstruction by single-particle analysis and electron tomography.