Transmission electron microtomography without the "missing wedge" for quantitative structural analysis

A three-dimensional (3D) visualization and structural analysis of a rod-shaped specimen of a zirconia/polymer nanocomposite material were carried out by transmission electron microtomography (TEMT) with particular emphasis on complete rotation of the specimen (tilt angular range: +/-90 degrees ). In order to achieve such an ideal experimental condition for the TEMT, improvements in the specimen as well as the sample holder were made. A rod-shaped specimen was necessary in order to obtain a high transmission of the specimen upon tilting to large angles. The image resolution of the reconstructed tomogram was isotropic, in sharp contrast to the anisotropic image resolution of the conventional TEMT with a limited angular range (the "missing wedge" problem). A volume fraction of zirconia, phi, evaluated from the 3D reconstruction was in quantitative agreement with the known composition of the nanocomposite. A series of 3D reconstructions was made from the tilt series with complete rotation by limiting the maximum tilt angle, alpha, from which a couple of structural parameters, the volume fraction and surface area per unit volume, Sigma, of the zirconia, were evaluated as a function of alpha. It was confirmed from actual experimental data that both phi and Sigma slightly decreased with the increasing alpha and reached constant values at around alpha=80 degrees , suggesting that the specimen may have to be tilted to +/-80 degrees for truly quantitative measurements.     

Difference Fourier analysis of "surface features" of bacteriorhodopsin using glucose-embedded and frozen-hydrated purple membrane

A difference Fourier map of the projected structure of bacteriorhodopsin has been synthesized from electron diffraction amplitudes collected from membranes prepared in the glucose-embedded state and the frozen-hydrated state. Phases of a recently published data set for glucose-embedded specimens were used for the difference Fourier map. Moderate resolution (9 A) and high resolution (4.25 A) maps both indicate that glucose is exchangeable for water in the region of the map corresponding to the lipid regions. We interpret this as indicating that there is a small surface depression in this region of the structure. The depth of this feature is estimated to be 1/6 the thickness of the protein region in the membrane. The data obtained in this study rules out the existence of an aqueous transmembrane channel, the dimensions of which are large enough to allow free exchange of glucose for water. Several new features are also observed in the protein region of the membrane. These features are probably due to segments of the polypeptide at the aqueous interface that are well ordered in frozen-hydrated specimens but not in glucose-embedded specimens. Candidate structures for the origin of these features are extensions of the helices, or linker regions connecting the helices.     

High-precision tilt stage for the high-voltage electron microscope

The high-voltage electron microscope is used to study thick samples (0.25 to several micrometers) to obtain three-dimensional information at ultrastructural resolution. Three-dimensional image reconstructions are often employed to extract, process and display this information. The sets of images used to form reconstructions must be recorded for precisely known specimen-beam orientations, especially if tomographic methods are employed. The design and operation of a precision (+/- 0.06 degrees) single-tilt stage to support this type of imaging is reported. All motions including two translations, height adjustment and tilting are accomplished via a single objective lens entry port. The specimen rod is supported on two rubber gaskets for vibration isolation, and motorized precision micrometers with encoder readouts for position monitoring drive the motions. The stage is stable to 0.6 nm for at least 16 s and is capable of tilt angles of +/- 70 degrees.     

Correction of high-resolution data for curvature of the Ewald sphere

At sufficiently high resolution, which depends on the wavelength of the electrons, the thickness of the sample exceeds the depth of field of the microscope. At this resolution, pairs of beams scattered at symmetric angles about the incident beam are no longer related by Friedel's law; that is, the Fourier coefficients that describe their amplitudes and phases are no longer complex conjugates of each other. Under these conditions, the Fourier coefficients extracted from the image are linear combinations of independent (as opposed to Friedel related) Fourier coefficients corresponding to the three-dimensional (3-D) structure. In order to regenerate the 3-D scattering density, the Fourier coefficients corresponding to the structure have to be recovered from the Fourier coefficients of each image. The requirement for different views of the structure in order to collect a full 3-D data set remains. Computer simulations are used to determine at what resolution, voltage and specimen thickness the extracted coefficients differ significantly from the Fourier coefficients needed for the 3-D structure. This paper presents the theory that describes this situation. It reminds us that the problem can be treated by considering the curvature of the Ewald sphere or equivalently by considering that different layers within the structure are imaged with different amounts of defocus. The paper presents several methods to extract the Fourier coefficients needed for a 3-D reconstruction. The simplest of the methods is to take images with different amounts of defocus. For helical structures, however, only one image is needed.     

Estimation of allowable errors for tilt parameter determination in protein electron crystallography

A three-dimensional reconstruction of a thin protein crystal requires an accurate assignment of amplitudes and phases in the three-dimensional reciprocal space. This assignment depends upon the tilt parameters which are experimentally determined. A theoretical estimate is made of the tolerable error in the determination of tilt parameters as a function of resolution and crystal thickness.     

Three-dimensional reconstruction from a single-exposure,random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli

We present a new reconstruction method that takes advantage of the fact that many biological macromolecular assemblies show a preferred orientation with respect to the plane of the specimen grid in the electron microscopic preparation. From one micrograph taken of such a specimen tilted by a large angle, a conical tilt series with random azimuthal angles can be extracted and used for a three-dimensional reconstruction. Our technique allows the determination of the molecular structure under low-dose conditions, which are not achievable with reconstruction methods that use conventional tilt series. The reconstruction method combines a number of existing image processing techniques with a newly developed weighted back-projection algorithm designed for three-dimensional reconstruction from projections taken with arbitrary projecting directions. The method is described as it was applied to the three-dimensional reconstruction of the structure of the 50S ribosomal subunit of Escherichia coli (E. coli).     

Three-dimensional reconstruction of imperfect two-dimensional crystals

An outline is given of the general methodology of 3D reconstruction on the basis of correlation averages of the 2D projections: this hybrid real space/Fourier space approach substantially alleviates one of the most serious limitations on obtaining high resolution 3D structures, namely crystal distortions. The paper discusses some of the technical problems involved, namely optimisation of tilt increments, a posteriori tilt angle determination, extraction of lattice line data from averaged unit cells, and stain/protein boundary determination. The approach is illustrated by application to a 2D crystal from a bacterial cell envelope.     

Reducing the missing wedge: High-resolution dual axis tomography of inorganic materials

Electron tomography is a powerful technique that can probe the three-dimensional (3-D) structure of materials. Recently, this technique has been successfully applied to inorganic materials using Z-contrast imaging in a scanning transmission electron microscope to image nanomaterials in 3-D with a resolution of 1 nm in all three spatial dimensions. However, an artifact intrinsic to this technique limits the amount of information obtainable from any object, namely the missing wedge. One way to circumvent this problem is to acquire data from two perpendicular tilt axes, a technique called "dual axis tomography." This paper presents the first dual axis data at high resolution for inorganic materials, and by studying a CdTe tetrapod sample, demonstrates the increase in information obtained using this technique.     

Transmembrane alpha-helices in the gap junction membrane channel: systematic search of packing models based on the pair potential function

Recent progress in the field of electron cryo-microscopy and image analysis has shown that there is an overwhelming need to interpret medium resolution (5 to 10 A) three-dimensional maps. Traditional methods of fitting amino acid residues into electron density using molecular modeling programs must be supplemented with further analysis. We have used a potential of mean force (PMF) method, derived from Boltzmann statistics in protein structure, to generate models for the packing of alpha-helices, using pairwise potentials between amino acid residues. The approach was tested using the three-dimensional map of a recombinant cardiac gap junction membrane channel provided by electron cryo-crystallography (Unger et al., 1997; 1999a, 1999b) which had a resolution of 7.5 A in the membrane plane and 21 A in the vertical direction. The dodecameric channel was formed by the end-to-end docking of two hexamers, each of which displayed 24 rods of density in the membrane interior, which was consistent with an alpha-helical conformation for the four transmembrane domains of each connexin subunit. Based on the three-dimensional map and the amino acid sequence for the 4 transmembrane domains determined by hydropathy analysis, we used the modeling utility SymServ (Macke et al., 1998) to build hexameric connexons with 24 transmembrane alpha-helices. Canonical alpha-helices were aligned to the axes of the rods of density and translated along the density so that the center of masses coincided. The PMF function was used to evaluate 162,000 conformations for each of the 24 possible alpha-helical packing models. Since the different packing models yielded different energy distributions, the pair potential function appears to be a promising tool for evaluating the packing of alpha-helices in membrane proteins. The analysis will be refined by energy calculations based on the expectations that the outer boundary of the channel will be formed by hydrophobic residues in contact with the lipids.     

一种时域平面扫描三维成像算法研究

提出了一种基于平面扫描模式下的三维成像时域算法。该算法在平面网格点上获取扫频幅相信息,经过相位补偿后变换到球面上,然后利用傅里叶逆变换将频域数据沿投影线转换为时域数据,对应球面的不同空间角度在投影线上作线性插值,最后通过二维角域积分获得目标的三维图像。仿真结果表明该算法聚焦效果良好。在微波暗室内构建了一套平面扫描三维成像系统,采用该算法处理后能获得高分辨率三维微波图像,成像的空间位置误差优于1 cm。     

Three-dimensional optical microscopy using tilted views

The resolution of an optical microscope is considerably less in the direction of the optical axis (z) than in the x–y plane. This is true of conventional or confocal microscopes. To alleviate this problem we used multiple tilted views to supply the ‘missing data’ and thus increase the resolution in z. A special tilting stage was constructed which allowed specimens to be rotated through large angles. The relative, translation, rotation and z-spacing between data sets were determined by a novel Wiener/phase cross-correlation function. Once brought to a common coordinate system the data sets can be combined by Fourier space techniques similar to those used in X-ray crystallography. We applied this technique to metaphase chromosomes from intact embryos of Drosophila melanogaster. As determined from significant intensity in the Fourier transform, the resolution of the final reconstruction was about 0?25 μm in x and y, and 0?4 μm in z.     

Assessment of resolution in biological electron crystallography.

The resolution of images or density maps produced by electron microscopy and electron crystallography can be objectively defined in terms of the spatial frequency of the highest resolution diffraction spot, or Fourier coefficient, included in the data processing. In practice, this objective definition of resolution is expected to be too optimistic if the amplitudes of the highest resolution structure factors are too weak, if the population of high resolution reflections is too sparse, or if the signal-to-noise ratio of the high resolution data is too low. Calculated examples are presented here which illustrate how the apparent resolution in images of a membrane protein, bacteriorhodopsin, can be reduced from a nominal value of 3.5 A by weak amplitudes, sparse data or high noise levels. These calculations provide concrete examples which can serve as a guide when estimating whether the objective definition of image resolution is likely to correspond to a practical, structurally useful estimate of image resolution.     

Three-dimensional reconstruction of a periodic specimen from a single view of an oblique section

Methods are described for producing a three-dimensional reconstruction from a single view of an oblique section through a two- or three-dimensional crystal. The image produced by the electron microscope corresponds to a projection through the thickness of the section, which smears out the details of the structure. This projection operation can be described mathematically by sets of linear projection equations or equivalently by convolution of the density in the unit cell with the section thickness. Solution of the projection equations or other methods of deconvolution reduces the smearing and gives a three-dimensional map of the density within the crystal superior to that obtained by direct inspection of the image. The degree of improvement attainable depends on the noise level in the image but computational experiments indicate that a factor of at least four should be achievable. The method, which is most powerful when the section thickness is small, has the advantage over conventional methods involving tilted that it is not affected by changes in section thickness on electron irradiation.     

Refinement procedure for the image alignment in high-resolution electron tomography

High-resolution electron tomography from a tilt series of transmission electron microscopy images requires an accurate image alignment procedure in order to maximise the resolution of the tomogram. This is the case in particular for ultra-high resolution where even very small misalignments between individual images can dramatically reduce the fidelity of the resultant reconstruction. A tomographic-reconstruction based and marker-free method is proposed, which uses an iterative optimisation of the tomogram resolution. The method utilises a search algorithm that maximises the contrast in tomogram sub-volumes. Unlike conventional cross-correlation analysis it provides the required correlation over a large tilt angle separation and guarantees a consistent alignment of images for the full range of object tilt angles. An assessment based on experimental reconstructions shows that the marker-free procedure is competitive to the reference of marker-based procedures at lower resolution and yields sub-pixel accuracy even for simulated high-resolution data.     

Fault detection and classification in automated assembly machines using machine vision

The geometry of rotary aircraft engine components is usually defined by thin mechanical elements and complex surfaces that are only achievable by 5-axis machining due to either limited access or the design itself. Such thin-walled characteristics make these components susceptible to vibrations while machining and usually require careful manipulation of the toolpath parameters to minimize cutting forces and vibration. Moreover, the tool suppliers’ approach leans towards the feature-build design of cutter geometry to increase the productivity and quality of a machined surface. Some examples of those recent improvements for rotary aircraft engine components are barrel-shaped tools that attempt to increase the contact radius on the tool-part interface to minimize step-over while conserving the scallop height to meet roughness tolerances. This research aims to fill a gap in the current literature by proposing a stability model for barrel-shaped tools. Stability contour maps make use of a mechanistic dynamic force model for barrel-shaped tools. The force model is also capable of including tool runout and orientation angles, tilt and lead, as named in most CAM software. By simulating dynamic forces on the time domain, a contour map is presented to address unstable vibrations. Since forced vibrations and surface location error (SLE) may also appear when milling aircraft parts, SLE and surface roughness are also determined. Finally, given the complexity and number of parameters, validation of the stability maps is performed through experimental chatter tests using a thin wall component.     

Analysis of density distribution for unsteady butane flow using three-dimensional digital speckle tomography

Transient and asymmetric density distributions have been investigated by three-dimensional digital speckle tomography. Multiple CCD images captured movements of speckles in three angles of view simultaneously because the flows were asymmetric and transient. The speckle movements between no flow and downward butane flow from a circular half opening have been calculated by a cross-correlation tracking method so that those distances can be transferred to deflection angles of laser rays for density gradients. The three-dimensional density fields have been reconstructed from the deflection angles by a real-time multiplicative algebraic reconstruction technique (MART).     

Theoretical analysis of the dynamic stiffness of conical hydrostatic thrust bearings under tilt,eccentricity and rotation

A theoretical study of the dynamic stiffness characteristics of capillary compensated annular recess conical hydrostatic thrust bearings under conditions of tilt, eccentricity and rotation is reported. The influences of aspect ratios, cone angles and resistance ratios on the dynamic stiffness are discussed.     

基于滤波对角化方法提升傅里叶变换质谱数据质量

傅里叶变换质谱仪能够达到很高的分辨率,在分子生物研究中得到广泛应用。数据处理方法,特别是底层信号的处理,对于提升数据质量至关重要。滤波对角化(filter diagonalization method,FDM)相比传统的快速傅里叶变换算法(fast Fourier transform method,FFT),能进一步提高图谱分辨率、降低信号强度测量误差。本工作通过仿真以及实际质谱数据分析,证明了相对FFT而言,FDM可将图谱的分辨率提高1个数量级左右,并且可以有效降低信号强度测量误差。另外,还研究了算法参数优化问题,为算法应用推广提供了参考。