Reprint of "Fiducial-less alignment of cryo-sections" [J. Struct. Biol. 159 (2007) 413-423

Cryo-electron tomography of vitreous sections is currently the most promising technique for visualizing arbitrary regions of eukaryotic cells or tissue at molecular resolution. Despite significant progress in the sample preparation techniques over the past few years, the three dimensional reconstruction using electron tomography is not as simple as in plunge frozen samples for various reasons, but mainly due to the effects of irradiation on the sections and the resulting poor alignment. Here, we present a new algorithm, which can provide a useful three-dimensional marker model after investigation of hundreds to thousands of observations calculated using local cross-correlation throughout the tilt series. The observations are chosen according to their coherence to a particular model and assigned to virtual markers. Through this type of measurement a merit figure can be calculated, precisely estimating the quality of the reconstruction. The merit figures of this alignment method are comparable to those obtained with plunge frozen samples using fiducial gold markers. An additional advantage of the algorithm is the implicit detection of areas in the sections that behave as rigid bodies and can thus be properly reconstructed.     

A procedure to deposit fiducial markers on vitreous cryo-sections for cellular tomography

We describe a novel approach for the accurate alignment of images in electron tomography of vitreous cryo-sections. Quantum dots, suspended in organic solvents at cryo-temperatures, are applied directly onto the sections and are subsequently used as fiducial markers to align the tilt series. Data collection can be performed from different regions of the vitreous sections, even when the sections touch the grid only at a few places. We present high-resolution tomograms of some organelles in cryo-sections of human skin cells using this method. The average error in image alignment was about 1nm and the resolution was estimated to be 5-7nm. Thus, the use of section-attached quantum dots as fiducial markers in electron tomography of vitreous cryo-sections facilitates high-resolution in situ 3D imaging of organelles and macromolecular complexes in their native hydrated state.     

Three-dimensional imaging of biological complexity

Over the past 5 years, thanks to advances in both instrumentation and computational speed, three-dimensional imaging techniques using the electron microscope have been greatly improved in two areas: electron tomography of cell organelles or cell sections and reconstruction of macromolecules from single particles. Ice embedment has brought a breakthrough in the degree of preservation of specimens under close-to-native conditions. The current challenge is to push the resolution of electron tomographic imaging to a point where macromolecular signatures can be recognized within the cellular context. We show first progress toward this goal by examples in two areas of application: the structure of the muscle triad junction and the architecture and fine structure of mitochondria. As techniques of cryo-microtomy are perfected, we hope to be able to apply tomography to high-pressure frozen sections of tissue.     

Tissue arrays as fiducial markers for section alignment in 3-D reconstruction technology

Combination of conventional histology and the three-dimensional spatial view of tissue structures offers new prospects for understanding and diagnosing nature and development of human diseases. The essential technical problem related to three-dimensional reconstruction in histopathology is represented by the correct alignment of serial sections. During the past years several methods have been proposed but failed to become popular because of their limits in terms of time consume and restricted applicability. We aimed to overcome this problem by applying the technology of Tissue Array, thus by positioning adequate fiducial markers from specific "donor" blocks into the "recipient" paraffin block of interest. Digitized pictures of serially cut sections were aligned according to the tissue markers embedded by Tissue Array, and then processed with specific softwares for three-dimensional reconstruction. Thirteen models, including fetal hearts, breast and thyroid carcinomas, were elaborated. We found the procedure to be easy, fast and reproducible. Moreover, by selectively embedding the fiducial markers according to specific angles, the Tissue Arrays can be exploited in order to establish the distance between sections. This original methodology of incorporating Tissue Arrays into paraffin blocks as fiducial markers for three-dimensional reconstruction has a potential impact on histology for research purposes and diagnostic applications.     

Marker-free image registration of electron tomography tilt-series

Background  

Tilt series are commonly used in electron tomography as a means of collecting three-dimensional information from two-dimensional projections. A common problem encountered is the projection alignment prior to 3D reconstruction. Current alignment techniques usually employ gold particles or image derived markers to correctly align the images. When these markers are not present, correlation between adjacent views is used to align them. However, sequential pairwise correlation is prone to bias and the resulting alignment is not always optimal.     

Automatic system for 3D reconstruction of the chick eye based on digital photographs

The geometry of anatomical specimens is very complex and accurate 3D reconstruction is important for morphological studies, finite element analysis (FEA) and rapid prototyping. Although magnetic resonance imaging, computed tomography and laser scanners can be used for reconstructing biological structures, the cost of the equipment is fairly high and specialised technicians are required to operate the equipment, making such approaches limiting in terms of accessibility. In this paper, a novel automatic system for 3D surface reconstruction of the chick eye from digital photographs of a serially sectioned specimen is presented as a potential cost-effective and practical alternative. The system is designed to allow for automatic detection of the external surface of the chick eye. Automatic alignment of the photographs is performed using a combination of coloured markers and an algorithm based on complex phase order likelihood that is robust to noise and illumination variations. Automatic segmentation of the external boundaries of the eye from the aligned photographs is performed using a novel level-set segmentation approach based on a complex phase order energy functional. The extracted boundaries are sampled to construct a 3D point cloud, and a combination of Delaunay triangulation and subdivision surfaces is employed to construct the final triangular mesh. Experimental results using digital photographs of the chick eye show that the proposed system is capable of producing accurate 3D reconstructions of the external surface of the eye. The 3D model geometry is similar to a real chick eye and could be used for morphological studies and FEA.     

On the ultrastructural organization of Trypanosoma cruzi using cryopreparation methods and electron tomography

The structural organization of Trypanosoma cruzi has been intensely investigated by different microscopy techniques. At the electron microscopy level, bi-dimensional analysis of thin sections of chemically fixed cells has been one of the most commonly used techniques, despite the known potential of generating artifacts during chemical fixation and the subsequent steps of sample preparation. In contrast, more sophisticated and elaborate techniques, such as cryofixation followed by freeze substitution that are known to preserve the samples in a more close-to-native state, have not been widely applied to T. cruzi. In addition, the 3D characterization of such cells has been carried out mostly using 3D reconstruction from serial sections, currently considered a low resolution technique when compared to electron tomography (ET). In this work, we re-visited the 3D ultrastructure of T. cruzi using a combination of two approaches: (1) analysis of both conventionally processed and cryofixed and freeze substituted cells and (2) 3D reconstruction of large volumes by serial electron tomography. The analysis of high-pressure frozen and freeze substituted parasites showed novel characteristics in a number of intracellular structures, both in their structure and content. Organelles generally showed a smooth and regular morphology in some cases presenting a characteristic electron dense content. Ribosomes and new microtubule sets showed an unexpected localization in the cell body. The improved preservation and imaging in 3D of T. cruzi cells using cryopreparation techniques has revealed some novel aspects of the ultrastructural organization of this parasite.     

A two-step alignment method for 3D computer-aided reconstruction based on fiducial markers and applied to mouse embryonic hearts.

An accurate three dimensional computer reconstruction of microscopic biological objects or distribution of molecules identified on serial sections must solve two major problems: 1) the alignment of sections using adequate extrinsic references (fiducial markers); 2) the impossibility of observing these references and the cellular or molecular structures in the microscope at the same magnification. To provide extrinsic references for objects embedded in soft media, we have modified and simplified the charcoal-paraffin method described by Langemeijer and Simons (1973). It consists of drilling three or four small holes into the paraffin block, sealing this block at the extremity of a glass holder and, from the other extremity of the holder attached to a rubber hose, aspirating a liquefied mixture of charcoal-paraffin to fill these cylindrical holes. An alignment procedure was developed using serial sections of mouse embryonic hearts with bromodeoxyuridine-labelled DNA synthesizing cells. From each fourth section, two sets of contours have been drawn and digitized: 1) at low magnification (about 40x), embryo body wall, heart, neural tube and extrinsic reference marks (black dots); 2) at higher magnification (240-300x): heart contours alone (without extrinsic references, but with individual labelled cells). Different operations of the computer-aided alignment, as well as checking of results by inverse alignment, are described in detail. This two-step alignment method offers a practical, efficient compromise between: a) purely subjective alignment based only on tissular landmarks interpreted by the operator; b) ideal perfect alignment based not only on adequate references, but on computerized correction of section deformation, as well.     

Automated Stitching of Microtubule Centerlines across Serial Electron Tomograms

Tracing microtubule centerlines in serial section electron tomography requires microtubules to be stitched across sections, that is lines from different sections need to be aligned, endpoints need to be matched at section boundaries to establish a correspondence between neighboring sections, and corresponding lines need to be connected across multiple sections. We present computational methods for these tasks: 1) An initial alignment is computed using a distance compatibility graph. 2) A fine alignment is then computed with a probabilistic variant of the iterative closest points algorithm, which we extended to handle the orientation of lines by introducing a periodic random variable to the probabilistic formulation. 3) Endpoint correspondence is established by formulating a matching problem in terms of a Markov random field and computing the best matching with belief propagation. Belief propagation is not generally guaranteed to converge to a minimum. We show how convergence can be achieved, nonetheless, with minimal manual input. In addition to stitching microtubule centerlines, the correspondence is also applied to transform and merge the electron tomograms. We applied the proposed methods to samples from the mitotic spindle in C. elegans, the meiotic spindle in X. laevis, and sub-pellicular microtubule arrays in T. brucei. The methods were able to stitch microtubules across section boundaries in good agreement with experts'' opinions for the spindle samples. Results, however, were not satisfactory for the microtubule arrays. For certain experiments, such as an analysis of the spindle, the proposed methods can replace manual expert tracing and thus enable the analysis of microtubules over long distances with reasonable manual effort.     

High resolution electron tomography and segmentation‐by‐modeling interpretation in Bsoft

Bsoft offers many tools for the processing of tomographic tilt series and the interpretation of tomograms. Since I introduced tomography into Bsoft almost two decades ago, the field has advanced significantly, requiring refinement of old algorithms and development of new ones. The current direct detectors allow us to collect data more efficiently and with better quality, progressing towards automation. The goal is then to also automate alignment of tilt series and reconstruction. I added an estimation of the specimen thickness as well as fiducialless alignment, to augment the existing fiducial‐based alignment. High‐resolution work requires correction for the contrast transfer function, in tomography complicated by the tilted specimen. For this, I developed a method to generate a power spectrum using the whole micrograph, compensating for tilting. This is followed by routine determination of the contrast transfer function, and correction for it during reconstruction. The next steps involve interpretation of the tomogram, either by subtomogram averaging where possible, or by segmentation and modeling otherwise. Such interpretation actually constitutes the main time‐consuming part of tomography and is less amenable to automation compared to the initial reconstruction.     

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.     

A model approach to assess diaphragmatic volume displacement

Diaphragmatic volume displacement (Vdi) is calculated from two models using measurements obtained from anteroposterior fluoroscopic images of supine anesthetized dogs. In model 1, diaphragmatic descent was treated as if it were a "piston in a cylinder." In contrast, model 2 incorporated thoracic configuration as well as inspiratory changes in rib cage diameter and diaphragm shape. In one dog, a computerized tomography reconstruction of Vdi was compared with Vdi calculated using the models. Vdi calculated from model 2 lay within 11% of the computerized tomographic value, whereas Vdi based on model 1 was 30% larger. In seven animals, radiopaque markers were sewn to the right costal diaphragm. Digitized fluoroscopic images were used to measure intermarker distance, an index of muscle shortening. For four tidal breaths per dog, in model 2 Vdi averaged 49 +/- 18% of tidal volume and was weakly correlated with costal diaphragm muscle shortening (R = 0.74). It is concluded that Vdi can be estimated from linear dimensions in the coronal plane, provided that inspiratory changes in rib cage diameter and diaphragmatic shape change are taken into account.     

Development and validation of a generic 3D model of the distal femur

The development and validation of a virtual generic 3D model of the distal femur using computer graphical methods is presented. The synthesis of the generic model requires the following steps: acquisition of bony 3D morphology using standard computed tomography (CT) imaging; alignment of 3D models reconstructed from CT images with a common coordinate system; computer graphical sectioning of the models; extraction of bone contours from the image sections; combining and averaging of extracted contours; and 3D reconstruction of the averaged contours. The generic models reconstructed from the averaged contours of six cadaver femora were validated by comparing their surface geometry on a point to point basis with that of the CT reconstructed reference models. The mean errors ranged from 0.99 to 2.5 mm and were in agreement with the qualitative assessment of the models.     

Multiphase method for automatic alignment of transmission electron microscope images using markers

In order to successfully perform the 3D reconstruction in electron tomography, transmission electron microscope images must be accurately aligned or registered. So far, the problem is solved by either manually showing the corresponding fiducial markers from the set of images or automatically using simple correlation between the images on several rotations and scales. The present solutions, however, share the problem of being inefficient and/or inaccurate. We therefore propose a method in which the registration is automated using conventional colloidal gold particles as reference markers between images. We approach the problem from the computer vision viewpoint; hence, the alignment problem is divided into several subproblems: (1) finding initial matches from successive images, (2) estimating the epipolar geometry between consecutive images, (3) finding and localizing the gold particles with subpixel accuracy in each image, (4) predicting the probable matching gold particles using the epipolar constraint and its uncertainty, (5) matching and tracking the gold beads through the tilt series, and (6) optimizing the transformation parameters for the whole image set. The results show not only the reliability of the suggested method but also a high level of accuracy in alignment, since practically all the visible gold markers can be used.     

Simultaneous alignment of dual-axis tilt series

We present a strategy for the alignment of dual-axis tomographic series, based on reference points and simultaneous alignment of both series. Each series is first aligned individually, an affine transformation is determined to bring the two series in a unique reference system, and all experimental coordinates are combined in a single system of equations. In case of severe shrinkage, a global and a local refinement of the orientation parameters are performed to correct all minors misalignments.The strategy is illustrated on tomographic experiments performed on sections from plastic-embedded biological samples. The efficiency in correcting the misalignment of gold particles and in improving the quality of the reconstruction is documented both visually and quantitatively.In our approach every region of the tomogram is associated with its own orientation parameters and can be eventually reconstructed with the preferred algorithm. This is convenient in the computation of 3D averages of equivalent structures. A simulation experiment is presented to show that the performances of this approach are superior to those of the method of rotation in direct space.     

A Rapid lmmunostaining Method for Frozen Sections

A simple and rapid one-step method for demonstrating immunohistochemical markers (leukocyte common antigen, cytokeratin, etc.) is described, which can help define the nature of poorly differentiated neoplasms for diagnosis using frozen section. Microwave irradiation was used to speed immunohistochemical analysis using “Enhanced Polymer One-step Staining” (EPOS) reagents on cryostat sections from a variety of pathologic samples. Reproducible results were obtained using EPOS reagents for leukocyte common antigen and cytokeratin. The overall procedure takes less than 10 min and can be completed during surgery.     

Development and validation of a generic 3D model of the distal femur

The development and validation of a virtual generic 3D model of the distal femur using computer graphical methods is presented. The synthesis of the generic model requires the following steps: acquisition of bony 3D morphology using standard computed tomography (CT) imaging; alignment of 3D models reconstructed from CT images with a common coordinate system; computer graphical sectioning of the models; extraction of bone contours from the image sections; combining and averaging of extracted contours; and 3D reconstruction of the averaged contours.

The generic models reconstructed from the averaged contours of six cadaver femora were validated by comparing their surface geometry on a point to point basis with that of the CT reconstructed reference models. The mean errors ranged from 0.99 to 2.5 mm and were in agreement with the qualitative assessment of the models.     

A microcomputer based system for three-dimensional reconstructions from tomographic or histologic sections

The reconstructions of three-dimensional (3-D) objects from serial two-dimensional (2-D) images can contribute to the understanding of many biologic structures, from organelles to organs and tissues. The 3-D reconstruction of sections can be divided into several major tasks: image acquisition, alignment of slices, internal object definition, object reconstruction and rotation of the completed image. A fast, versatile, interactive system was devised for the reconstruction of 3-D objects from serial 2-D images using a low-cost microcomputer, original programs and commercial software. The system allows reconstruction from any serial images, e.g., electron micrographs, histologic sections or computed tomograms. A photographic image or a microscopic field is acquired into the computer memory using a video digitizer. Slices are superimposed and aligned to each other using an operator-interactive program. A contour-(edge-) finding algorithm isolates an object of interest from the background image by "subtraction" of the image from an overlaid, slightly shifted identical image. Contours for each slice are input to a reconstruction procedure, which calculates the x, y and z coordinates of every point in a slice and the thickness and number of slices. It then calculates the illumination for every point using a given point source of light and an intensity-fading coefficient. Finally, the points are represented by cubes to provide dimension and reflective surfaces. A cube of appropriate shade and color represents in 2-D the equivalent of a 3-D object; this results in a very effective 3-D image. The reconstruction is rotated by recalculating the positions of every point defining the object and rebuilding the image.(ABSTRACT TRUNCATED AT 250 WORDS)     

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.     

Tilt-series and electron microscope alignment for the correction of the non-perpendicularity of beam and tilt-axis

In electron tomography the sample is tilted in the electron microscope and projections are recorded at different viewing angles. In the correct geometric setting, the tilt-axis of the object under scrutiny is perpendicular to the beam direction. However, we will demonstrate that this does not necessarily apply to all electron microscopes equipped with the default column alignment. The resulting effect is that a conical tilt is performed, which has to be considered in the reconstruction to avoid artifacts and to improve the resolution. A novel solution, with significantly improved convergence properties, will be introduced for calculating the three-dimensional marker model, which is necessary for the alignment of the tilt-series. Thereby, the angle between the beam direction and the tilt-axis is calculated, together with other geometrical distortions, like magnification and rotation changes, and incorporated in the reconstruction. Hereby, artifacts can be eliminated at the image processing basis, and the resolution can be significantly improved at the medium to high range frequencies. Synthetical and real data are used to demonstrate the obstructions caused by this effect and the quality improvement of the reconstructions. Finally, we also present a way to align the hardware of the microscope to correct for the non-perpendicularity between the beam direction and the tilt-axis, which is specifically tailored for tomographic applications.