Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipid bilayers.

We have used conical tomography to study the structure of integral proteins in their phospholipid bilayer environments. Complete conical series were collected from replicas of the water channel aquaporin-0 (AQP0), a 6.6 nm side tetramer with a molecular weight of approximately 120 kDa that was purified and reconstituted in liposomes. The replicas were tilted at 38 degrees , 50 degrees or 55 degrees and rotated by 2.5 degrees , 4 degrees , or 5 degrees increments until completing 360 degrees turns. The elliptical paths of between 6 and 12 freeze-fracture particles aligned the images to a common coordinate system. Using the weighted back projection algorithm, small volumes of the replicas were independently reconstructed to reconstitute the field. Using the Fourier Shell Correlation computed from reconstructions of even and odd projections of the series, we estimated a resolution of 2-3 nm, a value that was close to the thickness of the replica (approximately 1.5 nm). The 3D reconstructions exhibited isotropic resolution along the x-y plane, which simplified the analysis of particles oriented randomly in the membrane plane. In contrast to reconstructions from single particles imaged using random conical tilt [J. Mol. Biol. 325 (2003) 210], the reconstructions using conical tomography allowed the size and shape of individual particles representing the AQP0 channel to be identified without averaging or imposing symmetry. In conclusion, the reconstruction of freeze-fracture replicas with electron tomography has provided a novel experimental approach for the study of integral proteins inserted in phospholipid bilayers.

Correspondence analysis of sinogram lines. Sinogram trajectories in factor space replace raw images in the orientation of projections of macromolecular assemblies.

The lines of a large group of sinograms of projections with random orientation can be submitted to correspondence analysis. Since the number of samples per line is small, a small matrix is accumulated which is quick to orthogonalise. In the eigenvector space, the lines of a sinogram are represented by points describing a closed trajectory. Two trajectories of different sinograms intersect in the position of their common line. Determining where two trajectories cross each other is a problem of minimum chi2 distance in the space of 5-7 eigenvectors. An algorithm to determine common lines has been implemented and tested with phantom projections oriented at random, and corrupted with noise. The images were simulating a set collected with the two exposures technique, already proposed by the authors for three dimensional reconstruction from random projections. The preliminary models obtained with the new algorithm have been refined by a projection matching based on trajectories. This step requires determining which trajectory, in a set representing computed projections, matches at best with that of an experimental projection. This is a problem of minimum distance in a space with low dimensionality. The present algorithms, based on chi2 distances, run much faster than those based on correlation analysis and the quality of the reconstructed phantoms looks satisfactory.

Alignment of 3D structures of macromolecular assemblies.

MOTIVATION: A number of macromolecular assemblies are being reconstructed in 3D from electron micrographs. The analysis yields a 3D matrix representing the protein density map. In reconstruction processes and in comparing the results of different experiments, it is often necessary to obtain all models oriented the same way in three dimensions. The problem is not trivial since there exist no 3D counterpart of correlation analysis used for 2D images. It is usually solved by time consuming trial and error algorithms. RESULTS: 3D density distributions can be brought to a 'canonical' orientation. The tensor of inertia of the distribution is determined and its eigenvectors are oriented along the coordinate axes. The method is fast and essentially free of reference. It is suitable for structures whose inertial axes do not completely degenerate as they do in icosahedral viruses or if symmetry is cubic. Applications are presented for asymmetric objects and for molecules possessing symmetry axes higher than twofold. IMPLEMENTATION: The implementation simply requires the accumulation of the inertial tensor and its diagonalisation. Volume data rotation has been already illustrated in this journal by the authors.

A two-exposure technique for ice-embedded samples successfully reconstructs the chlorocruorin pigment of Sabella spallanzanii at 2. 1 Nm resolution.

A technique for reconstructing ice-embedded macromolecules from electron micrographs taken at two specimen tilts (+/-23 degrees ) has been used to determine the structure of chlorocruorin isolated from the Polychaete annelid Sabella spallanzanii. Images of individual molecules were extracted in couples from two micrographs of the same field of view so each couple consists of two projections of the same molecule. One couple was used as a fixed reference for alignment. Different references yielded reconstructions with different orientations. These were merged to give a model against which the orientation of 1624 first-exposure images was refined to give a final reconstruction at 2.1 nm resolution. The structure of this hematic pigment, essentially the same as that for Lumbricus terrestris, is a bilayer structure with overall symmetry D6, containing six hollow groups per layer. A hollow group is formed by six globular masses and has approximate threefold symmetry. Other structural elements connect the two layers and the hollow groups in a layer. This non-globin material occupies about 15% of the total molecular volume. The results show that the double-exposure strategy, previously described by some of the authors and tested in computer simulations, performs well in real experiments and could be used to obtain preliminary reconstructions in a semiautomatic way.

Three-dimensional reconstruction of metal replicas of the Helicobacter pylori vacuolating cytotoxin.

The Helicobacter pylori vacuolating cytotoxin (VacA) forms high molecular weight homooligomers which contain either six or seven copies of a 95-kDa polypeptide. Electron microscope visualization of carbon platinum replicas of quick-freeze, deepetched, preparations of VacA has revealed that the oligomers are arranged in flower-like structures with six- or sevenfold radial symmetry, depending on the number of 95-kDa oligomers that they contain. Each monomer is structured in two subunits of 37 and 58 kDa connected by an exposed loop which is a site for proteolytic cleavage. In preparations of VacA which had undergone extensive cleavage at the exposed loop, oligomers of both six- and seven-fold symmetry which appeared flatter were observed; these latter were interpreted as molecules which had lost a complete set of one of the subunits. We exploited a 3D reconstruction of metal replicas of quick-freeze, deep-etched, oligomers, representing the four types of molecules described. All the molecules appear to adhere with the same face toward the mica. Images of rotary shadowed oligomers were processed by multivariate statistical analysis to evidence clusters of equivalent and homogeneous oligomers. 3D reconstructions of the replicas so classified were performed by random conical tilt tomography. In the case of intact molecules (not cleaved) the reconstructions represent both the outer and the inner surfaces of the mold; the latter gives a reasonably accurate sense of the upper surface of the VacA oligomers. These data support the hypothesis that VacA is an AB type toxin and suggest a model in which the smaller of the two subunits is arranged in a uniform ring on the surface of the molecule in such a way as to contribute to the overall stability of the molecule.

Fast direct Fourier methods, based on one- and two-pass coordinate transformations, yield accurate reconstructions of x-ray CT clinical images.

The conversion from polar to Cartesian coordinates can be carried out with two-pass algorithms. The paper describes two different methods based on concentric square frames and octagonal frames and their results, obtained with accurate interpolations based on the "moving window Shannon reconstruction' (MWSR). The embedding of these algorithms in direct Fourier methods (DFMs) of tomographic reconstruction is discussed. With respect to one-pass methods and to the use of octagonal frames, the square frame method makes it possible to carry out the first pass, a radial resampling, in the direct space, before computing 1D Fourier transforms (FTs) of projections. Reconstructions of clinical images from the raw data of a third-generation x-ray tomograph are presented and compared with those obtained with one-pass DFMs and with the convolution back-projection method (CBPM) performed by the instrument. The simple algorithm using square frames yields results in complete agreement with other DFM protocols and the CBPM. On a general-purpose computer, the execution of DFM protocols based on one-pass and two-pass coordinate transformations is 35 to 55 times faster than the CBPM and make the algorithms attractive for modern instrumentation.

Fast sinogram computation and the sinogram-based alignment of images.

A direct Fourier method (DFM) to compute sinograms is described. Since the DFM is much faster than the customary rotation and projection process, novel uses of sinograms can be devised. As an example and an exercise on the properties of sinograms, a fast sinogram-based method to align large sets of images is described. The method is based on shift-invariant functions to detect rotations, and on tomographic reconstructions of cross-correlation functions to detect relative shifts. It has been implemented in a novel library, SIGNAL, used to align images of macromolecular assemblies observed in the electron microscope. A comparative analysis of the complexity of sinogram- and imagebased methods, as well as quite a few tests with EM images, show that SIGNAL runs faster, the accuracy being the same.

Image and volume data rotation with 1- and 3-pass algorithms.

Three different implementations of the 3-pass algorithm of image and volume data rotation are illustrated and discussed. The three protocols use interpolation in real domain, with a peculiar implementation of the Shannon reconstruction, or phase shifts in Fourier domain. Accuracy and speed of the three methods are compared with corresponding values obtained with a 1-pass method. The results indicate that for low or moderate accuracy, 1-pass is more convenient than 3-pass rotation for both accuracy and speed. Very accurate rotations can be obtained in reasonable time if all steps of 3-pass rotation are performed in the Fourier domain.

Oligomeric and subunit structure of the Helicobacter pylori vacuolating cytotoxin.

Disease-associated strains of Helicobacter pylori produce a potent toxin that is believed to play a key role in peptic ulcer disease in man. In vitro the toxin causes severe vacuolar degeneration in target cells and has thus been termed VacA (for vacuolating cytotoxin A). Cytotoxic activity is associated with a > 600-kD protein consisting of several copies of a 95-kD polypeptide that undergoes specific proteolytic cleavage after release from the bacteria to produce 37- and 58-kD fragments. Quick freeze, deep etch electron microscopy has revealed that the native cytotoxin is formed as regular oligomers with either six- or seven-fold radial symmetry. Within each monomer, two domains can clearly be distinguished, suggesting that the 37- and 58-kD fragments derive from proteolytic cleavage between discrete subunits of the monomer. Analysis of preparations of the toxin that had undergone extensive cleavage into the 37- and 58-kD subunits supports this interpretation and reveals that after cleavage the subunits remain associated in the oligomeric structure. The data suggest a structural similarity with AB-type toxins.

Three-dimensional reconstruction of helical structures with fast inversion of very large Fourier transforms.

A single projection of a helical distribution of matter allows one to obtain the complete three-dimensional reconstruction of the structure. This task is usually performed by a Fourier-Bessel algorithm, which is more efficient than a customary fast Fourier transform inversion. This article describes how to achieve such a result by a direct Fourier method in a reasonable time. Once the two-dimensional transform of the projection is obtained from the source image, it is possible to build up the three-dimensional transform array, in Cartesian coordinates, that yields the reconstruction by a straightforward Fourier inversion. Images of projected helices should be studied with high sampling rates to enhance the resolution, and the segments of helix should be long enough to give a satisfactory signal-to-noise ratio. These conditions result in three-dimensional transform arrays that would require one or more gigabytes of storage. The strategy proposed here requires much less storage and is fast enough to allow the reconstruction to be performed with different parameters and filters in a very short time without any sacrifice in resolution.

Flagellar structure in normal human spermatozoa and in spermatozoa that lack dynein arms.

Human sperm flagella were analyzed by electron microscopy and computer averaging in order to characterize normal flagella and to detect differences between normal and mutated spermatozoa. The A-tubules of normal spermatozoa were seen to have 13 protofilaments and a lumen containing a 'pentagon' and a 'sickle'. The incomplete B-tubule was seen to have 10 protofilaments with an angular separation such that a complete circle would have 16 protofilaments. A thin '11th filament' is located at the inner border between A- and B-tubules and, in the centriole, also between B- and C-tubules. The tail end piece has 18 microtubules of a conventional appearance. We conclude that the 9 axonemal doublets split distally into 2 microtubules and that normal microtubules with 13 protofilaments can grow from the incomplete B-tubules. The cell membrane in the end piece has a glycocalyx with regular periodicity. Spermatozoa from a man suffering from the immotile-cilia syndrome was also analyzed. His sperm flagella were seen to be abnormal in that the dynein arms are lacking, and, that the sickle is incomplete. In other respects his immotile spermatozoa were normal; spokes and central projections have the same appearance as in normal spermatozoa.

A direct Fourier method (DFM) for X-ray tomographic reconstructions and the accurate simulation of sinograms.

This article illustrates the reconstruction of tomographic images by a direct Fourier method (DFM) and the results obtained from simulations and from experimental X-ray sinograms. The implementation of DFM, especially with regard to the resampling of the 2D Fourier transform, is based on a technique of Shannon reconstruction, devised by the authors, and on novel interpolating kernels. A short account is given on the principles and the implementation aspects of the interpolation technique. The DFM protocol developed by the authors has been tested, both for parallel and fan geometry, on simulated sinograms obtained from real images and from phantoms. The technique used to compute accurate projections is also described, since it might be useful in restoring missing parts of sinograms with processes based on 'projections on convex sets' (POCS) techniques. The results obtained from simulations and from the raw data of a third generation tomograph are presented and discussed. A comparison among reconstructions obtained from complete sinograms and from half of them suggests that adequate images could be obtained with a radiation dose lower than that used to obtain the experimental sinograms.

FT3D: three-dimensional Fourier analysis on small Unix workstations for electron microscopy and tomographic studies.

FT3D is a self-contained package of tools for three-dimensional Fourier analysis, written in the C language for Unix workstations. It can evaluate direct transforms of three-dimensional real functions, inverse transforms, auto- and cross-correlations and spectra. The library has been developed to support three-dimensional reconstructions of biological structures from projections obtained in the electron microscope. This paper discusses some features of the library, which has been implemented in such a way as to profit from the resources of modern workstations. A table of elapsed times for jobs of different dimensions with different RAM buffers is reported for the particular hardware used in the authors' laboratory.

A strategy for the reconstruction of structures possessing axial symmetry: sectioned axonemes in sperm flagella.

The images of complex biological structures seen in the electron microscope, possessing an n-fold rotational symmetry, can be enhanced by averaging the axially repeating motif in order to improve their signal-to-noise ratio; this requires that the slices with n-fold symmetry do not exhibit distortions relative to one another. A strategy is proposed to detect the relative distortions and to remove them in order to obtain reliable results from the averaging process. Extensive use is made of cross-correlation analysis and of interpolation; because the procedure involves iterated resampling of the image, it is essential to adopt interpolation algorithms which preserve the spectral power. The procedure is illustrated by the analysis of transverse sections of the sperm flagellum axoneme of a stick insect; it might be used for the reconstruction of microtubules, nuclear pore complexes, virus capsids, and other supramolecular aggregates. The reconstructed images of axoneme sections reveal new information about the interactions between adjacent doublets; in particular, a double conjunction connecting the inner dynein arm with the nearest B-tubule has been consistently observed.

Bizarre flagellum of thrips spermatozoa (Thysanoptera, Insecta).

The flagellum of the thysanopteran spermatozoon has been examined by electron microscopy and computer-aided image analysis. The flagellum consists of 27 microtubular elements that probably are formed as outgrowths from three separate basal bodies. Nine of the elements are normal microtubular doublets that carry dynein arms and nine are doublets without dynein arms. The remaining nine elements are microtubular singlets that apparently bear dynein arms and have the same appearance as A-subtubules of microtubular doublets. The 27 elements are arranged in a fixed pattern that consists of nine groups, each of which begins with a microtubular singlet and ends with an arm-less microtubular doublet. Computer-aided image analysis has shown that the A-subtubules of the doublets and the microtubular singlets have lumens with very similar patterns. The sperm tail is known to have some motility; it generates fast waves running along its length. The amalgamated axonemes hence act as a functional flagellum. The thysanopteran sperm tail is the only type of flagellum known to us that consists of microtubules in a highly asymmetric array.

POLCA, a library running in a modern environment, implements a protocol for averaging randomly oriented images.

The library POLCA implements the averaging of biological structures whose images are recorded in digital form from electron micrographs. The averaging protocol is based upon a method developed about ten years ago, which allows one to operate on a sequence of objects oriented and displaced at random within their frame; the relative rotations and the displacements of the structures are detected with the use of correlation algorithms and modified to make all objects appear the same, apart from their noisy components. The average image is then obtained by a simple addition and the signal-to-noise ratio is improved by a factor equal to the square root of the number of objects used to calculate the average. With respect to the original implementation of the method, two novel features characterize the library: the first one deals with the functions that are cross-correlated to determine the relative rotations of the structures; the functions used here are the inverse transforms of the amplitude spectra (IAS functions), which give rise to sharp maxima when they are cross-correlated. The second peculiarity is the systematic adoption, in the transformations of coordinates and in other circumstances, of an interpolation technique based upon the Fourier series kernel. POLCA is written in C and runs on a VME machine under the UNIX V/68 operating system. A programming style has been adopted to exploit fully the machine resources.

Microtubules and their protofilaments in the flagellum of an insect spermatozoon.

Spermatozoa of stick insects have nine accessory tubules, which surround the nine outer microtubular doublets and the two inner microtubular singlets. When fixed in a fixative that was designed to minimize protein denaturation (glutaraldehyde and tannic acid, no osmium post-fixation but block staining with uranyl acetate in water) the accessory tubules were seen to contain 17 protofilaments of the same type as those in the 9 + 2 microtubular doublets and singlets. The protofilaments in accessory tubules and other microtubules were roughly triangular. When studied by Markham's photographic method a somewhat different tilt of the two longer sides was seen; this makes it possible to distinguish a polarity in the microtubules, i.e. to differentiate between a microtubule that is viewed from its (-)end to its (+)end from one that is viewed in the opposite direction. The dynein arms of the doublets can be used as an independent type of marker for the polarity. In a computer-aided analysis of the fine structure of the tail axoneme, the A-subtubules of the outer doublets were seen to be not quite equidistant; rather, there were somewhat widened electron-dense interspaces in the ring of protofilaments in four places. The locations of these widened interspaces coincide with the attachment sites for the spoke, the inner dynein arm, the outer dynein arm, and the intertubular material. It is tentatively concluded that proteins of these structures, and perhaps also other microtubule-associated proteins, may be anchored deep within the wall of a microtubule rather than just superficially along it.