No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Correlation of Topographic Surface and Volume Data from Three-Dimensional Electron Microscopy
Abstract
Three-dimensional(3D) reconstructions from tilt series in an electron microscope show in general an anisotropic resolution due to an instrumentally limited tilt angle. As a consequence, the information in the z direction is blurred, thus making it difficult to detect the boundary of the reconstructed structures. In contrast, high-resolution topography data from microscopic surface techniques provide exactly complementary information. The combination of topographic surface and volume data leads to a better understanding of the 3D structure. The new correlation procedure presented determines both the height scaling of the topographic surface and the relative position of surface and volume data, thus allowing information to be combined. Experimental data for crystalline T4 bacteriophage polyheads were used to test the new method. Three-dimensional volume data were reconstructed from a negatively stained tilt series. Topographic data for both surfaces were obtained by surface relief reconstruction of electron micrographs of freeze-dried and unidirectionally metal-shadowed polyheads. The combined visualization of volume data with the scaled and aligned surface data shows that the correlation technique yields meaningful results. The reported correlation method may be applied to surface data obtained by any microscopic technique yielding topographic data.
... In some situations (as for example for crystalline objects, cell membranes, etc.), these fine structures can be obtained to high resolution by modern scanning and microscopy techniques(e.g. [40]) and the full resolution with a FEM is often out of reach. Another source of roughness can arise from the coefficients (tensor) of the diffusion problem. ...
... where we used (40), the Cauchy-Schwarz inequality and the assumption on the tensor a ε and on the QF. Using an inequality similar to (50) gives the second assertion of the lemma and the proof is complete by noting that the arguments remain unchanged when δ > ε and δ/ε ∈ N. ...
... Our main motivation for implementing a reconstruction algorithm for crystals that works in real space and is iterative is not to replace the well established methods used at present but to create a framework in which we can easily incorporate information available from other sources. This information, such as surface reliefs from atomic or shadowing microscopies (see [15, 16] for a description of our work in this area), or a more suitable model of the imaging device (contrast transfer function; see [16] ) is more easily and naturally incorporated in a real space iterative method than in a Fourier space based algorithm. For example, in the ART connector using the traditional algorithm (top) and the new algorithm (middle). ...
A new algorithm for 3D reconstruction of two-dimensional crystals from projections is presented, and applied to biological macromolecules imaged using electron microscopy. Its main departure from the traditional approach is that it works in real space, rather than in Fourier space, and is iterative. This approach has the advantage of making it convenient to introduce additional constraints (such as the support of the function to be reconstructed, which may be known from alternative measurements) and has the potential of more accurately modeling the electron microscope image formation process.
... Recently, the ART algorithm has been further modified to allow 3D-reconstruction of 2D crystals in real-space (Marabini et al., 2002Marabini et al., , 2004 ). The main motivation for this work was not to replace the existing, wellestablished methods for 2D crystal reconstruction (Crowther et al., 1996), but to provide a framework in which prior information about the surface relief, as mentioned above, could be applied in the 2D-crystal case (Dimmeler et al., 2001). However, our tests indicate that the real-space algorithm behaves better than the traditional one, even without the incorporation of such additional information, especially when the number of projections is small. ...
11 pages, 2 figures.-- PMID: 15477099 [PubMed].-- Printed version published on Nov 2004. X-windows based microscopy image processing package (Xmipp) is a specialized suit of image processing programs, primarily aimed at obtaining the 3D reconstruction of biological specimens from large sets of projection images acquired by transmission electron microscopy. This public-domain software package was introduced to the electron microscopy field eight years ago, and since then it has changed drastically. New methodologies for the analysis of single-particle projection images have been added to classification, contrast transfer function correction, angular assignment, 3D reconstruction, reconstruction of crystals, etc. In addition, the package has been extended with functionalities for 2D crystal and electron tomography data. Furthermore, its current implementation in C++, with a highly modular design of well-documented data structures and functions, offers a convenient environment for the development of novel algorithms. In this paper, we present a general overview of a new generation of Xmipp that has been re-engineered to maximize flexibility and modularity, potentially facilitating its integration in future standardization efforts in the field. Moreover, by focusing on those developments that distinguish Xmipp from other packages available, we illustrate its added value to the electron microscopy community. We acknowledge partial support from the "Comunidad Autónoma de Madrid" through Grant CAM-07B-0032-2002, the "Comisión Interministerial de Ciencia y Tecnología" of Spain through Grants BIO2001-1237, BIO2001-4253-E, BIO2001-4339-E, and BIO2002-10855-E, the European Union through Grants QLK2-2000-00634, QLRI-2000-31237, QLRT-2000-0136, and QLRI-2001-00015, and the NIH through Grant HL70472. Partial support from the "Universidad San Pablo-CEU" Grant 17/02 is also acknowledged. Peer reviewed
... This supposition is consistent with the finding that the correlation coefficient between in vitro particles analyzed here and the published crystal structure (1J5E) [25] is quite similar to that between the in situ particles and the crystal structure. Therefore, the reconstruction should faithfully reproduce the overall morphology and the size of the 30S subunits [44]. By analyzing the reconstructed individual 30S ribosomal subunits, both in vitro and in situ, we can deduce that possible distortions arising from the vitrification and staining can essentially be disregarded at this resolution range, and should not affect the interpretation of biologically significant features [45]. ...
Cryo-electron tomography has been used to reconstruct the structures of individual ribosomal 30S subunits in Escherichia coli cells treated with rifampicin. Rifampicin inhibits transcription initiation, thus giving depletion of mRNA and accumulation of free 30S and 50S subunits in the cell. Here, we present the 3D morphologies of reconstructed individual 30S ribosomal subunits both in vitro and in situ from E. coli. The head, the platform, and the body of the structures show large conformational movements relative to each other. The particles were grouped into three conformational groups according to the ratio between width and height in the subunit solvent side view. Also, an S15 fusion protein derivative has been used as a physical reporter to localize S15 in the 30S subunit. The results demonstrate a considerable morphological heterogeneity and structural variability among 30S ribosomal subunits.
... However, Wtting high resolution structures into low/medium resolution volumes is still quite human-dependent and fully automatic and reliable methods are still under development. The information provided by cryo-electron microscopy may be complemented by other information sources such as Atomic Force Microscopy (Dimmeler et al. 2001; Engel and Muller 2000) or SAXS (Hamada et al. 2007) that help to constrain the search space in the reconstruction process. This extra information should result in an improvement of resolution, as long as the two sources of information correspond to the same conformation of the particle (Vestergaard et al. 2005). ...
Transmission electron microscopy is a powerful technique for studying the three-dimensional (3D) structure of a wide range of biological specimens. Knowledge of this structure is crucial for fully understanding complex relationships among macromolecular complexes and organelles in living cells. In this paper, we present the principles and main application domains of 3D transmission electron microscopy in structural biology. Moreover, we survey current developments needed in this field, and discuss the close relationship of 3D transmission electron microscopy with other experimental techniques aimed at obtaining structural and dynamical information from the scale of whole living cells to atomic structure of macromolecular complexes.
... This method has been successfully applied (e.g. Rockel et al., 2000; Walz et al., 1996; Dimmeler et al., 2001) to specimens of appropriate topology. However, the majority of biological structure is incompatible with the digital elevation map (Lupetti et al., 2005). ...
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.
... Our main motivation for implementing a reconstruction algorithm for crystals that works in real space and is iterative is not to replace the well-established methods used at present but to create a framework in which we can easily incorporate information available from other sources. This information, such as surface reliefs from atomic force or shadowing microscopies (see [33] and [40] for a description of our work in this area), or a more suitable model of the imaging device (contrast transfer function-see [33]), is more easily and naturally incorporated in a real space iterative method than in a Fourier space based noniterative algorithm. For example, in the ART-based method, the contrast transfer function can be taken into account by modifying the in the system matrix [see (3)] without any modification of the algorithm's logic. ...
A new algorithm for three-dimensional reconstruction of two-dimensional crystals from projections is presented, and its applicability to biological macromolecules imaged using transmission electron microscopy (TEM) is investigated. Its main departures from the traditional approach is that it works in real space, rather than in Fourier space, and it is iterative. This has the advantage of making it convenient to introduce additional constraints (such as the support of the function to be reconstructed, which may be known from alternative measurements) and has the potential of more accurately modeling the TEM image formation process. Phantom experiments indicate the superiority of the new approach even without the introduction of constraints in addition to the projection data.
Three-dimensional reconstructions producing computer-generated images have played an important role in furthering understanding in many areas in microscopical morphology, both in normal microanatomy and in cell pathology. This review article considers some recent developments in the techniques of three-dimensional reconstruction and some recent applications of three-dimensional reconstruction to problems in pathology.
We present a finite element method for the numerical solution of diffusion problems on rough surfaces. The problem is transformed to an elliptic homogenization problem in a two dimensional parameter domain with a rapidly oscillating diffusion tensor and source term. The finite element method is based on the heterogeneous multiscale methods of Weinan E and B. Engquist, Commun. Math. Sci. 1, No. 1, 87–132 (2003; Zbl 1093.35012)]. For periodic surface roughness of scale ε and amplitude O(ε), the method converges at a robust rate, i.e., independent of ε, to the homogenized solution.
Microtubules interact with a large variety of factors commonly referred to as either molecular motors (kinesins, dyneins) or structural microtubule-associated proteins (MAPs). MAPs do not exhibit motor activity, but regulate microtubule dynamics and their interactions with molecular motors, and organelles such as kinetochores or centrosomes. Structural investigations into microtubule-kinesin motor complexes are quite advanced today and by helical three-dimensional (3-D) analysis reveal a resolution of the motor-tubulin interface at <1.0 nm. However, due to their flexible structure MAPs like tau or MAP2C cannot be visualized in the same straightforward manner. Helical averaging usually reveals only the location of strong binding sites while the overall structure of the MAP remains unsolved. Other MAPs such as EB1 bind very selectively only to some parts of the microtubule lattice such as the lattice seam. Thus, they do not reveal a stoichiometric tubulin:MAP-binding ratio that would allow for a quantitative helical 3-D analysis. Therefore, to get a better view on the structure of microtubule-MAP complexes we often used a strategy that combined cryo-electron microscopy and helical or tomographic 3-D analysis with freeze-drying and high-resolution unidirectional surface shadowing. 3-D analysis of ice-embedded specimens reveals their full 3-D volume. This relies either on a repetitive structure following a helical symmetry that can be used for averaging or suffers from the limited resolution that is currently achievable with cryotomography. Surface metal shadowing exclusively images surface-exposed features at very high contrast, adding highly valuable information to 2-D or 3-D data of vitrified structures.
Electron tomography by conventional filtered back-projection is often seriously impaired by anisotropic resolution due to unavoidable limitation in specimen tilt-angles. We propose a new approach to overcome the problem for thin film-like replica-type specimens in which internal density is supposed as homogenous and contiguously distributed, by imposing a reasonable constraint of density-existing region in the reconstruction procedure. The objects were approximated as a distribution of binary voxels and the intensity of the projected images being proportional to the thickness along the projection ray. The new reconstruction algorithm consists of initial determination of approximate constraint region by a topographic analysis by stereo-photogrammetry, followed by iterative computation to find the unique solution of simultaneous equations, so that all the intensity distribution in tilt-series images are included within pre-determined voxel arrangement. During a trial run with a new methodology, we realized its significantly advantageous feature that much less number of projection images than conventional back-projection is required to perform the reconstruction of almost equivalent quality. Here, we show the performance of this novel algorithm by 3-D reconstruction of quick-freeze deep-etch replica specimens without any trace of spurious ghosting caused by missing-wedge problems.
Aquaporin-1 (AQP1) is an abundant protein in human erythrocyte membranes which functions as a specific and constitutively active water conducting pore. Solubilized and isolated as tetramer, it forms well-ordered two-dimensional (2D) crystals when reconstituted in the presence of lipids. Several high resolution projection maps of AQP1 have been determined, but information on its three-dimensional (3D) mass distribution is sparse. Here, we present surface reliefs at 0.9 nm resolution that were calculated from freeze-dried unidirectionally metal-shadowed AQP1 crystals as well as surface topographs recorded with the atomic force microscope of native crystals in buffer solution. Our results confirm the 3D map of negatively stained AQP1 crystals, which exhibited tetramers with four major protrusions on one side and a large central cavity on the other side of the membrane. Digestion of AQP1 crystals with carboxypeptidase Y, which cleaves off a 5 kDa intracellular C-terminal fragment, led to a reduction of the major protrusions, suggesting that the central cavity of the tetramer faces the outside of the cell. To interpret the results, sequence based structure predictions served as a guide.
A blinded evaluation of two groups of retrospective image registration techniques was performed using as a gold standard a prospective marker-based registration method, and we compared the performance of one group with the other. By grouping the techniques as volume-based or surface-based, we could make some interesting conclusions. In order to ensure blindness, all retrospective registrations were performed by participants who had no knowledge of the gold-standard results until after their results had been submitted. Image volumes of three modalities (X-ray CT, MRI and PET) were obtained from patients undergoing neurosurgery on whom bone-implanted fiducial markers were mounted. These volumes had all traces of the markers removed and were provided via the Internet to outside collaborators, who then performed retrospective registrations on the volumes, calculating transformations from CT to MRI and/or from PET to MRI. The accuracy of each registration was then evaluated. The accuracy is measured at multiple volumes of interest. The volume-based techniques in this study tended to give substantially more accurate and reliable results than the surface-based ones for the CT-to-MRI registration tasks, and slightly more accurate results for the PET-to-MRI tasks. Analysis of these results revealed that the rotational component of error was more pronounced for the surface-based group. It was also apparent that all of the registration techniques we examined have the potential to produce satisfactory results much of the time, but that visual inspection is necessary to guard against large errors.
Freeze-drying followed by heavy metal shadowing is a long established and straight forward approach to routinely study the structure of dehydrated macromolecules. Very thin specimens such as isolated membranes or single macromolecules are directly adsorbed on C-coated grids. After rapid freezing the grids are transferred into a suitable vacuum equipment for freeze-drying and heavy metal shadowing.
To improve the resolution power of shadowing films we introduced shadowing at very low specimen temperature (−250°C). To routinely do that without the danger of contamination we developed in collaboration with Balzers an UHV (p≤10 ⁻⁹ mbar) machine (BAF500K, Fig.2). It should be mentioned here that at −250°C the specimen surface acts as effective cryopump for practically all impinging residual gas molecules from the residual gas atmosphere.
Common high resolution shadowing films (Pt/C, Ta/W) have to be protected from alterations due to air contact by a relatively thick C-backing layer, when transferred via atmospheric conditions into the TEM. Such an additional C-coat contributes disturbingly to the contrast at high resolution.
Freeze-drying followed by heavy-metal shadowing is an established and straightforward approach to routine structural studies of dehydrated biological specimens (Nermut and Frank 1971; Kistler et al. 1977; Gross et al. 1985). Very thin specimens such as isolated membranes or isolated macromolecules can be directly adsorbed on carbon-coated grids. After rapid freezing, the grids are transferred into suitable high-vacuum equipment for freeze-drying and shadowing. After stabilizing the heavy-metal coat with carbon (C-backing), the specimens are warmed to room temperature and transferred via atmospheric conditions into the transmission electron microscope (TEM). In other words, the entire sandwich consisting of C-supporting film, biological specimen, metal coat and C-backing film is examined in the microscope.
Three-dimensional (3-D) image reconstruction of electron microscopy (EM) data offers a powerful tool in structural biology that provides important information about the structure and function of individual biomacromolecules, their oligomers, and supramolecular assemblies. Forming an important link between atomic-resolution X-ray or NMR data of individual proteins and their supramolecular complexes, 3-D EM data allow the combining of structural information from all sources to assess protein function at atomic detail. Within the last several years, a range of image reconstruction methods were introduced aiming to determine 3-D structures of biomacromolecular assemblies to intermediate resolution (i.e., ≤20 Å). To achieve a faithful representation of the specimen under investigation its preparation for EM is of critical importance. Whereas earlier 3-D reconstructions were predominantly obtained with negatively stained specimens, more recently the potential of cryofixation/ice embedding has definitely become widely recognized. Imaging the biomacromolecule itself rather than a heavy metal cast surrounding it, by freezing the sample in its physiological buffer environment, cryofixation/ice embedding was found to reduce adsorption artifacts and to reproduce certain structural details more accurately and faithfully. Most importantly, in addition to mapping out the overall size and shape of biomacromolecules, cryo-EM enables us to look “inside” biomacromolecules and image their secondary structure elements or even atomic detail. Despite these obvious advantages of ice embedding over negative staining, however, both preparation methods have their own strengths and limitations which should be carefully evaluated based on the particular structural and biological question asked.
Electron microscopy is a powerful technique for imaging complex biological macromolecules in order to further the understanding of their functions. When combined with sufficiently careful sample preparation procedures that preserve the native structure of the macromolecules and with sophisticated image processing procedures, electron microscopy can lead to very informative estimates of the three-dimensional (3D) structures of the specimens under study. 3D reconstruction from electron microscopic data is achieving high goals and exceeding expectations unthinkable only a few years ago. However, there are still some areas where either not enough work has been invested or the work has not as yet been fruitful. We describe image processing approaches that shed further light on some of these difficult areas. © 2000 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 11, 12–29, 2000
Images of freeze-dried and unidirectionally, heavy-metal shadowed specimens can be utilized for the computational reconstruction of the three-dimensional surface function of the object with little effort. To preserve the specimen surface as well as possible, samples are carefully freeze-dried and, after shadowing, transferred into the microscope under high-vacuum- and cryo-conditions and imaged under cryo-and low-dose-conditions. Such a transfer allows the omission of the usual additional carbon layer that causes a blurring of the image. The technique results in a routine resolution of 1.5 nm after application of a computational averaging process to the images; two- dimensional periodic objects are best suited for such a purpose. The actual reconstruction procedure requires several images of the object shadowed at distinct azimuthal angles in order to complement missing information in the shadow regions. Algorithms to determine the azimuthal and elevation shadowing angle for each single image are introduced. A procedure for performing an automatic alignment of the input images of symmetrical and asymmetrical objects is presented. It allows the determination of a common reference point with high accuracy and makes the multiple-image reconstruction, especially of asymmetric objects, routinely applicable. A procedure is described to calculate the overall surface function from the surface reconstructions of the bottom and top sides. The algorithm exploits constraints from other experiments such as height measurements from scanning probe microscopy and the molecular weight of the object. Novel ray tracing techniques are employed to generate an illuminated, perspective presentation of such a surface model. These techniques introduce an accurate determination of the surface normals of the discrete data and a shadowing procedure for obtaining realistic lighting effects. The combined processing sequence provides a procedure for achieving a three-dimensional surface model of an object at about 1.5 nm resolution and originating from optimally only two TEM-images.
Electron micrographs of the purple membrane have been recorded using liquid nitrogen and liquid helium cooling on three cryoelectron microscopes. The best micrographs show optical diffraction spots, arising from the two-dimensional crystal, out to resolutions of around 6 Å. Large areas of several of these micrographs have been analysed using a procedure which determines the strength of the very weak high resolution Fourier components of the image of the crystal. The procedure consists of reciprocal space filtering followed by real space correlation analysis to characterise image distortions, removal of the distortions by interpolation, and finally extraction of the amplitudes and phases of the Fourier components from the distortion-corrected image of the crystal. These raw image amplitudes and phases are then used, together with previously measured amplitude and phase information, to refine the beam tilt and crystal tilt, phase origin and amount of defocus and astigmatism of the image. The phases can then be corrected for the effects of the contrast transfer function, beam tilt and phase origin. The amplitudes of all the spots which are expected to be strong from their known electron diffraction intensity are observed to be significantly above the background noise level, and the independent phases from different images, and from symmetry-related directions in the same image, show excellent agreement out to a resolution of 3.5 Å. Although only images from untilted or slightly tilted ( < 5°) crystals have been analysed using the procedure described in this paper, a simple additional step enables analysis of images at any tilt angle, providing a complete practical method for high resolution analysis of images of two-dimensional crystalline arrays.
We have studied the aberrant tubular polyheads of bacteriophages T4D and T2L as a model system for capsid maturation. Six different types of polyhead surface lattice morphology, and the corresponding protein compositions are reported and discussed. Using in vitro systems to induce transformations between particular polyhead types, we have deduced that the structural classes represent successive points in a transitional pathway. In the first step, coarse polyheads (analogous to the prohead τ-particle) are proteolytically cleaved by a phagecoded protease, a fragment of the gene 21 product. This cleavage of P23 to P23∗ induces a co-operative lattice transformation in the protein of the surface shell, to a conformation equivalent to that of T2L giant phage capsids. These polyheads (derived either from T4 or T2L lysates) can accept further T4-coded proteins. In doing so, they pass through intermediate structural states, eventually reaching an end point whose unit cell morphology is indistinguishable from that of the giant T4 capsids. At least one protein (called soc (Ishii & Yanagida, 1975)) is bound stoichiometrically to P23∗ in the end-state conformation. The simulation of several aspects of capsid maturation (cleavage of P23 to P23∗, stabilization, and lattice expansion) in the polyhead pathway suggest that it parallels the major events of phage T-even capsid maturation, decoupled from any involvement of DNA packaging.
Vitrified Tobacco Mosaic Virus (TMV) and T4 polyhead suspensions have been studied by cryo-electron microscopy. The order of TMV particles is preserved to distances better than 0.3 nm when vitrified. In spite of the high beam sensitivity of unstained biological material, the resolution of images extends to 1.15 nm. Radial density distributions calculated from images of TMV and the helical aggregate of TMV protein (TMVP) show that the RNA is likely visualized in the virus. However, due to the imaging conditions of unstained vitrified specimens, the position of the RNA is erroneous. While TMV and TMVP do not show any departure from cylindrical symmetry, T4 polyheads are sensitive to the thickness of the ice layer in which they are embedded. To avoid flattening, T4 polyheads have to be embedded in an ice layer thicker than their diameter.
We have determined the nucleotide sequence of gene 23 of bacteriophage T4 by the methods of Maxam and Gilbert and of Sanger. The identities of approximately 80% of the amino acid residues of the major capsid protein which is encoded by gene 23 were determined additionally by Edman degradation of the intact protein and its peptides. Fifteen gene 23 amber mutation sites have been located within the sequence, and the 3' transcription termination site for genes 21, 22 and 23 has been identified.
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.
An adaptation of the 'correlation averaging' method is described which allows reliable and almost fully automatic image averaging in the case of near-periodic structures notwithstanding the presence of substantial crystal imperfections; methods for assessing resolution and symmetry without reliance on crystallinity are also discussed. Electron micrographs of negatively stained and rotary shadowed preparations of the HPI-layer protein from the cell envelope of Micrococcus radiodurans have been averaged using the method, and the projected structure is described to a resolution of about 1.9 nm.
SPECTRA is a program system that combines well tested and familiar algorithms and advanced graphics tools for (i) the display and indexing of the Fourier transform of images of crystalline specimens, (ii) refinement of the reciprocal lattice, (iii) output of amplitudes and phases of reflections and (iv) lattice distortion correction through cross-correlation map analysis. Because of the ease of identifying and indexing reflections, the user can include many reflections for reciprocal lattice refinement, leading to more accurate lattice determination. Automatic indexing is much faster than entering indices by hand, with less operator error. The user can run the procedure that corrects for lattice distortions with either standard parameters or storable parameters tailored to a particular specimen. SPECTRA's primary function is as a control program which acts as an interface between existing programs and the user. It was written in C with routines for the display, user interface and peak list search. Communication between the separate processes that make up SPECTRA is via the UNIX pipe mechanism and command files, the latter so that users may run, test or replace them or even run them as stand-alone programs outside this system.
Digital image processing is an essential step in the determination of macromolecular structures by electron microscopy. Centrally important procedures are the averaging of many images of the subunit to improve the signal, the correction for various transfer functions, and the generation of a three-dimensional map from a set of two-dimensional projections. The detailed way in which these computational procedures are best carried out depends on the symmetry of the object and the type of specimen preparation. Over many years a large set of programs has been written by various members of the Laboratory of Molecular Biology for processing images of two-dimensional crystals and of particles with helical or icosahedral symmetry. The philosophy has been to write stand-alone programs and the whole system is given coherence by the adoption of standard formats for the storage and interchange of different kinds of data. This paper describes the current state of the programs.
Algebraic reconstruction techniques (ART) are iterative procedures for solving systems of linear equations. They have been used in tomography to recover objects from their projections. In this work we apply an ART approach in which the basis functions used to describe the objects are not based on voxels, but are much smoother functions named "blobs". The data collection studied in this work follows the so-called "conical tilt geometry" that is commonly used in many applications of three-dimensional electron microscopy of biological macromolecules. The performance of ART with blobs is carefully compared with a currently well-known three dimensional (3D) reconstruction algorithm (weighted back projection) using a methodology which assigns a level of statistical significance to a claim of relative superiority of one algorithm over another for a particular task. The conclusion we reach is that ART with blobs produces high-quality reconstructions and is, in particular, superior to weighted backprojection in recovering features along the "vertical" direction. For the exact implementation recommended in this paper, the computational costs of ART are almost an order of magnitude smaller than those of WBP.
Recent progress in high-resolution shadowing for biological transmission elec-tron micrsocopy in
- Springer-Verlag
- Berlin
- H Gross
- K Krusche
- P Tittmann
Springer-Verlag, Berlin. Gross, H., Krusche, K., and Tittmann, P. (1990) Recent progress in high-resolution shadowing for biological transmission elec-tron micrsocopy in Proceedings XIIth International Congress on Electron Microscopy, Seattle, pp. 510 –511, San Francisco Press, San Francisco.
Reconstruction and representation of surface data from two-dimensional crystalline, biological macromolecules
- Fuchs