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

What can electron microscopy tell us about chaperoned protein folding?

Chaperonins form large, cage-like structures that act as protein folding machines. Recent developments in electron cryo-microscopy and image processing are helping to reveal the mechanism of chaperonin-mediated protein folding.

Estimation of variance distribution in three-dimensional reconstruction. I. Theory

A theory is developed for estimating the three-dimensional (3-D) variance of a 3-D image reconstructed from projections by weighted backprojection. The theory is applicable for any data-collection schemes that produce partially redundant sampling of the angular space. The particular data collection considered here, the single-exposure random-conical scheme, is used for the reconstruction of macromolecules in electron microscopy. In this context, the purpose of the 3-D variance estimation is to detect and localize the conformational variability, to assess the significance of structural differences between two experimentally related 3-D images, and to assess the significance of local features in a 3-D image. The 3-D variance estimate of each reconstruction voxel is obtained by (i) the comparison of closest points on Fourier sections associated with difference projections, (ii) the comparison of neighbor projections in real space, or (iii) the comparison of projections with reprojections of the reconstruction.

A model of the translational apparatus based on a three-dimensional reconstruction of the Escherichia coli ribosome

The morphology of the Escherichia coli ribosome, i.e., its shape at moderate to low (20-40 A (1 A = 0.1 nm)) resolution, provides important constraints in modeling both the folding of ribosomal RNA and the translational process. A new reconstruction, obtained by low-dose cryoelectron microscopy and image processing of single ribosomes, contains clues to the way in which the ribosome interacts with the key functional ligands: the mRNA and the A- and P-site tRNAs. It also suggests possible pathways of the nascent polypeptide chain. From an interpretation of these clues in the light of existing knowledge, a plausible model for the locations and interactions of key components of protein synthesis is suggested.

Three-dimensional architecture of the skeletal muscle ryanodine receptor

Recent advances in determining the three-dimensional architecture of the skeletal muscle ryanodine receptor/calcium release channel (RyR) by cryo-electron microscopy and three-dimensional reconstruction are discussed. The tetrameric receptor is characterized by a large 4-fold symmetric cytoplasmic assembly that consists of many domains separated by solvent-containing crevices and holes. Experimental evidence suggests that at least one regulatory ligand, calmodulin, binds to sites on the cytoplasmic assembly that are at least 10 nanometers from the transmembrane channel.

Structures of small subunit ribosomal RNAs in situ from Escherichia coli and Thermomyces lanuginosus

Small ribosomal subunits from the prokaryote Escherichia coli and the eukaryote Thermomyces lanuginosus were imaged electron spectroscopically, and single particle analysis used to yield three-dimensional reconstructions of the net phosphorus distribution representing the nucleic acid (RNA) backbone. This direct approach showed both ribosomal RNAs to have a three domain structure and other characteristic morphological features. The eukaryotic small ribosomal subunit had a prominent bill present in the head domain, while the prokaryotic subunit had a small vestigial bill. Both ribosomal subunits contained a thick 'collar' central domain which correlates to the site of the evolutionarily conserved ribosomal RNA core, and the location of the majority of ribosomal RNA bases that have been implicated in translation. The reconstruction of the prokaryotic subunit had a prominent protrusion extending from the collar, forming a channel approximately 1.5 nm wide and potentially representing a 'bridge' to the large subunit in the intact monosome. The basal domain of the prokaryotic ribosomal subunit was protein free. In this region of the eukaryotic subunit, there were two basal lobes composed of ribosomal RNA, consistent with previous hypotheses that this is a site for the 'non-conserved core' ribosomal RNA.

Three-dimensional reconstruction of the alpha D and beta C-hemocyanins of Helix pomatia from frozen-hydrated specimens

The three-dimensional (3D) reconstructions of the di-decameric forms of alpha D and beta C-hemocyanins of the Roman snail Helix pomatia and of the decameric half molecules of alpha D-hemocyanin were carried out on frozen-hydrated specimens observed in the electron microscope by using the random conical tilt series method. The three 3D volumes were examined by computing solid-body surface representations and slices through the volume and by eroding the structure progressively through raising of the threshold. The di-decameric molecule of alpha D and beta C-hemocyanins, reconstructed from side views, are very similar and are composed of a cylindrical wall, comprising ten oblique wall units, and of two collar complexes located at both ends of the cylinder, comprising each five arches and an annular collar made up of five collar units. Erosion of the structure reveals that the wall looks like a segment of a five-stranded right-handed helix and that each oblique wall unit resembles a figure 8 inclined to the right. The decameric half molecule of alpha D-hemocyanin, reconstructed from end-on views, resembles the whole molecule, except that the collar is thinner and appears composed of five independent collar complex units. It is suggested that the difference in structural appearance of the collar complex between the whole and the half alpha D-hemocyanin may be due to the missing cone artifact, induced by the angular limitations imposed by the goniometer of the electron microscope. The comparison between the alpha D-hemocyanin and the beta C-di-decameric hemocyanin at high thresholds suggests that in the beta C-hemocyanin the oblique wall units of each half molecule may be linked by two connections, whereas in alpha D-hemocyanin there may be only one. This difference in the number of connections may be responsible for the lower stability of the alpha D molecule at high salt concentration.

Cryo-electron microscopy and three-dimensional reconstruction of the calcium release channel/ryanodine receptor from skeletal muscle

The calcium release channel (CRC) from skeletal muscle is an unusually large tetrameric ion channel of the sarcoplasmic reticulum, and it is a major component of the triad junction, the site of excitation contraction coupling. The three-dimensional architecture of the CRC was determined from a random conical tilt series of images extracted from electron micrographs of isolated detergent-solubilized channels prepared in a frozen-hydrated state. Three major classes of fourfold symmetric images were identified, and three-dimensional reconstructions were determined for two of these. The two independent reconstructions were almost identical, being related to each other by a 180 degrees rotation about an axis in the plane of the specimen grid. The CRC consists of a large cytoplasmic assembly (29 x 29 x 12 nm) and a smaller transmembrane assembly that protrudes 7 nm from one of its faces. A cylindrical low-density region, 2-3 nm in apparent diameter, extends down the center of the transmembrane assembly, and possibly corresponds to the transmembrane Ca(2+)-conducting pathway. At its cytoplasmic end this channel-like feature appears to be plugged by a globular mass of density. The cytoplasmic assembly is apparently constructed from 10 or more domains that are loosely packed together such that greater than 50% of the volume enveloped by the assembly is occupied by solvent. The cytoplasmic assembly is suggestive of a scaffolding and seems well adapted to maintain the structural integrity of the triad junction while allowing ions to freely diffuse to and away from the transmembrane assembly.

Reversible interaction of beta-actin along the channel of the TCP-1 cytoplasmic chaperonin

The cytoplasm of eukaryotes contains a heteromeric toroidal chaperonin assembled from the t-complex TCP-1 and several other related polypeptides. The structure of the TCP-1 cytoplasmic chaperonin and that of the binary complex formed between this chaperonin and unfolded beta-actin have been studied using electron microscopy and image processing techniques. Two-dimensional averaging of front views reveals a circular stain-excluding mass surrounding a central stain-penetrating region in which the stain is excluded upon actin binding. Sections of a three-dimensional reconstruction of the chaperonin show that the inner core is an empty channel that becomes filled upon binary complex formation with unfolded beta-actin. Upon incubation with Mg-ATP, the beta-actin:chaperonin complex discharges the actin such that the chaperonin central cavity reappears. Side views from different forms of TCP-1 reveals that upon Mg-ATP binding, the cytoplasmic chaperonin undergoes a structural rearrangement that is confirmed using a new classification method.

The ribosome at improved resolution: new techniques for merging and orientation refinement in 3D cryo-electron microscopy of biological particles

Cryo-electron microscopy of single biological particles opens up new possibilities for structure analysis: the particle can be reconstructed in its native shape and internal features are preserved. To take advantage of these possibilities we have developed new methods of data collection and image processing and we have applied them to the 70S Escherichia coli ribosome. A method of orientation search is proposed, which makes it possible to relate random-conical data sets to one another even if they are collected from low-tilt micrographs. A technique for 3D alignment of projections is described and applied to the single-micrograph 3D reconstruction.

Three-dimensional reconstruction from random projections: orientational alignment via Radon transforms

A method for alignment of projections with unknown projecting directions towards a three-dimensional reference has been developed. The technique has been applied to the three-dimensional reconstruction from images of a frozen-hydrated preparation of 50S ribosomal subunits from Escherichia coli recorded in the electron microscope. The algorithm as used here combines the Single Exposure Conical Reconstruction Technique (SECReT) with a three-dimensional orientation search. The algorithm allows for the refinement of a reconstruction obtained with SECReT by refinement of the true projection angles, and by the inclusion of projections with a priori unknown random orientation. With model data it is demonstrated that the algorithm works reliably even for signal-to-noise ratios lower than 1.

Three-dimensional reconstruction of single particles negatively stained or in vitreous ice

The random-conical reconstruction method has been highly successful in three-dimensional imaging of macromolecules under low-dose conditions. This article summarizes the different steps of this technique as applied to molecules prepared with negative staining or vitreous ice, and sketches out the current directions of development. We anticipate that by using new instrumental developments, transfer function correction and computational refinement techniques, a resolution in the range of 7-10 A could ultimately be achieved.

Eukaryotic initiation factor 3 does not prevent association through physical blockage of the ribosomal subunit-subunit interface

The "native" 40 S ribosomal subunit, in which the protein eukaryotic initiation factor 3 is bound to the 40 S small ribosomal subunit, has been reconstructed to 48 A resolution. Comparison with a previous three-dimensional reconstruction of the "derived" 40 S subunit lacking any non-ribosomal components reveals the attachment site and morphology of the factor. It is a large (approximately 165 to 170 A long), bilobed, elongate structure, attached to the back lobes of the 40 S subunit by two strand-like features. Significantly, the factor is oriented away from the 60 S-subunit-40 S-subunit interface surface of the 40 S particle, suggesting that its anti-association activity is not accomplished via simple physical blockage of that surface.

Three-dimensional reconstruction of a complex of human alpha 2-macroglobulin with monomaleimido Nanogold (Au1.4nm) embedded in ice

Cysteine 949 and glutamine 952 are known to be part of the thiol ester site of each of the four subunits of human alpha 2-macroglobulin (alpha 2M). The hydrolysis of this thiol ester bound to methylamine results in the incorporation of the amine and liberation of a free sulfhydryl group that can be specifically labeled. Therefore, a high-resolution marker specific for the sulfhydryl groups, the monomaleimido Nanogold (Au1.4nm) cluster was used to bind this amino acid. After cryoelectron microscopy, a three-dimensional reconstruction of the alpha 2M-Nanogold conjugates (alpha 2M-Au1.4nm) was achieved, revealing the internal location of the thiol ester sites in the transformed alpha 2M molecules. From this study we propose three possible locations for the cysteine 949.

Detection, classification and 3D reconstruction of biological macromolecules on hypercube computers

In this work we present results of the mapping on hypercube computers of some of the key steps involved in the procedure for 3D structural determination from transmission electron microscopy images. The goal is the introduction of parallel processing tools in the field of electron microscopy image processing. We show how the rich topology of the hypercube, combined with an efficient programming strategy, allows for order-of-magnitude increase in computational capacity for such time-consuming tasks as calculation of multidimensional FFT's, cross-correlation coefficients, fuzzy partitioning functionals and the filtered back-projection 3D reconstruction method.

Three-dimensional reconstruction of the 70S Escherichia coli ribosome in ice: the distribution of ribosomal RNA

A reconstruction, at 40 A, of the Escherichia coli ribosome imaged by cryo-electron microscopy, obtained from 303 projections by a single-particle method of reconstruction, shows the two subunits with unprecedented clarity. In the interior of the subunits, a complex distribution of higher mass density is recognized, which is attributed to ribosomal RNA. The masses corresponding to the 16S and 23S components are linked in the region of the platform of the small subunit. Thus the topography of the rRNA regions responsible for protein synthesis can be described.

Three-dimensional reconstruction of native Androctonus australis hemocyanin

A sample of native 4 x 6-meric hemocyanin of Androctonus australis was negatively stained with the double-layer technique, and was observed by transmission electron microscopy under low-dose conditions with a 50 degree and 0 degree tilt. The three-dimensional reconstruction method from "Single-exposure, random conical tilt series" was then applied. Independent three-dimensional reconstructions were obtained from the top, side and 45 degree views. Despite a pronounced flattening effect, presumably due to the specimen preparation technique, the positions of the 24 subunits composing the oligomer were unequivocally determined. This experiment definitely solves the problem of the architectural organization of the subunits in the cheliceratan 4 x 6-meric hemocyanins. Moreover, distinction between the flip and flop faces and an attenuated rocking effect were observed.

Three-dimensional structure of the mammalian cytoplasmic ribosome

A three-dimensional reconstruction of the 80 S ribosome from rabbit reticulocytes has been calculated from low-dose electron micrographs of a negatively stained single-particle specimen. At 37 A resolution, the precise orientations of the 40 S and 60 S subunits within the monosome can be discerned. The translational domain centered on the upper portion of the subunit/subunit interface is quite open, allowing considerable space between the subunits for interactions with the non-ribosomal macromolecules involved in protein synthesis. Further, the cytosolic side of the monosome is strikingly more open than the membrane-attachment side, suggesting a greater ease of communication with the cytoplasm, which would facilitate the inwards and outwards diffusion of a number of ligands. Although the 60 S subunit portion of the 80 S structure shows essentially all of the major morphological features identified for the eubacterial 50 S large subunit, it appears to possess a region of additional mass that evidently accounts for the more ellipsoidal form of the eukaryotic subunit.

Classification of macromolecular assemblies studied as 'single particles'

In order to study proteins that do not occur in two- or three-dimensionally ordered form, one may take two different approaches: either search for conditions that induce the formation of crystals, and proceed with the established methods of X-ray or electron crystallography, or attempt to study the molecules in the form of single particles with the EM. Although many proteins have been successfully crystallized, and some general recipes for inducing ordered arrangement have been found (Mannella, 1984; Uzgiris & Kornberg, 1983), there exists a large number of proteins and protein assemblies that have resisted such attempts for a long time. Furthermore, there are macromolecular assemblies, associated with membranes and engaged in switching or gating, whose function is tied to their occurrence in isolated form, and hence are best studied without extraction from the membrane. For these reasons, the single-particle approach to the study of macromolecular structure (Franket al.1978, 1981; Radermacheret al.1987a, b; for recent reviews, see Franket al.1985, 1988e; Frank, 1989) has found numerous applications after initial technical and conceptual hurdles were overcome. Although atomic resolution cannot be achieved with this approach for a variety of reasons, a quantitative description of architecture on the quaternary level is nevertheless possible, as exemplified in the 3D studies of ribosomal particles (overviews, see Franket al.1988a) and, most recently, the junctional channel complex (Wagenknechtet al.1989a).

Three-dimensional reconstruction of the sevenfolded form of Bacillus subtilis Gro EL Chaperonin

Bacillus subtilis grown at 42 degrees C produces a major form of Gro EL-like chaperonin that has been analyzed by electron microscopy. Most of the views show a clear sevenfold symmetry when studied by rotational analysis. The particles were classified into defined families by multivariate analysis and supervised fuzzy-set classification methods, and those belonging to a sevenfold family were averaged to produce a two-dimensional representative projection. These selected particles were then used, when titled by 55 degrees in the microscope goniometer stage, as the starting projections for a three-dimensional reconstruction protocol based on the random conical tilt series method. The resulting reconstruction shows the Gro EL-like chaperonin from B. subtilis as a cylindrical body with seven well defined lobules arranged almost parallel to the longitudinal axis of the particle. There is a channel that is placed along this axis and appears fully open in both sides. The geometry of the channel is polar and presents differences in both faces of the particle.

Fuzzy sets-based classification of electron microscopy images of biological macromolecules with an application to ribosomal particles

Pattern recognition methods based on the theory of fuzzy sets are tested for their ability to classify electron microscopy images of biological specimens. The concept of fuzzy sets was chosen for its ability to represent classes of objects that are vaguely described from the measured data. A number of partitional clustering algorithms and an extensive set of cluster-validity functionals (some already reported and some newly developed) have been applied to a test-data set and to two real-data sets of images. One of the real-data sets corresponded to images of the Escherichia coli 50S ribosomal subunits depleted of proteins L7/L12 and the other set to images of the E. coli 70S monosome in the range of overlap views. These two latter sets had been previously studied by another clustering methodology. The new results obtained by the application of fuzzy clustering techniques will be compared to those previously obtained and some conclusions about the consistency of these classifications will be drawn from this comparison.

The application of the maximum entropy method to electron microscopic tomography

The maximum entropy method has been applied to single axis tilt electron microscopic tomography. Its application requires that the problem be correctly formulated and that the model for the noise in electron micrographs be developed. A suitable noise model was determined empirically. The maximum entropy method was applied to a reconstruction of a test object from projections to which noise had been added. These reconstructions were superior to those obtained by reciprocal space weighted back protection. The method was also robust towards the incorrect specification of the noise, the penalty being an increase in the time required for convergence rather than degradation of the quality of the reconstructed image. In the reconstruction of negatively stained chromatin fibres it was possible to obtain satisfactory images utilizing all the information in the projections, in contrast to conventional methods in which high resolution data are removed by the application of Fourier space filters.

Three-dimensional reconstruction of mammalian 40 S ribosomal subunit

The small (40 S) subunit from rabbit reticulocyte ribosomes has been reconstructed from electron micrographs of a negatively stained single-particle specimen to a resolution of 3.85 nm. The reconstruction reveals a morphology consisting of a broad wedge-shaped head structure set atop a quasi-cylindrical body. Distinctive features recognized in two-dimensional projections, such as the beak, back lobes, and feet, can now be localized in three dimensions. By reference to a recent reconstruction of the monomeric 80 S ribosome we can identify the interface and exterior surfaces of the subunit, thus enabling more detailed functional interpretations.

Electron microscope studies of human alpha 2-macroglobulin-chymotrypsin complex: demonstration that the two structures assigned to native and proteolyzed alpha 2-macroglobulin represent two views of the proteolyzed molecule

Electron microscope studies of native and protease-bound human alpha 2-macroglobulin have led to two contradictory models for these two structures. One viewpoint maintains that the native structure has the shape of )+(, which contracts on binding of the protease to the shape of ([). An opposing view proposes that the native structure has the shape of a padlock and that )+( and ([) are the side and end views of the proteolyzed molecule. In this investigation, electron microscope studies of the alpha-chymotrypsin-treated alpha 2-macroglobulin utilizing a tilt stage have shown that the two shapes [)+( and ([)] interconvert. This demonstrates that these two shapes represent the side and end views of the proteolyzed alpha 2-macroglobulin which are related by a 90 degree rotation of the prototype molecule.

Three-dimensional architecture of the calcium channel/foot structure of sarcoplasmic reticulum

The calcium channel responsible for the release of Ca2+ from the sarcoplasmic reticulum of skeletal muscle during excitation-contraction coupling has recently been identified and purified. The isolated calcium channel has been identified morphologically with the 'foot' structures which are associated with the junctional face membrane of the terminal cisternae of sarcoplasmic reticulum. In situ, the foot structure extends across the gap of the triad junction from the terminal cisternae of the reticulum to the transverse tubule. We describe here the three-dimensional architecture (3.7 nm resolution) of the calcium channel/foot structure from fast-twitch rabbit skeletal muscle, which we determined from electron micrographs of isolated, non-crystalline structures that had been tilted in the electron microscope. The reconstruction reveals two different faces and an internal structure in which stain accumulates at several interconnected locations, which could empty into the junctional gap of the triad junction. The detailed architecture of the channel complex is relevant to understanding both the physical path followed by calcium ions during excitation-contraction coupling and the association of the terminal cisternae and the transverse tubules in the triad junction.

Variations of the three-dimensional structure of the Escherichia coli ribosome in the range of overlap views. An application of the methods of multicone and local single-cone three-dimensional reconstruction

Electron microscopic techniques are among the most important tools for obtaining structural information of biological specimens. However, the three-dimensional (3D) structural analysis of asymmetrical specimens that do not form crystalline sheets has traditionally presented serious methodological obstacles to its accomplishment. One of the fundamental questions to be addressed in this type of structural study is in what way, and to what degree, does the 3D structural conformation depend on the orientation of the specimen with respect to the electron microscopic support films. As a step in studying this problem, we have analyzed the variations of the 3D structure of the Escherichia coli 70S monosome by performing four different 3D reconstructions of the 70S monosome from subsets of images in the so-called overlap range of views. These subsets were selected according to a multivariate statistical analysis performed on the total population of overlap-range specimen images. A certain amount of structural variability exists among the 3D reconstructions, although many of the main morphological characteristics, as the relative orientation between the ribosomal subunits, remain unchanged. We have also generalized the random conical reconstruction technique (Radermacher, M., T. Wagenknecht, A. Verschoor, and J. Frank. 1987. J. Microsc. 146: 113-136) to include those cases where the specimen exhibits a rocking behavior with respect to the support. The resulting Multicone Reconstruction Technique has been applied to computer-generated images as well as the E. coli 70S monosome images from part of the overlap range of views.

Three-dimensional reconstruction of the ribosome from Escherichia coli

Three-dimensional image reconstruction has been applied to electron micrographs of noncrystalline, negatively stained ribosomes obtained from Escherichia coli. Several independent reconstructions all show an overall appearance resembling models that had been derived earlier by direct visual interpretation of electron micrographs. The reconstructed ribosomes show numerous structural details not recognized previously, some of which may be functionally significant. A large elongate cavity (approximately 8-nm long x 5-nm wide x 6-nm [maximal] deep) is present on the surface of the ribosome near the base of its stalk and is identifiable as a portion of a feature termed the interface canyon, which was detected in prior reconstructions of the large ribosomal subunit (Radermacher, M., T. Wagenknecht, A. Verschoor, and J. Frank. 1987. EMBO (Eur. Mol. Biol. Organ.) J. 6:1107-1114). On the back of the ribosome, near the base of the central protuberance, is a hole leading to the interface canyon, which likely represents an exit site for the elongating polypeptide produced during protein biosynthesis. The exposed portion of the interface canyon appears well suited to bind two tRNA molecules in a configuration that is consistent with biochemical and structural data on the mechanism of peptide bond biosynthesis.

Image analysis of single macromolecules

A battery of sophisticated techniques is now available to extract three-dimensional structural information from electron micrographs of biological macromolecules occurring in the form of single particles. One of these techniques, the random-conical reconstruction method, which allows low-dose imaging, has been recently perfected and is being used routinely for the study of ribosomal architecture. The analysis of the 40S mammalian ribosomal subunit serves as an illustration of the various steps of image processing. The use of classification combined with 3-D reconstruction provides the means to investigate variations of the macromolecular structure (deformations, conformational changes, etc.) that are caused by the specimen preparation. An example is provided by the changes in the shape of the 70S monosome of E. coli as it changes its orientation on the carbon grid. The most challenging applications of the techniques discussed are in the area of cryo-microscopy of ice-embedded specimens. First studies of single macromolecules imaged in this way have indicated that the 3-D imaging methods and, specifically, the random-conical reconstruction method, will be applicable under these conditions.

Direct localization of the tRNA--anticodon interaction site on the Escherichia coli 30 S ribosomal subunit by electron microscopy and computerized image averaging

Previous immunoelectron microscopy studies have shown that the anticodon of valyl-tRNA, photocrosslinked to the ribosomal P site at the C1400 residue of the 16 S RNA, is located in the vicinity of the cleft of the small ribosomal subunit of Escherichia coli. In this study we used single-particle image-averaging techniques to demonstrate that the 30 S-bound tRNA molecule can be localized directly, without the need for specific antibody markers. In agreement with the immunoelectron microscopy results, we find that the tRNA molecule appears to be located deep in the cleft of the 30 S subunit. We believe that the use of computer image averaging to localize ligands bound to ribosomes and other macromolecular complexes will become widespread because of the superior sensitivity, precision and objectivity of this technique compared with conventional immunoelectron microscopy.

Three-dimensional reconstruction of single particles from random and nonrandom tilt series

To overcome the radiation damage-induced limitations to the resolution of three-dimensional reconstructions from electron microscopic tilt series, novel reconstruction schemes have been developed that require only a single exposure of the specimen. The tilt series collected with these methods have random projection directions. First, three-dimensional reconstruction techniques are described that are applicable to data obtained from tilt series with regular tilt geometry, followed by the extensions of these techniques to permit analysis of projection series with randomly spaced tilts. The main emphasis is placed on the weighted back-projection methods, which have recently been extended so as to be applicable to random tilt series. Besides a description of the algorithms, the complete procedure for a three-dimensional reconstruction from a single-exposure, random conical tilt series is explained, including the determination of the azimuthal angles, the alignment scheme for conical tilt series, the dependence of the achievable resolution on the number of projections for regular conical and single-axis geometries, and the method to calculate the actual resolution of two-dimensional image averages and of three-dimensional reconstructions using the phase residual and Fourier ring correlation criteria. Examples are given of biological specimens to which these three-dimensional reconstruction methods have been applied.

Three-dimensional structure of 50 S Escherichia coli ribosomal subunits depleted of proteins L7/L12

A structural study of Escherichia coli 50 S ribosomal subunits depleted selectively of proteins L7/L12 and visualized by low-dose electron microscopy has been carried out by multivariate statistical analysis, classification schemes and the new reconstruction technique from single-exposure, random-conical tilt series. This approach has allowed us to solve the three-dimensional structure of the depleted 50 S subunits at a resolution of 3 nm-1. In addition, two distinct morphological populations of subunits (cores) have been identified in the electron micrographs analyzed and have been separately studied in three dimensions. Depleted subunits in the two morphological states present as main features common to these two structures but different from those of the non-depleted subunit (1) the absence of the stalk, (2) a rearrangement of the stalk-base that changes the overall structure of this region. This morphological change is quite noticeable and important, since this region is mapped as a part of the GTPase center. The two conformations differ mainly in the orientation of the area between the L1 region and the head (the probable localization of the peptidyl transferase center) and in the accessibility of the region located below the head. A possible relationship of these structural changes to the functional dynamics of the ribosome is suggested.

Classification of images of biomolecular assemblies: a study of ribosomes and ribosomal subunits of Escherichia coli

Images of macromolecules obtained in the electron microscope are subjected to correspondence analysis. The structure inherent in the data in the resulting low-dimensional factor space is characterized by a mixed classification method which combines the dynamic clouds clustering technique with hierarchical ascendant classification (HAC). For our data, the rejection of marginal clusters obtained by dynamic clouds clustering appears as a crucial prerequisite for a stable performance of HAC. The method is applied to two sets of 204 and 177 images that show the 70S ribosome of Escherichia coli, in the range of overlap views as defined by A. Verschoor and co-workers, and to two sets of 480 and 496 images of the 50S subunit of E. coli depleted of L7/L12 proteins in the well-defined crown view. Reproducible classes are obtained, which are characterized by images reconstituted from factorial coordinates. These classes appear to be related to different orientations on the specimen grid (in the case of the 70S particle) and to different conformational states (50S subunit).

Electron microscopy and computer image averaging of ice-embedded large ribosomal subunits from Escherichia coli

Electron micrographs of frozen-hydrated, large ribosomal subunits from Escherichia coli have been analyzed by computer image processing. Images of subunits in the so-called "crown" orientation were analyzed by correlation alignment procedures developed for negatively stained specimens. Averages of the aligned images showed both similarities and differences to averages determined for negatively stained specimens. The L1 ridge is more dense and stalk-like in frozen-hydrated as compared with negatively stained subunits, possibly because it is associated with ribosomal RNA. The results show that it should be feasible to determine the three-dimensional structure of the large ribosomal subunit from micrographs of individual, frozen-hydrated subunits that have been tilted in the electron microscope.

Three-dimensional matching of macromolecular structures obtained from electron microscopy: an application to the 70S and 50S E. coli ribosomal particles

In this work we present a general computational method capable of finding the relative orientation of two structures represented by samples on a three-dimensional grid. It is shown that the three-dimensional shift and the three independent rotations necessary for the correct relative spatial placement of the two volumes can be obtained either from the auto-correlation function of the volumes or from a direct cross-correlation, depending on the specific problem to be solved. This method has been applied to the problem of fitting the 50S ribosomal subunit into the 70S monosome from E. coli, structures that were available as three-dimensional reconstructions from electron microscopical data.