Remarks on the Statistical Significance of Cross- Correlation Functions

It is shown that the theory of the statistical significance of crosscorrelation functions can be based on different approximations. The validity range of these approximations is discussed.

Influence of Electron Noise on Three-dimensional Image Reconstruction

A three-dimensional reconstruction requires the same integral dose as a conventional two-dimensional micrograph provided that the level of significance and the resolution are identical. The necessary dose D for one of the K projections in a reconstruction series is, therefore, the integral dose divided by K.

Marker-free image registration of electron tomography tilt-series

Background

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

Results

In this paper we introduce an algorithm to find regions of the tilt series which can be tracked within a subseries of the tilt series. These regions act as landmarks allowing the determination of the alignment parameters. We show our results with synthetic data as well as experimental cryo electron tomography.

Conclusion

Our algorithm is able to correctly align a single-tilt tomographic series without the help of fiducial markers thanks to the detection of thousands of small image patches that can be tracked over a short number of images in the series.

Aberration-corrected microscopy for structural biology applications

This study explores the potential of a C(s)-corrected transmission electron microscope for structural studies of biological samples, in particular isolated macromolecular complexes. A 300-kV transmission electron microscope, equipped with a C(s) corrector was employed to record sets of images at different defocus and C(s) settings. The experiments were designed to determine whether imaging with large defocus benefits from C(s) correction. Defocus contrast in biological imaging has a stronger influence on image resolution than any other parameter. We find the results are in good agreement with theoretical framework, verifying that the typical imaging conditions required for biological investigations are not affected by C(s) correction.

Fast 3D motif search of EM density maps using a locally normalized cross-correlation function

Three-dimensional motif search is becoming increasingly important both in the search for molecular signatures within a tomographic reconstruction, at low resolution, and in the search for atomic structures within high-resolution cryo-EM maps of macromolecular complexes. The present work describes the implementation of a fast local correlation algorithm suitable for template matching in the SPIDER environment. Two examples are given, one in each of the areas of application: (i). within a 7.8A single-particle reconstruction of the Escherichia coli ribosome, four proteins and one RNA structure were located with high accuracy; (ii). within a cryo-tomogram of sarcoplasmic reticulum vesicles, ryanodine receptors were located in positions that agreed with expert knowledge.

Noise reduction in electron tomographic reconstructions using nonlinear anisotropic diffusion

Electron tomography is a powerful technique capable of giving unique insights into the three-dimensional structural organization of pleomorphic biological objects. However, visualization and interpretation of the resulting volumetric data are hampered by an extremely low signal-to-noise ratio, especially when ice-embedded biological specimens are investigated. Usually, isosurface representation or volume rendering of such data is hindered without any further signal enhancement. We propose a novel technique for noise reduction based on nonlinear anisotropic diffusion. The approach combines efficient noise reduction with excellent signal preservation and is clearly superior to conventional methods (e.g., low-pass and median filtering) and invariant wavelet transform filtering. The gain in the signal-to-noise ratio is verified and demonstrated by means of Fourier shell correlation. Improved visualization performance after processing the 3D images is demonstrated with two examples, tomographic reconstructions of chromatin and of a mitochondrion. Parameter settings and discretization stencils are presented in detail.

Wavelet transform filtering and nonlinear anisotropic diffusion assessed for signal reconstruction performance on multidimensional biomedical data

Computer tomography (CT) techniques are the most widely applicable noninvasive methods for obtaining two- and three-dimensional insights into biological objects. They comprise CT for medical applications, as well as electron tomography used for investigating macromolecular and cellular specimens. Recent advances in the recording schemes improve the speed and resolution frontiers and provide new insights into structural organizations of different objects. However, many data sets suffer from a poor signal-to-noise ratio, which severely hinders the application of methods for automated data analysis, such as feature extraction, segmentation, and visualization. We propose the multidimensional implementation of two powerful signal reconstruction techniques, namely invariant wavelet filtering and nonlinear anisotropic diffusion. We establish quantitative measures to assess the signal reconstruction performance on synthetic data and biomedical images. The appropriate multidimensional implementations of wavelet and diffusion techniques allow for a superior performance over conventional noise-reduction methods. We derive the conditions for the choice between wavelet and diffusion techniques with respect to an optimal signal reconstruction performance. Results of applying the proposed methods in two very different imaging domains-molecular biology and clinical research-are provided.

Toward detecting and identifying macromolecules in a cellular context: template matching applied to electron tomograms

Electron tomography is the only technique available that allows us to visualize the three-dimensional structure of unfixed and unstained cells currently with a resolution of 6-8 nm, but with the prospect to reach 2-4 nm. This raises the possibility of detecting and identifying specific macromolecular complexes within their cellular context by virtue of their structural signature. Templates derived from the high-resolution structure of the molecule under scrutiny are used to search the reconstructed volume. Here we outline and test a computationally feasible two-step procedure: In a first step, mean-curvature motion is used for segmentation, yielding subvolumes that contain with a high probability macromolecules in the expected size range. Subsequently, the particles contained in the subvolumes are identified by cross-correlation, using a set of three-dimensional templates. With simulated and real tomographic data we demonstrate that such an approach is feasible and we explore the detection limits. Even structurally similar particles, such as the thermosome, GroEL, and the 20S proteasome can be identified with high fidelity. This opens up exciting prospects for mapping the territorial distribution of macromolecules and for analyzing molecular interactions in situ.

Electron microscopy and subunit-subunit interaction studies reveal a first architecture of COP9 signalosome

The COP9 signalosome is involved in signal transduction, whereas the 26 S proteasome lid is a regulatory subcomplex of the 26 S proteasome responsible for degradation of ubiquitinated proteins. COP9 signalosome and lid possess significant sequence homologies among their eight core subunits and are likely derived from a common ancestor. Surprisingly, from our two-dimensional electron microscopy data, a common architectural plan for the two complexes could not be deduced. None-the-less, the two particles have structural features in common. Both COP9 signalosome and lid lack any symmetry in subunit arrangement and exhibit a central groove, possibly qualified for scaffolding functions.Filter-binding assays with recombinant COP9 signalosome components revealed a multitude of subunit-subunit interactions, supporting the asymmetrical appearance of the complex in electron microscopy. On the basis of two-dimensional images and subunit interaction studies, a first architectural model of COP9 signalosome was created. The fact that four distinct classes of particle views were identified and that only 50 % of the selected particles could be classified indicates a high degree of heterogeneity in electron microscopic images. Different orientations with respect to the viewing axis and conformational variety, presumably due to different grades of phosphorylation, are possible reasons for the heterogeneous appearance of the complex. Our biochemical data show that recombinant COP9 signalosome subunits 2 and 7 are phosphorylated by the associated kinase activity. The modification of COP9 signalosome subunit 2 might be essential for c-Jun phosphorylation. Dephosphorylation does not inactivate the associated kinase activity. Although substrate phosphorylation by COP9 signalosome is significantly decreased by lambda protein phosphatase treatment, "autophosphorylation" is increased.

ATPase cycle controls the conformation of an archaeal chaperonin as visualized by cryo-electron microscopy

Chaperonins are double-ring protein folding machines fueled by ATP binding and hydrolysis. Conformational rearrangements upon ATPase cycling of the group I chaperonins, typified by the Escherichia coli GroEL/GroES system, have been thoroughly investigated by cryo-electron microscopy and X-ray crystallography. For archaeal group II chaperonins, however, these methods have so far failed to provide a correlation between the structural and the functional states. Here, we show that the conformation of the native alphabeta-thermosome of Thermoplasma acidophilum in vitrified ice is strictly regulated by adenine nucleotides.

The TOM core complex: the general protein import pore of the outer membrane of mitochondria

Translocation of nuclear-encoded preproteins across the outer membrane of mitochondria is mediated by the multicomponent transmembrane TOM complex. We have isolated the TOM core complex of Neurospora crassa by removing the receptors Tom70 and Tom20 from the isolated TOM holo complex by treatment with the detergent dodecyl maltoside. It consists of Tom40, Tom22, and the small Tom components, Tom6 and Tom7. This core complex was also purified directly from mitochondria after solubilization with dodecyl maltoside. The TOM core complex has the characteristics of the general insertion pore; it contains high-conductance channels and binds preprotein in a targeting sequence-dependent manner. It forms a double ring structure that, in contrast to the holo complex, lacks the third density seen in the latter particles. Three-dimensional reconstruction by electron tomography exhibits two open pores traversing the complex with a diameter of approximately 2.1 nm and a height of approximately 7 nm. Tom40 is the key structural element of the TOM core complex.

Structure of VAT, a CDC48/p97 ATPase homologue from the archaeon Thermoplasma acidophilum as studied by electron tomography

Valosine-containing protein-like ATPase from Thermoplasma acidophilum is a member of the superfamily of ATPases associated with a diversity of cellular activities and is closely related to CDC48 from yeast and p97 from higher eukaryotes and more distantly to N-ethylmaleimide-sensitive fusion protein. We have used electron tomography to obtain low-resolution (2-2.5 nm) three-dimensional maps of both the whole 500 kDa complex and the N-terminally truncated valosine-containing protein-like ATPase from T. acidophilum complex lacking the putative substrate binding domain.

Perspectives of molecular and cellular electron tomography

After a general introduction to three-dimensional electron microscopy and particularly to electron tomography (ET), the perspectives of applying ET to native (frozen-hydrated) cellular structures are discussed. In ET, a set of 2-D images of an object is recorded at different viewing directions and is then used for calculating a 3-D image. ET at a resolution of 2-5 nm would allow the 3-D organization of structural cellular components to be studied and would provide important information about spatial relationships and interactions. The question of whether it is a realistic long-term goal to visualize or--by sophisticated pattern recognition methods--identify macromolecules in cells frozen in toto or in frozen sections of cells is addressed. Because of the radiation sensitivity of biological specimens, a prerequisite of application of ET is the automation of the imaging process. Technical aspects of automated ET as realized in Martinsried and experiences are presented, and limitations of the technique are identified, both theoretically and experimentally. Possible improvements of instrumentation to overcome at least part of the limitations are discussed in some detail. Those means include increasing the accelerating voltage into the intermediate voltage range (300 to 500 kV), energy filtering, the use of a field emission gun, and a liquid-helium-cooled specimen stage. Two additional sections deal with ET of isolated macromolecules and of macromolecular structures in situ, and one section is devoted to possible methods for the detection of structures in volume data.

Denoising of electron tomographic reconstructions using multiscale transformations

The visualization of volume maps obtained by electron tomographic reconstruction is severely hampered by noise. As electron tomography is usually applied to individual, nonrepeatable structures, e.g., cell sections or cell organelles, the noise cannot be removed by averaging as is done implicitly in electron crystallography or explicitly in single particle analysis. In this paper, an approach for noise reduction is presented, based on a multiscale transformation, e.g., the wavelet transformation, in conjunction with a nonlinear filtration of the transform coefficients. After a brief introduction to the theoretical background, the effect of this type of noise reduction is demonstrated by test calculations as well as by applications to tomographic reconstructions of ice-embedded specimens. Regarding noise reduction and structure preservation, the method turns out to be superior to conventional filter techniques, such as the median filter or the Wiener filter. Results obtained with the use of different types of multiscale transformations are compared and the choice of suitable filter parameters is discussed.

Electron Tomography of Single Ice-Embedded Macromolecules: Three-Dimensional Alignment and Classification

From 3-D reconstructions of automatically recorded tilt series of ice-embedded macromolecules, several hundred 3-D images of single particles can be extracted. Here we describe correlation-based techniques to align the particles with respect to translation and orientation in 3-D and the calculation of an averaged reconstruction after application of the correct weighting function to the particle projections. Multivariate statistical analysis and classification are applied to the set of three-dimensionally reconstructed particles to investigate interimage variations on the 3-D level. Copyright 1997 Academic Press. Copyright 1997 Academic Press

Tricorn protease--the core of a modular proteolytic system

Large macromolecular assemblies have evolved as a means of compartmentalizing reactions in organisms lacking membrane-bounded compartments. A tricorn-shaped protease was isolated from the archaeon Thermoplasma and was shown to form a multisubunit proteolytic complex. The 120-kilodalton monomer assembled to form a hexameric toroid that could assemble further into a capsid structure. Tricorn protease appeared to act as the core of a proteolytic system; when it interacted with several smaller proteins, it displayed multicatalytic activities.

The EM Program Package: A Platform for Image Processing in Biological Electron Microscopy

EM is a software package developed for image processing in the field of biological electron microscopy. After a brief summary of its history, an outline of the package is given, by describing some characteristic features rather than by a complete report of all facilities. New developments, connected with the introduction of a UNIX version and the advent of automated electron microscopy, are described in more detail.

Structural studies on the 2.25-MDa homomultimeric phosphoenolpyruvate synthase from Staphylothermus marinus

The phosphoenolpyruvate synthase of the hyperthermophilic archaeon Staphylothermus marinus forms an unusually large homomultimeric complex of 93 kDa subunits. Electron image analysis of negatively stained and low-dose unstained preparations showed that the complex has a single, stable characteristic view and a well-preserved core with threefold rotational symmetry. The periphery of the assembly is composed of a nebulous, possibly flexible, component. Mass measurements by scanning transmission electron microscopy yielded a molecular weight of 2250 +/- 230 kDa, confirming the well-defined nature of the structure and indicating that it is composed of 24 +/- 2.5 subunits. The stability and symmetry of the characteristic projection views suggest a polyhedral three-dimensional architecture. The novel quaternary arrangement of this enzyme might be a consequence of its adaptation to an extreme environment.

Functional significance of symmetrical versus asymmetrical GroEL-GroES chaperonin complexes

The Escherichia coli chaperonin GroEL and its regulator GroES are thought to mediate adenosine triphosphate-dependent protein folding as an asymmetrical complex, with substrate protein bound within the GroEL cylinder. In contrast, a symmetrical complex formed between one GroEL and two GroES oligomers, with substrate protein binding to the outer surface of GroEL, was recently proposed to be the functional chaperonin unit. Electron microscopic and biochemical analyses have now shown that unphysiologically high magnesium concentrations and increased pH are required to assemble symmetrical complexes, the formation of which precludes the association of unfolded polypeptide. Thus, the functional significance of GroEL:(GroES)2 particles remains to be demonstrated.

Three-dimensional structure of lipid vesicles embedded in vitreous ice and investigated by automated electron tomography

Automated electron tomography is shown to be a suitable means to visualize the shape of phospholipid vesicles embedded in vitrified ice. With a slow-scan charge-coupled device camera as a recording device, the cumulative electron dose needed to record a data set of 60 projections at a magnification of 20,000X can be kept as low as 15 e-/A2 (or 1500 electrons/nm2). The membrane of the three-dimensionally reconstructed vesicles is clearly visible in two-dimensional sections through the three-dimensionally reconstructed volume. Some edges indicating a polygonal shape of the vesicles, frozen from the gel phase, are also clearly recognized. Because of the presently limited tilt angle range (+/- 60 degrees), the upper and lower "caps" of the vesicles (representing about 35% of the surface of the ellipsoidal particles) remain invisible in the three-dimensional reconstruction.

The molecular chaperone TF55. Assessment of symmetry

TF55-like factor from Sulfolobus solfataricus was purified to homogeneity and analyzed by electron microscopy and image analysis to determine the symmetries of these particles. Three different procedures were used to analyze the electron micrographs: (1) fuzzy-set based classification of the particles according to their rotational power spectra; (2) multivariate statistical analysis based on singular value decomposition; (3) circular harmonic analysis. Averages obtained from the three methods show unequivocally that the TF55-like complex presents a 9-fold symmetry.

Atomic force microscopy produces faithful high-resolution images of protein surfaces in an aqueous environment

The atomic force microscope has the potential to monitor structural changes of a biological system in its native environment. To correlate them with the biological function at a molecular level, high lateral and vertical resolution are required. Here we demonstrate that the atomic force microscope is capable of imaging the surface of the hexagonally packed intermediate layer of Deinococcus radiodurans in buffer solution with a lateral resolution of 1 nm and a vertical resolution of 0.1 nm. On average, these topographs differ from those determined by electron microscopy by <0.5 nm.

Subunit stoichiometry and three-dimensional arrangement in proteasomes from Thermoplasma acidophilum

The proteasome or multicatalytic proteinase from the archaebacterium Thermoplasma acidophilum is a 700 kDa multisubunit protein complex. Unlike proteasomes from eukaryotic cells which are composed of 10-20 different subunits, the Thermoplasma proteasome is made of only two types of subunit, alpha and beta, which have molecular weights of 25.8 and 22.3 kDa, respectively. In this communication we present a three-dimensional stoichiometric model of the archaebacterial proteasome deduced from electron microscopic investigations. The techniques which we have used include image analysis of negatively stained single particles, image analysis of metal decorated small three-dimensional crystals after freeze-etching and STEM mass measurements of freeze-dried particles. The archaebacterial and eukaryotic proteasomes are almost identical in size and shape; the subunits are arranged in four rings which are stacked together such that they collectively form a barrel-shaped complex. According to a previous immunoelectron microscopic investigation, the alpha-subunits form the two outer rings of the stack, while the two rings composed of beta-subunits, which are supposed to carry the active sites, are sandwiched between them. Each of the alpha- and beta-rings contains seven subunits; hence the stoichiometry of the whole proteasome is alpha 14 beta 14 and the symmetry is 7-fold. Image simulation experiments indicate that the alpha- and beta-subunits are not in register along the cylinder axis; rather it appears that the beta-rings are rotated with respect to the alpha-rings by approximately 25 degrees. In contrast to some previous reports we have not been able to find stoichiometric amounts of RNA associated with highly purified proteolytically active proteasome preparations.

The three-dimensional structure of proteasomes from Thermoplasma acidophilum as determined by electron microscopy using random conical tilting

The three-dimensional structure of proteasomes from the archaebacterium Thermoplasma acidophilum has been determined to a resolution of approximately 2 nm from electron micrographs of negatively stained preparations using the method of 'random conical tilting'. The particles turn out to be essentially cylinder-shaped barrels, 15 nm long and 11 nm wide, enclosing a tripartite inner compartiment. An account is given of some of the present limitations which prevent to attain a higher resolution and possible ways to overcome these limitations are indicated.

The multicatalytic proteinase (prosome) is ubiquitous from eukaryotes to archaebacteria

From the thermoacidophilic archaebacterium, Thermoplasma acidophilum, a proteolytically active particle has been isolated which is almost identical in size and shape with the multicatalytic proteinase (prosome) from rat. This result indicates that prosomes have been developed early in evolution and that they possibly serve functions common to all living cells.

Electron microscopy and image analysis of the multicatalytic proteinase

One electron micrographs, negatively stained multicatalytic proteinase molecules are viewed end-on (ring shaped) or side-on (rectangular shaped). For aurothioglucose, ammonium molybdate- and phosphotungstate-stained molecules, the dimensions measured are consistent. In contrast, uranyl acetate-staining reveals ring-shaped particles which vary in diameter between 12 and 16 nm. This is due to a partial collapse and substantial flattening of the structure. Digital image analysis of side-on views of the particles reveals a tripartite, reel-shaped structure. Within the ring-like, end-on projections of ammonium molybdate-stained molecules six local centres of mass can be discerned; their position appears to depart, however, from a true six-fold symmetry.

Correlation averaging of a badly distorted lattice: the surface protein of Pyrodictium occultum

The surface protein of the archaebacterium Pyrodictium occultum forms two-dimensional periodic arrays of extremely poor order. Two variants of correlation averaging have been applied in order to retrieve the unit cell structure from electron micrographs of negatively stained samples: straightforward correlation averaging correcting for lateral displacements only and a more elaborate approach, including a partial compensation for rotational disorder. Surprisingly, both routes yield virtually identical structures. Inclusion of molecular motifs from highly disordered domains, which are rejected in the "straightforward" approach, appears not to improve resolution, possibly because the high local strain tends to distort the individual molecules.

Three-dimensional structure of the regular surface layer (HPI layer) of Deinococcus radiodurans

The low-resolution structure of the regular surface layer of Deinococcus radiodurans has been determined from negatively stained specimens by three-dimensional electron microscopy. The layer has P6 symmetry, a lattice constant of 18 nm and a thickness of 6.5 nm. Three-dimensional reconstruction was performed by a hybrid real space/Fourier space approach that incorporates partial compensation of lattice distortions: The model obtained is discussed in the light of independent information about the surface structure of this layer, derived from metal shadowing and surface relief reconstruction. While agreement is quite satisfactory for the apparently more rigid inner surface, the outer surface shows severe flattening effects. The structure of the HPI layer is compared with other bacterial surface layers using a classification scheme that is outlined in the Appendix.

Structure of two-dimensional crystals of membrane-bound Na,K-ATPase as analyzed by correlation averaging

The structure of two-dimensional crystals of membrane-bound Na,K-ATPase from rabbit kidney has been analyzed with a correlation averaging procedure. Two principally different crystal forms are observed with p1 and p21 symmetry, respectively. In the p1 form the averaged projection structure shows a triangular shaped protein domain interpreted as a protomer (alpha beta-unit) of Na,K-ATPase. In the p21-form the stain-deficient area is extended toward a twofold symmetry axis. The results are in good agreement with a previous analysis where Fourier methods were applied to well ordered crystals of pig kidney Na,K-ATPase and illustrate that the correlation averaging procedure can be used for the analysis of membrane crystals of Na,K-ATPase showing curved lattice lines.

Three-dimensional reconstruction and averaging of 30 S ribosomal subunits of Escherichia coli from electron micrographs

From the micrographs of a tilt series, several particles of negatively stained 30 S ribosomal subunits of Escherichia coli were three-dimensionally reconstructed. Three of them showing similar orientation with respect to the supporting foil were averaged after alignment by newly developed three-dimensional correlation methods. As a main result we found a stained channel-like structure inside the particle. We tentatively propose that this corresponds, at least partially, to positively stained segments of the 16 S RNA.

The "EM" program system

"EM" is a computer program system concerned with the processing of electron micrographs. It provides facilities for two- and three-dimensional image reconstruction, correlation, filtering, etc. as well as for storage and display of image data. A description of the scientific aims, the system design, and the possibilities to display pictures is given. The handling of the command language is illustrated by some examples.