Automatic 3D alignment of projection images of randomly oriented objects

Unit quaternion description of spatial rotations in 3D electron cryo-microscopy

Electron cryo-microscopy (cryoEM) involves the estimation of spatial rotations, or saying orientations, of projection images or three-dimensional (3D) volumes. Euler angle system is widely used to describe spatial rotations in most cryoEM algorithms and software. In this review, we introduce unit quaternion as an alternate to Euler angles for describing spatial rotations, customize and develop corresponding tools for increasing demands of statistical analysis of spatial rotations in cryoEM. Some basic properties and definitions of quaternion are first recalled. Thereafter, distance and geodesic between rotations are introduced to aid comparisons and interpolations between rotations, which are prerequisites of statistics of rotations in 3D cryoEM. Furthermore, statistics of rotations are reviewed. Techniques potentially useful in cryoEM, such as calculations of the average rotation, generation of quasi-regular grids, sampling, inference with uniform distribution and angular central Gaussian (ACG) distribution, and estimation of rotation precision, are reviewed and developed. Finally, molecular symmetry presented in unit quaternion form is discussed. Unit quaternion system is shown as a convenient and comprehensive mathematical tool for cryoEM.

The structure of Escherichia coli signal recognition particle revealed by scanning transmission electron microscopy

Structural studies on various domains of the ribonucleoprotein signal recognition particle (SRP) have not converged on a single complete structure of bacterial SRP consistent with the biochemistry of the particle. We obtained a three-dimensional structure for Escherichia coli SRP by cryoscanning transmission electron microscopy and mapped the internal RNA by electron spectroscopic imaging. Crystallographic data were fit into the SRP reconstruction, and although the resulting model differed from previous models, they could be rationalized by movement through an interdomain linker of Ffh, the protein component of SRP. Fluorescence resonance energy transfer experiments determined interdomain distances that were consistent with our model of SRP. Docking our model onto the bacterial ribosome suggests a mechanism for signal recognition involving interdomain movement of Ffh into and out of the nascent chain exit site and suggests how SRP could interact and/or compete with the ribosome-bound chaperone, trigger factor, for a nascent chain during translation.

3D reconstruction of the Mu transposase and the Type 1 transpososome: a structural framework for Mu DNA transposition

Mu DNA transposition proceeds through a series of higher-order nucleoprotein complexes called transpososomes. The structural core of the transpososome is a tetramer of the transposase, Mu A, bound to the two transposon ends. High-resolution structural analysis of the intact transposase and the transpososome has not been successful to date. Here we report the structure of Mu A at 16-angstroms and the Type 1 transpososome at 34-angstroms resolution, by 3D reconstruction of images obtained by scanning transmission electron microscopy (STEM) at cryo-temperatures. Electron spectroscopic imaging (ESI) of the DNA-phosphorus was performed in conjunction with the structural investigation to derive the path of the DNA through the transpososome and to define the DNA-binding surface in the transposase. Our model of the transpososome fits well with the accumulated biochemical literature for this intricate transposition system, and lays a structural foundation for biochemical function, including catalysis in trans and the complex circuit of macromolecular interactions underlying Mu DNA transposition.

Quaternary organization of the Staphylothermus marinus phosphoenolpyruvate synthase: angular reconstitution from cryoelectron micrographs with molecular modeling

Digital electron images of frozen-hydrated preparations of the 2.25-MDa Staphylothermus marinus phosphoenolpyruvate synthase (EC 2.7.9.2) have been analyzed by single-particle classification and averaging and iterative quaternion-based angular reconstitution. Contrast transfer function correction of micrographs obtained at different defocus values was used to improve the informational quality of the projection averages. Three-dimensional reconstructions were obtained to roughly 3-nm spatial resolution, in which the 24 identical subunits were arranged to form an octahedral complex, although the amino-terminal nucleotide-binding domain was not resolved. An atomic model of the subunit was generated by homology modeling using as the reference the known X-ray crystallographic structure of the related enzyme pyruvate orthophosphate dikinase (EC 2.7.9.1) from Clostridium symbiosum (Protein Data Bank entry 1DIK). The S. marinus protein could be arranged into an assembly of 12 homodimers to match the three-dimensional reconstruction in terms of shape and size of the homodimers, as well as overall shape and size of the complex. The quaternary model indicated that active sites of three monomers were localized around cavities (or putative channels) centered at the threefold axes of rotational symmetry and that carboxyl-terminal alpha-helical segments of four monomers were localized at the fourfold axes of rotational symmetry where they could facilitate interdimer interaction. The quaternary arrangement also indicated numerous potential hydrophobic and electrostatic interactions at the interdimer interfaces that could contribute further to structural stability.

Angular reconstitution of the Staphylothermus marinus phosphoenolpyruvate synthase

The processes of single particle electron crystallography and three-dimensional angular reconstitution are applied to digital cryoelectron images of a macromolecular complex, the Staphylothermus marinus phosphoenolpyruvate synthase. In particular, the application of IQAD (iterative quaternionic angular determination) is exemplified in the context of more canonical approaches.

Cryoelectron microscopy of protein-lipid complexes of human myelin basic protein charge isomers differing in degree of citrullination

Myelin basic protein (MBP) is considered to be essential for the maintenance of stability of the myelin sheath. Reduction in cationicity of MBP, especially due to conversion of positively charged arginine residues to uncharged citrulline (Cit), has been found to be associated with multiple sclerosis (MS). Here, the interactions of an anionic phosphatidylserine/monosialoganglioside-G(M1) (4:1, w:w) lipid monolayer with 18.5-kDa MBP preparations from age-matched adult humans without MS (no Cit residues), with chronic MS (6 Cit), and with acute Marburg-type MS (18 Cit) were studied by transmission and ultralow dose scanning transmission electron microscopy under cryogenic conditions. Immunogold labeling and single particle electron crystallography were used to define the nature of the complexes visualized. These electron microscopical analyses showed that the three different MBP charge isomers all formed uniformly sized and regularly shaped protein-lipid complexes with G(M1), probably as hexamers, but exhibited differential association with and organization of the lipid. The least cationic Marburg MBP-Cit(18) formed the most open protein-lipid complex. The data show a disturbance in lipid-MBP interactions at the ultrastructural level that is related to degree of citrullination, and which may be involved in myelin degeneration in multiple sclerosis.

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

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

Marburg's variant of multiple sclerosis correlates with a less compact structure of myelin basic protein

Multiple sclerosis (MS) is an autoimmune disease in which the myelin sheath of the central nervous system is degraded, and the 18.5 kDa isoform of myelin basic protein (MBP) is reduced in cationicity. In a unique case of acute, fulminating MS (Marburg's variant), MBP is considerably less cationic than MBP from both normal, and chronic MS-afflicted individuals. This electron microscopical study has identified that, in vitro, the less cationic Marburg MBP isomer forms a more extended protein-lipid complex than MBP from healthy or chronic MS-afflicted individuals. This correlation implies that chemical modifications to MBP in vivo contribute directly to the structural instability of myelin, and subsequent autoantigenic presentation of this protein, observed in vivo in MS.

High resolution microanalysis and three-dimensional nucleosome structure associated with transcribing chromatin

The nucleosome is the ubiquitous and fundamental DNA-protein complex of the eukaryotic chromosome, participating in the packaging of DNA and in the regulation of gene expression. Biophysical studies have implicated changes in nucleosome structure from chromatin that is quiescent to active in transcription. Since DNA within the nucleosome contains a high concentration of phosphorus whereas histone proteins do not, the nucleosome structure is amenable to microanalytical electron energy loss mapping of phosphorus to delineate the DNA within the protein-nucleic acid particle. Nucleosomes associated with transcriptionally active genes were separated from nucleosomes associated with quiescent genes using mercury-affinity chromatography. The three-dimensional image reconstruction methods for the total nucleosome structure and for the 3D DNA-phosphorus distribution combined quaternion-assisted angular reconstitution of sets of single particles at random orientations and electron spectroscopic imaging. The structure of the active nucleosome has the conformation of an open clam-shell, C- or U-shaped in one view, elongated in another, and exhibits a protein asymmetry. A three-dimensional phosphorus map reveals a conformational change in nucleosomal DNA compared to DNA in the canonical nucleosome structure. It indicates an altered superhelicity and is consistent with unfolding of the particle. The results address conformational changes of the nucleosome and provide a direct structural linkage to biochemical and physiological changes which parallel gene expression.

A common-lines based method for determining orientations for N > 3 particle projections simultaneously

A method is proposed for determining the directions of projections. An arbitrary number of projections of unknown three-dimensional structure are simultaneously used as input. The method is based on common lines and uses a new discrepancy measure accounting for the uneven distribution of common lines in angular space. An application to the 70S Escherichia coli ribosome data obtained from an energy-filtering electron microscope is described.

Three-point repositioning of axes: three-dimensional alignment procedure for electron microscope tomography using three markers

A description is given of a new procedure to align series of tilted graphs, made with an electron microscope, for computer tomographic purposes. The procedure uses the coordinates of three projected markers to calculate parameters needed for the reconstruction. To that end the procedure computes the direction of the tilt-axis, the translation and rotation parameters, the tilt-angle of every micrograph, and the spatial coordinates of the individual markers with their centre of gravity as origin of the coordinate system. A searching technique, based on cross-correlation, is described to locate accurately the micrographs markers.

Structural states of the nucleosome

The nucleosome is the fundamental component of the eukaryotic chromosome, participating in the packaging of DNA and in the regulation of gene expression. Its numerous interactions imply a structural dynamism. Previous biophysical studies under limited sets of conditions have not been able to reconcile structural differences and transitions observed. We have determined a series of nucleosome conformations over a >10,000-fold range in salt concentration using a combination of biochemical methods, spectroscopic electron microscopy, and three-dimensional reconstruction techniques for randomly oriented single particles. This study indicates several ionic strength-dependent nucleosome conformations and also reconciles the differences between currently existing divergent models for the nucleosome. At low ionic environments, the particle appears highly elongated, becoming more compact and prolate ellipsoidal as ionic strength is increased to 10 mm NaCl. At 30 mM NaCl, the particle exhibits a spheroidal conformation. As ionic strength is increased to 150 mM NaCl, the nucleosome conformation changes and becomes oblate. Above 450 mM NaCl, the structure becomes highly elongated again. The result of this study is a unifying concept in which the three-dimensional structure of the nucleosome is inferred to be dynamic in response to ionic interactions and in accord with biochemical and genetic studies.

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.

Conformational characterization of nucleosomes by principal component analysis of their electron micrographs

Optimized fixation conditions were determined for protein-protein and protein-DNA crosslinking within calf-thymus nucleosomes in low monovalent salt concentrations. Nucleosomes were examined without heavy-atom staining by darkfield electron microscopy. The dimensions of these macromolecular complexes and those of HeLa core particles optimally fixed in divalent salt were analysed using principal component analysis. According to this analysis the structure of the calf-thymus nucleosomes was best presented by a prolate ellipsoid. Particle images had average major and minor axis lengths of 14.1 and 10.5 nm, respectively. In contrast, the HeLa nucleosomes were best modelled by an oblate ellipsoid from the analysis of their images, which had average major and minor axes of 13.3 and 11.5 nm. The applicability of this multivariate statistical analysis to the interpretation of macromolecular images is illustrated and discussed.