Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy

A computational procedure is described for assigning the absolute hand of the structure of a protein or assembly determined by single-particle electron microscopy. The procedure requires a pair of micrographs of the same particle field recorded at two tilt angles of a single tilt-axis specimen holder together with the three-dimensional map whose hand is being determined. For orientations determined from particles on one micrograph using the map, the agreement (average phase residual) between particle images on the second micrograph and map projections is determined for all possible choices of tilt angle and axis. Whether the agreement is better at the known tilt angle and axis of the microscope or its inverse indicates whether the map is of correct or incorrect hand. An increased discrimination of correct from incorrect hand (free hand difference), as well as accurate identification of the known values for the tilt angle and axis, can be used as targets for rapidly optimizing the search or refinement procedures used to determine particle orientations. Optimized refinement reduces the tendency for the model to match noise in a single image, thus improving the accuracy of the orientation determination and therefore the quality of the resulting map. The hand determination and refinement optimization procedure is applied to image pairs of the dihydrolipoyl acetyltransferase (E2) catalytic core of the pyruvate dehydrogenase complex from Bacillus stearothermophilus taken by low-dose electron cryomicroscopy. Structure factor amplitudes of a three-dimensional map of the E2 catalytic core obtained by averaging untilted images of 3667 icosahedral particles are compared to a scattering reference using a Guinier plot. A noise-dependent structure factor weight is derived and used in conjunction with a temperature factor (B=-1000A(2)) to restore high-resolution contrast without amplifying noise and to visualize molecular features to 8.7A resolution, according to a new objective criterion for resolution assessment proposed here.     

Accurate determination of local defocus and specimen tilt in electron microscopy

Accurate knowledge of defocus and tilt parameters is essential for the determination of three-dimensional protein structures at high resolution using electron microscopy. We present two computer programs, CTFFIND3 and CTFTILT, which determine defocus parameters from images of untilted specimens, as well as defocus and tilt parameters from images of tilted specimens, respectively. Both programs use a simple algorithm that fits the amplitude modulations visible in a power spectrum with a calculated contrast transfer function (CTF). The background present in the power spectrum is calculated using a low-pass filter. The background is then subtracted from the original power spectrum, allowing the fitting of only the oscillatory component of the CTF. CTFTILT determines specimen tilt parameters by measuring the defocus at a series of locations on the image while constraining them to a single plane. We tested the algorithm on images of two-dimensional crystals by comparing the results with those obtained using crystallographic methods. The images also contained contrast from carbon support film that added to the visibility of the CTF oscillations. The tests suggest that the fitting procedure is able to determine the image defocus with an error of about 10nm, whereas tilt axis and tilt angle are determined with an error of about 2 degrees and 1 degrees, respectively. Further tests were performed on images of single protein particles embedded in ice that were recorded from untilted or slightly tilted specimens. The visibility of the CTF oscillations from these images was reduced due to the lack of a carbon support film. Nevertheless, the test results suggest that the fitting procedure is able to determine image defocus and tilt angle with errors of about 100 nm and 6 degrees, respectively.     

Reprint of "Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)" [J. Struct. Biol. 160 (2007) 35-48

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L_2,3 edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell’s nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Dual-Axis Tomography: An Approach with Alignment Methods That Preserve Resolution

Tomographic reconstructions of biological specimens are now routinely being generated in our high voltage electron microscope by tilting the specimen around two orthogonal axes. Separate tomograms are computed from each tilt series. The two tomograms are aligned to each other with general 3-D linear transformations that can correct for distortions between the two tomograms, thus preserving the inherent resolution of the reconstruction throughout its volume. The 3-D Fourier transforms of the two tomograms are then selectively combined to achieve a single tomogram. Unlike a single-axis tomogram, a dual-axis tomogram shows good resolution for extended features at any orientation in the plane of the specimen; it also has improved resolution in the depth of the specimen. Calculations indicate that the improvements available from double tilting and from tilting to higher angles are largely additive. Actual and model data were used to assess whether varying the increment between tilted views in proportion to the cosine of the tilt angle would allow a reduction in the number of pictures required to achieve a given resolution of reconstruction. Analysis by Fourier sector correlation indicated that the variable tilt increment improved the reconstruction in some respects but degraded it in others. A varying tilt increment thus does not give an unqualified improvement, at least when using back-projection algorithms for the reconstruction.     

Mass distributions of a macromolecular assembly based on electrospray ionization mass spectrometric masses of the constituent subunits

Macromolecular assemblies containing multiple protein subunits and having masses in the megadalton (MDa) range are involved in most of the functions of a living cell. Because of variation in the number and masses of subunits, macromolecular assemblies do not have a unique mass, but rather a mass distribution. The giant extracelular erythrocruorins (Ers), ∼ 3.5 MDa, comprized of at least 180 polypeptide chains, are one of the best characterized assemblies. Three-dimensional reconstructions from cryoelectron microscopic images show them to be hexagonal bilayer complexes of 12 subassemblies, each comprised of 12 globin chains, anchored to a subassembly of 36 nonglobin linker chains. We have calculated the most probable mass distributions forLumbricus andRiftia assemblies and their globin and linker subassemblies, based on theLumbricus Er stoichiometry and using accurate subunit masses obtained by electrospray ionization mass spectrometry. The expected masses ofLumbricus andRiftia Ers are 3.517 MDa and 3.284 MDa, respectively, with a possible variation of ∼ 9% due to the breadth of the mass distributions. TheLumbricus Er mass is in astonishingly good agreement with the mean of 23 known masses, 3.524 ± 0.481 MDa.     

Helical Filaments of Human Dmc1 Protein on Single-Stranded DNA: A Cautionary Tale

Proteins in the RecA/Rad51/RadA family form nucleoprotein filaments on DNA that catalyze a strand exchange reaction as part of homologous genetic recombination. Because of the centrality of this system to many aspects of DNA repair, the generation of genetic diversity, and cancer when this system fails or is not properly regulated, these filaments have been the object of many biochemical and biophysical studies. A recent paper has argued that the human Dmc1 protein, a meiotic homolog of bacterial RecA and human Rad51, forms filaments on single-stranded DNA with ∼ 9 subunits per turn in contrast to the filaments formed on double-stranded DNA with ∼ 6.4 subunits per turn and that the stoichiometry of DNA binding is different between these two filaments. We show using scanning transmission electron microscopy that the Dmc1 filament formed on single-stranded DNA has a mass per unit length expected from ∼ 6.5 subunits per turn. More generally, we show how ambiguities in helical symmetry determination can generate incorrect solutions and why one sometimes must use other techniques, such as biochemistry, metal shadowing, or scanning transmission electron microscopy, to resolve these ambiguities. While three-dimensional reconstruction of helical filaments from EM images is a powerful tool, the intrinsic ambiguities that may be present with limited resolution are not sufficiently appreciated.     

The uncertainty of UTCI due to uncertainties in the determination of radiation fluxes derived from measured and observed meteorological data

In the present study, we investigate the determination accuracy of the Universal Thermal Climate Index (UTCI). We study especially the UTCI uncertainties due to uncertainties in radiation fluxes, whose impacts on UTCI are evaluated via the mean radiant temperature (Tmrt). We assume “normal conditions”, which means that usual meteorological information and data are available but no special additional measurements. First, the uncertainty arising only from the measurement uncertainties of the meteorological data is determined. Here, simulations show that uncertainties between 0.4 and 2 K due to the uncertainty of just one of the meteorological input parameters may be expected. We then analyse the determination accuracy when not all radiation data are available and modelling of the missing data is required. Since radiative transfer models require a lot of information that is usually not available, we concentrate only on the determination accuracy achievable with empirical models. The simulations show that uncertainties in the calculation of the diffuse irradiance may lead to Tmrt uncertainties of up to ±2.9 K. If long-wave radiation is missing, we may expect an uncertainty of ±2 K. If modelling of diffuse radiation and of longwave radiation is used for the calculation of Tmrt, we may then expect a determination uncertainty of ±3 K. If all radiative fluxes are modelled based on synoptic observation, the uncertainty in Tmrt is ±5.9 K. Because Tmrt is only one of the four input data required in the calculation of UTCI, the uncertainty in UTCI due to the uncertainty in radiation fluxes is less than ±2 K. The UTCI uncertainties due to uncertainties of the four meteorological input values are not larger than the 6 K reference intervals of the UTCI scale, which means that UTCI may only be wrong by one UTCI scale. This uncertainty may, however, be critical at the two temperature extremes, i.e. under extreme hot or extreme cold conditions.     

Towards a resolution of the long-standing controversy regarding the molecular mass of extracellular erythrocruorin of the earthworm Lumbricus terrestris

The published molecular mass of erythrocruorin of Lumbricus terrestris and related earthworm species covers a bewildering range of 3.23-4.5 MDa. A critical reexamination reveals that some mass determinations were underestimated and the results do cluster, not at one, but at two values of the molecular mass. One cluster corresponds to approximately 3.6 MDa, as predicted for a stoichiometry of 144 globin and 36 linker chains-the Vinogradov model for the hexagonal bilayer (HBL) assembly of Lumbricus erythrocruorin-and as estimated from the crystal structure of HBL at 5.5 A resolution [Proc. Natl. Acad. Sci. U. S. A. 97 (2000) 7107]. The other cluster corresponds to approximately 4.4 MDa. In addition, a molecular mass of 4.1 MDa, determined by multiangle laser light scattering (MALLS), stands apart of the two clusters, separated from the masses obtained by other methods of molecular mass determination.We propose a stoichiometry of 192 globin and 36 linker chains for the 4.4-MDa molecule. The 36 linkers and 144 out of 192 globin chains are identified with the HBL and the remaining 48 globins are allotted equally to the two halves of the axial cavity above and below the central torus of the structure. The proposed model is supported by the occurrence in some annelid species of erythrocruorin with centrally placed subunits [Biochim. Biophys. Acta 359 (1974) 210], and by the oxidation-dependent shedding of subunits in Lumbricus erythrocruorin. We propose further that the 4.1 MDa determination represents the weight average molecular mass of a population of molecules resulting from a partial dissociation of 4.4-MDa erythrocruorin. This interpretation seems reasonable on the background of the very low protein concentrations ( approximately 100 microg/ml and lower) prevailing at the MALLS experiment.     

Packaging of a polymer by a viral capsid: the interplay between polymer length and capsid size

We report a study of the in vitro self-assembly of virus-like particles formed by the capsid protein of cowpea chlorotic mottle virus and the anionic polymer poly(styrene sulfonate) (PSS) for five molecular masses ranging from 400 kDa to 3.4 MDa. The goal is to explore the effect on capsid size of the competition between the preferred curvature of the protein and the molecular mass of the packaged cargo. The capsid size distribution for each polymer was unimodal, but two distinct sizes were observed: 22 nm for the lower molecular masses, jumping to 27 nm at a molecular mass of 2 MDa. A model is provided for the formation of the virus-like particles that accounts for both the PSS and capsid protein self-interactions and the interactions between the protein and PSS. Our study suggests that the size of the encapsidated polymer cargo is the deciding factor for the selection of one distinct capsid size from several possible sizes with the same inherent symmetry.     

The crystal structure of a virus-like particle from the hyperthermophilic archaeon Pyrococcus furiosus provides insight into the evolution of viruses

Pyrococcus furiosus is a hyperthermophilic archaeal microorganism found near deep-sea thermal vents and its optimal growth temperature of 100 degrees C. Recently, a 38.8-kDa protein from P. furiosus DSM 3638 was isolated and characterized. Electron microscopy revealed that this protein aggregated as spheres of approximately 30 nm in diameter, which we designated P. furiosus virus-like particles (PfVs). X-ray crystallographic analysis at 3.6-A resolution revealed that each PfV consisted of 180 copies of the 38.8-kDa protein and retained T=3 icosahedral symmetry, as is often the case in spherical viruses. The total molecular mass of each particle was approximately 7 MDa. An examination of capsid structures suggested strong evolutionary links among PfV, tailed double-stranded DNA bacteriophages, and herpes viruses. The similar three-dimensional structures of the various coat proteins indicate that these viral capsids might have originated and evolved from a common ancestor. The structure of PfV provides a previously undescribed example of viral relationships across the three domains of life (Eukarya, Bacteria, and Archaea).     

Method for the determination of myosin head orientation from EPR spectra.

The determination of the iodoacetamide spin label orientation in myosin heads (Fajer, 1994) allows us for the first time to determine directly protein orientation from EPR spectra. Computational simulations have been used to determine the sensitivity of EPR to both torsional and tilting motions of myosin heads. For rigor heads (no nucleotide), we can detect 0.2 degree changes in the tilt angle and 4 degrees in the torsion of the head. Sensitivity decreases with increasing head disorder, but even in the presence of +/- 30 degrees disorder as expected for detached heads, 10 degree changes in the center of the orientational distribution can be detected. We have combined these numerical simulations with a Simplex optimization to compare the orientation of intrinsic heads, with the orientation of labeled extrinsic heads that have been infused into unlabeled muscle fibers. The near identity (within 2 degrees) of the orientational distribution in the two instances can be attributed to myosin elasticity taking up the mechanical strain induced by the mismatch of myosin and actin filament periodicity. A similar analysis of the spectra of fibers with ADP bound to myosin revealed a small (approximately 5 degrees-10 degrees) torsional reorientation, without a substantial change of the tilt angle (< 2 degrees).     

Automatic CTF correction for single particles based upon multivariate statistical analysis of individual power spectra

Three-dimensional electron cryomicroscopy of randomly oriented single particles is a method that is suitable for the determination of three-dimensional structures of macromolecular complexes at molecular resolution. However, the electron-microscopical projection images are modulated by a contrast transfer function (CTF) that prevents the calculation of three-dimensional reconstructions of biological complexes at high resolution from uncorrected images. We describe here an automated method for the accurate determination and correction of the CTF parameters defocus, twofold astigmatism and amplitude-contrast proportion from single-particle images. At the same time, the method allows the frequency-dependent signal decrease (B factor) and the non-convoluted background signal to be estimated. The method involves the classification of the power spectra of single-particle images into groups with similar CTF parameters; this is done by multivariate statistical analysis (MSA) and hierarchically ascending classification (HAC). Averaging over several power spectra generates class averages with enhanced signal-to-noise ratios. The correct CTF parameters can be deduced from these class averages by applying an iterative correlation procedure with theoretical CTF functions; they are then used to correct the raw images. Furthermore, the method enables the tilt axis of the sample holder to be determined and allows the elimination of individual poor-quality images that show high drift or charging effects.     

Practical Image Restoration of Thick Biological Specimens Using Multiple Focus Levels in Transmission Electron Microscopy

Three-dimensional electron tomographic studies of thick specimens such as cellular organelles or supramolecular structures require accurate interpretations of transmission electron micrograph intensities. In addition to microscope lens aberrations, thick specimen imaging is complicated by additional distortions resulting from multiple elastic and inelastic scattering. Extensive analysis of the mechanism of image formation using electron energy-loss spectroscopy and imaging as well as exit wavefront reconstruction demonstrated that multiple scattering does not contribute to the coherent component of the exit wave (Hanet al.,1996, 1995). Although exit wavefront restored images showed enhanced contrast and resolution, that technique, which requires the collection of more than 30 images at different focus levels, is not practical for routine data collection in 3D electron tomography, where usually over 100 projection views are required for each reconstruction. Using a 0.7-μm-thick specimen imaged at 200 keV, the accuracy of reconstructions using small numbers of defocused images and a simple linear filter (Schiske, 1968) was assessed by comparison to the complete exit wave restoration. We demonstrate that only four optimal focus levels are required to effectively restore the coherent component (deviation 5.1%). By contrast, the optimal single image (zero defocus) shows a 25.5% deviation to the exit wave restoration. Two pairs of under- and over-defocus images should be taken: one pair at quite high defocus (>10 μm) to differentiate the coherent (single elastic scattering) from the incoherent (multiple elastic and inelastic scattering) components, and the second pair to optimize information content at the highest desired resolution (e.g., 5 μm for (2.5 nm)⁻¹resolution). We also propose a new interpretation of the restored amplitude and phase components where the specimen mass-density is proportional to the logarithm of the amplitude component and linearly related to the phase component. This approach should greatly facilitate the collection of high resolution tomographic data from thick samples.     

A method for determining the crystal orientation for any tilt position when using a transmission electron microscope double-tilt specimen holder

A method is described in this short communiction which provides a rapid and precise determination of the crystal specimen orientation in any tilt position when using a doule-tilt holder in the transmission electron microscope (TEM). It is necessary to establish three pairs of tilt angles (α_i, β_i) (i = 1, 2, 3) where three recognized directions of the crystal specimen are aligned to the electron beam direction respectively, in order to determine the crystal specimen orientation for any tilt position in a double-tilt specimen holder. In addition, the tilt position (α, β), where any orientation [ u v w] is aligned to the beam direction, can be determined with the aid of this method.A software system for computer applications of the above method has beed developed.     

Molecular weight determination of plasmid DNA using electrospray ionization mass spectrometry.

Ionization and molecular weight (MW) determination of megadalton size plasmid DNA has been achieved using electrospray ionization (ESI) with Fourier transform ion cyclotron resonance (FTICR) mass spectrometry. DNA molecules were shown to remain intact through electrospray ionization by collection on a specially prepared surface, followed by agarose gel electrophoresis. Individual highly charged ions of plasmid DNA produced by ESI were trapped in an FTICR cell for up to several hours and reacted with acetic acid to induce charge state shifts. Measurements of mass-to-charge ratios for these multiple peaks arising from charge state shifting give MW measurements of individual ions with an average accuracy of 0.2%. The MW distribution was obtained by measurements for a number of individual ions from the same sample [plasmid DNA: pGEM-5S MW(cal) = 1.946 MDa], yielding a MW(obs) of 1.95 +/- 0.07 MDa for ions clustered in the vicinity of the expected MW.     

Structural studies of soluble oligomers of the Alzheimer beta-amyloid peptide

Recent studies have suggested that non-fibrillar soluble forms of Abeta peptides possess neurotoxic properties and may therefore play a role in the molecular pathogenesis of Alzheimer's disease. We have identified solution conditions under which two types of soluble oligomers of Abeta40 could be trapped and stabilized for an extended period of time. The first type of oligomers comprises a mixture of dimers/tetramers which are stable at neutral pH and low micromolar concentration, for a period of at least four weeks. The second type of oligomer comprises a narrow distribution of particles that are spherical when examined by electron microscopy and atomic force microscopy. The number average molecular mass of this distribution of particles is 0.94 MDa, and they are are stable at pH 3 for at least four weeks. Circular dichroism studies indicate that the dimers/tetramers possess irregular secondary structure that is not alpha-helix or beta-structure, while the 0.94 MDa particles contain beta-structure. Fluorescence resonance energy transfer experiments indicate that Abeta40 moieties in amyloid fibrils or protofibrils are more similar in structure to those in the 0.94 MDa particles than those in the dimers/tetramers. These findings indicate that soluble oligomeric forms of Abeta peptides can be trapped for extended periods of time, enabling their study by high resolution techniques that would not otherwise be possible.     

A Method for Helical RNA Global Structure Determination in Solution Using Small-Angle X-Ray Scattering and NMR Measurements

We report a “top-down” method that uses mainly duplexes' global orientations and overall molecular dimension and shape restraints, which were extracted from experimental NMR and small-angle X-ray scattering data, respectively, to determine global architectures of RNA molecules consisting of mostly A-form-like duplexes. The method is implemented in the G2G (from global measurement to global structure) toolkit of programs. We demonstrate the efficiency and accuracy of the method by determining the global structure of a 71-nt RNA using experimental data. The backbone root-mean-square deviation of the ensemble of the calculated global structures relative to the X-ray crystal structure is 3.0 ± 0.3 Å using the experimental data and is only 2.5 ± 0.2 Å for the three duplexes that were orientation restrained during the calculation. The global structure simplifies interpretation of multidimensional nuclear Overhauser spectra for high-resolution structure determination. The potential general application of the method for RNA structure determination is discussed.     

A quantitative description of in vitro assembly of human papillomavirus 16 virus-like particles

The full-length human papillomavirus 16 major capsid protein L1 is expressed in Saccharomyces cerevisiae as virus-like particles (VLPs). However, yeast-expressed human papillomavirus 16 particles are irregular in shape and are prone to aggregate. When disassembled and reassembled, the resulting particles have improved stability and solubility. We have examined VLP dissociation and reassembly to define the important features of the assembly mechanism. We found that the VLPs rapidly disassemble at pH 8.2 and low ionic strength in the presence of low concentrations of reducing agents. The pH dependence of assembly kinetics and extent of assembly under reducing conditions were differentially sensitive to ionic strength. Assembly at pH 5.2 was very fast and led to heavily aggregated particles. This sort of kinetic trap is expected for overinitiated assembly. We observed that reassembly at pH 6.2, 7.2, and 8.2 yielded regular particles over a broad range of ionic strength. At these three pH values, assembly was quantitative at 1 M NaCl. At pH 7.2, much more than at pH 6.2 or pH 8.2, assembly decreased monotonically with ionic strength. The free energy of association ranged from − 8 to − 10 kcal/mol per pentamer. The effect of pH on assembly was further investigated by examining dissociation of reassembled particles. Though indistinguishable by negative stain electron microscopy, particles assembled at pH 7.2 disassembled slower than pH 5.2, 6.2, or 8.2 VLPs. We hypothesize that pH 7.2 assembly reactions lead to formation of particles with conformationally different interactions.     

Cryo‐EM reveals the complex architecture of dynactin's shoulder region and pointed end

Dynactin is a 1.1 MDa complex that activates the molecular motor dynein for ultra‐processive transport along microtubules. In order to do this, it forms a tripartite complex with dynein and a coiled‐coil adaptor. Dynactin consists of an actin‐related filament whose length is defined by its flexible shoulder domain. Despite previous cryo‐EM structures, the molecular architecture of the shoulder and pointed end of the filament is still poorly understood due to the lack of high‐resolution information in these regions. Here we combine multiple cryo‐EM datasets and define precise masking strategies for particle signal subtraction and 3D classification. This overcomes domain flexibility and results in high‐resolution maps into which we can build the shoulder and pointed end. The unique architecture of the shoulder securely houses the p150 subunit and positions the four identical p50 subunits in different conformations to bind dynactin’s filament. The pointed end map allows us to build the first structure of p62 and reveals the molecular basis for cargo adaptor binding to different sites at the pointed end.     

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.