Scaling structure factor amplitudes in electron cryomicroscopy using X-Ray solution scattering

The structure factors derived from electron cryomicroscopic images are modified by the contrast transfer function of the microscope's objective lens and other influences. The phases of the structure factors can be corrected in a straightforward way when the positions of the contrast transfer function rings are determined. However, corrected amplitudes are also essential to yield an accurate distribution of mass in the reconstruction. The correct scale factors for the amplitudes are difficult to evaluate for data that are merged from many different micrographs. We opt to use X-ray solution scattering intensity from a concentrated suspension of the specimen to correct the amplitudes of the spherically averaged structure factors. When this approach is applied to the three-dimensional image data of ice-embedded acrosomal bundles, the core of a filament in a three-dimensional reconstruction of the acrosomal bundle becomes denser and matches more closely the outer density ascribed to scruin.     

Fourier amplitude decay of electron cryomicroscopic images of single particles and effects on structure determination

Several factors, including spatial and temporal coherence of the electron microscope, specimen movement, recording medium, and scanner optics, contribute to the decay of the measured Fourier amplitude in electron image intensities. We approximate the combination of these factors as a single Gaussian envelope function, the width of which is described by a single experimental B-factor. We present an improved method for estimating this B-factor from individual micrographs by combining the use of X-ray solution scattering and numerical fitting to the average power spectrum of particle images. A statistical estimation from over 200 micrographs of herpes simplex virus type-1 capsids was used to estimate the spread in the experimental B-factor of the data set. The B-factor is experimentally shown to be dependent on the objective lens defocus setting of the microscope. The average B-factor, the X-ray scattering intensity of the specimen, and the number of particles required to determine the structure at a lower resolution can be used to estimate the minimum fold increase in the number of particles that would be required to extend a single particle reconstruction to a specified higher resolution. We conclude that microscope and imaging improvements to reduce the experimental B-factor will be critical for obtaining an atomic resolution structure.     

Structural studies of tropomyosin by cryoelectron microscopy and x-ray diffraction.

A comparison has been made between cryoelectron microscope images and the x-ray structure of one projection of the Bailey tropomyosin crystal. The computed transforms of the electron micrographs extend to a resolution of approximately 18 A compared with the reflections from x-ray crystallography which extend to 15 A. After correction of the images for lattice distortions and the contrast transfer function, the structure factors were constrained to the plane group (pmg) symmetry of this projection. Amplitude and phase data for five images were compared with the corresponding view from the three-dimensional x-ray diffraction data (Phillips, G.N., Jr., J.P. Fillers, and C. Cohen. 1986. J. Mol. Biol. 192: 111-131). The average R factor between the electron microscopy and x-ray amplitudes was 15%, with an amplitude-weighted mean phase difference of 4.8 degrees. The density maps derived from cryoelectron microscopy contain structural features similar to those from x-ray diffraction: these include the width and run of the filaments and their woven appearance at the crossover regions. Preliminary images obtained from frozen-hydrated tropomyosin/troponin cocrystals suggest that this approach may provide structural details not readily obtainable from x-ray diffraction studies.     

Quantitation of molecular densities by cryo-electron microscopy. Determination of the radial density distribution of tobacco mosaic virus.

We have determined the absolute mass and radial scattering density distribution of tobacco mosaic virus in the frozen-hydrated state by energy-filtered low-dose bright-field transmission electron microscopy. The absolute magnitude of electron scattering from tobacco mosaic virus in 150 nm of ice was within 3.0% of that predicted, with inelastic scattering accounting for approximately 80% of the scattering contrast. In order to test the accuracy of the radial reconstruction, a computer model of tobacco mosaic virus was built from the atomic co-ordinates assuming uniform solvent density. The validity of the model was confirmed by comparison of X-ray scattering and predictions of the model (R factor = 0.05). First-order corrections for the microscope contrast transfer function were necessary and sufficient for conversion of the cryo-electron microscopy images into accurate representations of the mass density. At 1.9 nm resolution the compensated reconstruction and model had density peaks of similar magnitude at 2.4, 4.2, 6.0 and 7.8 nm radius and a central hole of 2 nm radius. Equatorial Fourier transforms of the corrected electron images were in excellent agreement with predictions of the model (R factor = 0.12). Thus, the uniform solvent approximation was adequate at 1.9 nm resolution to describe quantitatively X-ray scattering in liquid water and electron imaging in vitreous ice. This is the first demonstration that cryo-electron microscopy images can be used to quantitate the absolute mass, mass per unit length and internal density distributions of proteins and nucleic acids.     

Benefits and Limitations of Low-kV Macromolecular Imaging of Frozen-Hydrated Biological Samples

Object contrast is one of the most important parameters of macromolecular imaging. Low-voltage transmission electron microscopy has shown an increased atom contrast for carbon materials, indicating that amplitude contrast contributions increase at a higher rate than phase contrast and inelastic scattering. Here, we studied image contrast using ice-embedded tobacco mosaic virus particles as test samples at 20–80 keV electron energy. The particles showed the expected increase in contrast for lower energies, but at the same time the 2.3-nm-resolution measure decayed more rapidly. We found a pronounced signal loss below 60 keV, and therefore we conclude that increased inelastic scattering counteracts increased amplitude contrast. This model also implies that as long as the amplitude contrast does not increase with resolution, beam damage and multiple scattering will always win over increased contrast at the lowest energies. Therefore, we cannot expect that low-energy imaging of conventionally prepared samples would provide better data than state-of-the-art 200–300 keV imaging.     

Structural analysis of T4 DNA helix destabilizing protein (gp32 I) crystal by electron microscopy

Low dose electron diffraction and imaging techniques have been applied to the study of the crystalline structure of gp32*I, a DNA helix destabilizing protein derived from bacteriophage T4 gene 32 protein. A quantitative analysis of intensities from electron diffraction patterns from tilted, multilayered gp32*I crystal has provided the unit cell thickness of the crystal. The three-dimensional phases indicate that the space group P2(1)2(1)2. By taking into account the unit cell volume and the solvent content in the crystal, it was deduced that there is one gp32*I molecule in each asymmetric unit. A projected density map of unstained, glucose-embedded gp32*I crystal was synthesized with amplitudes from electron diffraction intensities and phases from electron images with reflections out to 7.6 A. Because of the similarity in the scattering density between glucose and protein, this projected map cannot be interpreted with certainty. A low resolution three-dimensional reconstruction shows that the protein molecule is about 90 A long and about 20 A in diameter. Because the dimer is formed around a dyad axis, the protein molecules comprising it must be arranged head-to-head. This dimeric arrangement of the proteins in the unit cell may be implicated as one of the conformational states of this protein in solution.     

Structure of myosin subfragment 1 from low-angle X-ray scattering

The X-ray scattering pattern produced by a solution of myosin subfragment 1 has been measured to a resolution (Bragg spacing) of 2 nm. We find that for subfragment 1 (S1) prepared by limited papain digestion in the presence of ethylenediaminetetraacetate the radius of gyration is 3.28 +/- 0.06 nm, the volume is 151 +/- 6 nm3, the surface area is 330 +/- 15 nm2, and the length of the maximum chord is 12.0 +/- 1.0 nm. The theoretical scattering patterns from several objects of uniform electron density have been calculated and compared with the observed scattering produced by S1. The recent three-dimensional electron micrograph reconstruction of S1-decorated actin by J. Seymour and E. O'Brien (private communication) generated the calculated pattern that best fit the observed scattering. This fit strongly suggests that this reconstruction resembles subfragment 1. The good correspondence between an S1 structure derived when S1 is attached to actin and a study of free S1 in solution strongly suggests that binding to actin does not grossly distort the shape of S1. This is consistent with the notion that S1 changes its orientation on actin, rather than its shape, in order to generate the contractile force in muscle.     

Effects of radiation damage with 400-kV electrons on frozen, hydrated actin bundles.

Electron images can be used to provide amplitudes and phases for the structural determination of biological specimens. Radiation damage limits the amount of structural information retrievable by computer processing. A 400-kV electron microscope was used to investigate radiation damage effects on frozen, hydrated actin bundles kept at -168 degrees C. The quality of phases within and among images in a damage series was evaluated quantitatively out to 16 A resolution. It was found that the phases of structure factors with good signal-to-noise ratio (IQ less than or equal to 4) can be reliably retrieved from images taken at a cumulative dose of at least 25 electrons/A2.     

Neutron and x-ray scatter studies of the histone octamer and amino and carboxyl domain trimmed octamers

The structure of the nucleosome has been under intense investigation using neutron crystallography, x-ray crystallography, and neutron solution scattering. However the dimension of the histone octamer inside the nucleosome is still a subject of controversy. The radius of gyration (Rg) of the octamer obtained from solution neutron scattering of core particles at 63% 2H2O, 37% 1H2O is 33 A, and x-ray crystallography study of isolated histone octamer gives a Rg of 32.5 A, while the reported values using x-ray crystallography of core particles from two individual studies are 29.7 and 30.4 A, respectively. We report here studies of isolated histone octamer and trypsin-limited digested octamer using both neutron solution scattering and small angle x-ray scattering. The Rg of the octamer obtained is 33 A, whereas that of the trimmed octamer is 29.8 A, similar to the structure obtained from the crystals of the core particles. The N-terminal domains of the core histones in the octamer have been shown by high resolution nuclear magnetic resonance (Schroth, G.P., Yau, P., Imai, B.S., Gatewood, J.M., and Bradbury, E.M. (1990) FEBS Lett. 268, 117-120) to be mobile and flexible; it is likely that these regions are disordered and "not seen" by x-ray crystallography.     

A statistical approach to computer processing of cryo-electron microscope images: virion classification and 3-D reconstruction

The scattering density of the virus is represented as a truncated weighted sum of orthonormal basis functions in spherical coordinates, where the angular dependence of each basis function has icosahedral symmetry. A statistical model of the image formation process is proposed and the maximum likelihood estimation method computed by an expectation-maximization algorithm is used to estimate the weights in the sum and thereby compute a 3-D reconstruction of the virus particle. If multiple types of virus particle are represented in the boxed images then multiple 3-D reconstructions are computed simultaneously without first requiring that the type of particle shown in each boxed image be determined. Examples of the procedure are described for viruses with known structure: (1). 3-D reconstruction of Flockhouse Virus from experimental images, (2). 3-D reconstruction of the capsid of Nudaurelia Omega Capensis Virus from synthetic images, and (3). 3-D reconstruction of both the capsid and the procapsid of Nudaurelia Omega Capensis Virus from a mixture of unclassified synthetic images.     

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.     

An ab initio algorithm for low-resolution 3-D reconstructions from cryoelectron microscopy images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

Small angle x-ray scattering of the hemoglobin from Biomphalaria glabrata

The hemoglobin from Biomphalaria glabrata is an extracellular respiratory protein of high molecular mass composed by subunits of 360 kDa, each one containing two 180 kDa chains linked by disulfide bridges. In this work, small angle x-ray scattering (SAXS) measurements were performed with the hemoglobin at pH 5.0 and 7.5. Radii of gyration of 98.6 +/- 0.5 and 101.8 +/- 0.2 A and maximum diameters of 300 +/- 10 and 305 +/- 10 A, respectively, were obtained from Guinier plot extrapolation and analytical curve fitting. The pair distance distribution functions p(r) corresponded to globular particles with a somewhat anisotropic shape for both preparations. Computer analysis of the low angle part of the scattering curve led to the determination of the low resolution envelope of the protein, revealing a P(222) symmetry. Shape reconstruction from ab initio calculations using the complete scattering curve furnished a compact prolate three-dimensional (3D) bead model for the protein. Hydrodynamic parameters were obtained from experiments and theoretical calculations using the 3D model. The results of the structural and biochemical studies reported herein indicate that the multisubunit structure of this hemoglobin is compatible with a tetrameric arrangement.     

An ab Initio Algorithm for Low-Resolution 3-D Reconstructions from Cryoelectron Microscopy Images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

The tetrameric form of ribosomal protein L7/L12 from Escherichia coli

A tetrameric form of the ribosomal protein L7/L12 has been prepared and its structure studied by using hydrodynamic methods, photon correlation spectroscopy, and small angle x-ray scattering. The tetrameric nature of the protein preparation is confirmed by three independent determinations of its molecular weight, with analysis of accurate sedimentation equilibrium data giving the most reliable estimate. The species has a Stokes radius of 4.0 +/- 0.1 nm and an absolute frictional ratio of 1.7. Taken together, the hydrodynamic measurements suggest the possibility of a flat structure, and this is consistent with the x-ray scattering results. The molecule has a radius of gyration of 3.6 +/- 0.05 nm and a maximum dimension of 11-12 nm. A geometric model consisting of four elongated monomers, arranged in a plane, is proposed.     

Size and molecular parameters of adenosine triphosphatase from Escherichia coli.

The Mg2+- and Ca2+-stimulated ATPase (bacterial coupling factor) has been investigated in solution with different independent techniques. The molecular weight of the five-subunit enzyme was found to be 345,000 +/- 5,000 by means of light scattering, 350,000 by sedimentation equilibrium experiments, and 358,000 by means of small-angle x-ray scattering. The radius of gyration was found to be 41.9 A, the volume 7.39 x 10(5) A3, and the surface to volume ratio 5.5 x 10(-2) A-1 from small-angle x-ray scattering measurements of the enzyme in solution. The degree of hydration was found to be 0.62 ml of H2O/g of ATPase. The translational diffusion coefficient was determined to be 3.47 x 10(-7) cm2 s-1 by means of inelastic light scattering. The distribution of the scattered intensity near the origin appears to be bimodal, suggesting that the ATPase molecule is composed of spherical parts bound together by a flexible polypeptide chain. The largest dimension of the ATPase in solution is 120.0 A, determined from the pair distribution function.     

Salt effects on the structure and internal dynamics of superhelical DNAs studied by light scattering and Brownian dynamics.

Using laser light scattering, we have measured the static and dynamic structure factor of two different superhelical DNAs, p1868 (1868 bp) and simian virus 40 (SV40) (5243 bp), in dilute aqueous solution at salt concentrations between 1 mM and 3 M NaCl. For both DNA molecules, Brownian dynamics (BD) simulations were also performed, using a previously described model. A Fourier mode decomposition procedure was used to compute theoretical light scattering autocorrelation functions (ACFs) from the BD trajectories. Both measured and computed autocorrelation functions were then subjected to the same multiexponential decomposition procedure. Simulated and measured relaxation times as a function of scattering angle were in very good agreement. Similarly, computed and measured static structure factors and radii of gyration agreed within experimental error. One main result of this study is that the amplitudes of the fast-relaxing component in the ACF show a peak at 1 M salt concentration. This nonmonotonic behavior might be caused by an initial increase in the amplitudes of internal motions due to diminishing long-range electrostatic repulsions, followed by a decrease at higher salt concentration due to a compaction of the structure.     

Structure of fully hydrated fluid phase DMPC and DLPC lipid bilayers using X-ray scattering from oriented multilamellar arrays and from unilamellar vesicles

Quantitative structures of the fully hydrated fluid phases of dimyristoylphosphatidylcholine (DMPC) and dilauroylphosphatidylcholine (DLPC) were obtained at 30 degrees C. Data for the relative form factors F(q(z)) for DMPC were obtained using a combination of four methods. 1), Volumetric data provided F(0). 2), Diffuse x-ray scattering from oriented stacks of bilayers provided relative form factors |F(q(z))| for high q(z), 0.22 < q(z) < 0.8 A(-1). 3), X-ray scattering from extruded unilamellar vesicles with diameter 600 A provided |F(q(z))| for low q(z), 0.1 < q(z) < 0.3 A(-1). 4), Previous measurements using a liquid crystallographic x-ray method provided |F(2 pi h/D)| for h = 1 and 2 for a range of nearly fully hydrated D-spacings. The data from method 4 overlap and validate the new unilamellar vesicles data for DMPC, so method 4 is not required for DLPC or future studies. We used hybrid electron density models to obtain structural results from these form factors. Comparison of the model electron density profiles with that of gel phase DMPC provides areas per lipid A, 60.6 +/- 0.5 A(2) for DMPC and 63.2 +/- 0.5 A(2) for DLPC. Constraints on the model provided by volume measurements and component volumes obtained from simulations put the electron density profiles rho(z) and the corresponding form factors F(q(z)) on absolute scales. Various thicknesses, such as the hydrophobic thickness and the steric thickness, are obtained and compared to literature values.     

Hydrodynamic diameters of murine mammary, Rous sarcoma, and feline leukemia RNA tumor viruses: studies by laser beat frequency light-scattering spectroscopy and electron microscopy.

We have studied purified preparations of murine mammary tumor virus (MuMTV), Rous sarcoma virus (RSV; Prague strain), and feline leukemia virus (FeLV) by laser beat frequency light-scattering spectroscopy, ultra-centrifugation, and electron microscopy. The laser beat frequency light-scattering spectroscopy measurements yield the light-scattering intensity, weighted diffusion coefficients. The corresponding average hydrodynamic diameters, as calculated from the diffusion coefficients by the Stokes-Einstein equation for MuMTV, RSV, and FeLV, respectively, are: 144 +/- 6 nm, 147 +/- 7 nm, and 168 +/- 6 nm. Portions of the purified RSV and MuMTV preparations, from which light-scattering samples were obtained, and portions of the actual FeLV light-scattering samples were examined by negatively stained, catalase crystal-calibrated electron microscopy. The light-scattering intensity weighted averages of the electron micrograph size distributions were calculated by weighing each size by its theoretical relative scattering intensity, as obtained from published tables computed according to the Mie scattering theory. These averages and the experimentally observed hydrodynamic diameters agreed to within +/- 5%, which is the combined experimental error in the electron microscopic and light-scattering techniques. We conclude that the size distributions of singlet particles observed in the electron micrographs are statistically true representations of the sedimentation-purified solution size distributions. The sedimentation coefficients (S20, w) for MuMTV, RSV, and FeLV, respectively, are: 595 +/- 29S, 689 +/- 35S, and 880 +/- 44S. Virus partial specific volumes were taken as the reciprocals of the buoyant densities, determined in sucrose density gradients. The Svedberg equation was used to calculate particle weights from the measured diffusion and sedimentation coefficients. The particle weights for MuMTV, RSV, and FeLV, respectively, are: (3.17 +/- 0.32) x 10(8), (4.17 +/- 0.42) x 10(8), and (5.50 +/- 0.55) x 10(8) daltons.     

From high symmetry to high resolution in biological electron microscopy: a commentary on Crowther (1971) ‘Procedures for three-dimensional reconstruction of spherical viruses by Fourier synthesis from electron micrographs’

Elucidation of the structure of biological macromolecules and larger assemblies has been essential to understanding the roles they play in living processes. Methods for three-dimensional structure determination of biological assemblies from images recorded in the electron microscope were therefore a key development. In his paper published in Philosophical Transactions B in 1971, Crowther described new computational procedures applied to the first three-dimensional reconstruction of an icosahedral virus from images of virus particles preserved in negative stain. The method for determining the relative orientation of randomly oriented particles and combining their images for reconstruction exploited the high symmetry of the virus particle. Computational methods for image analysis have since been extended to include biological assemblies without symmetry. Further experimental advances, combined with image analysis, have led to the method of cryomicroscopy, which is now used by structural biologists to study the structure and dynamics of biological machines and assemblies in atomic detail. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.