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.     

Focus gradient correction applied to tilt series image data used in electron tomography

The resolution in 3D reconstructions from tilt series is limited to the information below the first zero of the contrast transfer function unless the signal is corrected computationally. The restoration is usually based on the assumption of a linear space-invariant system and a linear relationship between object mass density and observed image contrast. The space-invariant model is no longer valid when applied to tilted micrographs because the defocus varies in a direction perpendicular to the tilt axis and with it the shape of the associated point spread function. In this paper, a method is presented for determining the defocus gradient in thin specimens such as sections and 2D crystals, and for restoration of the images subsequently used for 3D reconstruction. The alignment procedure for 3D reconstruction includes area matching and tilt geometry refinement. A map with limited resolution computed from uncorrected micrographs is compared to a volume computed from corrected micrographs with extended resolution.     

Three-dimensional image analysis of the complex of thin filaments and myosin molecules from skeletal muscle. I. Tilt angle of myosin subfragment-1 in the rigor complex

A three-dimensional image of the "rigor" complex of actin and chymotryptic myosin subfragment-1 was reconstituted from electron micrographs of negatively stained specimens. Data went out to 20 A radially and 26 A axially. The reconstituted images allowed us to deduce the angle between the major axis of the main part of myosin subfragment-1 and the axis of the actin helix. The subfragment-1 molecules were attached to the actin filament in a configuration in which they were tilted by only about 15 degrees from the plane perpendicular to the axis of the actin helix. The implication of the smaller tilt angle than the commonly accepted value is discussed.     

7A projection map of the S-layer protein sbpA obtained with trehalose-embedded monolayer crystals

Two-dimensional crystallization on lipid monolayers is a versatile tool to obtain structural information of proteins by electron microscopy. An inherent problem with this approach is to prepare samples in a way that preserves the crystalline order of the protein array and produces specimens that are sufficiently flat for high-resolution data collection at high tilt angles. As a test specimen to optimize the preparation of lipid monolayer crystals for electron microscopy imaging, we used the S-layer protein sbpA, a protein with potential for designing arrays of both biological and inorganic materials with engineered properties for a variety of nanotechnology applications. Sugar embedding is currently considered the best method to prepare two-dimensional crystals of membrane proteins reconstituted into lipid bilayers. We found that using a loop to transfer lipid monolayer crystals to an electron microscopy grid followed by embedding in trehalose and quick-freezing in liquid ethane also yielded the highest resolution images for sbpA lipid monolayer crystals. Using images of specimens prepared in this way we could calculate a projection map of sbpA at 7A resolution, one of the highest resolution projection structures obtained with lipid monolayer crystals to date.     

7 Å projection map of the S-layer protein sbpA obtained with trehalose-embedded monolayer crystals

Two-dimensional crystallization on lipid monolayers is a versatile tool to obtain structural information of proteins by electron microscopy. An inherent problem with this approach is to prepare samples in a way that preserves the crystalline order of the protein array and produces specimens that are sufficiently flat for high-resolution data collection at high tilt angles. As a test specimen to optimize the preparation of lipid monolayer crystals for electron microscopy imaging, we used the S-layer protein sbpA, a protein with potential for designing arrays of both biological and inorganic materials with engineered properties for a variety of nanotechnology applications. Sugar embedding is currently considered the best method to prepare two-dimensional crystals of membrane proteins reconstituted into lipid bilayers. We found that using a loop to transfer lipid monolayer crystals to an electron microscopy grid followed by embedding in trehalose and quick-freezing in liquid ethane also yielded the highest resolution images for sbpA lipid monolayer crystals. Using images of specimens prepared in this way we could calculate a projection map of sbpA at 7 Å resolution, one of the highest resolution projection structures obtained with lipid monolayer crystals to date.     

The tilting of the hydrocarbon chains in a single bilayer of phospholipid.

The tilt angle of the hydrocarbon chains to the planes of a dipalmitoryl lecithin single bilayer and multilayers were estimated by the asymmetry of the electron diffraction patterns of respective hydrated specimens. The chains in a single bilayer were found to be perpendicular to the bilayer plane, whereas the chains in the multilayers were found to be tilted with respect to the normal of the plane. Thermal analysis data also supported this conclusion.     

Electron crystallography of macromolecular periodic arrays on phospholipid monolayers

Electron crystallography has the potential of yielding structural information equivalent to x-ray diffraction. The major difficulty has been preparing specimens with the required structural order and size for diffraction and imaging in the electron microscope. 2D crystallization on phospholipid monolayers is capable of fulfilling both of these requirements. Crystals can form as a result of specific interactions with a protein's ligand or an analog, suitably linked to a lipid tail; or on a surface of complementary head-group charge. With such choices, the availability of a suitable lipid is limited only by synthetic chemistry. Ultimately, it is the quality and regularity of the protein-protein interactions that determine the crystalline order, as it is with any protein crystal. In the case of streptavidin, the monolayer crystal diffracts beyond 2.5 Å. A 3 Å projection map reconstructed from electron diffraction amplitudes and phases from images shows density which can be interpreted as β-sheets and clusters of side chains. It remains to be shown that the monolayer crystals are flat and diffract as well at high tilt angle as untilted. Technological issues such as charging must be resolved. With parallel advances in data collection and processing, electron crystallography of monolayer macromolecular crystals will eventually take its place beside x-ray crystallography and NMR as a routine and efficient structural technique.     

Structural differences between "dark" and "bright" isolated human osteonic lamellae

This investigation presents new insights into the structure of human secondary lamellae. Lamellar specimens that appear dark and bright on alternate osteon transverse sections under circularly polarizing light were isolated using a new technique, and examined by polarizing light microscopy, synchrotron X-ray diffraction, and confocal microscopy. A distribution of unidirectional collagen bundles and of two overlapping oblique bundles appears on circularly polarizing light microscopy images in relation to the angle between the specimen and the crossed Nicols' planes. The unidirectional collagen bundles observed at 45 degrees run parallel to the osteon axis in the dark lamellar specimens and perpendicular to it in the bright ones. Small and wide-angle micro-focus X-ray diffraction indicates that the dark lamellae are structurally quite homogeneous, with collagen fibers and apatite crystals preferentially oriented parallel to the osteon axis. Bright lamellar specimens exhibit different orientation patterns with the dominant ones bidirectional at +/-45 degrees with respect to the osteon axis. Accordingly, confocal microscopy evidences the presence of longitudinal bundles in dark lamellar specimens and oblique bundles in the bright ones. Radial bundles are evidenced in both lamellar types. The alternate osteon structure is described by a rather continuous multidirectional pattern, in which dark and bright lamellae display different mechanical and possibly biological functions.     

Two-dimensional structure of plant light-harvesting complex at 3.7 A [corrected] resolution by electron crystallography

The structure of the light-harvesting chlorophyll a/b-protein complex has been determined at 3.7 A resolution in projection by electron diffraction, electron microscopy and image analysis. Diffraction patterns and high-resolution spotscan images of two-dimensional crystals stabilized with tannin were recorded at low temperature. Phases of structure factors were obtained directly by image processing, after correction of the images for lattice distortions, defocus and beam tilt. Amplitudes were measured by electron diffraction. The projection map shows the detailed structure of the trimeric complex, suggesting the positions of two domains of potential structural and functional homology, of one membrane-spanning alpha-helix approximately perpendicular to the membrane plane and of several tightly bound lipid molecules.     

Single particle reconstructions of the transferrin-transferrin receptor complex obtained with different specimen preparation techniques

The outcome of three-dimensional (3D) reconstructions in single particle electron microscopy (EM) depends on a number of parameters. We have used the well-characterized structure of the transferrin (Tf)-transferrin receptor (TfR) complex to study how specimen preparation techniques influence the outcome of single particle EM reconstructions. The Tf-TfR complex is small (290kDa) and of low symmetry (2-fold). Angular reconstitution from images of vitrified specimens does not reliably converge on the correct structure. Random conical tilt reconstructions from negatively stained specimens are reliable, but show variable degrees of artifacts depending on the negative staining protocol. Alignment of class averages from vitrified specimens to a 3D negative stain reference model using FREALIGN largely eliminated artifacts in the resulting 3D maps, but not completely. Our results stress the need for critical evaluation of structures determined by single particle EM.     

Single versus dual-axis cryo-electron tomography of microtubules assembled in vitro: Limits and perspectives

Single-axis cryo-electron tomography of vitrified specimens has become a method of choice to reconstruct in three dimensions macromolecular assemblies in their cellular context or prepared from purified components. Here, we asked how a dual-axis acquisition scheme would improve three-dimensional reconstructions of microtubules assembled in vitro. We show that in single-axis tomograms, microtubules oriented close to the perpendicular of the tilt axis display diminished contrast, and ultimately transform into sets of parallel lines oriented in the direction of the electron beam when observed in cross-section. Analysis of their three-dimensional Fourier transform indicates that this imaging artifact is due to a decrease in the angular sampling of their equatorial components. Although the second orthogonal series does not fully complement the first one at the specimen level due to increased radiation damage, it still allows elongated features oriented in any directions to be correctly reconstructed, which might be essential for highly heterogeneous specimens such as cells.     

Electron Microscopic Observations on the Three-Dimensional Morphology of Apatite Crystallites of Human Dentine and Bone'

In sections of human dentine (carious and sound) and bone examined with the electron microscope, apatite crystallites were seen to present long thin profiles somewhat suggestive of a cylindrical shape, broad profiles indicative of a plate-like shape, and profiles intermediate between these two extremes. With a special stereoscopic specimen holder allowing the specimen to be tilted through an angle of 30° it was possible to record images of two profiles of the same crystallite from different angles and thus gain information concerning the 3-dimensional morphology of crystallites showing a thin profile. In all fields so examined, the thin-profile crystallites that were properly oriented with respect to the axis of tilt exhibited a different width dimension in each of the two micrographs. From this it is concluded that the thin profiles actually represented edge views of plate-like crystallites.     

Crystal structure and morphology of poly(12-dodecalactone)

Poly(12-dodecalactone) (PDDL) crystals in the form of chain-folded lamellae were prepared by isothermal crystallization from a 1-hexanol solution. The lozenge-shaped crystals with and without spiral growth have been studied by transmission electron microscopy and atomic force microscopy. Wide-angle X-ray diffraction data, obtained from PDDL lamellae sedimented to form oriented mats and annealed solvent-cast film, were supplemented with morphological and structural data from electron microscopy. PDDL crystallizes as an orthorhombic form with a P2(1)2(1)2(1) space group and lattice constants of a = 0.746 +/- 0.001 nm, b = 0.500 +/- 0.001 nm, and c (chain axis) = 3.281 +/- 0.003 nm. There are two chains per unit cell, which existed in an antiparallel arrangement. The fiber repeat distance is appropriate for an all-trans backbone conformation for the straight stems. Molecular packing of this structure has been studied in detail, taking into account both diffraction data and energy calculations. The setting angles, with respect to the a axis, were +/-43 degrees for the corner and center chains according to intensity measurements and structure factor calculations. The optimized shift along the crystallographic c axis is 0.1c (0.328 nm). A final model was obtained to yield R = 0.180 with X-ray diffraction data and R = 0.162 with electron diffraction data. A brief comparison is also made with related polymer structures.     

Characterization by electron microscopy of isolated particles and two-dimensional crystals of the CP47-D1-D2-cytochrome b-559 complex of photosystem II

A photosystem II complex containing the reaction center proteins D1 and D2, a 47-kDa chlorophyll-binding protein (CP47), and cytochrome b-559 was isolated with high yield, purity, and homogeneity; small but well-ordered two-dimensional crystals were prepared from the particles. The crystals and the isolated particles were analyzed by electron microscopy using negatively stained specimens. The information of 20 different digitized crystals was combined by alignment programs based on correlation methods to obtain a final average. The calculated diffraction pattern, with spots up to a resolution of 2.5 nm, and the optical diffraction pattern of a single crystal indicate that the plane group is p22121 (also called p2gg) and that the unit cell is rectangular with parameters of 23.5 x 16.0 nm, containing four stain-excluding monomers (two face-up and two face-down). In projection, the monomers have an asymmetrical shape with a length of 10 nm, a maximal width of 7.5 nm, and a height of 6 nm; their molecular mass is 175 +/- 40 kDa.     

ELECTRON MICROSCOPY OF STRUCTURAL DETAIL IN FROZEN BIOLOGICAL SPECIMENS

A procedure is described whereby preshadowed replicas can be obtained from frozen biological specimens which have been cut and then etched by sublimation of the ice from their surfaces. Electron micrographs showing details of the internal structure of plant virus crystals are presented to demonstrate the values of the procedure. Crystals of purified tobacco ringspot virus and squash mosaic virus and some portions of turnip yellow mosaic virus crystals have been shown to exhibit hexagonal packing. Sections through in situ crystals of tobacco mosaic virus show the rods to be parallel within each layer and arranged in a square net as viewed end on. Individual rods in each layer of the latter measure 300 mµ in length and are somewhat tilted with respect to the rods of adjacent layers. This results in the formation of a herring-bone appearance when a crystal is cut perpendicular to its hexagonal face. It is suggested that the procedure outlined here might well serve to supplement other procedures for the preparation of many cytological specimens for electron microscopy.     

Orientation of silk III at the air-water interface.

A threefold helical crystal structure of Bombyx mori silk fibroin has been observed in films prepared from aqueous silk fibroin solutions using the Langmuir Blodgett (LB) technique. The films were studied using a combination of transmission electron microscopy and electron diffraction techniques. Films prepared at a surface pressure of 16.7 mN/m have a uniaxially oriented crystalline texture, with the helical axis oriented perpendicular to the plane of the LB film. Films obtained from the air-water interface without compression have a different orientation, with the helical axes lying roughly in the plane of the film. In both cases the d-spacings observed in electron diffraction are the same and match a threefold helical model crystal structure, silk III, described in previous publications. Differences in the relative intensities of the observed reflections in both types of oriented samples, as compared to unoriented samples, allows estimations of orientation distributions and the calculations of orientation parameters. The orientation of the fibroin chain axis in the plane of the interfacial film for uncompressed samples is consistent with the amphiphilic behavior previously postulated to drive the formation of the threefold helical silk III conformation.     

Model for the structure of bacteriorhodopsin based on high-resolution electron cryo-microscopy

The light-driven proton pump bacteriorhodopsin occurs naturally as two-dimensional crystals. A three-dimensional density map of the structure, at near-atomic resolution, has been obtained by studying the crystals using electron cryo-microscopy to obtain electron diffraction patterns and high-resolution micrographs. New methods were developed for analysing micrographs from tilted specimens, incorporating methods previously developed for untilted specimens that enable large areas to be analysed and corrected for distortions. Data from 72 images, from both tilted and untilted specimens, were analysed to produce the phases of 2700 independent Fourier components of the structure. The amplitudes of these components were accurately measured from 150 diffraction patterns. Together, these data represent about half of the full three-dimensional transform to 3.5 A. The map of the structure has a resolution of 3.5 A in a direction parallel to the membrane plane but lower than this in the perpendicular direction. It shows many features in the density that are resolved from the main density of the seven alpha-helices. We interpret these features as the bulky aromatic side-chains of phenylalanine, tyrosine and tryptophan residues. There is also a very dense feature, which is the beta-ionone ring of the retinal chromophore. Using these bulky side-chains as guide points and taking account of bulges in the helices that indicate smaller side-chains such as leucine, a complete atomic model for bacteriorhodopsin between amino acid residues 8 and 225 has been built. There are 21 amino acid residues, contributed by all seven helices, surrounding the retinal and 26 residues, contributed by five helices, forming the proton pathway or channel. Ten of the amino acid residues in the middle of the proton channel are also part of the retinal binding site. The model also provides a useful basis for consideration of the mechanism of proton pumping and allows a consistent interpretation of a great deal of other experimental data. In particular, the structure suggests that pK changes in the Schiff base must act as the means by which light energy is converted into proton pumping pressure in the channel. Asp96 is on the pathway from the cytoplasm to the Schiff base and Asp85 is on the pathway from the Schiff base to the extracellular surface.     

Preparation and analysis of large, flat crystals of Ca(2+)-ATPase for electron crystallography.

Obtaining large, flat, well ordered crystals represents the key to structure determination by electron crystallography. Multilamellar crystals of Ca(2+)-ATPase are a good candidate for this methodology, and we have optimized methods of crystallization and of preparation for cryoelectron microscopy. In particular, high concentrations of glycerol were found to prevent nucleation and to reduce stacking; thus, by seeding solutions containing 40% glycerol, we obtained thin crystals that were 5-30 microns in diameter and 2-10 unit cells thick. We found that removing vesicles and minimizing concentrations of divalent cations were critical to preparing flat crystals in the frozen-hydrated state. Finally, we developed two methods for determining the number of lamellae composing individual crystals, information that is required for structure determination of this crystal form. The first method, using low magnification images of freeze-dried crystals, is more practical in our case. Nevertheless, the alternative method, involving analysis of Laue zones from electron diffraction patterns of slightly tilted crystals, may be of general use in structure determination from thin, three-dimensional crystals.     

Cryo-negative staining reduces electron-beam sensitivity of vitrified biological particles

Beam damage is the main resolution-limiting factor when biological particles are observed by cryoelectron microscopy in a thin vitrified solution film. Furthermore, the low contrast of the specimen frequently makes observation difficult and limits the possibility of image processing. Cryo-negative staining, in which the particles are vitrified in a thin layer of concentrated ammonium molybdate solution, makes it possible to visualize the particles with a much better signal-to-noise ratio (SNR) while keeping the specimen in a good state of preservation. We have observed the Escherichia coli GroEL chaperonin, prepared in a native vitrified solution and by cryo-negative staining after electron exposure from 1000 to 3000e(-)/nm(2). We have compared the resulting three-dimensional models obtained from these different conditions and have tested their fit with the atomic model of the protein subunit obtained from X-ray crystallography. It is found that, down to 1.5-nm resolution, the particles appear to be faithfully represented in the cryo-negatively stained preparation, but there is an approximately 10-fold increase of SNR compared with the native vitrified preparation. Furthermore, for the same range of irradiation and down to the same resolution, the particles seem unaffected by beam damage, whereas the damage is severe in the native vitrified particles.     

Two-dimensional crystallization of the ryanodine receptor Ca2+ release channel on lipid membranes

The ryanodine receptor (RyR) is the largest known membrane protein with a total molecular mass of 2.3 x 10(3) kDa. Well ordered, two-dimensional (2D) crystals are an essential prerequisite to enable RyR structure determination by electron crystallography. Conventionally, the 2D crystallization of membrane proteins is based on a 'trial-and-error' strategy, which is both time-consuming and chance-directed. By adopting a new strategy that utilizes protein sequence information and predicted transmembrane topology, we successfully crystallized the RyR on positively charged lipid membranes. Image processing of negatively stained crystals reveals that they are well ordered, with diffraction spots of IQ < or = 4 extending to approximately 20 angstroms, the resolution attainable in negative stain. The RyR crystals obtained on the charged lipid membrane have characteristics consistent with 2D arrays that have been observed in native sarcoplasmic reticulum of muscle tissues. These crystals provide ideal materials to enable structural analysis of RyR by high-resolution electron crystallography. Moreover, the reconstituted native-like 2D array provides an ideal model system to gain structural insights into the mechanism of RyR-mediated Ca2+ signaling processes, in which the intrinsic ability of RyR oligomers to organize into a 2D array plays a crucial role.