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Three-dimensional structure of a wide range of biological specimens can be computed from images collected by transmission electron microscopy. This information integrated with structural data obtained with other techniques (e.g., X-ray crystallography) helps structural biologists to understand the function of macromolecular complexes and organelles within cells. In this paper, we compare two three-dimensional transmission electron microscopy techniques that are becoming more and more related (at the image acquisition level as well as the image processing one): electron tomography and single-particle analysis. The first one is currently used to elucidate the three-dimensional structure of cellular components or smaller entire cells, whereas the second one has been traditionally applied to structural studies of macromolecules and macromolecular complexes. Also, we discuss possibilities for their integration with other structural biology techniques for an integrative study of living matter from proteins to whole cells.
Three-dimensional (3D) structural studies of biological matter, from proteins to whole cells, are of a great importance for fully understanding the function of macromolecular complexes and organelles within cells. The 3D structure of a cellular component is tightly related to its function within a cell, and the knowledge of both structure and function is necessary, for instance, to design drugs whose targets are particular proteins. The quality of the 3D structure is usually expressed in terms of resolution, which measures the level of detail contained in the structure. High resolution means the possibility of interpreting the structure at a high level of detail, which is mandatory for understanding its function.
Several complementary techniques have been developed for determining the 3D structure of biological specimens. In the case of molecules that can either auto-assemble or be coerced to assemble in 3D crystals, X-ray diffraction is traditionally used to determine their atomic structure. Moreover, since the development of synchrotron radiation in the sixties, structural biology blossomed, and nowadays, several hundreds of macromolecular structures are solved each year by X-ray crystallography. However, a large number of macromolecules diffract poorly or cannot be crystallized. For such samples, alternative approaches must be used. For example, for particles with low molecular weight (lower than 30 kDa), nuclear magnetic resonance is a very powerful technique. For larger macromolecular assemblies (molecular weights higher than 30 kDa) and other, larger cellular components, 3D transmission electron microscopy (TEM) techniques are the best exploration methods.
Although electron crystallography and helical–icosahedral reconstruction techniques are limited to the study of specimens having some special properties (crystalline or highly symmetric, respectively), single-particle analysis (SPA) and electron tomography (ET) are more general techniques, whose potential for combining and correlating starts attracting attention of many structural biology labs that have been specialized for one of the techniques and are now adopting the other as well. The goal of this paper is to briefly describe and compare these two techniques in the light of their potential combination.
In this section, we present the main principles of SPA and ET reconstructions, techniques for specimen protection against radiation damages and possibilities for automated image acquisition.
Diffraction, Fourier transform, central slice theoremand common lines
The Fourier transform plays a central role in image acquisition and in image processing for 3D reconstruction. In TEM, either an electron diffraction pattern in the back-focal plane or an image in the image plane can be recorded from an object. The space where the diffraction pattern forms is reciprocal space, whereas the space at the image plane is real space. The transformation from the real space to the reciprocal space is given by the Fourier transform. A diffraction pattern resembles the power spectrum (calculated from the Fourier transform) of the object that forms this diffraction pattern.
To explain the principle of 3D reconstruction, one usually uses the central slice theorem (DeRosier & Klug, 1968; Kak & Slaney, 1988). Thanks to this theorem, the 2D Fourier transforms of 2D projection images can be assembled in the 3D Fourier space, which then only should be inverted to provide the 3D real-space information about the structure of the studied specimen. More precisely, this theorem says that a central slice (i.e., a central plane) through the origin in reciprocal space corresponds to the projection in real space in a direction normal to the plane. Since any two central slices have a line in common (common line), a consequence of this theorem is that it is possible to determine the orientation of one projection plane with respect to other projection planes by determining a relative orientation of their commonlines.
Principles of SPA and ET reconstructions
SPA is used for studies of macromolecules and macromolecular assemblies whose structure and dynamic interactions can be analyzed in vitro, in isolation (e.g., proteins, ribosomes, viruses). The data collection for this approach consists in taking 2D projections of a sample containing many identical but differently oriented copies of the same object (Fig. 1(A)). Thus, when an even distribution of single particle orientations is observed on the specimen grid, this technique allows collecting all necessary data for the computation of a 3D average structure of the studied particles.
Conversely, ET is aimed at the study of systems maintaining their in vivo structural integrity as much as possible such as cells, cell portions or tissues, although it is also used for structural studies of isolated macromolecular complexes and organelles such as mitochondria (Nicastro et al., 2000). The data for ET reconstruction are collected by taking multiple 2D projections of the same specimen being gradually rotated around an axis perpendicular to the electron beam (Fig. 2(A)) or around two or more tilt axes (Penczek et al., 1995; Mastronarde, 1997; Messaoudi et al.,2006).
Structure preservation and contrast-enhancing methods
Before image acquisition, biological specimens must be protected against radiation generated in or by the microscope; otherwise, the interaction of electrons with non-protected organic matter damages its structure (Glaeser, 1971). Radiation damage is reduced at low temperatures. Cryo-electron microscopy (cryo-EM) is a protection method that preserves the specimen structure in near-physiological conditions. This technique consists of embedding the specimen in vitreous water using a rapid-freezing method such as plunge-freezing, where the specimen is rapidly plunged into liquid ethane (c. –150°C) thereby dropping its temperature at an approximate rate of 104°C s−1, followed by imaging of the frozen-hydrated specimens maintained at either liquid nitrogen or liquid helium temperatures (less than –160°C) (Dubochet et al., 1988).
In the case of SPA, cryo-EM grids with specimens embedded in 60- to 100-nm-thick vitreous water are readily prepared from aqueous suspensions. However, a problem of cryo-EM is that the electron doses required for a good SNR lead to unacceptable specimen damage (Hayward & Glaeser, 1979). Therefore, to acquire high-resolution images, the electron dose must be kept at a low level [e.g., 10 electrons Å−2 in the case of SPA and a 200-kV microscope (Jonic et al., 2007)]. This means that high-resolution images have a poor contrast and are dominated by noise (for an example of this type of image, see Fig. 1(B)).
Cryo-ET (ET of frozen-hydrated specimens) encounters at least three additional problems. First, the image contrast is low because of the small difference in mass density between unstained clusters of macromolecules and the frozen cytosol that surrounds them. It is therefore hard to visualize fine details of cellular sub-structure even when under-focussing the microscope objective lens to produce phase contrast (McIntosh et al., 2005).
Second, the method of plunge freezing gives the best results on relatively thin specimens (up to 500-nm-thick specimens, which include isolated organelles, small cells and thin parts of larger cells). Thicker specimens (e.g., thick parts of larger cells and tissues) are difficult to vitrify owing to lower cooling rates at the centre of the thick specimen (Studer et al., 1989). To vitrify thicker samples while avoiding the formation of ice crystals and their damage to specimen, special instrumentation is required. With high-pressure freezing, samples as thick as 500 μm can be vitrified with no ice crystals (Studer et al., 1989). Potential damaging effects of high pressure on the specimen structure are minimized if the pressure is increased quickly and followed immediately by rapid freezing.
The third problem encountered when using cryogenic techniques for ET is also related to the specimen thickness. Thick specimens should be cut in sections appropriate for electron microscopy (20–500 nm thick), whereas slices as thin as 20–100 nm may be required for a high-resolution serial section reconstruction (single images of individual thin sections are computationally merged to obtain a 3D reconstruction). Cutting of frozen-hydrated thick specimens at cryogenic temperatures is extremely difficult and many artefacts (such as knife marks, crevasses and compression) are generated during cryo-sectioning, which complicate the interpretation of the 3D reconstruction (Richter, 1994; Sartori Blanc et al., 1998). The production of cryo-sections is an art currently practiced by relatively few laboratories (Al-Amoudi et al., 2004a).
One alternative is to create plastic sections by freeze substitution; material is vitrified by high-pressure freezing and water is then substituted with organic solvents containing chemical fixatives at temperatures around –80°C (Zalokar, 1966; Kellenberger, 1991). The samples are warmed at a temperature around –40°C, embedded in plastic or resin and sectioned at room temperature. The contrast is often increased by post-staining with a heavy metal salt solution. An example of a freeze-substitution image is presented in Fig. 2(B).
This method is an improved version of a conventional one that consists in performing the following steps at room temperature: specimen chemical fixation, dehydration in organic solvents, embedding in resin or plastic, sectioning and post-staining. The improvement is that the structure is better preserved since the artefacts caused by chemical fixation and dehydration at room temperature are avoided. However, the method based on freeze substitution is not completely free of artefacts (Dubochet & Sartori Blanc, 2001). Moreover, cryo-EM images of thin frozen-hydrated sections show differences with respect to the images of plastic sections obtained after high-pressure freezing and freeze substitution (Al-Amoudiet al., 2004b).
Unfortunately, although the freeze-substitution method allows studies of whole cells and tissues and provides a good representation of membranous and larger supramolecular structures, it does not reach the resolution needed for a reliable interpretation at the molecular level mostly owing to radiation-induced distortions (Section ‘Resolution’).
Negative staining with heavy metal salts is often used for increasing the contrast in electron microscopy (Brenner & Horne, 1959). The heavy metals accumulate around the molecules of the specimen and also penetrate the cavities replacing water. Although the stain increases the contrast in images, it is not recommended for use in high-resolution structural studies because the images do not show faithfully the internal structure of biological material but only molecular surfaces accessible to the stain. However, staining can be useful in low-resolution studies aimed at obtaining an initial 3D model that can be further refined using high-resolution, unstained images.
Unlike the ET of stained plastic sections, cryo-ET of unstained cryo-sections has the potential to reach the resolution required for a reliable interpretation at the molecular level. Its broader use requires further development of methods for routinely cutting good-quality thin sections. A promising method for producing thin sections of frozen-hydrated specimens is focussed ion beam, which is commonly used in materials science to shape specimens for a variety of applications. It has been recently shown that focussed ion beam can be used for artefact-free thinning of whole frozen-hydrated cells, which leads to a successful reconstruction by cryo-ET (Marko et al., 2007).
Automation of electron microscopes started in the early 1990s (Dierksen et al., 1992). Nowadays, robots automatically loading samples in the microscope are being developed (Potter et al., 2004). Data-collection software for the microscope automatically surveys sample grids to select areas with appropriate ice thickness, autofocus and record images (Zheng et al., 2004; Lei & Frank, 2005; Nickell et al., 2005; Suloway et al., 2005; Stagg et al., 2006; Nickell et al., 2007). One can also automatically monitor specimen tilt (Ziese et al., 2003) or detect and discard images presenting defects such as charging, drift and absence of signal (Jonic et al., 2007). The common goal of all these ongoing developments is to allow a quasi-automatic computation of a 3D map at sub-nanometer resolution within a day or two after inserting the specimen grid in the microscope (Zhu et al., 2001). However, the acquisition is still mainly manual because these methods are not standard yet and especially because of difficulties in transferring specimen grids in the microscope in the case of cryo-techniques.
Regarding ET, the automation of data acquisition is indispensable for minimization of the exposure time. Since the same specimen is subjected to multiple exposures, the accumulated electron dose should be kept at a minimum. Ideally, the total time of a micrograph acquisition should be equal to the time of its recording. However, the recording is preceded by automated tracking and auto-focussing to compensate for the specimen lateral displacement and the displacement in the beam direction, respectively (Koster et al., 1997; Rath et al., 1997). They are performed on low-dose micrographs recorded at positions that are different from the final exposure position to minimize the received electron dose. Mechanical inaccuracies of the specimen holder are the main cause of the specimen movements during tilting, and ongoing development of procedures based upon a prediction of the specimen movement and highly stable specimen holders will lead to a faster acquisition under low-dose, cryo-conditions (Zheng et al., 2004).
Imaging of a 3D object at different orientations using a static electron source and detector system is equivalent to imaging of a static 3D object using an electron source and detector system that rotate around the object. Thus, each 2D projection image acquired in an electron microscope corresponds to one projection direction in the equivalent system (Fig. 3). The reconstruction of an object from its 2D projection images acquired in the electron microscope is therefore usually performed in two steps. In the first step, the object is centred and aligned rotationally with respect to the principal axes in each of the object's individual experimental images, and the projection direction is determined for each of these images. In the second step, a volume is reconstructed using these images and their orientation and position parameters computed in the previous step.
For the reconstruction using SPA, a sufficient number of copies of the studied object has to be extracted from the acquired micrographs. Many algorithms have been developed for automatic particle selection and their extraction from micrographs (Nicholson & Glaeser, 2001; Zhu et al., 2004).
Alignment for the first 3D model
There are two types of techniques for determining the orientation and position of 2D projections in 3D space: reference-free and reference-based. Reference-free methods are used to determine the alignment parameters for computing a first, low-resolution 3D model since they do not require any reference 3D model. Reference-based methods require a reference 3D model and refine the alignment parameters iteratively to determine a high-resolution 3D model. Reference-free methods are discussed in this section, whereas reference-based methods will be discussed in the section ‘Refinement of the alignment’.
In SPA, the orientation of each copy of the object has to be determined before starting the 3D reconstruction process. Two techniques are commonly used to determine the orientation of particles for the first 3D model: the method of random conical tilt series (Radermacher, 1988) and the techniques based on common lines (Crowther, 1971; van Heel, 1987; Goncharov, 1990; Penczek et al., 1996). According to the method of random conical tilt series, each field is imaged twice (with the specimen holder tilted at 45° and 0°). The orientation of the tilted particles is determined from the known tilt geometry and the alignment and classification of the untilted particle images. These parameters are then used with the tilted particle images for the computation of a first 3D reconstruction volume. The techniques that use common lines generally require the classification of particle images and computation of class averages to reduce noise for a correct image alignment. Geometrical relationships between class averages are then computed using the relative orientation of their common lines, and a first 3D reconstruction volume is then computed using the determined orientation parameters and the class averages. Three different projections are at least required to orient images of an entirely asymmetric particle and to determine the enantiomorphic type of the 3D structure.
In ET, projection images share a common line that corresponds to the tilt axis. Therefore, the determination of the tilt axis is essential for an accurate 3D reconstruction. Ideally, the object does not move during image acquisition. In this ideal case, the orientation of the tilt axis would be found as a common line present in all power spectra of the specimen tilt series. However, in practice, one generally has to perform a translational and rotational alignment of the projection images to determine the orientation of the tilt axis because of drifts that occur during image acquisition. These drifts have a mechanical origin but may be coupled with charging effects or thermal drifts in the case of samples observed at liquid nitrogen temperature. The post-acquisition 2D alignment can be performed using methods based on cross-correlation or using recognizable features such as gold fiducial markers added to the sample (Guckenberger, 1982; Lawrence, 1992; Owen & Landis, 1996; Brandt et al., 2001; Winkler & Taylor, 2006). Once the tilt series is aligned and the tilt parameters are determined, the 3D structure can be computed using any of the reconstruction methods described later.
The most widely used families of reconstruction algorithms in 3D TEM are direct Fourier inversion, backprojection and algebraic methods. The direct Fourier inversion methods use the central slice theorem to assemble the 2D Fourier transforms of the experimental images within an estimated 3D Fourier transform of the object (Kak & Slaney, 1988; Grigorieff, 1998; Penczek et al., 2004). Complicated interpolation schemes are required to compute the 3D Fourier transform on a regular grid (Lanzavecchia et al., 1999; Penczek et al., 2004). A 3D model of the object in real space is then obtained after the inverse 3D Fourier transformation.
Backprojection methods combine real-space experimental images in real 3D space to reconstruct a 3D object (Kak & Slaney, 1988). Simple linear real-space interpolation is usually sufficient in this case. Images are usually weighted before being summed in real 3D space to compensate for an uneven sampling in the reciprocal space (enhancement of low frequencies) (Harauz & van Heel, 1986; Radermacher et al., 1986; Radermacher, 1992). This method is known as weighted backprojection and it is particularly suited to conical-tilt geometry (Radermacher, 1988).
Algebraic methods express the reconstruction volume in real space as a weighted sum of shifted basis functions (e.g., voxels, blobs) and then estimate the weights through a linear equation system (Herman, 1980). The most popular algebraic methods in 3D TEM are Block ART (for Algebraic Reconstruction Technique) (Gordon et al., 1970; Marabini et al., 1998) and SIRT (for Simultaneous Iterative Reconstruction Technique) (Gilbert, 1972; Penczek et al., 1992). In the case of an uneven distribution of projection directions, it was shown that both weighted backprojection and algebraic methods produce elongations of the reconstructed volumes in the regions with the highest concentration of projection directions (Boissetet al., 1998; Sorzano et al., 2001). However, with the same data set, algebraic reconstruction methods with the proper selection of free parameters do not exhibit these elongations (Sorzano et al., 2001).
Refinement of the alignment
Many iterative algorithms have been developed to refine orientation and position of particle images with respect to a reference volume. There are two types of these algorithms. Both estimate the alignment parameters for an experimental image by minimizing the dissimilarity between the experimental image and 2D projections of the reference volume (reference projections). The first type of algorithms samples the space of test angles and the space of test translations uniformly, and compares the experimental image with only those reference projections that were computed using a set of reference, uniformly sampled projection directions (Penczek et al., 1994; Radermacher, 1994; Sorzano et al., 2004b). In each iteration, a 3D reconstruction is computed from experimental images using the current alignment parameters, and this volume is used in the next iteration as a reference. The sampling step for the computation of reference projections is reduced gradually during the iterative refinement to improve the alignment accuracy. The smaller is the step, the more accurate is the alignment, butthe slower is the determination of the alignment parameters.
The second type of refinement algorithms does not require a parameter such as a sampling step (Grigorieff, 1998; Jonic et al., 2005; Grigorieff, 2007). Reference projections for comparison with experimental images are computed with orientation and position parameters determined by gradient-based optimization algorithms. These methods determine the alignment parameters in Fourier space using the central slice theorem. This means that they are fast but may require more complicated interpolation schemes than the firsttype of algorithms. Traditionally, the refinement is done using the first type of algorithms until the algorithm gets close to the solution. Then, to perform a fast refinement around the lastly computed alignment parameters, the refinement is continued using the second type of refinement algorithms.
If microscopes were totally devoid of defects, their resolution would only be limited by the wavelength of the beam (Abbe, 1873). In this ideal case, even at 80 kV [the wavelength of 0.004 nm determining the theoretical limit of resolution of approximately 0.002 nm (Hawkes & Spence, 2007)], details as small as 0.002 nm could be reliably seen. However, such a high resolution is never achieved with 3D reconstruction practices. Other than the accuracy with which the individual images are aligned before the reconstruction and the accuracy of the reconstruction algorithm, many other practical factors limit the achievable resolution in practice. They will be discussed in this section as well as measurement of resolution.
Frozen-hydrated samples prepared by plunge freezing are likely to represent living cells because the sample is frozen within milliseconds and many of the cells will grow and divide when warmed rapidly to physiological temperatures (McIntosh, 2001). In high-pressure freezing, if the pressure is increased quickly and followed immediately by rapid freezing, the potentially damaging effects of high pressure are minimized and, as in plunge freezing, many frozen cells will live after thawing. However, once the freeze substitution takes place, the cells will not recover when warmed as all the water has been replaced by organic solvent.
Regarding the use of stain for contrast enhancement, the position of the stain might not accurately reflect the shapes of the macromolecules to which it binds. An additional problem encountered when using stain in ET is that the required electron dose can cause migration and agglomeration of the stain, which makes interpretation of the 3D reconstruction difficult.
The noise in experimental images is mainly caused by an insufficient sampling of the electron scattering from the specimen and by imperfections of the image detector. Three-dimensional reconstruction acts as a low-pass filter, which reduces the noise in three dimensions. However, the 3D structure is to some extent still obscured by the noise, which limits the usable resolution. This is especially true in the case of volumes obtained by cryo-ET (cryo-tomograms), which have extremely low SNRs. The low SNR is usually increased using a filtering algorithm (Stoschek & Hegerl, 1997; Frangakis & Hegerl, 2001; Jiang et al., 2003). These algorithms remove some noise but may, at the same time, remove a part of the signal. Denoising based on wavelet transforms preserves better the structural information (Stoschek & Hegerl, 1997).
Higher electron doses (e.g., greater than 10 electrons Å−2 in a 200-kV microscope) produce less noisy images but damage the sample through ionization, breaking of chemical bonds and formation of free radicals, deteriorating thus the resolution.
At room temperature, for instance, in the case of plastic sections prepared using high-pressure freezing with freeze substitution, the most striking effect of radiation damage is the shrinkage of sections (40–50% in the direction of the beam and 5–10% in the plane perpendicular to it) owing to the loss of mass (Lucic et al., 2005). This makes difficult an accurate 3D reconstruction and produces ambiguities in combining tomograms from neighbouring sections. Thus, an inaccurate representation of the native material due to preparation and beam-induced artefacts mainly limits the resolution achievable with this method.
The radiation damage at low temperatures causes a gradual deterioration of the achievable resolution, formation of bubbles of H2 gas from decomposed water in the sample but no mass loss (Leapman & Sun, 1995; Lucic et al., 2005). According to the principle of dose fractionation, the tolerable dose in ET should be divided among all tilt-series images; thus, the SNR of a tomogram is determined by the total dose for all images (McEwen et al., 1995). The total dose received by the object should be kept as low as possible, which requires a fast and automatic data acquisition (Koster et al., 1997). However, in practice, the dose per image is selected to be sufficient to produce enough detail in images for their accurate alignment.
Thickness of the sample
With the thicker samples that take advantage of ET, the likelihood that a beam electron will interact more than once with the sample is increased. In this case, the image is no longer a simple projection of the sample, which means that image resolution is reduced, unless a specific correction is made. In the case of inelastic scattering, the incident electrons lose energy while transferring it to the sample. This causes damage to the sample (ionization and formation of free radicals), which also reduces image quality. The inelastic electron scattering contributes to the formation of the background noise in the electron diffraction pattern. Therefore, when imaging thicker samples, the contrast improvement is often done using a filter that removes most of the electrons having lost energy (energy filtering), which improves the SNR (Grimm et al.,1996).
Only the smallest cells, the thinnest parts of cells and some isolated organelles are appropriate for ET without cutting the sample into slices of suitable thickness [200 nm or less for a microscope at 200 kV, 400 nm or less at 300 kV and 500 nm or less at 1000 kV (McIntosh et al., 2005)].
Resolution improvement in the case of thick samples will require improving the ability of CCD cameras to capture energetic electrons (e.g., 300 keV that work well for thicker specimens) and to better preserve structural information at high spatial frequencies (McIntosh et al., 2005).
Contrast transfer function
One of the factors limiting the resolution are imperfections of the electron microscope (spherical and chromatic aberrations, instabilities of magnetic lenses, instabilities of electron acceleration, additive noise, drift or charging etc.) that cause image deterioration (Frank, 2006a). Image formation with a majority of microscope imperfections is modeled by the contrast transfer function (CTF). The CTF is expressed in reciprocal space and its equivalent in real space is named point spread function as it describes how a single point is spread into a diffused spot when imaged in the microscope.
The development of methods for a more accurate estimation and correction of the CTF is an old topic in SPA, although still attractive. However, the development of methods for CTF estimation and correction in ET started only recently. The interest to correct for the CTF in ET has arisen only when reconstructions approaching molecular resolutions started being obtained in practice. However, the CTF estimation methods used in SPA cannot be applied directly in ET because of different image acquisition geometries in the two cases. Theoretical modelling of the CTF in ET to take into account the tilt of the sample grid and the specimen thickness is a research in progress (Lawrence et al., 2006; Philippsen et al., 2007). The correction of the CTF will require its correct estimation from images using the theoretical CTF model. Currently, this seems to be a very difficult task, especially in the case of low-dose tilt-series images of non-stained, frozen-hydrated specimens because of a very low SNR. Further improvements in the CCD camera design that will allow a better detection of moderate- to high-resolution structural details and a reduced noise level in acquired images are necessary to permit the CTF estimation and correction and, thus, make possible reaching resolutions below 3 nm.
The majority of objects studied by electron microscopy and certainly all cryo-specimens are phase objects. A phase object does not absorb radiation (the outgoing wave has the same amplitude as the incoming wave), but rather delays or advances the incoming wave, leading to an object wave that locally has a phase different from that in the rest of the object plane. When recording images, the amplitude information (i.e., the square of the wave functions) is only recorded, whereas the phase information is lost. Thus, the image registered in an ideal microscope will not show the phases that we are most interested in, but rather just a homogeneous grey image. The phase information becomes visible after defocussing the microscope (causing the lenses to deviate from the focus). The electron microscope has an aberration (spherical aberration) that causes additional phase shifts in the back focal plane. Combining under-focus and spherical aberration, one manipulates the phases of the diffracted beams with respect to the zero-order beam such that they interfere constructively in the image plane. In this way, one optimizes the instrument to convert the phase variations in the object plane into amplitude variations in the image plane, which means that the amplitudes in the registered image contain the information about the phases, which is exactly what we are interested in.
Given the right combination of under-focus and spherical aberration, one obtains an almost ideal phase-contrast microscope for a large frequency range. Zernike proposed the use of a phase plate in the back focal plane of the microscope to obtain exactly the same optical situation but without manipulating under-focus and spherical aberration (Zernike, 1942). The phase plate changes the relative length of the optical path of the diffracted beams with respect to the zero-order beam such that an extra phase difference is introduced between the two, which causes their interference. When using phase plates, CTF correction is not required (Danev & Nagayama, 2001, 2008). The phase plates have been shown to preserve low-frequency signal components well, which results in the improvement of the image contrast (Danev & Nagayama, 2001, 2007). Because of the potential for contrast improvement, they may find more applications in the future in imaging thick samples as in the ET case.
Missing projection directions
To determine the 3D structure of an object, one should collect its 2D projections from all possible directions. In ET practice, however, only a limited set of projections can be collected in the microscope because of specimen damage under the electron beam and to specimen tilt limitations in the microscope. Owing to the slab geometry of most specimens, the specimen appears thicker to electrons when increasing the tilt angle. A longer electron path through a thick sample than through a thin sample (the two samples tilted at the same angle) means that high tilt is useful for thinner specimens but not for thicker ones. The limiting factor at higher tilt angles is the thickness of the grid bars and the geometry of specimen holders. Thus, the maximum tilt angle is limited at around 70° since the electrons could still penetrate the sample at higher angles, albeit at a lower probability. However, specimen holders with geometries that will allow recording of projection images over a full 360° tilt range are in development [e.g., cylindrically symmetric specimen holders (Barnard et al., 1992)]. The consequences of being unable to acquire images from all directions are artefacts in the computed 3D structure. Thanks to the central slice theorem (DeRosier & Klug, 1968; Kak & Slaney, 1988), these artefacts can be explained by the empty regions in the 3D Fourier space in which no information about the specimen was recorded. A particular shape of the artefacts in the 3D Fourier space in the case of single tilt axis is a wedge, which corresponds to the wedge in which no information about the specimen was recorded owing to the maximum tilt angle limit (thus the name ‘missing wedge’ for this type of artefacts). The negative effects of the missing wedge can be partially overcome by using two (Penczek et al., 1995; Mastronarde, 1997) or more tilt axes (Messaoudi et al., 2006). Double-tilt axis geometry reduces the missing wedge artefact to a ‘missing pyramid’ artefact (Penczek et al., 1995; Mastronarde, 1997).
When taking images without tilting the specimen grid, as is the case in SPA, it is theoretically possible to acquire images from all projection directions (an example of a projection image acquired with this type of data collection geometry is shown in Fig. 1(B)). However, in practice, there might be missing projection directions because some particles may adopt preferred orientations. Hence, particles presenting some strong hydrophobic areas might always present these surface areas at the air–water interface of cryo-EM specimen grids (e.g., mammalian chaperonin CCTP).
When studying the specimen using SPA, structural variability of the sample is very often the main factor limiting the resolution. Macromolecules with structural flexibility may adopt different conformations to perform different molecular functions. However, reconstruction algorithms assume that images come from a homogeneous population (identical copies of a macromolecule). Several methods have been developed to study structural heterogeneity. These methods either separate projections in homogeneous classes using multi-reference classification or multivariate statistical classification (van Heel & Frank, 1981; van Heel & Stoffler-Meilicke, 1985; Lata et al., 2000; Heymann et al., 2003; Heymann et al., 2004), compute elastic geometric transformations between (pseudo)atomic coordinates of two provided 3D structural conformations (Tama et al., 2004), explicitly estimate the structural variability present in projections (Penczek et al., 2006b) and identify regions that are the most likely to vary from one image to another (Scheres et al., 2007).
Several measures of resolution of volumes reconstructed with SPA techniques have been proposed in the literature (Penczek, 2002; Unser et al., 2005; van Heel & Schatz, 2005; Sousa & Grigorieff, 2007). The most used in practice are those based on the Fourier shell correlation (FSC) (Harauz & van Heel, 1986; van Heel & Schatz, 2005). It comprises a division of the experimental-image data set in two sub-sets, a reconstruction of one volume from each sub-set, and a computation of the correlation between the 3D Fourier transforms of the volumes over shells of frequencies in the 3D Fourier space. A good agreement at low frequencies is indicated by the FSC value close to 1. The FSC falls gradually down for higher frequencies, which indicates a poor agreement between the two volumes at these frequencies. The resolution is thus usually determined as the Fourier shell radius for which the FSC falls below 0.5 (Bottcher et al., 1997), although the FSC thresholds other than 0.5 are also in use (Saxton & Baumeister, 1982; Orlova et al., 1997; Rosenthal & Henderson, 2003; van Heel & Schatz, 2005). A reliable resolution measure is only obtained when the two half data sets are aligned against two independent reference structures. When the alignment of images is done against the same reference, the resolution is over-estimated because the alignment introduces a correlation between the noise components present in the images (Grigorieff, 2000). However, the alignment against two independent references is rarely done in practice.
Regarding ET, a theoretically achievable resolution can be obtained from the Crowther criterion (Crowther et al., 1970). According to this criterion, the resolution is proportional to the size of the object in the direction of the electron beam and inversely proportional to the number of images in a tilt series used for the object reconstruction. This means that highest resolutions can be achieved with smallest objects and when using a large number of images. This criterion is only valid for spherical specimens and for constant tilt increment and, thus, has limited practical applications in ET. A practical use of this criterion is also limited by a poorly defined size of the object studied by ET (sub-cellular components have various sizes in a cell) and by a non-isotropic resolution due to a limited tilt-angle range (e.g., in single-axis tilt, the objects perpendicular to the plane defined by the direction of the electron beam and the tilt axis are almost not resolved; in double-axis tilt, the resolution is more isotropic because a smaller region in the 3D Fourier space remains uncovered by the projection data). Also, the resolution achievable in practice is affected by other factors that are not covered by this criterion (see above). The measures that are used in SPA to estimate the resolution of the reconstructed volumes can be directly applied to ET, although this is rarely done, mainly because of the anisotropy of resolution of tomograms and a small number of images. Yet, specific resolution measures have been designed for ET, for instance, the one that allows assessment of the dependence of the resolution on the tilt angle by comparing experimental projection images with the corresponding projections of the tomogram (Cardone et al., 2005). Currently, they are rarely used in practice, and the resolution is still usually estimated either from the position of the first zero of the CTF of projection images (an exact value of the defocus, which is maintained constant for all images in the tilt series, determines the position of the first zero of the oscillating CTF and, thus, the achievable resolution limit) or as the minimal distance between the points recognized to belong to two distinct objects.
Examples of reconstructed structures
Despite the imperfections of currently existing ET and SPA methods, important information has been obtained about the structure and the underlying biological function of many macromolecular complexes, organelles, parts of cells and entire cells.
Figures 1(B–D) show an application of cryo-EM and SPA methods to determine the 3D organization of the (αβ)6 1.2 MDa multi-enzymatic complex Glutamate synthase (GltS) from Escherichia coli. The GltS are found in bacteria, yeast and plants, where they form with glutamine synthetase an essential pathway for ammonia assimilation. The technique used to compute the 3D electron density map of the whole complex is described in Sorzano et al. (2007a) and the interactions and function of the GltS sub-units are discussed in Cottevieille et al. (2008). The structure was computed from low-dose cryo-EM images of a GltS sample on a holey carbon film vitrified by plunge freezing in liquid ethane (Fig. 1(B)). As the global shape of the GltS was unknown at the beginning, the random conical tilt series method was used to compute a first, low-resolution structure (Radermacher et al., 1987). This first model was refined using iterative projection matching combined with the CTF correction by Wiener filtering of volumes from focal series (Penczek et al., 1994, 1997) until the resolution stabilized at 9.5 Å. In each of the refinement iterations, the volume was symmetrized according to D3 point-group symmetry, which became evident since the first low-resolution model was computed. The final reconstructed structure is shown in Fig. 1(C). The 3D structure of the α sub-unit was solved by X-ray crystallography at atomic resolution [PDB code: 1ea0 (Binda et al., 2000)], whereas the 3D structure of the sub-unit β was derived from a homologous enzyme [PDB code: 1h7w (Dobritzsch et al., 2001)] by secondary structure prediction (Callebaut et al., 1997). These atomic structures were then fitted in the 3D electron density map semi-automatically using Chimera (Goddard et al., 2007; Fig. 1(D)). The interaction between sub-units were then studied in terms of contacts between the fitted structures (Cottevieilleet al., 2008).
Figures 2(B–D) show an application of ET of plastic sections to determine the 3D structural architecture of the mammalian Golgi from the pancreatic beta cell line, HIT-T15 [reproduced from Marsh (2005), with permission from Elsevier]. Immortalized HIT-T15 was prepared by high-pressure freezing and freeze substitution, followed by plastic embedding, and thick (400-nm) plastic sections were cut. Figure 2(B) shows 1 of 80 tilt-series images of a plastic section. One tilt series was collected for each of two tilt axes by imaging the specimen tilted over a range of ±60° in increments of 1.5°. Individual tilt-series images were first aligned with respect to each other by cross-correlation and were then more accurately aligned thanks to fiducial markers (10-nm colloidal gold) placed on the sample before image acquisition. One 3D reconstruction was computed for each of the two tilt series, and the two reconstructions were combined to produce a single, dual-axis tilt reconstruction. Figure 2(C) shows a slice extracted from the volume reconstructed at approximately 6-nm resolution. The same procedure was used to reconstruct 3D structures of additional 400-nm-thick sections to allow the study of a larger portion of the Golgi ribbon. The serial reconstructed volumes were mutually aligned and then combined to create a single, large volume (approximately3.1 × 3.2 × 1.2 μm). Visible structures in the Golgi region were then modelled (segmented), using the IMOD software package (Kremer et al., 1996). Membranes were segmented by placing points along the bilayers, connecting the points with coloured line segments and building closed contours that delimited distinct membrane-bounded compartments and vesicles for each tomographic slice. The structure of segmented objects was then studied as well as the relationships between the segmented objects and the surrounding objects (Fig. 2(D)).
Recent advances in the development of cryo-sectioning methods allowed more reliable cryo-ET studies of various organelles in frozen-hydrated skin and liver sections (Hsieh et al., 2006; Masich et al., 2006; Norlen et al., 2007). Three-dimensional reconstruction of microtubules in their cellular context has shown that it was possible to achieve a similar resolution with cryo-ET of frozen-hydrated sections to that achievable with plunge-frozen samples (approximately 4 nm), despite the artefacts inherent in the sections (Bouchet-Marquis et al., 2007). The latter example shows the power of tomograms from vitreous sections in allowing studies of macromolecular assemblies in their natural environment (Bouchet-Marquis et al., 2007).
Concluding remarks and perspectives: integrated approach to analysis of biological structural complexity
Neither of the two methods, SPA and ET, used alone can give a complete picture of complex structural organization of biological material. A multi-resolution approach in structural organization requires a multi-resolution approach for its analysis. This means that there is a need to integrate techniques specialized for different levels of detail (atoms, molecules, organelles and whole cells) (Frank et al., 2002).
It has been shown that SPA can be used to compute volumes with resolution that is sufficient for tracing helices (Ludtke et al., 2004; Saban et al., 2006; Connell et al., 2007). Moreover, this technique is the only one providing the structure of macromolecules that cannot be solved by other experimental techniques (e.g., electron crystallography, X-ray crystallography or nuclear magnetic resonance). When 3D atomic structures of the macromolecular sub-units are known [solved by an experimental technique or by structure prediction (Callebaut et al., 1997; Baker & Sali, 2001)], this complementary information can be used to study the interactions between the sub-units, the way in which they assemble and their function in the macromolecule. To this goal, known atomic structures of the sub-units are fitted in the 3D structure obtained by SPA, and their relative position and orientation are analyzed (as in the SPA example shown in this paper, Fig. 1(D)). For a reliable interpretation of the results of fitting, the resolution of the SPA reconstruction should be sub-nanometer. The fitting may be rigid or may take into account macromolecular flexibility (Tama et al., 2004; Velazquez-Muriel & Carazo, 2007). However, the fitting still requires human interaction because of a very different resolution of details in the two 3D structures, and development of fully automatic and reliable fitting methods is still inprogress.
Regarding ET, the most important issue is the interpretation of computed tomographic volumes. The interpretation of tomograms at the ultra-structural level requires their decomposition into structural components (e.g., membranes or organelles). In the majority of cases, a manual assignment of features is usually preferred to available segmentation algorithms. The interpretation of tomograms at the molecular level consists in recognition (location) of a priori known molecular shapes (from a library of macromolecular structures obtained by X-ray crystallography, nuclear magnetic resonance, electron crystallography, SPA etc.) and requires their discrimination in the case of different species. The information on the spatial relationships between the mapped macromolecular structures within the cell complements the macromolecular information provided by other approaches.
A reliable localization of proteins in samples preserved using high-pressure freezing with freeze substitution will require advances in techniques for tagging specific macromolecules with markers that are visible by TEM (McIntosh et al., 2005). Regarding cryo-ET, the labelling is a difficult task. Detection and identification of macromolecules in unlabelled tomograms can be done in a fully automated way using computational methods such as template matching (Frangakis et al., 2002). To accurately recognize and discriminate molecules without labels, the resolution of reconstructed volumes should be in the range of 2–3 nm (Bohm et al., 2000).
Therefore, there is an intense interest currently in developing new methods for cryo-ET (from sample preservation and sectioning to image processing) that will push the resolution towards the level of 2–3 nm. For example, combination of ET and SPA approaches has been shown to improve resolution in some cases. Hence, when the sample contains many identical copies of the same structure, particle volumes extracted from tomograms can be averaged (Walz et al., 1997) or traditional SPA classification and averaging strategies can be used to average projection images from identical particles and, thus, improve the SNR and the resolution of the reconstructed volume [e.g., the approach used to study the 3D structure of nuclear pore complex (Stoffler et al., 2003)]. However, these approaches require truly identical structures and not structures in different conformations. In addition, the signal in the individual images/volumes should be strong enough to allow an accurate image/volume alignment before averaging. The combined SPA and ET methods can also be used to generate sufficiently reliable initial models (from a relatively small number of macromolecular complexes) that could then be refined using traditional SPA approaches, using thousands of differently oriented individual particle images.
ET has a considerable potential for studying complexes with structural heterogeneity. For example, Fig. 4 shows the results of cryo-ET of a frozen-hydrated sample containing multiple copies of HIV-1 virions heterogeneous in size and shape [reproduced from Briggs et al. (2006), with permission from Elsevier]. This technique allowed the study of the diameter of the entire 3D virion structure and 3D morphology of the viral core of segmented virions. The virions were of an approximately spherical shape, with diameters between 106 and 183 nm, and of the 75 observed particles, 5 contained no well-defined core, 63 contained a single core, 3 contained 1 complete and 1 partial or indistinct core and 4 contained 2 cores (Briggs et al., 2006).
In the future, following the same principle of multi-resolution analysis of biological complexity, one might take advantage of integrating volumes from ET into even lower-resolution volumes representing whole large cells without sectioning, obtained from X-ray tomography (Le Gros et al., 2005) or even optical microscopy.
An extension of ET is its combination with chemical mapping by electron energy-loss spectroscopy that allows spatial localization of chemical components. It is already a well-established method in material sciences (Mobus et al., 2003; Gass et al., 2006) and is starting to be used in biology (Leapman et al., 2004).
A routine combination of TEM data with data obtained with other methods will be an important future goal, which is already giving rise to new fields such as correlative light–electron microscopy (Leapman, 2004). It consists in combining light microscopy with ET for an efficient location of a sub-micrometre object on a grid of few millimetres under low-dose conditions. Light microscope can be used to locate an approximate position of the object using molecules with fluorescent labels or by identifying large features that are visible in the light microscope. The located region is then zoomed. However, further technological developments are required for a routine use of this method.
We are grateful to European Commission for NoE ‘3D-EM’ contract no. LSHG-CT-2004-502828, Region Ile-de-France for convention SESAME 2000 E 1435, program C'Nano Ile-de-France for supporting 3D cryo-EM at IMPMC.