Cryo-Electron Tomography

  • Jürgen PlitzkoEmail author
  • Wolfgang P. Baumeister
Part of the Springer Handbooks book series (SHB)


Classical structural biology approaches rely on highly purified molecules which are isolated from their neighbors far from the complex macromolecular interaction network of the cell (ex situ). We have seen breathtaking results of such isolated molecular structures at atomic or near-atomic resolution obtained by single-particle cryo-electron microscopy (cryo-EM). However, many supra- and macromolecular complexes involved in key cellular processes cannot be studied in isolation; their function is so deeply rooted in their cellular context that it is impossible to isolate them without compromising their structural integrity. The challenge now is to apply cryo-EM to protein complexes and other biological objects in their natural environment, namely cells. Cryo-electron tomography (cryo-ET) offers this opportunity, and in this chapter we provide an overview of recent advances in sample preparation, data acquisition and data processing, including technology for focused ion beam milling, correlative light and electron microscopy, phase-plate imaging and direct electron detection. We show that these developments can be used synergistically to generate 3-D images of cells of unprecedented quality, enabling direct visualization of macromolecular complexes and their spatial coordination in undisturbed eukaryotic cell environments (in situ).

In his seminal paper of 1968, Roger G. Hart stated [4.1]:

Clearly, if recent improvements in electron microscopes are to be fully utilized in biology, contrast must be enhanced without drastic molecular alteration of the specimen or obscuration by extraneous material…Thus the polytropic montage seems to offer a means of determining the three-dimensional structures of low-contrast biological specimens at a resolution of \({\mathrm{3}}\,{\mathrm{\AA{}}}\), or the best resolution attainable with existing electron microscopes.

Fifty years after his visionary statement on tomography —which is synonymous with ‘‘the polytropic montage'' —the method is getting close to the realization of his vision. Today, biological specimens can be analyzed in their native state, which is the hydrated state (‘‘without drastic molecular alteration''), without contrast-enhancing agents (‘‘obscuration by extraneous material''), and with subnanometer resolution, but not yet ‘‘at a resolution of \({\mathrm{3}}\,{\mathrm{\AA{}}}\)''. Cryo-electron tomography ( ) enables the study of macromolecular and supramolecular structures in situ, i. e., in their functional cellular context. Whereas, cryo-electron microscopy ( ) of isolated macromolecular particles (ex situ) nowadays reaches near-atomic resolution and has become the most versatile method for structural biology (as recognized by the 2017 Nobel Prize in Chemistry), cryo-ET still needs improvements in technology and methodology to enter the realm of near-atomic resolution.

Since the introduction of the concept of tomography in the late 1960s, much has been achieved and several landmark papers have been published during this long journey (Fig. 4.1). Undoubtedly, the advances in instrumentation, in automation and in image processing have greatly expanded the capabilities of cryo-ET. This journey has been full of obstacles and methodological detours, and sometimes even dead ends. Fortunately, there have been more ups than downs, and since the beginning of the 21st century, cryo-electron tomography (cryo-ET) has begun to explore the mysteries of the cell's interior. The latter is reflected in the steady increase in publications and citations in this area, and more recently in the steady growth of laboratories that adopt and use this method.

Fig. 4.1

Developmental milestones leading to the practical realization of cryo-electron tomography (cryo-ET) at molecular resolution

The first version of this chapter on cryo-ET was written in 2005 and was slightly updated in the 2007 edition of Science of Microscopy. It is timely and appropriate now for another revision covering the more recent methodological and technological achievements. Although it has been more than a decade since the first chapter was written, the underlying principles are still the same [4.2]. In the recent past there has been a steady increase in reviews and book chapters on cryo-EM, and in particular on cryo-ET. Some of them deal with specific aspects of sample preparation, data acquisition and data processing (we apologize that we cannot refer to all of them here). What almost all have in common is the way cryo-electron tomography is described and performed—tilting a sample while taking projection images, reconstructing the volume and analyzing it. While this concept is straightforward, there are several factors that complicate tomography in practice. One of the biggest challenges is posed by the sample itself. Samples from viruses, cells, tissue or entire organisms should remain unperturbed by chemical fixation or staining, and they must be made thin enough to be electron-transparent. The Martinsried way of doing tomography as of today is an end-to-end process (sometimes also called the cryo-ET workflow ), where the sample and the associated sample preparation are of utmost importance. This workflow includes vitrification of the sample, correlative fluorescence microscopy for identification and localization of features of interest, focused ion beam milling to make the samples thin enough, and finally, cryo-TEM for tomography. Only with suitably thin samples can molecular resolution be attained, as resolution scales with thickness in almost every TEM application. Powerful image processing platforms exist for the mining of the rich information contained in cellular tomograms.

There is no doubt that data quality (in tomography) has benefited greatly from advances in automation and microscope hardware, and in particular from the new generation of direct electron detection devices and the recent availability of durable phase plates. And it is clear that the availability of massively parallel computing power (such as GPUs) and the development of advanced and automated computational analysis methods have contributed considerably to the rise of cryo-ET [4.3]). Therefore, this revised chapter will focus on today's cryo-ET workflow, its limitations and its potential for performing structural biology in situ at molecular resolution. Recent applications of this method are presented, along with an outlook on future developments.

4.1 A Short Overview

The basis for doing cryo-electron tomography (cryo-ET) is provided by the transmission electron microscope (TEM), which was invented in the 1930s, and commercial instruments that became available shortly thereafter. The development of the TEM and the first biological applications are inextricably linked to the two Ruska brothers, Ernst and Helmut Ruska [4.4]. Despite the prospects of attaining much higher resolution with electron microscopes than was possible with light microscopes, many biologists remained skeptical with regard to their usefulness. The main problem was, and still is, the radiation sensitivity of biological material, and burning them to a cinder upon longer exposures to the electron beam [4.5]. It took decades of developing measures for protecting biological samples from exposure to the damaging effects of the hostile environment (vacuum, electron bombardment) inside the TEM. Gentle dehydration and substitution of water by polymers became key protective measures, along with metal coating and embedding in high-contrast metal salts. The introduction of ultramicrotomes [4.6, 4.7] was a major step forward, which over time has enabled the establishment of the principles of cellular architecture (ultrastructure), in particular cellular compartmentalization, and has given shape to cell biology as we know it today.

Unlike molecular structures, cellular structures are subject to stochastic variations and hence are pleomorphic. The crowded interior of a cell resembles huge factories in which the macromolecular components interact in the form of transient interaction networks or in the form of more or less stable machines and assemblies [4.8]. The challenge in cellular structural biology is to avoid, or at least minimize, any perturbations of this fragile system.

Already in the 1960s, Fernandez-Moran advocated the use of frozen-hydrated samples and introduced the concept of cryo-electron microscopy [4.10, 4.9]. The full potential of structural preservation in frozen-hydrated samples was first demonstrated by electron diffraction on catalase crystals, which showed preservation to better than \({\mathrm{4}}\,{\mathrm{\AA{}}}\) [4.11, 4.12]. However, the formation of crystalline ice during the freezing process was a major problem, and could damage the biological structures. The first report on amorphous ice obtained by slow condensation of water vapor on the outside of a copper wire dates back to 1935 [4.13, 4.14]. Half a century later, Brueggeller and Mayer succeeded in vitrifying micrometer-sized water droplets by injection into \({\mathrm{90}}\,{\mathrm{K}}\)-cooled liquid ethane [4.15]. The high cooling rates achieved with this jet-freezing method made it possible to cool the water droplets through the glass transition, which led to amorphous ice. In 1981, Dubochet and McDowall introduced vitrification by plunge-freezing as a generic method for the production of biological samples for electron microscopy [4.16, 4.17, 4.18], a technique that would revolutionize electron microscopy of biological samples. Plunge-freezing allows the sample to be kept in a fully hydrated state, with the added advantage that the sample is less sensitive to radiation when imaged at the low temperature required to maintain its vitrified state [4.19]. While contrast is low in frozen-hydrated samples, it allows the imaging of modulations of intrinsic mass densities instead of relying on contrast enhancement, through the addition of electron-dense stains. The achievable resolution is therefore not limited by the sample preparation, as is the case with staining or plastic embedding.

The elimination of artifacts was clearly one of the achievements in obtaining higher-resolution images of biological structures, but because of their pleomorphic nature, single two-dimensional () images are clearly insufficient for a complete structural characterization, which can only be performed in three dimensions (). Because of the large depth of field of the electron microscope, images are only 2-D projections of the sample, and almost all information about the third dimension is lost. As already mentioned, sectioning can help, especially serial sectioning, where the desired structure is cut serially. Up to this time, however, the series cuts were only carried out on samples embedded in epoxy resin. The resolution was limited to the layer thickness (\(\approx{\mathrm{50}}\,{\mathrm{nm}}\)), and any information about the molecular organization was lost. But it was clear that information retrieval down to the supramolecular level for all three dimensions is indispensable for an in-depth structural analysis of native biological samples.

In the late 1960s and early 1970s, three groups independently experimented with the possibility of three-dimensional microscopy, namely electron tomography [4.1, 4.20, 4.21, 4.22]. Likely inspired by the tomographic methods invented for medical examinations [4.23, 4.24], they developed acquisition schemes to access the 3-D information by recording images from different orientations or from differently oriented particles. DeRosier and Klug studied the helical tails of T4-bacteriophages, and with a single electron micrograph they were able to present a complete 3-D reconstruction. By selecting an object with the a priori knowledge of its helical symmetry, they avoided a complicated data acquisition procedure. In the same year, Hart reported very precisely on his idea: the polytropic montage. He investigated the rod-shaped tobacco mosaic virus (TMV). Hart and later Hoppe chose a more complicated and cumbersome acquisition process: the manual rotation of the object perpendicular to the incoming electron beam and the acquisition of single projections from different viewing angles. They reported on the 3-D representation out of a series of images acquired over a large angular regime. In the late 1960s, when the common electron microscopist used photographic plates, these procedures were inevitably very cumbersome and time-consuming, and of course, reconstruction calculations were only possible with large supercomputers. With the introduction of charge-coupled devices (CCDs) for image recording in EM in the early 1990s [4.25, 4.26] and the introduction of computer-controlled EMs, attempts were made to improve the pioneering work with the prospect of implementing it for routine and rapid use [4.27, 4.28, 4.29]. Together with suitable cryo-preparation techniques of biological samples, cryogenic electron tomography (cryo-ET) promised to be the method of choice for further structural work in molecular biology. However, it was not until the mid-1990s that the first reports on applications of automated cryo-ET appeared [4.30, 4.31, 4.32, 4.33, 4.34].

In recent years, CCD cameras have been replaced by direct detectors. While the concept of direct detection of charged particles is not new (it dates back to the 1980s), a new technology was needed to make such detectors resistant to prolonged exposure to electron bombardment [4.35, 4.36]. This was achieved by a special radiation-hard chip design coupled with a high readout speed, and in 2012 the first commercial products became available. The gain in sensitivity and speed of today's direct detectors literally allows us to see more details and correct beam-induced sample movements that would otherwise degrade image quality [4.37, 4.38, 4.39] (Fig. 4.2), a fact that was of utmost importance for the preservation of atomic resolution structures by cryo-EM, and that also improved the quality of the data in cryo-ET.

Cryo-ET was, at first, limited to thin vitrified samples such as viruses, isolated organelles and small prokaryotic cells [4.40, 4.41, 4.42, 4.43, 4.44, 4.45, 4.46]. Thicker specimens, such as eukaryotic cells, tissue and organisms, were largely inaccessible without further preparation steps. Cryo-sectioning on high-pressure frozen (HPF) samples was the only method of obtaining sufficiently thin samples for tomography [4.43, 4.47, 4.48, 4.49]. Great efforts have been made to overcome some of the difficulties involved, such as mechanical distortions, knife marks and crevices in thicker sections (\(> {\mathrm{100}}\,{\mathrm{nm}}\)). While the ease of use of this technique has improved [4.50, 4.51, 4.52], none of the invented tricks really solved the problems (i. e., inhomogeneous distortions), and cryo-ultramicrotomy has remained a real feat of craftsmanship to this day.

An alternative sectioning/thinning technique emerged around 2007: cryo-focused ion beam milling (FIB ) [4.53]. FIB instruments are ubiquitous in the material sciences and are a standard for TEM sample preparation in light of their unsurpassed site-specific preparation capabilities. However, the use of a focused ion beam, typically gallium ions, to obtain electron-transparent regions from frozen-hydrated samples without compromising both the integrity and the vitreous state seemed impossible at first. Fortunately, it has turned out that FIB milling of vitreous samples does not cause devitrification or other impassable artifacts [4.55, 4.56], and the first tomographic experiments soon followed [4.53, 4.57, 4.58]. Further technical developments have been made since then, such as improved cryo-FIB workflows, the on-the-grid or in situ cryo-lamella preparation technique for plunge-frozen cells on EM grids, and even lift-out approaches for HPF samples [4.59, 4.60].

However, correlated or multiscale microscopy methods are indispensable for enabling and expediting the search for interesting features in larger cellular volumes. Therefore, the development and application of correlative light and electron microscopy ( ) methods for frozen-hydrated samples was (and still is) of great interest [4.61, 4.62, 4.63, 4.64], especially for guiding the preparation steps [4.65]. Meanwhile, there are several different routes for cryo-CLEM, which has become a central element in most of today's cryo-ET studies [4.66, 4.67].

A few years ago, a new type of phase plate for cryo-EM—the Volta phase plate ( )—was introduced, which significantly improved the contrast, visibility of fine features and subtomogram averaging [4.68]. Phase plates had already been proposed and theoretically considered in the early days of transmission electron microscopy [4.69]. However, although various types of phase plates were tested over time, no practical device was produced for several decades. The VPP is very similar to the originally proposed Zernike-type phase plate [4.70], but without a hole, and the phase shift is self-created by the electron beam. It can be easily implemented in automated data acquisition schemes, and combines ease of use with durability. Volta phase plate-assisted cryo-ET has already enabled the localization and analysis of individual protein complexes in situ and the visualization of cellular structures in unprecedented detail [4.71, 4.72, 4.73, 4.74, 4.75, 4.76, 4.77].

The rate of developments in and for cryo-electron tomography (cryo-ET) was moderate in the first decades, but accelerated steadily and noticeably in the 21st century. Progress in computer technology has clearly set the pace and pushed the method forward. Here, we detail the application of cryo-ET by following the workflow from sample preparation to image acquisition, and finally, image analysis (Fig. 4.3).

Fig. 4.2

Advances in cryo-EM instrumentation. The data output in cryo-EM is steadily growing due to advancements in technology and the performance of modern electron microscopes. Milestones are illustrated here and arranged according to their complexity and their contribution to the increased data output. Figure adapted from [4.3]

Fig. 4.3

Cryo-ET workflow: from sample preparation to image processing. Crucial points and a rough estimate on the time frame are depicted. Adapted from [4.54], with permission from Elsevier

4.2 Cryo-Electron Tomography: The Workflow

Today, structural biology has a powerful armamentarium of methods at its disposal for determining the high-resolution structures of molecules of biological relevance. For quite some time, x-ray crystallography was the premier method, and has contributed the majority of entries to the Protein Data Bank (PDB). It was later complemented by nuclear magnetic resonance (NMR) spectroscopy. Following the resolution revolution [4.78], cryo-electron microscopy single-particle analysis has become a major player; it is particularly powerful for the structural determination of multi-subunit complexes and membrane proteins where attempts to obtain crystals of good quality often fail. What all three methods have in common is the need to isolate and purify the molecules of interest. This reductionist or divide-and-conquer approach—powerful as it is—has its limitations [4.3]. Information about the interactions between the many molecular species in their functional environment —the intact cells —is lost. However, it is this very network of interactions which underlies cellular functions [4.74, 4.79]. Hence, there is a need for methods that allow visualization of cellular landscapes at high resolution, i. e., to do structural biology in situ. Suitable techniques should span a wide range of length scales to enable the integration of information from both ends of the resolution spectrum. Fluorescence light microscopy ( ) is the most popular method for studying live cell processes; it allows for the direct detection of cellular structures and macromolecules of interest via molecule-specific labeling. It is perfectly suited for investigating cellular dynamics with high specificity and over a broad range of both spatial and temporal orders of magnitude. With the advent of super-resolution techniques [4.80] see Chap.  22 (STED [4.81], RESOLFT [4.82], PALM [4.83, 4.84], STORM [4.85]), protein colocalization with precision close to \({\mathrm{20}}\,{\mathrm{nm}}\) can be reached. Despite the technical improvements in FLM, one major limitation remains: only labeled structures can be detected, and the surrounding environment remains invisible. In recent years, cryo-electron tomography (cryo-ET) has emerged as a powerful, label-free method for the visualization of cellular landscapes with molecular resolution.

The need to study biological systems on different scales—from organisms to atoms—has made the integration of various methods indispensable. This is a unified methodology that is capable of navigating cellular landscapes, targeting features of interest, acquiring structural information and analyzing complex cellular samples. The successful combination of various techniques into a robust and reliable workflow was and still is a major challenge. However, over the course of several years (almost a decade), technology and methodology was developed, and a workflow for structural studies of cellular samples was designed and implemented. The general cryo-ET workflow is shown in Fig. 4.3, starting with sample preparation, all the way to image processing [4.54]. Derivations and adaptations of this workflow exist [4.86, 4.87, 4.88, 4.89, 4.90, 4.91], but basically all of them are composed of the same sequence of steps and procedures: Vitrification , correlative fluorescence microscopy ( ), micromachining by focused ion beam milling ( ), cryo-ET , and finally, computational methods for image processing. The most critical points are the handling and transfer steps, which must be carefully controlled throughout the process in order to avoid adverse contamination and structural damage to the sample. In addition, suitable software tools must be available to ensure the transfer of the information gathered in these steps from one system to another.

Owing to this workflow, purification is no longer required, and thus both classical organelles and other cellular assemblies arising from phase separation can now be studied at high resolution in situ in both prokaryotic and eukaryotic cells. Meanwhile, entire molecular assemblies can be studied at high resolution in a close to lifelike state, which is reflected in the growing number of publications following this strictly in situ approach [4.100, 4.101, 4.71, 4.92, 4.93, 4.94, 4.95, 4.96, 4.97, 4.98, 4.99]. The ability to generate quantitative maps of molecular constituents has been dubbed visual proteomics  [4.102], and what looked like a vision is now coming true. Large portions of the proteomic space can now be detected, visualized and quantified in an unbiased manner and at high resolution, and this will have profound implications for the way biological systems can be understood and modeled (Fig. 4.4a-d).

Fig. 4.4a-d

Exemplary in situ cryo-ET studies of cellular compartments. (a) The molecular sociology at the HeLa nuclear periphery. From [4.71]. Reprinted with permission from AAAS. (b) Nucleolus-like structure formed in bacteria during phage infection. From [4.100]. Reprinted with permission from AAAS (c) PolyQ inclusions in HeLa cells as a model for Huntington's disease. Adapted from [4.98], with permission from Elsevier and (d) Rubisco in the pyrenoid of C. reinhardtii, which behaves like a liquid droplet. Adapted from [4.95], with permission from Elsevier

4.2.1 Sample Preparation

In the preparation of biological samples for electron microscopy, chemical fixation, dehydration and staining were obligatory, and they are still used today, especially for larger samples (> 200 \({\upmu}\)m). Whereas these steps were necessary to stabilize the sample for the ambient conditions within an electron microscope, dehydration can severely alter or even damage the cellular ultrastructure and molecular organization. The introduction of sample preservation by vitrification , i. e., the rapid freezing of aqueous protein solutions or entire cells, which yields amorphous instead of crystalline ice [4.11, 4.12, 4.17], changed this situation. Cryo-preservation by vitrification allows us to maintain the native structure of the biological material and avoids alterations or modifications as known from conventionally used techniques. Three different methods are available today for obtaining frozen-hydrated samples for cryo-EM : plunge freezing (PF) [4.16], jet or spray freezing (JF) [4.15] and high-pressure freezing (HPF) [4.103]. By far the most commonly used technique for cryo-EM and ET is plunge freezing , as it is compatible with protein complexes, fractionated cell material and whole cells, and it can be automated [4.104, 4.105]. For large specimens, such as organisms or tissue, HPF can be used up to a thickness of \({\mathrm{200}}\,{\mathrm{{\upmu}m}}\) without the formation of crystalline ice [4.106, 4.107]. For the latter, however, suitable processing steps after freezing, e. g., sectioning or thinning, are indispensable.

4.2.2 Correlative Microscopy

Larger samples require an additional step to identify and locate specific regions or features. This is especially important when examining transient events or characteristics of heterogeneous cell populations. In addition, it is important to reduce the area/volume to be searched, as cryo-ET offers only a limited field of view [4.61, 4.62, 4.63, 4.64, 4.66]. The inherent low contrast of frozen-hydrated samples, along with their radiation sensitivity, requires methods to navigate the cell volume carefully and with high precision. Cryo-fluorescence microscopy combined with the specific fluorescence labeling of structures assists in the search and the analysis of vitrified samples before electron microscopy. If used in a correlative way (cryo-CLEM), it can greatly expedite this search in two or even three dimensions, and it further allows us to target suitable preparation areas [4.65]. However, cryo-light microscopy is still far from reaching the same resolution as that at room temperature. This is attributed to the unavailability of objectives/lenses combining larger working distances and high numerical apertures (NA) or even immersion objectives that can be used at cryogenic temperatures [4.108, 4.67]. To overcome this, far-field super-resolution fluorescence light microscopy techniques have been adapted to cryogenic conditions [4.108, 4.109, 4.110].

4.2.3 Cryo-FIB Milling

Biological samples thicker than about \({\mathrm{500}}\,{\mathrm{nm}}\) are no longer electron-transparent, and as the resolution scales with thickness, high-resolution data can no longer be obtained. Even the smallest eukaryotic cells exceed the limits of electron transmissivity. Therefore, in situ cryo-ET in the stricter sense [4.111] would be rather confined, e. g., to small cells such as prokaryotes or peripheral areas of eukaryotic cells that are thin enough. The apparent increase in thickness during tilting of the sample further exacerbates this. High-resolution cryo-electron tomography of intact cells therefore requires in most cases a preparation/thinning step to make thicker cell areas accessible.

Already in the 1950s [4.9], the basis for the thinning of frozen samples by mechanical sectioning had been developed, but its routine application was achieved only many years later. Cryo-electron microtomy of vitreous sections (i. e., CEMOVIS) [4.112, 4.113] made it possible to observe cells in an almost native state. But the necessary craftsmanship and the associated artifacts (i. e., waviness, crevices and sample compression), especially with thicker sections (> \({\mathrm{50}}\,{\mathrm{nm}}\)), limited its broader application for high-resolution cryo-ET [4.114]. To avoid sectioning artifacts, an approach derived from materials science was adapted for the preparation/thinning of frozen-hydrated samples: focused ion beam (FIB) milling [4.115, 4.53, 4.57]. FIB milling/thinning is usually performed using a dual-beam microscope that combines a scanning electron microscope (SEM) for imaging and an ion beam microscope for material removal. However, milling frozen-hydrated samples requires special stages operating at nitrogen temperature and special protocols adapted to the properties of the biological materials. Over the past 10 years, the requirements for milling of frozen-hydrated biological material have been fulfilled, and today cryo-focused ion beam milling (cryo-FIB) can be routinely used to produce electron-transparent and distortion-free samples of different geometry (wedges or lamellae) and thickness (\(<{\mathrm{200}}\,{\mathrm{nm}}\)) [4.116, 4.117]. In addition, the exquisite imaging properties of the dual-beam instruments enable correlative imaging, and when they are combined with cryo-FLM, specific biological structures can be navigated, targeted and excised with subcellular precision [4.65]. This micromachining technique enables the investigation of the intricate molecular scenery of cells with high resolution, and almost unaffected by artifacts. FIB milling is most commonly performed on isolated cells, but lamellae from tissues and multicellular organisms can also be produced and examined by cryo-ET [4.118, 4.59]. Even lift-out approaches for high-pressure frozen samples have recently been successfully implemented [4.60].

4.2.4 Cryo-ET

In cryo-electron tomography , the sample is rotated incrementally around an axis (from \({+}60^{\circ}\) to \({-}60^{\circ}\)), and a projection image is taken for each tilting angle. In order to avoid radiation damage, therefore, the tolerable electron dose must be distributed over all projections of a tilting series. The available dose per image is therefore much lower in comparison to single-particle cryo-EM, and cryo-ET projections have much lower contrast, with a significantly lower signal-to-noise ratio ( ). In order to cover the angular space as completely as possible and to divide the available total electron dose as best as possible, there are several different tilting and sampling schemes—unidirectional, bidirectional, symmetrical [4.119]—which are implemented in fully automatic acquisition routines [4.120, 4.121, 4.122, 4.123, 4.124, 4.125, 4.126] and which have led to increased data output. However, a minimum of contrast and signal is still required to align the tilt series for subsequent reconstruction. Therefore, further measures must be taken to enhance the contrast and to amplify the signal.

Additional contrast can be generated by defocusing the objective lens, but this limits the achievable resolution. Defocusing, however, requires extra post-recording computational image analysis techniques to determine and correct its detrimental effects, i. e., contrast transfer function correction [4.127]. In order to improve the phase contrast without defocusing, phase plates for cryo-electron microscopy have recently been introduced, which allow image acquisition in focus [4.128]. The hole-free Volta phase plate (VPP), for example, increases the contrast in cryo-EM and allows an exact structure determination, especially for very small molecules (\(<{\mathrm{100}}\,{\mathrm{kDa}}\)) [4.129, 4.68]. Contrast enhancement is particularly important for cryo-ET, since here the possibilities for averaging molecular structures/complexes in tomograms (i. e., subtomogram averaging) are more restricted than in single-particle cryo-EM due to the lower dose, the smaller number of particle copies and the limited tilting/sampling range.

The signal boost for low-dose cryo-EM images can be achieved by improving the performance of the detection devices. Until recently, CCD cameras (charge-coupled devices) were the preferred detectors for cryo-ET. However, CCDs detected electrons indirectly, and the necessary conversion step led to a very low signal yield. In the meantime, CCDs were supplanted by electron detectors, which detect the incoming electron signal directly and surpass CCDs in terms of sensitivity and speed. Their ability to count each incoming electron, coupled with their high readout speed of several hundred fps (frames per second), provided the significant SNR gain in recorded images and was critical to the resolution revolution in single-particle cryo-EM [4.78], and together with the phase plate has greatly advanced cryo-ET [4.71, 4.72, 4.73, 4.75, 4.76, 4.77].

4.2.5 Image Processing

Data processing of tomographic data sets has developed steadily over the past 10 years and has become significantly faster since the introduction of direct electron detectors in recent years. Today, there are various software solutions available for preprocessing, alignment, reconstruction and visualization of cryo-ET data sets [4.130]. The alignment of the individual tilt images is usually done by tracking high-density reference markers (e. g., fiducials), such as gold nanoparticles, which must be applied to the sample before vitrification. Therefore, their use for the alignment of FIB-cut lamellae is impaired or they must be applied after milling [4.118], the latter of which could compromise the quality and integrity of the fragile sample. Alternatively, cross-correlation-based alignment methods can be used to establish a relationship between the positions within each tilt image and its final position in the reconstructed tomograms, an approach that is often less accurate than fiducial tracking, and it can be particularly error-prone if the tilt is high and/or the signal is low. For FIB lamellae, patch tracking is commonly used, where multiple and overlapping image patches are traced through the tilt series, and the tracked positions are then treated as a reference model as in fiducial tracking. After the alignment of the projection images, the next step is the reconstruction of the 3-D volume. Several iterative reconstruction algorithms exist, such as the simultaneous iterative or simultaneous algebraic reconstruction technique ( or ) [4.131, 4.132]. However, the most commonly used algorithm is the noniterative weighted back-projection ( ), as it preserves the high-resolution information most reliably [4.133]. The resulting 3-D volumes can be analyzed directly and either manually or semiautomatically annotated. In particular, larger structures such as membranes or organelles, as well as large macromolecular complexes (e. g., ribosomes, proteasomes), can be easily identified without the need for special software tools. However, manual annotation is impractical for larger data sets (e. g., several dozen tomograms). To quantitatively investigate molecular structures in situ, fully automated segmentation and annotation methods have to be used [4.134, 4.135, 4.136]. To identify and locate macromolecular complexes based on structurally known features (i. e., shape and size), the most common approach is template matching . In template matching, a correlation volume is usually generated, where the pixel values represent the correlation scores, i. e., their correspondence to the reference used. Both the localization and the orientation of the picked particles in relation to the reference can be obtained with subnanometer accuracy, thus allowing the analysis of their relative positions in 3-D. Particularly with larger data sets containing heterogeneous particles with less descriptive shape, however, caution is required to avoid model or template bias. In addition, volumes can be extracted around the located positions and iteratively aligned and averaged, a procedure known as subtomogram averaging (STA) [4.134, 4.137, 4.138, 4.43]. As with single-particle analysis, the particles are averaged, so that the SNR is increased with respect to the individual subtomograms. However, averaging of subtomograms can be more demanding than single-particle analysis due to the lower particle count and their higher variability, as well as the higher background and noise levels. Nevertheless, the target structures can be located in their native environment, and thus many different states can be detected that include the presence of labile or transient interaction partners. For the latter, however, advanced routines are required to divide the initial subtomogram averages into homogeneous subsets (i. e., classes), and in particular those that reduce human interaction to a minimum, as is the case, for example, with autofocused 3-D classification [4.134].

4.3 Technical Details of the Cryo-ET Workflow

4.3.1 Sample Preparation: Vitrification

Already in the 1960s, Fernández-Morán advocated the use of frozen-hydrated samples and introduced the concept of cryo-electron microscopy [4.10, 4.9]. However, the full potential of structural preservation in frozen-hydrated samples was first demonstrated by electron diffraction on catalase crystals, which showed preservation to better than \({\mathrm{4}}\,{\mathrm{\AA{}}}\) [4.11, 4.12]. However, a major problem was the formation of crystalline ice during the freezing process, which could damage the biological structures. The first report on amorphous ice obtained by slow condensation of water vapor on the outside of a copper wire dates back to 1935 [4.13, 4.14]. Half a century later, Brueggeller and Mayer succeeded in vitrifying micrometer-sized water droplets by injection into \({\mathrm{90}}\,{\mathrm{K}}\) cooled liquid ethane [4.15]. The high cooling rates of about \(E5{-}E6\,{\mathrm{K\mskip 3.0mus^{-1}}}\) achieved with this jet-freezing method made it possible to cool the water droplets through the glass transition, which led to amorphous ice (devitrification temperature \(\approx-{\mathrm{137}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)). In 1981, Dubochet and McDowall introduced vitrification by plunge-freezing as a generic method for the production of biological samples for electron microscopy [4.139, 4.16, 4.17, 4.18]. In 1984 Adrian et al [4.140] reported on their work on the first successful investigation of a shock-frozen biological object.

The sample (\(\approx 3{-}4\,{\mathrm{{\upmu}L}}\)) is typically applied to a holey carbon grid and briefly blotted (i. e., blotting \(=\) removal of excess solution) with filter paper to produce a thin aqueous film required for vitrification. The grid is then rapidly plunged into a liquid cryogen cooled by liquid nitrogen. Cryogens typically used are liquid ethane, propane or a mixture of both. These cryogens have a much higher thermal conductivity than liquid nitrogen, ensuring a significantly faster heat transfer for proper vitrification. Furthermore, the Leidenfrost effect is greatly reduced, which would otherwise cause the formation of a warm and insulating gas layer around the sample, affecting the freezing rates. Pure ethane or propane will solidify when left at liquid nitrogen temperature, while the mixture has a lower freezing point, allowing the cryogen to remain liquid at liquid nitrogen temperatures and making its application more convenient [4.141]. Plunge-freezing allows the sample to be kept in a fully hydrated state, with the added advantage that the sample is less sensitive to radiation when imaged at the low temperature required to maintain its vitrified state [4.142, 4.19].

Existing cryo-plungers vary slightly in design and functionality. Commercially available instruments have been introduced over the years (FEI/Thermo Fisher, Leica and Gatan) with the additional possibility to adjust and control some of the preparation parameters, such as humidity, temperature and air pressure, in specially designed environmental chambers. Moreover, the whole process—except for the introduction of the sample, which still has to be done manually—is computer-controlled and automated to facilitate the sample preparation process and expand its reproducibility [4.104, 4.105].

Successful vitrification requires cooling rates higher than \({\mathrm{10^{4}}}\,{\mathrm{K{\,}s^{-1}}}\). For samples that are too thick or of poor thermal conductivity, such cooling rates cannot be obtained solely by plunge-freezing. The ice throughout the sample volume is therefore not fully vitrified, but partially crystalline, which can damage the structure or hinder subsequent analysis [4.143]. Pure water can only be vitrified to a thickness of \(\approx{\mathrm{1}}\,{\mathrm{{\upmu}m}}\); however, intracellular proteins and other macromolecules act as cryoprotectants and can increase the vitrification depth up to \(\approx{\mathrm{10}}\,{\mathrm{{\upmu}m}}\) for some biological materials. For an even thicker specimen, the vitrification depth can be increased 10-fold by freezing at high pressures where ice nucleation and growth is suppressed [4.103, 4.144, 4.145]. High-pressure freezing (HPF) can be used up to a thickness of \({\mathrm{200}}\,{\mathrm{{\upmu}m}}\) [4.106, 4.107, 4.146]; however, HPF samples require additional preparation techniques (e. g., cryo-sectioning or FIB milling) prior to imaging (Fig. 4.5a-f) [4.147].

Fig. 4.5a-f

Preparation of vitreous specimens for cryo-electron microscopy (cryo-EM) and tomography (cryo-ET) (a). Cryo-SEM micrograph of a self-supported FIB lamella and (b) a frozen-hydrated section. (c) 2-D projection of isolated 20S proteasomes, and \(x\)-\(y\) slices from tomographic reconstructions of: (dEscherichia coli, (e) of a region of a FIB-milled HeLa cell, and (f) of a cryo-section from an organotypic slice culture of rat hippocampus showing the compression along the cutting direction on the egg-shaped synaptic vesicles. Republished with permission of Annual Reviews, from [4.147]

4.3.2 Cryo-FIB Milling

With the advent of cryo-preparation systems for focused ion beam microscopes, a fundamentally different method for thinning frozen-hydrated samples became feasible. FIB instruments were originally developed for material science applications and were used for the direct modification of semiconductor devices, the fabrication of optoelectronic components and fault analysis [4.148]. The FIB technique for TEM specimen preparation was introduced more than 20 years ago and is now a standard preparation method in the materials sciences because of its unsurpassed site-specific preparation abilities [4.149]. However, applying this technique to frozen-hydrated biological specimens requires hardware and protocols adapted to cryogenic needs.

During the milling procedure, the frozen-hydrated sample is kept in high vacuum and is exposed to a beam of focused ions. Heavy ions, such as gallium (\(\mathrm{Ga^{+}}\)), are typically used. The controlled bombardment of the sample with these ions results in the removal of atoms from the specimen surface through sputtering. In particular, FIB milling avoids the mechanical cutting artifacts associated with cryo-ultramicrotomy [4.114]. Nonetheless, subtle ion-induced structural alterations, due to local heating or the formation of a damaged layer on the milled surface (as a consequence of the ion impacts), can be expected. Moreover, the surfaces of the milled areas are not completely planar, and streak-like surface irregularities along the milling direction can sometimes be observed. Such parallel striations are related to compositional changes within the ice-embedded specimen, which result in differential sputtering rates and thus preferential milling, referred to as curtaining  [4.150].

To date, it has been shown that FIB milling of vitreous ice with an ion current of \({\mathrm{10}}\,{\mathrm{pA}}\) (at a nominal incidence angle of \(75^{\circ}\) from the normal) does not induce heating to the extent that devitrification occurs [4.56]. Moreover, simulations indicate that the \(\mathrm{Ga^{+}}\) implantation zone can be restricted to a relatively tolerable superficial layer of \(10{-}20\,{\mathrm{nm}}\) when oblique or grazing angles of incidence are chosen [4.151].

The successful application of the cryo-FIB technique to frozen-hydrated biological material is directly tied to robust hardware implementation and reliable operational protocols. Several requirements must be considered, including temperature stability, protection against contamination, sample and beam stability over longer preparation periods, and the suitability of the thinned area for tomography. Temperature stability is one of the main aspects, as the sample temperature must always be below the devitrification point of approximately \(-{\mathrm{135}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). In addition, strong heating during ion milling must be prevented. Although ion-induced damage cannot be completely avoided, it should be limited to a very thin surface layer. Ideally, the sample should remain free from frost or other potential contaminants during all preparation and necessary transfer steps. Processing times should be minimized in order to avoid sample alterations and detrimental drift effects. Finally, the ablated area of the sample must be correspondingly thin and appropriately oriented for cryo-electron tomography (e. g., with respect to the orthogonal tilting directions).

One of the biggest challenges in the routine application of FIB milling to cellular samples is multiple transfer, during which samples can be contaminated or lost. This is particularly a problem when cryo-correlation microscopy is required, adding another manipulation step to the overall workflow. For this reason, various engineering solutions have been implemented to facilitate sample mounting and transfer for light microscopy, FIB and cryo-TEM instruments. Several different column-mounted cryo-SEM preparation systems are commercially available (e. g., FEI, Quorum, Leica, Hummingbird). These systems enable the transfer of specimens onto a stable SEM cold stage for further observation or manipulation.

Typically, an EM grid with vitrified cells is mounted into a loading station in a special cryo-holder or shuttle and then transferred to an actively cooled cryo-stage within a FIB instrument [4.58]. The stage temperature is normally kept at \(-150\) to \(-{\mathrm{170}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). Target cells are identified by imaging secondary electrons or by correlative methods [4.65]. Various milling strategies are currently being used for milling cells directly on EM sample carriers; parallel milling, wedge milling or lamella milling [4.152, 4.153]. One of these is the lamella milling of cells directly on the EM grid (i. e., on-the-grid lamella milling ) in order to avoid further tampering with the thin and fragile lamellae, as is necessary, for example, in lift-out approaches. Lift-out approaches are frequently used in materials science at room temperature [4.154, 4.155] where the lifting is done with a micromanipulator device, followed by placement in a special half-grid so that the electron beam of the TEM is normal to the cross-sectional area of the lamella. The lift-out approach poses a particular challenge for samples that must remain vitrified, and it is also a rather time-consuming procedure [4.60]. For these reasons, on-the-grid lamellar milling or simply wedge milling are currently favored.

Lamella milling on the grid is accomplished by removing material with the ion beam above and below the target region, producing a self-supported, thin and electron-transparent lamella (Fig. 4.6a-c). In order to prevent ion beam erosion at the front face of the lamella and to obtain a homogeneous surface structure (i. e., to avoid curtaining), a protective layer of organometallic platinum is deposited with the aid of the gas injection system (GIS) [4.156]. This deposition process is driven solely by the thermal gradient between the deposition gas and the cold sample surface, and the interaction with the ion beam transforms the condensed organometallic gas into a conductive and protective layer. In order to avoid radiation effects through the needle (\({\mathrm{25}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)), a large needle–sample distance is required (e. g., \(> {\mathrm{3}}\,{\mathrm{mm}}\)). The target area of the cell must then be positioned so that milling at shallow angles is possible. Typical angles of incidence for the gallium beam are \(5{-}15^{\circ}\) from the grid surface. This is followed by the acquisition of an overview image of the intended target cell by a secondary electron image and the positioning of two rectangular milling patterns. The two patterns are drawn above and below the area intended for the lamella preparation, and the distance between them determines the final thickness of the lamella. Milling of the patterns can be performed in succession or in parallel, the latter by fast scanning of the ion beam iteratively over both areas. The final result of a milling experiment can be observed by imaging the top view of a lamella with the electron beam.

Fig. 4.6a-c

Geometry of FIB on-the-grid lamella preparation. (a) Cryo-SEM micrograph of a frozen-hydrated cell embedded in a thin layer of ice and attached to the holey carbon support film. (b) Corresponding region after FIB milling yielding the lamella, which is supported on the sides by the remaining bulk ice material. (c) Cartoon illustrating the resulting lamella. Figure 4.6a-ca,b adapted from [4.152, 4.58]

The respective cell dimensions determine the lamella size. To ensure sufficient lateral support of the lamella, the samples should cover less than two-thirds of the visible width of the cell. Doing otherwise may cause the lamella to bend. The on-the-grid thinning procedure is carried out in several steps: Coarse milling with a high ion beam current of \({\mathrm{300}}\,{\mathrm{pA}}\) is used for the rapid removal of frozen-hydrated bulk material, followed by fine milling steps at much lower currents. The final fine milling steps are combined with placing and redefining the rectangular patterns closer to each other to define the final lamella thickness. Reducing the milling currents to lower and even lower currents (e. g., \(10{-}50\,{\mathrm{pA}}\)) will minimize radiation-related damage to the milling surfaces. In this way, several lamellae can be prepared on an EM grid before transfer to the cryo-EM for tomography experiments (Fig. 4.7a-c).

Fig. 4.7a-c

Cryo-EM/ET on a FIB lamella of a HeLa cell. (a) 2-D TEM montage of a HeLa cell FIB lamella. Lamella top with an organometallic Pt layer. (b\(x\),\(y\) slice from a tomographic volume acquired at the framed area in (a), showing a variety of organelles and cytoskeletal structures within the cytoplasm. (c) Corresponding \(x\),\(z\) slice of the tomographic volume in (b). Adapted from [4.117], with permission from Elsevier

Cryo-FIB thinning can be applied to vitrified biological material obtained by either plunge-freezing or high-pressure freezing. The successful combination of cryo-FIB milling and cryo-ET, meanwhile, has been shown for several applications using plunge-frozen specimens on EM grids [4.71, 4.72, 4.73, 4.75, 4.76, 4.77, 4.97, 4.98, 4.99], and several approaches have been developed to utilize high-pressure frozen samples as well [4.115, 4.60]. A general disadvantage of the FIB milling technique is that the features of interest show little or no contrast and are hidden under a layer of amorphous ice, which necessitates careful identification and targeting of appropriate milling sites (Sect. 4.3.3).

4.3.3 Correlative Microscopy

The field of view in cryo-electron tomography covers at most a few square micrometers. Localizing specific areas of interest on an EM grid, three orders of magnitude larger, often exceeds the time required to record a tomographic tilt series. This screening process is frequently aggravated by the low signal-to-noise ratios (SNR) of single cryo-EM projection images. However, the degree of damage caused by the cumulative electron dose becomes evident only after data collection. Due to these restrictions, structures of interest can be difficult to identify within low-dose electron micrographs, which are dominated by noise that obscures finer structural detail. Furthermore, without a priori information, it is almost impossible to assess the functional state of a structure, since electron micrographs represent only a series of static snapshots from which the sequence of events must be inferred. Here, fluorescence microscopy can offer a solution, permitting independent and unambiguous confirmation of the functional state of a feature of interest, albeit at low resolution and devoid of the structural context in which the events occur.

The use of optical microscopy to screen the cellular landscape and identify features of interest before magnifying these features via cryo-EM provides a powerful approach for studying cellular processes. In general, the biological sample can be immobilized by vitrification techniques either before or after imaging with the light microscope. Imaging in physiological conditions has the advantage that oil-immersion objectives with high numerical apertures (NA) can be used. This in turn enables investigations at higher spatial resolution, which can be further increased through the application of super-resolution techniques such as PALM/STORM. However, molecular reorganization occurs during the time required to transfer the cells to a vitrification device, complicating the accurate correlation of LM and EM observations. In practice, transfer to a vitrification device can take at least \({\mathrm{30}}\,{\mathrm{s}}\) for thin-film vitrification and several minutes for high-pressure freezing. The latter method is notably prolonged, since medium or buffer must be supplemented with a high-molecular-weight cryoprotectant to ensure uniform vitrification throughout the sample. Thin-film vitrification occurs in about \({\mathrm{5}}\,{\mathrm{ms}}\) [4.157], while high-pressure freezing can be accomplished within \(15{-}20\,{\mathrm{ms}}\). However, it remains a challenge to gain temporal control over the freezing process [4.158] or to capture events at specific stages by time-resolved vitrification [4.159, 4.160, 4.161].

In order to image exactly the same structure in the electron microscope as was previously observed by light microscopy, it is necessary to perform fluorescence microscopy after vitrification. Such a cryo-fluorescence microscopy approach enables a direct correlation of the frozen-hydrated sample between the two imaging modalities (Fig. 4.8a-c). Unlike approaches that image the specimen before vitrification, this method is not affected by structural changes that occur during the time between fluorescence observation and cryo-immobilization. However, the specimen must be observed at temperatures below the devitrification point (\(<-{\mathrm{135}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)), which excludes the use of standard immersion objectives (although a liquid propane immersion lens has been proposed [4.162]). Consequently, the attainable resolution in cryo-fluorescence microscopy is limited by the NA of air objective lenses. For routine cryo-CLEM experiments (wide field), the measured resolution using fluorescent beads for calibration is between \(400{-}500\,{\mathrm{nm}}\), and the overall correlation precision is in the range of \(50{-}100\,{\mathrm{nm}}\), which has been demonstrated in proof-of-principle experiments [4.163, 4.64]. Far-field super-resolution fluorescence light microscopy techniques, meanwhile, have been adapted to cryogenic conditions [4.108, 4.109, 4.110] with reported resolution down to \(\approx{\mathrm{40}}\,{\mathrm{nm}}\). However, optical aberrations (e. g., scattering of light in the frozen medium), subtle changes in sample quality and the locally varying ice thickness on a grid can affect the achievable resolution and complicate accurate colocalization.

Fig. 4.8a-c

Principle of cryo-correlation microscopy. Correlation applied to synchronized HeLa cell culture for targeting fluorescence-labeled lipid droplets. (a) Maximum intensity projection of the spinning-disk confocal volume. Green shows general neutral lipid droplets dye. Red shows neutral fatty acids dye. (b) FIB image at the same sample position overlaid with FLM data. (c) Cryo-TEM montage of lamella containing the targeted lipid droplets. Adapted from [4.65], with permission from Elsevier

Fluorescence labeling techniques are of fundamental importance in successful cryo-correlative studies [4.164, 4.165]. The labeling of intracellular epitopes in living cells before freezing, either by electron-dense markers or fluorescent antibodies or compounds, is not only invasive but also notoriously difficult. Immunocytochemistry labeling cannot be performed under cryogenic conditions, since antibodies do not have access to target sites embedded in the ice and unbound labels cannot be removed via washing steps. Currently, the best labels for cryo-correlative microscopy are clonable fusion proteins, such as green fluorescent protein ( ). These fluorophores are expressed within the cell, enabling noninvasive screening for cellular phenotypes and localization of low-copy-number structures on an EM grid. However, currently available fluorescent proteins do not provide contrast to EM micrographs. Clearly, there is demand for a genetically engineered electron-dense contrast agent suitable for both light and electron microscopy. The first attempts to generate such a label were based on fusing a small metal-binding protein, metallothionein, to a target protein. This approach tried to leverage the capacity of metallothionein to initiate gold cluster formation [4.166]. However, this approach has several shortcomings, including nonspecific intracellular aggregation and adverse physiological effects.

Fluorescence microscopy of vitrified biological specimens directly on EM grids requires dedicated instrumentation that ideally can be adapted to various existing light microscopy platforms. For this purpose, different nitrogen-cooled cryo-stage systems have been developed [4.167, 4.168, 4.169, 4.57, 4.61, 4.62, 4.64, 4.65], and some are commercially available. However, all systems must comply with the basic requirements for a cryogenic workflow:
  1. 1.

    Temperature stability: the vitrified specimen must be kept at temperatures below the devitrification point of approximately \(-{\mathrm{135}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\) at all times

  2. 2.

    Protection from contamination: contamination by ice crystals or frost particles on the EM grid surface must be avoided by proper isolation and shielding of the sample

  3. 3.

    Appropriate specimen holder: the system must be adapted to hold standard EM grids.

These technical demands impose major constraints on the resolution and signal detection of light microscopy.

To avoid potential cytotoxic effects caused by copper ions, eukaryotic cells are typically cultivated on gold EM grids. These gold grids are particularly malleable and can be easily deformed by the gripping and clamping tools used throughout the workflow. This obstacle can be circumvented by stabilizing the grid after vitrification in a rigid specimen support, i. e., AutoGrids (FEI Company, Eindhoven, The Netherlands). They are also known as C-clip rings and made of a rigid reinforcement ring that provides steadier specimen support during the multiple transfer and handling steps [4.116, 4.117, 4.57]. This is of special importance if the grid is transferred from one system to another.

4.3.4 Cryo-ET


Due to their great depth of field, electron microscopic images are essentially two-dimensional projections of the entire three-dimensional object in the electron beam. Thus, features from different \(z\)-levels within the object overlap in the resulting micrograph and cannot be separated. The traditional way to extract meaningful information from an electron micrograph is to reduce the \(z\)-dimension of the object (e. g., using an ultramicrotome), i. e., to image almost two-dimensional objects. As previously stated, this approach has its limitations.

The first practical formulation for applied tomography was achieved in the 1950s [4.170]; however, Johan Radon first outlined the mathematical principles behind the technique in 1917 [4.171] (English translation in Deans [4.172]). The Radon transformation is the integral transformation of a known function over straight lines. Radon also describes an inverse function that can be used to calculate an unknown function with a given Radon transformation. In electron tomography, this inverse formula is used to obtain the a priori unknown three-dimensional (3-D) density of the object from two-dimensional (2-D) projections.

Each 2-D projection of a tilt series corresponds to a part of the Fourier transformation of the 3-D object to be imaged, and each 2-D projection at a given angle is a central section through the 3-D Fourier transformation of that object (central slice or projection slice theorem). Thus, if a sufficiently large number of 2-D projections are recorded from all angles, we should be able to get a complete description of the 3-D object over the full range of frequencies. If we now use the inverse Fourier transformation of the superposition of all these Fourier-transformed 2-D projections, the real-space object can be reconstructed. This direct Fourier reconstruction approach was formulated by Bracewell [4.170] and was used for the first tomographic reconstruction from electron microscope images [4.20]. It is also used to determine atomic structures in electron [4.173] and x-ray crystallography [4.174], where it is referred to as Fourier synthesis .

In computer tomography, the instrument revolves around the sample—the patient—and takes images at different angles. In electron microscopy, the instrument remains static, instead the sample is tilted incrementally and a micrograph is recorded for each tilting angle. This limited tilt range results from the limited spacing of the objective pole pieces, the holder's geometry and also the planar geometry of the object itself. At higher angles of inclination (e. g., \(\pm 90^{\circ}\)) the electron beam is blocked by the holder and possibly by the EM grid, depending on the position of the structure within a grid mesh. This angular gap can be well represented in reciprocal space (i. e., Fourier space), where a wedge-shaped, blind area is formed, the so-called missing wedge . However, the requirement for a distortion-free 3-D reconstruction, all projections of the sample over the entire tilt range (\(\pm 90^{\circ}\)) [4.175], is not fulfilled, which leads to imperfections in the reconstructed object. The resolution of the 3-D reconstruction is direction-dependent: parallel to the tilt axis it is determined by the instrument itself; perpendicular to the tilt axis, it is directly related to the angular increment and to the number of projections. Along the beam direction, projections lack some information (missing wedge), which leads to an elongation of structures in the final reconstruction. Furthermore, resolution is influenced by the applicable electron dose and the detector performance. By combining two orthogonal tilt series (dual-axis tomography ) the missing wedge is reduced to a missing pyramid, thus increasing the amount of information by almost \({\mathrm{20}}\%\). Although the maximum resolution is not necessarily increased, the achievable resolution is clearly more isotropic, and structures hidden in the uniaxial case, due to their orientation relative to the tilt axis and their position relative to the missing wedge, emerge in a biaxial acquisition scheme.

In recent years, only a few studies have been conducted using a dual-axis acquisition scheme [4.176, 4.177, 4.178, 4.179, 4.180, 4.181], as dual-axis tilting is associated with additional difficulties. Besides some purely technical aspects such as the alignment of two separate tilt series and the increased acquisition time, the dose accumulation on the sample from two tilt series remains the challenge. However, the missing wedge (or pyramid) and its effects require special attention and special routines for processing and mining tomograms (e. g., subtomogram averaging or template matching).

Tilt-Series Acquisition

A tilt series can be acquired in various schemes: unidirectional, bidirectional and dose-symmetrical (i. e., dual-walkup), each with a constant angular increment [4.119]. A scheme with decreasing increments for higher tilt angles, the Saxton scheme [4.182], was proposed to reduce the resolution anisotropy which arises at higher tilt angles due to the increase in specimen thickness. However, schemes with a constant angle increment are the most common, since they perform better with still noisy micrographs. The unidirectional tilt scheme makes a linear sweep from one angular extreme to the other, while the bidirectional tilt scheme is divided into two separate branches, or tilt series. The dual-walkup tilt scheme shows a near-symmetrical accumulated electron dose. The tilt increments typically range from \(0.5^{\circ}\) to \(5^{\circ}\). A bidirectional tilt scheme is better suited for automated data acquisition, since targeting of the desired image area is done at the tilt series starting angle \(0^{\circ}\). However, a disadvantage is that the projections on both sides of the start angle will have different accumulated doses, and beam-induced sample alterations can complicate the alignment of the two tilt branches. The dose-symmetrical scheme maximizes the transfer of high-resolution information by collecting the low-tilt images early on before radiation damage has accumulated. This tilting scheme starts at zero degrees and travels to the highest tilts in both directions in an alternating fashion (\(0^{\circ}\), \(+3^{\circ}\), \(-3^{\circ}\), \(-6^{\circ}\), \(+6^{\circ}\), \(+9^{\circ}\), \(-9^{\circ}\), \(-12^{\circ}\), …). Depending on the microscope hardware and the stage design , some instruments will show more drift after tilt, which may increase acquisition time, and microscopes with removable side-entry holders are unlikely to be sufficiently stable for this type of data collection.

Tilting is exclusively mechanical, which leads to a major practical difficulty: the inability to precisely adjust the eucentric height of the specimen throughout the tilt series. The eucentric plane is normal to the optics axis, so a point on the optics axis should not move sideways when tilted around the holder axis. But even today, shifts in the \(x\), \(y\) and \(z\) directions occur during an angular acquisition. Shifts in the \(z\) direction lead to changes in focus and make 3-D reconstruction more difficult, or even render a reconstruction meaningless in uncorrected cases. Therefore, the \(x\)-\(y\) position (tracking) and the \(z\) position (autofocus) must be controlled and corrected iteratively. Even today, data acquisition for tomography is more time-consuming, for example, than in the single-particle case. However, the microscope hardware improved over the past decade, and together with advanced automation routines (i. e., batch acquisition), the throughput increased from a few tomograms to more than a dozen per day. Meanwhile, several software packages are available and routinely used to set up and control automated tilt-series acquisition schemes, including SerialEM [4.121], TOM Toolbox [4.183] and UCSF Tomography [4.184], and commercial packages such as Xplore3D™ Tomography Suite (FEI/Thermo Fisher Scientific), Latitude-T (Gatan) or EM-Tomo (TVIPS).

Contrast Enhancement: The Volta Phase Plate (VPP)

The basic limitation in cryo-EM and cryo-ET is still the radiation sensitivity of biological materials and the need to minimize recording time and dose. This dose limit problem is exacerbated by the low contrast of frozen-hydrated biological samples, as they are predominantly composed of light elements. As a result, the signal-to-noise ratio (SNR) of individual images/projections is relatively low, and structural information can only be retrieved by averaging. The contrast of vitrified biological samples is due mainly to the modulation of the phase, and not of the amplitude [4.56]. This means that they behave like weak-phase objects, and in order to extract a maximum of information at a given dose, it is necessary to amplify this phase component. Traditionally, this is achieved by defocusing the objective lens and is generally referred to as defocusing phase contrast ( ). Defocusing provides good information transfer at medium to high spatial frequencies, but at low spatial frequencies the transfer is significantly lower. DPC images therefore have a high-pass filter-like appearance and an overall low contrast. A direct interpretation of the recordings is thus made more difficult, and it is necessary to apply various image restoration techniques. Another possibility for improving the phase contrast is the use of phase plates, as in light microscopy. Phase plates are devices that generate phase contrast without the need for defocusing and over a wide range of spatial frequencies [4.185]. Already in the early days of transmission electron microscopy, there were both theoretical and practical considerations regarding the applicability of phase plates, and different types were tested over the years, but with little success [4.69, 4.70]. During the early 2000s, the thin-film Zernike phase plate ( ) was introduced, which is made of a thin amorphous carbon film with a small hole in the center [4.128]. Over 10 years, the ZPP has been tested and used in proof-of-principle applications [4.186], but it showed a number of practical problems that made routine use almost impossible [4.187]. One of these problems was the short life of the ZPP, which required replacement after only a few days of operation in the electron microscope. Furthermore, the exact centering of the hole on the beam path was an elaborate task and could not be automated, so that the data acquisition had to be performed manually. In 2014 a new type of phase plate was introduced—the Volta phase plate ( )—which is very similar in design to the ZPP but without a central hole [4.68]. With the VPP, the phase shift is generated by the interaction of the electron beam with the continuous carbon film. The now-accepted hypothesis is that the beam causes physicochemical changes on the surface of the film, which lead to a local change of the working function and thus to a local surface potential difference. These surface changes are only temporary, and after a few days this potential disappears and the carbon film is back in its original state so that this position can be used and reused again. This gives the VPP a very long practical life, and if it is not mechanically damaged, the film can be used for years. The VPP does not require precise centering, and its application can easily be implemented in automated data acquisition solutions.

The Volta phase plate is a thin (\(\approx{\mathrm{12}}\,{\mathrm{nm}}\)) continuous carbon film, which is positioned in the back focal plane of the microscope (i. e., the position of the objective aperture), so that the beam is maximally condensed to around \({\mathrm{25}}\,{\mathrm{nm}}\) diameter on the phase plate (Figs. 4.9a-c and 4.10a,b). This is called on-plane condition . An initial conditioning exposure of a freshly selected phase plate position results in the development of a Volta potential which in turn induces a phase shift of the unscattered relative to the scattered electrons. Essential for the performance of the VPP is the heating of the film (\({\mathrm{250}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)) to prevent beam-induced contamination and charging during its application. Contamination on the film's surface will result in charging, and this will lead to a deterioration of the VPP performance.

Fig. 4.9a-c

Volta phase plate principle and contrast enhancement. (a) The Volta phase plate comprises a continuous amorphous carbon film and is positioned in the back-focal plane of the objective lens. (b\(x\),\(y\) slice of a reconstruction (FIB-milled HeLa cell) taken without the phase plate at a defocus of \({\mathrm{6}}\,{\mathrm{{\upmu}m}}\) and (c\(x\),\(y\) slice of a reconstruction (FIB-milled HeLa cell) taken with the Volta phase plate at a defocus of \({\mathrm{0.5}}\,{\mathrm{{\upmu}m}}\)

Fig. 4.10a,b

Side-by-side Fourier transforms of high-magnification images taken without (a) and with a VPP (b). The CTFs for both sides are shown for a defocus of \({\mathrm{500}}\,{\mathrm{nm}}\). Adapted from [4.68]

The VPP has some practical limitations . Because it uses a carbon film in the beam path, some of the electrons are scattered, which leads to signal losses of \(\approx{\mathrm{18}}\%\) at \({\mathrm{200}}\,{\mathrm{kV}}\) and \({\mathrm{15}}\%\) at \({\mathrm{300}}\,{\mathrm{kV}}\) [4.68]. Additionally, different positions on the VPP can introduce varying amounts of astigmatism (up to \(\approx{\mathrm{1000}}\,{\mathrm{\AA{}}}\)) due to local variations in the film quality or wrinkling of the film. Furthermore, the variable phase shift (i. e., phase shift development over time) complicates the fitting of the contrast transfer function (CTF ).

However, electrostatic charging of the specimen is the main problem when using the VPP for cryo-ET. Vitrified samples are largely nonconductive and can thus be charged by the electron beam. Such charge phenomena can lead to beam movements on the phase plate or the beam can deform because the charge acts like an electrostatic lens. The only practicable solution to prevent or minimize the charging of the sample is to use conductive carrier foils or to coat the samples with conductive material [4.117]. The latter coating step is especially of relevance for thin cryo-FIB lamella. Cryo-ET with the VPP can be performed either in focus or with a mild defocus (\(0.5{-}3\,{\mathrm{{\upmu}m}}\)). However, as previously stated, the SNR of a single tomographic projection is much lower than a single particle image, since the tolerable dose is distributed over the entire tilt series and since \({\mathrm{15}}\%\) of the signal is lost in the phase plate film. This limits the ability to fit the CTF at such low defocus values. During the tilt-series acquisition, the performance is further limited by the ability to focus accurately and maintain the phase shift [4.188].

In order to avoid electrostatic charging or scattering effects of a phase plate, no additional material should be present in the beam path. Recently, it has been shown that a phase shift can also be generated by a high-intensity focused laser beam [4.189, 4.190]. Such a laser phase plate sounds very promising, and it could become a permanent phase contrast solution for cryo-EM, since a constant and tunable phase shift can be produced at the push of a button.

Direct Electron Detection: The Resolution Revolution

The resolution revolution in cryo-EM is directly related to the development and availability of high-end electron detectors [4.185]. The main characteristic of these new cameras is the ability to directly detect the signal coming from electrons accelerated up to \({\mathrm{300}}\,{\mathrm{keV}}\). These cameras possess a very high readout speed (several hundred frames a second) which is directly linked to their high sensitivity: they allow for single electron counting, thus every event can be registered/detected.

The concept of direct detection for charged particles is not really new (it dates back to the 1980s); however, the new aspect lies in the fact that today's direct detectors can withstand the constant bombardment of harmful and high-speed electrons. The question arises: How is this possible? The answer to this is pretty simple: reduce the amount of detector material, and the electrons will interact with and furthermore shrink the size of the transistors needed for registration of the signals. The continuous scaling of microelectronics was key to the continuous gain in computation speed (e. g., see Moore's law) and, in the end, to the gain in detection sensitivity we are experiencing today [4.35].

In transmission electron microscopy, CCD cameras have been used since the 1990s [4.25]. However, CCDs are easily destroyed by direct exposure to high-energy incident electrons. To decelerate the electrons and to convert their signal into photons, CCD chips for TEM had to be coupled to a phosphor or scintillator. To direct and amplify the generated photons, fiber optics or lens optics had to be used as well [4.191]. However, every part of this CCD stack, but especially the scintillator, broadens the signal substantially, and this compromises the performance of such detectors. The final signal yield was poor and the transistor architecture used only allowed sequential readout. Thus, one exposure time resulted in only one integrated image, and for high-resolution purposes, conventional film was (back then) the detector of choice.

Direct detectors are built from a single chip consisting of fast CMOS transistors with a detection layer directly incorporated into it (CMOS pixel). The thickness of this epilayer determines the sensitivity, and since each and every active pixel reads out simultaneously on its own, the readout speed is determined solely by the CMOS design/technology that is used and how many analog-to-digital converters (ADCs) are incorporated. And the beauty is that all camera functions can be placed directly on the imaging sensor, namely the chip. Today's sensors offer readout speeds in the range of \(40{-}1000\,{\mathrm{fps}}\), and all available cameras allow electron counting. The nice side effect of this speed is the resistance to radiation damage. To reduce the amount of noise contributed by the backscattering of electrons in the silicon substrate material, all chips are back-thinned to a thickness less than that of paper. In addition, back-thinning also contributes to increased detector lifetime, since less energy is deposited in the sensitive layer [4.36].

This boost in sensitivity and speed have enabled us to literally see more detail and to correct for detrimental sample or image motion. The correction for beam-induced specimen movement, which otherwise blurs the recorded images, was paramount in obtaining atomic-resolution structures by cryo-EM [4.37, 4.39]. While the roots/causes of beam-induced motion are still controversial and highly debated, we now have the means to study it in more detail and, even without knowing its origin, to correct for it. The ability to count every incident electron is the second major feature of these detectors. Counting greatly increases the gain in the signal-to-noise ratio of the recorded images. But one must keep in mind that for counting single electron events, one has to decrease the intensity of the illumination by a factor of several hundred (if compared to integrated imaging). While cryo-microscopists are well aware of keeping the electron dose on their specimen within acceptable limits, now they have also to keep the dose rate within bounds to enable counting.

The performance of imaging detectors is measured by the amount of additional noise they add to the image. This is quantified by detective quantum efficiency ( ), which describes the ratio of detected to incidental information as a function of spatial frequency (Fig. 4.11a,b [4.192]). To design and build a perfect detector with \({\mathrm{100}}\%\) efficiency might be wishful thinking and technically impossible. However, we still can improve current designs for better performance to come close to the ideal. Speed is one thing, which can be dramatically improved. The CMOS technology currently used for electron detection (transistor size of 350 or \({\mathrm{180}}\,{\mathrm{nm}}\)) is already more than 10 years old, but used because it was proven, available and affordable in the chip foundries across the world. Nevertheless, the transistor size has further decreased to a few tens of nm, and we can expect several thousand fps (instead of a few hundred). We will also see bigger arrays, going from the standard \(4096\times{}4096\) pixel arrays (\({\mathrm{4}}\,{\mathrm{k}}\)) up to \({\mathrm{8}}\,{\mathrm{k}}\) or \({\mathrm{10}}\,{\mathrm{k}}\), the latter similar to the size of the film that was used formerly. Efforts will continue to define the optimal pixel size with a suitable sensitivity layer thickness, to increase sensitivity and increase the signal-to noise readout, and to minimize missed or overlapping events in electron counting.

Fig. 4.11a,b

Comparison of the detection quantum efficiency (DQE) at 300 keV as a function of spatial frequency. (a) DQE for direct electron detectors: DE-20 (green), Falcon II (red), Falcon 3EC (orange) and K2 Summit (blue). (b) Corresponding DQEs of photographic film (dark gray) and a CCD camera (US 4000; purple). After [4.192]

There are currently three comparable and commercially available direct electron detectors: K2 Summit (Gatan Inc.), Falcon 3EC (Thermo Fisher Scientific) and DE-Series (Direct Electron). The K2 Summit direct electron detector performs better at low and medium spatial frequencies, which are essential for tomography, and is only slightly surpassed by the Falcon 3EC at high spatial frequencies.

4.3.5 Image Processing

Preprocessing: Movie Frame Alignment

Individual projections from the tilt series recorded in film mode on a direct electron detector must be processed before aligning of the tilt series and reconstruction of the tomogram in order to correct for beam-induced specimen movement that, if not corrected, blurs the captured images [4.193]. The beam-induced sample movement (for a detailed description see book chapter by Glaeser [4.194]) can be split into two components: a uniform full-frame movement and nonuniform local movements that can vary across the image. Motion correction is accomplished by registering identical features in the subframes, followed by summing the registered subframes to produce a motion-corrected image. A number of published algorithms can be used to align the frames in one movie stack [4.195, 4.196, 4.197, 4.37]. However, in contrast to frame alignment from a single-particle acquisition, frames coming from a tilt series have usually been obtained with a much lower electron dose. Therefore, algorithms with moving averages can sometimes be favored, especially if there are no high-contrast features present such as gold fiducials that facilitate image alignment despite the lower dose.

To additionally consider the effects of radiation-induced loss of information individual tilt images can be filtered depending on the radiation exposure [4.198, 4.37]. These exposure or radiation weighting schemes are essentially dose-dependent low-pass filters, where each image is filtered according to the accumulated electron dose [4.199]. Filtering reduces noise and increases contrast in the final reconstruction, and also improves alignment in subtomogram averaging [4.130, 4.200].

Preprocessing: Defocus Determination and CTF Correction

Projections from a tilt series have a lower SNR than single-particle images owing to the low dose used in each tilted image and to the greater sample thickness, which effectively increases with increasing tilt angle. This in turn leads to weaker Thon rings and makes defocus determination more difficult and, depending on the detector used, more challenging. Another factor that influences the defocus determination is the nonuniform defocus present in tilted images [4.127, 4.201, 4.202]. This defocus gradient perpendicular to the tilt axis is due to height differences in the image and depends on the sample thickness and tilt angle. For tilted images, the mean defocus is the defocus on the tilt axis that must be determined. Several algorithms have been developed to determine the mean defocus value of a tilted image based on periodogram averaging of strips running parallel to the tilting axis. Within each strip there are minimal defocus variations, and using multiple strips, a series of defocus measurements perpendicular to the tilt axis can be made [4.127, 4.201, 4.202, 4.203]. Periodogram averaging is one way to improve the Thon rings; downsampling of the complete Fourier transformation and radial averaging are further possibilities [4.204]. Thus, the mean defocus, the defocus gradient or both can be calculated. In cases where these methods do not yet provide enough signal to measure the defocus, extended acquisition schemes can be employed and power spectra can be averaged from several images to improve the SNR for subsequent defocus determination [4.205, 4.206].

For the VPP tilt series, extended acquisition schemes are also necessary, if the acquisition takes place in focus, and therefore no defocus correction (i. e., CTF correction) has to be carried out. Focusing is done several times for each tilt image at two positions on opposite sides of the target area. The resulting nominal defocus, which is interpolated from the two focusing areas, can be a good approach to the target area, if the height differences of the sample stay within bounds. While this strategy has been beneficial for single-particle acquisition with the VPP, tilt series taken up with this approach resulted in an increased tomographic alignment error and consequently in lower resolution [4.188, 4.207]. This error is likely due to deformation of the specimen as a result of radiation damage at the focusing areas after several focusing rounds. Thus, the benefits of the beam-induced deformation of the sample outweigh the advantage of more precise focusing due to the lengthy focusing protocol. VPP data with small defocus values (up to \({\mathrm{3}}\,{\mathrm{{\upmu}m}}\)) require CTF determination and correction similar to defocus phase-contrast ( ) images with an extended imaging model, including the VPP-induced phase shift.

CTF correction of tilted images can be performed locally on strips parallel to the tilt axis [4.127, 4.201], or globally, i. e., CTF correction of the entire image instead [4.208, 4.209]. For the latter, there are two approaches: one for CTF correction per tilted image using a processing filter similar to the stripwise approach, and one for 3-D-CTF correction during tomogram reconstruction [4.210]. The 3-D-CTF correction considers the defocus change in relation to the thickness of the sample and is computationally expensive. However, if subtomogram averaging is the goal, one can determine the local defocus (of each particle) and perform a local CTF correction. Local CTF correction can be performed by extracting the 2-D projections of each particle from each tilted image, performing a CTF correction, and then directly reconstructing a subtomogram with each particle [4.211, 4.212] or CTF correction can be performed on the Fourier slices of a subtomogram extracted from a non-CTF-corrected tomogram [4.213, 4.214]. While the first approach is accurate as long as the projection to be corrected is large enough to include the full point spread function, the second allows the CTF to be further refined during reconstruction [4.210, 4.215, 4.216].

Preprocessing: Tilt-Series Alignment

Tilt-series or tomogram alignment generally includes determining displacements between the images in a tilt series, accurately determining the orientation of the tilt axis and the tilt angles, and compensating for image deformations or distortions (for a detailed account see [4.217, 4.218]). These alignment parameters are most frequently determined using high-contrast gold beads (fiducials) embedded in the ice throughout the field of view [4.219]. Their positions can be determined either manually by visual inspection or automatically with the help of picking algorithms [4.220]. However, gold beads are added either to the sample solution or directly onto the carbon foil prior to the vitrification process, thus they are surrounding the cells to be imaged, and thus they are absent in cryo-FIB lamella or cryo-sections. They can be added after milling or sectioning [4.118, 4.221, 4.222] by dipping the lamella or sections into a solution containing gold beads. However, such procedures entail risks that can lead to a catastrophic loss of the fragile, pre-prepared sample, wasting hours of sample preparation.

Tilt series can also be aligned without the use of fiducials, i. e., by feature or patch tracking. Tracking image features through the entire set of tilted projections can be difficult, since features change their appearance during tilting (i. e., alteration by radiation exposure), and cross-correlation-based alignment methods assume that the sample behaves as a rotating rigid body [4.223]. Much greater success was achieved with patch tracking [4.224, 4.225]. This is based on the calculation of the cross correlation (CC) between multiple and overlapping image patches through the tilt series and treats the tracked positions like a fiducial model. The obtained trace values are then used to align the tilt stack [4.217, 4.225, 4.226]. While less accurate than fiducial-based alignments, especially at high tilts, patch tracking can be applied to samples such as lamellae or sections.


After preprocessing and alignment, the tilt series can be used to create a 3-D reconstruction—a tomogram . Various methods are available for the reconstruction of tomograms (reviewed [4.227, 4.228]). The direct interpretation of the projection-slice theorem would suggest a reconstruction algorithm based in Fourier space [4.229]. Although the first 3-D reconstruction by DeRosier and Klug [4.20] was carried out in Fourier space, it is common to use real-space-based reconstruction algorithms, because the practical implementation of Fourier space reconstruction is not as simple as an inverse transform. The projection data are always sampled at discrete angles, leaving regular gaps in Fourier space. The inverse transform inherently requires a continuous function, and thus it is still required to fill the gaps in Fourier space [4.230]. However, the quality of a Fourier-space reconstruction is greatly affected by the type of interpolation implemented, as examined by Smith et al [4.231]. Reconstruction of the 3-D structure factors based on the Fourier-transformed projections and direct inversion to real space would be a natural choice. Progress has been made in that respect, and direct inversion [4.232, 4.233, 4.234] has already demonstrated its advantages in terms of accuracy and speed [4.233]. However, by far the most widely utilized algorithm is weighted back-projection ( ) [4.133, 4.235]. Nowadays, iterative, typically real-space-based reconstruction techniques are also well established (reviewed in [4.236]), such as the algebraic reconstruction technique (  [4.237, 4.238]), the simultaneous iterative reconstruction technique (  [4.132, 4.239]) and the simultaneous algebraic reconstruction technique  [4.131]), despite the fact that some were subject to criticism early on [4.240] (for a detailed review of reconstruction algorithms we refer to [4.227, 4.241]). There are a number of other iterative methods, including the progressive stochastic reconstruction technique (  [4.215]), the maximum entropy method (MEM  [4.242]) and Fourier space methods  [4.211, 4.243]. As with real-space methods, they compare each image with the corresponding center section and update the volume iteratively to minimize the difference. Iterative methods provide tomograms with better contrast and less noise; they are usually easier to interpret than tomograms reconstructed with WBP. The higher contrast in tomograms generated by iterative methods reflects a better, lower-resolution signal, which is beneficial for the alignment of subtomograms (Sect. 4.3.5, Subtomogram Averaging and Classification). However, when these methods are used, information with higher resolution below the noise level may be lost. In WBP, the high-resolution signal is retained, and it can be amplified and restored during subtomogram averaging; therefore, it is still the most commonly used in combination with subtomogram averaging.

The theory of back-projection is based on a simple principle: a point in space can be unambiguously described by three arbitrary rays passing through that point. As the complexity of the object grows, however, more rays are needed to describe it uniquely. A projection of a three-dimensional object is the opposite end of such a ray and thus describes part of the complexity of the object. By reversing the projection and smearing it along the path it was taken, one can produce a ray that uniquely describes the object in this projection direction, a process called back-projection. With an adequate number of projections from different directions, the superposition of all back-projected rays yields the shape of the original object: a reconstruction technique known as direct back-projection. Direct back projection produces objects that are exceptionally blurred. While low frequencies are clearly amplified, fine spatial details may be poorly reproduced. This is an effect of the uneven sampling of spatial frequencies in the series of original projections. Each of the acquired projections is a line intersecting the center of Fourier space. This means that there are far more sampling points in the center of Fourier space (assuming we sample each projection uniformly) than at the edge. Consequently, high spatial frequencies will be undersampled and low spatial frequencies oversampled, resulting in a blurred reconstruction. In order to correct this blur in real space and restore the frequency equilibrium in Fourier space, it is thus necessary to apply weighting schemes that take into account the different sampling densities in Fourier space. In weighted back-projection, the projections in Fourier space are first weighted by a function before being back-projected. Assuming an infinitely small tilt increment, the weighting must be proportional to the amount of the spatial frequency orthogonal to the tilt axis (analytical weighting ); more precise weighting (exact weighting ) must consider the shape function of the object to approximate the sampling density in Fourier space, normally using a sine function [4.229, 4.244]. The weighted micrographs can then be back-projected into the reconstruction body, most often by trilinear interpolation. New iterative methods are being developed specifically for subtomogram averaging to achieve higher contrast while maintaining high-resolution information [4.211, 4.215, 4.245].

Visualization: Segmentation

Tomograms can be presented either as stacks of two-dimensional (2-D) images (slices) or as three-dimensional (3-D) images generated by surface or volume rendering (Fig. 4.12a,b). While this may be sufficient for a qualitative description of the tomogram, a more quantitative analysis requires that the features of interest are identified with high accuracy and precisely localized. The annotation and segmentation of the tomogram is a challenging task, because the signal-to-noise ratio ( ) of the data sets recorded under minimal dose conditions is poor and contains distortions resulting from incomplete data (missing wedge) [4.247, 4.248]. Existing segmentation methods, which are widely used in biomedical imaging, fail to work with the noisy and low-contrast data typical of cryo-electron tomography.

Fig. 4.12a,b

Segmentation example. Molecular architecture of the Chlamydomonas Golgi apparatus and transport vesicles revealed by in situ cryo-ET. (a) A slice through a cellular tomogram containing a representative Golgi stack and (b) corresponding 3-D segmentation, showing the native morphology of the ER (yellow), four cis cisternae (green), cis vesicles (light green), four medial cisternae (magenta), medial vesicles (light pink), the trans cisterna (blue), trans vesicles (light blue) and the TGN (purple). Other membranes, the nuclear envelope, nuclear pore complexes and ribosomes are shown in gray. Adapted from [4.246]

Denoising is often a prerequisite for segmentation: the SNR needs to be increased, particularly in a tomogram, to distinguish different structural elements [4.249]. The simplest form of denoising is low-pass filtering the data. Since the SNR is lower in higher frequencies, low-pass filtering automatically yields an increase of the overall SNR. Denoising procedures, such as band-pass frequency filtering, nonlocal means filtering and iterative reconstruction schemes, can be performed during or after tomogram reconstruction. Nonlinear anisotropic diffusion ( ) is a particularly successful denoising method in cryo-ET [4.250, 4.251, 4.252, 4.253] and is still used today. The algorithm uses simulated diffusion to reduce the noise a measure of the probability based on multiple correlation coefficients improved detection accuracy and sensitivity compared to the probability scores using single templates.

Proper denoising can aid in tomogram interpretation and is particularly useful for the segmentation of supramolecular structures and organelles [4.247, 4.254, 4.255]. While tomogram segmentation is optional, there are several reasons to mask cellular compartments (see below).

Tomogram segmentation can be performed either manually or automatically, with several toolboxes available (reviewed in [4.248, 4.256, 4.257, 4.258]). Automated segmentation procedures for cryo-tomograms have the advantage that they avoid tedious and error-prone manual segmentation of noisy 3-D images. Given that we now produce many tomograms per microscope per day, automated analysis has become even more critical and a major time-limiting factor in the processing pipeline [4.259].

Procedures were developed for segmentation of more prominent cellular structures such as lipid membranes [4.260, 4.261, 4.262, 4.263, 4.264, 4.265] and cytoskeletal filaments [4.247, 4.266]. The latest automatic segmentation algorithms produce accurate results, which can be refined by providing boundary conditions [4.255, 4.263, 4.267]. However, each class of characteristics typically required its own development effort. Manual segmentation is still required today for more complex cellular architectures that involve interpretation and a priori knowledge. A generalizable algorithm for the annotation and segmentation of any feature is highly desirable, but is not yet available.

Identification of Complexes in Tomograms: Template Matching

Tomogram analysis on the molecular level requires precise detection of specific macromolecules. However, identifying all detectable macromolecular complexes in cellular tomograms (i. e., visual proteomics) is a considerable challenge [4.102, 4.135, 4.268, 4.269]. In cellular samples, most complexes are not accessible to labeling by electron dense tags because lipid membranes enclose them. Identification of macromolecules based on their structural signature is the most general approach to assign densities to specific macromolecules. Conceptually, this approach is part of the above segmentation approach according to structurally known features.

Algorithms for particle identification are based on correlation of a template density with the experimental tomogram [4.134, 4.136, 4.249, 4.270]. The correlation coefficient is a measure for the probability that a feature corresponds to a specific macromolecule. In the simplest form, a specific feature is assigned to the template yielding the highest correlation. An existing particle structure can be used to create such a reference or structural template. Atomic models (i. e., the list of atomic coordinates) of the macromolecule of interest, derived from both cryo-EM single-particle analysis and x-ray crystallography, usually form the basis and are easily available via the Protein Database (PDB), a repository for experimentally determined structures. Both the imaging conditions (e. g., defocusing, pixel size, etc.) and the loss of information due to the missing wedge must also be taken into account when composing such a template. Typically, the electrostatic potential of the macromolecule is first calculated from the coordinates and identities of the individual atoms in the atomic model. The resulting electron density map is then convoluted with the CTF (representing the imaging parameters used for tilt-series acquisition) and finally, low-pass-filtered and scaled to the pixel size of the tomogram (Fig. 4.13).

Fig. 4.13

Template matching and subtomogram averaging overview. A template based on known structures or geometrical shapes (e. g., spheres, cylinder) can be used to locate macromolecular complexes in tomograms. Subvolumes can be then extracted, averaged and classified from multiple tomograms to obtain a higher-resolution structure and/or different conformational state. Finally, the structures of the identified particles can be mapped back into the tomogram at their positions and with their orientations. Adapted from [4.102]

For the purpose of determining the similarity between the reference and the structures within a tomogram, the reference is moved pixel-by-pixel in all three spatial directions throughout the entire tomogram. By assigning the determined cross-correlation coefficient to the respective middle voxel in the tomographic subvolume, a first correlation volume is generated. As the complexes in the tomogram can be oriented arbitrarily, this pixelwise cross correlation is determined with a series of different orientations for the reference structure. When scanning this angular space, only the highest cross-correlation coefficient is kept for each voxel. In the resulting 3-D correlation volume, the positions of the possible candidates for the macromolecular complex of interest are displayed that are directly derived from the maxima (peaks) of the calculated cross-correlation function. In certain cases, however, high cross-correlation values are also obtained for other structures which do not necessarily correspond to the sought macromolecular complex (false positives), a fact that is strongly influenced by the inherent low signal-to-noise ratio in the tomogram. Various methods are available for distinguishing between true and false positives of the cross-correlation function; however, the simplest approach is still manual inspection [4.135, 4.271]. More elegant and also faster than the visual check is the cross-correlation-based pattern recognition with a mirrored reference structure. Importantly, the cross-correlation coefficients for the right and left reference are quite similar for false-positive peaks. For the right reference structure, on the other hand, a significantly higher correlation coefficient for a true-positive peak can be expected. However, this additional calculation step can be avoided if a classification step is carried out anyway. The classification of subvolumes of detected positions can be used to distinguish true- and false-positive peaks. This is especially the case when characteristics are classified that are not necessarily contained in the reference structure. Restricting the search volume to the cell body also reduces false positives, excluding gold fiducial markers and contaminants that are often assigned high scores by template matching [4.272, 4.273, 4.45]. A de novo template matching and subtomogram averaging procedure without external structural information can also be used to identify macromolecules found in the tomograms [4.99]. Here, identical structures within a tomogram can be manually selected, aligned and averaged to obtain a first average structure, which is then used as the first template for template matching. This template can then be iteratively refined after several rounds of classification and averaging until the final structure(s) are obtained.

Template matching identifies molecular structures in the tomogram with subnanometer accuracy. In addition to obtaining the positions and orientations, it also enables the assignment of each macromolecule to its location and its neighborhood within the cell. For example, ribosomes bound to the nuclear envelope and ribosomes bound to the endoplasmic reticulum can be reliably distinguished [4.96]. Or, in the case of neuronal poly-GA aggregates, the association with a conspicuous number of functionally impaired 26S proteasomes could be established, as well as the fact that other macromolecules (i. e., ribosomes, TRIC/CCT chaperonins) are excluded from the interior of the aggregate [4.99] (Fig. 4.14a-c).

Fig. 4.14a-c

Template matching/subtomogram averaging example on neuronal poly-GA aggregates prepared by FIB milling. (a\(x\),\(y\) slice of an aggregate. (b) 3-D rendering of an aggregate within a neuron. Mapping macromolecules within poly-GA aggregates (red twisted ribbons) shows a substantial recruitment of 26S proteasomes (light green) and other macromolecules either within or at the periphery of the aggregate: ribosomes (yellow), TRiC/CCT chaperonins (purple). (c) Subtomogram classification of 26S proteasomes. One ground state shown in light green, at \({\mathrm{11.8}}\,{\mathrm{\AA{}}}\) resolution, and one substrate processing state shown in light blue at \({\mathrm{12.8}}\,{\mathrm{\AA{}}}\) resolution (semitransparent maps of the two displayed states are superimposed with the atomic models. Reprinted from [4.99], with permission from Elsevier)

The combination of template matching and tomogram segmentation makes it possible to determine the exact concentrations of molecular complexes within defined cell compartments, and to analyze the clustering of macromolecules and their positioning in comparison to other complexes, membranes or the cytoskeleton. In combination with subtomogram averaging and classification (see below), it also facilitates the mapping of the in situ distributions of macromolecules in different conformations or states of aggregation and can thus provide important insights into the spatial regulation of protein function within the cell; as such, it is an unrivaled method [4.200, 4.254, 4.274, 4.275, 4.75, 4.76, 4.92, 4.93, 4.94, 4.96, 4.97, 4.98, 4.99].

Subtomogram Averaging and Classification

Single-particle analysis and subtomogram averaging have many things in common: selection of particles and their positions, alignment with respect to their orientations and averaging over a large number of particles to increase signal-to-noise ratio (SNR) and resolution. The main difference, however, is that the particles are represented by three-dimensional volumes and not by two-dimensional projections [4.130, 4.200, 4.33].

For the alignment of the subtomograms, different rotations and shifts in relation to a reference are sampled iteratively, and the cross correlation is maximized. Since the missing wedge is present in the subtomogram, the cross correlation in Fourier space is calculated only for the components experimentally sampled in the subtomogram (constrained cross correlation  [4.134, 4.137, 4.138]). Subtomograms are then averaged, including the determined rotations and translations. The resulting structure is used as a reference for the next alignment round, and the process repeated iteratively until rotations and translations converge. To reduce the risk of overfitting during alignment, an adaptive band-pass filter can be applied to the reference based on the resolution determined for the preceding iteration [4.134].

While the translation search is generally performed in Fourier space, the rotation search can be performed either in real space [4.276] or in Fourier space using spherical harmonics [4.211, 4.277, 4.278]. The latter is called fast rotation matching ( ) because this search for rotations is significantly faster than for procedures in real space and offers the possibility of sampling rotations globally. It further enables reference-free alignment, in which subtomograms are first aligned, for example, to a structureless sphere and not to a reference structure. Reference-free does not mean that no reference is used per se, but that external references are excluded. Reference-free alignment minimizes one of the largest problems in aligning and subsequently averaging subtomograms—the template bias—because without a template there is no bias. In addition, reference-free alignment can detect structures of unknown macromolecular complexes, i. e., de novo. The reference bias can be further minimized by increasing the low-frequency contrast using the Volta phase plate [4.76].

The influence of noise is another major problem in aligning the subtomograms, since subtomograms contain much more random noise than real features. This poses a risk, as this noise may be fitted to real attributes in the 3-D map. During the iteration cycles, some of these noise features can gradually build up. One way to minimize the buildup of overfitted noise is to divide the data set into two halves that are processed completely independently, a procedure known today as gold-standard alignment [4.279, 4.280]). By independently determining the Fourier shell correlation of the two completely independent halves of the data, the resolution can be evaluated without the contribution of artificially correlated noise, and this information can be used to adjust the band-pass filter.

Macromolecules in the native cell environment possess a high degree of heterogeneity with respect to their conformations, interaction partners and states of aggregation. Therefore, an additional classification step will inevitably be needed for the initial subtomogram averages, in order to find subsets of more homogeneous particles [4.130, 4.276, 4.33]. Assessment routines, e. g., scoring functions, iteratively sort the subvolumes during a classification according to their similarity into classes [4.134, 4.281, 4.282]. Procedures such as autofocused 3-D classification also minimize human interaction. For this purpose, the differences within a group of aligned subvolumes are used (i. e., the grayscale variance of their mean value) to automatically generate masks for the weighting function [4.281]. This algorithm provides reliable detection and separation of even the finest variations in structure and conformation [4.200, 4.274, 4.96]. Additional classification rounds may help to determine more homogeneous subclasses, provided there are sufficient subvolumes to allow for a correct alignment. The characterization of various conformations or assembly states can also be supported by fitting atomic structures or subunits into the classified averages [4.283, 4.97, 4.99] (Fig. 4.14a-c).

In situ cryo-ET has the advantage that complexes suspended within the cell volume do not normally have preferential orientations, a phenomenon observed predominantly in single-particle cryo-EM. Even if there are preferred orientations in a tomogram, these preferred orientations may vary between different tomograms of the same cells, so that subtomogram averaging can generate relatively isotropic structures from a moderate number of subvolumes [4.246, 4.284, 4.285, 4.96, 4.97, 4.99].

4.4 Perspectives and Outlook

While reducing complexity may have been a necessary step in the past to obtain high-resolution data from macromolecular complexes, recent improvements in data processing, sample preparation and cryo-electron microscope hardware have enabled in situ cryo-electron tomography studies that show more details of intracellular processes than ever before. Advanced sample preparation techniques such as focused ion beam milling eliminate the need for purification and fractionation to meet the physical requirements of cryo-ET. In this way, entire networks of different molecular actors can be modeled in their native environment in high resolution and quantitatively.

Despite this progress, however, there is room for further improvement in the workflow for cryo-ET described herein. Limiting factors include the material-dependent vitrification quality of plunge-frozen and HPF specimens, the contamination (i. e., ice crystal) introduced during transfers and the fragility of the TEM grids during handling, transfer and storage. Vitrification approaches for tissue and organisms in particular are based exclusively on high-pressure freezing, a technology that has not changed substantially since its invention [4.144]. Even the most modern HPF machines cannot vitrify samples thicker than \(200{-}300\,{\mathrm{{\upmu}m}}\), and incomplete vitrification results have been a problem ever since. However, the same holds true for plunge-freezing, where incomplete vitrification of mammalian cells can be directly observed in FIB lamellae. After all, different biological systems always require adjustments of the individual preparation steps, as the properties of the individual biological samples can vary greatly. New approaches are therefore urgently needed, and efforts must be made to revive the technology, i. e., of high-pressure freezing, and make it suitable for the challenges ahead.

Cryo-CLEM in particular continues to suffer from a significant resolution gap between cryo-ET and FLM. High-resolution fluorescence imaging has opened new avenues for experiments at room temperature, and a similar effect is expected under cryogenic conditions. The routine implementation of super-resolution methods at liquid nitrogen temperatures, possibly with the aid of special immersion lenses [4.286], will make it possible to combine the power of genetically encoded tags, and thus the molecular identity, with the high-resolution information of cryo-EM. Miniaturization and integration of fluorescence microscopes (SR microscopes) into other machines in the workflow for cryo-ET described here, such as the focused ion beam, could also help to further streamline sample processing. The overall preparation speed and success rate are other aspects where improvements will be crucial. Standard cryo-FIB milling on plunge-frozen grids can deliver one suitable TEM lamella per hour, and the production of a single cryo-lift-out lamella from high-pressure frozen bulk material will take considerably longer, since the low material removal rates of Ga ions limit the volumes and depths that can be probed. FIB milling is a task that can be automated, parallelized and eventually performed unattended overnight. Additionally, to avoid the low and slow removal rates of conventional Ga ion FIBs, novel plasma FIBs (PFIBs) using noble gas ions (e. g., Xe), which promise faster removal rates (up to 60 times as high), could be an interesting option [4.287]. The potential of PFIBs for cryo-applications, however, has yet to be explored.

Since the current resolution revolution was largely driven by the development of direct electron detector cameras, its further improvement seems equally important. Higher pixel densities and sensitivity, along with faster readout of frames, further reduce sample damage and preserve high-resolution information. At the same time, progress in hardware instrumentation must be accompanied by improvements in the software that controls the microscopes and performs the image processing. With more stable cryo-ET stages, for example, there are more efficient ways to acquire tomograms. Tilt schemes that distribute the electron in a dose-symmetrical manner around the low tilt angles were recently proposed and have already proven their merits [4.119]. In this way, the damage caused by the electron beam can be further reduced, and the data quality and the resolution of the resulting subtomogram averages can be significantly improved. In subtomogram averaging, however, image alignment is still an important factor limiting resolution. In order to push the resolution limit further, it will thus be necessary to implement new approaches for aligning the tilt series. These include physical methods such as the introduction of cell-permeable nanoparticles as fiducial markers or software-based solutions using intracellular complexes that can be used to denoise and align the individual tilt images. Finally, the search through large data sets for both known and unknown structures requires new implementations of template matching. For known complexes, precalculated orientations could be used to find correct orientations [4.288], and neuronal networks could be trained to recognize a whole range of molecular actors simultaneously. As more and more information about different organisms is gathered, it is becoming increasingly important to archive this data and make it available to various research areas. Thus, it is conceivable that databases will be created in which tomographic data from various institutions will be stored. Such meta-databases could then be searched and annotated by different groups to further complete the subcellular protein network present in the data. With further progress in both software and hardware, the use of in situ cryo-ET will continue to grow and provide a more complete picture of cellular landscapes in an almost lifelike state.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of Molecular Structural BiologyMax Planck Institute of BiochemistryMartinsriedGermany

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