18.2.1 Use of Electron Radiation for Imaging of Biological Machinery

To use any kind of radiation for imaging at a certain resolution, it must: (i) be focusable and (ii) have a wavelength that matches the resolution sought. In other words, for a wave to experience an object as an obstacle it needs to be of a similar size. For example, raindrops cannot inflict any meaningful perturbation on ocean waves. Light microscopy is a powerful imaging methodology, because photons can be easily focused (with a precisely shaped piece of glass, known as a lens) and observed – eyes are detectors of unparalleled performance. However, atoms in molecules are roughly 1 Ångstrom (0.1 nm) apart. Therefore, visible light with the shortest wavelength of ∼400 nm cannot provide sufficient resolution for molecular structure determination. X‐rays have a short wavelength (∼Ångstrom) and excellent penetration of solid matter (fracture clinics, airport security), but are hard to focus. Neutrons, currently used in diffraction experiments like X‐rays, can be emitted with sub‐Ångstrom wavelengths. However, at present it is not known how to make a neutron lens.

Electron radiation has the two crucial properties (ability to be focused and the short wavelength) that led to its use in EMs for high resolution imaging. First, the wavelength of the electron radiation is in the picometre range and is thus suitable for investigating biological structure, theoretically to atomic level resolution. Second, the charge carried by electrons enables their deflection by an electromagnetic field and hence electron beams can be focused with magnetic lenses – as light is focused by glass lenses – to produce images. The imaging ability of cryo‐TEM has a great advantage for structure determination over X‐ray or neutron diffraction experiments. Diffraction patterns (also produced in microscopes at the back focal plane of the objective lens, Figure 18.2, 18.3) contain only amplitude information, leading to the classical phasing problem of X‐ray and neutron diffraction techniques. Crucially, information about both amplitudes and phases of the scattered/diffracted waves are captured in TEM images.

18.2.2 Electron Beam Interaction with a Biological Sample

Unlike X‐rays, electrons have a resting mass that imposes limits on their ability to penetrate samples. The so‐called mean free path of an electron is in the range of ∼200–300 nm depending on microscope voltage. Thus, the ideal cryo‐TEM sample would only be marginally thicker than the longest dimension of the molecule or region of interest, such that the sample is as thin as possible, while not being squashed (Figure 18.1b).

Atoms of the specimen interact with incident electrons in various ways, depending on their electrostatic (Coulomb) potential (proportional to atomic number) and the beam energy [4]. Considering interactions with heavy atoms, it is sufficient to interpret incident electrons (also called primary electrons) as a stream of particles with defined velocities and trajectories, being scattered at high angles – including backscattering – by the large electrostatic fields of those heavy atoms. Such scattering is negligible in biological TEM, since biological matter is mainly built of light elements, such as hydrogen (H), carbon (C), oxygen (O), nitrogen (N) and phosphorus (P). These atoms mostly only weakly scatter primary electrons.

To understand weak scattering and its consequences, the particle approximation of an electron is no longer helpful. It is best to think of each primary electron as a single plane wave, traversing space in a certain direction and with a certain energy (wavelength). This interpretation is overall much more broadly applicable, but also more abstract. Every such electron passes through the specimen individually and interacts with the whole sample (Figure 18.2). Weak scattering means that a portion of this incident wave passes through the sample without effect, i.e. unscattered, but the electrostatic potentials of sample atoms – multiple scattering centres – will also cause perturbations that can be envisaged as ripples in this single plane wave. These ripples interfere, giving rise to new wave fronts (Figure 18.2). Upon such interaction with the sample, the primary electron wave can lose some of its energy, exciting the sample electrons to higher orbitals. This is immediately followed by a decay to a lower energy state, accompanied by X‐ray emission or by an ejection of a so‐called secondary electron in any direction from an outer orbital. This is called inelastic scattering, resulting in a longer wavelength of the transmitted wave (Figure 18.1b). However, when the primary electron wave does not lose energy after impinging on sample atoms, the information about them is transmitted by the scattered component waves, retaining the original wavelength, but with a phase altered by ∼¼ of a wavelength (∼90°) relative to the unscattered component wave. This is called elastic scattering. At voltages used in typical cryo‐TEM experiments, inelastic scattering is around three times more likely than elastic scattering [5].

Elastic scattering contributes useful structural information to the final image, while inelastic scattering lowers the signal‐to‐noise ratio (SNR) in the image. This is because the inelastically scattered wave: (i) is focused more strongly (out of the image plane) due to its lower energy (longer wavelength) compared to both the unscattered and the elastically scattered component waves and causes blurring of fine image features; (ii) causes deposition of energy in the sample, resulting in damage through ionisation, induction of free radicals and emission of X‐rays. Due to this radiation damage, the maximum dose in a typical cryo‐TEM experiment must be limited (∼50 e‐/Ų on the sample). However, the finest structural details are immediately compromised as soon as the sample is exposed to the electron beam. In particular, negatively charged side chains of acidic amino acid residues are exceptionally susceptible and are almost immediately destroyed in imaging experiments. A final consideration for imaging is that in order to accurately capture structural information about the sample, an elastically scattered electron wave should only be scattered once before transmission through the sample. In samples that are thicker than ∼200 nm, multiple scattering events can also affect the SNR.

Constructive interference of the elastically scattered waves will occur when Bragg's law is satisfied (equation in Figure 18.2) as determined by the spacing of the scattering centres (sample atoms). These scattered component waves can be depicted as rays perpendicular to their fronts in order to follow their fate in an optical system (Figure 18.2). This is further explored in the next section, which focuses on image formation.

18.2.3 Image Formation: The Weak Phase Object Challenge

Regardless of the type of cryo‐TEM imaging experiment – single particle data collection or successive tomographic tilt views – the primary image is always a 2D projection of a 3D specimen (Figure 18.1d, single particle example). Density variation in the direction perpendicular to the electron beam is projected and recorded as intensity variation in the resultant image. The image contrast is the difference between the intensities of the brightest and the darkest point in the image, divided by the average intensity of the image. Modulation in these intensities – defined as amplitude contrast – can arise directly from strong scattering of incident electrons by the sample, i.e. scattering at high angles, including backscattering mentioned earlier. These strongly scattered waves can be blocked by diaphragms called apertures accompanying lenses in microscopes (see later). Therefore, a simplistic explanation for the emergence of the amplitude contrast in a microscope is that rays travelling around a dense object pass through and rays colliding with it are removed by the optical system. However, since cells, viruses and biomolecules are composed mainly of H, C, O, N and P, as noted above, they produce very low intensity modulation (amplitude contrast) against the background of similar atoms from the surrounding vitrified solvent. A thin, unstained biological specimen generates amplitude contrast estimated to be ∼7% at 120 kV and ∼4% at 300 kV [6]. Therefore, biological samples are generally considered as weak phase objects; the projection of their electron potential is encoded in the phase variation of the emergent composite wave [7].

The direction (angle) and strength (amplitude) of each scattered wave depends on the distance (d in Figure 18.2) between the scattering centres (sample atoms) and their number, respectively. Thus, fine features in the sample (e.g. distance between atoms in the adjacent amino acid side chains in a protein) produce scattering at relatively high angles (scattering angle α in Figure 18.2), whereas larger features (atoms spaced between particular secondary structures or domains of a protein) produce scattering at lower angles. All of the oscillations within the single electron wave, including all of the scattered components and the unscattered primary component, can be considered as separate rays of electron radiation, as mentioned above (Figure 18.2). An electron lens collects all those rays and focuses them, giving rise to positive (constructive) and negative (destructive) interference of the scattered waves with the unscattered primary wave. The resultant waves manifest in a so‐called diffraction pattern at the back focal plane of the lens (Figure 18.2), where each instance of productive interference contributes a discrete signal – a single spot in the diffraction pattern. Such signal decomposition is known as Fourier transformation and each constituent wave is a separate Fourier component that represents specific distance between scattering centres (d in Figure 18.2). In Fourier space (also called reciprocal space) this distance is called spatial frequency. The fine features (small d), generating high scattering angles, correspond to high spatial frequencies (edges of the diffraction pattern), while the coarser features, generating low scattering angles, correspond to low spatial frequencies (middle of the diffraction pattern). Further on the optical path of the lens is the image plane, where the rays are recombined to form a projection image approximation of the sample (Fourier synthesis) (Figure 18.2).

Crucially, phase contrast produced in biological TEM must be expressed as (or converted to) amplitude contrast to be detected by an imaging device that can only measure signal intensity modulation. Therefore, the phase shift produced by the sample needs to be such that it produces detectable amplitude contrast in the image: maximum contrast is derived from either ∼180° (negative interference) or 360° (identical to 0°, positive interference) phase shifts. Overall visibility of any object in the image is critically dependent on the phase difference between the scattered waves at low spatial frequencies corresponding to object shape in the image and the unscattered wave. Since low spatial frequencies are represented by rays nearly parallel to the optical axis of the lens (Figure 18.2), their optical path length is similar to that of the unscattered wave component. This means that the two waves remain only ∼90° shifted in phase, are unproductive in terms of image formation and thus these critical low frequencies remain invisible at focus under perfect lens conditions (assumed in Figure 18.2). In practice, adequate amplitude contrast such that the sample can be seen is obtained by imposing additional shifts in the phase of the scattered component waves. A later section will explain how this is achieved in a TEM.

18.2.4 Basic Anatomy of a TEM

At the top of a TEM column is an electron source or gun (Figure 18.3a). Electrons are extracted by high voltage (100–300 kV) from so‐called filaments. The extraction voltage defines the wavelength of the electron radiation. There are three types of filaments: (i) bent tungsten wire heated up to 3000 °C in low end microscopes, which thermally emit electrons like a light bulb; (ii) lanthanum hexaboride (LaB6) crystal, with emission from a smaller area (∼5 μm) and with lower temperature; and (iii) a field emission gun (FEG) in high performance microscopes, where electrons escape from the very sharp tip (∼10 nm) of a tungsten crystal coated with ZrO₂ to lower the work function of tungsten for electrons. This allows them to be pulled off the tip by a strong and uniform electric field with uniform energies, even at room temperature. Each of these sources emit electron beams with different homogeneity or coherence. There are two types of coherence: (i) spatial coherence, where electrons emerge in the same direction, and (ii) temporal coherence, where electrons emerge with the same speed or energy, allowing uniform focusing of all the rays. Tungsten wire filaments produce relatively incoherent electrons, LaB6 filaments produce beams with intermediate coherence and field emission from a small area produces the most coherent beam. In this last case, the electrons are then accelerated in the accelerator stack, e.g. for 300 kV settings through voltages of −300 to 0 kV (electrons travel towards positive potential – here ground) to ∼3/4 of the speed of light, before entering the optical system of the microscope column (Figure 18.3a).

As previously mentioned, the column of a TEM instrument needs to be under ultrahigh vacuum to avoid performance‐dampening contamination and scattering from gas molecules that generate image noise. EM lenses are magnetic fields induced by the passing of current through copper coils (Figure 18.3b, white lines). First, the beam passes through the condenser lens system, which converts the divergent beam into a parallel one and directs it on to the specimen (Figure 18.3a). The specimen is located inside the objective lens system, producing the first magnified image of the specimen. The projector lens system further magnifies the image that can be displayed on a fluorescent viewing screen (not included in most modern TEM designs) or recorded by an imaging device (Figure 18.3a). All lens systems have four basic components (starting from top): (i) deflectors, moving the incoming beam to the optical axis of the microscope; (ii) the lenses themselves, focusing the beam at the specified distance (magnification is image distance from the centre of the lenses, divided by the distance from the same point to the object); (iii) stigmators, correcting for imperfection in the shape of the magnetic field of the lenses (see below); and (iv) apertures, which limit the most incoherent rays at the periphery of the beam, thus increasing contrast (Figure 18.3a). Paradoxically, it is thanks to a common imperfection of lenses (Figure 18.3b) that we can see anything in classical biological cryo‐TEM. The next section will discuss lens aberrations alongside other systematic defects of a TEM and their influence on image formation.

18.2.5 Systematic TEM Defects and Their Influence on Image Formation

Electromagnetic lenses come with typical performance limitations familiar from traditional optical systems, of which the most prominent are: (i) spherical aberration, where the periphery of the lens focuses the beam more strongly than its centre (Figure 18.3b); (ii) chromatic aberration, where longer wavelength (lower energy) waves are focused more strongly than shorter wavelengths; and (iii) astigmatism, where the lens focuses the beam more strongly in one direction, producing ellipsoidal distortion of every feature in the image. All these defects have obviously adverse consequences for the transmitted image, but some can be partly offset with available or emerging technologies, such as spherical and chromatic aberration correctors (Cs and Cc correctors, respectively). Because astigmatism results from an asymmetric magnetic field in the lens, it can be largely compensated for by additional stigmator coils. Chromatic aberration is detrimental because the temporal incoherence (significant energy spread) of the beam – due to, for example, voltage variation at the source, as well as the inelastic (energy‐loss) events – causes degradation of the image by blurring its fine details. This can be partly remedied with a pre‐column monochromator and/or an in‐column (omega) or post‐column (GIF) energy filter set to a desired electron energy range (Figure 18.3a) to sharpen the image.

Crucially, spherical aberration of the objective lens, aside from its obvious resolution‐degrading effect, plays a key role in imaging. Such distortion facilitates increases in the phase shift between the scattered component waves and the unscattered component wave, which converts the undetectable phase contrast into detectable amplitude contrast in the image. The Cs is a fixed parameter specific to a microscope, but the overall effect is oscillatory due to the wave nature of the signal (phase contrast), and is described by the phase contrast transfer function (CTF) of the microscope:

where Δz = defocus, λ = wavelength and k = spatial frequency. It was found that image contrast increases with increasing defocus, revealing that defocusing combined with spherical aberration increases the observed phase shift [8]. In practice, micrographs are taken at up to several micrometres under focus (negative defocus).

Imaging out of focus is a hallmark of the classical biological cryo‐TEM and produces specific effects in the projection images and their Fourier transforms. The primary consequence of defocusing is the modulation of the CTF oscillation, giving rise to the so‐called Thon rings in the Fourier transform of micrographs (Figure 18.4a). The rings represent the decomposition of the signal from the amorphous material (specimen support film and/or specimen) in the image into discrete spatial frequencies (Fourier components), equivalent to the diffraction pattern (image formed at the back focal plane of the objective lens). As previously discussed, in such a spectrum, the low spatial frequencies (corresponding to coarse features of the image) are located near the origin (middle) of the spectrum and the higher spatial frequencies (representing the finer features) progress towards its outer edge. The phases of the Thon rings alternately switch between positive and negative contrast with the overall rate dependent on the amount of defocus: the further away from focus, the more frequent the oscillation, with oscillations increasing towards higher spatial frequencies (the effect of Cs) (Figure 18.4).

At every CTF node, where the function crosses the 0‐amplitude axis, there is no contrast transfer, so the relevant spatial frequency information is absent. The loss of information, strongly skewed towards high frequencies, increases with the number of nodes, resulting in a characteristic image coarsening with increasing defocus. The specimen outline becomes more visible but at the expense of structural detail (loss of high resolution information). This is illustrated in Figure 18.4b, where the first contrast lobe of the curve representing lower defocus (light blue) has a maximum shifted towards higher frequencies and with fewer zero crossings in the higher spatial frequency region compared to the curve representing higher defocus (dark blue). Furthermore, the oscillations on either side of the horizontal axis indicate that certain Fourier components are inverted.

18.2.6 CTF Detection and Correction

Since any amount of defocus inevitably causes loss of information, it is necessary to compensate for the loss by collecting data at a range of defoci to fill in the zeros of the CTF, especially for high resolution information. The CTF also inverts Fourier components, which corrupts the image. Therefore, to obtain a more faithful projection image of the sample, and thus correctly interpret the data, the CTF lobes with negative amplitudes need to be inverted. This can be achieved, for example, by dividing the Fourier transform of the micrograph by the CTF of the microscope, after which the image is recovered by inverse Fourier transform. An alternative strategy, called phase flipping (as illustrated in Figure 18.4c), involves simply reversing the sign of the CTF lobes with negative amplitudes. Variations on these approaches are described in the literature [9]. These are the most basic version of the procedure known as CTF correction, which first requires detection of the exact defocus value of the micrograph. This can be done in Fourier space by fitting a simulated CTF curve to Thon rings derived from the image. CTF correction parameters are usually established for each micrograph in the dataset before it is incorporated into any 3D reconstruction pipeline, where the correction is applied.

Thus, with the contrast gain through spherical aberration and defocusing comes the necessity of CTF correction. This becomes much more challenging in cryo‐ET tilt series. An alternative way to introduce phase shift to the scattered wave than defocus imaging is to use a phase plate inserted at the diffraction (back focal) plane of the objective lens. The concept of a phase plate comes from light microscopy; its early adaptations for EM – such as a Zernike phase plate (ZPP) – despite promising results, had practical limitations, including lifetime and alignment [10]. The more recently introduced Volta phase plate (VPP) is a continuous piece of carbon film, constantly heated to ∼250 °C, which, by some mechanism not fully understood, produces a nearly ∼90° phase shift in the scattered electron waves. In principle, the VPP works in focus, but in practice it is not easy to find the exact point of focus. Thus, data collected with a VPP is usually minimally defocused and CTF corrected [ 10,11].

18.2.7 Resolution Limiting Factors

Besides stable aberrations discussed earlier, there are a number of irregular disturbances that limit the information transfer of a TEM, including: mechanical vibrations in the column and fluctuations in lens currents (as resistivity is sensitive to temperature instability of the lens cooling system). Distortion and dampening of the signal due to both stable and unstable defects is therefore intrinsic to TEM imaging; it manifests in decay of the CTF amplitude towards high frequencies (Figure 18.4a), because the finer the detail, the more it suffers from those imperfections (dampening factors). The stable dampening factors combine to generate a net envelope function of a given microscope that describes the total systematic signal falloff. The CTF is always multiplied by this envelope function, so these two functions always appear together and can be further modulated by irregular (incidental) disturbances, superposing their own envelope function on the CTF. The gradual attenuation of high spatial frequencies is best illustrated by the fading of Thon rings (Figure 18.4a). The extent of Thon ring visualisation gives an idea about the resolution of the data collected in each image and may be used as a guide for selection of micrographs to be included in the 3D reconstruction. More sophisticated CTF correction calculations involve compensation for the amplitude decay towards high spatial frequencies.

In real space, the same concept is described by the point spread function (PSF) of the microscope, which is an inverse Fourier transform of the CTF. PSF can therefore be thought of as being like the brush with which the microscope paints the image, meaning that every point of the object is convoluted in its projection image with the unique PSF of a given TEM system. This distortion is partially removed by CTF correction, but the TEM projection image always suffers non‐recoverable loss of information at CTF zeroes.

A major challenge in data collection for biological TEM comes from the damage to the sample incurred during imaging and from the beam‐induced sample movement. To consider this more completely, we now describe the properties of cryo‐TEM samples and the procedures for preparing them.

18.3.1 Sample Preparation for Cryo‐TEM

Sample quality is widely recognised as a major bottleneck in cryo‐TEM structure determination experiments [12]. While each sample requires bespoke optimization, general considerations are summarised here. Central to any cryo‐TEM experiment is the preservation and maintenance of the sample in a layer of so‐called vitreous ice [13]. Vitreous ice is a non‐crystalline, glass‐like form of solid water, in which the biological sample remains hydrated. Vitreous ice is metastable, readily transforming into other crystalline forms of ice if warmed above −150 °C. Therefore, once vitrification has been achieved, the sample must be maintained at liquid nitrogen temperatures during transfer into the microscope and for data collection.

A TEM sample must be prepared such that it is sufficiently thin for imaging. Typically, the sample is applied to a support layer, often made of a thin (5–10 nm) electron‐transparent film of carbon; this support layer is itself supported by a copper mesh disc, 3 mm in diameter and together with a mesh and support layer constitute ‘the EM grid’ (Figure 18.1a). Variations in the material of both the mesh and the support have been implemented, but it is important that both: (i) are somewhat physically tough (given their dimensions) in order to withstand sample preparation steps, (ii) are non‐ferromagnetic to avoid distortion of the electron beam, (iii) can rapidly conduct heat away from the sample and (iv) are electrically conductive to minimise charge accumulation arising from incident electrons. Prior to sample application, the normally hydrophobic support surface is typically treated (for example by exposure to low energy plasma) to make it hydrophilic and thereby enable sample spreading and adherence.

The goal in typical molecular cryo‐TEM experiments is to determine an atomic/near‐atomic resolution structure or set of structures. Thorough biochemical and biophysical analysis of the sample to establish its compositional homogeneity is vital prior to initiation of structural experiments. This should include >98% purity by sodium dodecyl sulphate‐polyacrylamide gel electrophoresis (SDS‐PAGE), unambiguous chromatograms from size exclusion chromatography, ideally size exclusion chromatography‐multiangle light scattering (SEC‐MALS) analysis, yielding approximate molecular dimensions and validation of biologically relevant activity. Cryo‐TEM is an inefficient and very expensive tool for screening biochemical sample quality. The best image contrast will be achieved if the sample is embedded in a film of pure frozen water. While the molecular stability of molecular complexes in water is unlikely and their physiological relevance uncertain, EM‐optimised buffers should also be established.

With a biochemically high quality sample in hand, it is very important to first check its stability, behaviour and appearance by negative stain TEM [14]. In a typical negative stain experiment, a relatively low concentration (∼0.01–0.05 mg/ml) of sample is applied to the carbon surface of a TEM grid. Excess liquid is blotted away and a thin layer of heavy metal stain – such as 1% (w/v) uranyl acetate (pH 4.2) or 2% methylamine tungstate (pH 6.8) – is applied on top of the sample and allowed to dry (∼1 minute on the lab bench). The stain dries around the sample of interest, forming a cast of heavy metal that strongly scatters electrons in the TEM, thereby offering a high (amplitude) contrast view of the stained sample. Commonly used stains have high density and stability, small grain size and are chemically inert, giving confidence that the resulting images provide reliable information about the sample. However, it will be clear from this outline that the limitations of negative stain experiments include a requirement that the samples are dehydrated, potentially distorted by the stain and that the images provide a view of the cast formed by the stain rather than of the sample itself. Nevertheless, negative stain TEM experiments have the distinct advantage of being quick and straightforward to perform, allowing multiple samples/conditions to be efficiently screened.

Once sample quality and parameters for stability have been established, preparation of cryo‐TEM samples can proceed. As a rule of thumb, higher sample concentrations (∼0.1–2 mg/ml) will be required for cryo‐TEM experiments than for negative stain studies of the same sample. However, there are a very large number of parameters that can affect sample distribution on cryo‐TEM grids – e.g. buffer contents, grid type, grid surface treatment – such that protein concentration will be just one of multiple experimental variables to be optimised during cryo‐TEM grid preparation. As for negative stain experiments, cryo‐TEM sample preparation typically involves application of a small volume of sample to the treated surface of a carbon‐coated copper grid. However, unlike negative stain experiments, most cryo‐TEM samples will be applied to a layer of carbon that has holes in it, typically with a diameter of between 1 and 4 μm. During sample preparation, excess liquid is blotted away from the surface of the grid, leaving a very thin (∼100 nm) layer of sample suspended within the holes in the carbon support. The grid is then plunged immediately into liquid cryogen maintained at ∼−183 °C, at which temperature the sample is vitrified (Figure 18.5). The rate of freezing is critical to the success of this step, requiring freezing speeds of 10⁵–10⁶ deg/s [13], thereby preventing reordering of water molecules into ice crystals. The choice of cryogen is clearly vital, since it must be liquid below −180 °C. Typically this is liquid ethane, liquid propane or a mixture of the two [15]. Although liquid nitrogen is a much more commonly available cryogen, it cannot be used for vitrification because when it contacts warmer objects – such as the EM grid – it boils, forming an insulating layer of nitrogen gas. This so‐called Leidenfrost effect means that the rapid rates of freezing necessary for vitrification cannot be achieved. Liquid nitrogen (at –196 °C) is, however, routinely used for preservation of cryo‐TEM samples, both for storage and during imaging in the microscope.

Water is a poor thermal conductor, so the samples must be sufficiently thin (<1 μm) to achieve the rapid freezing required for vitrification. However, with these thin samples, fast freezing can be achieved using homemade devices that effectively drop the grid (held tightly in a pair of tweezers) a distance of ∼30 cm into the cryogen under gravity. Hydraulically controlled devices are also available commercially. The rate of water evaporation from these thin samples is very high and, if uncontrolled, can result in increases in sample ionic strength, which can in turn affect sample stability and appearance. This can be readily controlled by enclosing the grid preparation steps in a small chamber with high humidity [16].

A successful freezing experiment will result in multiple well‐preserved cryo‐TEM grids, typically stored in small plastic grid boxes under liquid nitrogen. In theory, the sample will be evenly distributed across the entire grid surface in a uniform layer of ice and present with all possible orientations. On a single such cryo‐TEM grid with 80 000 holes (∼800 grid squares and ∼100 holes per square) and a ‘typical’ sample distribution yielding ∼1500 particles perhole, a dataset arising from such an idealised grid would be more than adequate to yield an atomic resolution reconstruction [5]. In practice, this rarely happens. For example, there is often a gradient of ice across the grid, giving areas where the ice is too thick to visualise particles and/or too thin, thereby excluding larger particles [17]. Crystalline ice contamination can adhere to the surface of the vitreous ice layer occluding embedded particles; this contamination often occurs during storage or transfer into the microscope or less often during data collection. A topic of great current interest for the cryo‐TEM field is the effect of the air–water interface in the thin sample film immediately prior to freezing. Although the precise nature of these effects is not well understood, the way in which a given sample interacts with this interface may profoundly affect the dispersion that is ultimately visualised in the TEM and may include denaturation of sensitive samples previously visualised by negative stain. Experimental conditions for optimal sample preparation must be empirically determined for each new sample [12].

18.3.2 Cryo‐TEM Data Collection

Once a cryo‐TEM sample has been prepared, it must be transferred into the microscope and maintained there without devitrification. The grid is held within the sample holder by a metal ring around its perimeter, with the entire holder maintained under liquid nitrogen. According to the holder/microscope combination, the grid may be inserted into the microscope in a so‐called side entry holder. In this configuration, the grid is kept cold inside the microscope via a liquid nitrogen‐containing external dewar, which conducts heat away from it. This dewar requires topping up every few hours and causes instability because, for example, vibrations from the bubbling liquid nitrogen cause vibrations of the sample itself, blurring features of interest in the images. More modern microscopes use individual cartridges for holding grids, which are inserted via a top entry stage and maintained by internal cooling with liquid nitrogen, allowing for much improved sample stability [24]. Automated sample transfer systems that allow loading of multiple grids have brought further improvements in sample stability and data collection efficiency.

An important parameter to consider in advance of cryo‐TEM data collection is the desired/realistically achievable resolution of the structural experiment. In data collection terms, this will depend on the magnification at which data are collected and the physical pixel size of the image detector (see below); together these parameters define the digital pixel size in the images. As stated by the Nyquist theorem, the best attainable resolution in any imaging experiment is twice the pixel size. Whether the properties of a given specimen will allow this theoretical resolution to be achieved cannot be determined a priori. However, it is important that data collection parameters do not impose limits on this unnecessarily.

18.3.2.3 Data Collection Strategies for Cryo‐Electron Tomography (Cryo‐ET)

All the considerations of the sensitivity of the specimen to electron dose and the use of low dose imaging also apply to cryo‐ET samples. However, the goals of cryo‐ET data collection are different to SPA. Tomography is particularly useful for gaining structural insight into irregular objects, such as cellular compartments, isolated organelles or viruses with flexible capsids, and for in situ studies of cellular components, such as cytoskeletal filamentous networks or membrane protein complexes [34, pp. 7–12]. In such samples, averaging of different copies of the object of interest is rarely possible, so 3D information must be acquired using a different approach. Different views of the individual object are obtained by physically tilting the sample holder – and thus the sample of interest – within the TEM, enabling a series of 2D projections to be recorded over a range of angles (the ‘tilt series’; see Figure 18.6). At least 30 projections of the same region are collected through a tilt series.

The extent of sample tilting is physically limited by the way the grid sits within the microscope, yielding maximum tilts of ∼ ±70°. Thus, a considerable portion of spatial information (in Fourier space) is missing from the tilt series (the ‘missing wedge’), ultimately causing distortion in the 3D reconstruction. In addition, as sample tilt increases, so does its thickness, causing a higher number of inelastic scattering events and increasing the noise further in already noisy data. The use of energy filters – either within the TEM column or after it – that exclude inelastically scattered electrons can improve cryo‐ET data SNR (Figure 18.3a). Even in modern microscopes, tilted samples are fundamentally less stable within the microscope. However, because cryo‐ET experiments do not impose any requirements on the type of sample to be studied, they are very widely applicable. As well as complex cell samples, SPA samples can also be studied in cryo‐ET experiments, which may be useful, for example, to investigate the variability of a particle population or its distribution in the ice layer.

18.3.3 Image Processing for Cryo‐TEM Samples

18.3.3.2 Structure Determination Strategies for SPA

Structure determination by cryo‐TEM is based on the central section theorem [1], which states that the Fourier transform of a 2D projection from a 3D specimen corresponds to the central section through the 3D Fourier transform of the 3D object. Therefore, the 3D Fourier transform of the object can be built by combining multiple 2D Fourier transforms from all possible angular projections (Figure 18.7). Ultimately, the 3D structure in real space can be calculated using inverse Fourier transformation. Inevitably, this involves a certain level of interpolation, since the angular space is never completely filled with data. Although not all SPA algorithms work in Fourier space, these structural principles still apply.

SPA structure determination therefore requires that the many thousands (sometimes millions) of individual noisy 2D projections of the sample are oriented with respect to each other and combined to yield the 3D structure. In general, the larger the dataset, the higher the expected resolution in the final reconstruction. Many excellent and detailed reviews have been written, both about theoretical considerations at each processing step [ 9,42,43] and about the particular features associated with individual software packages [44–50]. In addition, as the properties of cryo‐TEM images and movies are better understood, it has become possible to automate more steps in the processing pipeline. Software is also increasingly user‐friendly, with GUIs being common. Here we aim to summarise qualitatively the key steps involved.

A first step in any SPA processing scheme involves picking individual particles from the micrographs and placing them in a digital 2D box of defined size on which further processing steps will be performed. For the early phases of any new project, manual particle picking is recommended to become familiar with the data. However, automated particle picking is the only realistic option for the very large datasets usually collected for high resolution structural determination. Picking algorithms typically require a target template – often a set of low resolution projections – and usually incorporate some false‐positives (‘junk’) into the data, which can be removed later. After initial structures are calculated from a given dataset, they can be used to generate new projections to reinterrogate the micrographs, potentially extracting more useful particles. As would be expected, particle picking becomes increasingly challenging for smaller and/or more heterogeneous samples.

After this, computational alignment of all the 2D particle views is performed, followed by 2D classification – sometimes relatively crude – of these views using statistical methods, and calculation of 2D averages of similarly appearing particle projections. Junk particles can be easily recognised and removed at this stage. The averaging provides 2D views from the dataset with much improved SNR. This first processing stage provides vital information about the range of views present; it is often the case that molecular complexes assume a more limited range of orientations in the cryo‐TEM ice layer, adopting so‐called preferred orientations. Further sample optimization or collection of even more data is typically used to deal with this problem. Initial indications about sample heterogeneity – either contamination by other molecules or conformational heterogeneity – may also be evident at this stage. Increasingly, with high quality and large datasets, evidence of secondary structural information is often seen in the 2D classes, providing confidence to proceed. If not, reviewing sample quality or imaging conditions may be required.

The next critical step in the processing pipeline is the determination of the angular relationship between the 2D views to generate the 3D structure. Until recently, most reconstruction algorithms required an initial 3D model of the target structure to provide simulated reference 2D projections against which the 2D data were matched. Such a model needs to be filtered to include only very low‐resolution features (a lowpass filter at ∼40 Å). This filtering step reduces the very real possibility of the noisy cryo‐TEM images aligning to any reference and reproducing its structure, regardless of whether there are genuine similarities between the model and the sample (so‐called Einstein‐from‐noise effect [51]). In the case of samples where such suitable prior structural knowledge exists, this projection matching approach works well and the resulting 3D structures can be validated with the emergence of novel features consistent with the input data. However, the absence of a suitable model for a completely new molecule or complex is a ‘catch‐22’ situation. In these cases, low resolution initial models may be generated using cryo‐ET, but often a featureless 3D blob of the appropriate dimensions also works well. The major challenge for very small macromolecular complexes (<100 kD) is the ability to accurately distinguish different 2D views.

Recent innovations in image processing implement the use of maximum likelihood algorithms [ 44,49,52,53] and have transformed computational approaches to cryo‐EM structure determination. Furthermore, stochastic gradient descent allows de novo 3D structure determination, removing the need for an initial reference model and the risk of model bias [54]. Together with the implementation of user‐friendly interfaces and GPUs for calculations, 3D reconstructions can now be determined in a matter of hours, rather than over the course of weeks, as was the case previously. 3D classification is now also readily performed, such that SPA experiments typically result in the determination of a set of 3D structures that can capture functionally relevant conformational heterogeneity. Improved efficiency of processing also allows many more processing parameters to be tested to identify the optimal set for a given sample. Expert image processing labs will typically develop processing pipelines that use the best aspects of multiple software packages tuned according to the particular sample.

18.4.1 Case Study 1: Single Particle Analysis of Microtubule Stabilisation by a Neuronal Microtubule‐Associated Protein Doublecortin

Microtubules (MTs) are dynamic polymers of α/β‐tubulin dimers (110 kDa) that play a central role in cell division, intracellular transport and cell migration. Individual tubulin dimers can be studied with different structural biology techniques, but MTs are perfectly suited to cryo‐TEM structure determination, due to their size (∼300 Å diameter and ∼μm length).

Tubulin assembles longitudinally in a head‐to‐tail manner, forming protofilaments (PFs). The cylindrical structure of an MT emerges through lateral association of PFs, preferentially forming homotypic lateral contacts, i.e. α‐ and β‐tubulin lie next to each other. In vitro, MTs polymerise with a range of PF numbers, but in cells most MTs have a 13‐PF architecture. This architecture necessitates that at one site called the seam, α‐ and β‐tubulin form heterotypic lateral contacts, breaking the otherwise helical symmetry of an MT cylinder. Thus 13‐PF MTs are pseudo‐helical.

Many proteins in cells bind to MTs, regulating their behaviour and extending their repertoire of functions. One such protein is doublecortin (DCX), which nucleates and stabilises MTs [56]. DCX comprises two ubiquitin‐like domains, the N‐terminal doublecortin and the C‐terminal doublecortin domains (NDC and CDC, respectively) connected by a 42‐residue linker. It is specifically expressed in immature neurons, where it is indispensable for neuronal migration [57,58]. DCX mutations cause defective brain development (lissencephaly or smooth brain) associated with severe intellectual disability and epilepsy.

One of us (CM) has been researching a doublecortin‐microtubule (DCX‐MT) interaction using cryo‐TEM since 2004 [56], initially using data collection on film with a 120 kV FEG microscope and Fourier–Bessel reconstruction methods on the subpopulation of in vitro polymerised MTs with strict helical symmetry (PHOELIX [59]). More recently, SPA approaches to MT reconstruction have been introduced [60,61] that can be applied to pseudo‐helical 13‐PF MTs. In this approach, the long MT tube is treated as a series of connected single particles. The alignment parameters of the adjacent MT segments are linked by the overall MT architecture, but can be refined separately, allowing distortions in the MT lattice to be corrected. The presence of the seam can also be taken into account. Implementation of SPA approaches led to calculation of structures of 13‐PF MTs bound by DCX in the Moores lab, the first sets using 200 kV FEG microscope and film [62,63]. Most recently, we have used 300 kV microscope and a DED for data collection (Manka and Moores [64]), again using the SPA method for structure determination. Comparison of the DCX‐MT structures over time provides an insightful overview of the progress in cryo‐TEM technology (Figure 18.8) and how the increasing resolution of a biological structure aids understanding of the biological system in question.

The DCX‐MT structure from 2004 revealed that DCX binds to MTs between PFs, providing the first structural insight into the mechanism of MT nucleation and stabilisation by DCX. From this structure, it became clear that DCX stabilises lateral association of PFs. The structure from 2010 reached subnanometre resolution, providing separation of protein secondary structures. This enabled differentiation between similar α‐ and β‐tubulin subunits based on a difference in the length of one of their loops (Figure 18.1, coloured red). Another facet of MT stabilisation by DCX was then revealed: that it binds the MT lattice in the vertex of four tubulin dimers, thus stabilising not only lateral but also longitudinal lattice contacts. The most recent near‐atomic resolution DCX‐MT reconstruction allowed direct atomic model refinement in the density. With the resolution reaching ∼3.4 Å in the MT lattice core (Figure 18.8), it is now possible to study molecular interfaces in the complex with high precision. Of note, the nucleotides bound to tubulin are also readily visualised in these reconstructions and shed light on GTPase‐linked mechanisms of MT dynamic instability [64]. Below we summarise sample preparation, data collection conditions and image processing for the highest‐resolution DCX‐MT structure.

18.4.1.2 Image Processing and 3D Reconstruction

Movie frames were aligned with MotionCor2 [65] before MT segments were cut along MTs with 652 × 652 pixel boxes (Figure 18.9a) using an EMAN software package [66]. The boxes spanned ∼11 tubulin dimers and overlapped by ∼8 dimers.

These segments were subsequently treated as single‐particle input to Chuff [ 60, 62], a custom‐designed multiscript processing pipeline using the software Spider [67] and Frealign [68]. The initial seam finding alignment was done in Spider by projection matching to a model 13‐PF DCX‐MT reference filtered to 30 Å. The CTF parameters were estimated with CTFFIND3 [69] and the CTF correction was performed during local refinement within Frealign, producing isotropic 3D reconstructions. Pseudo‐helical symmetry was applied and independently processed half‐maps were combined in Relion 1.4 [52] and subjected to its standard post‐processing routine, involving: (i) estimation of map resolution based on FSC between the two half‐maps, (ii) computation of the average sharpening B‐factor using the EMBfactor program [70], and (iii) map sharpening using the computed B‐factor value. The resolution of the final map was estimated to be 3.8 Å using 0.143 FSC cut‐off criterion. Tubulin atomic models were refined in the cryo‐EM density. Molecular visualisations were prepared using UCSF Chimaera [71].

18.4.2 Case Study 2: Insight into the Human Immunodeficiency Virus Type 1 (HIV‐1) Assembly Using Subtomogram Averaging

Despite ∼30 years of HIV research and anti‐retroviral drug development, the acquired immune deficiency syndrome (AIDS) pandemic is still ongoing, with ∼37 million people worldwide infected with the still incurable HIV [72]. The virus primarily infects CD4+ T cells in the lymphoid tissues, but also harms bone marrow and thymus, preventing T cell regeneration. Severe depletion of the CD4+ T cells leads to excess pathogen load and chronic inflammation.

The seven stages of the HIV lifecycle can be divided to an early phase – (i) binding to the surface of the host cell, (ii) fusion, (iii) reverse transcription of viral RNA, (iv) integration of viral DNA into host cell genome – and late phase – (v) virus gene expression, (vi) assembly of the main capsid protein Gag (55 kDa) and other proteins at the plasma membrane, and (vii) release of the immature virus. Maturation into the infectious virion is initiated by Gag cleavage at five sites (Figure 18.10, cartoon) by the virus' own protease, triggering dramatic rearrangement of the capsid core structure. This can be prevented by maturation inhibitor (MI) drugs, such as amprenavir (APV) or bevirimat (BVM). Despite therapy, the virus DNA persists indefinitely integrated with the DNA of the long‐lived memory CD4+ T cells.

The Gag polyprotein has been a major focus of interest as a mediator of virus maturation. It assembles into a spherically shaped poly‐hexameric array at the plasma membrane of the infected cell and bends the membrane, inducing budding. Gag consists of 5 domains: N‐terminal matrix domain (MA), followed by two capsid (CA) domains (NTD and CTD), nucleocapsid (NC) domain and the C‐terminal p6 domain. The CA and NC domains are connected by spacer‐peptide 1 (SP1) and spacer‐peptide 2 (SP2) connects the NC domain with the p6 domain (Figure 18.10, cartoon).

The Gag lattice is incomplete (randomly truncated sphere) and exhibits irregular defects; thus, the immature virus particles are heterogeneous in size and morphology, making cryo‐ET and subtomogram averaging the ideal method for structural investigation. Using this approach, Briggs and colleagues reported breakthrough 3D reconstructions of the CA‐SP1 region within the immature HIV‐1 capsid, first in 2015 at subnanometre resolution [73] and then in 2016 – using optimised cryo‐ET protocol (see below) – at near‐atomic resolution [74].

The first study revealed the positions of the CA domains by fitting all of their alpha‐helices to the 8.8 Å resolution density, thus providing insight into the tertiary and quaternary structures of the assembly (Figure 18.10, middle panels). Crucially, the arrangement of capsid N‐terminal domain (CA‐NTD) was completely different than that predicted from the in vitro assembled homologues [75]. This highlights the importance and the power of the in situ subtomogram averaging. However, the highest resolution (3.9 Å) in the 2016 study was achieved using ΔMACANCSP2 virus‐like particles (VLPs, without surrounding cell membrane), assembled in vitro in the arrangement identical to that in the isolated viruses.

The MA and NC domains did not appear in the averages in either study, as expected from their flexible linkage downstream of the SP1, causing their spatially disordered arrangement relative to the CA‐SP1 core. In the 2015 study, the SP1 region seemed to form a six‐rod‐like bundle around a hollow centre, but no high‐resolution nuclear magnetic resonance (NMR) or X‐ray structures of that region were known, so it remained unmodelled (Figure 18.1, asterisk). The 2016 study [74] presented the CA‐SP1 capsid structure at 3.9 Å resolution, which enabled ab initio modelling of that vital region, including a critical CA‐SP1 cleavage site (Figure 18.10, right‐hand panels).

Below we focus on the improvements in the cryo‐ET and image processing protocol employed in the 2016 study [74] that have led to the resolution boost.

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Website Resources

1. https://www.ibiology.org/techniques/transmission‐electron‐microscopy
2. https://www.ibiology.org/biophysics/single‐particle‐cryo‐em/#part‐1
3. http://cryo‐em‐course.caltech.edu/videos
4. https://www.jove.com/video/52311/do‐s‐don‐ts‐cryo‐electron‐microscopy‐primer‐on‐sample‐preparation
5. https://www.jove.com/video/57199/variations‐on‐negative‐stain‐electron‐microscopy‐methods‐tools‐for