Electron Tomography: A Three-Dimensional Analytic Tool for Hard and Soft Materials Research

Abstract

Three-dimensional (3D) structural analysis is essential to understand the relationship between the structure and function of an object. Many analytical techniques, such as X-ray diffraction, neutron spectroscopy, and electron microscopy imaging, are used to provide structural information. Transmission electron microscopy (TEM), one of the most popular analytic tools, has been widely used for structural analysis in both physical and biological sciences for many decades, in which 3D objects are projected into two-dimensional (2D) images. In many cases, 2D-projection images are insufficient to understand the relationship between the 3D structure and the function of nanoscale objects. Electron tomography (ET) is a technique that retrieves 3D structural information from a tilt series of 2D projections, and is gradually becoming a mature technology with sub-nanometer resolution. Distinct methods to overcome sample-based limitations have been separately developed in both physical and biological science, although they share some basic concepts of ET. This review discusses the common basis for 3D characterization, and specifies difficulties and solutions regarding both hard and soft materials research. It is hoped that novel solutions based on current state-of-the-art techniques for advanced applications in hybrid matter systems can be motivated.

Keywords: STEM; electron tomography; three-dimensional structural analysis; transmission electron microscopy (TEM).

Figure 1

A schematic diagram of the historical resolution of visible light microscopes and transmission electron microscopes. a) The left panel shows a time line for the improvement of the resolution of microscopes versus the year of development. Reproduced with permission.^[6] Copyright 2009, Oxford University Press. b–d) Three different types of TEM electron sources: a W filament, a LaB₆ filament, and an FEG. b) Reproduced with permission.^[7] Copyright 1991, Springer; c,d) Reproduced with permission.^[8] Copyright 2009, Springer.

Figure 2

A diagram of the mathematical concept of the projection theorem in 2D (directly extendible to 3D). A projection of a 2D object in real space is reduced to a 1D measurement of the projected density. The Fourier transform of the 1D projection is equivalent to a central section at the original projection direction through the object’s full Fourier transform.

Figure 3

The theoretical sampling (dotted lines) of reciprocal space by a tomographic tilt series from ±70° with equal angular increments. The blue triangles indicate the missing wedge of information between 70° and 90°, which impacts resolution along the original projection direction. Notice the oversampling of information at low spatial frequencies near the zero frequency, which is compensated for in the WBP reconstruction method.

Figure 4

a) The mismatch between information sampled by a 17-image tilt series with equal angular increments (red dots) and a square Cartesian grid. The interpolation method used to combine this data can strongly influence the final reconstruction. Radon back-projection is used to avoid interpolation in space interpolation. b) A simplified example of Radon back-projection for a set of 3 low-tilt projections producing 5 possible object locations (black dots). c) The addition of a high-tilt projection uniquely defines the existence and location of only 3 objects.

Figure 5

A comparison of the CTF for STEM (red) and TEM (blue). The phase portion of the CTF for TEM is plotted at Scherzer defocus (maximum resolution). STEM shows a monotonically decreasing function for increasing spatial frequency. TEM has low information transfer at low frequencies (<0.1 Å⁻¹). However, TEM provides relatively high transfer compared to STEM near the maximum linear resolution at the first zero crossing of the TEM CTF (ca. 0.32 Å⁻¹). The oscillatory nature of the TEM transfer function above the first zero crossing complicates analysis of TEM images at high resolution especially for crystalline materials. Importantly, TEM provides relatively high SNR for a given dose compared to STEM, which are not considered in this comparison.

Figure 6

A comparison between the lateral and depth resolution of focused STEM beams for: a) an uncorrected 200 kV FEI Tecnai STEM and b) an aberration-corrected 300 kV FEI Titan. The intensity scale shows low intensity for blue and high intensity for red. The drastically reduced probe dimensions (both lateral and depth) of aberration-corrected STEM have important implications for electron tomography because the entire object may not be in focus.

Figure 7

An example of the limited 3D-reconstruction resolution achieved using only defocus in aberration-corrected HAADF-STEM. The image is a cross-section through a set of images at different defocus values of ca. 5 nm diameter gold nanoparticles on a carbon substrate using an aberration-corrected STEM at 300 kV with a 30 mrad semiconvergence angle. The depth of focus is estimated to be ca. 6 nm. The lateral extent of the nanoparticles (horizontal axis) is well defined and the thickness (vertical axis) is highly elongated due to signal from the focused and unfocused parts of electron beam.

Figure 8

Unlike normal tilting ET, data acquisition for equally sloped tomography (EST) uses specific tilt-angles that directly map into reciprocal space on a grid of concentric squares without interpolation. The pPFFT⁻¹ accurately calculates the density map in real space on a rectangular grid. For clarity, the diagram shows a small set of 4 tilt angles with 22.5° between tilt images. Notice the colored vertical lines in reciprocal space, which mark equal slope increments between projections. Since projections acquired using EST perfectly map to reciprocal space, iterative calculations that transform the data between real and reciprocal space (used to improve the reconstruction resolution) are exact and produce no artifacts.

Figure 9

Concepts of Fresnel contrast in Lorentz (field-free) microscopy. The diagram on the left shows the paths of electrons passing through grains of a magnetic material with opposing in-plane magnetization. The paths bend according to the direction of the magnetic field yielding bright and dark contrast at domain walls. The image intensities in a series of defocused images at a) under-focus, b) over-focus and c) in-focus can be used to estimate d) the electron wave phase shifts due to the magnetic field of the sample. These relative phase shifts can be related to the magnetic properties of the object. Adapted with permission.^[130] Copyright 2014, Elsevier.

Figure 10

A schematic diagram of optimized negative-staining (OpNS) procedures. a) Incubation station designed to hold a glow-discharged TEM grid pre-coated with a thin carbon film, which incubates a 3 μL sample solution above an ice bath. b) Staining workstation designed to hold water droplets and stain droplets above an ice bed while minimizing stain exposure to light. c) Overview of the staining procedure. The TEM grid with sample was prepared via 3× water washing, 3× UF stain exposure and followed by backside blotting with a filter. The grid was then dried immediately by nitrogen gas. Reproduced with permission.^[181] Copyright 2014, The Authors, published by Journal of Vizualized Experiments (JoVE).

Figure 11

TEM images of proteins with known structure using OpNS. a) Survey view of a small and asymmetric protein, 53 kDa CETP (dashed circles) by OpNS. b) 30 representative images of CETP particles. c) Two representative images of CETP particles with particle orientation identified by their tapered tip end (N-terminal β-barrel domain) and globular tip end (C-terminal β-barrel domain), d) which is consistent with the CETP structure, obtained from X-ray crystallography (PDB: 2OBD), in size and shape. e) The high-contrast images were used to reconstruct a 3D volume at 1.4 nm resolution. f) Survey view of another protein with known structure, GroEL, and g) 9 representative particles images prepared by OpNS. h) Survey view of a third protein with known structure, proteasome, and i) 9 representative particle images prepared by OpNS. Scale bars: a) 50 nm; e) 3 nm; f) and h) 50 nm. a–e) Reproduced with permission.^[162] Copyright 2012, rights managed by Nature Publishing Group; f–i) Reproduced with permission.^[181] Copyright 2014, The Authors, published by Journal of Vizualized Experiments (JoVE).

Figure 12

A schematic diagram of cryo-EM sample-preparation procedures. a) A 3–4 μL sample solution is deposited onto the holey carbon coated TEM grid, which was previously glow-discharged. b) The grid is then incubated for approximately one minute. c–e) Excess solution is removed by blotting with filter paper (c), and then quickly plunged into liquid ethane [(d,e) Reproduced with permission.^[192] Copyright 1999, Hanspeter Niederstrasser/Snaggled Works]. f) The frozen grid, with vitrified ice covering the carbon film holes, is then transferred to liquid nitrogen for storage. g) The grid is imaged under liquid nitrogen temperature of −170 °C to −180 °C. h) An electron beam passing through the vitrified ice projects the 3D sample into a 2D image, which is recorded by CCD. h) Reproduced with permission.^[193] Copyright 2010, Greg Pintilie.

Figure 13

Images of a small and asymmetric protein CETP (53 kDa) imaged using cryo-positive staining (cryo-PS) showing high-resolution details. a) Five representative images of CETP particles prepared by cryo-positive staining (with reversed contrast and a circular-shaped soft mask). b) By applying particle-shaped soft masks on each particle image, the masked images are compared with (c) the structure of CETP (obtained by X-ray crystallography and shown in ribbon structure) at similar viewing angles. Similar structural features are marked by arrows. Reproduced with permission.^[162] Copyright 2012, rights managed by Nature Publishing Group.

Figure 14

Phase-plate TEM imaging of a cyanophage virus assembling inside marine cyanobacteria. a) Sectional overview of a late-stage infected Syn5 including labeled cellular components and phages: carboxysomes (C), infecting phages (I), ribosomes (R) and thylakoid membranes (T). b–e) Higher-magnification views of sections and their corresponding 3D reconstructions of cellular components of thylakoid membrane (green) (b); carboxysome (blue) (c); ribosome (purple) (d); A Syn5 cyanophage (red) (e) on the cell’s surface during infection. Yellow: cell envelope; magenta: phage progeny. Scale bars: 50 nm (b,c); 60 nm (d,e). Reproduced with permission.^[230] Copyright 2013, Nature Publishing Group.

Figure 15

3D reconstruction of bacteriophage T7 virion infection of Escherichia coli minicells by cryo-electron tomography. a–c) Three selected sections of large-volume 3D reconstructions of T7 infection of E. coli. d–f) Higher-magnification views of the sections of the subvolumes. g,h) A central slice and 3D surface view of a selected sub-volume average from 3352 virions. i,j) A central slice and 3D surface view of another selected sub-volume average from 1886 virions. Reproduced with permission.^[241] Copyright 2013, American Association for the Advancement of Science (AAAS).

Figure 16

IPET 3D reconstructions of two IgG antibody particles by negative-staining ET and two HDL particles by cryo-EM. a) Nine representative images from a tilt series of a single-instance IgG antibody by negative-staining (NS) ET displayed in the left-most column. The IPET method obtains the 3D model of an individual protein via an iterative refinement processes. b) The iso-surface of the final 3D reconstruction of an individual antibody particle. c) Flexible docking of the structure obtained by X-ray crystallography (PDB entry 1IGT) into each domain of IgG shows a good fit. d–f) Another example of an individual IgG antibody particle. g–i) A 17 nm nascent HDL particle embedded in ice, imaged by cryo-EM tomography and reconstructed by the IPET method. The high-density portion corresponds to the protein component, primarily consisting of apolipoprotein A-I (apoA-I), forms a discoidal shape (a ring shape). j–l) Another example of a 17 nm nascent HDL particle by cryo-EM tomography. The 3D reconstruction showed the similar structural feature to the first HDL particle. Our cryoET reconstructions are consistent with other cryoEM observations. a–l) Reproduced with permission.^[38] Copyright 2012, The Authors, Published by PLoS ONE.

Figure 17

The details of the total number of 3D density maps deposited in the EM data bank (EMDB). a) Cumulative number of 3D maps released per year. The rate of deposition of density maps has increased significantly in recent years. b) Distribution of available density maps (2802 in total) as a function of technique used: single particle reconstruction (more than ca. 78%) and ET methods (ca. 20%); including subvolume averaging (ca. 10%), helical structures (ca. 7%), general ET (ca. 3%). Electron crystallography adds ca. 1% to the EMDB. Plots and pie chart were produced from data published by the EMDB.^[269]