High-resolution electron crystallography of protein molecules

An image processing approach to crystal structure determination

In crystallography, finding the spatial arrangement of the average unit cell contents requires solution of the phase problem. As described in Chapter 1, the Fourier transform relationship between an image and its diffraction pattern can be experimentally realized in one direction if only intensity data are recorded. Since the image intensity is linearly proportional to the crystal potential, when the weak phase object approximation is valid, the directly computed transform finds the crystallographic phases (the Fourier transform of relative mass shifts). Structure factor magnitudes are all that one can obtain from recorded diffraction intensities, on the other hand, and the phase interactions of the scattered beams are lost. (However, an intensity transform, assuming all-zero phases, can also be useful, as will be shown.) Using high-resolution electron micrographs as an independent source of crystallographic phase information, therefore, demonstrates a potential advantage of electron crystallography over x-ray crystallography. On the other hand, great care must be taken to ensure that all measured data are adequately near the single scattering approximation to guarantee the success of ab initio structure analyses (see Chapter 5).

Determining the structure of a protein complex using electron microscopy requires the calculation of a 3D density map from 2D images of single particles. Since the individual images are taken at low electron dose to avoid radiation damage, they are noisy and difficult to align with each other. This can result in incorrect maps, making validation essential. Pairs of electron micrographs taken at known angles to each other (tilt-pairs) can be used to measure the accuracy of assigned projection orientations and verify the soundness of calculated maps. Here we establish a statistical framework for evaluating images and density maps using tilt-pairs. The directional distribution of such angular data is modelled using a Fisher distribution on the unit sphere. This provides a simple, quantitative and easily comparable metric, the concentration parameter κ, for evaluating the quality of datasets and density maps that is independent of the data collection and analysis methods. A large κ is indicative of good agreement between the particle images and the 3D density map. For structure validation, we recommend and a p-value <0.01. The statistical framework herein allows one to objectively answer the question: Is a reconstructed density map correct within a particular confidence interval?

Cryo-electron microscopy (Cryo-EM) is widely used in molecular structure determination and drug discovery. Experimental cryo-EM images suffer from the noises introduced by electron beam dose and sample preparation. Although many approaches have been proposed to improve the signal-to-noise ratio (SNR) for cryo-EM image denoising, the noises are still presented after 3D reconstruction and can obstruct the analysis and visualization of the 3D density map. Here we present DeepTracer-Denoising, a method for 3D electron density map denoising. We employ a 3D Neural Network to learn the pattern of noises and the biological structure from density maps. Our method is designed to work on medium to high-resolution maps ranging from 2.5 A to 10.0A. It is configurated with two modes to tackle both background noise and structural noise in a 3D density map. Our method can correctly identify 97.70% background noise while preserving 96.46% density of the native structure. For the maps that contain structural noise, DeepTracer-Denoising achieves an overall accuracy of 98.95%.

Electron crystallography is especially useful for studying the structure and function of membrane proteins — key molecules with important functions in neural and other cells. Electron crystallography is now an established technique for analyzing the structures of membrane proteins in lipid bilayers that closely simulate their natural biological environment. Utilizing cryo-electron microscopes with helium-cooled specimen stages that were developed through a personal motivation to understand the functions of neural systems from a structural point of view, the structures of membrane proteins can be analyzed at a higher than 3 Å resolution. This review covers four objectives. First, I introduce the new research field of structural physiology. Second, I recount some of the struggles involved in developing cryo-electron microscopes. Third, I review the structural and functional analyses of membrane proteins mainly by electron crystallography using cryo-electron microscopes. Finally, I discuss multifunctional channels named “adhennels” based on structures analyzed using electron and X-ray crystallography.

Electron crystallography of zeolites: structure information from HREM images and electron diffraction patterns

Many of the techniques that have been developed in X-ray crystallography are being applied in electron crystallographic studies of proteins. Electron crystallography has the advantage of measuring structure factor phases directly from high resolution images with an accuracy substantially higher than is common in X-ray crystallography. However, electron diffraction amplitudes are often not as precise as those obtained in X-ray work. We discuss here some approaches to maximizing the reliability of the diffraction amplitudes through choice of exposure and data processing schemes. With accurate measurement of diffraction data, Fourier difference methods can be used in electron crystallographic studies of small, localized changes of proteins that exist in two-dimensional crystals. The mathematical basis for the power of these methods in detecting small changes is reviewed. We then discuss several issues related to optimizing the quality of the diffraction data and derive an expression for the best exposure for recording diffraction patterns. An application of Fourier difference maps in localizing drug binding sites on the protein tubulin is discussed.

Comparison of phase contrast transmission electron microscopy with optimized scanning transmission annular dark field imaging for protein imaging

By using a high resolution electron microscopy we studied planar, linear and point defects occurring in some oxides, particularly Nb and its ternary oxides. In those studies, the image formation of the crystal defects is based on the phase contrast and is different from that of the conventional method (using the diffraction contrast). The electron micrographs of crystals taken under some strict imaging conditions showed roughly distributions of electrostatic potentials in the crystals and the positions of individual metal atoms were resolved. Justification of this intuitive interpretation of the image contrast is provided under some conditions by theoretical calculation of the image using a weak phase object approximation.

Scanning transmission electron microscopy (STEM) has been widely utilized with annular detectors such as annular dark field (ADF) and annular bright field (ABF).Recently, segmented and pixelated detectors have allowed for the detection of detailed electron scattering intensity in the diffraction plane.Utilizing this richer information, low-dose STEM imaging capabilities have been discussed [1,2].Optimum-bright field (OBF) STEM, a non-iterative imaging technique developed recently, uses a segmented or pixelated detector for low-dose observation [3].OBF images are reconstructed from multiple images recorded simultaneously with a segmented/pixelated detector (Fig. 1).The reconstruction process ensures that the reconstructed image achieves the maximum signal-to-noise ratio (SNR) under the weak phase object approximation (WPOA).As the reconstruction process is noniterative, OBF images can be displayed synchronously with the probe scan.OBF STEM is starting to be used as a dose-efficient imaging technique for beam-sensitive materials.Recently, we demonstrated low-dose atomic resolution observations of FAU-type zeolite using OBF STEM, successfully visualizing all atomic sites [4].Figure 2 compares the OBF image with integrated differential phase contrast (iDPC), annular bright field (ABF), and bright field (BF) imaging techniques.The OBF image displays the highest SNR, clearly visualizing both oxygen and silicon sites.Additionally, since the noise in the OBF image can be considered as white noise, its interpretation is straightforward.In contrast, noise in the iDPC image is intensified in the low-frequency region, leading to reduced image contrast.Although OBF STEM is a promising technique for low-dose observations, adjusting observation conditions such as aberrations and crystal orientations for beam-sensitive specimens remains challenging.However, OBF reconstruction can account for residual aberrations and crystal misorientation.We developed a method to estimate actual observation conditions, including residual aberrations, crystal misorientation, and specimen thickness, using data recorded by a pixelated detector.Under the conditions of a thick weak phase object approximation (tWPOA) [5,6], we formulated a mathematical expression that defines the relationship between the 4D dataset and observation condition parameters.We found that it is possible to estimate these parameters separately by fitting the dataset to the corresponding mathematical expressions.We tested this method on a low-dose observation of FAU-type zeolite, with the dataset intentionally recorded under suboptimal observation conditions.The OBF reconstructed image assuming ideal observation conditions appeared opaque due to residual aberrations and crystal misorientation.In contrast, the OBF image that took into account the estimated observation condition parameters accurately visualized all atomic sites of FAU-type zeolite.This method significantly enhances the efficiency of low-dose observations.Moreover, if real-time estimation becomes feasible, the dataset could be recorded under nearly ideal conditions by adjusting the electron microscope based on the estimated parameters [7].

The aim of structural biology has been always the study of biological macromolecules structures and their mechanistic behaviour at molecular level. To achieve its goal, multiple biophysical methods and approaches have become part of the structural biology toolbox. Considered as one of the pillars of structural biology, X-ray crystallography has been the most successful method for solving three-dimensional protein structures at atomic level to date. It is however limited by the success in obtaining well-ordered protein crystals that diffract at high resolution. This is especially true for challenging targets such as membrane proteins (MPs). Understanding structure-function relationships of MPs at the biochemical level is vital for medicine and drug discovery as they play critical roles in many cellular processes. Though difficult, structure determination of MPs by X-ray crystallography has significantly improved in the last two decades, mainly due to many relevant technological and methodological developments. Today, numerous MP crystal structures have been solved, revealing many of their mechanisms of action. Yet the field of structural biology has also been through significant technological breakthroughs in recent years, particularly in the fields of single particle electron microscopy (cryo-EM) and X-ray free electron lasers (XFELs). Here we summarise the most important advancements in the field of MP crystallography and the significance of these developments in the present era of modern structural biology.

X-ray crystallography and single-particle analysis cryogenic electron microscopy are essential techniques for uncovering the three-dimensional structures of biological macromolecules. Both techniques rely on the Fourier transform to calculate experimental maps. However, one of the crucial parameters, resolution, is rather broadly defined. Here, the methods to determine the resolution in X-ray crystallography and single-particle analysis are summarized. In X-ray crystallography, it is becoming increasingly more common to include reflections discarded previously by traditionally used standards, allowing for the inclusion of incomplete and anisotropic reflections into the refinement process. In general, the resolution is the smallest lattice spacing given by Bragg’s law for a particular set of X-ray diffraction intensities; however, typically the resolution is truncated by the user during the data processing based on certain parameters and later it is used during refinement. However, at which resolution to perform such a truncation is not always clear and this makes it very confusing for the novices entering the structural biology field. Furthermore, it is argued that the effective resolution should be also reported as it is a more descriptive measure accounting for anisotropy and incompleteness of the data. In single particle cryo-EM, the situation is not much better, as multiple ways exist to determine the resolution, such as Fourier shell correlation, spectral signal-to-noise ratio and the Fourier neighbor correlation. The most widely accepted is the Fourier shell correlation using a threshold of 0.143 to define the resolution (so-called “gold-standard”), although it is still debated whether this is the correct threshold. Besides, the resolution obtained from the Fourier shell correlation is an estimate of varying resolution across the density map. In reality, the interpretability of the map is more important than the numerical value of the resolution.

Electron crystallography is a powerful technique for studying the structure and function of membrane proteins, not only in the ground state, but also in active conformations. When combined with high-resolution structures obtained by X-ray crystallography, electron crystallography can provide insights into the mechanism of the protein. In this chapter we discuss obtaining a three-dimensional map of membrane proteins by electron crystallography and how to combine these maps with atomic resolution models in order to study the function of membrane proteins. We argue that this approach is particularly powerful as it combines the high resolution attainable by X-ray crystallography with the visualization of the subject in the near-native environment of the membrane, by electron cryo-microscopy. This point has been illustrated by the analysis of the protein translocation complex SecYEG.

A new lanthanum oxide, KLa5O5(VO4)2, was synthesized using a flux growth technique that involved solid-state reaction under an air atmosphere at 900 °C. The crystal structure was solved and refined using an innovative approach recently established and based on three-dimensional (3D) electron diffraction data, using precession of the electron beam and then validated against Rietveld refinement and denisty functional theory (DFT) calculations. It crystallizes in a monoclinic unit cell with space group C2/m and has unit cell parameters of a = 20.2282(14) Å, b = 5.8639(4) Å, c = 12.6060(9) Å, and β = 117.64(1)°. Its structure is built on Cresnel-like two-dimensional (2D) units (La5O5) of 4*3 (OLa4) tetrahedra, which run parallel to (001) plane, being surrounded by isolated VO4 tetrahedra. Four isolated vanadate groups create channels that host K(+) ions. Substitution of K(+) cations by another alkali metal is possible, going from lithium to rubidium. Li substitution led to a similar phase with a primitive monoclinic unit cell. A complementary selected area electron diffraction (SAED) study highlighted diffuse streaks associated with stacking faults observed on high-resolution electron microscopy (HREM) images of the lithium compound. Finally, preliminary catalytic tests for ethanol oxidation are reported, as well as luminescence evidence. This paper also describes how solid-state chemists can take advantages of recent progresses in electron crystallography, assisted by DFT calculations and powder X-ray diffraction (PXRD) refinements, to propose new structural types with potential applications to the physicist community.

Membrane proteins are still heavily under-represented in the protein data bank (PDB), owing to multiple bottlenecks. The typical low abundance of membrane proteins in their natural hosts makes it necessary to overexpress these proteins either in heterologous systems or through in vitro translation/cell-free expression. Heterologous expression of proteins, in turn, leads to multiple obstacles, owing to the unpredictability of compatibility of the target protein for expression in a given host. The highly hydrophobic and (or) amphipathic nature of membrane proteins also leads to challenges in producing a homogeneous, stable, and pure sample for structural studies. Circumventing these hurdles has become possible through the introduction of novel protein production protocols; efficient protein isolation and sample preparation methods; and, improvement in hardware and software for structural characterization. Combined, these advances have made the past 10-15 years very exciting and eventful for the field of membrane protein structural biology, with an exponential growth in the number of solved membrane protein structures. In this review, we focus on both the advances and diversity of protein production and purification methods that have allowed this growth in structural knowledge of membrane proteins through X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, and cryo-electron microscopy (cryo-EM).