Patch averaging of electron images of GP3*I crystals with variable thickness

Recording high-resolution images of two-dimensional crystals of membrane proteins

Principles underlying the recording of high-quality/resolution images of two-dimensional crystals of membrane proteins are discussed in the context of instrumental conditions and operational procedures. A detailed example of low-dose microscope settings is provided along with an overview of a program that implements a computer-aided data acquisition procedure.

Single-particle reconstruction of biological macromolecules in electron microscopy--30 years

This essay gives the autho's personal account on the development of concepts underlying single-particle reconstruction, a technique in electron microscopy of macromolecular assemblies with a remarkable record of achievements as of late. The ribosome proved to be an ideal testing ground for the development of specimen preparation methods, cryo-EM techniques, and algorithms, with discoveries along the way as a rich reward. Increasingly, cryo-EM and single-particle reconstruction, in combination with classification techniques, is revealing dynamic information on functional molecular machines uninhibited by molecular contacts.

Application of two-dimensional crystallography and image processing to atomic resolution Z-contrast images

Zone axis images recorded using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM or Z-contrast imaging) reveal the atomic structure with a resolution that is defined by the probe size of the microscope. In most cases, the full images contain many sub-images of the crystal unit cell and/or interface structure. Thanks to the repetitive nature of these images, it is possible to apply standard image processing techniques that have been developed for the electron crystallography of biological macromolecules and have been used widely in other fields of electron microscopy for both organic and inorganic materials. These methods can be used to enhance the signal-to-noise present in the original images, to remove distortions in the images that arise from either the instrumentation or the specimen itself and to quantify properties of the material in ways that are difficult without such data processing. In this paper, we describe briefly the theory behind these image processing techniques and demonstrate them for aberration-corrected, high-resolution HAADF-STEM images of Si(46) clathrates developed for hydrogen storage.

Cross-correlation and merging of crystallographic reflections derived from cryoelectron micrographs of 3D crystals: application to the Limulus acrosomal bundle

A method is described for merging in reciprocal space of electron microscopic data from three-dimensional crystals of the acrosomal bundle. Permutation of indices was required to find the proper alignment of data from different bundles. The method utilizes a statistical evaluation of the significance of the cross-correlation results to indicate the proper order for merging. The three-dimensional (3D) merging is a reference-free operation that does not depend on choosing a "zero-tilt" user-defined starting point. Results from the merging are given and the merged 3D data to 9.5A resolution is evaluated for coherence. General issues such as statistical significance of cross-correlation function peaks, symmetry evaluation, and phase coherence as a function of amplitude are discussed.

Multivariate analysis of single unit cells in electron crystallography

High-resolution electron cryomicroscopy of two-dimensional protein crystals is associated with extremely noisy raw data in which even the crystal lattice often cannot be discerned. Correlation averaging procedures, aimed at calculating the total average of all unit cells of crystals in order to reduce noise, are now used routinely in electron crystallography. Multivariate statistical analysis (MSA) may be used for finding not only the average structure but also for quantifying the systematic departures from that average within the population of individual unit cells. We show that the MSA approach is applicable to single unit-cell images in the low-dose (< 10 electrons/A2), high-resolution (< 5 A) realm using 400 keV electron spot-scan images of ice-embedded gp32*I protein crystals. Our feasibility study opens a pathway toward exploiting these naturally occurring variations on the unit-cell theme in order to achieve higher-resolution three-dimensional reconstruction results, or to better understand the dynamic behaviour of molecules within two-dimensional crystals. We explain how single unit-cell images can be processed and classified into homogeneous groups, and we review how the results of such discriminate averaging may subsequently be exploited within the context of conventional "h, k"-space electron crystallographic approaches. Variations among the individual unit cells may thus be one of the most significant resolution-limiting factors currently experienced in electron crystallography. The quantitative assessment and exploitation of such variations may lead to an increased performance of electron crystallographic procedures.

Electron crystallography of macromolecules

Numerous technical advances in electron crystallography have facilitated determination of the three-dimensional structures of macromolecules, especially those that form two-dimensional or helical periodic arrays. Several recent studies have demonstrated the utility of this technique for visualizing secondary structure such as alpha-helices and beta-sheets of membrane proteins and, in one case, the entire polypeptide backbone. Electron crystallography, therefore, has great potential as a tool for studying structural problems that are relevant to both molecular biology and biotechnology.

Teaching electron diffraction and imaging of macromolecules

Electron microscopic analysis can be used to determine the three-dimensional structures of macromolecules at resolutions ranging between 3 and 30 A. It differs from nuclear magnetic resonance spectroscopy or x-ray crystallography in that it allows an object's Coulomb potential functions to be determined directly from images and can be used to study relatively complex macromolecular assemblies in a crystalline or noncrystalline state. Electron imaging already has provided valuable structural information about various biological systems, including membrane proteins, protein-nucleic acid complexes, contractile and motile protein assemblies, viruses, and transport complexes for ions or macromolecules. This article, organized as a series of lectures, presents the biophysical principles of three-dimensional analysis of objects possessing different symmetries.

SPECTRA: a system for processing electron images of crystals

SPECTRA is a program system that combines well tested and familiar algorithms and advanced graphics tools for (i) the display and indexing of the Fourier transform of images of crystalline specimens, (ii) refinement of the reciprocal lattice, (iii) output of amplitudes and phases of reflections and (iv) lattice distortion correction through cross-correlation map analysis. Because of the ease of identifying and indexing reflections, the user can include many reflections for reciprocal lattice refinement, leading to more accurate lattice determination. Automatic indexing is much faster than entering indices by hand, with less operator error. The user can run the procedure that corrects for lattice distortions with either standard parameters or storable parameters tailored to a particular specimen. SPECTRA's primary function is as a control program which acts as an interface between existing programs and the user. It was written in C with routines for the display, user interface and peak list search. Communication between the separate processes that make up SPECTRA is via the UNIX pipe mechanism and command files, the latter so that users may run, test or replace them or even run them as stand-alone programs outside this system.

Flopping polypeptide chains and Suleika's subtle imperfections: analysis of variations in the electron micrograph of a purple membrane crystal

Patch averaging, a method of data analysis combining correlation averaging with multivariate statistical analysis, was applied to a high-resolution image of a purple membrane thin crystal. The observed variational patterns fall in two categories: non-crystallographic, related to small electron-optical distortions of the microscope, and crystallographic, conceivably related to variations in the locations of flexible segments of the polypeptide chain on the surface of the membrane.