Automated determination of parameters describing power spectra of micrograph images in electron microscopy

Automated pipelines for rapid evaluation during cryoEM data acquisition

Cryo-electron microscopy (cryoEM) has become a popular method for determining high-resolution structures of biomolecules. However, data processing can be time-consuming, particularly for new researchers entering the field. To improve data quality and increase data collection efficiency, several software packages have been developed for on-the-fly data processing with various degrees of automation. These software packages allow researchers to perform tasks such as motion correction, CTF estimation, 2D classification, and 3D reconstruction in real-time, with minimal human input. On-the-fly data processing can not only improve data collection efficiency but also increase the productivity of instrumentation in high demand. However, the various software packages available differ in their performance, computational requirements, and levels of automation. In this review, we describe the minimal metrics used to assess data quality during data collection, outline the features of an ideal on-the-fly data processing software systems, and provide results from using three of these systems.

Single-Particle Cryo-EM of Membrane Proteins

In the recent years, the protein databank has been fueled by the exponential growth of high-resolution electron cryo-microscopy (cryo-EM) structures. This trend will be further accelerated through the continuous software and method developments and the increasing availability of imaging centers, which will open cryo-EM to a wide array of researchers with their diverse scientific goals and questions. Especially for structural biology of membrane proteins, cryo-EM offers significant advantages as it can overcome multiple limitations of classical methods. Most importantly, in cryo-EM, the sample is prepared as a vitrified suspension, which abolishes the need for crystallization, reduces the required sample amount and allows usage of a wide arsenal of hydrophobic environments. Despite recent improvements, high-resolution cryo-EM still poses some significant challenges, and standardized procedures, especially for the characterization of membrane proteins, are missing. While there can be no ultimate recipe toward a high-resolution cryo-EM structure for every membrane protein, certain factors seem to be universally relevant. Here, we share the protocols that have been successfully used in our laboratory. We hope that this may be a useful resource to other researchers in the field and may increase their chances of success.

Reducing bias and variance for CTF estimation in single particle cryo-EM

When using an electron microscope for imaging of particles embedded in vitreous ice, the recorded image, or micrograph, is a significantly degraded version of the tomographic projection of the sample. Apart from noise, the image is affected by the optical configuration of the microscope. This transformation is typically modeled as a convolution with a point spread function. The Fourier transform of this function, known as the contrast transfer function (CTF), is oscillatory, attenuating and amplifying different frequency bands, and sometimes flipping their signs. High-resolution reconstruction requires this CTF to be accounted for, but as its form depends on experimental parameters, it must first be estimated from the micrograph. We present a new method for CTF estimation based on multitaper techniques that reduce bias and variance in the estimate. We also use known properties of the CTF and the background power spectrum to further reduce the variance through background subtraction and steerable basis projection. We show that the resulting power spectrum estimates better capture the zero-crossings of the CTF and yield accurate CTF estimates on several experimental micrographs.

Real-time cryo-electron microscopy data preprocessing with Warp

The acquisition of cryo-electron microscopy (cryo-EM) data from biological specimens must be tightly coupled to data preprocessing to ensure the best data quality and microscope usage. Here we describe Warp, a software that automates all preprocessing steps of cryo-EM data acquisition and enables real-time evaluation. Warp corrects micrographs for global and local motion, estimates the local defocus and monitors key parameters for each recorded micrograph or tomographic tilt series in real time. The software further includes deep-learning-based models for accurate particle picking and image denoising. The output from Warp can be fed into established programs for particle classification and 3D-map refinement. Our benchmarks show improvement in the nominal resolution, which went from 3.9 Å to 3.2 Å, of a published cryo-EM data set for influenza virus hemagglutinin. Warp is easy to install from http://github.com/cramerlab/warp and computationally inexpensive, and has an intuitive, streamlined user interface.

Identification of interfaces involved in weak interactions with application to F-actin-aldolase rafts

Macromolecular interactions occur with widely varying affinities. Strong interactions form well defined interfaces but weak interactions are more dynamic and variable. Weak interactions can collectively lead to large structures such as microvilli via cooperativity and are often the precursors of much stronger interactions, e.g. the initial actin-myosin interaction during muscle contraction. Electron tomography combined with subvolume alignment and classification is an ideal method for the study of weak interactions because a 3-D image is obtained for the individual interactions, which subsequently are characterized collectively. Here we describe a method to characterize heterogeneous F-actin-aldolase interactions in 2-D rafts using electron tomography. By forming separate averages of the two constituents and fitting an atomic structure to each average, together with the alignment information which relates the raw motif to the average, an atomic model of each crosslink is determined and a frequency map of contact residues is computed. The approach should be applicable to any large structure composed of constituents that interact weakly and heterogeneously.

Real-time detection and single-pass minimization of TEM objective lens astigmatism

Minimization of the astigmatism of the objective lens is a critical daily instrument alignment task essential for high resolution TEM imaging. Fast and sensitive detection of astigmatism is needed to provide real-time feedback and adjust the stigmators to efficiently reduce astigmatism. Currently the method used by many microscopists is to visually examine the roundness of a diffractogram (Thon rings) and iteratively adjust the stigmators to make the Thon rings circular. This subjective method is limited by poor sensitivity and potentially biased by the astigmatism of human eyes. In this study, an s² power spectra based method, s²stigmator, was developed to allow fast and sensitive detection of the astigmatism in TEM live images. The "radar"-style display provides real-time feedback to guide the adjustment of the objective lens stigmators. Such unique capability allowed us to discover the mapping of the two stigmators to the astigmatism amplitude and angle, which led us to develop a single-pass tuning strategy capable of significantly quicker minimization of the objective lens astigmatism.

CTFFIND4: Fast and accurate defocus estimation from electron micrographs

CTFFIND is a widely-used program for the estimation of objective lens defocus parameters from transmission electron micrographs. Defocus parameters are estimated by fitting a model of the microscope's contrast transfer function (CTF) to an image's amplitude spectrum. Here we describe modifications to the algorithm which make it significantly faster and more suitable for use with images collected using modern technologies such as dose fractionation and phase plates. We show that this new version preserves the accuracy of the original algorithm while allowing for higher throughput. We also describe a measure of the quality of the fit as a function of spatial frequency and suggest this can be used to define the highest resolution at which CTF oscillations were successfully modeled.

Visualization and quality assessment of the contrast transfer function estimation

The contrast transfer function (CTF) describes an undesirable distortion of image data from a transmission electron microscope. Many users of full-featured processing packages are often new to electron microscopy and are unfamiliar with the CTF concept. Here we present a common graphical output to clearly demonstrate the CTF fit quality independent of estimation software. Separately, many software programs exist to estimate the four CTF parameters, but their results are difficult to compare across multiple runs and it is all but impossible to select the best parameters to use for further processing. A new measurement is presented based on the correlation falloff of the calculated CTF oscillations against the normalized oscillating signal of the data, called the CTF resolution. It was devised to provide a robust numerical quality metric of every CTF estimation for high-throughput screening of micrographs and to select the best parameters for each micrograph. These new CTF visualizations and quantitative measures will help users better assess the quality of their CTF parameters and provide a mechanism to choose the best CTF tool for their data.

CTER-rapid estimation of CTF parameters with error assessment

In structural electron microscopy, the accurate estimation of the Contrast Transfer Function (CTF) parameters, particularly defocus and astigmatism, is of utmost importance for both initial evaluation of micrograph quality and for subsequent structure determination. Due to increases in the rate of data collection on modern microscopes equipped with new generation cameras, it is also important that the CTF estimation can be done rapidly and with minimal user intervention. Finally, in order to minimize the necessity for manual screening of the micrographs by a user it is necessary to provide an assessment of the errors of fitted parameters values. In this work we introduce CTER, a CTF parameters estimation method distinguished by its computational efficiency. The efficiency of the method makes it suitable for high-throughput EM data collection, and enables the use of a statistical resampling technique, bootstrap, that yields standard deviations of estimated defocus and astigmatism amplitude and angle, thus facilitating the automation of the process of screening out inferior micrograph data. Furthermore, CTER also outputs the spatial frequency limit imposed by reciprocal space aliasing of the discrete form of the CTF and the finite window size. We demonstrate the efficiency and accuracy of CTER using a data set collected on a 300kV Tecnai Polara (FEI) using the K2 Summit DED camera in super-resolution counting mode. Using CTER we obtained a structure of the 80S ribosome whose large subunit had a resolution of 4.03Å without, and 3.85Å with, inclusion of astigmatism parameters.

Single particle cryo-electron microscopy and 3-D reconstruction of viruses

With fast progresses in instrumentation, image processing algorithms, and computational resources, single particle electron cryo-microscopy (cryo-EM) 3-D reconstruction of icosahedral viruses has now reached near-atomic resolutions (3-4 Å). With comparable resolutions and more predictable outcomes, cryo-EM is now considered a preferred method over X-ray crystallography for determination of atomic structure of icosahedral viruses. At near-atomic resolutions, all-atom models or backbone models can be reliably built that allow residue level understanding of viral assembly and conformational changes among different stages of viral life cycle. With the developments of asymmetric reconstruction, it is now possible to visualize the complete structure of a complex virus with not only its icosahedral shell but also its multiple non-icosahedral structural features. In this chapter, we will describe single particle cryo-EM experimental and computational procedures for both near-atomic resolution reconstruction of icosahedral viruses and asymmetric reconstruction of viruses with both icosahedral and non-icosahedral structure components. Procedures for rigorous validation of the reconstructions and resolution evaluations using truly independent de novo initial models and refinements are also introduced.

Maximizing the potential of electron cryomicroscopy data collected using direct detectors

Single-particle electron cryomicroscopy is undergoing a technical revolution due to the recent developments of direct detectors. These new recording devices detect electrons directly (i.e. without conversion into light) and feature significantly improved detective quantum efficiencies and readout rates as compared to photographic films or CCDs. We evaluated here the potential of one such detector (Gatan K2 Summit) to enable the achievement of near-atomic resolution reconstructions of biological specimens when coupled to a widely used, mid-range transmission electron microscope (FEI TF20 Twin). Compensating for beam-induced motion and stage drift provided a 4.4Å resolution map of Sulfolobus turreted icosahedral virus (STIV), which we used as a test particle in this study. Several motion correction and dose fractionation procedures were explored and we describe their influence on the resolution of the final reconstruction. We also compared the quality of this data to that collected with a FEI Titan Krios microscope equipped with a Falcon I direct detector, which provides a benchmark for data collected using a high-end electron microscope.

FASTDEF: fast defocus and astigmatism estimation for high-throughput transmission electron microscopy

In this work we present a fast and automated algorithm for estimating the contrast transfer function (CTF) of a transmission electron microscope. The approach is very suitable for High Throughput work because: (a) it does not require any initial defocus estimation, (b) it is almost an order of magnitude faster than existing approaches, (c) it opens the way to well-defined extensions to the estimation of higher order aberrations, at the same time that provides defocus and astigmatism estimations comparable in accuracy to well established methods, such as Xmipp and CTFFIND3 approaches. The new algorithm is based on obtaining the wrapped modulating phase of the power spectra density pattern by the use of a quadrature filter. This phase is further unwrapped in order to obtain the continuous and smooth absolute phase map; then a Zernike polynomial fitting is performed and the defocus and astigmatism parameters are determined. While the method does not require an initial estimation of the defocus parameters or any non-linear optimization procedure, these approaches can be used if further refinement is desired. Results of the CTF estimation method are presented for standard negative stained images, cryo-electron microscopy images in the absence of carbon support, as well as micrographs with only ice. Additionally, we have also tested the proposed method with micrographs acquired from tilted and untilted samples, obtaining good results. The algorithm is freely available as a part of the Xmipp package [http://xmipp.cnb.csic.es].

A graph theory method for determination of cryo-EM image focuses

Accurate determination of micrograph focuses is essential for averaging multiple images to reach high-resolution 3-D reconstructions in electron cryo-microscopy (cryo-EM). Current methods use iterative fitting of focus-dependent simulated power spectra to the power spectra of experimental images, with the fitting performed independently for different images. Here we have developed a novel graph theory based method in which the rotational average focus and individual angular sector focuses of all images are determined simultaneously in closed form using the least square solution of overdetermined linear equations. The new method was shown to be fast, accurate, and robust in tests with large datasets of experimental low dose cryo-EM images. Its integration with three classic power spectra fitting methods also allows cross validation of the results by these vastly different methods. The new integrated focus determination method will improve reliability of automated focus determination for large-scale data processing that is increasingly common in the cryo-EM field.

Subunit organization of the membrane-bound HIV-1 envelope glycoprotein trimer

The trimeric human immunodeficiency virus type 1 (HIV-1) envelope glycoprotein (Env) spike is a molecular machine that mediates virus entry into host cells and is the sole target for virus-neutralizing antibodies. The mature Env spike results from cleavage of a trimeric glycoprotein precursor, gp160, into three gp120 and three gp41 subunits. Here, we describe an ~11-Å cryo-EM structure of the trimeric HIV-1 Env precursor in its unliganded state. The three gp120 and three gp41 subunits form a cage-like structure with an interior void surrounding the trimer axis. Interprotomer contacts are limited to the gp41 transmembrane region, the torus-like gp41 ectodomain and a trimer-association domain of gp120 composed of the V1, V2 and V3 variable regions. The cage-like architecture, which is unique among characterized viral envelope proteins, restricts antibody access, reflecting requirements imposed by HIV-1 persistence in the host.

Defocus estimation from stroboscopic cryo-electron microscopy data

Defocus estimation is an important step for improving the resolution of single particle reconstructions. It can be troublesome to estimate the defocus from low-dose cryo-electron microscopy (cryo-EM) data, particularly if there is not sufficient contrast present in the Fourier transform of the micrograph. Most existing approaches estimate the defocus from the presence of Thon rings within the power spectrum, employing image enhancement techniques to highlight these rings. In this paper, an approach to estimating the defocus from a stroboscopic image series is described. The image series is used to obtain two statistical metrics: figure of merit (FOM) and Q-factor. These metrics have been used to estimate the defoci from low-dose stroboscopic cryo-EM data consisting of a variable number of images.

Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy

Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfil predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3-4Å resolution. This review summarizes technical developments, both in instrumentation and in computation, that have led to the new structures, which advance our understanding of virus assembly and cell entry.

A novel approximation method of CTF amplitude correction for 3D single particle reconstruction

The typical resolution of three-dimensional reconstruction by cryo-EM single particle analysis is now being pushed up to and beyond the nanometer scale. Correction of the contrast transfer function (CTF) of electron microscopic images is essential for achieving such a high resolution. Various correction methods exist and are employed in popular reconstruction software packages. Here, we present a novel approximation method that corrects the amplitude modulation introduced by the contrast transfer function by convoluting the images with a piecewise continuous function. Our new approach can easily be implemented and incorporated into other packages. The implemented method yielded higher resolution reconstructions with data sets from both highly symmetric and asymmetric structures. It is an efficient alternative correction method that allows quick convergence of the 3D reconstruction and has a high tolerance for noisy images, thus easing a bottleneck in practical reconstruction of macromolecules.

Automation in single-particle electron microscopy connecting the pieces

Throughout the history of single-particle electron microscopy (EM), automated technologies have seen varying degrees of emphasis and development, usually depending upon the contemporary demands of the field. We are currently faced with increasingly sophisticated devices for specimen preparation, vast increases in the size of collected data sets, comprehensive algorithms for image processing, sophisticated tools for quality assessment, and an influx of interested scientists from outside the field who might lack the skills of experienced microscopists. This situation places automated techniques in high demand. In this chapter, we provide a generic definition of and discuss some of the most important advances in automated approaches to specimen preparation, grid handling, robotic screening, microscope calibrations, data acquisition, image processing, and computational infrastructure. Each section describes the general problem and then provides examples of how that problem has been addressed through automation, highlighting available processing packages, and sometimes describing the particular approach at the National Resource for Automated Molecular Microscopy (NRAMM). We contrast the more familiar manual procedures with automated approaches, emphasizing breakthroughs as well as current limitations. Finally, we speculate on future directions and improvements in automated technologies. Our overall goal is to present automation as more than simply a tool to save time. Rather, we aim to illustrate that automation is a comprehensive and versatile strategy that can deliver biological information on an unprecedented scale beyond the scope available with classical manual approaches.

Fourier-Bessel reconstruction of helical assemblies

Helical symmetry is commonly used for building macromolecular assemblies. Helical symmetry is naturally present in viruses and cytoskeletal filaments and also occurs during crystallization of isolated proteins, such as Ca-ATPase and the nicotinic acetyl choline receptor. Structure determination of helical assemblies by electron microscopy has a long history dating back to the original work on three-dimensional (3D) reconstruction. A helix offers distinct advantages for structure determination. Not only can one improve resolution by averaging across the constituent subunits, but each helical assembly provides multiple views of these subunits and thus provides a complete 3D data set. This review focuses on Fourier methods of helical reconstruction, covering the theoretical background, a step-by-step guide to the process, and a practical example based on previous work with Ca-ATPase. Given recent results from helical reconstructions at atomic resolution and the development of graphical user interfaces to aid in the process, these methods are likely to continue to make an important contribution to the field of structural biology.

Image restoration in cryo-electron microscopy

Image restoration techniques are used to obtain, given experimental measurements, the best possible approximation of the original object within the limits imposed by instrumental conditions and noise level in the data. In molecular electron microscopy (EM), we are mainly interested in linear methods that preserve the respective relationships between mass densities within the restored map. Here, we describe the methodology of image restoration in structural EM, and more specifically, we will focus on the problem of the optimum recovery of Fourier amplitudes given electron microscope data collected under various defocus settings. We discuss in detail two classes of commonly used linear methods, the first of which consists of methods based on pseudoinverse restoration, and which is further subdivided into mean-square error, chi-square error, and constrained based restorations, where the methods in the latter two subclasses explicitly incorporates non-white distribution of noise in the data. The second class of methods is based on the Wiener filtration approach. We show that the Wiener filter-based methodology can be used to obtain a solution to the problem of amplitude correction (or "sharpening") of the EM map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparative interpretation. Finally, we present a semiheuristic Wiener filter-based solution to the problem of image restoration given sets of heterogeneous solutions. We conclude the chapter with a discussion of image restoration protocols implemented in commonly used single particle software packages.

Error analysis in the determination of the electron microscopical contrast transfer function parameters from experimental power Spectra

BACKGROUND

The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.

RESULTS

In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.

CONCLUSION

We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Radial averages of astigmatic TEM images

The Contrast Transfer Function (CTF) of an image, which modulates images taken from a Transmission Electron Microscope (TEM), is usually determined from the radial average of the power spectrum of the image (Frank, J., Three-dimensional Electron Microscopy of Macromolecular Assemblies, Oxford University Press, Oxford, 2006). The CTF is primarily defined by the defocus. If the defocus estimate is accurate enough then it is possible to demodulate the image, which is popularly known as the CTF correction. However, it is known that the radial average is somewhat attenuated if the image is astigmatic (see Fernando, K.V., Fuller, S.D., 2007. Determination of astigmatism in TEM images. Journal of Structural Biology 157, 189-200) but this distortion due to astigmatism has not been fully studied or understood up to now. We have discovered the exact mathematical relationship between the radial averages of TEM images with and without astigmatism. This relationship is determined by a zeroth order Bessel function of the first kind and hence we can exactly quantify this distortion in the radial averages of signal and power spectra of astigmatic images. The argument to this Bessel function is similar to an aberration function (without the spherical aberration term) except that the defocus parameter is replaced by the differences of the defoci in the major and minor axes of astigmatism. The ill effects due this Bessel function are twofold. Since the zeroth order Bessel function is a decaying oscillatory function, it introduces additional zeros to the radial average and it also attenuates the CTF signal in the radial averages. Using our analysis, it is possible to simulate the effects of astigmatism in radial averages by imposing Bessel functions on idealized radial averages of images which are not astigmatic. We validate our theory using astigmatic TEM images.

Fast, robust, and accurate determination of transmission electron microscopy contrast transfer function

Transmission electron microscopy, as most imaging devices, introduces optical aberrations that in the case of thin specimens are usually modeled in Fourier space by the so-called contrast transfer function (CTF). Accurate determination of the CTF is crucial for its posterior correction. Furthermore, the CTF estimation must be fast and robust if high-throughput three-dimensional electron microscopy (3DEM) studies are to be carried out. In this paper we present a robust algorithm that fits a theoretical CTF model to the power spectrum density (PSD) measured on a specific micrograph or micrograph area. Our algorithm is capable of estimating the envelope of the CTF which is absolutely needed for the correction of the CTF amplitude changes.

3D electron microscopy of biological nanomachines: principles and applications

Transmission electron microscopy is a powerful technique for studying the three-dimensional (3D) structure of a wide range of biological specimens. Knowledge of this structure is crucial for fully understanding complex relationships among macromolecular complexes and organelles in living cells. In this paper, we present the principles and main application domains of 3D transmission electron microscopy in structural biology. Moreover, we survey current developments needed in this field, and discuss the close relationship of 3D transmission electron microscopy with other experimental techniques aimed at obtaining structural and dynamical information from the scale of whole living cells to atomic structure of macromolecular complexes.

Determination of astigmatism in TEM images

We have developed a new two-step algorithm to determine the astigmatism of images from transmission electron microscopes (TEMs). Instead of computing the radial average of the power spectrum, we divide the power spectrum of a TEM image 1 to m (typically 32) sectors. We use a technique based on perturbation analysis of the contrast transfer function (CTF) to assimilate sector averages of the power spectrum of an image, which are incoherent in the presence of astigmatism, to a coherent radial average corresponding to a nominal defocus value. This is based on the fact that small defocus change from a nominal value can be considered to be equivalent to a perturbation on the spatial frequency spectra. Thus, instead of measuring the angular defocus variations, we optimise the frequency change required to obtain a coherent radial average. Numerically, this is achieved by minimizing sigma(2)/sigma(1) of a matrix formed from the sector averages, where sigma(i) denotes the ith singular value of the matrix. After the minimisation procedure, the second singular value should be very small compared with the first singular value, indicating that the matrix is nearly rank unity. In the second step, the nominal defocus can be obtained from the coherent radial average using any good defocus estimation program, which assumes zero astigmatism. The defocus value at a sector can be obtained from this nominal defocus value and one of the parameters from the unconstrained optima. Our algorithm is tested on astigmatic images of carbon film, 2D crystals of bacteriorhodopsin and cryo-images of HIV cores.

A novel method for improvement of visualization of power spectra for sorting cryo-electron micrographs and their local areas

In a context of automation of cryo-electron microscopy, we developed a novel method for improving visibility of diffraction rings in the power spectra of cryo-electron micrographs of vitreous ice (without carbon film or high concentration of diffracting material). We used these enhanced spectra to semi-automatically detect and remove micrographs and/or local areas introducing errors in the global 3D map (drifted and charged areas) or those unable to increase global signal-to-noise ratio (non-diffracting areas). Our strategy also allows a detection of micrographs/areas with a strong astigmatism. These images should be removed when using algorithms that do not correct astigmatism. Our sorting method is simple and fast since it uses the normalized cross-correlation between enhanced spectra and their copies rotated by 90 degrees. It owes its success mainly to the novel pre-processing of power spectra. The improved visibility also allows an easier visual check of accuracy of sorting. We show that our algorithm can even improve the visibility of diffraction rings of cryo-electron micrographs of pure water. Moreover, we show that this visibility depends strongly on ice thickness. This algorithm is implemented in the Xmipp (open-source image processing package) and is freely available for implementation in any other software package.

The endosome-associated protein Hrs is hexameric and controls cargo sorting as a "master molecule"

The structure of the endosomal-associated protein, Hrs, has been determined with cryo-electron microscopy. Hrs interacts with a number of proteins, including SNAP-25 and STAM1, forming a complex that binds ubiquitin moieties. Analytical ultracentrifugation studies revealed that Hrs exists as a hexamer. The symmetry and the structure of the hexameric form of Hrs were determined with the single-particle reconstruction method. Hrs comprises three antiparallel dimers with a central core and distinct caps on either end. Crystal structures of VHS and FYVE domains fit into the Hrs end caps in the EM density map. Thus, the location of domains that interact with the endosomal membrane, the VHS, FYVE, and C-terminal domains, facilitates the anchorage of Hrs to the membrane, initiating the functional processes of Hrs on the endosome. Based on our model, the Hrs hexamer interacts with the membrane and acts as a "master molecule" that presents multiple sites for protein binding.

CTF determination and correction in electron cryotomography

Electron cryotomography (cryoET) has the potential to elucidate the structure of complex biological specimens at molecular resolution but technical and computational improvements are still needed. This work addresses the determination and correction of the contrast transfer function (CTF) of the electron microscope in cryoET. Our approach to CTF detection and defocus determination depends on strip-based periodogram averaging, extended throughout the tilt series to overcome the low contrast conditions found in cryoET. A method for CTF correction that deals with the defocus gradient in images of tilted specimens is also proposed. These approaches to CTF determination and correction have been applied here to several examples of cryoET of pleomorphic specimens and of single particles. CTF correction is essential for improving the resolution, particularly in those studies that combine cryoET with single particle averaging techniques.

XMIPP: a new generation of an open-source image processing package for electron microscopy

X-windows based microscopy image processing package (Xmipp) is a specialized suit of image processing programs, primarily aimed at obtaining the 3D reconstruction of biological specimens from large sets of projection images acquired by transmission electron microscopy. This public-domain software package was introduced to the electron microscopy field eight years ago, and since then it has changed drastically. New methodologies for the analysis of single-particle projection images have been added to classification, contrast transfer function correction, angular assignment, 3D reconstruction, reconstruction of crystals, etc. In addition, the package has been extended with functionalities for 2D crystal and electron tomography data. Furthermore, its current implementation in C++, with a highly modular design of well-documented data structures and functions, offers a convenient environment for the development of novel algorithms. In this paper, we present a general overview of a new generation of Xmipp that has been re-engineered to maximize flexibility and modularity, potentially facilitating its integration in future standardization efforts in the field. Moreover, by focusing on those developments that distinguish Xmipp from other packages available, we illustrate its added value to the electron microscopy community.

ACE: automated CTF estimation

We present a completely automated algorithm for estimating the parameters of the contrast transfer function (CTF) of a transmission electron microscope. The primary contribution of this paper is the determination of the astigmatism prior to the estimation of the CTF parameters. The CTF parameter estimation is then reduced to a 1D problem using elliptical averaging. We have also implemented an automated method to calculate lower and upper cutoff frequencies to eliminate regions of the power spectrum which perturb the estimation of the CTF parameters. The algorithm comprises three optimization subproblems, two of which are proven to be convex. Results of the CTF estimation method are presented for images of carbon support films as well as for images of single particles embedded in ice and suspended over holes in the support film. A MATLAB implementation of the algorithm, called ACE, is freely available.

Noise bias in the refinement of structures derived from single particles

One of the main goals in the determination of three-dimensional macromolecular structures from electron microscope images of individual molecules and complexes (single particles) is a sufficiently high spatial resolution, about 4 A, at which the interpretation with an atomic model becomes possible. To reach high resolution, an iterative refinement procedure using an expectation maximization algorithm is often used that leads to a more accurate alignment of the positional and orientational parameters for each particle. We show here the results of refinement algorithms that use a phase residual, a linear correlation coefficient, or a weighted correlation coefficient to align individual particles. The algorithms were applied to computer-generated data sets that contained projections from model structures, as well as noise. The algorithms show different degrees of over-fitting, especially at high resolution where the signal is weak. We demonstrate that the degree of over-fitting is reduced with a weighting scheme that depends on the signal-to-noise ratio in the data. The weighting also improves the accuracy of resolution measurement by the commonly used Fourier shell correlation. The performance of the refinement algorithms is compared to that using a maximum likelihood approach. The weighted correlation coefficient was implemented in the computer program FREALIGN.

Rearrangement of the 16S precursor subunits is essential for the formation of the active 20S proteasome

Proteasome-dependent proteolysis is essential for a number of key cellular processes and requires a sophisticated biogenesis pathway to function. Here, we have arrested the assembly process in its dynamic progression at the short-lived 16S state. Structural analysis of the 16S proteasome precursor intermediates by electron microscopy, and single particle analysis reveals major conformational changes in the structure of the beta-ring in comparison with one-half of the 20S proteasome. The individual beta-subunits in the 16S precursor complex rotate with respect to their positions in the x-ray crystallographic structure of the fully assembled 20S. This rearrangement results in a movement of the catalytic residue threonine-1 from the protected location in 16S precursor complexes to a more exposed position in the 20S structure. Thereby, our findings provide a molecular explanation for the structural rearrangements necessary for the dimerization of two 16S precursor complexes and the subsequent final maturation to active 20S proteasomes.