Contrast Transfer Function Parameters Research Articles

A generalized framework for the image formation model and disentanglement of CTF parameters in cryo-electron microscopy

In cryo-electron microscopy (cryo-EM), the microscope has a point spread function, whose Fourier transform, known as the Contrast Transfer Function (CTF), is determined by various parameters with a physical meaning (including height of the sample, magnetic lens aberrations, operating voltage, amplitude contrast, etc.). Some of the parameters are under experimental control, but they can also contain some experimental uncertainty and fluctuate over the course of data collection. While it is routine to use point estimates for the CTF parameters in a simplified forward model of image formation, we characterize here the uncertainty of the CTF by (1) framing the forward model of image formation as a probabilistic graphical model, (2) deriving conditional probabilities that leverage analytical linking functions, and (3) compare these results with existing approaches that model noise in frequency space, such as the “B-factor envelope” and the “white/coloured noise model”.

Gctf: Real-time CTF determination and correction.

Accurate estimation of the contrast transfer function (CTF) is critical for a near-atomic resolution cryo electron microscopy (cryoEM) reconstruction. Here, a GPU-accelerated computer program, Gctf, for accurate and robust, real-time CTF determination is presented. The main target of Gctf is to maximize the cross-correlation of a simulated CTF with the logarithmic amplitude spectra (LAS) of observed micrographs after background subtraction. Novel approaches in Gctf improve both speed and accuracy. In addition to GPU acceleration (e.g. 10–50×), a fast ‘1-dimensional search plus 2-dimensional refinement (1S2R)’ procedure further speeds up Gctf. Based on the global CTF determination, the local defocus for each particle and for single frames of movies is accurately refined, which improves CTF parameters of all particles for subsequent image processing. Novel diagnosis method using equiphase averaging (EPA) and self-consistency verification procedures have also been implemented in the program for practical use, especially for aims of near-atomic reconstruction. Gctf is an independent program and the outputs can be easily imported into other cryoEM software such as Relion (Scheres, 2012) and Frealign (Grigorieff, 2007). The results from several representative datasets are shown and discussed in this paper.

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.

CTF Challenge: Result summary

Image formation in bright field electron microscopy can be described with the help of the contrast transfer function (CTF). In this work the authors describe the "CTF Estimation Challenge", called by the Madrid Instruct Image Processing Center (I2PC) in collaboration with the National Center for Macromolecular Imaging (NCMI) at Houston. Correcting for the effects of the CTF requires accurate knowledge of the CTF parameters, but these have often been difficult to determine. In this challenge, researchers have had the opportunity to test their ability in estimating some of the key parameters of the electron microscope CTF on a large micrograph data set produced by well-known laboratories on a wide set of experimental conditions. This work presents the first analysis of the results of the CTF Estimation Challenge, including an assessment of the performance of the different software packages under different conditions, so as to identify those areas of research where further developments would be desirable in order to achieve high-resolution structural information.

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.

Contrast transfer function correction applied to cryo-electron tomography and sub-tomogram averaging

Cryo-electron tomography together with averaging of sub-tomograms containing identical particles can reveal the structure of proteins or protein complexes in their native environment. The resolution of this technique is limited by the contrast transfer function (CTF) of the microscope. The CTF is not routinely corrected in cryo-electron tomography because of difficulties including CTF detection, due to the low signal to noise ratio, and CTF correction, since images are characterised by a spatially variant CTF. Here we simulate the effects of the CTF on the resolution of the final reconstruction, before and after CTF correction, and consider the effect of errors and approximations in defocus determination. We show that errors in defocus determination are well tolerated when correcting a series of tomograms collected at a range of defocus values. We apply methods for determining the CTF parameters in low signal to noise images of tilted specimens, for monitoring defocus changes using observed magnification changes, and for correcting the CTF prior to reconstruction. Using bacteriophage PRD1 as a test sample, we demonstrate that this approach gives an improvement in the structure obtained by sub-tomogram averaging from cryo-electron tomograms.

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

BackgroundThe 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.ResultsIn 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.ConclusionWe 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.

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.

Application of template matching technique to particle detection in electron micrographs

Template matching together with the comprehensive theory of image formation in electron microscope provides an optimal (in Bayesian sense) tool for solving one of the outstanding problems in single particle analysis, i.e., automatic selection of particle views from noisy micrograph fields. The method is based on the assumption that the reference three-dimensional structure is known and that the relevant parameters of the model of the image formation process can be estimated. In the first stage of the procedure, a set of possible particle views is generated using the available reference structure. The template images are constructed as linear combinations of available particle views using a clustering technique. Next, the micrograph noise characteristic is established using an automated contrast transfer function (CTF) estimation procedure. Finally, the CTF parameters calculated are used to construct a matched filter and correlation functions corresponding to the available template images are calculated. In order to alleviate the problem of the biased caused by varying image formation conditions, a decision making strategy based on the predicted distribution of correlation coefficients is proposed. It is demonstrated that due to the inclusion of CTF considerations, the template matching method performed very well in a broad range of microscopy conditions.

Automatic CTF correction for single particles based upon multivariate statistical analysis of individual power spectra

Three-dimensional electron cryomicroscopy of randomly oriented single particles is a method that is suitable for the determination of three-dimensional structures of macromolecular complexes at molecular resolution. However, the electron-microscopical projection images are modulated by a contrast transfer function (CTF) that prevents the calculation of three-dimensional reconstructions of biological complexes at high resolution from uncorrected images. We describe here an automated method for the accurate determination and correction of the CTF parameters defocus, twofold astigmatism and amplitude-contrast proportion from single-particle images. At the same time, the method allows the frequency-dependent signal decrease ( B factor) and the non-convoluted background signal to be estimated. The method involves the classification of the power spectra of single-particle images into groups with similar CTF parameters; this is done by multivariate statistical analysis (MSA) and hierarchically ascending classification (HAC). Averaging over several power spectra generates class averages with enhanced signal-to-noise ratios. The correct CTF parameters can be deduced from these class averages by applying an iterative correlation procedure with theoretical CTF functions; they are then used to correct the raw images. Furthermore, the method enables the tilt axis of the sample holder to be determined and allows the elimination of individual poor-quality images that show high drift or charging effects.

EMAN: Semiautomated Software for High-Resolution Single-Particle Reconstructions

We present EMAN (Electron Micrograph ANalysis), a software package for performing semiautomated single-particle reconstructions from transmission electron micrographs. The goal of this project is to provide software capable of performing single-particle reconstructions beyond 10 Å as such high-resolution data become available. A complete single-particle reconstruction algorithm is implemented. Options are available to generate an initial model for particles with no symmetry, a single axis of rotational symmetry, or icosahedral symmetry. Model refinement is an iterative process, which utilizes classification by model-based projection matching. CTF (contrast transfer function) parameters are determined using a new paradigm in which data from multiple micrographs are fit simultaneously. Amplitude and phase CTF correction is then performed automatically as part of the refinement loop. A graphical user interface is provided, so even those with little image processing experience will be able to begin performing reconstructions. Advanced users can directly use the lower level shell commands and even expand the package utilizing EMAN's extensive image-processing library. The package was written from scratch in C++ and is provided free of charge on our Web site. We present an overview of the package as well as several conformance tests with simulated data.

Determination of the defocus value of micrographs of ice-embedded specimen without carbon support film

It is well recognized that the contrast transfer function (CTF) of an electron microscope modulates the image contrast The effects of this CTF are to reverse the sign of the phases and to alter the amplitudes at different spatial frequencies. These changes are dependent on the defocus of the objective lens in a given microscope setting. Therefore, it is necessary to determine the defocus experimentally in order to correct the phase reversal and the amplitudes due to the CTF for attaining a high resolution reconstruction. The most straightforward way of determining the defocus value is to determine the positions of the Thon rings in the CTF by optical or computed transforms. In a crystalline specimen, the defocus value of an image can be refined against the electron diffraction amplitude. For specimen of which the x-ray structure is known, one can also use the x-ray structure factor to determine the CTF parameters.