goCTF: Geometrically optimized CTF determination for single-particle cryo-EM

Preferred particle orientation represents a recurring problem in single-particle cryogenic electron microcopy (cryo-EM). A specimen-independent approach through tilting has been attempted to increase particle orientation coverage, thus minimizing anisotropic three-dimensional (3D) reconstruction. However, focus gradient is a critical issue hindering tilt applications from being a general practice in single-particle cryo-EM. The present study describes a newly developed geometrically optimized approach, goCTF, to reliably determine the global focus gradient. A novel strategy of determining contrast transfer function (CTF) parameters from a sector of the signal preserved power spectrum is applied to increase reliability. Subsequently, per-particle based local focus refinement is conducted in an iterative manner to further improve the defocus accuracy. Novel diagnosis methods using a standard deviation defocus plot and goodness of fit heatmap have also been proposed to evaluate CTF fitting quality prior to 3D refinement. In a benchmark study, goCTF processed a published single-particle cryo-EM dataset for influenza hemagglutinin trimer collected at a 40-degree specimen tilt. The resulting 3D reconstruction map was improved from 4.1?Å to 3.7?Å resolution. The goCTF program is built on the open-source code of CTFFIND4, which adopts a consistent user interface for ease of use.     

Automatic particle pickup method using a neural network has high accuracy by applying an initial weight derived from eigenimages: a new reference free method for single-particle analysis

The single-particle analysis is a structure-determining method for electron microscope (EM) images which does not require crystal. In this method, the projections are picked up and averaged by the images of similar Euler angles to improve the signal to noise ratio, and then create a 3-D reconstruction. The selection of a large number of particles from the cryo-EM micrographs is a pre-requisite for obtaining a high resolution. To pickup a low-contrast cryo-EM protein image, we have recently found that a three-layer pyramidal-type neural network is successful in detecting such a faint image, which had been difficult to detect by other methods. The connection weights between the input and hidden layers, which work as a matching filter, have revealed that they reflect characters of the particle projections in the training data. The images stored in terms of the connection weights were complex, more similar to the eigenimages which are created by the principal component analysis of the learning images rather than to the averages of the particle projections. When we set the initial learning weights according to the eigenimages in advance, the learning period was able to be shortened to less than half the time of the NN whose initial weights had been set randomly. Further, the pickup accuracy increased from 90 to 98%, and a combination of the matching filters were found to work as an integrated matching filter there. The integrated filters were amazingly similar to averaged projections and can be used directly as references for further two-dimensional averaging. Therefore, this research also presents a brand-new reference-free method for single-particle analysis.     

A Fast Image Alignment Approach for 2D Classification of Cryo-EM Images Using Spectral Clustering

Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy (cryo-EM) is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-EM is an important procedure for producing high-quality initial 3D structures, where image alignment is a fundamental step. In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters of rotation angles and translational shifts between the two projection images, which can obtain subpixel and subangle accuracy. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed image alignment algorithm and a spectral clustering algorithm are used to compute class averages for single-particle 3D reconstruction. The proposed image alignment algorithm is firstly tested on a Lena image and two cryo-EM datasets. Results show that the proposed image alignment algorithm can estimate the alignment parameters accurately and efficiently. The proposed method is also used to reconstruct preliminary 3D structures from a simulated cryo-EM dataset and a real cryo-EM dataset and to compare them with RELION. Experimental results show that the proposed method can obtain more high-quality class averages than RELION and can obtain higher reconstruction resolution than RELION even without iteration.     

Structural Information, Resolution, and Noise in High-Resolution Atomic Force Microscopy Topographs

AFM has developed into a powerful tool in structural biology, providing topographs of proteins under close-to-native conditions and featuring an outstanding signal/noise ratio. However, the imaging mechanism exhibits particularities: fast and slow scan axis represent two independent image acquisition axes. Additionally, unknown tip geometry and tip-sample interaction render the contrast transfer function nondefinable. Hence, the interpretation of AFM topographs remained difficult. How can noise and distortions present in AFM images be quantified? How does the number of molecule topographs merged influence the structural information provided by averages? What is the resolution of topographs? Here, we find that in high-resolution AFM topographs, many molecule images are only slightly disturbed by noise, distortions, and tip-sample interactions. To identify these high-quality particles, we propose a selection criterion based on the internal symmetry of the imaged protein. We introduce a novel feature-based resolution analysis and show that AFM topographs of different proteins contain structural information beginning at different resolution thresholds: 10 Å (AqpZ), 12 Å (AQP0), 13 Å (AQP2), and 20 Å (light-harvesting-complex-2). Importantly, we highlight that the best single-molecule images are more accurate molecular representations than ensemble averages, because averaging downsizes the z-dimension and “blurs” structural details.Abbreviations: 2D, two-dimensional; 3D, three-dimensional; ACV, auto-correlation value; AFM, atomic force microscopy; AQP0, aquaporin-0; AQP2, aquaporin-2; AqpZ, aquaporin-Z; bR, bacteriorhodopsin; CCV, cross-correlation value; CTF, contrast transfer function; DPR, differential phase residual; EM, electron microscopy; FRC, Fourier ring correlation; FSC, Fourier shell correlation; IS, internal symmetry; LH2, light-harvesting-complex 2; RMSD, root mean-square deviation; SD, standard deviation; SNR, signal/noise ratio; SSNR, spectral signal/noise ratio     

Edged watershed segmentation: A semi-interactive algorithm for segmentation of low-resolution maps from electron cryomicroscopy

Electron cryomicroscopy (cryo-EM) allows for the structural analysis of large protein complexes that may be difficult to study by other means. Frequently, maps of complexes from cryo-EM are obtained at resolutions between 10 and 25 Å. To aid in the interpretation of these medium- to low-resolution maps, they may be subdivided into three-dimensional segments representing subunits or subcomplexes. This division is often accomplished using a manual segmentation approach. While extremely useful, manual segmentation is subjective. We have developed a novel semi-interactive segmentation algorithm that can incorporate prior knowledge of subunit composition or structure without biasing the boundaries between subunits or subcomplexes. This algorithm has been characterized with experimental and simulated cryo-EM density maps at resolutions between 10 and 25 Å.     

Direct electron detection yields cryo-EM reconstructions at resolutions beyond 3/4 Nyquist frequency

One limitation in electron cryo-microscopy (cryo-EM) is the inability to recover high-resolution signal from the image-recording media at the full-resolution limit of the transmission electron microscope. Direct electron detection using CMOS-based sensors for digitally recording images has the potential to alleviate this shortcoming. Here, we report a practical performance evaluation of a Direct Detection Device (DDD®) for biological cryo-EM at two different microscope voltages: 200 and 300 kV. Our DDD images of amorphous and graphitized carbon show strong per-pixel contrast with image resolution near the theoretical sampling limit of the data. Single-particle reconstructions of two frozen-hydrated bacteriophages, P22 and ε15, establish that the DDD is capable of recording usable signal for 3D reconstructions at about 4/5 of the Nyquist frequency, which is a vast improvement over the performance of conventional imaging media. We anticipate the unparalleled performance of this digital recording device will dramatically benefit cryo-EM for routine tomographic and single-particle structural determination of biological specimens.     

Three-dimensional spectral signal-to-noise ratio for a class of reconstruction algorithms

A three-dimensional (3D) version of the spectral signal-to-noise ratio (SSNR)-based resolution measure is introduced. The measure is defined for a class of 3D reconstruction algorithms that use interpolation in Fourier space. The statistical properties of the SSNR are discussed and related to the properties of another resolution measure, the Fourier shell correlation (FSC). The new measure was tested on 3D structures calculated from a simulated set of quasi-evenly spaced 2D projections using a nearest-neighbor interpolation and a gridding algorithm. In the latter case, the results agree very well with the FSC-based estimate, with the exception of very high SSNR values. The main applicability of the 3D SSNR is tomography, where due to the small number of projections collected, FSC cannot be used. The new measure was applied to three sets of tomographic data. It was demonstrated that the measure is sufficiently sensitive to yield theoretically expected results. Therefore, the 3D SSNR opens up the possibility of evaluating the quality of tomographic reconstructions in an objective manner. The 3D distribution of SSNR is of major interest in single-particle analysis. It is shown that the new measure can be used to evaluate the anisotropy of 3D reconstructions. The distribution of SSNR is characterized by three anisotropy indices derived from principal axes of the 3D inertia covariance matrix of the SSNR. These indices are used to construct a 3D Fourier filter which, when applied to a 3D reconstruction of a macromolecule, maximizes the SNR in real space and minimizes real-space artifacts caused by uneven distribution of 2D projections.     

Developing a denoising filter for electron microscopy and tomography data in the cloud

The low radiation conditions and the predominantly phase-object image formation of cryo-electron microscopy (cryo-EM) result in extremely high noise levels and low contrast in the recorded micrographs. The process of single particle or tomographic 3D reconstruction does not completely eliminate this noise and is even capable of introducing new sources of noise during alignment or when correcting for instrument parameters. The recently developed Digital Paths Supervised Variance (DPSV) denoising filter uses local variance information to control regional noise in a robust and adaptive manner. The performance of the DPSV filter was evaluated in this review qualitatively and quantitatively using simulated and experimental data from cryo-EM and tomography in two and three dimensions. We also assessed the benefit of filtering experimental reconstructions for visualization purposes and for enhancing the accuracy of feature detection. The DPSV filter eliminates high-frequency noise artifacts (density gaps), which would normally preclude the accurate segmentation of tomography reconstructions or the detection of alpha-helices in single-particle reconstructions. This collaborative software development project was carried out entirely by virtual interactions among the authors using publicly available development and file sharing tools.     

Analysis of Video-Based Microscopic Particle Trajectories Using Kalman Filtering

The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes.     

Detecting consistent common lines in cryo-EM by voting

The single-particle reconstruction problem of electron cryo-microscopy (cryo-EM) is to find the three-dimensional structure of a macromolecule given its two-dimensional noisy projection images at unknown random directions. Ab initio estimates of the 3D structure are often obtained by the “Angular Reconstitution” method, in which a coordinate system is established from three projections, and the orientation of the particle giving rise to each image is deduced from common lines among the images. However, a reliable detection of common lines is difficult due to the low signal-to-noise ratio of the images. In this paper we describe a global self-correcting voting procedure in which all projection images participate to decide the identity of the consistent common lines. The algorithm determines which common line pairs were detected correctly and which are spurious. We show that the voting procedure succeeds at relatively low detection rates and that its performance improves as the number of projection images increases. We demonstrate the algorithm for both simulative and experimental images of the 50S ribosomal subunit.     

In silico reconstitution of DNA replication. Lessons from single-molecule imaging and cryo-tomography applied to single-particle cryo-EM

DNA replication has been reconstituted in vitro with yeast proteins, and the minimal system requires the coordinated assembly of 16 distinct replication factors, consisting of 42 polypeptides. To understand the molecular interplay between these factors at the single residue level, new structural biology tools are being developed. Inspired by advances in single-molecule fluorescence imaging and cryo-tomography, novel single-particle cryo-EM experiments have been used to characterise the structural mechanism for the loading of the replicative helicase. Here, we discuss how in silico reconstitution of single-particle cryo-EM data can help describe dynamic systems that are difficult to approach with conventional three-dimensional classification tools.     

Automatic cryo-EM particle selection for membrane proteins in spherical liposomes

Random spherically constrained (RSC) single particle reconstruction is a method to obtain structures of membrane proteins embedded in lipid vesicles (liposomes). As in all single-particle cryo-EM methods, structure determination is greatly aided by reliable detection of protein “particles” in micrographs. After fitting and subtraction of the membrane density from a micrograph, normalized cross-correlation (NCC) and estimates of the particle signal amplitude are used to detect particles, using as references the projections of a 3D model. At each pixel position, the NCC is computed with only those references that are allowed by the geometric constraint of the particle’s embedding in the spherical vesicle membrane. We describe an efficient algorithm for computing this position-dependent correlation, and demonstrate its application to selection of membrane-protein particles, GluA2 glutamate receptors, which present very different views from different projection directions.     

A Bayesian view on cryo-EM structure determination

Three-dimensional (3D) structure determination by single-particle analysis of cryo-electron microscopy (cryo-EM) images requires many parameters to be determined from extremely noisy data. This makes the method prone to overfitting, that is, when structures describe noise rather than signal, in particular near their resolution limit where noise levels are highest. Cryo-EM structures are typically filtered using ad hoc procedures to prevent overfitting, but the tuning of arbitrary parameters may lead to subjectivity in the results. I describe a Bayesian interpretation of cryo-EM structure determination, where smoothness in the reconstructed density is imposed through a Gaussian prior in the Fourier domain. The statistical framework dictates how data and prior knowledge should be combined, so that the optimal 3D linear filter is obtained without the need for arbitrariness and objective resolution estimates may be obtained. Application to experimental data indicates that the statistical approach yields more reliable structures than existing methods and is capable of detecting smaller classes in data sets that contain multiple different structures.     

A novel mirror-symmetry analysis approach for the study of macromolecular assemblies imaged by electron microscopy

Multivariate statistical symmetry analysis is widely employed in single-particle electron-microscopy studies for the detection of symmetry components within a set of noisy two-dimensional images. So far, this technique has been used to retrieve information from the analysis of end-on view oriented particles only. Here, we propose a method to detect symmetry components from side- and tilted-view oriented particles. This method is validated using a number of in silico generated as well as real datasets, can be used to analyze stoichiometrically heterogeneous datasets, and is useful for separating particle datasets with respect to their symmetry components. Additionally, translational components in lock-washer ring configurations can be detected. Most relevantly, this method represents a powerful tool for the characterisation of distinct symmetry components within multi-layered protein assemblies, and any putative symmetry mismatch between layers. Such configurations have often been postulated, though rarely observed directly, and are thought to have a crucial role in conferring dynamicity to molecular machineries like nucleic acid packaging motors, ClpAP/ClpXP proteases, flagellar motors and the F1/F0 ATPase.     

Robust filtering and particle picking in micrograph images towards 3D reconstruction of purified proteins with cryo-electron microscopy

In order to make a high resolution model of macromolecular structures from cryo-electron microscope (cryo-EM) raw images one has to be precise at every processing step from particle picking to 3D image reconstruction. In this paper we propose a collection of novel methods for filtering cryo-EM images and for automatic picking of particles. These methods have been developed for two cases: (1) when particles can be identified and (2) when particle are not distinguishable. The advantages of these methods are demonstrated in standard purified protein samples and to generalize them we do not use any ad hoc presumption of the geometry of the particle projections. We have also suggested a filtering method to increase the signal-to-noise (S/N) ratio which has proved to be useful for other levels of reconstruction, i.e., finding orientations and 3D model reconstruction.     

A Local Agreement Filtering Algorithm for Transmission EM Reconstructions

We present LAFTER, an algorithm for de-noising single particle reconstructions from cryo-EM.Single particle analysis entails the reconstruction of high-resolution volumes from tens of thousands of particle images with low individual signal-to-noise. Imperfections in this process result in substantial variations in the local signal-to-noise ratio within the resulting reconstruction, complicating the interpretation of molecular structure. An effective local de-noising filter could therefore improve interpretability and maximise the amount of useful information obtained from cryo-EM maps.LAFTER is a local de-noising algorithm based on a pair of serial real-space filters. It compares independent half-set reconstructions to identify and retain shared features that have power greater than the noise. It is capable of recovering features across a wide range of signal-to-noise ratios, and we demonstrate recovery of the strongest features at Fourier shell correlation (FSC) values as low as 0.144 over a 256³-voxel cube. A fast and computationally efficient implementation of LAFTER is freely available.We also propose a new way to evaluate the effectiveness of real-space filters for noise suppression, based on the correspondence between two FSC curves: 1) the FSC between the filtered and unfiltered volumes, and 2) C_ref, the FSC between the unfiltered volume and a hypothetical noiseless volume, which can readily be estimated from the FSC between two half-set reconstructions.     

New insights into GPCR coupling and dimerisation from cryo-EM structures

Over the past three years (2020–2022) more structures of GPCRs have been determined than in the previous twenty years (2000–2019), primarily of GPCR complexes that are large enough for structure determination by single-particle cryo-EM. This review will present some structural highlights that have advanced our molecular understanding of promiscuous G protein coupling, how a G protein receptor kinase and β-arrestins couple to GPCRs, and GPCR dimerisation. We will also discuss advances in the use of gene fusions, nanobodies, and F_ab fragments to facilitate the structure determination of GPCRs in the inactive state that, on their own, are too small for structure determination by single-particle cryo-EM.     

Classical detection theory and the cryo-EM particle selection problem

Particle selection is an essential but tedious step in the determination of macromolecular structures by single particle reconstruction. This paper presents an automatic, multi-reference particle detection scheme that is based on the classical matched filter principle. It makes use of a pre-whitening filter to standardize the noise, a reduced representation of the references by means of principal component analysis, and a statistic for distinguishing particles from image artifacts. Standardizing the noise allows the noise-induced false-positive frequency to be estimated, and also allows the distribution of the discrimination statistic to be calculated a priori. The method is demonstrated with an annotated dataset of cryo-EM images.     

TMaCS: A hybrid template matching and classification system for partially-automated particle selection

Selection of particle images from electron micrographs presents a bottleneck in determining the structures of macromolecular assemblies by single particle electron cryomicroscopy (cryo-EM). The problem is particularly important when an experimentalist wants to improve the resolution of a 3D map by increasing by tens or hundreds of thousands of images the size of the dataset used for calculating the map. Although several existing methods for automatic particle image selection work well for large protein complexes that produce high-contrast images, it is well known in the cryo-EM community that small complexes that give low-contrast images are often refractory to existing automated particle image selection schemes. Here we develop a method for partially-automated particle image selection when an initial 3D map of the protein under investigation is already available. Candidate particle images are selected from micrographs by template matching with template images derived from projections of the existing 3D map. The candidate particle images are then used to train a support vector machine, which classifies the candidates as particle images or non-particle images. In a final step in the analysis, the selected particle images are subjected to projection matching against the initial 3D map, with the correlation coefficient between the particle image and the best matching map projection used to assess the reliability of the particle image. We show that this approach is able to rapidly select particle images from micrographs of a rotary ATPase, a type of membrane protein complex involved in many aspects of biology.     

Applications of the molecular dynamics flexible fitting method

In recent years, cryo-electron microscopy (cryo-EM) has established itself as a key method in structural biology, permitting the structural characterization of large biomolecular complexes in various functional states. The data obtained through single-particle cryo-EM has recently seen a leap in resolution thanks to landmark advances in experimental and computational techniques, resulting in sub-nanometer resolution structures being obtained routinely. The remaining gap between these data and revealing the mechanisms of molecular function can be closed through hybrid modeling tools that incorporate known atomic structures into the cryo-EM data. One such tool, molecular dynamics flexible fitting (MDFF), uses molecular dynamics simulations to combine structures from X-ray crystallography with cryo-EM density maps to derive atomic models of large biomolecular complexes. The structures furnished by MDFF can be used subsequently in computational investigations aimed at revealing the dynamics of the complexes under study. In the present work, recent applications of MDFF are presented, including the interpretation of cryo-EM data of the ribosome at different stages of translation and the structure of a membrane-curvature-inducing photosynthetic complex.