Detecting circular and rectangular particles based on geometric feature detection in electron micrographs

Accurate and automatic particle detection from cryo-electron microscopy (cryo-EM images) is very important for high-resolution reconstruction of large macromolecular structures. In this paper, we present a method for particle picking based on shape feature detection. Two fundamental concepts of computational geometry, namely, the distance transform and the Voronoi diagram, are used for detection of critical features as well as for accurate location of particles from the images or micrographs. Unlike the conventional template-matching methods, our approach detects the particles based on their boundary features instead of intensities. The geometric features derived from the boundaries provide an efficient way for locating particles quickly and accurately, which avoids a brute-force searching for the best position/orientation. Our approach is fully automatic and has been successfully applied to detect particles with approximately circular or rectangular shapes (e.g., KLH particles). Particle detection can be enhanced by multiple sets of parameters used in edge detection and/or by anisotropic filtering. We also discuss the extension of this approach to other types of particles with certain geometric features.     

Cryo-electron microscope image denoising based on the geodesic distance

Background

To perform a three-dimensional (3-D) reconstruction of electron cryomicroscopy (cryo-EM) images of viruses, it is necessary to determine the similarity of image blocks of the two-dimensional (2-D) projections of the virus. The projections containing high resolution information are typically very noisy. Instead of the traditional Euler metric, this paper proposes a new method, based on the geodesic metric, to measure the similarity of blocks.

Results

Our method is a 2-D image denoising approach. A data set of 2243 cytoplasmic polyhedrosis virus (CPV) capsid particle images in different orientations was used to test the proposed method. Relative to Block-matching and three-dimensional filtering (BM3D), Stein’s unbiased risk estimator (SURE), Bayes shrink and K-means singular value decomposition (K-SVD), the experimental results show that the proposed method can achieve a peak signal-to-noise ratio (PSNR) of 45.65. The method can remove the noise from the cryo-EM image and improve the accuracy of particle picking.

Conclusions

The main contribution of the proposed model is to apply the geodesic distance to measure the similarity of image blocks. We conclude that manifold learning methods can effectively eliminate the noise of the cryo-EM image and improve the accuracy of particle picking.

     

An adaptation of the Wiener filter suitable for analyzing images of isolated single particles

The Wiener filter is a standard means of optimizing the signal in sums of aligned, noisy images obtained by electron cryo-microscopy (cryo-EM). However, estimation of the resolution-dependent (“spectral”) signal-to-noise ratio (SSNR) from the input data has remained problematic, and error reduction due to specific application of the SSNR term within a Wiener filter has not been reported. Here we describe an adjustment to the Wiener filter for optimal summation of images of isolated particles surrounded by large regions of featureless background, as is typically the case in single-particle cryo-EM applications. We show that the density within the particle area can be optimized, in the least-squares sense, by scaling the SSNR term found in the conventional Wiener filter by a factor that reflects the fraction of the image field occupied by the particle. We also give related expressions that allow the SSNR to be computed for application in this new filter, by incorporating a masking step into a Fourier Ring Correlation (FRC), a standard resolution measure. Furthermore, we show that this masked FRC estimation scheme substantially improves on the accuracy of conventional SSNR estimation methods. We demonstrate the validity of our new approach in numeric tests with simulated data corresponding to realistic cryo-EM imaging conditions. This variation of the Wiener filter and accompanying derivation should prove useful for a variety of single-particle cryo-EM applications, including 3D reconstruction.     

Fast automatic particle picking from cryo-electron micrographs using a locally normalized cross-correlation function: a case study

Recent progress in single-particle reconstruction methods and cryo-EM techniques has led to the determination of macromolecular structures with unprecedented resolution. The number of particles that goes into the reconstruction is a key determinant in achieving high resolution. Interactive manual picking of particles from an electron micrograph is a very time-consuming, tedious, and inefficient process. We have implemented a fast automatic particle picking procedure in the SPIDER environment. The procedure makes use of template matching schemes and employs a recently developed locally normalized correlation algorithm based on Fourier techniques. As a test, we have used this procedure to pick 70S Escherichia coli ribosomes from a cryo-electron micrograph. Different search strategies including use of a circular mask and asymmetric masks for different orientations of the particle have been explored, and their relative efficiencies are discussed. The results indicate that the procedure can be optimally used to pick ribosomes in a fully automatic way within the limit of selecting less than 10% false positives while missing about 15% of true positives.     

Deep generative modeling for volume reconstruction in cryo-electron microscopy

Advances in cryo-electron microscopy (cryo-EM) for high-resolution imaging of biomolecules in solution have provided new challenges and opportunities for algorithm development for 3D reconstruction. Next-generation volume reconstruction algorithms that combine generative modelling with end-to-end unsupervised deep learning techniques have shown promise, but many technical and theoretical hurdles remain, especially when applied to experimental cryo-EM images. In light of the proliferation of such methods, we propose here a critical review of recent advances in the field of deep generative modelling for cryo-EM reconstruction. The present review aims to (i) provide a unified statistical framework using terminology familiar to machine learning researchers with no specific background in cryo-EM, (ii) review the current methods in this framework, and (iii) outline outstanding bottlenecks and avenues for improvements in the field.     

Conformational heterogeneity and probability distributions from single-particle cryo-electron microscopy

Single-particle cryo-electron microscopy (cryo-EM) is a technique that takes projection images of biomolecules frozen at cryogenic temperatures. A major advantage of this technique is its ability to image single biomolecules in heterogeneous conformations. While this poses a challenge for data analysis, recent algorithmic advances have enabled the recovery of heterogeneous conformations from the noisy imaging data. Here, we review methods for the reconstruction and heterogeneity analysis of cryo-EM images, ranging from linear-transformation-based methods to nonlinear deep generative models. We overview the dimensionality-reduction techniques used in heterogeneous 3D reconstruction methods and specify what information each method can infer from the data. Then, we review the methods that use cryo-EM images to estimate probability distributions over conformations in reduced subspaces or predefined by atomistic simulations. We conclude with the ongoing challenges for the cryo-EM community.     

Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction

Cryo-electron microscopy (cryo-EM), combined with image processing, is an increasingly powerful tool for structure determination of macromolecular protein complexes and assemblies. In fact, single particle electron microscopy¹ and two-dimensional (2D) electron crystallography² have become relatively routine methodologies and a large number of structures have been solved using these methods. At the same time, image processing and three-dimensional (3D) reconstruction of helical objects has rapidly developed, especially, the iterative helical real-space reconstruction (IHRSR) method³, which uses single particle analysis tools in conjunction with helical symmetry. Many biological entities function in filamentous or helical forms, including actin filaments⁴, microtubules⁵, amyloid fibers⁶, tobacco mosaic viruses⁷, and bacteria flagella⁸, and, because a 3D density map of a helical entity can be attained from a single projection image, compared to the many images required for 3D reconstruction of a non-helical object, with the IHRSR method, structural analysis of such flexible and disordered helical assemblies is now attainable.In this video article, we provide detailed protocols for obtaining a 3D density map of a helical protein assembly (HIV-1 capsid⁹ is our example), including protocols for cryo-EM specimen preparation, low dose data collection by cryo-EM, indexing of helical diffraction patterns, and image processing and 3D reconstruction using IHRSR. Compared to other techniques, cryo-EM offers optimal specimen preservation under near native conditions. Samples are embedded in a thin layer of vitreous ice, by rapid freezing, and imaged in electron microscopes at liquid nitrogen temperature, under low dose conditions to minimize the radiation damage. Sample images are obtained under near native conditions at the expense of low signal and low contrast in the recorded micrographs. Fortunately, the process of helical reconstruction has largely been automated, with the exception of indexing the helical diffraction pattern. Here, we describe an approach to index helical structure and determine helical symmetries (helical parameters) from digitized micrographs, an essential step for 3D helical reconstruction. Briefly, we obtain an initial 3D density map by applying the IHRSR method. This initial map is then iteratively refined by introducing constraints for the alignment parameters of each segment, thus controlling their degrees of freedom. Further improvement is achieved by correcting for the contrast transfer function (CTF) of the electron microscope (amplitude and phase correction) and by optimizing the helical symmetry of the assembly.     

Automatic particle selection from electron micrographs using machine learning techniques

The 3D reconstruction of biological specimens using Electron Microscopy is currently capable of achieving subnanometer resolution. Unfortunately, this goal requires gathering tens of thousands of projection images that are frequently selected manually from micrographs. In this paper we introduce a new automatic particle selection that learns from the user which particles are of interest. The training phase is semi-supervised so that the user can correct the algorithm during picking and specifically identify incorrectly picked particles. By treating such errors specially, the algorithm attempts to minimize the number of false positives. We show that our algorithm is able to produce datasets with fewer wrongly selected particles than previously reported methods. Another advantage is that we avoid the need for an initial reference volume from which to generate picking projections by instead learning which particles to pick from the user. This package has been made publicly available in the open-source package Xmipp.     

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.     

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.     

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.     

Auto-accumulation method using simulated annealing enables fully automatic particle pickup completely free from a matching template or learning data

Single-particle analysis is a 3-D structure determining method using electron microscopy (EM). In this method, a large number of projections is required to create 3-D reconstruction. In order to enable completely automatic pickup without a matching template or a training data set, we established a brand-new method in which the frames to pickup particles are randomly shifted and rotated over the electron micrograph and, using the total average image of the framed images as an index, each frame reaches a particle. In this process, shifts are selected to increase the contrast of the average. By iterated shifts and further selection of the shifts, the frames are induced to shift so as to surround particles. In this algorithm, hundreds of frames are initially distributed randomly over the electron micrograph in which multi-particle images are dispersed. Starting with these frames, one of them is selected and shifted randomly, and acceptance or non-acceptance of its new position is judged using the simulated annealing (SA) method in which the contrast score of the total average image is adopted as an index. After iteration of this process, the position of each frame converges so as to surround a particle and the framed images are picked up. This method is the first unsupervised fully automatic particle picking method which is applicable to EM of various kinds of proteins, especially to low-contrasted cryo-EM protein images.     

A Zernike-moment-based non-local denoising filter for cryo-EM images

Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other methods such as X-ray crystallography and nuclear magnetic resonance analysis find difficult. The signal-to-noise ratio of cryo-EM images is low and the contrast is very weak, and therefore, the images are very noisy and require filtering. In this paper, a filtering method based on non-local means and Zernike moments is proposed. The method takes into account the rotational symmetry of some biological molecules to enhance the signal-to-noise ratio of cryo-EM images. The method may be useful in cryo-EM image processing such as the automatic selection of particles, orientation determination, and the building of initial models.     

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.     

Model-based particle picking for cryo-electron microscopy

We describe an algorithm for finding particle images in cryo-EM micrographs. The algorithm starts from a crude 3D map of the target particle, computed from a relatively small number of manually picked images, and then projects the map in many different directions to give synthetic 2D templates. The templates are clustered and averaged and then cross-correlated with the micrographs. A probabilistic model of the imaging process then scores cross-correlation peaks to produce the final picks. We give quantitative results on two quite different target particles: keyhole limpet hemocyanin and p97 AAA ATPase. On these particles our automatic particle picker shows human performance level, as measured by the Fourier shell correlations of 3D reconstructions.     

Rapid increase of near atomic resolution virus capsid structures determined by cryo-electron microscopy

The recent technological advances in electron microscopes, detectors, as well as image processing and reconstruction software have brought single particle cryo-electron microscopy (cryo-EM) into prominence for determining structures of bio-molecules at near atomic resolution. This has been particularly true for virus capsids, ribosomes, and other large assemblies, which have been the ideal specimens for structural studies by cryo-EM approaches. An analysis of time series metadata of virus structures on the methods of structure determination, resolution of the structures, and size of the virus particles revealed a rapid increase in the virus structures determined by cryo-EM at near atomic resolution since 2010. In addition, the data highlight the median resolution (～3.0?Å) and size (～310.0?Å in diameter) of the virus particles determined by X-ray crystallography while no such limits exist for cryo-EM structures, which have a median diameter of 508?Å. Notably, cryo-EM virus structures in the last four years have a median resolution of 3.9?Å. Taken together with minimal sample requirements, not needing diffraction quality crystals, and being able to achieve similar resolutions of the crystal structures makes cryo-EM the method of choice for current and future virus capsid structure determinations.     

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.     

Wavelets filtering for classification of very noisy electron microscopic single particles images- application on structure determination of VP5-VP19C recombinant

Background

Images of frozen hydrated [vitrified] virus particles were taken close-to-focus in an electron microscope containing structural signals at high spatial frequencies. These images had very low contrast due to the high levels of noise present in the image. The low contrast made particle selection, classification and orientation determination very difficult. The final purpose of the classification is to improve the signal-to-noise ratio of the particle representing the class, which is usually the average. In this paper, the proposed method is based on wavelet filtering and multi-resolution processing for the classification and reconstruction of this very noisy data. A multivariate statistical analysis (MSA) is used for this classification.

Results

The MSA classification method is noise dependant. A set of 2600 projections from a 3D map of a herpes simplex virus -to which noise was added- was classified by MSA. The classification shows the power of wavelet filtering in enhancing the quality of class averages (used in 3D reconstruction) compared to Fourier band pass filtering. A 3D reconstruction of a recombinant virus (VP5-VP19C) is presented as an application of multi-resolution processing for classification and reconstruction.

Conclusion

The wavelet filtering and multi-resolution processing method proposed in this paper offers a new way for processing very noisy images obtained from electron cryo-microscopes. The multi-resolution and filtering improves the speed and accuracy of classification, which is vital for the 3D reconstruction of biological objects. The VP5-VP19C recombinant virus reconstruction presented here is an example, which demonstrates the power of this method. Without this processing, it is not possible to get the correct 3D map of this virus.

     

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.     

Streptavidin crystals as nanostructured supports and image-calibration references for cryo-EM data collection

For cryo-EM structural studies, we seek to image membrane proteins as single particles embedded in proteoliposomes. One technical difficulty has been the low density of liposomes that can be trapped in the approximately 100nm ice layer that spans holes in the perforated carbon support film of EM grids. Inspired by the use of two-dimensional (2D) streptavidin crystals as an affinity surface for biotinylated DNA (Crucifix et al., 2004), we propose to use the crystals to tether liposomes doped with biotinylated lipids. The 2D crystal image also serves as a calibration of the image formation process, providing an absolute conversion from electrostatic potentials in the specimen to the EM image intensity, and serving as a quality control of acquired cryo-EM images. We were able to grow streptavidin crystals covering more than 90% of the holes in an EM grid, and which remained stable even under negative stain. The liposome density in the resulting cryo-EM sample was uniform and high due to the high-affinity binding of biotin to streptavidin. Using computational methods, the 2D crystal background can be removed from images without noticeable effect on image properties.