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.     

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.

     

Cryo-EM image alignment: From pair-wise to joint with deep unsupervised difference learning

Cryo-electron microscopy (cryo-EM) single-particle analysis is a revolutionary imaging technique to resolve and visualize biomacromolecules. Image alignment in cryo-EM is an important and basic step to improve the precision of the image distance calculation. However, it is a very challenging task due to high noise and low signal-to-noise ratio. Therefore, we propose a new deep unsupervised difference learning (UDL) strategy with novel pseudo-label guided learning network architecture and apply it to pair-wise image alignment in cryo-EM. The training framework is fully unsupervised. Furthermore, a variant of UDL called joint UDL (JUDL), is also proposed, which is capable of utilizing the similarity information of the whole dataset and thus further increase the alignment precision. Assessments on both real-world and synthetic cryo-EM single-particle image datasets suggest the new unsupervised joint alignment method can achieve more accurate alignment results. Our method is highly efficient by taking advantages of GPU devices. The source code of our methods is publicly available at “http://www.csbio.sjtu.edu.cn/bioinf/JointUDL/” for academic use.     

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.     

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.     

Noise Reduction in Electron Tomographic Reconstructions Using Nonlinear Anisotropic Diffusion

Electron tomography is a powerful technique capable of giving unique insights into the three-dimensional structural organization of pleomorphic biological objects. However, visualization and interpretation of the resulting volumetric data are hampered by an extremely low signal-to-noise ratio, especially when ice-embedded biological specimens are investigated. Usually, isosurface representation or volume rendering of such data is hindered without any further signal enhancement. We propose a novel technique for noise reduction based on nonlinear anisotropic diffusion. The approach combines efficient noise reduction with excellent signal preservation and is clearly superior to conventional methods (e.g., low-pass and median filtering) and invariant wavelet transform filtering. The gain in the signal-to-noise ratio is verified and demonstrated by means of Fourier shell correlation. Improved visualization performance after processing the 3D images is demonstrated with two examples, tomographic reconstructions of chromatin and of a mitochondrion. Parameter settings and discretization stencils are presented in detail.     

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.     

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.

     

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.     

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.     

The resolution dependence of optimal exposures in liquid nitrogen temperature electron cryomicroscopy of catalase crystals

Electron beam damage is the fundamental limit to resolution in electron cryomicroscopy (cryo-EM) of frozen, hydrated specimens. Radiation damage increases with the number of electrons used to obtain an image and affects information at higher spatial frequencies before low-resolution information. For the experimentalist, a balance exists between electron exposures sufficient to obtain a useful signal-to-noise ratio (SNR) in images and exposures that limit the damage to structural features. In single particle cryo-EM this balance is particularly delicate: low-resolution features must be imaged with a sufficient SNR to allow image alignment so that high-resolution features recorded below the noise level can be recovered by averaging independent images. By measuring the fading of Fourier components from images obtained at 200 kV of thin crystals of catalase embedded in ice, we have determined the electron exposures that will maximize the SNR at resolutions between 86 and 2.9 Å. These data allow for a rational choice of exposure for single particle cryo-EM. For example, for 20 Å resolution, the SNR is maximized at ～20 e^?/Ų, whereas for 3 Å resolution, it is maximized at ～10 e^?/Ų. We illustrate the effects of exposure in single particle cryo-EM with data collected at ～12–15 and ～24–30 e^?/Ų.     

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.     

Practical performance evaluation of a 10k × 10k CCD for electron cryo-microscopy

Electron cryo-microscopy (cryo-EM) images are commonly collected using either charge-coupled devices (CCD) or photographic film. Both film and the current generation of 16 megapixel (4k × 4k) CCD cameras have yielded high-resolution structures. Yet, despite the many advantages of CCD cameras, more than two times as many structures of biological macromolecules have been published in recent years using photographic film. The continued preference to film, especially for subnanometer-resolution structures, may be partially influenced by the finer sampling and larger effective specimen imaging area offered by film. Large format digital cameras may finally allow them to overtake film as the preferred detector for cryo-EM. We have evaluated a 111-megapixel (10k × 10k) CCD camera with a 9 μm pixel size. The spectral signal-to-noise ratios of low dose images of carbon film indicate that this detector is capable of providing signal up to at least 2/5 Nyquist frequency potentially retrievable for 3D reconstructions of biological specimens, resulting in more than double the effective specimen imaging area of existing 4k × 4k CCD cameras. We verified our estimates using frozen-hydrated ε15 bacteriophage as a biological test specimen with previously determined structure, yielding a ～7 ? resolution single particle reconstruction from only 80 CCD frames. Finally, we explored the limits of current CCD technology by comparing the performance of this detector to various CCD cameras used for recording data yielding subnanometer resolution cryo-EM structures submitted to the electron microscopy data bank (http://www.emdatabank.org/).     

基于Renyi熵滤波的光声图像重建算法设计与实现

针对光声图像重建过程中存在的原始光声信号信噪比差、重建图像对比度低、分辨率不足等问题,提出了基于Renyi熵的光声图像重建滤波算法.该算法首先根据原始光声信号的Renyi熵分布情况,确定分割阈值,并滤除杂波信号;再利用滤波后的光声数据进行延时叠加光声图像重建.利用该滤波算法分别处理铅笔芯横截面(零维)、头发丝(一维)以及小鼠大脑皮层血管(二维)等不同维度样本的光声信号,实验结果表明:相比Renyi熵处理之前,重建图像对比度平均增强了32.45%,分辨率平均提高了30.78%,信噪比提高了47.66%,均方误差降低了35.01%;相比典型的滤波处理算法(模极大值法和阈值去噪法),本研究中图像的对比度、分辨率和信噪比分别提高了25.94%/10.60%、27.90%/19.48%、35.21%/10.60%,均方误差减小了28.57%/16.66%.因此,选择利用Renyi熵滤波算法处理光声信号,从而使光声图像重建质量得到大幅改善.     

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.     

Vitrification of thick samples for soft X-ray cryo-tomography by high pressure freezing

Soft X-ray cryo-microscopy (cryo-XT) offers an ideal complement to electron cryo-microscopy (cryo-EM). Cryo-XT is applicable to samples more than an order of magnitude thicker than cryo-EM, albeit at a more modest resolution of tens of nanometers. Furthermore, the natural contrast obtained in the “water-window” by differential absorption by organic matter vs water yields detailed images of organelles, membranes, protein complexes, and other cellular components. Cryo-XT is thus ideally suited for tomography of eukaryotic cells. The increase in sample thickness places more stringent demands on sample preparation, however. The standard method for cryo-EM, i.e., plunging to a cryogenic fluid such as liquid ethane, is no longer ideally suited to obtain vitrification of thick samples for cryo-XT. High pressure freezing is an alternative approach, most closely associated with freeze-substitution and embedding, or with electron cryo-microscopy of vitreous sections (CEMOVIS). We show here that high pressure freezing can be adapted to soft X-ray tomography of whole vitrified samples, yielding a highly reliable method that avoids crystallization artifacts and potentially offers improved imaging conditions in samples not amenable to plunge-freezing.     

Preprocessing of two-dimensional gel electrophoresis images

Proteomics produces a huge amount of two-dimensional gel electrophoresis images. Their analysis can yield a lot of information concerning proteins responsible for different diseases or new unidentified proteins. However, an automatic analysis of such images requires an efficient tool for reducing noise in images. This allows proper detection of the spots' borders, which is important in protein quantification (as the spots' areas are used to determine the amounts of protein present in an analyzed mixture). Also in the feature-based matching methods the detected features (spots) can be described by additional attributes, such as area or shape. In our study, a comparison of different methods of noise reduction is performed in order to find out a method best suited for reducing noise in gel images. Among the compared methods there are the classical methods of linear filtering, e.g., the mean and Gaussian filtering, the nonlinear method, i.e., median filtering, and also the methods better suited for processing of nonstationary signals, such as spatially adaptive linear filtering and filtering in the wavelet domain. The best results are obtained by filtering of gel images in the wavelet domain, using the BayesThresh method of threshold value determination.     

Mean curvature motion facilitates the segmentation and surface visualization of electron tomograms

Three-dimensional visualization of biological samples is essential for understanding their architecture and function. However, it is often challenging due to the macromolecular crowdedness of the samples and low signal-to-noise ratio of the cryo-electron tomograms. Denoising and segmentation techniques address this challenge by increasing the signal-to-noise ratio and by simplifying the data in images. Here, mean curvature motion is presented as a method that can be applied to segmentation results, created either manually or automatically, to significantly improve both the visual quality and downstream computational handling. Mean curvature motion is a process based on nonlinear anisotropic diffusion that smooths along edges and causes high-curvature features, such as noise, to disappear. In combination with level-set methods for image erosion and dilation, the application of mean curvature motion to electron tomograms and segmentations removes sharp edges or spikes in the visualized surfaces, produces an improved surface quality, and improves overall visualization and interpretation of the three-dimensional images.     

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.     

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach.