Cryo-EM image alignment based on nonuniform fast Fourier transform

Simcryocluster: a semantic similarity clustering method of cryo-EM images by adopting contrastive learning

BACKGROUND

Cryo-electron microscopy (Cryo-EM) plays an increasingly important role in the determination of the three-dimensional (3D) structure of macromolecules. In order to achieve 3D reconstruction results close to atomic resolution, 2D single-particle image classification is not only conducive to single-particle selection, but also a key step that affects 3D reconstruction. The main task is to cluster and align 2D single-grain images into non-heterogeneous groups to obtain sharper single-grain images by averaging calculations. The main difficulties are that the cryo-EM single-particle image has a low signal-to-noise ratio (SNR), cannot manually label the data, and the projection direction is random and the distribution is unknown. Therefore, in the low SNR scenario, how to obtain the characteristic information of the effective particles, improve the clustering accuracy, and thus improve the reconstruction accuracy, is a key problem in the 2D image analysis of single particles of cryo-EM.

RESULTS

Aiming at the above problems, we propose a learnable deep clustering method and a fast alignment weighted averaging method based on frequency domain space to effectively improve the class averaging results and improve the reconstruction accuracy. In particular, it is very prominent in the feature extraction and dimensionality reduction module. Compared with the classification method based on Bayesian and great likelihood, a large amount of single particle data is required to estimate the relative angle orientation of macromolecular single particles in the 3D structure, and we propose that the clustering method shows good results.

CONCLUSIONS

SimcryoCluster can use the contrastive learning method to perform well in the unlabeled high-noise cryo-EM single particle image classification task, making it an important tool for cryo-EM protein structure determination.

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.

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.

Fast Cryo-EM Image Alignment Algorithm Using Power Spectrum Features

Cryo-electron microscopy (cryo-EM) single-particle image analysis is a powerful technique to resolve structures of biomacromolecules, while the challenge is that the cryo-EM image is of a low signal-to-noise ratio. For both two-dimensional image analysis and three-dimensional density map analysis, image alignment is an important step to improve the precision of the image distance calculation. In this paper, we introduce a new algorithm for performing two-dimensional pairwise alignment for cryo-EM particle images, which is based on the Fourier transform and power spectrum analysis. Compared to the existing heuristic iterative alignment methods, our method utilizes the signal distribution and signal feature on images' power spectrum to directly compute the alignment parameters. It does not require iterative computations and is robust against the cryo-EM image noise. Both theoretical analysis and experimental results suggest that our power-spectrum-feature-based alignment method is highly computational-efficient and is capable of offering effective alignment results. This new alignment algorithm is publicly available at: www.csbio.sjtu.edu.cn/bioinf/EMAF/for academic use.

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Single-particle cryo-electron microscopy (cryo-EM) reconstructs the three-dimensional (3D) structure of biomolecules from a large set of 2D projection images with random and unknown orientations. A crucial step in the single-particle cryo-EM pipeline is 3D refinement, which resolves a highresolution 3D structure from an initial approximate volume by refining the estimation of the orientation of each projection. In this work, we propose a new approach that refines the projection angles on the continuum. We formulate the optimization problem over the density map and the orientations jointly. The density map is updated using the efficient alternating-direction method of multipliers, while the orientations are updated through a semicoordinate- wise gradient descent for which we provide an explicit derivation of the gradient. Our method eliminates the requirement for a fine discretization of the orientation space and does away with the classical but computationally expensive templatematching step. Numerical results demonstrate the feasibility and performance of our approach compared to several baselines.

A joint method for marker-free alignment of tilt series in electron tomography

MOTIVATION

Electron tomography (ET) is a widely used technology for 3D macro-molecular structure reconstruction. To obtain a satisfiable tomogram reconstruction, several key processes are involved, one of which is the calibration of projection parameters of the tilt series. Although fiducial marker-based alignment for tilt series has been well studied, marker-free alignment remains a challenge, which requires identifying and tracking the identical objects (landmarks) through different projections. However, the tracking of these landmarks is usually affected by the pixel density (intensity) change caused by the geometry difference in different views. The tracked landmarks will be used to determine the projection parameters. Meanwhile, different projection parameters will also affect the localization of landmarks. Currently, there is no alignment method that takes interrelationship between the projection parameters and the landmarks.

RESULTS

Here, we propose a novel, joint method for marker-free alignment of tilt series in ET, by utilizing the information underlying the interrelationship between the projection model and the landmarks. The proposed method is the first joint solution that combines the extrinsic (track-based) alignment and the intrinsic (intensity-based) alignment, in which the localization of landmarks and projection parameters keep refining each other until convergence. This iterative approach makes our solution robust to different initial parameters and extreme geometric changes, which ensures a better reconstruction for marker-free ET. Comprehensive experimental results on three real datasets show that our new method achieved a significant improvement in alignment accuracy and reconstruction quality, compared to the state-of-the-art methods.

AVAILABILITY AND IMPLEMENTATION

The main program is available at https://github.com/icthrm/joint-marker-free-alignment.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Single-particle XFEL 3D reconstruction of ribosome-size particles based on Fourier slice matching: requirements to reach subnanometer resolution

Three-dimensional (3D) structures of biomolecules provide insight into their functions. Using X-ray free-electron laser (XFEL) scattering experiments, it was possible to observe biomolecules that are difficult to crystallize, under conditions that are similar to their natural environment. However, resolving 3D structure from XFEL data is not without its challenges. For example, strong beam intensity is required to obtain sufficient diffraction signal and the beam incidence angles to the molecule need to be estimated for diffraction patterns with significant noise. Therefore, it is important to quantitatively assess how the experimental conditions such as the amount of data and their quality affect the expected resolution of the resulting 3D models. In this study, as an example, the restoration of 3D structure of ribosome from two-dimensional diffraction patterns created by simulation is shown. Tests are performed using the diffraction patterns simulated for different beam intensities and using different numbers of these patterns. Guidelines for selecting parameters for slice-matching 3D reconstruction procedures are established. Also, the minimum requirements for XFEL experimental conditions to obtain diffraction patterns for reconstructing molecular structures to a high-resolution of a few nanometers are discussed.

Single-particle cryo-EM-Improved ab initio 3D reconstruction with SIMPLE/PRIME

Cryogenic electron microscopy (cryo-EM) and single-particle analysis now enables the determination of high-resolution structures of macromolecular assemblies that have resisted X-ray crystallography and other approaches. We developed the SIMPLE open-source image-processing suite for analysing cryo-EM images of single-particles. A core component of SIMPLE is the probabilistic PRIME algorithm for identifying clusters of images in 2D and determine relative orientations of single-particle projections in 3D. Here, we extend our previous work on PRIME and introduce new stochastic optimization algorithms that improve the robustness of the approach. Our refined method for identification of homogeneous subsets of images in accurate register substantially improves the resolution of the cluster centers and of the ab initio 3D reconstructions derived from them. We now obtain maps with a resolution better than 10 Å by exclusively processing cluster centers. Excellent parallel code performance on over-the-counter laptops and CPU workstations is demonstrated.

Refined Cryo-EM Structure of the T4 Tail Tube: Exploring the Lowest Dose Limit

The bacteriophage T4 contractile tail (containing a tube and sheath) was the first biological assembly reconstructed in three dimensions by electron microscopy at a resolution of ∼35 Å in 1968. A single-particle reconstruction of the T4 baseplate was able to generate a 4.1 Å resolution map for the first two rings of the tube using the overall baseplate for alignment. We have now reconstructed the T4 tail tube at a resolution of 3.4 Å, more than a 1,000-fold increase in information content for the tube from 1968. We have used legacy software (Spider) to show that we can do better than the typical 2/3 Nyquist frequency. A reasonable map can be generated with only 1.5 electrons/Ų using the higher dose images for alignment, but increasing the dose results in a better map, consistent with other reports that electron dose does not represent the main limitation on resolution in cryo-electron microscopy.

Three-dimensional reconstruction for coherent diffraction patterns obtained by XFEL

The three-dimensional (3D) structural analysis of single particles using an X-ray free-electron laser (XFEL) is a new structural biology technique that enables observations of molecules that are difficult to crystallize, such as flexible biomolecular complexes and living tissue in the state close to physiological conditions. In order to restore the 3D structure from the diffraction patterns obtained by the XFEL, computational algorithms are necessary as the orientation of the incident beam with respect to the sample needs to be estimated. A program package for XFEL single-particle analysis based on the Xmipp software package, that is commonly used for image processing in 3D cryo-electron microscopy, has been developed. The reconstruction program has been tested using diffraction patterns of an aerosol nanoparticle obtained by tomographic coherent X-ray diffraction microscopy.

A Stochastic Hill Climbing Approach for Simultaneous 2D Alignment and Clustering of Cryogenic Electron Microscopy Images

A critical step in the analysis of novel cryogenic electron microscopy (cryo-EM) single-particle datasets is the identification of homogeneous subsets of images. Methods for solving this problem are important for data quality assessment, ab initio 3D reconstruction, and analysis of population diversity due to the heterogeneous nature of macromolecules. Here we formulate a stochastic algorithm for identification of homogeneous subsets of images. The purpose of the method is to generate improved 2D class averages that can be used to produce a reliable 3D starting model in a rapid and unbiased fashion. We show that our method overcomes inherent limitations of widely used clustering approaches and proceed to test the approach on six publicly available experimental cryo-EM datasets. We conclude that, in each instance, ab initio 3D reconstructions of quality suitable for initialization of high-resolution refinement are produced from the cluster centers.

Principles of cryo-EM single-particle image processing

Single-particle reconstruction is the process by which 3D density maps are obtained from a set of low-dose cryo-EM images of individual macromolecules. This review considers the fundamental principles of this process and the steps in the overall workflow for single-particle image processing. Also considered are the limits that image signal-to-noise ratio places on resolution and the distinguishing of heterogeneous particle populations.

Cryogenic electron microscopy and single-particle analysis

About 20 years ago, the first three-dimensional (3D) reconstructions at subnanometer (<10-Å) resolution of an icosahedral virus assembly were obtained by cryogenic electron microscopy (cryo-EM) and single-particle analysis. Since then, thousands of structures have been determined to resolutions ranging from 30 Å to near atomic (<4 Å). Almost overnight, the recent development of direct electron detectors and the attendant improvement in analysis software have advanced the technology considerably. Near-atomic-resolution reconstructions can now be obtained, not only for megadalton macromolecular complexes or highly symmetrical assemblies but also for proteins of only a few hundred kilodaltons. We discuss the developments that led to this breakthrough in high-resolution structure determination by cryo-EM and point to challenges that lie ahead.

Magnetic microbubble-mediated ultrasound-MRI registration based on robust optical flow model

Background

As a dual-modality contrast agent, magnetic microbubbles (MMBs) can not only improve contrast of ultrasound (US) image, but can also serve as a contrast agent of magnetic resonance image (MRI). With the help of MMBs, a new registration method between US image and MRI is presented.

Methods

In this method, MMBs were used in both ultrasound and magnetic resonance imaging process to enhance the most important information of interest. In order to reduce the influence of the speckle noise to registration, semi-automatic segmentations of US image and MRI were carried out by using active contour model. After that, a robust optical flow model between US image segmentation (floating image) and MRI segmentation (reference image) was built, and the vector flow field was estimated by using the Coarse-to-fine Gaussian pyramid and graduated non-convexity (GNC) schemes.

Results

Qualitative and quantitative analyses of multiple group comparison experiments showed that registration results using all methods tested in this paper without MMBs were unsatisfactory. On the contrary, the proposed method combined with MMBs led to the best registration results.

Conclusion

The proposed algorithm combined with MMBs contends with larger deformation and performs well not only for local deformation but also for global deformation. The comparison experiments also demonstrated that ultrasound-MRI registration using the above-mentioned method might be a promising method for obtaining more accurate image information.

Oriented matrix promotes directional tubulogenesis

Detailed control over the structural organization of scaffolds and engineered tissue constructs is a critical need in the quest to engineer functional tissues using biomaterials. This work presents a new approach to spatially direct endothelial tubulogenesis. Micropatterned fibronectin substrates were used to control lung fibroblast adhesion and growth and the subsequent deposition of fibroblast-derived matrix during culture. The fibroblast-derived matrix produced on the micropatterned substrates was tightly oriented by these patterns, with an average variation of only 8.5°. Further, regions of this oriented extracellular matrix provided directional control of developing endothelial tubes to within 10° of the original micropatterned substrate design. Endothelial cells seeded directly onto the micropatterned substrate did not form tubes. A metric for matrix anisotropy showed a relationship between the fibroblast-derived matrix and the endothelial tubes that were subsequently developed on the same micropatterns with a resulting aspect ratio over 1.5 for endothelial tubulogenesis. Micropatterns in "L" and "Y" shapes were used to direct endothelial tubes to turn and branch with the same level of precision. These data demonstrate that anisotropic fibroblast-derived matrices instruct the alignment and shape of endothelial tube networks, thereby introducing an approach that could be adapted for future design of microvascular implants featuring organ-specific natural matrix that patterns microvascular growth.

Structure of the mammalian 80S initiation complex with initiation factor 5B on HCV-IRES RNA

The universally conserved eukaryotic initiation factor (eIF) 5B, a translational GTPase, is essential for canonical translation initiation. It is also required for initiation facilitated by the internal ribosomal entry site (IRES) of hepatitis C virus (HCV) RNA. eIF5B promotes joining of 60S ribosomal subunits to 40S ribosomal subunits bound by initiator tRNA (Met-tRNAi(Met)). However, the exact molecular mechanism by which eIF5B acts has not been established. Here we present cryo-EM reconstructions of the mammalian 80S-HCV-IRES-Met-tRNAi(Met)-eIF5B-GMPPNP complex. We obtained two substates distinguished by the rotational state of the ribosomal subunits and the configuration of initiator tRNA in the peptidyl (P) site. Accordingly, a combination of conformational changes in the 80S ribosome and in initiator tRNA facilitates binding of the Met-tRNAi(Met) to the 60S P site and redefines the role of eIF5B as a tRNA-reorientation factor.

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

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

Assembly of macromolecular complexes by satisfaction of spatial restraints from electron microscopy images

To obtain a structural model of a macromolecular assembly by single-particle EM, a large number of particle images need to be collected, aligned, clustered, averaged, and finally assembled via reconstruction into a 3D density map. This process is limited by the number and quality of the particle images, the accuracy of the initial model, and the compositional and conformational heterogeneity. Here, we describe a structure determination method that avoids the reconstruction procedure. The atomic structures of the individual complex components are assembled by optimizing a match against 2D EM class-average images, an excluded volume criterion, geometric complementarity, and optional restraints from proteomics and chemical cross-linking experiments. The optimization relies on a simulated annealing Monte Carlo search and a divide-and-conquer message-passing algorithm. Using simulated and experimentally determined EM class averages for 12 and 4 protein assemblies, respectively, we show that a few class averages can indeed result in accurate models for complexes of as many as five subunits. Thus, integrative structural biology can now benefit from the relative ease with which the EM class averages are determined.

A Stochastic Kinematic Model of Class Averaging in Single-Particle Electron Microscopy

Single-particle electron microscopy is an experimental technique that is used to determine the 3D structure of biological macromolecules and the complexes that they form. In general, image processing techniques and reconstruction algorithms are applied to micrographs, which are two-dimensional (2D) images taken by electron microscopes. Each of these planar images can be thought of as a projection of the macromolecular structure of interest from an a priori unknown direction. A class is defined as a collection of projection images with a high degree of similarity, presumably resulting from taking projections along similar directions. In practice, micrographs are very noisy and those in each class are aligned and averaged in order to reduce the background noise. Errors in the alignment process are inevitable due to noise in the electron micrographs. This error results in blurry averaged images. In this paper, we investigate how blurring parameters are related to the properties of the background noise in the case when the alignment is achieved by matching the mass centers and the principal axes of the experimental images. We observe that the background noise in micrographs can be treated as Gaussian. Using the mean and variance of the background Gaussian noise, we derive equations for the mean and variance of translational and rotational misalignments in the class averaging process. This defines a Gaussian probability density on the Euclidean motion group of the plane. Our formulation is validated by convolving the derived blurring function representing the stochasticity of the image alignments with the underlying noiseless projection and comparing with the original blurry image.

An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy

Maximum-likelihood (ML) estimation has very desirable properties for reconstructing 3D volumes from noisy cryo-EM images of single macromolecular particles. Current implementations of ML estimation make use of the Expectation-Maximization (EM) algorithm or its variants. However, the EM algorithm is notoriously computation-intensive, as it involves integrals over all orientations and positions for each particle image. We present a strategy to speedup the EM algorithm using domain reduction. Domain reduction uses a coarse grid to evaluate regions in the integration domain that contribute most to the integral. The integral is evaluated with a fine grid in these regions. In the simulations reported in this paper, domain reduction gives speedups which exceed a factor of 10 in early iterations and which exceed a factor of 60 in terminal iterations.

Deblurring of Class-Averaged Images in Single-Particle Electron Microscopy

This paper proposes a method for deblurring of class-averaged images in single-particle electron microscopy (EM). Since EM images of biological samples are very noisy, the images which are nominally identical projection images are often grouped, aligned and averaged in order to cancel or reduce the background noise. However, the noise in the individual EM images generates errors in the alignment process, which creates an inherent limit on the accuracy of the resulting class averages. This inaccurate class average due to the alignment errors can be viewed as the result of a convolution of an underlying clear image with a blurring function. In this work, we develop a deconvolution method that gives an estimate for the underlying clear image from a blurred class-averaged image using precomputed statistics of misalignment. Since this convolution is over the group of rigid body motions of the plane, SE(2), we use the Fourier transform for SE(2) in order to convert the convolution into a matrix multiplication in the corresponding Fourier space. For practical implementation we use a Hermite-function-based image modeling technique, because Hermite expansions enable lossless Cartesian-polar coordinate conversion using the Laguerre-Fourier expansions, and Hermite expansion and Laguerre-Fourier expansion retain their structures under the Fourier transform. Based on these mathematical properties, we can obtain the deconvolution of the blurred class average using simple matrix multiplication. Tests of the proposed deconvolution method using synthetic and experimental EM images confirm the performance of our method.

Fundamentals of three-dimensional reconstruction from projections

Three-dimensional (3D) reconstruction of an object mass density from the set of its 2D line projections lies at a core of both single-particle reconstruction technique and electron tomography. Both techniques utilize electron microscope to collect a set of projections of either multiple objects representing in principle the same macromolecular complex in an isolated form, or a subcellular structure isolated in situ. Therefore, the goal of macromolecular electron microscopy is to invert the projection transformation to recover the distribution of the mass density of the original object. The problem is interesting in that in its discrete form it is ill-posed and not invertible. Various algorithms have been proposed to cope with the practical difficulties of this inversion problem and their differ widely in terms of their robustness with respect to noise in the data, completeness of the collected projection dataset, errors in projections orientation parameters, abilities to efficiently handle large datasets, and other obstacles typically encountered in molecular electron microscopy. Here, we review the theoretical foundations of 3D reconstruction from line projections followed by an overview of reconstruction algorithms routinely used in practice of electron microscopy.

Conformational averaging in structural biology: issues, challenges and computational solutions

Most experimental methods in structural biology provide time- and ensemble-averaged signals and, consequently, molecular structures based on such signals often exhibit only idealized, average features. Second, most experimental signals are only indirectly related to real, molecular geometries, and solving a structure typically involves a complicated procedure, which may not always result in a unique solution. To what extent do such conformationally-averaged, non-linear experimental signals and structural models derived from them accurately represent the underlying microscopic reality? Are there some structural motifs that are actually artificially more likely to be "seen" in an experiment simply due to the averaging artifact? Finally, what are the practical consequences of ignoring the averaging effects when it comes to functional and mechanistic implications that we try to glean from experimentally-based structural models? In this review, we critically address the work that has been aimed at studying such questions. We summarize the details of experimental methods typically used in structural biology (most notably nuclear magnetic resonance, X-ray crystallography and different types of spectroscopy), discuss their individual susceptibility to conformational (motional) averaging, and review several theoretical approaches, most importantly molecular dynamics simulations that are increasingly being used to aid experimentalists in interpreting structural biology experiments.