A common task in cryo-electron microscopy (cryo-EM) data processing is to compare three-dimensional density maps of macromolecules. In this paper, we propose an algorithm for aligning three-dimensional density maps that exploits common lines between projection images of the maps. The algorithm is fully automatic and handles rotations, reflections (handedness), and translations between the maps. In addition, the algorithm is applicable to any type of molecular symmetry without requiring any information regarding the symmetry of the maps. We evaluate our alignment algorithm on publicly available density maps, demonstrating its accuracy and efficiency. The algorithm is available at https://github.com/ShkolniskyLab/emalign.
Single particle cryo-electron microscopy is a vital tool for 3D characterization of protein structures. A typical workflow involves acquiring projection images of a collection of randomly oriented particles, picking and classifying individual particle projections by orientation, and finally using the individual particle projections to reconstruct a 3D map of the electron density profile. The reconstruction is challenging because of the low signal-to-noise ratio of the data, the unknown orientation of the particles, and the sparsity of data especially when dealing with flexible proteins where t…
SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of British Columbia（不列颠哥伦比亚大学）
Cryogenic electron microscopy (cryo-EM) provides images from different copies of the same biomolecule in arbitrary orientations. Here, we present an end-to-end unsupervised approach that learns individual particle orientations from cryo-EM data while reconstructing the average 3D map of the biomolecule, starting from a random initialization. The approach relies on an auto-encoder architecture where the latent space is explicitly interpreted as orientations used by the decoder to form an image according to the linear projection model. We evaluate our method on simulated data and show that it is…
Cryo-Electron Microscopy (Cryo-EM) is a Nobel prize-winning technology for determining the 3D structure of particles at near-atomic resolution. A fundamental step in the recovering of the 3D single-particle structure is to align its 2D projections; thus, the construction of a canonical representation with a fixed rotation angle is required. Most approaches use discrete clustering which fails to capture the continuous nature of image rotation, others suffer from low-quality image reconstruction. We propose a novel method that leverages the recent development in the generative adversarial networ…
Simons Machine Learning Center, Simons Electron Microscopy Center, New York Structural Biology Center（西蒙斯机器学习中心、西蒙斯电子显微镜中心、纽约结构生物学中心）
Over the past decade, cryogenic electron microscopy (cryo-EM) has emerged as a primary method for determining near-native, near-atomic resolution 3D structures of biological macromolecules. In order to meet increasing demand for cryo-EM, automated methods to improve throughput and efficiency while lowering costs are needed. Currently, all high-magnification cryo-EM data collection softwares require human input and manual tuning of parameters. Expert operators must navigate low- and medium-magnification images to find good high-magnification collection locations. Automating this is non-trivial:…
University of Illinois at Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Chicago（芝加哥大学）
We develop in this paper a novel intrinsic classification algorithm -- multi-frequency class averaging (MFCA) -- for classifying noisy projection images obtained from three-dimensional cryo-electron microscopy (cryo-EM) by the similarity among their viewing directions. This new algorithm leverages multiple irreducible representations of the unitary group to introduce additional redundancy into the representation of the optimal in-plane rotational alignment, extending and outperforming the existing class averaging algorithm that uses only a single representation. The formal algebraic model and …
Stanford University（斯坦福大学）；SLAC National Accelerator（SLAC国家加速器实验室）
Cryo-electron microscopy (cryo-EM) is capable of producing reconstructed 3D images of biomolecules at near-atomic resolution. As such, it represents one of the most promising imaging techniques in structural biology. However, raw cryo-EM images are only highly corrupted - noisy and band-pass filtered - 2D projections of the target 3D biomolecules. Reconstructing the 3D molecular shape starts with the removal of image outliers, the estimation of the orientation of the biomolecule that has produced the given 2D image, and the estimation of camera parameters to correct for intensity defects. Curr…
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Massachusetts Institute of Technology（麻省理工学院）；University of Chicago（芝加哥大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）
Recent breakthroughs in high-resolution imaging of biomolecules in solution with cryo-electron microscopy (cryo-EM) have unlocked new doors for the reconstruction of molecular volumes, thereby promising further advances in biology, chemistry, and pharmacological research. Recent next-generation volume reconstruction algorithms that combine generative modeling with end-to-end unsupervised deep learning techniques have shown promising preliminary results, but still face considerable technical and theoretical hurdles when applied to experimental cryo-EM images. In light of the proliferation of su…
Institute of Statistical Science, Academia Sinica（中央研究院統計科學研究所）；Institute of Chemistry, Academia Sinica（中央研究院化學研究所）
Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The se…
Using cryogenic transmission electron microscopy, we revealed three dimensional (3D) structural details of the electrochemically plated lithium (Li) flakes and their solid electrolyte interphase (SEI), including the composite SEI skin-layer and SEI fossil pieces buried inside the Li matrix. As the SEI skin-layer is largely comprised of nanocrystalline LiF and Li2O in amorphous polymeric matrix, when complete Li stripping occurs, the compromised SEI three-dimensional framework buckles, forming nanoscale bends and wrinkles. We showed that the flexibility and resilience of the SEI skin-layer play…
Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating indiv…
A main task in cryo-electron microscopy single particle reconstruction is to find a three-dimensional model of a molecule given a set of its randomly oriented and positioned noisy projection-images. In this work, we propose an algorithm for ab-initio reconstruction for molecules with tetrahedral or octahedral symmetry. The algorithm exploits the multiple common lines between each pair of projection-images as well as self common lines within each image. It is robust to noise in the input images as it integrates the information from all images at once. The applicability of the proposed algorithm…
Different tasks in the computational pipeline of single-particle cryo-electron microscopy (cryo-EM) require enhancing the quality of the highly noisy raw images. To this end, we develop an efficient algorithm for signal enhancement of cryo-EM images. The enhanced images can be used for a variety of downstream tasks, such as 2-D classification, removing uninformative images, constructing {ab initio} models, generating templates for particle picking, providing a quick assessment of the data set, dimensionality reduction, and symmetry detection. The algorithm includes built-in quality measures to…
Single-particle cryo-electron microscopy (cryo-EM) is a leading technology to resolve the structure of molecules. Early in the process, the user detects potential particle images in the raw data. Typically, there are many false detections as a result of high levels of noise and contamination. Currently, removing the false detections requires human intervention to sort the hundred thousands of images. We propose a statistically-established unsupervised algorithm to remove non-particle images. We model the particle images as a union of low-dimensional subspaces, assuming non-particle images are …
Cryo-electron microscopy (cryo-EM) has revolutionized experimental protein structure determination. Despite advances in high resolution reconstruction, a majority of cryo-EM experiments provide either a single state of the studied macromolecule, or a relatively small number of its conformations. This reduces the effectiveness of the technique for proteins with flexible regions, which are known to play a key role in protein function. Recent methods for capturing conformational heterogeneity in cryo-EM data model it in volume space, making recovery of continuous atomic structures challenging. He…
Recovering a Molecule's 3D Dynamics from Liquid-phase Electron Microscopy Movies
National Biomedical Imaging Center, Peking University（北京大学国家生物医学成像中心）；College of Future Technology, Peking University（北京大学未来技术学院）；College of Chemistry and Molecular Engineering, Peking University（北京大学化学与分子工程学院）；DP Technology, Ltd.（深度势能科技有限公司）
