Denoising of high-resolution single-particle electron-microscopy density maps by their approximation using three-dimensional Gaussian functions

Emerging Themes in CryoEM─Single Particle Analysis Image Processing

Cryo-electron microscopy (CryoEM) has become a vital technique in structural biology. It is an interdisciplinary field that takes advantage of advances in biochemistry, physics, and image processing, among other disciplines. Innovations in these three basic pillars have contributed to the boosting of CryoEM in the past decade. This work reviews the main contributions in image processing to the current reconstruction workflow of single particle analysis (SPA) by CryoEM. Our review emphasizes the time evolution of the algorithms across the different steps of the workflow differentiating between two groups of approaches: analytical methods and deep learning algorithms. We present an analysis of the current state of the art. Finally, we discuss the emerging problems and challenges still to be addressed in the evolution of CryoEM image processing methods in SPA.

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth of structural data arising from cryoEM and other structural biology methods, has driven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.

Advances in Xmipp for Cryo-Electron Microscopy: From Xmipp to Scipion

Xmipp is an open-source software package consisting of multiple programs for processing data originating from electron microscopy and electron tomography, designed and managed by the Biocomputing Unit of the Spanish National Center for Biotechnology, although with contributions from many other developers over the world. During its 25 years of existence, Xmipp underwent multiple changes and updates. While there were many publications related to new programs and functionality added to Xmipp, there is no single publication on the Xmipp as a package since 2013. In this article, we give an overview of the changes and new work since 2013, describe technologies and techniques used during the development, and take a peek at the future of the package.

Bayesian Random Tomography of Particle Systems

Random tomography is a common problem in imaging science and refers to the task of reconstructing a three-dimensional volume from two-dimensional projection images acquired in unknown random directions. We present a Bayesian approach to random tomography. At the center of our approach is a meshless representation of the unknown volume as a mixture of spherical Gaussians. Each Gaussian can be interpreted as a particle such that the unknown volume is represented by a particle cloud. The particle representation allows us to speed up the computation of projection images and to represent a large variety of structures accurately and efficiently. We develop Markov chain Monte Carlo algorithms to infer the particle positions as well as the unknown orientations. Posterior sampling is challenging due to the high dimensionality and multimodality of the posterior distribution. We tackle these challenges by using Hamiltonian Monte Carlo and a global rotational sampling strategy. We test the approach on various simulated and real datasets.

Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy.

Exploiting prior knowledge about biological macromolecules in cryo-EM structure determination

Three-dimensional reconstruction of the electron-scattering potential of biological macromolecules from electron cryo-microscopy (cryo-EM) projection images is an ill-posed problem. The most popular cryo-EM software solutions to date rely on a regularization approach that is based on the prior assumption that the scattering potential varies smoothly over three-dimensional space. Although this approach has been hugely successful in recent years, the amount of prior knowledge that it exploits compares unfavorably with the knowledge about biological structures that has been accumulated over decades of research in structural biology. Here, a regularization framework for cryo-EM structure determination is presented that exploits prior knowledge about biological structures through a convolutional neural network that is trained on known macromolecular structures. This neural network is inserted into the iterative cryo-EM structure-determination process through an approach that is inspired by regularization by denoising. It is shown that the new regularization approach yields better reconstructions than the current state of the art for simulated data, and options to extend this work for application to experimental cryo-EM data are discussed.

Hybrid Electron Microscopy Normal Mode Analysis with Scipion

Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) method was introduced in 2014. HEMNMA computes normal modes of a reference model (an atomic structure or an electron microscopy map) of a molecular complex and uses this model and its normal modes to analyze single-particle images of the complex to obtain information on its continuous conformational changes, by determining the full distribution of conformational variability from the images. An advantage of HEMNMA is a simultaneous determination of all parameters of each image (particle conformation, orientation, and shift) through their iterative optimization, which allows applications of HEMNMA even when the effects of conformational changes dominate those of orientational changes. HEMNMA was first implemented in Xmipp and was using MATLAB for statistical analysis of obtained conformational distributions and for fitting of underlying trajectories of conformational changes. A HEMNMA implementation independent of MATLAB is now available as part of a plugin of Scipion V2.0 (http://scipion.i2pc.es). This plugin, named ContinuousFlex, can be installed by following the instructions at https://pypi.org/project/scipion-em-continuousflex. In this article, we present this new HEMNMA software, which is user-friendly, totally free, and open-source. STATEMENT FOR A BROADER AUDIENCE: This article presents Hybrid Electron Microscopy Normal Mode Analysis (HEMNMA) software that allows analyzing single-particle images of a complex to obtain information on continuous conformational changes of the complex, by determining the full distribution of conformational variability from the images. The HEMNMA software is user-friendly, totally free, open-source, and available as part of ContinuousFlex plugin (https://pypi.org/project/scipion-em-continuousflex) of Scipion V2.0 (http://scipion.i2pc.es).

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Bayesian Weighing of Electron Cryo-Microscopy Data for Integrative Structural Modeling

Cryo-electron microscopy (cryo-EM) has become a mainstream technique for determining the structures of complex biological systems. However, accurate integrative structural modeling has been hampered by the challenges in objectively weighing cryo-EM data against other sources of information due to the presence of random and systematic errors, as well as correlations, in the data. To address these challenges, we introduce a Bayesian scoring function that efficiently and accurately ranks alternative structural models of a macromolecular system based on their consistency with a cryo-EM density map as well as other experimental and prior information. The accuracy of this approach is benchmarked using complexes of known structure and illustrated in three applications: the structural determination of the GroEL/GroES, RNA polymerase II, and exosome complexes. The approach is implemented in the open-source Integrative Modeling Platform (http://integrativemodeling.org), thus enabling integrative structure determination by combining cryo-EM data with other sources of information.

A methodology using Gaussian-based density map approximation to assess sets of cryo-electron microscopy density maps

This article presents a methodology to assess a set of density maps, as used in the Blind Assessment Phase of the 2015/2016 Map Challenge (EMDataBank Validation Challenges). The synthetic and experimental cryo-electron microscopy (cryo-EM) density maps obtained by different single particle analysis protocols and by different participants, submitted in the Challenge Phase for assessment, were analyzed with this methodology and the obtained results are presented and discussed here. The goal of using such a methodology was to blindly identify the density maps with globally similar structural information, meaning the maps with the structural information mostly "reproduced" by different protocols. To this end, the density maps are "coarsened" using Gaussian-based approximations, with the same input approximation parameters for all maps of the target biological complex. The approximated maps are then represented in a common reduced-dimension (here, 3D) space of their correlation-coefficient-based distances, in which close maps mean similar maps. The distance analysis allows identifying maps with the most "reproduced" structural information by different protocols. The obtained results are also discussed taking into account the detailed information about the protocols that has been released after the end of the Blind Assessment Phase.

Integrative structure and functional anatomy of a nuclear pore complex

Despite the central role of Nuclear Pore Complexes (NPCs) as gatekeepers of RNA and protein transport between the cytoplasm and nucleoplasm, their large size and dynamic nature have impeded a full structural and functional elucidation. Here, we have determined a subnanometer precision structure for the entire 552-protein yeast NPC by satisfying diverse data including stoichiometry, a cryo-electron tomography map, and chemical cross-links. The structure reveals the NPC’s functional elements in unprecedented detail. The NPC is built of sturdy diagonal columns to which are attached connector cables, imbuing both strength and flexibility, while tying together all other elements of the NPC, including membrane-interacting regions and RNA processing platforms. Inwardly-directed anchors create a high density of transport factor-docking Phe-Gly repeats in the central channel, organized in distinct functional units. Taken together, this integrative structure allows us to rationalize the architecture, transport mechanism, and evolutionary origins of the NPC.

Gaussian-input Gaussian mixture model for representing density maps and atomic models

A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm.

Versatility of Approximating Single-Particle Electron Microscopy Density Maps Using Pseudoatoms and Approximation-Accuracy Control

Three-dimensional Gaussian functions have been shown useful in representing electron microscopy (EM) density maps for studying macromolecular structure and dynamics. Methods that require setting a desired number of Gaussian functions or a maximum number of iterations may result in suboptimal representations of the structure. An alternative is to set a desired error of approximation of the given EM map and then optimize the number of Gaussian functions to achieve this approximation error. In this article, we review different applications of such an approach that uses spherical Gaussian functions of fixed standard deviation, referred to as pseudoatoms. Some of these applications use EM-map normal mode analysis (NMA) with elastic network model (ENM) (applications such as predicting conformational changes of macromolecular complexes or exploring actual conformational changes by normal-mode-based analysis of experimental data) while some other do not use NMA (denoising of EM density maps). In applications based on NMA and ENM, the advantage of using pseudoatoms in EM-map coarse-grain models is that the ENM springs are easily assigned among neighboring grains thanks to their spherical shape and uniformed size. EM-map denoising based on the map coarse-graining was so far only shown using pseudoatoms as grains.