Directly reconstructing principal components of heterogeneous particles from cryo-EM images

Cryo-EM heterogeneity analysis using regularized covariance estimation and kernel regression

Proteins and the complexes they form are central to nearly all cellular processes. Their flexibility, expressed through a continuum of states, provides a window into their biological functions. Cryogenic electron microscopy (cryo-EM) is an ideal tool to study these dynamic states as it captures specimens in noncrystalline conditions and enables high-resolution reconstructions. However, analyzing the heterogeneous distributions of conformations from cryo-EM data is challenging. We present RECOVAR, a method for analyzing these distributions based on principal component analysis (PCA) computed using a REgularized COVARiance estimator. RECOVAR is fast, robust, interpretable, expressive, and competitive with state-of-the-art neural network methods on heterogeneous cryo-EM datasets. The regularized covariance method efficiently computes a large number of high-resolution principal components that can encode rich heterogeneous distributions of conformations and does so robustly thanks to an automatic regularization scheme. The reconstruction method based on adaptive kernel regression resolves conformational states to a higher resolution than all other tested methods on extensive independent benchmarks while remaining highly interpretable. Additionally, we exploit favorable properties of the PCA embedding to estimate the conformational density accurately. This density allows for better interpretability of the latent space by identifying stable states and low free-energy motions. Finally, we present a scheme to navigate the high-dimensional latent space by automatically identifying these low free-energy trajectories. We make the code freely available at https://github.com/ma-gilles/recovar.

Evaluating Cryo-TEM Reconstruction Accuracy of Self-Assembled Polymer Nanostructures

Cryogenic transmission electron microscopy (cryo-TEM) combined with single particle analysis (SPA) is an emerging imaging approach for soft materials. However, the accuracy of SPA-reconstructed nanostructures, particularly those formed by synthetic polymers, remains uncertain due to potential packing heterogeneity of the nanostructures. In this study, the combination of molecular dynamics (MD) simulations and image simulations is utilized to validate the accuracy of cryo-TEM 3D reconstructions of self-assembled polypeptoid fibril nanostructures. Using CryoSPARC software, image simulations, 2D classifications, ab initio reconstructions, and homogenous refinements are performed. By comparing the results with atomic models, the recovery of molecular details is assessed, heterogeneous structures are identified, and the influence of extraction location on the reconstructions is evaluated. These findings confirm the fidelity of single particle analysis in accurately resolving complex structural characteristics and heterogeneous structures, exhibiting its potential as a valuable tool for detailed structural analysis of synthetic polymers and soft materials.

CryoSTAR: leveraging structural priors and constraints for cryo-EM heterogeneous reconstruction

Resolving conformational heterogeneity in cryogenic electron microscopy datasets remains an important challenge in structural biology. Previous methods have often been restricted to working exclusively on volumetric densities, neglecting the potential of incorporating any preexisting structural knowledge as prior or constraints. Here we present cryoSTAR, which harnesses atomic model information as structural regularization to elucidate such heterogeneity. Our method uniquely outputs both coarse-grained models and density maps, showcasing the molecular conformational changes at different levels. Validated against four diverse experimental datasets, spanning large complexes, a membrane protein and a small single-chain protein, our results consistently demonstrate an efficient and effective solution to conformational heterogeneity with minimal human bias. By integrating atomic model insights with cryogenic electron microscopy data, cryoSTAR represents a meaningful step forward, paving the way for a deeper understanding of dynamic biological processes.

Cryo-EM Heterogeneity Analysis using Regularized Covariance Estimation and Kernel Regression

Proteins and the complexes they form are central to nearly all cellular processes. Their flexibility, expressed through a continuum of states, provides a window into their biological functions. Cryogenic electron microscopy (cryo-EM) is an ideal tool to study these dynamic states as it captures specimens in non-crystalline conditions and enables high-resolution reconstructions. However, analyzing the heterogeneous distributions of conformations from cryo-EM data is challenging. We present RECOVAR, a method for analyzing these distributions based on principal component analysis (PCA) computed using a REgularized COVARiance estimator. RECOVAR is fast, robust, interpretable, expressive, and competitive with the state-of-art neural network methods on heterogeneous cryo-EM datasets. The regularized covariance method efficiently computes a large number of high-resolution principal components that can encode rich heterogeneous distributions of conformations and does so robustly thanks to an automatic regularization scheme. The novel reconstruction method based on adaptive kernel regression resolves conformational states to a higher resolution than all other tested methods on extensive independent benchmarks while remaining highly interpretable. Additionally, we exploit favorable properties of the PCA embedding to estimate the conformational density accurately. This density allows for better interpretability of the latent space by identifying stable states and low free-energy motions. Finally, we present a scheme to navigate the high-dimensional latent space by automatically identifying these low free-energy trajectories. We make the code freely available at https://github.com/ma-gilles/recovar.

Four-dimensional imaging for cryo-electron microscopy experiments using molecular simulations and manifold learning

Elucidating protein conformational changes is essential because conformational changes are closely related to the functions of proteins. Cryo-electron microscopy (cryo-EM) experiment can be used to reconstruct protein conformational changes via a method that involves using the experimental data (two-dimensional protein images). In this study, a reconstruction method, referred to as the "four-dimensional imaging," was proposed. In our four-dimensional imaging technique, the protein conformational change was obtained using the two-dimensional protein images (the three-dimensional electron density maps used in previously proposed techniques were not used). The protein conformation for each two-dimensional protein image was obtained using our original protocol with molecular dynamics simulations. Using a manifold-learning technique and two-dimensional protein images, the protein conformations were arranged according to the conformational change of the protein. By arranging the protein conformations according to the arrangement of the protein images, four-dimensional imaging is constructed. A simulation for a cryo-EM experiment demonstrated the validity of our four-dimensional imaging technique.

MDSPACE and MDTOMO Software for Extracting Continuous Conformational Landscapes from Datasets of Single Particle Images and Subtomograms Based on Molecular Dynamics Simulations: Latest Developments in ContinuousFlex Software Package

Cryo electron microscopy (cryo-EM) instrumentation allows obtaining 3D reconstruction of the structure of biomolecular complexes in vitro (purified complexes studied by single particle analysis) and in situ (complexes studied in cells by cryo electron tomography). Standard cryo-EM approaches allow high-resolution reconstruction of only a few conformational states of a molecular complex, as they rely on data classification into a given number of classes to increase the resolution of the reconstruction from the most populated classes while discarding all other classes. Such discrete classification approaches result in a partial picture of the full conformational variability of the complex, due to continuous conformational transitions with many, uncountable intermediate states. In this article, we present the software with a user-friendly graphical interface for running two recently introduced methods, namely, MDSPACE and MDTOMO, to obtain continuous conformational landscapes of biomolecules by analyzing in vitro and in situ cryo-EM data (single particle images and subtomograms) based on molecular dynamics simulations of an available atomic model of one of the conformations. The MDSPACE and MDTOMO software is part of the open-source ContinuousFlex software package (starting from version 3.4.2 of ContinuousFlex), which can be run as a plugin of the Scipion software package (version 3.1 and later), broadly used in the cryo-EM field.

KsgA facilitates ribosomal small subunit maturation by proofreading a key structural lesion

Ribosome assembly is orchestrated by many assembly factors, including ribosomal RNA methyltransferases, whose precise role is poorly understood. Here, we leverage the power of cryo-EM and machine learning to discover that the E. coli methyltransferase KsgA performs a 'proofreading' function in the assembly of the small ribosomal subunit by recognizing and partially disassembling particles that have matured but are not competent for translation. We propose that this activity allows inactive particles an opportunity to reassemble into an active state, thereby increasing overall assembly fidelity. Detailed structural quantifications in our datasets additionally enabled the expansion of the Nomura assembly map to highlight rRNA helix and r-protein interdependencies, detailing how the binding and docking of these elements are tightly coupled. These results have wide-ranging implications for our understanding of the quality-control mechanisms governing ribosome biogenesis and showcase the power of heterogeneity analysis in cryo-EM to unveil functionally relevant information in biological systems.

Novel Artificial Intelligence-Based Approaches for Ab Initio Structure Determination and Atomic Model Building for Cryo-Electron Microscopy

Single particle cryo-electron microscopy (cryo-EM) has emerged as the prevailing method for near-atomic structure determination, shedding light on the important molecular mechanisms of biological macromolecules. However, the inherent dynamics and structural variability of biological complexes coupled with the large number of experimental images generated by a cryo-EM experiment make data processing nontrivial. In particular, ab initio reconstruction and atomic model building remain major bottlenecks that demand substantial computational resources and manual intervention. Approaches utilizing recent innovations in artificial intelligence (AI) technology, particularly deep learning, have the potential to overcome the limitations that cannot be adequately addressed by traditional image processing approaches. Here, we review newly proposed AI-based methods for ab initio volume generation, heterogeneous 3D reconstruction, and atomic model building. We highlight the advancements made by the implementation of AI methods, as well as discuss remaining limitations and areas for future development.

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.

MDTOMO method for continuous conformational variability analysis in cryo electron subtomograms based on molecular dynamics simulations

Cryo electron tomography (cryo-ET) allows observing macromolecular complexes in their native environment. The common routine of subtomogram averaging (STA) allows obtaining the three-dimensional (3D) structure of abundant macromolecular complexes, and can be coupled with discrete classification to reveal conformational heterogeneity of the sample. However, the number of complexes extracted from cryo-ET data is usually small, which restricts the discrete-classification results to a small number of enough populated states and, thus, results in a largely incomplete conformational landscape. Alternative approaches are currently being investigated to explore the continuity of the conformational landscapes that in situ cryo-ET studies could provide. In this article, we present MDTOMO, a method for analyzing continuous conformational variability in cryo-ET subtomograms based on Molecular Dynamics (MD) simulations. MDTOMO allows obtaining an atomic-scale model of conformational variability and the corresponding free-energy landscape, from a given set of cryo-ET subtomograms. The article presents the performance of MDTOMO on a synthetic ABC exporter dataset and an in situ SARS-CoV-2 spike dataset. MDTOMO allows analyzing dynamic properties of molecular complexes to understand their biological functions, which could also be useful for structure-based drug discovery.

3DFlex: determining structure and motion of flexible proteins from cryo-EM

Modeling flexible macromolecules is one of the foremost challenges in single-particle cryogenic-electron microscopy (cryo-EM), with the potential to illuminate fundamental questions in structural biology. We introduce Three-Dimensional Flexible Refinement (3DFlex), a motion-based neural network model for continuous molecular heterogeneity for cryo-EM data. 3DFlex exploits knowledge that conformational variability of a protein is often the result of physical processes that transport density over space and tend to preserve local geometry. From two-dimensional image data, 3DFlex enables the determination of high-resolution 3D density, and provides an explicit model of a flexible protein's motion over its conformational landscape. Experimentally, for large molecular machines (tri-snRNP spliceosome complex, translocating ribosome) and small flexible proteins (TRPV1 ion channel, αVβ8 integrin, SARS-CoV-2 spike), 3DFlex learns nonrigid molecular motions while resolving details of moving secondary structure elements. 3DFlex can improve 3D density resolution beyond the limits of existing methods because particle images contribute coherent signal over the conformational landscape.

Methods for Cryo-EM Single Particle Reconstruction of Macromolecules Having Continuous Heterogeneity

Macromolecules change their shape (conformation) in the process of carrying out their functions. The imaging by cryo-electron microscopy of rapidly-frozen, individual copies of macromolecules (single particles) is a powerful and general approach to understanding the motions and energy landscapes of macromolecules. Widely-used computational methods already allow the recovery of a few distinct conformations from heterogeneous single-particle samples, but the treatment of complex forms of heterogeneity such as the continuum of possible transitory states and flexible regions remains largely an open problem. In recent years there has been a surge of new approaches for treating the more general problem of continuous heterogeneity. This paper surveys the current state of the art in this area.

MDSPACE: Extracting Continuous Conformational Landscapes from Cryo-EM Single Particle Datasets Using 3D-to-2D Flexible Fitting based on Molecular Dynamics Simulation

This article presents an original approach for extracting atomic-resolution landscapes of continuous conformational variability of biomolecular complexes from cryo electron microscopy (cryo-EM) single particle images. This approach is based on a new 3D-to-2D flexible fitting method, which uses molecular dynamics (MD) simulation and is embedded in an iterative conformational-landscape refinement scheme. This new approach is referred to as MDSPACE, which stands for Molecular Dynamics simulation for Single Particle Analysis of Continuous Conformational hEterogeneity. The article describes the MDSPACE approach and shows its performance using synthetic and experimental datasets.

Exploring the Structural Variability of Dynamic Biological Complexes by Single-Particle Cryo-Electron Microscopy

Biological macromolecules and assemblies precisely rearrange their atomic 3D structures to execute cellular functions. Understanding the mechanisms by which these molecular machines operate requires insight into the ensemble of structural states they occupy during the functional cycle. Single-particle cryo-electron microscopy (cryo-EM) has become the preferred method to provide near-atomic resolution, structural information about dynamic biological macromolecules elusive to other structure determination methods. Recent advances in cryo-EM methodology have allowed structural biologists not only to probe the structural intermediates of biochemical reactions, but also to resolve different compositional and conformational states present within the same dataset. This article reviews newly developed sample preparation and single-particle analysis (SPA) techniques for high-resolution structure determination of intrinsically dynamic and heterogeneous samples, shedding light upon the intricate mechanisms employed by molecular machines and helping to guide drug discovery efforts.

Amortized Inference for Heterogeneous Reconstruction in Cryo-EM

Cryo-electron microscopy (cryo-EM) is an imaging modality that provides unique insights into the dynamics of proteins and other building blocks of life. The algorithmic challenge of jointly estimating the poses, 3D structure, and conformational heterogeneity of a biomolecule from millions of noisy and randomly oriented 2D projections in a computationally efficient manner, however, remains unsolved. Our method, cryoFIRE, performs ab initio heterogeneous reconstruction with unknown poses in an amortized framework, thereby avoiding the computationally expensive step of pose search while enabling the analysis of conformational heterogeneity. Poses and conformation are jointly estimated by an encoder while a physics-based decoder aggregates the images into an implicit neural representation of the conformational space. We show that our method can provide one order of magnitude speedup on datasets containing millions of images without any loss of accuracy. We validate that the joint estimation of poses and conformations can be amortized over the size of the dataset. For the first time, we prove that an amortized method can extract interpretable dynamic information from experimental datasets.

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.

DeepHEMNMA: ResNet-based hybrid analysis of continuous conformational heterogeneity in cryo-EM single particle images

Single-particle cryo-electron microscopy (cryo-EM) is a technique for biomolecular structure reconstruction from vitrified samples containing many copies of a biomolecular complex (known as single particles) at random unknown 3D orientations and positions. Cryo-EM allows reconstructing multiple conformations of the complexes from images of the same sample, which usually requires many rounds of 2D and 3D classifications to disentangle and interpret the combined conformational, orientational, and translational heterogeneity. The elucidation of different conformations is the key to understand molecular mechanisms behind the biological functions of the complexes and the key to novel drug discovery. Continuous conformational heterogeneity, due to gradual conformational transitions giving raise to many intermediate conformational states of the complexes, is both an obstacle for high-resolution 3D reconstruction of the conformational states and an opportunity to obtain information about multiple coexisting conformational states at once. HEMNMA method, specifically developed for analyzing continuous conformational heterogeneity in cryo-EM, determines the conformation, orientation, and position of the complex in each single particle image by image analysis using normal modes (the motion directions simulated for a given atomic structure or EM map), which in turn allows determining the full conformational space of the complex but at the price of high computational cost. In this article, we present a new method, referred to as DeepHEMNMA, which speeds up HEMNMA by combining it with a residual neural network (ResNet) based deep learning approach. The performance of DeepHEMNMA is shown using synthetic and experimental single particle images.

Artificial Intelligence in Cryo-Electron Microscopy

Cryo-electron microscopy (cryo-EM) has become an unrivaled tool for determining the structure of macromolecular complexes. The biological function of macromolecular complexes is inextricably tied to the flexibility of these complexes. Single particle cryo-EM can reveal the conformational heterogeneity of a biochemically pure sample, leading to well-founded mechanistic hypotheses about the roles these complexes play in biology. However, the processing of increasingly large, complex datasets using traditional data processing strategies is exceedingly expensive in both user time and computational resources. Current innovations in data processing capitalize on artificial intelligence (AI) to improve the efficiency of data analysis and validation. Here, we review new tools that use AI to automate the data analysis steps of particle picking, 3D map reconstruction, and local resolution determination. We discuss how the application of AI moves the field forward, and what obstacles remain. We also introduce potential future applications of AI to use cryo-EM in understanding protein communities in cells.

Visualizing Conformational Space of Functional Biomolecular Complexes by Deep Manifold Learning

The cellular functions are executed by biological macromolecular complexes in nonequilibrium dynamic processes, which exhibit a vast diversity of conformational states. Solving the conformational continuum of important biomolecular complexes at the atomic level is essential to understanding their functional mechanisms and guiding structure-based drug discovery. Here, we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions that approximately visualize the conformational space of biomolecular complexes of interest. AlphaCryo4D integrates 3D deep residual learning with manifold embedding of pseudo-energy landscapes, which simultaneously improves 3D classification accuracy and reconstruction resolution via an energy-based particle-voting algorithm. In blind assessments using simulated heterogeneous datasets, AlphaCryo4D achieved 3D classification accuracy three times those of alternative methods and reconstructed continuous conformational changes of a 130-kDa protein at sub-3 Å resolution. By applying this approach to analyze several experimental datasets of the proteasome, ribosome and spliceosome, we demonstrate its potential generality in exploring hidden conformational space or transient states of macromolecular complexes that remain hitherto invisible. Integration of this approach with time-resolved cryo-EM further allows visualization of conformational continuum in a nonequilibrium regime at the atomic level, thus potentially enabling therapeutic discovery against highly dynamic biomolecular targets.

Probing Structural Perturbation of Biomolecules by Extracting Cryo-EM Data Heterogeneity

Single-particle cryogenic electron microscopy (cryo-EM) has become an indispensable tool to probe high-resolution structural detail of biomolecules. It enables direct visualization of the biomolecules and opens a possibility for averaging molecular images to reconstruct a three-dimensional Coulomb potential density map. Newly developed algorithms for data analysis allow for the extraction of structural heterogeneity from a massive and low signal-to-noise-ratio (SNR) cryo-EM dataset, expanding our understanding of multiple conformational states, or further implications in dynamics, of the target biomolecule. This review provides an overview that briefly describes the workflow of single-particle cryo-EM, including imaging and data processing, and new methods developed for analyzing the data heterogeneity to understand the structural variability of biomolecules.

Hierarchical autoclassification of cryo-EM samples and macromolecular energy landscape determination

BACKGROUND AND OBJECTIVE

Cryo-electron microscopy using single particle analysis is a powerful technique for obtaining 3D reconstructions of macromolecules in near native conditions. One of its major advances is its capacity to reveal conformations of dynamic molecular complexes. Most popular and successful current approaches to analyzing heterogeneous complexes are founded on Bayesian inference. However, these 3D classification methods require the tuning of specific parameters by the user and the use of complicated 3D re-classification procedures for samples affected by extensive heterogeneity. Thus, the success of these approaches highly depends on the user experience. We introduce a robust approach to identify many different conformations presented in a cryo-EM dataset based on Bayesian inference through Relion classification methods that does not require tuning of parameters and reclassification strategies.

METHODS

The algorithm allows both 2D and 3D classification and is based on a hierarchical clustering approach that runs automatically without requiring typical inputs, such as the number of conformations present in the dataset or the required classification iterations. This approach is applied to robustly determine the energy landscapes of macromolecules.

RESULTS

We tested the performance of the methods proposed here using four different datasets, comprising structurally homogeneous and highly heterogeneous cases. In all cases, the approach provided excellent results. The routines are publicly available as part of the CryoMethods plugin included in the Scipion package.

CONCLUSIONS

Our results show that the proposed method can be used to align and classify homogeneous and heterogeneous datasets without requiring previous alignment information or any prior knowledge about the number of co-existing conformations. The approach can be used for both 2D and 3D autoclassification and only requires an initial volume. In addition, the approach is robust to the "attractor" problem providing many different conformations/views for samples affected by extensive heterogeneity. The obtained 3D classes can render high resolution 3D structures, while the obtained energy landscapes can be used to determine structural trajectories.

Catalytic trajectory of a dimeric nonribosomal peptide synthetase subunit with an inserted epimerase domain

Nonribosomal peptide synthetases (NRPSs) are modular assembly-line megaenzymes that synthesize diverse metabolites with wide-ranging biological activities. The structural dynamics of synthetic elongation has remained unclear. Here, we present cryo-EM structures of PchE, an NRPS elongation module, in distinct conformations. The domain organization reveals a unique “H”-shaped head-to-tail dimeric architecture. The capture of both aryl and peptidyl carrier protein-tethered substrates and intermediates inside the heterocyclization domain and l-cysteinyl adenylate in the adenylation domain illustrates the catalytic and recognition residues. The multilevel structural transitions guided by the adenylation C-terminal subdomain in combination with the inserted epimerase and the conformational changes of the heterocyclization tunnel are controlled by two residues. Moreover, we visualized the direct structural dynamics of the full catalytic cycle from thiolation to epimerization. This study establishes the catalytic trajectory of PchE and sheds light on the rational re-engineering of domain-inserted dimeric NRPSs for the production of novel pharmaceutical agents.

The catalytic domains in nonribosomal peptide synthetases (NRPSs) are responsible for a choreography of events that elongates substrates into natural products. Here, the authors present cryo-EM structures of a siderophore-producing dimeric NRPS elongation module in multiple distinct conformations, which provides insight into the mechanisms of catalytic trajectory.

Machine Learning for Structure Determination in Single-Particle Cryo-Electron Microscopy: A Systematic Review

Recently, single-particle cryo-electron microscopy (cryo-EM) has become an indispensable method for determining macromolecular structures at high resolution to deeply explore the relevant molecular mechanism. Its recent breakthrough is mainly because of the rapid advances in hardware and image processing algorithms, especially machine learning. As an essential support of single-particle cryo-EM, machine learning has powered many aspects of structure determination and greatly promoted its development. In this article, we provide a systematic review of the applications of machine learning in this field. Our review begins with a brief introduction of single-particle cryo-EM, followed by the specific tasks and challenges of its image processing. Then, focusing on the workflow of structure determination, we describe relevant machine learning algorithms and applications at different steps, including particle picking, 2-D clustering, 3-D reconstruction, and other steps. As different tasks exhibit distinct characteristics, we introduce the evaluation metrics for each task and summarize their dynamics of technology development. Finally, we discuss the open issues and potential trends in this promising field.

Cryo-EM Analyses Permit Visualization of Structural Polymorphism of Biological Macromolecules

The functions of biological macromolecules are often associated with conformational malleability of the structures. This phenomenon of chemically identical molecules with different structures is coined structural polymorphism. Conventionally, structural polymorphism is observed directly by structural determination at the density map level from X-ray crystal diffraction. Although crystallography approach can report the conformation of a macromolecule with the position of each atom accurately defined in it, the exploration of structural polymorphism and interpreting biological function in terms of crystal structures is largely constrained by the crystal packing. An alternative approach to studying the macromolecule of interest in solution is thus desirable. With the advancement of instrumentation and computational methods for image analysis and reconstruction, cryo-electron microscope (cryo-EM) has been transformed to be able to produce “in solution” structures of macromolecules routinely with resolutions comparable to crystallography but without the need of crystals. Since the sample preparation of single-particle cryo-EM allows for all forms co-existing in solution to be simultaneously frozen, the image data contain rich information as to structural polymorphism. The ensemble of structure information can be subsequently disentangled through three-dimensional (3D) classification analyses. In this review, we highlight important examples of protein structural polymorphism in relation to allostery, subunit cooperativity and function plasticity recently revealed by cryo-EM analyses, and review recent developments in 3D classification algorithms including neural network/deep learning approaches that would enable cryo-EM analyese in this regard. Finally, we brief the frontier of cryo-EM structure determination of RNA molecules where resolving the structural polymorphism is at dawn.

TomoFlow: Analysis of Continuous Conformational Variability of Macromolecules in Cryogenic Subtomograms based on 3D Dense Optical Flow

Cryogenic Electron Tomography (cryo-ET) allows structural and dynamics studies of macromolecules in situ. Averaging different copies of imaged macromolecules is commonly used to obtain their structure at higher resolution and discrete classification to analyze their dynamics. Instrumental and data processing developments are progressively equipping cryo-ET studies with the ability to escape the trap of classification into a complete continuous conformational variability analysis. In this work, we propose TomoFlow, a method for analyzing macromolecular continuous conformational variability in cryo-ET subtomograms based on a three-dimensional dense optical flow (OF) approach. The resultant lower-dimensional conformational space allows generating movies of macromolecular motion and obtaining subtomogram averages by grouping conformationally similar subtomograms. The animations and the subtomogram group averages reveal accurate trajectories of macromolecular motion based on a novel mathematical model that makes use of OF properties. This paper describes TomoFlow with tests on simulated datasets generated using different techniques, namely Normal Mode Analysis and Molecular Dynamics Simulation. It also shows an application of TomoFlow on a dataset of nucleosomes in situ, which provided promising results coherent with previous findings using the same dataset but without imposing any prior knowledge on the analysis of the conformational variability. The method is discussed with its potential uses and limitations.

Approximating deformation fields for the analysis of continuous heterogeneity of biological macromolecules by 3D Zernike polynomials

Structural biology has evolved greatly due to the advances introduced in fields like electron microscopy. This image-capturing technique, combined with improved algorithms and current data processing software, allows the recovery of different conformational states of a macromolecule, opening new possibilities for the study of its flexibility and dynamic events. However, the ensemble analysis of these different conformations, and in particular their placement into a common variable space in which the differences and similarities can be easily recognized, is not an easy matter. To simplify the analysis of continuous heterogeneity data, this work proposes a new automatic algorithm that relies on a mathematical basis defined over the sphere to estimate the deformation fields describing conformational transitions among different structures. Thanks to the approximation of these deformation fields, it is possible to describe the forces acting on the molecules due to the presence of different motions. It is also possible to represent and compare several structures in a low-dimensional mapping, which summarizes the structural characteristics of different states. All these analyses are integrated into a common framework, providing the user with the ability to combine them seamlessly. In addition, this new approach is a significant step forward compared with principal component analysis and normal mode analysis of cryo-electron microscopy maps, avoiding the need to select components or modes and producing localized analysis.

Rieske head domain dynamics and indazole-derivative inhibition of Candida albicans complex III

Electron transfer between respiratory complexes drives transmembrane proton translocation, which powers ATP synthesis and membrane transport. The homodimeric respiratory complex III (CIII₂) oxidizes ubiquinol to ubiquinone, transferring electrons to cytochrome c and translocating protons through a mechanism known as the Q cycle. The Q cycle involves ubiquinol oxidation and ubiquinone reduction at two different sites within each CIII monomer, as well as movement of the head domain of the Rieske subunit. We determined structures of Candida albicans CIII₂ by cryoelectron microscopy (cryo-EM), revealing endogenous ubiquinone and visualizing the continuum of Rieske head domain conformations. Analysis of these conformations does not indicate cooperativity in the Rieske head domain position or ligand binding in the two CIIIs of the CIII₂ dimer. Cryo-EM with the indazole derivative Inz-5, which inhibits fungal CIII₂ and is fungicidal when administered with fungistatic azole drugs, showed that Inz-5 inhibition alters the equilibrium of Rieske head domain positions.

A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments

Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature it has the potential to provide information about a biomolecule's conformational variability and underlying free-energy landscape. However, treating cryo-EM as a single-molecule technique is challenging because of the low signal-to-noise ratio (SNR) in individual particles. In this work, we propose the cryo-BIFE method (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. We test the framework on several synthetic systems where the imaging parameters and conditions were controlled. We found that for realistic cryo-EM environments and relevant biomolecular systems, it is possible to recover the underlying free energy, with the pose accuracy and SNR as crucial determinants. We then use the method to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of [Formula: see text]. We expect our tool for extracting free-energy profiles from cryo-EM images to enable more complete characterization of the thermodynamic ensemble of biomolecules.

Principal component analysis is limited to low-resolution analysis in cryoEM

Principal component analysis (PCA) has been widely proposed to analyze flexibility and heterogeneity in cryo-electron microscopy (cryoEM). In this paper, it is argued that (i) PCA is an excellent technique to describe continuous flexibility at low resolution (but not so much at high resolution) and (ii) PCA components should be analyzed in a concerted manner (and not independently).

HEMNMA-3D: Cryo Electron Tomography Method Based on Normal Mode Analysis to Study Continuous Conformational Variability of Macromolecular Complexes

Cryogenic electron tomography (cryo-ET) allows structural determination of biomolecules in their native environment (in situ). Its potential of providing information on the dynamics of macromolecular complexes in cells is still largely unexploited, due to the challenges of the data analysis. The crowded cell environment and continuous conformational changes of complexes make difficult disentangling the data heterogeneity. We present HEMNMA-3D, which is, to the best of our knowledge, the first method for analyzing cryo electron subtomograms in terms of continuous conformational changes of complexes. HEMNMA-3D uses a combination of elastic and rigid-body 3D-to-3D iterative alignments of a flexible 3D reference (atomic structure or electron microscopy density map) to match the conformation, orientation, and position of the complex in each subtomogram. The elastic matching combines molecular mechanics simulation (Normal Mode Analysis of the 3D reference) and experimental, subtomogram data analysis. The rigid-body alignment includes compensation for the missing wedge, due to the limited tilt angle of cryo-ET. The conformational parameters (amplitudes of normal modes) of the complexes in subtomograms obtained through the alignment are processed to visualize the distribution of conformations in a space of lower dimension (typically, 2D or 3D) referred to as space of conformations. This allows a visually interpretable insight into the dynamics of the complexes, by calculating 3D averages of subtomograms with similar conformations from selected (densest) regions and by recording movies of the 3D reference's displacement along selected trajectories through the densest regions. We describe HEMNMA-3D and show its validation using synthetic datasets. We apply HEMNMA-3D to an experimental dataset describing in situ nucleosome conformational variability. HEMNMA-3D software is available freely (open-source) as part of ContinuousFlex plugin of Scipion V3.0 (http://scipion.i2pc.es).

3D variability analysis: Resolving continuous flexibility and discrete heterogeneity from single particle cryo-EM

Single particle cryo-EM excels in determining static structures of protein molecules, but existing 3D reconstruction methods have been ineffective in modelling flexible proteins. We introduce 3D variability analysis (3DVA), an algorithm that fits a linear subspace model of conformational change to cryo-EM data at high resolution. 3DVA enables the resolution and visualization of detailed molecular motions of both large and small proteins, revealing new biological insight from single particle cryo-EM data. Experimental results demonstrate the ability of 3DVA to resolve multiple flexible motions of α-helices in the sub-50 kDa transmembrane domain of a GPCR complex, bending modes of a sodium ion channel, five types of symmetric and symmetry-breaking flexibility in a proteasome, large motions in a spliceosome complex, and discrete conformational states of a ribosome assembly. 3DVA is implemented in the cryoSPARC software package.

CryoDRGN: reconstruction of heterogeneous cryo-EM structures using neural networks

Cryo-electron microscopy (cryo-EM) single-particle analysis has proven powerful in determining the structures of rigid macromolecules. However, many imaged protein complexes exhibit conformational and compositional heterogeneity that poses a major challenge to existing three-dimensional reconstruction methods. Here, we present cryoDRGN, an algorithm that leverages the representation power of deep neural networks to directly reconstruct continuous distributions of 3D density maps and map per-particle heterogeneity of single-particle cryo-EM datasets. Using cryoDRGN, we uncovered residual heterogeneity in high-resolution datasets of the 80S ribosome and the RAG complex, revealed a new structural state of the assembling 50S ribosome, and visualized large-scale continuous motions of a spliceosome complex. CryoDRGN contains interactive tools to visualize a dataset's distribution of per-particle variability, generate density maps for exploratory analysis, extract particle subsets for use with other tools and generate trajectories to visualize molecular motions. CryoDRGN is open-source software freely available at http://cryodrgn.csail.mit.edu .

A set of common movements within GPCR-G-protein complexes from variability analysis of cryo-EM datasets

G-protein coupled receptors (GPCRs) are among the most versatile signal transducers in the cell. Once activated, GPCRs sample a large conformational space and couple to G-proteins to initiate distinct signaling pathways. The dynamical behavior of GPCR-G-protein complexes is difficult characterize structurally, and it might hinder obtaining routine high-resolution density maps in single-particle reconstructions. Here, we used variability analysis on the rhodopsin-G_i-Fab16 complex cryo-EM dataset, and the results provide insights into the dynamic nature of the receptor-complex interaction. We compare the outcome of this analysis with recent results obtained on the cannabinoid-G_i- and secretin-G_s-receptor complexes. Despite differences related to the biochemical compositions of the three samples, a set of consensus movements emerges. We anticipate that systematic variability analysis on GPCR-G-protein complexes may provide useful information not only at the biological level, but also for improving the preparation of more stable samples for cryo-EM single-particle analysis.

Continuous flexibility analysis of SARS-CoV-2 spike prefusion structures

Using a new consensus-based image-processing approach together with principal component analysis, the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state have been analysed. These studies revealed concerted motions involving the receptor-binding domain (RBD), N-terminal domain, and subdomains 1 and 2 around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. It is shown that in this data set there are not well defined, stable spike conformations, but virtually a continuum of states. An ensemble map was obtained with minimum bias, from which the extremes of the change along the direction of maximal variance were modeled by flexible fitting. The results provide a warning of the potential image-processing classification instability of these complicated data sets, which has a direct impact on the interpretability of the results.

Structural Heterogeneities of the Ribosome: New Frontiers and Opportunities for Cryo-EM

The extent of ribosomal heterogeneity has caught increasing interest over the past few years, as recent studies have highlighted the presence of structural variations of the ribosome. More precisely, the heterogeneity of the ribosome covers multiple scales, including the dynamical aspects of ribosomal motion at the single particle level, specialization at the cellular and subcellular scale, or evolutionary differences across species. Upon solving the ribosome atomic structure at medium to high resolution, cryogenic electron microscopy (cryo-EM) has enabled investigating all these forms of heterogeneity. In this review, we present some recent advances in quantifying ribosome heterogeneity, with a focus on the conformational and evolutionary variations of the ribosome and their functional implications. These efforts highlight the need for new computational methods and comparative tools, to comprehensively model the continuous conformational transition pathways of the ribosome, as well as its evolution. While developing these methods presents some important challenges, it also provides an opportunity to extend our interpretation and usage of cryo-EM data, which would more generally benefit the study of molecular dynamics and evolution of proteins and other complexes.

Continuous flexibility analysis of SARS-CoV-2 Spike prefusion structures

With the help of novel processing workflows and algorithms, we have obtained a better understanding of the flexibility and conformational dynamics of the SARS-CoV-2 spike in the prefusion state. We have re-analyzed previous cryo-EM data combining 3D clustering approaches with ways to explore a continuous flexibility space based on 3D Principal Component Analysis. These advanced analyses revealed a concerted motion involving the receptor-binding domain (RBD), N-terminal domain (NTD), and subdomain 1 and 2 (SD1 & SD2) around the previously characterized 1-RBD-up state, which have been modeled as elastic deformations. We show that in this dataset there are not well-defined, stable, spike conformations, but virtually a continuum of states moving in a concerted fashion. We obtained an improved resolution ensemble map with minimum bias, from which we model by flexible fitting the extremes of the change along the direction of maximal variance. Moreover, a high-resolution structure of a recently described biochemically stabilized form of the spike is shown to greatly reduce the dynamics observed for the wild-type spike. Our results provide new detailed avenues to potentially restrain the spike dynamics for structure-based drug and vaccine design and at the same time give a warning of the potential image processing classification instability of these complicated datasets, having a direct impact on the interpretability of the results.

Advances in methods for atomic resolution macromolecular structure determination

Recent technical advances have dramatically increased the power and scope of structural biology. New developments in high-resolution cryo-electron microscopy, serial X-ray crystallography, and electron diffraction have been especially transformative. Here we highlight some of the latest advances and current challenges at the frontiers of atomic resolution methods for elucidating the structures and dynamical properties of macromolecules and their complexes.

Computational Methods for Single-Particle Electron Cryomicroscopy

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the three-dimensional molecular structure needs to be determined from many noisy two-dimensional tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications.

Need for Cross-Validation of Single Particle Cryo-EM

Cross-validation is used to determine the validity of a model on unseen data by assessing if the model is overfitted to noise. It is widely used in many fields, from artificial intelligence to structural biology in X-ray crystallography and nuclear magnetic resonance. Although there are concerns of map overfitting in cryo-electron microscopy (cryo-EM), cross-validation is rarely used. The problem is that establishing a performance metric of the maps over unseen data (given by 2D-projection images) is difficult due to the low signal-to-noise ratios in the individual particles. Here, I present recent advances for cryo-EM map reconstruction. I highlight that the gold-standard procedure can fail to detect map overfitting in certain cases, showing the necessity of assessing the map quality on unbiased data. Finally, I describe the challenges and advantages of developing a robust cross-validation methodology for cryo-EM.

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.

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).

Reconstruction of Stochastic 3D Signals With Symmetric Statistics From 2D Projection Images Motivated by Cryo-Electron Microscopy

Cryo-electron microscopy provides 2D projection images of the 3D electron scattering intensity of many instances of the particle under study (e.g., a virus). Both symmetry (rotational point groups) and heterogeneity are important aspects of biological particles and both aspects can be combined by describing the electron scattering intensity of the particle as a stochastic process with a symmetric probability law and, therefore, symmetric moments. A maximum likelihood estimator implemented by an expectation-maximization algorithm is described, which estimates the unknown statistics of the electron scattering intensity stochastic process from the images of instances of the particle. The algorithm is demonstrated on the bacteriophage HK97 and the virus [Formula: see text]. The results are contrasted with the existing algorithms, which assume that each instance of the particle has the symmetry rather than the less restrictive assumption that the probability law has the symmetry.

Modelling structures in cryo-EM maps

Recent advances in structure determination of sub-cellular structures using cryo-electron microscopy and tomography have enabled us to understand their architecture in a more detailed manner and gain insight into their function. The choice of approach to use for atomic model building, fitting, refinement and validation in the 3D map resulting from these experiments depends primarily on the resolution of the map and the prior information on the corresponding model. Here, we survey some of such methods and approaches and highlight their uses in specific recent examples.

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.

Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the three-dimensional (3D) electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy two-dimensional images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For n images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O ( n N 4 + κ N 6 log N ) , where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in six dimensions. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed nonconsistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.

Likelihood-based structural analysis of electron microscopy images

Likelihood-based analysis of single-particle electron microscopy images has contributed much to the recent improvements in resolution. By treating particle orientations and classes probabilistically, uncertainties in the reconstruction process are explicitly accounted for, and the risk of bias towards the initial model is diminished. As a result, the quality and reliability of the reconstructions have greatly improved at manageable computational cost. Likelihood-based analysis of electron microscopy images also offers a route to direct coordinate refinement for dynamic systems, as an alternative to 3D density reconstruction. Here, we review recent developments in the algorithms used for reconstructions of high-resolution maps, and in the integrative framework of combining likelihood methods with simulations to address conformational variability in cryo-electron microscopy.

Allosteric effects in bacteriophage HK97 procapsids revealed directly from covariance analysis of cryo EM data

The information content of cryo EM data sets exceeds that of the electron scattering potential (cryo EM) density initially derived for structure determination. Previously we demonstrated the power of data variance analysis for characterizing regions of cryo EM density that displayed functionally important variance anomalies associated with maturation cleavage events in Nudaurelia Omega Capensis Virus and the presence or absence of a maturation protease in bacteriophage HK97 procapsids. Here we extend the analysis in two ways. First, instead of imposing icosahedral symmetry on every particle in the data set during the variance analysis, we only assume that the data set as a whole has icosahedral symmetry. This change removes artifacts of high variance along icosahedral symmetry axes, but retains all of the features previously reported in the HK97 data set. Second we present a covariance analysis that reveals correlations in structural dynamics (variance) between the interior of the HK97 procapsid with the protease and regions of the exterior (not seen in the absence of the protease). The latter analysis corresponds well with hydrogen deuterium exchange studies previously published that reveal the same correlation.

Massively parallel unsupervised single-particle cryo-EM data clustering via statistical manifold learning

Structural heterogeneity in single-particle cryo-electron microscopy (cryo-EM) data represents a major challenge for high-resolution structure determination. Unsupervised classification may serve as the first step in the assessment of structural heterogeneity. However, traditional algorithms for unsupervised classification, such as K-means clustering and maximum likelihood optimization, may classify images into wrong classes with decreasing signal-to-noise-ratio (SNR) in the image data, yet demand increased computational costs. Overcoming these limitations requires further development of clustering algorithms for high-performance cryo-EM data processing. Here we introduce an unsupervised single-particle clustering algorithm derived from a statistical manifold learning framework called generative topographic mapping (GTM). We show that unsupervised GTM clustering improves classification accuracy by about 40% in the absence of input references for data with lower SNRs. Applications to several experimental datasets suggest that our algorithm can detect subtle structural differences among classes via a hierarchical clustering strategy. After code optimization over a high-performance computing (HPC) environment, our software implementation was able to generate thousands of reference-free class averages within hours in a massively parallel fashion, which allows a significant improvement on ab initio 3D reconstruction and assists in the computational purification of homogeneous datasets for high-resolution visualization.

StructMap: Elastic Distance Analysis of Electron Microscopy Maps for Studying Conformational Changes

Single-particle electron microscopy (EM) has been shown to be very powerful for studying structures and associated conformational changes of macromolecular complexes. In the context of analyzing conformational changes of complexes, distinct EM density maps obtained by image analysis and three-dimensional (3D) reconstruction are usually analyzed in 3D for interpretation of structural differences. However, graphic visualization of these differences based on a quantitative analysis of elastic transformations (deformations) among density maps has not been done yet due to a lack of appropriate methods. Here, we present an approach that allows such visualization. This approach is based on statistical analysis of distances among elastically aligned pairs of EM maps (one map is deformed to fit the other map), and results in visualizing EM maps as points in a lower-dimensional distance space. The distances among points in the new space can be analyzed in terms of clusters or trajectories of points related to potential conformational changes. The results of the method are shown with synthetic and experimental EM maps at different resolutions.