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Vuillemot R, Harastani M, Hamitouche I, Jonic S. 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. Int J Mol Sci 2023; 25:20. [PMID: 38203192 PMCID: PMC10779004 DOI: 10.3390/ijms25010020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 12/16/2023] [Accepted: 12/17/2023] [Indexed: 01/12/2024] Open
Abstract
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.
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Affiliation(s)
| | | | | | - Slavica Jonic
- IMPMC-UMR 7590 CNRS, Sorbonne Université, MNHN, 75005 Paris, France
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2
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DiIorio MC, Kulczyk AW. Novel Artificial Intelligence-Based Approaches for Ab Initio Structure Determination and Atomic Model Building for Cryo-Electron Microscopy. MICROMACHINES 2023; 14:1674. [PMID: 37763837 PMCID: PMC10534518 DOI: 10.3390/mi14091674] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Revised: 08/21/2023] [Accepted: 08/25/2023] [Indexed: 09/29/2023]
Abstract
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.
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Affiliation(s)
- Megan C. DiIorio
- Institute for Quantitative Biomedicine, Rutgers University, 174 Frelinghuysen Road, Piscataway, NJ 08854, USA
| | - Arkadiusz W. Kulczyk
- Institute for Quantitative Biomedicine, Rutgers University, 174 Frelinghuysen Road, Piscataway, NJ 08854, USA
- Department of Biochemistry & Microbiology, Rutgers University, 76 Lipman Drive, New Brunswick, NJ 08901, USA
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3
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Punjani A, Fleet DJ. 3DFlex: determining structure and motion of flexible proteins from cryo-EM. Nat Methods 2023:10.1038/s41592-023-01853-8. [PMID: 37169929 DOI: 10.1038/s41592-023-01853-8] [Citation(s) in RCA: 53] [Impact Index Per Article: 53.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 03/16/2023] [Indexed: 05/13/2023]
Abstract
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.
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Affiliation(s)
- Ali Punjani
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada.
- Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada.
- Structura Biotechnology Inc., Toronto, Ontario, Canada.
| | - David J Fleet
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada.
- Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada.
- Google Research, Toronto, Ontario, Canada.
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4
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Toader B, Sigworth FJ, Lederman RR. Methods for Cryo-EM Single Particle Reconstruction of Macromolecules Having Continuous Heterogeneity. J Mol Biol 2023; 435:168020. [PMID: 36863660 PMCID: PMC10164696 DOI: 10.1016/j.jmb.2023.168020] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Revised: 02/15/2023] [Accepted: 02/16/2023] [Indexed: 03/02/2023]
Abstract
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.
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Affiliation(s)
- Bogdan Toader
- Department of Statistics and Data Science, Yale University, United States.
| | - Fred J Sigworth
- Department of Cellular and Molecular Physiology, Yale University, United States
| | - Roy R Lederman
- Department of Statistics and Data Science, Yale University, United States. https://twitter.com/roylederman
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5
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Herreros D, Kiska J, Ramirez E, Filipovic J, Carazo JM, Sorzano COS. ZART: A novel multiresolution reconstruction algorithm with motion-blur correction for single particle analysis. J Mol Biol 2023; 435:168088. [PMID: 37030648 DOI: 10.1016/j.jmb.2023.168088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 03/31/2023] [Accepted: 04/01/2023] [Indexed: 04/10/2023]
Abstract
One of the main purposes of CryoEM Single Particle Analysis is to reconstruct the three-dimensional structure of a macromolecule thanks to the acquisition of many particle images representing different poses of the sample. By estimating the orientation of each projected particle, it is possible to recover the underlying 3D volume by multiple 3D reconstruction methods, usually working either in Fourier or in real space. However, the reconstruction from the projected images works under the assumption that all particles in the dataset correspond to the same conformation of the macromolecule. Although this requisite holds for some macromolecules, it is not true for flexible specimens, leading to motion-induced artefacts in the reconstructed CryoEM maps. In this work, we introduce a new Algebraic Reconstruction Technique called ZART, which is able to include continuous flexibility information during the reconstruction process to improve local resolution and reduce motion blurring. The conformational changes are modelled through Zernike3D polynomials. Our implementation allows for a multiresolution description of the macromolecule adapting itself to the local resolution of the reconstructed map. In addition, ZART has also proven to be a useful algorithm in cases where flexibility is not so dominant, as it improves the overall aspect of the reconstructed maps by improving their local and global resolution.
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Affiliation(s)
- D Herreros
- Centro Nacional de Biotecnologia-CSIC, C/ Darwin, 3, 28049, Cantoblanco, Madrid, Spain.
| | - J Kiska
- Institute of Computer Science, Masaryk University, Botanická 68a, 60200 Brno, Czech Republic
| | - E Ramirez
- Centro Nacional de Biotecnologia-CSIC, C/ Darwin, 3, 28049, Cantoblanco, Madrid, Spain
| | - J Filipovic
- Institute of Computer Science, Masaryk University, Botanická 68a, 60200 Brno, Czech Republic
| | - J M Carazo
- Centro Nacional de Biotecnologia-CSIC, C/ Darwin, 3, 28049, Cantoblanco, Madrid, Spain.
| | - C O S Sorzano
- Centro Nacional de Biotecnologia-CSIC, C/ Darwin, 3, 28049, Cantoblanco, Madrid, Spain.
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6
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Herreros D, Lederman RR, Krieger JM, Jiménez-Moreno A, Martínez M, Myška D, Strelak D, Filipovic J, Sorzano COS, Carazo JM. Estimating conformational landscapes from Cryo-EM particles by 3D Zernike polynomials. Nat Commun 2023; 14:154. [PMID: 36631472 PMCID: PMC9832421 DOI: 10.1038/s41467-023-35791-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2022] [Accepted: 12/29/2022] [Indexed: 01/12/2023] Open
Abstract
The new developments in Cryo-EM Single Particle Analysis are helping us to understand how the macromolecular structure and function meet to drive biological processes. By capturing many states at the particle level, it is possible to address how macromolecules explore different conformations, information that is classically extracted through 3D classification. However, the limitations of classical approaches prevent us from fully understanding the complete conformational landscape due to the reduced number of discrete states accurately reconstructed. To characterize the whole structural spectrum of a macromolecule, we propose an extension of our Zernike3D approach, able to extract per-image continuous flexibility information directly from a particle dataset. Also, our method can be seamlessly applied to images, maps or atomic models, opening integrative possibilities. Furthermore, we introduce the ZART reconstruction algorithm, which considers the Zernike3D deformation fields to revert particle conformational changes during the reconstruction process, thus minimizing the blurring induced by molecular motions.
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Affiliation(s)
- D Herreros
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain.
| | - R R Lederman
- The Department of Statistics and Data Science, Yale University, New Haven, CT, USA
| | - J M Krieger
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain
| | - A Jiménez-Moreno
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain
| | - M Martínez
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain
| | - D Myška
- Institute of Computer Science, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic
| | - D Strelak
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain.,Faculty of Informatics, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic
| | - J Filipovic
- Institute of Computer Science, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic
| | - C O S Sorzano
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain
| | - J M Carazo
- Centro Nacional de Biotecnologia-CSIC, C/Darwin, 3, 28049, Cantoblanco, Madrid, Spain
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Vuillemot R, Mirzaei A, Harastani M, Hamitouche I, Fréchin L, Klaholz BP, Miyashita O, Tama F, Rouiller I, Jonic S. MDSPACE: Extracting Continuous Conformational Landscapes from Cryo-EM Single Particle Datasets Using 3D-to-2D Flexible Fitting based on Molecular Dynamics Simulation. J Mol Biol 2023; 435:167951. [PMID: 36638910 DOI: 10.1016/j.jmb.2023.167951] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2022] [Revised: 12/08/2022] [Accepted: 01/03/2023] [Indexed: 01/12/2023]
Abstract
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.
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Affiliation(s)
- Rémi Vuillemot
- IMPMC-UMR 7590 CNRS, Sorbonne Université, Muséum National d'Histoire Naturelle, Paris, France; Department of Biochemistry & Pharmacology and Bio21 Molecular Science and Biotechnology Institute, The University of Melbourne, Victoria, Australia
| | - Alex Mirzaei
- IMPMC-UMR 7590 CNRS, Sorbonne Université, Muséum National d'Histoire Naturelle, Paris, France
| | - Mohamad Harastani
- IMPMC-UMR 7590 CNRS, Sorbonne Université, Muséum National d'Histoire Naturelle, Paris, France
| | - Ilyes Hamitouche
- IMPMC-UMR 7590 CNRS, Sorbonne Université, Muséum National d'Histoire Naturelle, Paris, France
| | - Léo Fréchin
- Centre for Integrative Biology, Department of Integrated Structural Biology, IGBMC-UMR 7104 CNRS, U964 Inserm, Université de Strasbourg, Strasbourg, France
| | - Bruno P Klaholz
- Centre for Integrative Biology, Department of Integrated Structural Biology, IGBMC-UMR 7104 CNRS, U964 Inserm, Université de Strasbourg, Strasbourg, France
| | | | - Florence Tama
- RIKEN Center for Computational Science, Kobe, Japan; Institute of Transformative Biomolecules, Graduate School of Science, Nagoya University, Nagoya, Japan; Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Isabelle Rouiller
- Department of Biochemistry & Pharmacology and Bio21 Molecular Science and Biotechnology Institute, The University of Melbourne, Victoria, Australia
| | - Slavica Jonic
- IMPMC-UMR 7590 CNRS, Sorbonne Université, Muséum National d'Histoire Naturelle, Paris, France.
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8
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Hamitouche I, Jonic S. DeepHEMNMA: ResNet-based hybrid analysis of continuous conformational heterogeneity in cryo-EM single particle images. Front Mol Biosci 2022; 9:965645. [PMID: 36158571 PMCID: PMC9493108 DOI: 10.3389/fmolb.2022.965645] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 08/08/2022] [Indexed: 11/13/2022] Open
Abstract
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.
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9
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Visualizing Conformational Space of Functional Biomolecular Complexes by Deep Manifold Learning. Int J Mol Sci 2022; 23:ijms23168872. [PMID: 36012133 PMCID: PMC9408802 DOI: 10.3390/ijms23168872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2022] [Revised: 07/29/2022] [Accepted: 08/03/2022] [Indexed: 11/17/2022] Open
Abstract
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.
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DeVore K, Chiu PL. Probing Structural Perturbation of Biomolecules by Extracting Cryo-EM Data Heterogeneity. Biomolecules 2022; 12:biom12050628. [PMID: 35625556 PMCID: PMC9138638 DOI: 10.3390/biom12050628] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 04/15/2022] [Accepted: 04/18/2022] [Indexed: 02/04/2023] Open
Abstract
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.
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Giraldo-Barreto J, Ortiz S, Thiede EH, Palacio-Rodriguez K, Carpenter B, Barnett AH, Cossio P. A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments. Sci Rep 2021; 11:13657. [PMID: 34211017 PMCID: PMC8249403 DOI: 10.1038/s41598-021-92621-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 06/01/2021] [Indexed: 11/08/2022] Open
Abstract
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.
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Affiliation(s)
- Julian Giraldo-Barreto
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia
- Magnetism and Simulation Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia
| | - Sebastian Ortiz
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia
| | - Erik H Thiede
- Center for Computational Mathematics, Flatiron Institute, New York City, USA
| | - Karen Palacio-Rodriguez
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, Paris, France
| | - Bob Carpenter
- Center for Computational Mathematics, Flatiron Institute, New York City, USA
| | - Alex H Barnett
- Center for Computational Mathematics, Flatiron Institute, New York City, USA
| | - Pilar Cossio
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia.
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438, Frankfurt am Main, Germany.
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12
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Abstract
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.
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Affiliation(s)
- Amit Singer
- Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
| | - Fred J Sigworth
- Departments of Cellular and Molecular Physiology, Biomedical Engineering, and Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA
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