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Van Veen D, Galaz-Montoya JG, Shen L, Baldwin P, Chaudhari AS, Lyumkis D, Schmid MF, Chiu W, Pauly J. Missing Wedge Completion via Unsupervised Learning with Coordinate Networks. Int J Mol Sci 2024; 25:5473. [PMID: 38791508 PMCID: PMC11121946 DOI: 10.3390/ijms25105473] [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: 04/10/2024] [Revised: 04/29/2024] [Accepted: 04/30/2024] [Indexed: 05/26/2024] Open
Abstract
Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3-20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.
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Affiliation(s)
- Dave Van Veen
- Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA;
| | - Jesús G. Galaz-Montoya
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA; (J.G.G.-M.); (W.C.)
| | - Liyue Shen
- Department of Electrical and Computer Engineering, University of Michigan, Ann Arbor, MI 48109, USA;
| | - Philip Baldwin
- Department of Biochemistry and Molecular Pharmacology, Baylor College of Medicine, Houston, TX 77030, USA;
- Department of Genetics, The Salk Institute of Biological Sciences, La Jolla, CA 92037, USA;
| | | | - Dmitry Lyumkis
- Department of Genetics, The Salk Institute of Biological Sciences, La Jolla, CA 92037, USA;
- Graduate School of Biological Sciences, University of California San Diego, La Jolla, CA 92037, USA
| | - Michael F. Schmid
- Division of CryoEM and Bioimaging, SSRL, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA;
| | - Wah Chiu
- Department of Bioengineering, Stanford University, Stanford, CA 94305, USA; (J.G.G.-M.); (W.C.)
- Division of CryoEM and Bioimaging, SSRL, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA;
- Department of Microbiology and Immunology, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - John Pauly
- Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA;
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2
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Van Veen D, Galaz-Montoya JG, Shen L, Baldwin P, Chaudhari AS, Lyumkis D, Schmid MF, Chiu W, Pauly J. Missing Wedge Completion via Unsupervised Learning with Coordinate Networks. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.04.12.589090. [PMID: 38712113 PMCID: PMC11071277 DOI: 10.1101/2024.04.12.589090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2024]
Abstract
Cryogenic electron tomography (cryoET) is a powerful tool in structural biology, enabling detailed 3D imaging of biological specimens at a resolution of nanometers. Despite its potential, cryoET faces challenges such as the missing wedge problem, which limits reconstruction quality due to incomplete data collection angles. Recently, supervised deep learning methods leveraging convolutional neural networks (CNNs) have considerably addressed this issue; however, their pretraining requirements render them susceptible to inaccuracies and artifacts, particularly when representative training data is scarce. To overcome these limitations, we introduce a proof-of-concept unsupervised learning approach using coordinate networks (CNs) that optimizes network weights directly against input projections. This eliminates the need for pretraining, reducing reconstruction runtime by 3 - 20× compared to supervised methods. Our in silico results show improved shape completion and reduction of missing wedge artifacts, assessed through several voxel-based image quality metrics in real space and a novel directional Fourier Shell Correlation (FSC) metric. Our study illuminates benefits and considerations of both supervised and unsupervised approaches, guiding the development of improved reconstruction strategies.
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Affiliation(s)
- Dave Van Veen
- Dept. of Electrical Engineering, Stanford University
| | | | - Liyue Shen
- Dept. of Electrical and Computer Engineering, University of Michigan
| | - Philip Baldwin
- Dept. of Biochemistry and Molecular Pharmacology, Baylor College of Medicine
- Dept. of Genetics, The Salk Institute for Biological Sciences
| | | | - Dmitry Lyumkis
- Dept. of Genetics, The Salk Institute for Biological Sciences
- Graduate School of Biological Sciences, University of California San Diego
| | - Michael F. Schmid
- Division of CryoEM and Bioimaging, SSRL, SLAC National Accelerator Laboratory
| | - Wah Chiu
- Dept. of Bioengineering, Stanford University
- Division of CryoEM and Bioimaging, SSRL, SLAC National Accelerator Laboratory
- Dept. of Microbiology and Immunology, Stanford University
| | - John Pauly
- Dept. of Electrical Engineering, Stanford University
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3
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Zhu D, Cao D, Zhang X. Virus structures revealed by advanced cryoelectron microscopy methods. Structure 2023; 31:1348-1359. [PMID: 37797619 DOI: 10.1016/j.str.2023.09.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 08/25/2023] [Accepted: 09/11/2023] [Indexed: 10/07/2023]
Abstract
Before the resolution revolution, cryoelectron microscopy (cryo-EM) single-particle analysis (SPA) already achieved resolutions beyond 4 Å for certain icosahedral viruses, enabling ab initio atomic model building of these viruses. As the only samples that achieved such high resolution at that time, cryo-EM method development was closely intertwined with the improvement of reconstructions of symmetrical viruses. Viral morphology exhibits significant diversity, ranging from small to large, uniform to non-uniform, and from containing single symmetry to multiple symmetries. Furthermore, viruses undergo conformational changes during their life cycle. Several methods, such as asymmetric reconstruction, Ewald sphere correction, cryoelectron tomography (cryo-ET), and sub-tomogram averaging (STA), have been developed and applied to determine virus structures in vivo and in vitro. This review outlines current advanced cryo-EM methods for high-resolution structure determination of viruses and summarizes accomplishments obtained with these approaches. Moreover, persisting challenges in comprehending virus structures are discussed and we propose potential solutions.
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Affiliation(s)
- Dongjie Zhu
- National Laboratory of Biomacromolecules, CAS Center for Excellence in Biomacromolecules, Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, China
| | - Duanfang Cao
- National Laboratory of Biomacromolecules, CAS Center for Excellence in Biomacromolecules, Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, China; University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xinzheng Zhang
- National Laboratory of Biomacromolecules, CAS Center for Excellence in Biomacromolecules, Institute of Biophysics, Chinese Academy of Sciences, Beijing 100101, China; University of Chinese Academy of Sciences, Beijing 100049, China.
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4
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Zhao C, Lu D, Zhao Q, Ren C, Zhang H, Zhai J, Gou J, Zhu S, Zhang Y, Gong X. Computational methods for in situ structural studies with cryogenic electron tomography. Front Cell Infect Microbiol 2023; 13:1135013. [PMID: 37868346 PMCID: PMC10586593 DOI: 10.3389/fcimb.2023.1135013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Accepted: 08/29/2023] [Indexed: 10/24/2023] Open
Abstract
Cryo-electron tomography (cryo-ET) plays a critical role in imaging microorganisms in situ in terms of further analyzing the working mechanisms of viruses and drug exploitation, among others. A data processing workflow for cryo-ET has been developed to reconstruct three-dimensional density maps and further build atomic models from a tilt series of two-dimensional projections. Low signal-to-noise ratio (SNR) and missing wedge are two major factors that make the reconstruction procedure challenging. Because only few near-atomic resolution structures have been reconstructed in cryo-ET, there is still much room to design new approaches to improve universal reconstruction resolutions. This review summarizes classical mathematical models and deep learning methods among general reconstruction steps. Moreover, we also discuss current limitations and prospects. This review can provide software and methods for each step of the entire procedure from tilt series by cryo-ET to 3D atomic structures. In addition, it can also help more experts in various fields comprehend a recent research trend in cryo-ET. Furthermore, we hope that more researchers can collaborate in developing computational methods and mathematical models for high-resolution three-dimensional structures from cryo-ET datasets.
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Affiliation(s)
- Cuicui Zhao
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Da Lu
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Qian Zhao
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Chongjiao Ren
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Huangtao Zhang
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Jiaqi Zhai
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Jiaxin Gou
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Shilin Zhu
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Yaqi Zhang
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
| | - Xinqi Gong
- Mathematical Intelligence Application LAB, Institute for Mathematical Sciences, Renmin University of China, Beijing, China
- Beijing Academy of Intelligence, Beijing, China
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5
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Koeck PJB. Alternative Forward Models for Imaging Thick Specimens in Transmission Electron Microscopy. MICROSCOPY AND MICROANALYSIS : THE OFFICIAL JOURNAL OF MICROSCOPY SOCIETY OF AMERICA, MICROBEAM ANALYSIS SOCIETY, MICROSCOPICAL SOCIETY OF CANADA 2023; 29:1071-1076. [PMID: 37749689 DOI: 10.1093/micmic/ozad038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Revised: 02/10/2023] [Accepted: 03/09/2023] [Indexed: 09/27/2023]
Abstract
I have investigated two different forward models for image formation in transmission electron microscopy of thick specimens, the 3DCtf model, which introduces a defocus gradient in the linear approximation, and the multislice model. An important result is that the 3DCtf model does not seem to be compatible with the multislice image formation model. A second very useful finding is that the exit wave in the multislice model has an imaginary part, which, in first-order approximation, is a pure projection of the specimen and is not affected by the defocus gradient. The defocus gradient only comes into play in real valued and higher-order imaginary terms. If the multislice model is closer to reality than the 3DCtf-model, then the best way to retrieve the specimen projection for thicker specimens should be a procedure for retrieving the exit wave's imaginary term, for example using images recorded at different defocus values.
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Affiliation(s)
- Philip Johannes Barrett Koeck
- School of Engineering Sciences in Chemistry, Biotechnology and Health, Royal Institute of Technology, Hälsovägen 11 C, 14152 Huddinge, Sweden
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6
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Danita C, Chiu W, Galaz-Montoya JG. Efficient manual annotation of cryogenic electron tomograms using IMOD. STAR Protoc 2022; 3:101658. [PMID: 36097385 PMCID: PMC9463458 DOI: 10.1016/j.xpro.2022.101658] [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: 12/02/2021] [Revised: 03/28/2022] [Accepted: 08/01/2022] [Indexed: 11/24/2022] Open
Abstract
Annotation highlights and segmentation isolates features in cryogenic electron tomograms to improve visualization and quantification of features (for example, their size and abundance, and spatial relationships with other features), facilitating phenotypic structural analyses of cellular tomograms. Here, we present a manual annotation protocol using the open-source software IMOD and describe segmentation of three types of common cellular features: membranes, large globules, and filaments. IMOD’s interpolation function can improve the speed of manual annotation up to an order of magnitude. Interpolation between sparsely annotated slices speeds up manual annotation Manual annotation differentiates between similar features in different contexts Turning annotations into segmentations shows actual data instead of representations of it
Publisher’s note: Undertaking any experimental protocol requires adherence to local institutional guidelines for laboratory safety and ethics.
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7
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Journal of Structural Biology – Paper of the Year 2020. J Struct Biol 2021. [DOI: 10.1016/j.jsb.2021.107762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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8
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TomoAlign: A novel approach to correcting sample motion and 3D CTF in CryoET. J Struct Biol 2021; 213:107778. [PMID: 34416376 DOI: 10.1016/j.jsb.2021.107778] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 07/16/2021] [Accepted: 08/08/2021] [Indexed: 11/23/2022]
Abstract
TomoAlign is a software package that integrates tools to mitigate two important resolution limiting factors in cryoET, namely the beam-induced sample motion and the contrast transfer function (CTF) of the microscope. The package is especially focused on cryoET of thick specimens where fiducial markers are required for accurate tilt-series alignment and sample motion estimation. TomoAlign models the beam-induced sample motion undergone during the tilt-series acquisition. The motion models are used to produce motion-corrected subtilt-series centered on the particles of interest. In addition, the defocus of each particle at each tilt image is determined and can be corrected, resulting in motion-corrected and CTF-corrected subtilt-series from which the subtomograms can be computed. Alternatively, the CTF information can be passed on so that CTF correction can be carried out entirely within external packages like Relion. TomoAlign serves as a versatile tool that can streamline the cryoET workflow from initial alignment of tilt-series to final subtomogram averaging during in situ structure determination.
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9
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Pyle E, Zanetti G. Current data processing strategies for cryo-electron tomography and subtomogram averaging. Biochem J 2021; 478:1827-1845. [PMID: 34003255 PMCID: PMC8133831 DOI: 10.1042/bcj20200715] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Revised: 04/19/2021] [Accepted: 04/26/2021] [Indexed: 12/25/2022]
Abstract
Cryo-electron tomography (cryo-ET) can be used to reconstruct three-dimensional (3D) volumes, or tomograms, from a series of tilted two-dimensional images of biological objects in their near-native states in situ or in vitro. 3D subvolumes, or subtomograms, containing particles of interest can be extracted from tomograms, aligned, and averaged in a process called subtomogram averaging (STA). STA overcomes the low signal to noise ratio within the individual subtomograms to generate structures of the particle(s) of interest. In recent years, cryo-ET with STA has increasingly been capable of reaching subnanometer resolution due to improvements in microscope hardware and data processing strategies. There has also been an increase in the number and quality of software packages available to process cryo-ET data with STA. In this review, we describe and assess the data processing strategies available for cryo-ET data and highlight the recent software developments which have enabled the extraction of high-resolution information from cryo-ET datasets.
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Affiliation(s)
- Euan Pyle
- Institute of Structural and Molecular Biology, Birkbeck College, Malet St., London WC1E 7HX, U.K
| | - Giulia Zanetti
- Institute of Structural and Molecular Biology, Birkbeck College, Malet St., London WC1E 7HX, U.K
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10
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Peck A, Yao Q, Brewster AS, Zwart PH, Heumann JM, Sauter NK, Jensen GJ. Challenges in solving structures from radiation-damaged tomograms of protein nanocrystals assessed by simulation. Acta Crystallogr D Struct Biol 2021; 77:572-586. [PMID: 33950014 PMCID: PMC8098477 DOI: 10.1107/s2059798321002369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Accepted: 03/02/2021] [Indexed: 11/11/2022] Open
Abstract
Structure-determination methods are needed to resolve the atomic details that underlie protein function. X-ray crystallography has provided most of our knowledge of protein structure, but is constrained by the need for large, well ordered crystals and the loss of phase information. The rapidly developing methods of serial femtosecond crystallography, micro-electron diffraction and single-particle reconstruction circumvent the first of these limitations by enabling data collection from nanocrystals or purified proteins. However, the first two methods also suffer from the phase problem, while many proteins fall below the molecular-weight threshold required for single-particle reconstruction. Cryo-electron tomography of protein nanocrystals has the potential to overcome these obstacles of mainstream structure-determination methods. Here, a data-processing scheme is presented that combines routines from X-ray crystallography and new algorithms that have been developed to solve structures from tomograms of nanocrystals. This pipeline handles image-processing challenges specific to tomographic sampling of periodic specimens and is validated using simulated crystals. The tolerance of this workflow to the effects of radiation damage is also assessed. The simulations indicate a trade-off between a wider tilt range to facilitate merging data from multiple tomograms and a smaller tilt increment to improve phase accuracy. Since phase errors, but not merging errors, can be overcome with additional data sets, these results recommend distributing the dose over a wide angular range rather than using a finer sampling interval to solve the protein structure.
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Affiliation(s)
- Ariana Peck
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - Qing Yao
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - Aaron S. Brewster
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Petrus H. Zwart
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
- Center for Advanced Mathematics in Energy Research Applications, Lawrence Berkeley National Laboratory, Berkeley CA 94720, USA
| | - John M. Heumann
- Department of Molecular, Cellular and Developmental Biology, University of Colorado Boulder, Boulder, CO 80309, USA
| | - Nicholas K. Sauter
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Grant J. Jensen
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA 91125, USA
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11
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Kazantsev IG, Matej S, Lewitt RM, Olsen UL, Poulsen HF, Yarovenko IP, Prokhorov IV. Modelling and Simulation of Compton Scatter Image Formation in Positron Emission Tomography. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2020; 28:923-932. [PMID: 34690436 PMCID: PMC8535948 DOI: 10.1515/jiip-2020-0052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the Positron Emission Tomography. The formula of the forward model has been obtained using the Single Scatter Simulation approximation under simplified assumptions and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions. Good fits of the formula-based and statistically generated profiles of scatter projections are observed in the presented numerical results.
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Affiliation(s)
- Ivan G Kazantsev
- Institute of Computational Mathemtics and Mathematical Geophysics, 630090 Novosibirsk, Russia
| | - Samuel Matej
- University of Pennsylvania, Department of Radiology, Philadelphia, PA 19104, USA
| | - Robert M Lewitt
- University of Pennsylvania, Department of Radiology, Philadelphia, PA 19104, USA
| | - Ulrik L Olsen
- Technical University of Denmark, Department of Physics, Fysikvej 307, 2800 Kgs. Lyngby, Denmark
| | - Henning F Poulsen
- Technical University of Denmark, Department of Physics, Fysikvej 307, 2800 Kgs. Lyngby, Denmark
| | - Ivan P Yarovenko
- Institute of Applied Mathematics, 7 Radio, 690041, Vladivostok, Russia
| | - Igor V Prokhorov
- Institute of Applied Mathematics, 7 Radio, 690041, Vladivostok, Russia
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12
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Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons. Ultramicroscopy 2020; 218:113094. [DOI: 10.1016/j.ultramic.2020.113094] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2019] [Revised: 07/06/2020] [Accepted: 08/09/2020] [Indexed: 11/18/2022]
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13
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Weinhardt V, Chen JH, Ekman AA, Guo J, Remesh SG, Hammel M, McDermott G, Chao W, Oh S, Le Gros MA, Larabell CA. Switchable resolution in soft x-ray tomography of single cells. PLoS One 2020; 15:e0227601. [PMID: 31978064 PMCID: PMC6980406 DOI: 10.1371/journal.pone.0227601] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2019] [Accepted: 12/24/2019] [Indexed: 11/18/2022] Open
Abstract
The diversity of living cells, in both size and internal complexity, calls for imaging methods with adaptable spatial resolution. Soft x-ray tomography (SXT) is a three-dimensional imaging technique ideally suited to visualizing and quantifying the internal organization of single cells of varying sizes in a near-native state. The achievable resolution of the soft x-ray microscope is largely determined by the objective lens, but switching between objectives is extremely time-consuming and typically undertaken only during microscope maintenance procedures. Since the resolution of the optic is inversely proportional to the depth of focus, an optic capable of imaging the thickest cells is routinely selected. This unnecessarily limits the achievable resolution in smaller cells and eliminates the ability to obtain high-resolution images of regions of interest in larger cells. Here, we describe developments to overcome this shortfall and allow selection of microscope optics best suited to the specimen characteristics and data requirements. We demonstrate that switchable objective capability advances the flexibility of SXT to enable imaging cells ranging in size from bacteria to yeast and mammalian cells without physically modifying the microscope, and we demonstrate the use of this technology to image the same specimen with both optics.
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Affiliation(s)
- Venera Weinhardt
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Jian-Hua Chen
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Axel A. Ekman
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Jessica Guo
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Soumya G. Remesh
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
| | - Michal Hammel
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
| | - Gerry McDermott
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Weilun Chao
- Center for X-ray Optics, Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
| | - Sharon Oh
- Center for X-ray Optics, Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
| | - Mark A. Le Gros
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
| | - Carolyn A. Larabell
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, California, United States of America
- Department of Anatomy, University of California San Francisco, San Francisco, California, United States of America
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14
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Brillault L, Landsberg MJ. Preparation of Proteins and Macromolecular Assemblies for Cryo-electron Microscopy. Methods Mol Biol 2020; 2073:221-246. [PMID: 31612445 DOI: 10.1007/978-1-4939-9869-2_13] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Cryo-electron microscopy has become popular as the penultimate step on the road to structure determination for many proteins and macromolecular assemblies. The process of obtaining high-resolution images of a purified biomolecular complex in an electron microscope often follows a long, and in many cases exhaustive screening process in which many iterative rounds of protein purification are employed and the sample preparation procedure progressively re-evaluated in order to improve the distribution of particles visualized under the electron microscope, and thus maximize the opportunity for high-resolution structure determination. Typically, negative stain electron microscopy is employed to obtain a preliminary assessment of the sample quality, followed by cryo-EM which first requires the identification of optimal vitrification conditions. The original methods for frozen-hydrated specimen preparation developed over 40 years ago still enjoy widespread use today, although recent developments have set the scene for a future where more systematic and high-throughput approaches to the preparation of vitrified biomolecular complexes may be routinely employed. Here we summarize current approaches and ongoing innovations for the preparation of frozen-hydrated single particle specimens for cryo-EM, highlighting some of the commonly encountered problems and approaches that may help overcome these.
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Affiliation(s)
- Lou Brillault
- School of Chemistry and Molecular Biosciences, The University of Queensland, St. Lucia, QLD, Australia
| | - Michael J Landsberg
- School of Chemistry and Molecular Biosciences, The University of Queensland, St. Lucia, QLD, Australia.
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15
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Abstract
Cryo-electron tomography (cryo-ET) allows three-dimensional (3D) visualization of frozen-hydrated biological samples, such as protein complexes and cell organelles, in near-native environments at nanometer scale. Protein complexes that are present in multiple copies in a set of tomograms can be extracted, mutually aligned, and averaged to yield a signal-enhanced 3D structure up to sub-nanometer or even near-atomic resolution. This technique, called subtomogram averaging (StA), is powered by improvements in EM hardware and image processing software. Importantly, StA provides unique biological insights into the structure and function of cellular machinery in close-to-native contexts. In this chapter, we describe the principles and key steps of StA. We briefly cover sample preparation and data collection with an emphasis on image processing procedures related to tomographic reconstruction, subtomogram alignment, averaging, and classification. We conclude by summarizing current limitations and future directions of this technique with a focus on high-resolution StA.
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16
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Markova EA, Zanetti G. Visualizing membrane trafficking through the electron microscope: cryo-tomography of coat complexes. ACTA CRYSTALLOGRAPHICA SECTION D-STRUCTURAL BIOLOGY 2019; 75:467-474. [PMID: 31063149 PMCID: PMC6503763 DOI: 10.1107/s2059798319005011] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Accepted: 04/12/2019] [Indexed: 11/23/2022]
Abstract
The study of coat protein assemblies on membranes by cryo-electron tomography and subtomogram averaging is discussed, outlining the methodological advancements that enabled the gain of crucial structural insight. Coat proteins mediate vesicular transport between intracellular compartments, which is essential for the distribution of molecules within the eukaryotic cell. The global arrangement of coat proteins on the membrane is key to their function, and cryo-electron tomography and subtomogram averaging have been used to study membrane-bound coat proteins, providing crucial structural insight. This review outlines a workflow for the structural elucidation of coat proteins, incorporating recent developments in the collection and processing of cryo-electron tomography data. Recent work on coat protein I, coat protein II and retromer performed on in vitro reconstitutions or in situ is summarized. These studies have answered long-standing questions regarding the mechanisms of membrane binding, polymerization and assembly regulation of coat proteins.
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Affiliation(s)
- Evgenia A Markova
- Institute of Structural and Molecular Biology, Birkbeck College, Malet Street, London WC1E 7HX, England
| | - Giulia Zanetti
- Institute of Structural and Molecular Biology, Birkbeck College, Malet Street, London WC1E 7HX, England
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17
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Malyshev IV, Chkhalo NI. A method of z-tomography using high-aperture soft X-ray microscopy. Ultramicroscopy 2019; 202:76-86. [PMID: 31003162 DOI: 10.1016/j.ultramic.2019.04.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2018] [Revised: 02/19/2019] [Accepted: 04/10/2019] [Indexed: 11/25/2022]
Abstract
Multilayer normal-incidence mirrors allow the numerical aperture (NA=0.3-0.5) of a projection lens to be significantly increased in the spectral ranges of the water (λ = 2.3-4.4 nm) and carbon (λ = 4.4-7 nm) windows, in comparison with the Fresnel zone plates. The low depth of focus of high-aperture optics (tens of nm) makes it possible to use z-tomography to reconstruct the structure of samples in soft X-ray microscopy. The presence of strong absorption prevents the direct use of a powerful deconvolution apparatus developed for fluorescence optical microscopy to improve the clarity of the image. In this article, the "intensity restoration algorithm" is proposed that takes into account the absorption effect before standard deconvolution. For an imagine lens with NA = 0.3 and a working wavelength of 3.37 nm, the results of simulating an image of a protein cell and its deconvolutionary processing are presented, before and after applying the proposed method. After its application, the deconvolution efficiency is significantly increased. A "full-period" resolution of 40 nm was obtained for the image of a simulated protein cell.
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Affiliation(s)
- Ilya V Malyshev
- Institute for Physics of Microstructures of RAS, GSP-105, 603950 Nizhny Novgorod, Russia.
| | - Nikolay I Chkhalo
- Institute for Physics of Microstructures of RAS, GSP-105, 603950 Nizhny Novgorod, Russia
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18
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Abstract
Cryogenic electron microscopy (cryo-EM) enables structure determination of macromolecular objects and their assemblies. Although the techniques have been developing for nearly four decades, they have gained widespread attention in recent years due to technical advances on numerous fronts, enabling traditional microscopists to break into the world of molecular structural biology. Many samples can now be routinely analyzed at near-atomic resolution using standard imaging and image analysis techniques. However, numerous challenges to conventional workflows remain, and continued technical advances open entirely novel opportunities for discovery and exploration. Here, I will review some of the main methods surrounding cryo-EM with an emphasis specifically on single-particle analysis, and I will highlight challenges, open questions, and opportunities for methodology development.
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Affiliation(s)
- Dmitry Lyumkis
- From the Laboratory of Genetics and Helmsley Center for Genomic Medicine, The Salk Institute for Biological Studies, La Jolla, California 92037
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19
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Himes BA, Zhang P. emClarity: software for high-resolution cryo-electron tomography and subtomogram averaging. Nat Methods 2018; 15:955-961. [PMID: 30349041 PMCID: PMC6281437 DOI: 10.1038/s41592-018-0167-z] [Citation(s) in RCA: 158] [Impact Index Per Article: 26.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2017] [Accepted: 07/25/2018] [Indexed: 11/17/2022]
Abstract
Macromolecular complexes are intrinsically flexible and often challenging to purify for structure determination by single particle cryoEM. Such complexes may be studied using cryo-electron tomography combined with sub-tomogram alignment and classification, which in exceptional cases reaches sub-nanometer resolution, yielding insight into structure-function relationships. Extending this approach to specimens that exhibit conformational or compositional heterogeneity, and that may be present at low abundance, remains challenging. To address this challenge, we developed emClarity (https://github.com/bHimes/emClarity/wiki), a GPU-accelerated image processing package, which features an iterative tomographic tilt-series refinement algorithm using sub-tomograms as fiducial markers and a 3D-samping function compensated, multi-scale Principle Component Analysis classification method. We demonstrate substantial improvements in the resolution of maps and in the separation of different functional states of macromolecular complexes, compared to those generated using current state-of-the-art software.
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Affiliation(s)
- Benjamin A Himes
- Department of Structural Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA.,Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA
| | - Peijun Zhang
- Department of Structural Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA. .,Division of Structural Biology, Wellcome Trust Centre for Human Genetics, University of Oxford, Oxford, UK. .,Electron Bio-Imaging Centre, Diamond Light Source, Didcot, UK.
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20
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Pfeffer S, Mahamid J. Unravelling molecular complexity in structural cell biology. Curr Opin Struct Biol 2018; 52:111-118. [PMID: 30339965 DOI: 10.1016/j.sbi.2018.08.009] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Revised: 06/18/2018] [Accepted: 08/29/2018] [Indexed: 12/14/2022]
Abstract
Structural and cell biology have traditionally been separate disciplines and employed techniques that were well defined within the realm of either one or the other. Recent technological breakthroughs propelled electron microscopy of frozen hydrated specimens (cryo-EM) followed by single-particle analysis (SPA) to become a widely applied approach for obtaining near-atomic resolution structures of purified macromolecules. In parallel, ongoing developments on sample preparation are increasingly successful in bringing molecular views into cell biology. Cryo-electron tomography (cryo-ET) has so far served as the main imaging modality employed in these efforts towards obtaining three-dimensional (3D) volumes of heterogeneous molecular assemblies. We review the state-of-the-art in cryo-ET and computational processing and describe the current opportunities and frontiers for in-cell applications.
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Affiliation(s)
- Stefan Pfeffer
- Centre for Molecular Biology of Heidelberg University (ZMBH), 69120 Heidelberg, Germany
| | - Julia Mahamid
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, 69117 Heidelberg, Germany.
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21
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Sub-2 Å Ewald curvature corrected structure of an AAV2 capsid variant. Nat Commun 2018; 9:3628. [PMID: 30194371 PMCID: PMC6128836 DOI: 10.1038/s41467-018-06076-6] [Citation(s) in RCA: 59] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Accepted: 08/11/2018] [Indexed: 01/08/2023] Open
Abstract
Single-particle cryogenic electron microscopy (cryo-EM) provides a powerful methodology for structural biologists, but the resolutions typically attained with experimentally determined structures have lagged behind microscope capabilities. Here, we exploit several technical advances to improve resolution, including per-particle contrast transfer function (CTF) refinement and correction for Ewald sphere curvature. The latter is demonstrated with several experimental samples and should become more standard as resolutions increase or at lower microscope accelerating voltages. The combined application of the described methods to micrographs recorded on a Titan Krios enables structure determination at ~1.86-Å resolution of an adeno-associated virus serotype 2 variant (AAV2), an important gene-delivery vehicle. The resulting structural details provide an improved model for understanding the biology of AAV that will guide future vector development for gene therapy. Single-particle cryo-EM is a powerful method for macromolecular structure determination. Here the authors demonstrate that Ewald sphere curvature correction, sub-Angstrom pixilation and per-particle CTF refinement can improve map quality and resolution and present the 1.86 Å cryo-EM structure of an adeno-associated virus serotype 2 variant.
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22
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Ekman A, Weinhardt V, Chen JH, McDermott G, Le Gros MA, Larabell C. PSF correction in soft X-ray tomography. J Struct Biol 2018; 204:9-18. [PMID: 29908247 DOI: 10.1016/j.jsb.2018.06.003] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Revised: 06/05/2018] [Accepted: 06/07/2018] [Indexed: 11/29/2022]
Abstract
In this article, we introduce a linear approximation of the forward model of soft X-ray tomography, such that the reconstruction is solvable by standard iterative schemes. This linear model takes into account the three-dimensional point spread function (PSF) of the optical system, which consequently enhances the reconstruction of data. The feasibility of the model is demonstrated on both simulated and experimental data, based on theoretically estimated and experimentally measured PSFs.
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Affiliation(s)
- Axel Ekman
- Department of Anatomy, University of California, San Francisco, CA 94143, USA
| | - Venera Weinhardt
- Department of Anatomy, University of California, San Francisco, CA 94143, USA; Molecular Biophysics and Integrated Bioimaging, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Jian-Hua Chen
- Department of Anatomy, University of California, San Francisco, CA 94143, USA
| | - Gerry McDermott
- Department of Anatomy, University of California, San Francisco, CA 94143, USA
| | - Mark A Le Gros
- Department of Anatomy, University of California, San Francisco, CA 94143, USA; Molecular Biophysics and Integrated Bioimaging, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Carolyn Larabell
- Department of Anatomy, University of California, San Francisco, CA 94143, USA; Molecular Biophysics and Integrated Bioimaging, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
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23
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Pushing the resolution limit by correcting the Ewald sphere effect in single-particle Cryo-EM reconstructions. Nat Commun 2018; 9:1552. [PMID: 29674632 PMCID: PMC5908801 DOI: 10.1038/s41467-018-04051-9] [Citation(s) in RCA: 64] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2018] [Accepted: 03/28/2018] [Indexed: 01/05/2023] Open
Abstract
The Ewald sphere effect is generally neglected when using the Central Projection Theorem for cryo electron microscopy single-particle reconstructions. This can reduce the resolution of a reconstruction. Here we estimate the attainable resolution and report a “block-based” reconstruction method for extending the resolution limit. We find the Ewald sphere effect limits the resolution of large objects, especially large viruses. After processing two real datasets of large viruses, we show that our procedure can extend the resolution for both datasets and can accommodate the flexibility associated with large protein complexes. Conventional reconstruction methods used in cryo-EM single particle analysis do not take the depth of field effect into account. Here the authors present a block-based reconstruction method to deal with the depth of field effect and show that this approach can improve the resolution of cryo-EM virus structures.
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24
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Ewald sphere correction using a single side-band image processing algorithm. Ultramicroscopy 2018; 187:26-33. [PMID: 29413409 PMCID: PMC5862657 DOI: 10.1016/j.ultramic.2017.11.001] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Accepted: 11/03/2017] [Indexed: 11/22/2022]
Abstract
Curvature of the Ewald sphere limits the resolution at which Fourier components in an image can be approximated as corresponding to a projection of the object. Since the radius of the Ewald sphere is inversely proportional to the wavelength of the imaging electrons, this normally imposes a limit on the thickness of specimen for which images can be easily interpreted to a particular resolution. Here we present a computational method for precisely correcting for the curvature of the Ewald sphere using defocused images that delocalise the high-resolution Fourier components from the primary image. By correcting for each approximately Friedel-symmetry-related sideband separately using two distinct complex transforms that effectively move the displaced Fourier components back to where they belong in the structure, we can determine the amplitude and phase of each of the Fourier components separately. This precisely accounts for the effect of Ewald sphere curvature over a bandwidth defined by the defocus and the size of the particle being imaged. We demonstrate this processing algorithm using: 1. simulated images of a particle with only a single, high-resolution Fourier component, and 2. experimental images of gold nanoparticles embedded in ice. Processing micrographs with this algorithm will allow higher resolution imaging of thicker specimens at lower energies without any image degradation or blurring due to errors made by the assumption of a flat Ewald sphere. Although the procedure will work best on images recorded with higher defocus settings than used normally, it should still improve 3D single-particle structure determination using images recorded at any defocus and any electron energy. Finally, since the Ewald sphere curvature is in a known direction in the third dimension which is parallel to the direction of view, this algorithm automatically determines the absolute hand of the specimen without the need for pairs of images with a known tilt angle difference.
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25
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Downing KH, Glaeser RM. Estimating the effect of finite depth of field in single-particle cryo-EM. Ultramicroscopy 2017; 184:94-99. [PMID: 28869854 DOI: 10.1016/j.ultramic.2017.08.007] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2017] [Revised: 08/05/2017] [Accepted: 08/15/2017] [Indexed: 01/30/2023]
Abstract
The extent to which the resolution varies within a three-dimensional (3-D) reconstruction, when the diameter of an object is large, is investigated computationally. Numerical simulation is used to model ideal three-dimensional point-spread functions at different radial positions within an object. It is shown that reconstructed density maps are affected less than might have been expected when particles are larger than the depth of field. This favorable outcome is attributed mainly to the fact that a point which lies outside the depth of field relative to the center, for some orientations of the object, will also lie within the depth of field for other orientations. We find, as a result, that the diameter of a particle can be as much as four times the depth of field (as defined by a 90° phase-error criterion) before curvature of the Ewald sphere becomes a limiting factor in determining the resolution that can be achieved.
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Affiliation(s)
- Kenneth H Downing
- Lawrence Berkeley National Laboratory, University of California, Berkeley CA 94720, USA
| | - Robert M Glaeser
- Lawrence Berkeley National Laboratory, University of California, Berkeley CA 94720, USA.
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26
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Turoňová B, Schur FKM, Wan W, Briggs JAG. Efficient 3D-CTF correction for cryo-electron tomography using NovaCTF improves subtomogram averaging resolution to 3.4Å. J Struct Biol 2017; 199:187-195. [PMID: 28743638 PMCID: PMC5614107 DOI: 10.1016/j.jsb.2017.07.007] [Citation(s) in RCA: 155] [Impact Index Per Article: 22.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2017] [Revised: 07/07/2017] [Accepted: 07/21/2017] [Indexed: 11/17/2022]
Abstract
Cryo-electron tomography (cryo-ET) allows cellular ultrastructures and macromolecular complexes to be imaged in three-dimensions in their native environments. Cryo-electron tomograms are reconstructed from projection images taken at defined tilt-angles. In order to recover high-resolution information from cryo-electron tomograms, it is necessary to measure and correct for the contrast transfer function (CTF) of the microscope. Most commonly, this is performed using protocols that approximate the sample as a two-dimensional (2D) plane. This approximation accounts for differences in defocus and therefore CTF across the tilted sample. It does not account for differences in defocus of objects at different heights within the sample; instead, a 3D approach is required. Currently available approaches for 3D-CTF correction are computationally expensive and have not been widely implemented. Here we simulate the benefits of 3D-CTF correction for high-resolution subtomogram averaging, and present a user-friendly, computationally-efficient 3D-CTF correction tool, NovaCTF, that is compatible with standard tomogram reconstruction workflows in IMOD. We validate the approach on synthetic data and test it using subtomogram averaging of real data. Consistent with our simulations, we find that 3D-CTF correction allows high-resolution structures to be obtained with much smaller subtomogram averaging datasets than are required using 2D-CTF. We also show that using equivalent dataset sizes, 3D-CTF correction can be used to obtain higher-resolution structures. We present a 3.4 Å resolution structure determined by subtomogram averaging.
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Affiliation(s)
- Beata Turoňová
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1, Heidelberg, Germany
| | - Florian K M Schur
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1, Heidelberg, Germany
| | - William Wan
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1, Heidelberg, Germany
| | - John A G Briggs
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, Meyerhofstrasse 1, Heidelberg, Germany; Structural Studies Division, MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge, UK.
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27
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Galaz-Montoya JG, Ludtke SJ. The advent of structural biology in situ by single particle cryo-electron tomography. BIOPHYSICS REPORTS 2017; 3:17-35. [PMID: 28781998 PMCID: PMC5516000 DOI: 10.1007/s41048-017-0040-0] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2017] [Accepted: 03/30/2017] [Indexed: 01/06/2023] Open
Abstract
Single particle tomography (SPT), also known as subtomogram averaging, is a powerful technique uniquely poised to address questions in structural biology that are not amenable to more traditional approaches like X-ray crystallography, nuclear magnetic resonance, and conventional cryoEM single particle analysis. Owing to its potential for in situ structural biology at subnanometer resolution, SPT has been gaining enormous momentum in the last five years and is becoming a prominent, widely used technique. This method can be applied to unambiguously determine the structures of macromolecular complexes that exhibit compositional and conformational heterogeneity, both in vitro and in situ. Here we review the development of SPT, highlighting its applications and identifying areas of ongoing development.
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Affiliation(s)
- Jesús G Galaz-Montoya
- National Center for Macromolecular Imaging, Verna and Marrs McLean Department of Biochemistry and Molecular Biology, Baylor College of Medicine, Houston, TX 77030 USA
| | - Steven J Ludtke
- National Center for Macromolecular Imaging, Verna and Marrs McLean Department of Biochemistry and Molecular Biology, Baylor College of Medicine, Houston, TX 77030 USA
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28
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Three-dimensional CTF correction improves the resolution of electron tomograms. J Struct Biol 2016; 197:114-122. [PMID: 27343995 DOI: 10.1016/j.jsb.2016.06.016] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2016] [Revised: 06/20/2016] [Accepted: 06/21/2016] [Indexed: 11/22/2022]
Abstract
Correction of the contrast transfer function (CTF) of the microscope is a necessary step, in order to achieve high resolution from averaged electron microscopic images. Thereby, the CTF is first estimated and subsequently the electron micrograph is corrected, so that the negative oscillations of the CTF are equalized. Typically, the CTF correction is performed in 2D and the tilt-induced focus gradient is taken into account. Most often, the sample-thickness-induced focus gradient is ignored. Theoretical considerations, as well as implementation suggestions, for a 3D CTF correction that considers both gradients have been proposed before, although an implementation achieving a resolution improvement has been lacking, primarily due to computational reasons. Here, we present a comprehensive solution for a 3D CTF correction based on the Jensen-Kornberg scheme, which performs a slice-by-slice correction of the CTF within the tomographic reconstruction. We show that the computational requirements are comparable to those of 2D CTF correction. Using the examples of mitochondrial ribosomes and tobacco mosaic virus we demonstrate the improvement of the reconstruction quality with the 3D CTF correction, and the resolution gain on sub-tomogram averaging. More interestingly, for tomographic applications, the quality of the individual sub-tomograms before averaging increases significantly. We find that 3D CTF correction always produces equal or better results than 2D CTF correction.
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29
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Abstract
Cryo-electron tomography (cryo-ET) allows 3D volumes to be reconstructed from a set of 2D projection images of a tilted biological sample. It allows densities to be resolved in 3D that would otherwise overlap in 2D projection images. Cryo-ET can be applied to resolve structural features in complex native environments, such as within the cell. Analogous to single-particle reconstruction in cryo-electron microscopy, structures present in multiple copies within tomograms can be extracted, aligned, and averaged, thus increasing the signal-to-noise ratio and resolution. This reconstruction approach, termed subtomogram averaging, can be used to determine protein structures in situ. It can also be applied to facilitate more conventional 2D image analysis approaches. In this chapter, we provide an introduction to cryo-ET and subtomogram averaging. We describe the overall workflow, including tomographic data collection, preprocessing, tomogram reconstruction, subtomogram alignment and averaging, classification, and postprocessing. We consider theoretical issues and practical considerations for each step in the workflow, along with descriptions of recent methodological advances and remaining limitations.
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Affiliation(s)
- W Wan
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, Heidelberg, Germany
| | - J A G Briggs
- Structural and Computational Biology Unit, European Molecular Biology Laboratory, Heidelberg, Germany.
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30
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Selin M, Fogelqvist E, Werner S, Hertz HM. Tomographic reconstruction in soft x-ray microscopy using focus-stack back-projection. OPTICS LETTERS 2015; 40:2201-2204. [PMID: 26393699 DOI: 10.1364/ol.40.002201] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Tomographic reconstruction in soft x-ray microscopy is a powerful technique for obtaining high-resolution 3D images of biological samples. However, the depth of focus of such zone-plate-based microscopes is typically shorter than the thickness of many relevant biological objects, challenging the validity of the projection assumption used in conventional reconstruction algorithms. In order to make full use of the soft x-ray microscopes' high resolution, the tomographic reconstruction needs to take the depth of focus into account. Here we present a method to achieve high resolution in the full sample when the depth of focus is short compared to the sample thickness. The method relies on the back-projection of focus-stacked image data from x-ray microscopy. We demonstrate the method on theoretical and experimental data.
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31
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KOECK P, KARSHIKOFF A. Limitations of the linear and the projection approximations in three-dimensional transmission electron microscopy of fully hydrated proteins. J Microsc 2015; 259:197-209. [DOI: 10.1111/jmi.12253] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2014] [Accepted: 03/09/2015] [Indexed: 11/29/2022]
Affiliation(s)
- P.J.B. KOECK
- Royal Institute of Technology; School of Technology and Health; Handen Sweden
- Department of Biosciences and Nutrition; Karolinska Institutet; Huddinge Sweden
| | - A. KARSHIKOFF
- Department of Biosciences and Nutrition; Karolinska Institutet; Huddinge Sweden
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32
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Kirchenbuechler D, Mutsafi Y, Horowitz B, Levin-Zaidman S, Fass D, G. Wolf S, Elbaum M. Cryo-STEM Tomography of Intact Vitrified Fibroblasts. AIMS BIOPHYSICS 2015. [DOI: 10.3934/biophy.2015.3.259] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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33
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Quantifying resolution limiting factors in subtomogram averaged cryo-electron tomography using simulations. J Struct Biol 2014; 187:103-111. [PMID: 24998892 DOI: 10.1016/j.jsb.2014.06.007] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2013] [Revised: 06/22/2014] [Accepted: 06/23/2014] [Indexed: 11/21/2022]
Abstract
Cryo-electron tomography (CET) is the only available technique capable of characterizing the structure of biological macromolecules in conditions close to the native state. With the advent of subtomogram averaging, as a post-processing step to CET, resolutions in the (sub-) nanometer range have become within reach. In addition to advances in instrumentation and experiments, the reconstruction scheme has improved by inclusion of more accurate contrast transfer function (CTF) correction methods, better defocus estimation, and better alignments of the tilt-series and subtomograms. To quantify the importance of each contribution, we have split the full process from data collection to reconstruction into different steps. For the purpose of evaluation we have acquired tilt-series of ribosomes in such a way that we could precisely determine the defocus of each macromolecule. Then, we simulated tilt-series using the InSilicoTEM package and applied tomogram reconstruction and subtomogram averaging. Through large scale simulations under different conditions and parameter settings we find that tilt-series alignment is the resolution limiting factor for our experimental data. Using simulations, we find that when this alignment inaccuracy is alleviated, tilted CTF correction improves the final resolution, or equivalently, the same resolution can be achieved using less particles. Furthermore, we predict from which resolution onwards better CTF correction and defocus estimation methods are required. We obtain a final average using 3198 ribosomes with a resolution of 2.2nm on the experimental data. Our simulations suggest that with the same number of particles a resolution of 1.2nm could be achieved by improving the tilt-series alignment.
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34
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Voortman LM, Franken EM, van Vliet LJ, Rieger B. Fast, spatially varying CTF correction in TEM. Ultramicroscopy 2012; 118:26-34. [DOI: 10.1016/j.ultramic.2012.05.002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2012] [Revised: 05/02/2012] [Accepted: 05/04/2012] [Indexed: 10/28/2022]
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35
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Zhang X, Zhou ZH. Limiting factors in atomic resolution cryo electron microscopy: no simple tricks. J Struct Biol 2011; 175:253-63. [PMID: 21627992 PMCID: PMC3710782 DOI: 10.1016/j.jsb.2011.05.004] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2010] [Revised: 05/03/2011] [Accepted: 05/05/2011] [Indexed: 01/25/2023]
Abstract
To bring cryo electron microscopy (cryoEM) of large biological complexes to atomic resolution, several factors--in both cryoEM image acquisition and 3D reconstruction--that may be neglected at low resolution become significantly limiting. Here we present thorough analyses of four limiting factors: (a) electron-beam tilt, (b) inaccurate determination of defocus values, (c) focus gradient through particles, and (d) particularly for large particles, dynamic (multiple) scattering of electrons. We also propose strategies to cope with these factors: (a) the divergence and direction tilt components of electron-beam tilt could be reduced by maintaining parallel illumination and by using a coma-free alignment procedure, respectively. Moreover, the effect of all beam tilt components, including spiral tilt, could be eliminated by use of a spherical aberration corrector. (b) More accurate measurement of defocus value could be obtained by imaging areas adjacent to the target area at high electron dose and by measuring the image shift induced by tilting the electron beam. (c) Each known Fourier coefficient in the Fourier transform of a cryoEM image is the sum of two Fourier coefficients of the 3D structure, one on each of two curved 'characteristic surfaces' in 3D Fourier space. We describe a simple model-based iterative method that could recover these two Fourier coefficients on the two characteristic surfaces. (d) The effect of dynamic scattering could be corrected by deconvolution of a transfer function. These analyses and our proposed strategies offer useful guidance for future experimental designs targeting atomic resolution cryoEM reconstruction.
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Affiliation(s)
- Xing Zhang
- Department of Microbiology, Immunology & Molecular Genetics, University of California, Los Angeles, 237 BSRB, 615 Charles E. Young Dr. S., Los Angeles, CA 90095-7364, USA California NanoSystems Institute, University of California, Los Angeles, Box 957227, 570 Westwood Plaza, Bldg 114, Los Angeles, CA 90095-7227, USA
| | - Z. Hong Zhou
- Department of Microbiology, Immunology & Molecular Genetics, University of California, Los Angeles, 237 BSRB, 615 Charles E. Young Dr. S., Los Angeles, CA 90095-7364, USA California NanoSystems Institute, University of California, Los Angeles, Box 957227, 570 Westwood Plaza, Bldg 114, Los Angeles, CA 90095-7227, USA
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36
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Voortman LM, Stallinga S, Schoenmakers RHM, van Vliet LJ, Rieger B. A fast algorithm for computing and correcting the CTF for tilted, thick specimens in TEM. Ultramicroscopy 2011; 111:1029-36. [PMID: 21740865 DOI: 10.1016/j.ultramic.2011.03.001] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2010] [Revised: 12/15/2010] [Accepted: 03/01/2011] [Indexed: 10/18/2022]
Abstract
Today, the resolution in phase-contrast cryo-electron tomography is for a significant part limited by the contrast transfer function (CTF) of the microscope. The CTF is a function of defocus and thus varies spatially as a result of the tilting of the specimen and the finite specimen thickness. Models that include spatial dependencies have not been adopted in daily practice because of their high computational complexity. Here we present an algorithm which reduces the processing time for computing the 'tilted' CTF by more than a factor 100. Our implementation of the full 3D CTF has a processing time on the order of a Radon transform of a full tilt-series. We derive and validate an expression for the damping envelope function describing the loss of resolution due to specimen thickness. Using simulations we quantify the effects of specimen thickness on the accuracy of various forward models. We study the influence of spatially varying CTF correction and subsequent tomographic reconstruction by simulation and present a new approach for space-variant phase-flipping. We show that our CTF correction strategies are successful in increasing the resolution after tomographic reconstruction.
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Affiliation(s)
- Lenard M Voortman
- Quantitative Imaging Group, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands.
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Kazantsev IG, Klukowska J, Herman GT, Cernetic L. Fully three-dimensional defocus-gradient corrected backprojection in cryoelectron microscopy. Ultramicroscopy 2010; 110:1128-42. [PMID: 20462697 DOI: 10.1016/j.ultramic.2010.04.002] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2009] [Revised: 02/04/2010] [Accepted: 04/13/2010] [Indexed: 11/18/2022]
Abstract
Recognizing that the microscope depth of field is a significant resolution-limiting factor in 3D cryoelectron microscopy, Jensen and Kornberg proposed a concept they called defocus-gradient corrected backprojection (DGCBP) and illustrated by computer simulations that DGCBP can effectively eliminate the depth of field limitation. They did not provide a mathematical justification for their concept. Our paper provides this, by showing (in the idealized case of noiseless data being available for all projection directions) that the reconstructions obtained based on DGCBP from data produced with distance-dependent blurring are essentially the same as what is obtained by a classical method of reconstruction of a 3D object from its line integrals. The approach is general enough to be applicable for correcting for any distance-dependent blurring during projection data collection. We present a new implementation of the DGCBP concept, one that closely follows the mathematics of its justifications, and illustrate it using mathematically described phantoms and their reconstructions from finitely many distance-dependently blurred projections.
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Affiliation(s)
- Ivan G Kazantsev
- RISØ, Materials Research Department, Technical University of Denmark, DK-4000, Roskilde, Denmark.
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38
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Abstract
To avoid the challenges of crystallization and the size limitations of NMR, it has long been hoped that single-particle cryo-electron microscopy (cryo-EM) would eventually yield atomically interpretable reconstructions. For the most favorable class of specimens (large icosahedral viruses), one of the key obstacles is curvature of the Ewald sphere, which leads to a breakdown of the Projection Theorem used by conventional three-dimensional (3D) reconstruction programs. Here, we review the basic problem and our implementation of the "paraboloid" reconstruction method, which overcomes the limitation by averaging information from images recorded from different points of view.
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Zhou ZH. Towards atomic resolution structural determination by single-particle cryo-electron microscopy. Curr Opin Struct Biol 2008; 18:218-28. [PMID: 18403197 PMCID: PMC2714865 DOI: 10.1016/j.sbi.2008.03.004] [Citation(s) in RCA: 145] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2008] [Revised: 03/01/2008] [Accepted: 03/04/2008] [Indexed: 11/19/2022]
Abstract
Recent advances in cryo-electron microscopy and single-particle reconstruction (collectively referred to as 'cryoEM') have made it possible to determine the three-dimensional (3D) structures of several macromolecular complexes at near-atomic resolution ( approximately 3.8-4.5A). These achievements were accomplished by overcoming the challenges in sample handling, instrumentation, image processing, and model building. At near-atomic resolution, many detailed structural features can be resolved, such as the turns and deep grooves of helices, strand separation in beta sheets, and densities for loops and bulky amino acid side chains. Such structural data of the cytoplasmic polyhedrosis virus (CPV), the Epsilon 15 bacteriophage and the GroEL complex have provided valuable constraints for atomic model building using integrative tools, thus significantly enhancing the value of the cryoEM structures. The CPV structure revealed a drastic conformational change from a helix to a beta hairpin associated with RNA packaging and replication, coupling of RNA processing and release, and the long sought-after polyhedrin-binding domain. These latest advances in single-particle cryoEM provide exciting opportunities for the 3D structural determination of viruses and macromolecular complexes that are either too large or too heterogeneous to be investigated by conventional X-ray crystallography or nuclear magnetic resonance (NMR) methods.
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Affiliation(s)
- Z Hong Zhou
- Department of Microbiology, Immunology & Molecular Genetics and the California NanoSystems Institute, University of California at Los Angeles, 237 BSRB, 615 Charles E. Young Dr. S., Los Angeles, CA 90095-7364, USA.
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40
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Yan X, Chipman PR, Castberg T, Bratbak G, Baker TS. The marine algal virus PpV01 has an icosahedral capsid with T=219 quasisymmetry. J Virol 2005; 79:9236-43. [PMID: 15994818 PMCID: PMC1168743 DOI: 10.1128/jvi.79.14.9236-9243.2005] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Phaeocystis pouchetii virus (PpV01) infects and lyses the haptophyte Phaeocystis pouchetii (Hariot) Lagerheim and was first isolated from Norwegian coastal waters. We have used electron cryomicroscopy and three-dimensional image reconstruction methods to examine the native morphology of PpV01 at a resolution of 3 nm. The icosahedral capsid of PpV01 has a maximum diameter of 220 nm and is composed of 2,192 capsomers arranged with T=219 quasisymmetry. One specific capsomer in each asymmetric unit contains a fiber-like protrusion. Density attributed to the presence of a lipid membrane appears just below (inside) the capsid. PpV01 is the largest icosahedral virus whose capsid structure has been determined in three dimensions from images of vitrified samples. Striking similarities in the structures of PpV01 and a number of other large double-stranded DNA viruses are consistent with a growing body of evidence that they share a common evolutionary origin.
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Affiliation(s)
- Xiaodong Yan
- Department of Biological Sciences, Purdue University, West Lafayette, Indiana 47907, USA
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41
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Winkler H, Taylor KA. Focus gradient correction applied to tilt series image data used in electron tomography. J Struct Biol 2003; 143:24-32. [PMID: 12892723 DOI: 10.1016/s1047-8477(03)00120-5] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The resolution in 3D reconstructions from tilt series is limited to the information below the first zero of the contrast transfer function unless the signal is corrected computationally. The restoration is usually based on the assumption of a linear space-invariant system and a linear relationship between object mass density and observed image contrast. The space-invariant model is no longer valid when applied to tilted micrographs because the defocus varies in a direction perpendicular to the tilt axis and with it the shape of the associated point spread function. In this paper, a method is presented for determining the defocus gradient in thin specimens such as sections and 2D crystals, and for restoration of the images subsequently used for 3D reconstruction. The alignment procedure for 3D reconstruction includes area matching and tilt geometry refinement. A map with limited resolution computed from uncorrected micrographs is compared to a volume computed from corrected micrographs with extended resolution.
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Affiliation(s)
- Hanspeter Winkler
- Institute of Molecular Biophysics, Florida State University, Mail Code 4380, Tallahassee, FL 32306-4380, USA
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Abstract
To determine the structure of a biological particle to high resolution by electron microscopy, image averaging is required to combine information from different views and to increase the signal-to-noise ratio. Starting from the number of noiseless views necessary to resolve features of a given size, four general factors are considered that increase the number of images actually needed: (1) the physics of electron scattering introduces shot noise, (2) thermal motion and particle inhomogeneity cause the scattered electrons to describe a mixture of structures, (3) the microscope system fails to usefully record all the information carried by the scattered electrons, and (4) image misalignment leads to information loss through incoherent averaging. The compound effect of factors 2-4 is approximated by the product of envelope functions. The problem of incoherent image averaging is developed in detail through derivation of five envelope functions that account for small errors in 11 "alignment" parameters describing particle location, orientation, defocus, magnification, and beam tilt. The analysis provides target error tolerances for single particle analysis to near-atomic (3.5 A) resolution, and this prospect is shown to depend critically on image quality, defocus determination, and microscope alignment.
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Affiliation(s)
- G J Jensen
- Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720-0001, USA.
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