1932

Abstract

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) 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 3D molecular structure needs to be determined from many noisy 2D 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, which also play a significant role in many other data science applications.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-biodatasci-021020-093826
2020-07-20
2024-06-24
Loading full text...

Full text loading...

/deliver/fulltext/biodatasci/3/1/annurev-biodatasci-021020-093826.html?itemId=/content/journals/10.1146/annurev-biodatasci-021020-093826&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Nogales E. 2016. The development of cryo-EM into a mainstream structural biology technique. Nat. Methods 13:24–27
    [Google Scholar]
  2. 2. 
    Henderson R. 1995. The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules. Q. Rev. Biophys. 28:171–93
    [Google Scholar]
  3. 3. 
    Frank J. 2006. Three-Dimensional Electron Microscopy of Macromolecular Assemblies New York: Academic
    [Google Scholar]
  4. 4. 
    Glaeser RM. 1999. Electron crystallography: present excitement, a nod to the past, anticipating the future. J. Struct. Biol. 128:3–14
    [Google Scholar]
  5. 5. 
    Holton JM, Frankel KA. 2010. The minimum crystal size needed for a complete diffraction data set. Acta Crystallogr. D 66:393–408
    [Google Scholar]
  6. 6. 
    Sathyanarayanan N, Cannone G, Gakhar L, Katagihallimath N, Sowdhamini R et al. 2019. Molecular basis for metabolite channeling in a ring opening enzyme of the phenylacetate degradation pathway. Nat. Commun. 10:4127
    [Google Scholar]
  7. 7. 
    Dubochet J, Lepault J, Freeman R, Berriman J, Homo JC 1982. Electron microscopy of frozen water and aqueous solutions. J. Microsc. 128:219–37
    [Google Scholar]
  8. 8. 
    Erickson H, Klug A. 1971. Measurement and compensation of defocusing and aberrations by Fourier processing of electron micrographs. Philos. Trans. R. Soc. Lond. B 261:105–18
    [Google Scholar]
  9. 9. 
    Wade R. 1992. A brief look at imaging and contrast transfer. Ultramicroscopy 46:145–56
    [Google Scholar]
  10. 10. 
    Smith MT, Rubinstein JL. 2014. Beyond blob-ology. Science 345:617–19
    [Google Scholar]
  11. 11. 
    Li X, Mooney P, Zheng S, Booth CR, Braunfeld MB et al. 2013. Electron counting and beam-induced motion correction enable near-atomic-resolution single-particle cryo-EM. Nat. Methods 10:584–90
    [Google Scholar]
  12. 12. 
    McMullan G, Faruqi A, Henderson R 2016. Direct electron detectors. The Resolution Revolution: Recent Advances in cryoEM RA Crowther 1–17 New York: Academic
    [Google Scholar]
  13. 13. 
    Brilot AF, Chen JZ, Cheng A, Pan J, Harrison SC et al. 2012. Beam-induced motion of vitrified specimen on holey carbon film. J. Struct. Biol. 177:630–37
    [Google Scholar]
  14. 14. 
    Liao M, Cao E, Julius D, Cheng Y 2013. Structure of the TRPV1 ion channel determined by electron cryo-microscopy. Nature 504:107–12
    [Google Scholar]
  15. 15. 
    Amunts A, Brown A, Bai X-C, Llácer JL, Hussain T et al. 2014. Structure of the yeast mitochondrial large ribosomal subunit. Science 343:1485–89
    [Google Scholar]
  16. 16. 
    Bartesaghi A, Aguerrebere C, Falconieri V, Banerjee S, Earl LA et al. 2018. Atomic resolution cryo-EM structure of β-galactosidase. Structure 26:848–56
    [Google Scholar]
  17. 17. 
    Kühlbrandt W. 2014. The resolution revolution. Science 343:1443–44
    [Google Scholar]
  18. 18. 
    Ripstein Z, Rubinstein J. 2016. Processing of cryo-EM movie data. Methods Enzymol 579:103–24
    [Google Scholar]
  19. 19. 
    Zheng SQ, Palovcak E, Armache JP, Verba KA, Cheng Y, Agard DA 2017. MotionCor2: anisotropic correction of beam-induced motion for improved cryo-electron microscopy. Nat. Methods 14:4331–32
    [Google Scholar]
  20. 20. 
    Grant T, Grigorieff N. 2015. Measuring the optimal exposure for single particle cryo-EM using a 2.6 Å reconstruction of rotavirus VP6. eLife 4:e06980
    [Google Scholar]
  21. 21. 
    Rohou A, Grigorieff N. 2015. CTFFIND4: fast and accurate defocus estimation from electron micrographs. J. Struct. Biol. 192:216–21
    [Google Scholar]
  22. 22. 
    Zhang K. 2016. Gctf: Real-time CTF determination and correction. J. Struct. Biol. 193:1–12
    [Google Scholar]
  23. 23. 
    Sindelar CV, Grigorieff N. 2011. An adaptation of the Wiener filter suitable for analyzing images of isolated single particles. J. Struct. Biol. 176:60–74
    [Google Scholar]
  24. 24. 
    Sigworth FJ. 2004. Classical detection theory and the cryo-EM particle selection problem. J. Struct. Biol. 145:111–22
    [Google Scholar]
  25. 25. 
    Danev R, Baumeister W. 2016. Cryo-EM single particle analysis with the Volta phase plate. eLife 5:e13046
    [Google Scholar]
  26. 26. 
    Khoshouei M, Radjainia M, Baumeister W, Danev R 2017. Cryo-EM structure of haemoglobin at 3.2 Å determined with the Volta phase plate. Nat. Commun. 8:16099
    [Google Scholar]
  27. 27. 
    Frank J, Wagenknecht T. 1983. Automatic selection of molecular images from electron micrographs. Ultramicroscopy 12:169–75
    [Google Scholar]
  28. 28. 
    Chen JZ, Grigorieff N. 2007. SIGNATURE: a single-particle selection system for molecular electron microscopy. J. Struct. Biol. 157:168–73
    [Google Scholar]
  29. 29. 
    Scheres SH. 2015. Semi-automated selection of cryo-EM particles in RELION-1.3. J. Struct. Biol. 189:114–22
    [Google Scholar]
  30. 30. 
    Voss N, Yoshioka C, Radermacher M, Potter C, Carragher B 2009. DoG picker and TiltPicker: software tools to facilitate particle selection in single particle electron microscopy. J. Struct. Biol. 166:205–13
    [Google Scholar]
  31. 31. 
    Shatsky M, Hall RJ, Brenner SE, Glaeser RM 2009. A method for the alignment of heterogeneous macromolecules from electron microscopy. J. Struct. Biol. 166:67–78
    [Google Scholar]
  32. 32. 
    Henderson R. 2013. Avoiding the pitfalls of single particle cryo-electron microscopy: Einstein from noise. PNAS 110:18037–41
    [Google Scholar]
  33. 33. 
    Heimowitz A, Andén J, Singer A 2018. APPLE picker: automatic particle picking, a low-effort cryo-EM framework. J. Struct. Biol. 204:215–27
    [Google Scholar]
  34. 34. 
    Wang F, Gong H, Liu G, Li M, Yan C et al. 2016. DeepPicker: a deep learning approach for fully automated particle picking in cryo-EM. J. Struct. Biol. 195:325–36
    [Google Scholar]
  35. 35. 
    Wagner T, Merino F, Stabrin M, Moriya T, Antoni C et al. 2019. SPHIRE-crYOLO is a fast and accurate fully automated particle picker for cryo-EM. Commun. Biol. 2:218
    [Google Scholar]
  36. 36. 
    Bepler T, Morin A, Rapp M, Brasch J, Shapiro L et al. 2019. Positive-unlabeled convolutional neural networks for particle picking in cryo-electron micrographs. Nat. Methods 16:1153–60
    [Google Scholar]
  37. 37. 
    Herman GT. 2009. Fundamentals of Computerized Tomography: Image Reconstruction from Projections London: Springer
    [Google Scholar]
  38. 38. 
    Wasserman L. 2013. All of Statistics: A Concise Course in Statistical Inference New York: Springer Sci. Bus. Media
    [Google Scholar]
  39. 39. 
    Neyman J, Scott EL. 1948. Consistent estimates based on partially consistent observations. Econometrica 16:1–32
    [Google Scholar]
  40. 40. 
    Dempster A, Laird N, Rubin D 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B 39:1–38
    [Google Scholar]
  41. 41. 
    Sigworth F. 1998. A maximum-likelihood approach to single-particle image refinement. J. Struct. Biol. 122:328–39
    [Google Scholar]
  42. 42. 
    Penczek PA, Renka R, Schomberg H 2004. Gridding-based direct Fourier inversion of the three-dimensional ray transform. J. Opt. Soc. Am. A 21:499–509
    [Google Scholar]
  43. 43. 
    Dutt A, Rokhlin V. 1993. Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Comput. 14:1368–93
    [Google Scholar]
  44. 44. 
    Wang L, Shkolnisky Y, Singer A 2013. A Fourier-based approach for iterative 3D reconstruction from cryo-EM images. arXiv 1307.5824 [math.NA]
  45. 45. 
    Marabini R, Herman GT, Carazo JM 1998. 3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). Ultramicroscopy 72:53–65
    [Google Scholar]
  46. 46. 
    Natterer F. 1986. The Mathematics of Computerized Tomography New York: Wiley
    [Google Scholar]
  47. 47. 
    Barnett AH, Magland J, af Klinteberg L 2019. A parallel nonuniform fast Fourier transform library based on an exponential of semicircle kernel. SIAM J. Sci. Comput. 41:C479–504
    [Google Scholar]
  48. 48. 
    Grigorieff N. 2007. FREALIGN: high-resolution refinement of single particle structures. J. Struct. Biol. 157:117–25
    [Google Scholar]
  49. 49. 
    Harauz G, Ottensmeyer F. 1983. Direct three-dimensional reconstruction for macromolecular complexes from electron micrographs. Ultramicroscopy 12:309–19
    [Google Scholar]
  50. 50. 
    Harauz G, Ottensmeyer F. 1984. Nucleosome reconstruction via phosphorous mapping. Science 226:936–41
    [Google Scholar]
  51. 51. 
    Punjani A, Rubinstein JL, Fleet DJ, Brubaker MA 2017. cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination. Nat. Methods 14:290–96
    [Google Scholar]
  52. 52. 
    Tagare HD, Barthel A, Sigworth FJ 2010. An adaptive expectation–maximization algorithm with GPU implementation for electron cryomicroscopy. J. Struct. Biol. 171:256–65
    [Google Scholar]
  53. 53. 
    Scheres S. 2012. RELION: implementation of a Bayesian approach to cryo-EM structure determination. J. Struct. Biol. 180:519–30
    [Google Scholar]
  54. 54. 
    Dvornek NC, Sigworth FJ, Tagare HD 2015. SubspaceEM: a fast maximum-a-posteriori algorithm for cryo-EM single particle reconstruction. J. Struct. Biol. 190:200–14
    [Google Scholar]
  55. 55. 
    Scheres SH, Valle M, Grob P, Nogales E, Carazo JM 2009. Maximum likelihood refinement of electron microscopy data with normalization errors. J. Struct. Biol. 166:234–40
    [Google Scholar]
  56. 56. 
    Scheres SH. 2016. Processing of structurally heterogeneous cryo-EM data in RELION. Methods Enzymol 579:125–57
    [Google Scholar]
  57. 57. 
    Zivanov J, Nakane T, Scheres SH 2019. A Bayesian approach to beam-induced motion correction in cryo-EM single-particle analysis. IUCrJ 6:5–17
    [Google Scholar]
  58. 58. 
    Kimanius D, Forsberg BO, Scheres SH, Lindahl E 2016. Accelerated cryo-EM structure determination with parallelisation using GPUs in RELION-2. eLife 5:e18722
    [Google Scholar]
  59. 59. 
    Zivanov J, Nakane T, Forsberg BO, Kimanius D, Hagen WJ et al. 2018. New tools for automated high-resolution cryo-EM structure determination in RELION-3. eLife 7:e42166
    [Google Scholar]
  60. 60. 
    Scheres SH. 2012. A Bayesian view on cryo-EM structure determination. J. Mol. Biol. 415:406–18
    [Google Scholar]
  61. 61. 
    Ullrich K, van den Berg R, Brubaker M, Fleet D, Welling M 2019. Differentiable probabilistic models of scientific imaging with the Fourier slice theorem. Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI 2019) Pap148 http://auai.org/uai2019/proceedings/papers/148.pdf
    [Google Scholar]
  62. 62. 
    Kaipio J, Somersalo E. 2006. Statistical and Computational Inverse Problems New York: Springer
    [Google Scholar]
  63. 63. 
    Scheres SH, Valle M, Nuñez R, Sorzano CO, Marabini R et al. 2005. Maximum-likelihood multi-reference refinement for electron microscopy images. J. Mol. Biol. 348:139–49
    [Google Scholar]
  64. 64. 
    Sorzano C, Bilbao-Castro J, Shkolnisky Y, Alcorlo M, Melero R et al. 2010. A clustering approach to multireference alignment of single-particle projections in electron microscopy. J. Struct. Biol. 171:197–206
    [Google Scholar]
  65. 65. 
    Bottou L, Curtis FE, Nocedal J 2018. Optimization methods for large-scale machine learning. SIAM Rev 60:223–311
    [Google Scholar]
  66. 66. 
    Glaeser RM. 2016. How good can cryo-EM become. ? Nat. Methods 13:28–32
    [Google Scholar]
  67. 67. 
    Subramaniam S, Kühlbrandt W, Henderson R 2016. CryoEM at IUCrJ: a new era. IUCrJ 3:3–7
    [Google Scholar]
  68. 68. 
    Sorzano COS, Carazo JM. 2017. Challenges ahead electron microscopy for structural biology from the image processing point of view. arXiv 1701.00326 [cs.CV]
  69. 69. 
    Scheres SH, Gao H, Valle M, Herman GT, Eggermont PP et al. 2007. Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization. Nat. Methods 4:27–29
    [Google Scholar]
  70. 70. 
    Ludtke SJ. 2016. Single-particle refinement and variability analysis in EMAN2.1. Methods Enzymol 579:159–89
    [Google Scholar]
  71. 71. 
    de la Rosa-Trevín J, Otón J, Marabini R, Zaldivar A, Vargas J et al. 2013. Xmipp 3.0: an improved software suite for image processing in electron microscopy. J. Struct. Biol. 184:321–28
    [Google Scholar]
  72. 72. 
    Lyumkis D, Brilot AF, Theobald DL, Grigorieff N 2013. Likelihood-based classification of cryo-EM images using FREALIGN. J. Struct. Biol. 183:377–88
    [Google Scholar]
  73. 73. 
    Grant T, Rohou A, Grigorieff N 2018. cisTEM, user-friendly software for single-particle image processing. eLife 7:e35383
    [Google Scholar]
  74. 74. 
    Sorzano C, Jiménez A, Mota J, Vilas J, Maluenda D et al. 2019. Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy. Acta Crystallogr. F 75:19–32
    [Google Scholar]
  75. 75. 
    Liu W, Frank J. 1995. Estimation of variance distribution in three-dimensional reconstruction. I. Theory. J. Opt. Soc. Am. A 12:2615–27
    [Google Scholar]
  76. 76. 
    Liu W, Boisset N, Frank J 1995. Estimation of variance distribution in three-dimensional reconstruction. II. Applications. J. Opt. Soc. Am. A 12:2628–35
    [Google Scholar]
  77. 77. 
    Penczek PA. 2002. Variance in three-dimensional reconstructions from projections. Proceedings of the 2002 IEEE International Symposium on Biomedical Imaging749–52 New York: IEEE
    [Google Scholar]
  78. 78. 
    Penczek PA, Yang C, Frank J, Spahn CM 2006. Estimation of variance in single-particle reconstruction using the bootstrap technique. J. Struct. Biol. 154:168–83
    [Google Scholar]
  79. 79. 
    Zhang W, Kimmel M, Spahn CM, Penczek PA 2008. Heterogeneity of large macromolecular complexes revealed by 3D cryo-EM variance analysis. Structure 16:1770–76
    [Google Scholar]
  80. 80. 
    Penczek P, Kimmel M, Spahn C 2011. Identifying conformational states of macromolecules by eigen-analysis of resampled cryo-EM images. Structure 19:1582–90
    [Google Scholar]
  81. 81. 
    Liao H, Frank J. 2010. Classification by bootstrapping in single particle methods. Proceedings of the 2010 IEEE International Symposium on Biomedical Imaging169–72 New York: IEEE
    [Google Scholar]
  82. 82. 
    Zheng Y, Wang Q, Doerschuk PC 2012. Three-dimensional reconstruction of the statistics of heterogeneous objects from a collection of one projection image of each object. J. Opt. Soc. Am. A 29:959–70
    [Google Scholar]
  83. 83. 
    Wang Q, Matsui T, Domitrovic T, Zheng Y, Doerschuk PC, Johnson JE 2013. Dynamics in cryo EM reconstructions visualized with maximum-likelihood derived variance maps. J. Struct. Biol. 181:195–206
    [Google Scholar]
  84. 84. 
    Xu N, Veesler D, Doerschuk PC, Johnson JE 2018. Allosteric effects in bacteriophage HK97 procapsids revealed directly from covariance analysis of cryo EM data. J. Struct. Biol. 202:129–41
    [Google Scholar]
  85. 85. 
    Tagare HD, Kucukelbir A, Sigworth FJ, Wang H, Rao M 2015. Directly reconstructing principal components of heterogeneous particles from cryo-EM images. J. Struct. Biol. 191:245–62
    [Google Scholar]
  86. 86. 
    Klaholz BP. 2015. Structure sorting of multiple macromolecular states in heterogeneous cryo-EM samples by 3D multivariate statistical analysis. Open J. Stat. 5:820–36
    [Google Scholar]
  87. 87. 
    Katsevich E, Katsevich A, Singer A 2015. Covariance matrix estimation for the cryo-EM heterogeneity problem. SIAM J. Imaging Sci. 8:126–85
    [Google Scholar]
  88. 88. 
    Andén J, Katsevich E, Singer A 2015. Covariance estimation using conjugate gradient for 3D classification in cryo-EM. Proceedings of the 2015 IEEE 12th International Symposium on Biomedical Imaging200–204 New York: IEEE
    [Google Scholar]
  89. 89. 
    Andén J, Singer A. 2018. Structural variability from noisy tomographic projections. SIAM J. Imaging Sci. 11:1441–92
    [Google Scholar]
  90. 90. 
    Jin Q, Sorzano COS, de La Rosa-Trevín JM, Bilbao-Castro JR, Nunez-Ramirez R et al. 2014. Iterative elastic 3D-to-2D alignment method using normal modes for studying structural dynamics of large macromolecular complexes. Structure 22:496–506
    [Google Scholar]
  91. 91. 
    Sorzano COS, de La Rosa-Trevín JM, Tama F, Jonić S 2014. Hybrid electron microscopy normal mode analysis graphical interface and protocol. J. Struct. Biol. 188:134–41
    [Google Scholar]
  92. 92. 
    Jonić S. 2017. Computational methods for analyzing conformational variability of macromolecular complexes from cryo-electron microscopy images. Curr. Opin. Struct. Biol. 43:114–21
    [Google Scholar]
  93. 93. 
    Schilbach S, Hantsche M, Tegunov D, Dienemann C, Wigge C et al. 2017. Structures of transcription pre-initiation complex with TFIIH and Mediator. Nature 551:204–9
    [Google Scholar]
  94. 94. 
    Dashti A, Schwander P, Langlois R, Fung R, Li W et al. 2014. Trajectories of the ribosome as a Brownian nanomachine. PNAS 111:17492–97
    [Google Scholar]
  95. 95. 
    Frank J, Ourmazd A. 2016. Continuous changes in structure mapped by manifold embedding of single-particle data in cryo-EM. Methods 100:61–67
    [Google Scholar]
  96. 96. 
    Dashti A, Shekhar MS, Hail DB, Mashayekhi G, Schwander P et al. 2018. Functional pathways of biomolecules retrieved from single-particle snapshots. bioRxiv 291922. https://doi.org/10.1101/291922
    [Crossref]
  97. 97. 
    Moscovich A, Halevi A, Andén J, Singer A 2020. Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes. Inverse Probl 36:024003
    [Google Scholar]
  98. 98. 
    Shan H, Wang Z, Zhang F, Xiong Y, Yin CC, Sun F 2016. A local-optimization refinement algorithm in single particle analysis for macromolecular complex with multiple rigid modules. Protein Cell 7:46–62
    [Google Scholar]
  99. 99. 
    Nakane T, Kimanius D, Lindahl E, Scheres SH 2018. Characterisation of molecular motions in cryo-EM single-particle data by multi-body refinement in RELION. eLife 7:e36861
    [Google Scholar]
  100. 100. 
    Lederman RR, Andén J, Singer A 2020. Hyper-molecules: on the representation and recovery of dynamical structures for applications in flexible macro-molecules in cryo-EM. Inverse Probl 36:044005
    [Google Scholar]
  101. 101. 
    Zhong ED, Bepler T, Davis JH, Berger B 2019. Reconstructing continuously heterogeneous structures from single particle cryo-EM with deep generative models. arXiv 1909.05215 [q-bio.QM]
  102. 102. 
    Bepler T, Zhong E, Kelley K, Brignole E, Berger B 2019. Explicitly disentangling image content from translation and rotation with spatial-VAE. Proceedings of the 33rd Conference on Advances in Neural Information Processing Systems https://papers.nips.cc/paper/9677-explicitly-disentangling-image-content-from-translation-and-rotation-with-spatial-vae.pdf
    [Google Scholar]
  103. 103. 
    Tan YZ, Baldwin PR, Davis JH, Williamson JR, Potter CS et al. 2017. Addressing preferred specimen orientation in single-particle cryo-EM through tilting. Nat. Methods 14:793–96
    [Google Scholar]
  104. 104. 
    Rickgauer JP, Grigorieff N, Denk W 2017. Single-protein detection in crowded molecular environments in cryo-EM images. eLife 6:e25648
    [Google Scholar]
  105. 105. 
    Glaeser RM. 2019. How good can single-particle cryo-EM become? What remains before it approaches its physical limits. ? Annu. Rev. Biophys. 48:45–61
    [Google Scholar]
  106. 106. 
    Russo CJ, Henderson R. 2018. Microscopic charge fluctuations cause minimal contrast loss in cryoEM. Ultramicroscopy 187:56–63
    [Google Scholar]
  107. 107. 
    McMullan G, Vinothkumar K, Henderson R 2015. Thon rings from amorphous ice and implications of beam-induced Brownian motion in single particle electron cryo-microscopy. Ultramicroscopy 158:26–32
    [Google Scholar]
/content/journals/10.1146/annurev-biodatasci-021020-093826
Loading
/content/journals/10.1146/annurev-biodatasci-021020-093826
Loading

Data & Media loading...

Supplementary Data

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error