A Bayesian View on Cryo-EM Structure Determination

Overview

Journal J Mol Biol

Publisher Elsevier

Specialties Microbiology
Molecular Biology

Date 2011 Nov 22

PMID 22100448

Citations 458

Authors

Sjors H W Scheres

Affiliations

Soon will be listed here.

Abstract

Three-dimensional (3D) structure determination by single-particle analysis of cryo-electron microscopy (cryo-EM) images requires many parameters to be determined from extremely noisy data. This makes the method prone to overfitting, that is, when structures describe noise rather than signal, in particular near their resolution limit where noise levels are highest. Cryo-EM structures are typically filtered using ad hoc procedures to prevent overfitting, but the tuning of arbitrary parameters may lead to subjectivity in the results. I describe a Bayesian interpretation of cryo-EM structure determination, where smoothness in the reconstructed density is imposed through a Gaussian prior in the Fourier domain. The statistical framework dictates how data and prior knowledge should be combined, so that the optimal 3D linear filter is obtained without the need for arbitrariness and objective resolution estimates may be obtained. Application to experimental data indicates that the statistical approach yields more reliable structures than existing methods and is capable of detecting smaller classes in data sets that contain multiple different structures.

Citing Articles

Structural basis of Nipah virus RNA synthesis.

Sala F, Ditter K, Dybkov O, Urlaub H, Hillen H Nat Commun. 2025; 16(1):2261.

PMID: 40050611 PMC: 11885841. DOI: 10.1038/s41467-025-57219-5.

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

Gilles M, Singer A Proc Natl Acad Sci U S A. 2025; 122(9):e2419140122.

PMID: 40009640 PMC: 11892586. DOI: 10.1073/pnas.2419140122.

Balanced plant helper NLR activation by a modified host protein complex.

Huang S, Wang J, Song R, Jia A, Xiao Y, Sun Y Nature. 2025; 639(8054):447-455.

PMID: 39939760 DOI: 10.1038/s41586-024-08521-7.

Biochemical and structural bases for talin ABSs-F-actin interactions.

Biertumpfel C, Yamada Y, Vasquez-Montes V, Truong T, Cada A, Mizuno N Proc Natl Acad Sci U S A. 2025; 122(6):e2405922122.

PMID: 39903122 PMC: 11831117. DOI: 10.1073/pnas.2405922122.

Aerolysin Nanopore Structures Revealed at High Resolution in a Lipid Environment.

Anton J, Iacovache I, Bada Juarez J, Abriata L, Perrin L, Cao C J Am Chem Soc. 2025; 147(6):4984-4992.

PMID: 39900531 PMC: 11826888. DOI: 10.1021/jacs.4c14288.

References

Ludtke S, Baldwin P, Chiu W . EMAN: semiautomated software for high-resolution single-particle reconstructions. J Struct Biol. 1999; 128(1):82-97. DOI: 10.1006/jsbi.1999.4174. View

Sindelar C, Grigorieff N . An adaptation of the Wiener filter suitable for analyzing images of isolated single particles. J Struct Biol. 2011; 176(1):60-74. PMC: 3184790. DOI: 10.1016/j.jsb.2011.06.010. View

Iizuka R, Yoshida T, Shomura Y, Miki K, Maruyama T, Odaka M . ATP binding is critical for the conformational change from an open to closed state in archaeal group II chaperonin. J Biol Chem. 2003; 278(45):44959-65. DOI: 10.1074/jbc.M305484200. View

Stagg S, Lander G, Pulokas J, Fellmann D, Cheng A, Quispe J . Automated cryoEM data acquisition and analysis of 284742 particles of GroEL. J Struct Biol. 2006; 155(3):470-81. DOI: 10.1016/j.jsb.2006.04.005. View

Pipe J, Menon P . Sampling density compensation in MRI: rationale and an iterative numerical solution. Magn Reson Med. 1999; 41(1):179-86. DOI: 10.1002/(sici)1522-2594(199901)41:1<179::aid-mrm25>3.0.co;2-v. View

Scheres S, Nunez-Ramirez R, Gomez-Llorente Y, San Martin C, Eggermont P, Carazo J . Modeling experimental image formation for likelihood-based classification of electron microscopy data. Structure. 2007; 15(10):1167-77. PMC: 2277044. DOI: 10.1016/j.str.2007.09.003. View

Suloway C, Pulokas J, Fellmann D, Cheng A, Guerra F, Quispe J . Automated molecular microscopy: the new Leginon system. J Struct Biol. 2005; 151(1):41-60. DOI: 10.1016/j.jsb.2005.03.010. View

Penczek P . Three-dimensional spectral signal-to-noise ratio for a class of reconstruction algorithms. J Struct Biol. 2002; 138(1-2):34-46. DOI: 10.1016/s1047-8477(02)00033-3. View

Grigorieff N, Harrison S . Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy. Curr Opin Struct Biol. 2011; 21(2):265-73. PMC: 3088881. DOI: 10.1016/j.sbi.2011.01.008. View

10.

Sorzano C, Marabini R, Velazquez-Muriel J, Bilbao-Castro J, Scheres S, Carazo J . XMIPP: a new generation of an open-source image processing package for electron microscopy. J Struct Biol. 2004; 148(2):194-204. DOI: 10.1016/j.jsb.2004.06.006. View

11.

Wang L, Sigworth F . Structure of the BK potassium channel in a lipid membrane from electron cryomicroscopy. Nature. 2009; 461(7261):292-5. PMC: 2797367. DOI: 10.1038/nature08291. View

12.

Penczek P . Image restoration in cryo-electron microscopy. Methods Enzymol. 2010; 482:35-72. PMC: 3166661. DOI: 10.1016/S0076-6879(10)82002-6. View

13.

Liao H, Frank J . CLASSIFICATION BY BOOTSTRAPPING IN SINGLE PARTICLE METHODS. Proc IEEE Int Symp Biomed Imaging. 2010; 2010:169-172. PMC: 2924593. DOI: 10.1109/ISBI.2010.5490386. View

14.

Murshudov G, Vagin A, Dodson E . Refinement of macromolecular structures by the maximum-likelihood method. Acta Crystallogr D Biol Crystallogr. 1997; 53(Pt 3):240-55. DOI: 10.1107/S0907444996012255. View

15.

Baxter W, Grassucci R, Gao H, Frank J . Determination of signal-to-noise ratios and spectral SNRs in cryo-EM low-dose imaging of molecules. J Struct Biol. 2009; 166(2):126-32. PMC: 2700974. DOI: 10.1016/j.jsb.2009.02.012. View

16.

Scheres S . Visualizing molecular machines in action: Single-particle analysis with structural variability. Adv Protein Chem Struct Biol. 2010; 81:89-119. DOI: 10.1016/B978-0-12-381357-2.00004-9. View

17.

Elad N, Clare D, Saibil H, Orlova E . Detection and separation of heterogeneity in molecular complexes by statistical analysis of their two-dimensional projections. J Struct Biol. 2008; 162(1):108-20. DOI: 10.1016/j.jsb.2007.11.007. View

18.

Faruqi A, McMullan G . Electronic detectors for electron microscopy. Q Rev Biophys. 2011; 44(3):357-90. DOI: 10.1017/S0033583511000035. View

19.

Sigworth F, Doerschuk P, Carazo J, Scheres S . An introduction to maximum-likelihood methods in cryo-EM. Methods Enzymol. 2010; 482:263-94. PMC: 3051286. DOI: 10.1016/S0076-6879(10)82011-7. View

20.

Rosenthal P, Henderson R . Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy. J Mol Biol. 2003; 333(4):721-45. DOI: 10.1016/j.jmb.2003.07.013. View