Skip to main content
SpringerLink
Log in

Single particle cryo-EM image registration based on Fourier–Bessel transform and fast Laguerre projection method

  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

Abstract

When constructing the three-dimensional model of a particle by means of single particle cryo-electron microscopy, an important step is particle projection alignment, which are grouped by their spatial similarities. This step helps to improve the quality of the microscopic particle projection images by averaging the aligned projections. In this work we present a two-dimensional image registration method, that can be effectively applied for projection alignment in single particle cryo-electron microscopy. The proposed method is based on calculating the correlation function between a pair of images and with the use of the Fourier–Bessel transform. We apply Laguerre projection method to calculate the Fourier-Bessel transform. For additional acceleration of calculations, it is suggested to use the fast algorithm for calculating projection coefficients, based on the Gauss-Laguerre quadrature in the calculation of the Hankel transform. The application of Laguerre projection method for the Fourier-Bessel transform calculation significantly accelerates the registration, and the use of fast projection coefficients calculation algorithm gives additional speed-up to the Laguerre projection methodwithout major registration errors. The experimental results on synthetic data with different level of noise have demonstrated the effectiveness of the proposed registration method. In addition, experiments on real data have clearly proved the applicability of the method to cryo-EM images.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Cheng, Y., Grigorieff, N., Penczek, P.A., Walz, T.: A primer to single-particle cryo-electron microscopy. Cell 161(3), 438–449 (2015)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Vilas, J.L., Carazo, J.M., Sorzano, C.O.S.: Emerging themes in cryo-EM single particle analysis image processing. Chem. Rev. 122(17), 13,915–13,951 (2022)

    Article  Google Scholar 

  3. Joyeux, L., Penczek, P.A.: Efficiency of 2D alignment methods. Ultramicroscopy 92(2), 33–46 (2002)

    Article  CAS  PubMed  Google Scholar 

  4. Anoshina, N.A., Krylov, A.S., Sorokin, D.V.: Correlation-based 2D registration method for single particle cryo-EM images. In: 2017 Seventh International Conference on Image Processing Theory, Tools and Applications (IPTA), pp. 1–6. IEEE, (2017)

    Google Scholar 

  5. Cong, Y., Kovacs, J.A., Wriggers, W.: 2D fast rotational matching for image processing of biophysical data. J. Struct. Biol. 144(1-2), 51–60 (2003)

    Article  PubMed  Google Scholar 

  6. Guizar-Sicairos, M., Thurman, S.T., Fienup, J.R.: Efficient subpixel image registration algorithms. Opt. Lett. 33(2), 156–158 (2008)

    Article  ADS  PubMed  Google Scholar 

  7. Kovacs, J.A., Abagyan, R., Yeager, M.: Fast Bessel matching. J. Comput. Theor. Nanosci. 4(1), 84–95 (2007)

    CAS  Google Scholar 

  8. Penczek, P., Radermacher, M., Frank, J.: Three-dimensional reconstruction of single particles embedded in ice. Ultramicroscopy 40(1), 33–53 (1992)

    Article  CAS  PubMed  Google Scholar 

  9. Wang, X., Lu, Y., Liu, J.: A fast image alignment approach for 2D classification of cryo-EM images using spectral clustering. CIMB 43(3), 1652–1668 (2021)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Wilson, C.A., Theriot, J.A.: A correlation-based approach to calculate rotation and translation of moving cells. IEEE Trans. Image Process. 15(7), 1939–1951 (2006)

    Article  ADS  PubMed  Google Scholar 

  11. Yang, Z., Penczek, P.A.: Cryo-EM image alignment based on nonuniform fast Fourier transform. Ultramicroscopy 108(9), 959–969 (2008)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Yang, Z., Fang, J., Chittuluru, J., Asturias, F.J., Penczek, P.A.: Iterative stable alignment and clustering of 2D transmission electron microscope images. Structure 20(2), 237–247 (2012)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Zhao, Z., Singer, A.: Rotationally invariant image representation for viewing direction classification in cryo-EM. J. Struct. Biol. 186(1), 153–166 (2014)

    Article  PubMed  PubMed Central  Google Scholar 

  14. Punjani, A., Rubinstein, J.L., Fleet, D.J., Brubaker, M.A.: Cryosparc: Algorithms for rapid unsupervised cryo-EM structure determination. Nat. Methods 14(3), 290–296 (2017)

    Article  CAS  PubMed  Google Scholar 

  15. Scheres, S.H.: Relion: implementation of a bayesian approach to cryo-EM structure determination. J. Struct. Biol. 180(3), 519–530 (2012)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Grigorieff, N.: Frealign: high-resolution refinement of single particle structures. J. Struct. Biol. 157(1), 117–125 (2007)

    Article  CAS  PubMed  Google Scholar 

  17. Wang, F., Gong, H., Liu, G., Li, M., Yan, C., Xia, T., Li, X., Zeng, J.: Deeppicker: A deep learning approach for fully automated particle picking in cryo-EM. J. Struct. Biol. 195(3), 325–336 (2016)

    Article  PubMed  Google Scholar 

  18. Gupta, H., McCann, M.T., Donati, L., Unser, M.: Cryogan: A new reconstruction paradigm for single-particle cryo-EM via deep adversarial learning. IEEE Trans. Comput. Imaging 7, 759–774 (2021)

    Google Scholar 

  19. Palovcak, E., Asarnow, D., Campbell, M.G., Yu, Z., Cheng, Y.: Enhancing the signal-to-noise ratio and generating contrast for cryo-EM images with convolutional neural networks. IUCrJ 7(6), 1142–1150 (2020)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Vilenkin, N.I.: Special functions and the theory of group representations, vol. 22. American Mathematical Soc (1978)

    Google Scholar 

  21. Sorokin, D., Krylov, A.: Laguerre projection method for finite Hankel transform of arbitrary order. Mosc. Univ. Comput. Math. Cybern. 34, 149–156 (2010)

    Article  MathSciNet  Google Scholar 

  22. Sorokin, D., Krylov, A.: A projection local image descriptor. Pattern Recognit. Image Analysis 22, 380–385 (2012)

    Article  Google Scholar 

  23. Krylov, V. I.: Approximate calculation of integrals, Nauka, Moscow (1967), pp. 116–147

    Google Scholar 

  24. Aberth, O.: Iteration methods for finding all zeros of a polynomial simultaneously. Math. Comp. 27(122), 339–344 (1973)

    Article  MathSciNet  Google Scholar 

  25. Anoshina, N.A., Sagindykov, T.B., Sorokin, D.V.: A method for generation of synthetic 2D and 3D cryo-EM images. Program. Comput. Softw. 44(4), 240–247 (2018)

    Article  Google Scholar 

  26. Electron microscopy data bank. https://www.ebi.ac.uk/emdb/

  27. Rosenthal, P.B., Henderson, R.: Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy. J. Mol. Biol. 333(4), 721–745 (2003)

    Article  CAS  PubMed  Google Scholar 

Download references

Funding

The research was funded by the Russian Science Foundation grant 22-21-00125.

Author information

Authors and Affiliations

  1. Laboratory of Mathematical Methods of Image Processing, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russian Federation

    N. A. Anoshina & D. V. Sorokin

Authors
  1. N. A. Anoshina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. V. Sorokin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. A. Anoshina.

Additional information

Translated from Prikladnaya Matematika i Informatika, No. 73, 2023, pp. 4–22

This article is a translation of the original article published in Russian in the journal Prikladnaya Matematika i Informatika. The translation was done with the help of an artificial intelligence machine translation tool, and subsequently reviewed and revised by an expert with knowledge of the field. Springer Nature works continuously to further the development of tools for the production of journals, books and on the related technologies to support the authors.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anoshina, N., Sorokin, D. Single particle cryo-EM image registration based on Fourier–Bessel transform and fast Laguerre projection method. Comput Math Model (2024). https://doi.org/10.1007/s10598-024-09591-y

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10598-024-09591-y

Keywords

Search

Navigation