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Determination of the Shape of a Helix Particle Based on Small-Angle X-ray Scattering Data: Modification of the “Simulated Annealing” Algorithm

  • DIFFRACTION AND SCATTERING OF IONIZING RADIATIONS
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Abstract

The modified “simulated annealing” algorithm implemented in the DAMMINV software allows one to obtain 10 to 15 different nanoparticle models fitting small-angle X-ray scattering data. This method is based on the mode of intermittent weights of the objective function, which balances between minimization of the penalty coefficients, responsible for the model meaningfulness, and the discrepancy between the experimental and model scattering data. The effect of noise on the scattering curves on the quality of three-dimensional helix shape reconstruction has been investigated, and the results are compared with the data obtained using standard programs. The method has been verified on noise-free model data and data with superimposed Poisson noise by the example of a helix particle with a thickness of turns comparable to the characteristic size of the space between them. A comparative analysis of the reconstructed models and the three-dimensional shapes obtained using standard modes of the “simulated annealing” algorithm has been performed.

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REFERENCES

  1. D. I. Svergun and L. A. Feigin, X-ray and Small-Angle Neutron Scattering (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  2. M. V. Petoukhov, D. Franke, A. V. Shkumatov, et al., J. Appl. Crystallogr. 45, 342 (2012). https://doi.org/10.1107/S0021889812007662

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  3. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983). https://doi.org/10.1126/science.220.4598.671

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  4. D. I. Svergun, Biophys. J. 78, 2879 (1999). https://doi.org/10.1016/S0006-3495(99)77443-6

    Article  Google Scholar 

  5. D. Franke and D. I. Svergun, J. Appl. Crystallogr. 42, 342 (2009). https://doi.org/10.1107/S0021889809000338

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. D. I. Svergun and H. B. Stuhrmann, Acta Crystallogr. A 47, 736 (1991). https://doi.org/10.1107/S0108767391006414

    Article  ADS  Google Scholar 

  7. D. I. Svergun, V. V. Volkov, M. B. Kozin, et al., Acta Crystallogr. A 52, 419 (1996). https://doi.org/10.1107/S0108767396000177

    Article  ADS  Google Scholar 

  8. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, 1949).

    Google Scholar 

  9. T. D. Grant, Nat. Methods 15, 191 (2018). https://doi.org/10.1038/nmeth.4581

    Article  CAS  PubMed  Google Scholar 

  10. H. He, C. Liu, and H. Liu, iScience 23, 100906 (2020).

  11. V. V. Volkov, Crystallogr. Rep. 66, 793 (2021). https://doi.org/10.31857/S0023476121050234

    Article  Google Scholar 

  12. V. A. Grigor’ev, P. V. Konarev, and V. V. Volkov, Usp. Khim. Khim. Tekhnol. 36, 53 (2022).

    Google Scholar 

  13. G. Marsaglia and W. W. Tsang, SIAM J. Sci. Stat. Comput. 5, 349 (1984). https://doi.org/10.1137/0905026

    Article  Google Scholar 

  14. L. Devroye, Computing 26, 197 (1981). https://doi.org/10.1007/BF02243478

    Article  MathSciNet  Google Scholar 

  15. J. Durbin and G. S. Watson, Biometrika 37, 409 (1950). https://doi.org/10.1093/biomet/37.3-4.409

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  16. J. Durbin and G. S. Watson, Biometrika 38, 159 (1951). https://doi.org/10.2307/2332325

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  17. M. Kozin and D. Svergun, J. Appl. Crystallogr. 34, 33 (2001). https://doi.org/10.1107/S0021889800014126

    Article  ADS  CAS  Google Scholar 

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Funding

This study was supported by the Ministry of Science and Higher Education of Russian Federation within the State assignment for the Federal Scientific Research Centre “Crystallography and Photonics” of the Russian Academy of Sciences.

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Authors and Affiliations

  1. Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, 119333, Moscow, Russia

    V. A. Grigorev, P. V. Konarev & V. V. Volkov

Authors
  1. V. A. Grigorev
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  2. P. V. Konarev
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  3. V. V. Volkov
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Correspondence to V. A. Grigorev.

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Translated by A. Sin’kov

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Grigorev, V.A., Konarev, P.V. & Volkov, V.V. Determination of the Shape of a Helix Particle Based on Small-Angle X-ray Scattering Data: Modification of the “Simulated Annealing” Algorithm. Crystallogr. Rep. 68, 938–942 (2023). https://doi.org/10.1134/S1063774523601016

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