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Phasing Serial Crystallography Data

  • Richard A. KirianEmail author
  • Joe P. J. Chen
  • John C. H. Spence
Chapter

Abstract

The development of serial femtosecond crystallography (SFX) at X-ray free electron lasers (X-ray FELs) allows for the use of tiny protein crystals down to just a few unit cells along an edge, measured at physiological temperatures, and with a time resolution far better than can be achieved with synchrotrons or electron microscopes. The unique properties of the X-ray FEL source has furthermore resulted in the appearance of entirely new ideas for solving the crystallographic phase problem. At the same time, in combination with work on phasing single-particle data (with one bioparticle per shot), SFX has stimulated research into new phasing methods for serial crystallography (SC) at synchrotrons, and protein crystallography in general. In the sense that these new phasing methods depend on the application of constraints, they might be considered developments of traditional “direct methods” such as density modification approaches.

Notes

Acknowledgments

Supported by NSF STC BioXFEL award 1231306.

References

  1. 1.
    Millane, R. P. (1990). Phase retrieval in crystallography and optics. Journal of the Optical Society of America A, 7(3), 394–411.CrossRefGoogle Scholar
  2. 2.
    Sayre, D. (1952). Some implications of a theorem due to Shannon. Acta Crystallographica, 5(6), 843–843.CrossRefGoogle Scholar
  3. 3.
    Gerchberg, R. W., & Saxton, W. O. (1972). A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik (Stuttgart), 35, 237–246.Google Scholar
  4. 4.
    Fienup, J. R. (1982). Phase retrieval algorithms: A comparison. Applied Optics, 21(15), 2758–2769.CrossRefGoogle Scholar
  5. 5.
    Marchesini, S. (2007). A unified evaluation of iterative projection algorithms for phase retrieval. The Review of Scientific Instruments, 78, 011301.CrossRefGoogle Scholar
  6. 6.
    Millane, R. P., & Lo, V. L. (2013). Iterative projection algorithms in protein crystallography. Acta Crystallographica Section A: Foundations and Advances, A69, 517.Google Scholar
  7. 7.
    Spence, J. C. H. (2017b). In P. Hawkes & J. C. H. Spence (Eds.), Science of microscopy (pp. 1196–1227). New York: Springer.Google Scholar
  8. 8.
    Bragg, L., & Perutz, M. F. (1952). The structure of haemoglobin. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 213(1115), 425–435 The Royal Society.Google Scholar
  9. 9.
    Elser, V., & Millane, R. P. (2008). Reconstruction of an object from its symmetry-averaged diffraction pattern. Acta Crystallographica Section A: Foundations of Crystallography, 64(2), 273–279.CrossRefGoogle Scholar
  10. 10.
    Schlichting, I. (2017). Experimental phasing of serial femtosecond crystallography data. IUCrJ, 4, 517–517.CrossRefGoogle Scholar
  11. 11.
    Thibault, P., & Elser, V. (2010). X-ray diffraction microscopy. Annual Review of Condensed Matter Physics, 1, 237–255.CrossRefGoogle Scholar
  12. 12.
    Rupp, B. (2010). Biomolecular crystallography: Principles, practice, and application to structural biology. New York: Garland Science.Google Scholar
  13. 13.
    Hendrickson, W. A. (2014). Anomalous diffraction in crystallographic phase evaluation. Quarterly Reviews of Biophysics, 47(1), 49–93.  https://doi.org/10.1017/S0033583514000018.CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    Spence, J. C. H. (2017). XFELs for structure and dynamics in biology. IUCrJ, 4, 322–339.CrossRefGoogle Scholar
  15. 15.
    Barends, T. R., Foucar, L., Shoeman, R. L., Bari, S., Epp, S. W., Hartmann, R., et al. (2013a). Anomalous signal from S atoms in protein crystallographic data from an X-ray free-electron laser. Acta Crystallographica Section A: Foundations and Advances, D69, 838–842.CrossRefGoogle Scholar
  16. 16.
    Nass, K., Meinhart, A., Barends, T. R., Foucar, L., Gorel, A., Aquila, A., et al. (2016). Protein structure determination by single-wavelength anomalous diffraction phasing of X-ray free-electron laser data. IUCrJ, 3(3), 180–191.CrossRefGoogle Scholar
  17. 17.
    Yamashita, K., Pan, D., Okuda, T., Sugahara, M., Kodan, A., Yamaguchi, T., et al. (2015). An isomorphous replacement method for efficient de novo phasing for serial femtosecond crystallography. Scientific Reports, 5, 14017.CrossRefGoogle Scholar
  18. 18.
    Yamashita, K., Kuwabara, N., Nakane, T., et al. (2017). Experimental phase determination with selenomethionine or mercury-derivatization in serial femtosecond crystallography. IUCrJ, 4, 639–647.CrossRefGoogle Scholar
  19. 19.
    Hunter, M. S., Yoon, C. H., DeMirci, H., Sierra, R. G., Dao, E. H., Ahmadi, R., et al. (2016). Selenium single-wavelength anomalous diffraction de novo phasing using an X-ray-free electron laser. Nature Communications, 7, 13388.CrossRefGoogle Scholar
  20. 20.
    Colletier, J.-P., Sawaya, M. R., Gingery, M., et al. (2016). De novo phasing with X-ray laser reveals mosquito larvicide BinAB structure. Nature, 539, 43–47.  https://doi.org/10.1038/nature19825.CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Barends, T. R. M., et al. (2013b). De novo protein crystal structure determination from X-ray free-electron laser data. Nature, 505, 244–247.CrossRefGoogle Scholar
  22. 22.
    Nakane, T., Song, C., Suzuki, M., Nango, E., Kobayashi, J., Masuda, T., et al. (2015). Native sulfur/chlorine SAD phasing for serial femtosecond crystallography. Acta Crystallographica Section D: Biological Crystallography, 71(12), 2519–2525.CrossRefGoogle Scholar
  23. 23.
    Batyuk, A., Galli, L., Ishchenko, A., Han, G. W., Gati, C., Popov, P. A., et al. (2016). Native phasing of x-ray free-electron laser data for a G protein–coupled receptor. Science Advances, 2(9), e1600292.CrossRefGoogle Scholar
  24. 24.
    Gorel, A., Motomura, K., Fukuzawa, H., Doak, R. B., Grünbein, M. L., Hilpert, M., et al. (2017). Multi-wavelength anomalous diffraction de novo phasing using a two-colour X-ray free-electron laser with wide tunability. Nature Communications, 8, 1170.  https://doi.org/10.1038/s41467-017-00754-7.CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Shapiro, D. A., Chapman, H. N., DePonte, D., Doak, R. B., Fromme, P., Hembree, G., et al. (2008). Powder diffraction from a continuous microjet of submicrometer protein crystals. Journal of Synchrotron Radiation, 15(6), 593–599.CrossRefGoogle Scholar
  26. 26.
    Spence, J. C., & Doak, R. B. (2004). Single molecule diffraction. Physical Review Letters, 92(19), 198102.CrossRefGoogle Scholar
  27. 27.
    Kirian, R. A., Wang, X., Weierstall, U., et al. (2010). Femtosecond protein nanocrystallography - data analysis methods. Optics Express, 18(6), 5713–5723.CrossRefGoogle Scholar
  28. 28.
    Perutz, M. F. (1954). The structure of haemoglobin. III. Direct determination of the molecular transform. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 225(1161), 264–286 The Royal Society.Google Scholar
  29. 29.
    Chapman, H. N., Fromme, P., Barty, A., et al. (2011). Femtosecond X-ray protein nanocrystallography. Nature, 470, 73–77.PubMedPubMedCentralGoogle Scholar
  30. 30.
    Spence, J. C. H., Kirian, R. A., Wang, X. Y., Weierstall, U., Schmidt, K. E., White, T., et al. (2011). Phasing of coherent femtosecond X-ray diffraction from size-varying nanocrystals. Optics Express, 19(4), 2866–2873.  https://doi.org/10.1364/Oe.19.002866.CrossRefPubMedGoogle Scholar
  31. 31.
    Chen, J. P. J., Arnal, R. D., Morgan, A. J., Bean, R. J., Beyerlein, K. R., Chapman, H. N., et al. (2016). Reconstruction of an object from diffraction intensities averaged over multiple object clusters. Journal of Optics, 18(11), 114003.CrossRefGoogle Scholar
  32. 32.
    Chen, J. P. J., & Millane, R. P. (2014). Diffraction by nanocrystals II. Journal of the Optical Society of America A, 31(8), 1730–1737.CrossRefGoogle Scholar
  33. 33.
    Elser, V. (2013). Direct phasing of nanocrystal diffraction. Acta Crystallographica Section A: Foundations of Crystallography, 69(6), 559–569.Google Scholar
  34. 34.
    Kirian, R. A., Bean, R. J., Beyerlein, K. R., Yefanov, O. M., White, T. A., Barty, A., et al. (2014). Phasing coherently illuminated nanocrystals bounded by partial unit cells. Philosophical Transactions of the Royal Society B, 369(1647), 20130331.CrossRefGoogle Scholar
  35. 35.
    Kirian, R. A., Bean, R. J., Beyerlein, K. R., Barthelmess, M., Yoon, C. H., Wang, F. L., et al. (2015). Direct phasing of finite crystals illuminated with a free-electron laser. Physical Review X, 5(1), 011015.CrossRefGoogle Scholar
  36. 36.
    Spence, J. C. H., Zatsepin, N. A., & Li, C. (2014). Coherent convergent-beam time-resolved X-ray diffraction. Philosophical Transactions of the Royal Society B: Biological Sciences, 369(1647), 20130325.CrossRefGoogle Scholar
  37. 37.
    Ravelli, R., Leiros, H., Pan, B. C., Caffrey, M., & McSweeney, S. (2003). Specific radiation damage can be used to solve macromolecular crystal structures. Structure/Folding and Design, 11(2), 217–224.PubMedGoogle Scholar
  38. 38.
    Son, S. K., Chapman, H. N., & Santra, R. (2011). Multiwavelength anomalous diffraction at high X-ray intensity. Physical Review Letters, 107(21), 218102.CrossRefGoogle Scholar
  39. 39.
    Galli, L., Son, S. K., Klinge, M., Bajt, S., Barty, A., Bean, R., et al. (2015a). Electronic damage in S atoms in a native protein crystal induced by an intense X-ray free-electron laser pulse. Structural Dynamics, 2(4), 041703.CrossRefGoogle Scholar
  40. 40.
    Galli, L., Son, S. K., Barends, T. R., White, T. A., Barty, A., Botha, S., et al. (2015b). Towards phasing using high X-ray intensity. IUCrJ, 2(6), 627–634.CrossRefGoogle Scholar
  41. 41.
    Galli, L., Son, S. K., White, T. A., Santra, R., Chapman, H. N., & Nanao, M. H. (2015c). Towards RIP using free-electron laser SFX data. Journal of Synchrotron Radiation, 22(2), 249–255.CrossRefGoogle Scholar
  42. 42.
    Hosemann, R., & Bagchi, S. N. (1954). On homometric structures. Acta Cryst, 7, 237–241.CrossRefGoogle Scholar
  43. 43.
    Bricogne, G. (1974). Geometric sources of redundancy in intensity data and their use for phase determination. Acta Crystallographica Section A: Foundations and Advances, A30, 395–405.CrossRefGoogle Scholar
  44. 44.
    Crowther, R. A. (1969). The use of non-crystallographic symmetry for phase determination. Acta Cryst, B25, 2571–2580.CrossRefGoogle Scholar
  45. 45.
    Miao, J., Sayre, D., & Chapman, H. N. (1998). Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects. Journal of the Optical Society of America A, 15(6), 1662–1669.CrossRefGoogle Scholar
  46. 46.
    Thibault, P. (2007). Algorithmic methods in diffraction microscopy. PhD Thesis, Cornell University.Google Scholar
  47. 47.
    Millane, R. P., & Arnal, R. D. (2015). Uniqueness of the macromolecular crystallographic phase problem. Acta Crystallographica Section A: Foundations and Advances, A71, 592–598.CrossRefGoogle Scholar
  48. 48.
    Liu, Z.-C., Xu, R., & Dong, Y.-H. (2012). Phase retrieval in protein crystallography. Acta Crystallographica Section A: Foundations of Crystallography, A68, 256–265.Google Scholar
  49. 49.
    He, H., & Su, W. P. (2015). Direct phasing of protein crystals with high solvent content. Acta Crystallographica Section A, Foundations and Advances, 71(Pt 1), 92–98.CrossRefGoogle Scholar
  50. 50.
    He, H., Fang, H., Miller, M. D., Phillips Jr., G. N., & Su, W. P. (2016). Improving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithm. Acta Crystallographica Section A: Foundations and Advances, 72(5), 539–547.CrossRefGoogle Scholar
  51. 51.
    Spence, J. C. H., Weierstall, U., Fricke, T. T., Glaeser, R. M., & Downing, K. (2003). Journal of Structural Biology, 144, 209–218.CrossRefGoogle Scholar
  52. 52.
    Frank, M., Carlson, D. B., Hunter, M. S., Williams, G. J., Messerschmidt, M., Zatsepin, N. A., et al. (2014). Femtosecond X-ray diffraction from two-dimensional protein crystals. IUCrJ, 1(2), 95–100.CrossRefGoogle Scholar
  53. 53.
    Arnal, R. D., & Millane, R. P. (2017). The phase problem for two-dimensional crystals. I. Theory. Acta Crystallographica Section A: Foundations and Advances, 73, 438–448.CrossRefGoogle Scholar
  54. 54.
    Oszlanyi, G., & Suto, A. (2004). Ab initio structure solution by charge flipping. Acta Crystallographica Section A: Foundations and Advances, A60, 134.Google Scholar
  55. 55.
    Wu, J., Leinenweber, K., Spence, J. C., & O'Keeffe, M. (2006). Ab initio phasing of X-ray powder diffraction patterns by charge flipping. Nature Materials, 5(8), 647–652.CrossRefGoogle Scholar
  56. 56.
    Oszlanyi, G., & Suto, A. (2008). The charge flipping algorithm. Acta Crystallographica Section A: Foundations of Crystallography, A64, 123–134.Google Scholar
  57. 57.
    Dashti, A., Schwander, P., Langlois, R., Fung, R., Li, W., Hosseinizadeh, A., et al. (2014). Trajectories of the ribosome as a Brownian nanomachine. PNAS, 111(49), 17492–17497.CrossRefGoogle Scholar
  58. 58.
    Hosseinizadeh, A., Mashayekhi, G., Copperman, J., et al. (2017). Conformational landscape of a virus by single-particle X-ray scattering. Nature Methods, 14, 877–881.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Richard A. Kirian
    • 1
    Email author
  • Joe P. J. Chen
    • 1
  • John C. H. Spence
    • 1
  1. 1.Department of PhysicsArizona State UniversityTempeUSA

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