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Conformational landscape of a virus by single-particle X-ray scattering


Using a manifold-based analysis of experimental diffraction snapshots from an X-ray free electron laser, we determine the three-dimensional structure and conformational landscape of the PR772 virus to a detector-limited resolution of 9 nm. Our results indicate that a single conformational coordinate controls reorganization of the genome, growth of a tubular structure from a portal vertex and release of the genome. These results demonstrate that single-particle X-ray scattering has the potential to shed light on key biological processes.

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Figure 1: 3D diffraction volume and structure obtained without conformational analysis.
Figure 2: 3D structures revealed by conformational analysis assuming icosahedral symmetry.
Figure 3: Conformational probability distribution.
Figure 4: 3D structures revealed by conformational analysis without imposing icosahedral symmetry.


  1. 1

    Neutze, R., Wouts, R., van der Spoel, D., Weckert, E. & Hajdu, J. Potential for biomolecular imaging with femtosecond X-ray pulses. Nature 406, 752–757 (2000).

    CAS  PubMed  PubMed Central  Google Scholar 

  2. 2

    Breedlove, J.R. Jr. & Trammell, G.T. Molecular microscopy: fundamental limitations. Science 170, 1310–1313 (1970).

    CAS  PubMed  Google Scholar 

  3. 3

    Solem, J.C. & Baldwin, G.C. Microholography of living organisms. Science 218, 229–235 (1982).

    CAS  PubMed  Google Scholar 

  4. 4

    Miao, J., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999).

    CAS  Google Scholar 

  5. 5

    Fung, R., Shneerson, V., Saldin, D.K. & Ourmazd, A. Structure from fleeting illumination of faint spinning objects in flight. Nat. Phys. 5, 64–67 (2009).

    CAS  Google Scholar 

  6. 6

    Loh, N.T. & Elser, V. Reconstruction algorithm for single-particle diffraction imaging experiments. Phys. Rev. E 80, 026705 (2009).

    Google Scholar 

  7. 7

    Seibert, M.M. et al. Single mimivirus particles intercepted and imaged with an X-ray laser. Nature 470, 78–81 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. 8

    Hantke, M.F. et al. High-throughput imaging of heterogeneous cell organelles with an X-ray laser. Nat. Photonics 8, 943–949 (2014).

    CAS  Google Scholar 

  9. 9

    Kuhn, R.J., Dowd, K.A., Beth Post, C. & Pierson, T.C. Shake, rattle, and roll: impact of the dynamics of flavivirus particles on their interactions with the host. Virology 479-480, 508–517 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  10. 10

    Mateu, M.G. Assembly, stability and dynamics of virus capsids. Arch. Biochem. Biophys. 531, 65–79 (2013).

    CAS  PubMed  Google Scholar 

  11. 11

    Xu, R. et al. Single-shot three-dimensional structure determination of nanocrystals with femtosecond X-ray free-electron laser pulses. Nat. Commun. 5, 4061 (2014).

    CAS  PubMed  Google Scholar 

  12. 12

    Ekeberg, T. et al. Three-dimensional reconstruction of the giant mimivirus particle with an x-ray free-electron laser. Phys. Rev. Lett. 114, 098102 (2015).

    PubMed  Google Scholar 

  13. 13

    Loh, N.D. et al. Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns. Phys. Rev. Lett. 104, 225501 (2010).

    CAS  PubMed  Google Scholar 

  14. 14

    Moore, P.B. How should we think about the ribosome? Annu. Rev. Biophys. 41, 1–19 (2012).

    CAS  PubMed  Google Scholar 

  15. 15

    Changeux, J.P. & Edelstein, S. Conformational selection or induced fit? 50 years of debate resolved. F1000 Biol. Rep. 3, 19 (2011).

    PubMed  PubMed Central  Google Scholar 

  16. 16

    Ye, L., Van Eps, N., Zimmer, M., Ernst, O.P. & Prosser, R.S. Activation of the A2A adenosine G-protein-coupled receptor by conformational selection. Nature 533, 265–268 (2016).

    CAS  PubMed  Google Scholar 

  17. 17

    Yu, I.M. et al. Structure of the immature dengue virus at low pH primes proteolytic maturation. Science 319, 1834–1837 (2008).

    CAS  PubMed  Google Scholar 

  18. 18

    Henrich, B. et al. The adaptive gain integrating pixel detector AGIP a detector for the European XFEL. Nucl. Instrum. Methods Phys. Res. A 633, S11–S14 (2011).

    CAS  Google Scholar 

  19. 19

    Jarzynski, C. Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690–2693 (1997).

    CAS  Google Scholar 

  20. 20

    Jarzynski, C. Equilibrium free energy differences from nonequilibrium measurements. Phys. Rev. E 56, 5018–5035 (1997).

    CAS  Google Scholar 

  21. 21

    Crooks, G.E. Path-ensemble averages in systems driven far from equilibrium. Phys. Rev. E 61, 2361 (2000).

    CAS  Google Scholar 

  22. 22

    Pressé, S. Principles of maximum entropy andn maximum caliber in statistical physics. Rev. Mod. Phys. 85, 1115–1141 (2013).

    Google Scholar 

  23. 23

    Schwander, P., Fung, R. & Ourmazd, A. Conformations of macromolecules and their complexes from heterogeneous datasets. Phil. Trans. R. Soc. Lond. B 369, 20130567 (2014).

    CAS  Google Scholar 

  24. 24

    Dashti, A. et al. Trajectories of the ribosome as a Brownian nanomachine. Proc. Natl. Acad. Sci. USA 111, 17492–17497 (2014).

    CAS  PubMed  Google Scholar 

  25. 25

    Frank, J. & Ourmazd, A. Continuous changes in structure mapped by manifold embedding of single-particle data in cryo-EM. Methods 100, 61–67 (2016).

    CAS  PubMed  Google Scholar 

  26. 26

    Reddy, H.K.N. et al. Coherent soft X-ray diffraction imaging of coliphage PR772 at the Linac coherent light source. Sci. Data 4, 170079 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  27. 27

    Hosseinizadeh, A., Dashti, A., Schwander, P., Fung, R. & Ourmazd, A. Single-particle structure determination by X-ray free-electron lasers: possibilities and challenges. Struct. Dyn. 2, 041601 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  28. 28

    Hosseinizadeh, A. et al. High-resolution structure of viruses from random diffraction snapshots. Phil. Trans. R. Soc. Lond. B 369, 20130326 (2014).

    CAS  Google Scholar 

  29. 29

    Scheres, S.H. & Chen, S. Prevention of overfitting in cryo-EM structure determination. Nat. Methods 9, 853–854 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  30. 30

    Peralta, B. et al. Mechanism of membranous tunnelling nanotube formation in viral genome delivery. PLoS Biol. 11, e1001667 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. 31

    Santos-Pérez, I. et al. Membrane-assisted viral DNA ejection. Biochim. Biophys. Acta 1861, 664–672 (2017).

    Google Scholar 

  32. 32

    Incardona, N.L. & Kaesberg, P. A pH-induced structural change in bromegrass mosiac virus. Biophys. J. 4, 11–21 (1964).

    CAS  PubMed  PubMed Central  Google Scholar 

  33. 33

    Speir, J.A., Munshi, S., Wang, G., Baker, T.S. & Johnson, J.E. Structures of the native and swollen forms of cowpea chlorotic mottle virus determined by X-ray crystallography and cryo-electron microscopy. Structure 3, 63–78 (1995).

    CAS  PubMed  PubMed Central  Google Scholar 

  34. 34

    Ayyer, K., Lan, T.Y., Elser, V. & Loh, N.D. Dragonfly: an implementation of the expand-maximize-compress algorithm for single-particle imaging. J. Appl. Crystallogr. 49, 1320–1335 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  35. 35

    Frank, J. Three-Dimensional Electron Microscopy of Macromolecular Assemblies 2nd edn. (Oxford University Press, 2006).

  36. 36

    Coifman, R.R. et al. Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc. Natl. Acad. Sci. USA 102, 7426–7431 (2005).

    CAS  PubMed  Google Scholar 

  37. 37

    Giannakis, D. & Majda, A.J. Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability. Proc. Natl. Acad. Sci. USA 109, 2222–2227 (2012).

    CAS  PubMed  Google Scholar 

  38. 38

    Giannakis, D., Schwander, P. & Ourmazd, A. The symmetries of image formation by scattering. I. Theoretical framework. Opt. Express 20, 12799–12826 (2012).

    PubMed  Google Scholar 

  39. 39

    Schwander, P., Giannakis, D., Yoon, C.H. & Ourmazd, A. The symmetries of image formation by scattering. II. Applications. Opt. Express 20, 12827–12849 (2012).

    PubMed  Google Scholar 

  40. 40

    White, T.A. CrystFEL: a software suite for snapshot serial crystallography. J. Appl. Crystallogr. 45, 335–341 (2012).

    CAS  Google Scholar 

  41. 41

    Fienup, J.R. Phase retrieval algorithms: a comparison. Appl. Opt. 21, 2758–2769 (1982).

    CAS  PubMed  Google Scholar 

  42. 42

    Coifman, R.R., Shkolnisky, Y., Sigworth, F.J. & Singer, A. Graph Laplacian tomography from unknown random projections. IEEE Trans. Image Process. 17, 1891–1899 (2008).

    PubMed  Google Scholar 

  43. 43

    Marchesini, S. et al. X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B 68, 140101 (2003).

    Google Scholar 

  44. 44

    Dashti, A., Komarov, I. & D'Souza, R.M.D. Efficient computation of k-nearest neighbour graphs for large high-dimensional data sets on GPU clusters. PLoS One 8, e74113 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

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We acknowledge valuable discussions with H. Chapman, E. Lattman, J. Spence and I. Vartaniants. The research conducted at University of Wisconsin–Milwaukee was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under contract DE-SC0002164 (A.O., algorithm design and development) and by the US National Science Foundation (NSF) under contract STC 1231306 (A.O., numerical trial models and data analysis; M.S., data analysis) and under contract number 1551489 (A.O., underlying analytical models). The research at Arizona State University was supported by the NSF under contract STC 1231306 (B.G.H.). Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract DE-AC02-76SF00515.

Author information




A.H.: algorithmic design, data preprocessing, single-particle hit finding, orientation and structural recovery, preparation of paper. G.M.: conformational analysis, preparation of paper. J.C.: conformational analysis and validation, preparation of paper. P.S.: experimental and algorithmic design, code development, data preprocessing, data analysis, experiments at LCLS, preparation of paper. A.D., R.S. and R.F.: data-analytical contributions. M.S.: analysis of results, preparation of paper. C.H.Y.: experimental design, data collection. B.G.H.: sample selection, preparation and characterization, experiments at LCLS, preparation of paper. G.J.W.: planning and execution of experiment and discussions of data and analysis. A.A.: experimental design, data collection, preparation of paper. A.O.: experimental and algorithmic design, data analysis and interpretation, preparation of paper.

Corresponding author

Correspondence to Abbas Ourmazd.

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Integrated supplementary information

Supplementary Figure 1 2D snapshots obtained by direct phasing of individual diffraction snapshots.

Each row shows five representative snapshots assigned to an extreme value of the conformational parameter τ. Note the reduction in the projected inner density between the two rows. (Rainbow color code, with dark red corresponding to the highest density.)

Supplementary Figure 2 Reliability of the reconstructed diffraction volume.

R-split as a function of the magnitude of the scattering vector q, indicating reliable reconstruction up to the detector-limited resolution of 9 nm. The analysis was performed by random splitting, without substitution, of the 37,550 snapshots into two disjoint datasets.

Source data

Supplementary Figure 3 Spatial resolution of 3D density.

Fourier Shell Correlation (FSC) vs. the magnitude of the scattering vector q obtained from splitting the 37,550 snapshots into two random disjoint subsets. The resolution is limited to 9 nm by the detector geometry.

Source data

Supplementary Figure 4 Spherically averaged radial densities of 3D structures obtained without imposing icosahedral symmetry.

The conformational coordinate ranges from 0 (black curve) to 1 (red curve). Averages (circles) and standard deviations (error bars) pertain to twenty 3D iterative phasing calculations using all 37,550 single-particle snapshots. Spline fits are guides to the eye.

Source data

Supplementary Figure 5 A representative experimental XFEL diffraction snapshot of the PR772 virus before and after preprocessing.

(a) A raw snapshot. (b) Same snapshot after background correction. The dark horizontal line in each snapshot is due to the gap between the two detector panels. Intensity is shown in the rainbow color code, with red corresponding to the highest intensity.

Supplementary Figure 6 Diffusion map manifolds formed by experimental XFEL diffraction snapshots of the PR772 virus.

(a) Manifold obtained by embedding 135,375 preprocessed XFEL snapshots (“hits”). (b) Distribution of single- and multi-particle snapshots on the same manifold. The general parabolic shape stems from changes in the incident beam intensity intersecting the particles. (c) Manifold of single-particle snapshots after outlier removal. A total of 37,550 single-particle snapshots were extracted by this analysis.

Source data

Supplementary Figure 7 Comparison of icosahedral Wigner D functions with diffusion map manifolds obtained from simulated and experimental diffraction snapshots.

(a) Icosahedral Wigner D-functions sampled in 30,000 randomly selected orientations. (b) DM eigenfunctions obtained from 30,000 simulated, noise-free snapshots of an icosahedral capsid. (c) Manifold from 37,550 simulated snapshots of an icosahedral capsid with experimental signal-to-noise ratio (SNR) and detector gap. (d) Manifold from 37,550 experimental single-particle PR772 snapshots. (e) Eigenvalue spectrum for an icosahedral capsid simulated at the experimental SNR. (f) Eigenvalue spectrum for the PR772 virus.

Source data

Supplementary Figure 8 Diffusion map eigenvalue spectra for experimental and simulated diffraction snapshots of PR772 virus.

(a) Spectrum for 37,550 single-particle experimental snapshots of PR772 virus. (b) Spectrum resulting from the same number of simulated snapshots of an icosahedral capsid stretched by 10% along one 5-fold axis. Note the differences between the eigenvalue spectra.

Source data

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–8 and Supplementary Note (PDF 1339 kb)

Life Sciences Reporting Summary

Life Sciences Reporting Summary (PDF 160 kb)

Supplementary Data

Single-particle indices (XLSX 1153 kb)

3D conformational movie with imposed icosahedral symmetry.

Evolution of the 3D structure of the PR772 virus, and the occupancy along the dominant conformational reaction coordinate. These results were obtained assuming icosahedral symmetry. (MOV 800 kb)

3D conformational movie without imposing icosahedral symmetry.

Evolution of the 3D structure of the PR772 virus, and the occupancy along the conformational reaction coordinate without imposing icosahedral symmetry. Note the protrusion of a tubular structure, and the concentration of the genome toward the tube. (MOV 418 kb)

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Hosseinizadeh, A., Mashayekhi, G., Copperman, J. et al. Conformational landscape of a virus by single-particle X-ray scattering. Nat Methods 14, 877–881 (2017).

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