Abstract

We report a new classification scheme with computation complexity well within the capacity of a PC for coherent X-ray imaging of single biomolecules. In contrast to current methods, which are based on data from large scattering angles, we propose to classify the orientations of the biomolecule using data from small angle scattering, where the signals are relatively strong. Further we integrate data to form radial and azimuthal distributions of the scattering pattern to reduce the variance caused by the shot noise. Classification based on these two distributions are shown to successfully recognize not only the patterns from molecules of the same orientation but also those that differ by an in-plane rotation.

© 2011 OSA

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2011 (1)

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

2009 (4)

N.-T. D. Loh and V. Elser, “Reconstruction algorithm for single-particle diffraction imaging experiments,” Phy. Rev. E 80, 026705 (2009).
[CrossRef]

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

D. K. Saldin, V. L. Shneerson, R. Fung, and A. Ourmazd, “Structure of isolated biomolecules obtained from ultrashort x-ray pulses: exploiting the symmetry of random orientations,” J. Phys.: Condens. Matter 21, 134014 (2009).
[CrossRef]

J. Lipfert, D. Herschlag, and S. Doniach, “Riboswitch conformations revealed by small-angle x-ray scattering,” Methods Mol. Biol. 540, 141–159 (2009).
[CrossRef] [PubMed]

2008 (1)

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

2007 (2)

G. Bortel and G. Faigel, “Classification of continuous diffraction patterns: a numerical study,” J. Struct. Biol. 158, 10–18 (2007).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

2006 (2)

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

2005 (1)

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

2004 (1)

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

2003 (4)

G. Huldt, A. Szoke, and J. Hajdu, “Diffraction imaging of single particles and biomolecules,” J. Struct. Biol. 144, 219–227 (2003).
[CrossRef] [PubMed]

Y. Nishino, J. Miao, and T. Ishikawa, “Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities,” Phys. Rev. B 68, 220101 (2003).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

2002 (2)

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

J. C. H. Spence, U. Weierstall, and M. Howells, “Phase recovery and lensless imaging by iterative methods in optical x-ray and electron diffraction,” PPhilos. Trans. R. Soc. London, Ser. A 360, 875–895 (2002).
[CrossRef]

2001 (1)

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

2000 (2)

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

M. van Heel, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

1999 (1)

J. Miao, Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

1998 (2)

D. Sayre, H. N. Chapman, and J. Miao, “On the extendibility of x-ray crystallography to noncrystals,” Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 323–239 (1998).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

1992 (1)

1987 (1)

M. van Heel, “Angular reconstruction: a posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy 21, 111–124 (1987).
[CrossRef] [PubMed]

1965 (1)

R. Miles, “On random rotations in r3,” Biometrika 52, 636–639 (1965).

1955 (1)

G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).

Abergel, C.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Amirbekian, B.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Anderson, E. H.

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

Andreasson, J.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Aquila, A.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Bajt, S.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Barty, A.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

Beetz, T.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Benner, W. H.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Bogan, M. J.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Bortel, G.

G. Bortel and G. Faigel, “Classification of continuous diffraction patterns: a numerical study,” J. Struct. Biol. 158, 10–18 (2007).
[CrossRef]

Bunk, O.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Caleman, C.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Chapman, H.

Chapman, H. N.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

D. Sayre, H. N. Chapman, and J. Miao, “On the extendibility of x-ray crystallography to noncrystals,” Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 323–239 (1998).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Charalambous,

J. Miao, Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Claverie, J.-M.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Coppola, N.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Cui, C.

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

DePonte, D. P.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Doniach, S.

J. Lipfert, D. Herschlag, and S. Doniach, “Riboswitch conformations revealed by small-angle x-ray scattering,” Methods Mol. Biol. 540, 141–159 (2009).
[CrossRef] [PubMed]

Ekeberg, T.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Elser, V.

N.-T. D. Loh and V. Elser, “Reconstruction algorithm for single-particle diffraction imaging experiments,” Phy. Rev. E 80, 026705 (2009).
[CrossRef]

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Faigel, G.

G. Bortel and G. Faigel, “Classification of continuous diffraction patterns: a numerical study,” J. Struct. Biol. 158, 10–18 (2007).
[CrossRef]

Farrow, N. A.

Frank, M.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Fung, R.

D. K. Saldin, V. L. Shneerson, R. Fung, and A. Ourmazd, “Structure of isolated biomolecules obtained from ultrashort x-ray pulses: exploiting the symmetry of random orientations,” J. Phys.: Condens. Matter 21, 134014 (2009).
[CrossRef]

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

Gumprecht, L.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Hajdu, J.

G. Huldt, A. Szoke, and J. Hajdu, “Diffraction imaging of single particles and biomolecules,” J. Struct. Biol. 144, 219–227 (2003).
[CrossRef] [PubMed]

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

Hantke, M.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Hau-Riege, S.

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

Hau-Riege, S. P.

He, H.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

Herschlag, D.

J. Lipfert, D. Herschlag, and S. Doniach, “Riboswitch conformations revealed by small-angle x-ray scattering,” Methods Mol. Biol. 540, 141–159 (2009).
[CrossRef] [PubMed]

Howells, M.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

J. C. H. Spence, U. Weierstall, and M. Howells, “Phase recovery and lensless imaging by iterative methods in optical x-ray and electron diffraction,” PPhilos. Trans. R. Soc. London, Ser. A 360, 875–895 (2002).
[CrossRef]

Howells, M. R.

Huldt, G.

G. Huldt, A. Szoke, and J. Hajdu, “Diffraction imaging of single particles and biomolecules,” J. Struct. Biol. 144, 219–227 (2003).
[CrossRef] [PubMed]

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Ishikawa, T.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Y. Nishino, J. Miao, and T. Ishikawa, “Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities,” Phys. Rev. B 68, 220101 (2003).
[CrossRef]

Ishkawa, T.

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

Iwan, B.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Jacobsen, C.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Jiang, H.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Johnson, B.

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Jonsson, O.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Kirz, J.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

J. Miao, Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Lai, B.

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

Liang, M.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Lima, E.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Lipfert, J.

J. Lipfert, D. Herschlag, and S. Doniach, “Riboswitch conformations revealed by small-angle x-ray scattering,” Methods Mol. Biol. 540, 141–159 (2009).
[CrossRef] [PubMed]

Loh, N.-T. D.

N.-T. D. Loh and V. Elser, “Reconstruction algorithm for single-particle diffraction imaging experiments,” Phy. Rev. E 80, 026705 (2009).
[CrossRef]

London, R. A.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

Maia, F. R. N. C.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Mancuso, A.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Marchesini, S.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

Martin, A.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Miao, H.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Miao, J.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Y. Nishino, J. Miao, and T. Ishikawa, “Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities,” Phys. Rev. B 68, 220101 (2003).
[CrossRef]

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

J. Miao, Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

D. Sayre, H. N. Chapman, and J. Miao, “On the extendibility of x-ray crystallography to noncrystals,” Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 323–239 (1998).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Miles, R.

R. Miles, “On random rotations in r3,” Biometrika 52, 636–639 (1965).

Neiman, A. M.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Neutze, R.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

Nishino, Y.

Y. Nishino, J. Miao, and T. Ishikawa, “Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities,” Phys. Rev. B 68, 220101 (2003).
[CrossRef]

Noy, A.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

Odic, D.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Ohodgson, K. O.

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

Ottensmeyer, F. P.

Ourmazd, A.

D. K. Saldin, V. L. Shneerson, R. Fung, and A. Ourmazd, “Structure of isolated biomolecules obtained from ultrashort x-ray pulses: exploiting the symmetry of random orientations,” J. Phys.: Condens. Matter 21, 134014 (2009).
[CrossRef]

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

Padmore, H.

Peng, L.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Pfeifer, M. A.

G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).

Pfeifer, M.A.

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

Pfeiffer, F.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Pitney, J.

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

Robinson, I.

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).

Rocker, A.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Rodenburg, J. M.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Rosen, R.

Saldin, D. K.

D. K. Saldin, V. L. Shneerson, R. Fung, and A. Ourmazd, “Structure of isolated biomolecules obtained from ultrashort x-ray pulses: exploiting the symmetry of random orientations,” J. Phys.: Condens. Matter 21, 134014 (2009).
[CrossRef]

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

Sayre, D.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

J. Miao, Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

D. Sayre, H. N. Chapman, and J. Miao, “On the extendibility of x-ray crystallography to noncrystals,” Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 323–239 (1998).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Schulz, J.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Seibert, M. M.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Seltzer, V.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Shah, S. S.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Shapir, D.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Shapiro, D.

Shneerson, V.

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

Shneerson, V. L.

D. K. Saldin, V. L. Shneerson, R. Fung, and A. Ourmazd, “Structure of isolated biomolecules obtained from ultrashort x-ray pulses: exploiting the symmetry of random orientations,” J. Phys.: Condens. Matter 21, 134014 (2009).
[CrossRef]

Song, C.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Spence, J. C. H.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

J. C. H. Spence, U. Weierstall, and M. Howells, “Phase recovery and lensless imaging by iterative methods in optical x-ray and electron diffraction,” PPhilos. Trans. R. Soc. London, Ser. A 360, 875–895 (2002).
[CrossRef]

Spiller, E.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Stern, S.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Sun, R.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Svenda, M.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Szke, A.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Szoke, A.

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

G. Huldt, A. Szoke, and J. Hajdu, “Diffraction imaging of single particles and biomolecules,” J. Struct. Biol. 144, 219–227 (2003).
[CrossRef] [PubMed]

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

Szoke, H.

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

Thibault, P.

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

van der Spoel, D.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

van Heel, M.

M. van Heel, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

M. van Heel, “Angular reconstruction: a posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy 21, 111–124 (1987).
[CrossRef] [PubMed]

Vartanyants, I.

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).

Weckert, E.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

Weierstall, U.

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

S. Marchesini, H. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, “Coherent x-ray diffractive imaging: applications and limitations,” Opt. Express 11, 2344–2353 (2003).
[CrossRef] [PubMed]

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

J. C. H. Spence, U. Weierstall, and M. Howells, “Phase recovery and lensless imaging by iterative methods in optical x-ray and electron diffraction,” PPhilos. Trans. R. Soc. London, Ser. A 360, 875–895 (2002).
[CrossRef]

Westphal, D.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

White, T. A.

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

Williams, G.

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).

Woods, B. W.

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Wouts, R.

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

Zhou, Z. H.

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

Acta Crystallogr. Sect. A: Found. Crystallogr. (1)

S. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, “Speden: reconstructing single particles from their diffraction patterns,” Acta Crystallogr. Sect. A: Found. Crystallogr. 60, 294–305 (2004).
[CrossRef]

Acta Crystallogr., Sect. A: Found. Crystallogr. (1)

D. Sayre, H. N. Chapman, and J. Miao, “On the extendibility of x-ray crystallography to noncrystals,” Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 323–239 (1998).
[CrossRef]

Biometrika (1)

R. Miles, “On random rotations in r3,” Biometrika 52, 636–639 (1965).

J. Opt. Soc. Am. A (3)

J. Phys.: Condens. Matter (1)

D. K. Saldin, V. L. Shneerson, R. Fung, and A. Ourmazd, “Structure of isolated biomolecules obtained from ultrashort x-ray pulses: exploiting the symmetry of random orientations,” J. Phys.: Condens. Matter 21, 134014 (2009).
[CrossRef]

J. Struct. Biol. (2)

G. Bortel and G. Faigel, “Classification of continuous diffraction patterns: a numerical study,” J. Struct. Biol. 158, 10–18 (2007).
[CrossRef]

G. Huldt, A. Szoke, and J. Hajdu, “Diffraction imaging of single particles and biomolecules,” J. Struct. Biol. 144, 219–227 (2003).
[CrossRef] [PubMed]

Methods Mol. Biol. (1)

J. Lipfert, D. Herschlag, and S. Doniach, “Riboswitch conformations revealed by small-angle x-ray scattering,” Methods Mol. Biol. 540, 141–159 (2009).
[CrossRef] [PubMed]

Nat. Phys. (1)

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

Nature (3)

M. M. Seibert, T. Ekeberg, F. R. N. C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D. P. DePonte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M. Liang, T. A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, and J.-M. Claverie, “Single mimivirus particles intercepted and imaged with an x-ray laser,” Nature 470, 78–81 (2011).
[CrossRef] [PubMed]

J. Miao, Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond x-ray pulses,” Nature 406, 753–757 (2000).
[CrossRef]

Opt. Express (1)

Phy. Rev. B (1)

S. Marchesini, H. He, H. N. Chapman, S. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phy. Rev. B 68, 140101 (2003).
[CrossRef]

Phy. Rev. E (1)

N.-T. D. Loh and V. Elser, “Reconstruction algorithm for single-particle diffraction imaging experiments,” Phy. Rev. E 80, 026705 (2009).
[CrossRef]

Phy. Rev. Lett. (2)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard x-ray lensless imaging of extended objects,” Phy. Rev. Lett. 98, 034801 (2007).
[CrossRef]

I. Robinson, I. Vartanyants, G. Williams, M.A. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phy. Rev. Lett. 87(19), 195505 (2001).
[CrossRef]

Phys. Rev. B (1)

Y. Nishino, J. Miao, and T. Ishikawa, “Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities,” Phys. Rev. B 68, 220101 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).

J. Miao, T. Ishkawa, B. Johnson, E. H. Anderson, B. Lai, and K. O. Ohodgson, “High resoluton 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088302 (2002).
[CrossRef]

C. Song, H. Jiang, A. Mancuso, B. Amirbekian, L. Peng, R. Sun, S. S. Shah, Z. H. Zhou, T. Ishikawa, and J. Miao, “Quantitative imaging of single, unstained viruses with coherent x rays,” Phys. Rev. Lett. 101, 158101 (2008).
[CrossRef] [PubMed]

PPhilos. Trans. R. Soc. London, Ser. A (1)

J. C. H. Spence, U. Weierstall, and M. Howells, “Phase recovery and lensless imaging by iterative methods in optical x-ray and electron diffraction,” PPhilos. Trans. R. Soc. London, Ser. A 360, 875–895 (2002).
[CrossRef]

Proc. FEL (1)

H. N. Chapman, S. Bajt, A. Barty, W. H. Benner, M. J. Bogan, M. Frank, S. P. Hau-Riege, R. A. London, S. Marchesini, E. Spiller, A. Szke, and B. W. Woods, “Ultrafast coherent diffraction imaging with x-ray free-electron lasers,” Proc. FEL , 805–811 (2006).

Proc. Natl. Acad. Sci. U.S.A. (1)

D. Shapir, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 102(43), 15343–15346 (2005).
[CrossRef]

Q. Rev. Biophys. (1)

M. van Heel, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Ultramicroscopy (1)

M. van Heel, “Angular reconstruction: a posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy 21, 111–124 (1987).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Typical simulated scattering patterns of a DNA polymerase delta (PDB ID:3IAY). The data are shown in logarithmic scale. The radius of the hole in the center of the detector array is 3.72 mm. Left: “noise free” pattern; Middle: incident photon number is 2 × 1014 and the number of collected photons is 818875; Right: incident photon number is 2 × 1012 and the number of collected photons is 8114.

Fig. 2
Fig. 2

Detector array is divided into radial (a) or azimuthal segments (b).

Fig. 3
Fig. 3

Typical radical (a) and azimuthal (b) distributions. Three cases are studied: the mean value case (dotted line); the 2 × 1014 photon number case (solid line) and the 2 × 1012 photon number case (dashed line).

Fig. 4
Fig. 4

Surface plots of the radial (left column) and azimuthal (right column) distributions of the scattering patterns when the biomolecule rotates about the x-axis (a,b), y-axis (c,d), and z-axis (e–f). The incident photon number is 2 × 1014.

Fig. 5
Fig. 5

The radial distance as a function of the rotation angle when the protein rotates about y, and z respectively. The curve for rotation along z is shown in pink; in blue for rotation along y. Two incident photon levels are studied here: (a) 1014; (b) 1012; The mean values of the distances are shown in the solid lines; The color-shaded areas represent ±σ around the mean values for both the rotation about y and z respectively. σ is the variance. (c)–(d) are zoomed-in versions of (a) and (b) respectively.

Fig. 6
Fig. 6

Azimuthal distance reaches minimum at the in-plane rotation angle. Two incident photon number levels are studied: 2 × 1014(solid line) and 2 × 1012(dashed line).

Fig. 7
Fig. 7

(a) Scattering pattern from a single measurement; (b) Scattering pattern after averaging over 19 patterns with different in-plane rotations; (c) “Noise free” pattern.

Tables (1)

Tables Icon

Table 1 Accuracy of the In-Plane Rotation Classificationa

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

I ( x , y ) = Φ inc r e 2 Ω pix | n = 1 N atom f n ( x n , y n , z n ) exp ( j 2 π x x n + y y n λ z ) | 2 ,
ρ n + 1 = ρ n + Δ ρ n , n = 0 , 1 , 2 , N 1 ; Δ ρ n + 1 = ( 1 + ( Δ ρ n ρ n ) 2 ) Δ ρ n ,
I ρ ( n ) = ρ n ρ n + 1 0 2 π I ( ρ , θ ) d θ ρ d ρ ρ min ρ max 0 2 π I ( ρ , θ ) d θ ρ d ρ , n = 0 , 1 , 2 , N 1
I θ ( n ) = θ n θ n + 1 ρ min ρ max I ( ρ , θ ) ρ d ρ d θ 0 π ρ min ρ max I ( ρ , θ ) ρ d ρ d θ , n = 0 , 1 , 2 , 179.
R ( ϕ ) = R z ( γ ) R y ( β ) R z ( α ) ; π α , γ π , 0 β π ,
p ( α , β , γ ) = sin β 8 π 2 .
p eff ( α , cos β , γ ) = 1 2 π 2 , 0 α , β , γ π .
N inplane = N total 1 / 3 n .
D ρ ( I ref , I test ) = | n = 1 N ( I ρ ref ( n ) I ρ test ( n ) ) 2 | 1 / 2 ,
I θ ( θ , θ shift ) = I θ test ( θ θ shift ) ,
D θ ( I ref , I test , θ shift ) = | 0 π ( I θ ref I θ test ( θ θ shift ) ) 2 d θ | 1 / 2 ,
N in d = N total × ( N total 1 ) × N total 1 / 3 N total .
η = N true N classified ,
| δ r | = a 2 δ θ .

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