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In-plane rotation classification for coherent X-ray imaging of single biomoleculesKaiqin Chu, James Evans, Nina Rohringer, Stefan Hau-Riege, Alexander Graf, Matthias Frank, Zachary J. Smith, and Stephen Lane »View Author Affiliations
Kaiqin Chu,1,*
James Evans,2
Nina Rohringer,3,4
Stefan Hau-Riege,4
Alexander Graf,4
Matthias Frank,4
Zachary J. Smith,1
and Stephen Lane1,4
1Center for Biophotonics Science and Technology, Sacramento, California 95817, USA 2Molecular and Cellular Biology, University of California at Davis, Davis, California 95616, USA 3Max Planck Advanced Study Group, Center for Free-Electron Laser Science, c/o DESY, 22607 Hamburg, Germany 4Lawrence Livermore National Laboratory, Livermore, California 94550, USA *Corresponding author: kqchu@ucdavis.edu |
Optics Express, Vol. 19, Issue 12, pp. 11691-11704 (2011)
http://dx.doi.org/10.1364/OE.19.011691
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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
OCIS Codes
(260.1960) Physical optics : Diffraction theory
(290.5840) Scattering : Scattering, molecules
(290.2558) Scattering : Forward scattering
(110.3200) Imaging systems : Inverse scattering
ToC Category:
X-ray Optics
History
Original Manuscript: February 15, 2011
Revised Manuscript: May 7, 2011
Manuscript Accepted: May 25, 2011
Published: June 1, 2011
Virtual Issues
Vol. 6, Iss. 7 Virtual Journal for Biomedical Optics
Citation
Kaiqin Chu, James Evans, Nina Rohringer, Stefan Hau-Riege, Alexander Graf, Matthias Frank, Zachary J. Smith, and Stephen Lane, "In-plane rotation classification for coherent X-ray imaging of single biomolecules," Opt. Express 19, 11691-11704 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11691
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References
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- 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]
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- 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]
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- G. Bortel and G. Faigel, “Classification of continuous diffraction patterns: a numerical study,” J. Struct. Biol. 158, 10–18 (2007). [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).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
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- 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]
- 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]
- 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]
- 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).
- 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]
- 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]
- 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).
- 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]
- 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]
- 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]
- 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]
- M. van Heel, “Angular reconstruction: a posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy 21, 111–124 (1987). [CrossRef] [PubMed]
- 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).
- 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]
- 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]
- 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]
- 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]
- 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).
- 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).
- 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]
- 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.
- 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.
- 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
- R. Miles, “On random rotations in r3,” Biometrika 52, 636–639 (1965).
J. Opt. Soc. Am. A
- N. A. Farrow and F. P. Ottensmeyer, “A posteriori determination of relative projection directions of arbitrarily oriented macromolecules,” J. Opt. Soc. Am. A 9, 1749–1760 (1992). [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]
- 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]
J. Phys.: Condens. Matter
- 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.
- 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.
- 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.
- 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
- 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
- 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]
Phy. Rev. B
- 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
- 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.
- 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
- 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.
- 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
- 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
- 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.
- 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.
- M. van Heel, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000). [CrossRef]
Ultramicroscopy
- M. van Heel, “Angular reconstruction: a posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy 21, 111–124 (1987). [CrossRef] [PubMed]
2011, Seibert, Nature
- 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]
- 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]
- 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]
- 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]
- 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).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- M. van Heel, “Angular reconstruction: a posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy 21, 111–124 (1987). [CrossRef] [PubMed]
- R. Miles, “On random rotations in r3,” Biometrika 52, 636–639 (1965).
- G. Williams, M. A. Pfeifer, I. Vartanyants, and I. Robinson, “Three-dimensional imaging of microstructure in au nanocrystals,” Phys. Rev. Lett. 90, 195505 (2003).
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