Abstract

We consider the problem of phase determination for continuous diffraction patterns obtained from a beam of identical, aligned large molecules (such as proteins), each coated with a layer of water or vitreous ice. Many laser-aligned molecules are assumed to lie within a wide continuous x-ray beam at any instant. An iterative phasing method is developed to extract the common target structure in three dimensions from diffraction patterns of these doped ice balls. Several measurements of the diffraction intensity in reciprocal space are needed. We found iteratively two boundaries (supports) (between protein and ice and the outer iceball support) by using the charge-flipping and multiple hybrid input–output algorithms, working with multiple sets of measured data. The approach is applied to simulated data from hydrated lysozyme proteins generated by the serial crystallography method of laser-aligned protein-beam diffraction proposed by Spence and Doak [Phys. Rev. Lett. 92, 198102 (2004) ]. We consider also the effect of empty ice balls on the patterns. The algorithm can also be used to align images with different randomly chosen origins, so that the same embedded subunits overlap.

© 2005 Optical Society of America

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References

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  1. J. C. H. Spence, B. Doak, “Single molecule diffraction,” Phys. Rev. Lett. 92, 198102 (2004).
    [CrossRef] [PubMed]
  2. J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
    [CrossRef]
  3. H. Stapelfeldt, T. Seideman, “Colloquium: aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
    [CrossRef]
  4. H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
    [CrossRef]
  5. L. S. Bartell, J. Huang, “Supercooling of water below the anomalous range near 226 K,” J. Phys. Chem. 90, 7455–7457 (1994).
    [CrossRef]
  6. M. Faubel, S. Schlemmer, J. P. Toennies, “A molecular-beam study of the evaporation of water from a liquid jet,” Z. Phys. D At. Mol. Clusters 10, 269–277 (1988).
    [CrossRef]
  7. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
    [CrossRef] [PubMed]
  8. H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
    [CrossRef]
  9. S. Marchesini, H. He, H. Chapman, S. Hau-Riege, A. Noy, M. Howells, U. Weierstall, J. C. H. Spence, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
    [CrossRef]
  10. R. W. Gerchberg, W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).
  11. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  12. J. W. Miao, C. Charalambous, J. Kirz, D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature (London) 400, 342–344 (1999).
    [CrossRef]
  13. J. Miao, D. Sayre, “On possible extensions of x-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A Found. Crystallogr. 56, 596–605 (2000).
    [CrossRef]
  14. U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
    [CrossRef]
  15. G. Oszlányi, A. Sütő, “ Ab initio structure solution by charge flipping,” Acta Crystallogr. Sect. A Found. Crystallogr. 60, 134–l41 (2004).
    [CrossRef]
  16. J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
    [CrossRef]
  17. J. S. Wu, U. Weierstall, J. C. H. Spence, C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29, 2737–2739 (2004).
    [CrossRef] [PubMed]
  18. M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
    [CrossRef]
  19. T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
    [CrossRef] [PubMed]
  20. R. Diamond, “Real-space refinement of structure of hen egg-white lysozyme,” J. Mol. Biol. 82, 371–391 (1974).
    [CrossRef] [PubMed]
  21. S. W. Peterson, H. A. Levy, “A single-crystal neutron diffraction study of heavy ice,” Acta Crystallogr. 10, 70–76 (1957).
    [CrossRef]
  22. Y. Teshima, T. Ogama, “Dense packing of equal circles on a sphere by the minimum-zenith method: symmetrical arrangement,” Forma 15, 347–364 (2000).

2005

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

2004

J. C. H. Spence, B. Doak, “Single molecule diffraction,” Phys. Rev. Lett. 92, 198102 (2004).
[CrossRef] [PubMed]

G. Oszlányi, A. Sütő, “ Ab initio structure solution by charge flipping,” Acta Crystallogr. Sect. A Found. Crystallogr. 60, 134–l41 (2004).
[CrossRef]

J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
[CrossRef]

J. S. Wu, U. Weierstall, J. C. H. Spence, C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29, 2737–2739 (2004).
[CrossRef] [PubMed]

2003

H. Stapelfeldt, T. Seideman, “Colloquium: aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

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

2001

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

2000

J. Miao, D. Sayre, “On possible extensions of x-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A Found. Crystallogr. 56, 596–605 (2000).
[CrossRef]

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Y. Teshima, T. Ogama, “Dense packing of equal circles on a sphere by the minimum-zenith method: symmetrical arrangement,” Forma 15, 347–364 (2000).

1999

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

1994

T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
[CrossRef] [PubMed]

L. S. Bartell, J. Huang, “Supercooling of water below the anomalous range near 226 K,” J. Phys. Chem. 90, 7455–7457 (1994).
[CrossRef]

1988

M. Faubel, S. Schlemmer, J. P. Toennies, “A molecular-beam study of the evaporation of water from a liquid jet,” Z. Phys. D At. Mol. Clusters 10, 269–277 (1988).
[CrossRef]

1982

1974

R. Diamond, “Real-space refinement of structure of hen egg-white lysozyme,” J. Mol. Biol. 82, 371–391 (1974).
[CrossRef] [PubMed]

1972

R. W. Gerchberg, W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1957

S. W. Peterson, H. A. Levy, “A single-crystal neutron diffraction study of heavy ice,” Acta Crystallogr. 10, 70–76 (1957).
[CrossRef]

Bartell, L. S.

L. S. Bartell, J. Huang, “Supercooling of water below the anomalous range near 226 K,” J. Phys. Chem. 90, 7455–7457 (1994).
[CrossRef]

Caspar, D. L. D.

T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
[CrossRef] [PubMed]

Chapman, H.

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

Charalambous, C.

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

Chen, Q.

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

Cohen, D.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

DeRosier, D. J.

T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
[CrossRef] [PubMed]

Diamond, R.

R. Diamond, “Real-space refinement of structure of hen egg-white lysozyme,” J. Mol. Biol. 82, 371–391 (1974).
[CrossRef] [PubMed]

Diaz-Avalos, R.

T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
[CrossRef] [PubMed]

Doak, B.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

J. C. H. Spence, B. Doak, “Single molecule diffraction,” Phys. Rev. Lett. 92, 198102 (2004).
[CrossRef] [PubMed]

Faubel, M.

M. Faubel, S. Schlemmer, J. P. Toennies, “A molecular-beam study of the evaporation of water from a liquid jet,” Z. Phys. D At. Mol. Clusters 10, 269–277 (1988).
[CrossRef]

Fienup, J. R.

Finn, R.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Fromme, P.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

Gao, M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Gowen, B.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Groy, T.

J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
[CrossRef]

Hau-Riege, S.

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

He, H.

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

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

Hembree, G.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

Howells, M.

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

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

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

Huang, J.

L. S. Bartell, J. Huang, “Supercooling of water below the anomalous range near 226 K,” J. Phys. Chem. 90, 7455–7457 (1994).
[CrossRef]

Isaacson, M.

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

Kirz, J.

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

Koch, C. T.

Levy, H. A.

S. W. Peterson, H. A. Levy, “A single-crystal neutron diffraction study of heavy ice,” Acta Crystallogr. 10, 70–76 (1957).
[CrossRef]

Marchesini, S.

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

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

Matadeen, R.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Miao, J.

J. Miao, D. Sayre, “On possible extensions of x-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A Found. Crystallogr. 56, 596–605 (2000).
[CrossRef]

Miao, J. W.

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

Minemoto, S.

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

Nagahara, L. A.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

Nanjo, H.

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

Noy, A.

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

O’Keeffe, M.

J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
[CrossRef]

Ogama, T.

Y. Teshima, T. Ogama, “Dense packing of equal circles on a sphere by the minimum-zenith method: symmetrical arrangement,” Forma 15, 347–364 (2000).

Orlova, E. V.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Oszlányi, G.

G. Oszlányi, A. Sütő, “ Ab initio structure solution by charge flipping,” Acta Crystallogr. Sect. A Found. Crystallogr. 60, 134–l41 (2004).
[CrossRef]

Panepucci, R. R.

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

Pape, T.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Patwardhan, A.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Peterson, S. W.

S. W. Peterson, H. A. Levy, “A single-crystal neutron diffraction study of heavy ice,” Acta Crystallogr. 10, 70–76 (1957).
[CrossRef]

Ranck, J. L.

T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
[CrossRef] [PubMed]

Ruiz, T.

T. Ruiz, J. L. Ranck, R. Diaz-Avalos, D. L. D. Caspar, D. J. DeRosier, “Electron diffraction of helical particles,” Ultramicroscopy 55, 383–395 (1994).
[CrossRef] [PubMed]

Sakai, H.

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “Practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Sayre, D.

J. Miao, D. Sayre, “On possible extensions of x-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A Found. Crystallogr. 56, 596–605 (2000).
[CrossRef]

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

Schatz, M.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Schlemmer, S.

M. Faubel, S. Schlemmer, J. P. Toennies, “A molecular-beam study of the evaporation of water from a liquid jet,” Z. Phys. D At. Mol. Clusters 10, 269–277 (1988).
[CrossRef]

Schmidt, K.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

Schmidt, R.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Seideman, T.

H. Stapelfeldt, T. Seideman, “Colloquium: aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

Spence, J. C. H.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

J. C. H. Spence, B. Doak, “Single molecule diffraction,” Phys. Rev. Lett. 92, 198102 (2004).
[CrossRef] [PubMed]

J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
[CrossRef]

J. S. Wu, U. Weierstall, J. C. H. Spence, C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29, 2737–2739 (2004).
[CrossRef] [PubMed]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

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

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

Stapelfeldt, H.

H. Stapelfeldt, T. Seideman, “Colloquium: aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

Stark, H.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

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G. Oszlányi, A. Sütő, “ Ab initio structure solution by charge flipping,” Acta Crystallogr. Sect. A Found. Crystallogr. 60, 134–l41 (2004).
[CrossRef]

Suzuki, T.

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

Tanji, H.

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

Teshima, Y.

Y. Teshima, T. Ogama, “Dense packing of equal circles on a sphere by the minimum-zenith method: symmetrical arrangement,” Forma 15, 347–364 (2000).

Toennies, J. P.

M. Faubel, S. Schlemmer, J. P. Toennies, “A molecular-beam study of the evaporation of water from a liquid jet,” Z. Phys. D At. Mol. Clusters 10, 269–277 (1988).
[CrossRef]

van Heel, M.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

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J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

Weierstall, U.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

J. S. Wu, U. Weierstall, J. C. H. Spence, C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29, 2737–2739 (2004).
[CrossRef] [PubMed]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

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

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
[CrossRef]

Wu, J. S.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
[CrossRef]

J. S. Wu, U. Weierstall, J. C. H. Spence, C. T. Koch, “Iterative phase retrieval without support,” Opt. Lett. 29, 2737–2739 (2004).
[CrossRef] [PubMed]

Zhang, R.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

Zuo, J. M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

Acta Crystallogr.

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[CrossRef]

Acta Crystallogr. Sect. A Found. Crystallogr.

J. C. H. Spence, K. Schmidt, J. S. Wu, G. Hembree, U. Weierstall, B. Doak, P. Fromme, “Diffraction and imaging from a beam of laser-aligned proteins: resolution limits,” Acta Crystallogr. Sect. A Found. Crystallogr. 61, 237–245 (2005).
[CrossRef]

H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, J. C. H. Spence, “Experimental lensless soft-x-ray imaging using iterative algorithms: phasing diffuse scattering,” Acta Crystallogr. Sect. A Found. Crystallogr. 59, 143–152 (2003).
[CrossRef]

J. Miao, D. Sayre, “On possible extensions of x-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A Found. Crystallogr. 56, 596–605 (2000).
[CrossRef]

G. Oszlányi, A. Sütő, “ Ab initio structure solution by charge flipping,” Acta Crystallogr. Sect. A Found. Crystallogr. 60, 134–l41 (2004).
[CrossRef]

J. S. Wu, J. C. H. Spence, M. O’Keeffe, T. Groy, “Application of a modified Oszlányi and Sütő Ab initio charge-flipping algorithm to experimental data,” Acta Crystallogr. Sect. A Found. Crystallogr. 60326–330 (2004).
[CrossRef]

Appl. Opt.

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[CrossRef]

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Phys. Rev. B

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

Phys. Rev. Lett.

J. C. H. Spence, B. Doak, “Single molecule diffraction,” Phys. Rev. Lett. 92, 198102 (2004).
[CrossRef] [PubMed]

H. Sakai, S. Minemoto, H. Nanjo, H. Tanji, T. Suzuki, “Controlling the orientation of polar molecules with combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 90, 083001 (2003).
[CrossRef]

Q. Rev. Biophys.

M. van Heel, B. Gowen, R. Matadeen, E. V. Orlova, R. Finn, T. Pape, D. Cohen, H. Stark, R. Schmidt, M. Schatz, A. Patwardhan, “Single-particle electron cryo-microscopy: towards atomic resolution,” Q. Rev. Biophys. 33, 307–369 (2000).
[CrossRef]

Rev. Mod. Phys.

H. Stapelfeldt, T. Seideman, “Colloquium: aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75, 543–557 (2003).
[CrossRef]

Science

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef] [PubMed]

Ultramicroscopy

U. Weierstall, Q. Chen, J. C. H. Spence, M. Howells, M. Isaacson, R. R. Panepucci, “Image reconstruction from electron and x-ray diffraction patterns using iterative algorithms: experiment and simulation,” Ultramicroscopy 90, 171–195 (2001).
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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Illustration of the core-passing multiple HIO algorithm for three sets of data, F 1 ( u ) , F 2 ( u ) , and F 3 ( u ) . The outer support s out ( x ) is illustrated by circles, and the molecular support s mole ( x ) is shown by octagons. The core that forms by the molecular support passes to the next estimate in the algorithm.

Fig. 2
Fig. 2

Tetrahedrally bonded H 2 O cluster used to build a model of vitreous ice. It is the average environment of an H 2 O molecule in amorphous ice, as determined by neutron diffraction.[21]

Fig. 3
Fig. 3

Three projections along the (a) [100], (b) [010], and (c) [001] directions of the potential (at resolution of 3 Å) of a lysozyme molecule inside an amorphous ice ball (diameter of 6.5 nm) and its oversampled electron diffraction projected along the (d) [ 100 ] * , (e) [ 010 ] * , and (f) [ 001 ] * directions. ( * means direction in reciprocal space as opposed to that in real space.)

Fig. 4
Fig. 4

R versus iteration number for the reconstruction of g n 1 ( x ) working with a dynamic support generated by a volume ratio of 0.5. ER, error reduction.

Fig. 5
Fig. 5

Three projections along the (a) [100], (b) [010], (c) [001] directions of the reconstructed potential g 160 1 ( x ) for lysozyme, masked by the current support at iteration 160. The molecular support can be found on the basis of it.

Fig. 6
Fig. 6

R factor versus iteration number for extraction of the lysozyme molecule shown in Fig. 7 with both outer and molecular supports.

Fig. 7
Fig. 7

Three projections along the (a) [100], (b) [010], and (c) [001] directions of the reconstructed and subtracted potential of the lysozyme molecule.

Fig. 8
Fig. 8

Crystallographic residual R1 and R2 versus the number of lysozyme (5LYZ) protein molecules passing through the electron beam. R1 reaches 0.07 when the number of molecules is 400. This shows that when protein molecules are coated only with thin jackets the elastic background caused by empty ice balls passing with them can be removed by collecting another diffraction pattern merely from empty vitreous ice balls and subtracting it with normalization.

Equations (11)

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

I = F 1 ( u ) + F 2 ( u ) + + F Q ( u ) = Q F mol ( u ) + q = 1 Q F p amorph ( u ) + q = 1 Q coh ( F mol ( u ) , F q amorph ( u ) ) .
I Q = F mol ( u ) + [ q = 1 Q F p amorph ( u ) + q = 1 Q coh ( F mol ( u ) , F q amorph ( u ) ) ] Q .
I ̱ one = F mol ( u ) + F amorph ( u ) + coh ( F mol , F amorph ) ,
g n ( x ) = J 1 { J [ g n ( x ) ] F ( u ) J [ g n ( x ) ] } ,
g n + 1 ( x ) = { g n ( x ) x s out ( x ) 0 x s out ( x ) .
g n + 1 ( x ) = { g n ( x ) x s out ( x ) g n ( x ) β g n ( x ) x s out ( x ) ,
g n + 1 ( x ) = { g n ( x ) x s out ( x ) g n ( x ) x s out ( x ) .
g n k SU ( x ) = { g n p ( x ) x s mol ( x ) g n k ( x ) x s mol ( x ) ,
p = { m if k = 1 k 1 if k 1 .
R = F ( u ) G ( u ) F ( u ) ,
R 1 = [ F jacket ( u ) c F ice ( u ) ] F 5 LYZ ( u ) F 5 LYZ ( u ) ,

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