Advertisement

Three-Dimensional Structure Determination by Electron Microscopy (Nonperiodic Specimens)

  • W. Hoppe
  • R. Hegerl
Part of the Topics in Current Physics book series (TCPHY, volume 13)

Abstract

The three-dimensional reconstruction of individual molecules from a set of electron micrographs is comparable to the “reconstruction” of structures in X-ray crystallography. Basically the electron microscope is equivalent to a diffractometer, since the specimen is illuminated by a parallel primary beam with a well-defined wavelength and orientation. The Fourier inversion of an electron micrograph delivers the distorted structure factors in a well-defined plane or weakly curved surface of the three-dimensional reciprocal space. Extraction of the undistorted structure factors and reconstruction is possible if a sufficient number of micrographs with different orientations of the object is available. Structure factors within a certain resolution in reciprocal space must be known to give a well defined reconstruction. Unlike X-ray crystallography, no “phase problem” exists since the phases of the structure factors can be deduced from the micrographs.

Keywords

Image Point Primary Beam Reciprocal Space Fourier Space Image Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

References

  1. 4.1
    W. Hoppe, D. Typke: “Three-Dimensional Reconstruction of Aperiodic Objects in Electron Microscopy”, in Advances in Structure Research by Diffraction Method, Vol.7, ed. by W. Hoppe, R. Mason (Pergamon Press, Oxford, and Vieweg, Braunschweig 1978 ) pp. 137–190Google Scholar
  2. 4.2
    W. Hoppe, P. Bussler, A. Feltynowski, N. Hunsmann, A. Hirt: “Some Experience with Computerized Image Reconstruction Methods”, in Image Processing and Computer-Aided Design in Electron Optics, ed. by P.W. Hawkes ( Academic Press, London 1973 ) pp. 91–126Google Scholar
  3. 4.3
    R. Hegerl, W. Hoppe: Z. Naturforsch. 31a, 1717–1721 (1976)ADSGoogle Scholar
  4. 4.4
    A. Jones: J. Appi. Cryst. 11, 268 (1978)CrossRefGoogle Scholar
  5. 4.5
    W. Hoppe: Acta Cryst. k26, 414–426 (1970)CrossRefGoogle Scholar
  6. 4.6
    W. Hoppe: Naturwiss. 61, 239–249 (1974)ADSCrossRefGoogle Scholar
  7. 4.7
    J. Kieffer: Radiology 33, 560–585 (1939)Google Scholar
  8. 4.8
    P. Edholm: The tomogram. Its formation and content. Acta Radiol., Suppl 193 (1960)Google Scholar
  9. 4.9
    R.N. Bracewel1, A.C. Riddle: Astrophys. J. 150, 427–434 (1967)ADSCrossRefGoogle Scholar
  10. 4.10
    D.W. Sweeney, C.M. Vest: Appi. Opt. 11, 205–207 (1972)ADSCrossRefGoogle Scholar
  11. 4.11
    R.G. Hart: Science 159, 1464–1467 (1968)ADSCrossRefGoogle Scholar
  12. 4.12
    D.J. DeRosier, A. Klug: Nature (London) 217, 130–134 (1968)ADSCrossRefGoogle Scholar
  13. 4.13
    W. Hoppe, R. Langer, G. Knesch, Ch. Poppe: Naturwiss. 55, 333–336 (1968)ADSCrossRefGoogle Scholar
  14. 4.14
    J.G. Colsher: Comput. Graphics Image Process. 6, 513–537 (1977)CrossRefGoogle Scholar
  15. 4.15
    J.G. Colsher: Thesis, University of California (1976)Google Scholar
  16. 4.16
    R.A. Crowther, A. Klug: Ann. Rev. Biochem. 44, 161–182 (1975)CrossRefGoogle Scholar
  17. 4.17
    W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1090–1100 (1970); Phil. Trans. Roy. Soc. London 261, 71–94 (1971)CrossRefGoogle Scholar
  18. 4.18
    J. Frank, P. Bussler, R. Langer, W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1105–1115 (1970)Google Scholar
  19. 4.19
    R. Langer, J. Frank, A. Feltynowski, W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1120–1126 (1970)Google Scholar
  20. 4.20
    W. Hoppe: Manchester (1972) pp.612–617Google Scholar
  21. 4.21
    W. Hoppe: Naturwiss. 48, 736–737 (1961)ADSCrossRefGoogle Scholar
  22. 4.22
    W. Hoppe: Optik 20, 599–606 (1963)Google Scholar
  23. 4.23
    G. Möllenstedt, R. Speidel, W. Hoppe, R. Langer, K.-H. Katerbau, F. Thon: Rome (1968) Vol. 1, pp. 125–126Google Scholar
  24. 4.24
    W. Hoppe, H. Wenzl, H.J. Schramm: Jerusalem (1976) Vol. 2, pp. 58–60Google Scholar
  25. 4.25
    W. Hoppe, H. Wenzl, H.J. Schramm: Hoppe-Seyler’s Z. Physiol. Chem. 358, 1069–1076 (1977)CrossRefGoogle Scholar
  26. 4.26
    D.F. Parsons: Science 186, 407–414 (1974)ADSCrossRefGoogle Scholar
  27. 4.27
    R.M. Glaeser: J. Ultrastruct. Res. 36, 466–482 (1971)CrossRefGoogle Scholar
  28. 4.28
    R. Henderson, P.N.T. Unwin: Nature (London) 257, 28–32 (1975)ADSCrossRefGoogle Scholar
  29. 4.29
    W. Hoppe, J. Gassmann, N. Hunsmann, H.J. Schramm, M. Sturm: Hoppe-Seyler’s Z. Physiol. Chem. 355, 1483–1487 (1974)Google Scholar
  30. 4.30
    W. Hoppe, H.J. Schramm, M. Sturm, 31a, 1370–1379 (1976)Google Scholar
  31. 4.31
    W. Hoppe, H.J. Schramm, M. Sturm, 31a, 645–655 (1976)Google Scholar
  32. 4.32
    W. Hoppe, H.J. Schramm, M. Sturm, N. Hunsmann, J. Gassmann: Z. Naturforsch. 31a, 1380–1390 (1976)ADSGoogle Scholar
  33. 4.33
    W. Hoppe, B. Grill: U1tramicroscopy 2, 153–168 (1977)CrossRefGoogle Scholar
  34. 4.34
    J. Frank: Jerusalem (1976) Vol. 1, pp. 273–274Google Scholar
  35. 4.35
    J. Frank: U1tramicroscopy 1, 159–162 (1975)CrossRefGoogle Scholar
  36. 4.36
    J. Frank: “Optical Use of Image Information Using Signal Detection and Averaging Techniques”, in Short Wavelength Microscopy, Ann. N.Y. Acad. Sei. 306, 112–120 (1978)Google Scholar
  37. 4.37
    W. Hoppe: Z. Naturforsch. 30a, 1188–1199 (1975)ADSGoogle Scholar
  38. 4.38
    W. Hoppe: “Trace Structure Analysis”, in Short Wavelength Microscopy, Ann. N.Y. Acad. Sei. 306, 121–144 (1978)Google Scholar
  39. 4.39
    O Scherzer: Optik 501–516 (1971)Google Scholar
  40. 4.40
    H. Rose: Optik 1–24 (1971); Optik 34, 285–311 (1971)Google Scholar
  41. 4.41
    E. Plies, W. Hoppe: Optik 46, 75–92 (1976)Google Scholar
  42. 4.42
    W. Hoppe, R. Guckenberger: Z. Naturforsch. 29a, 1931–1932 (1974)ADSGoogle Scholar
  43. 4.43
    W. Hoppe: Naturwiss. 61, 534–536 (1974)ADSCrossRefGoogle Scholar
  44. 4.44
    P. Schiske: Rome (1968) Vol. 1, pp. 145–146Google Scholar
  45. 4.45
    W. Hoppe, R. Langer, F. Thon: Optik 30, 538–545 (1970)Google Scholar
  46. 4.46
    W. Hoppe: Z. Naturforsch. 26a, 1155–1168 (1971)ADSGoogle Scholar
  47. 4.47
    W. Hoppe: Optik 29, 617–621 (1969)Google Scholar
  48. 4.48
    C. E. Shannon, W. Weaver: The Mathematical Theory of Communication (University of Illinois Press 1975 )Google Scholar
  49. 4.49
    J.L. Harris: J. Opt. Soc. Am. 54, 931–936 (1964)ADSCrossRefGoogle Scholar
  50. 4.50
    R.A. Crowther, D.J. DeRosier, A. Klug: Proc. Roy. Soc. Lond. (1970)Google Scholar
  51. 4.51
    V. Knauer: Diplomarbeit, TU München (1976)Google Scholar
  52. 4.52
    W. Hoppe: Z. Naturforsch. 27a, 919–929 (1972)ADSGoogle Scholar
  53. 4.53
    D. Typke, W. Hoppe, W. Sessler, M. Burger: Jerusalem (1976) Vol.1Google Scholar
  54. 4.54
    W. Hoppe, N. Hunsmann, H.J. Schramm, M. Sturm, B. Grill, J. Gassmann: Jerusalem (1976) Vol. 1, pp.8–13Google Scholar
  55. 4.55
    M. Radermacher, W. Hoppe: Toronto (1978) Vol.1, pp.218–219Google Scholar
  56. 4.56
    R.A. Crowther, L.A. Amos, A. Klug: Manchester (1972) pp. 593–597Google Scholar
  57. 4.57
    A.M. Cormack: J. Appl. Phys. 35, 2908–2913 (1964)zbMATHADSCrossRefGoogle Scholar
  58. 4.58
    P.R. Smith, T.M. Peters, R.H.T. Bates: J. Phys. Äff, 361–382 (1973)Google Scholar
  59. 4.59
    E. Zeitler: Optik 39, 396–415 (1974)Google Scholar
  60. 4.60
    A. Klug, R.A. Crowther: Nature 235, 435–440 (1972)ADSCrossRefGoogle Scholar
  61. 4.61
    N. Hunsmann: Thesis, TU München (1975)Google Scholar
  62. 4.62
    R. Gordon, R. Bender, G.T. Herman: J. Theor. Biol. 29, 471–481 (1970)CrossRefGoogle Scholar
  63. 4.63
    P.F.C. Gilbert: J. Theor. Biol. 36, 105–117 (1972)CrossRefGoogle Scholar
  64. 4.64
    R.A. Crowther, A. Klug: Nature 251, 490–492 (1974)ADSCrossRefGoogle Scholar
  65. 4.65
    M. Goitein: Nucl. Instrum. Methods 101, 509–518 (1971)ADSCrossRefGoogle Scholar
  66. 4.66
    W. Hoppe, R. Huber, J. Gassmann: Acta Cryst. 16, A4 (1963)Google Scholar
  67. 4.67
    W. Hoppe, J. Gassmann: Acta Cryst. B24, 97–107 (1968)CrossRefGoogle Scholar
  68. 4.68
    W. Hoppe, J. Gassmann, K. Zechmeister: “Some Automatic Procedures for the Solution of Crystal Structures with Direct Methods and Phase Correction”, Cvystallogvaphic Computing IX, ed. by F.R. Ahmed ( Munksgaard, Copenhagen 1970 ) pp. 26–36Google Scholar
  69. 4.69
    J. Gassmann: “Improvement and Extension of Approximate Phase Sets in Struc ture Determination”, in Crystallographies Computing II, ed. by F.R. Ahmed ( Munksgaard, Copenhagen 1976 ) pp. 144–154Google Scholar
  70. 4.70
    E. Zeitler, M.G.R. Thomson: Optik 31, 258–280 (1970)Google Scholar
  71. 4.71
    O Scherzer: Ber. Bunsenges. Phys. Chem. 74, 1154–1167 (1970)Google Scholar
  72. 4.72
    W. Hoppe: Acta Cryst. k25, 508–514 (1969)CrossRefGoogle Scholar
  73. 4.73
    W. Hoppe: Acta Cryst. A25, 495–501 (1969)CrossRefGoogle Scholar
  74. 4.74
    R. Hegerl, W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1148–1154 (1970)Google Scholar
  75. 4.75
    H. Rose: Optik 416–436 (1974)Google Scholar
  76. 4.76
    L.H. Veneklasen: Optik 44, 447–468 (1975)Google Scholar
  77. 4.77
    D. Gabor: Nature 161, 777–778 (1948)ADSCrossRefGoogle Scholar

Additonal References

  1. W. Hoppe, J. Gassmann: “Comments on the 3-D reconstruction of periodic structures”, in Electronic Microscopy in Molecular Dimensions. State of the Art and Strategies for the Future, ed. by W. Baumeister (Springer, Berlin, Heidelberg, New York 1980 ) In preparationGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • W. Hoppe
  • R. Hegerl

There are no affiliations available

Personalised recommendations