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A general theory for the evaluation of X-ray diagrams of biomembranes and other lamellar systems

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Physical Chemistry

Part of the book series: Advances in Polymer Science ((POLYMER,volume 30))

Abstract

In the following contribution the development of a new evaluation theory for X-ray diffraction diagrams of biomembranes and other lamellar systems is presented. This theory is more comprehensive than other theories applied hitherto, since statistical lattice distortions, distortions of the lattice-cell, membrane undulations and different interspatial electron densities as well as “Lorentz” correction are considered.

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6 References

  1. Zernicke, F., Prins, J. A.: Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung. Z. f. Physik 41, 184 (1927)

    Article  Google Scholar 

  2. Kratky, O.: Die Struktur des flüssigen Quecksilbers. Physikal. Zeitschr. 34, 482 (1933)

    CAS  Google Scholar 

  3. Levine, Y. K., Wilkins, M. H. F.: Structure of oriented Lipid Bilayers. Nature 230, 69 (1971)

    Article  CAS  Google Scholar 

  4. Engelmann, D. M.: Lipid bilayer Structure in the Membrane of Mycoplasma laidlawii. J. Mol. Biol. 58, 153 (1971)

    Article  Google Scholar 

  5. Blaurock, A. E.: X-Ray Diffraction Pattern from a Bilayer with Protein outside. Biophysical J. 13, 281 (1973)

    CAS  Google Scholar 

  6. Blaurock, A. E.: The Structure of a Lipid-Cyt. C Membrane. Biophysical J. 13, 290 (1973)

    CAS  Google Scholar 

  7. Lee, R. E., Worthington, C. R., Glew, R. H.: The Bilayer Nature of Deposits Occurring in Gaucher's Disease. Arch. of Biochem. & Biophys. 159, 259 (1973)

    Article  CAS  Google Scholar 

  8. Franks, N. P.: Structural Analysis of Hydrated Egg-Lecithin and Cholesterol Bilayers. I. X-Ray Diffraction. J. Mol. Biol. 100, 345 (1976)

    Article  CAS  Google Scholar 

  9. Worcester, D. L., Franks, N. P.: Structural Analysis of Hydrated Egg Lecithin and Cholesterol Bilayers. II. Neutron Diffraction. J. Mol. Biol. 359, 100 (1976)

    Google Scholar 

  10. Podo, F., Cain, J. E., Blasie, J. K.: Structural and Dynamical Studies of Mixed Chlorophyll/Phosphatidylcholine Bilayers via X-Ray Diffraction, Absorption Polarization Spectroscopy and Nuclear Magnetic Resonance. BBA 419, 19 (1976)

    CAS  Google Scholar 

  11. Khare, R. S., Worthington, C. R.: An X-Ray Diffraction Study of Sphingomyelin-Cholesterol Interaction in Oriented Bilayers. Mol. Cryst. Liq. Cryst. 38, 195 (1977)

    Article  CAS  Google Scholar 

  12. Casper, D. L. D., Kirschner, D. A.: Myelin Membrane Structure at 10 Å Resolution. Nature 231, 46 (1971)

    Article  Google Scholar 

  13. McIntosh, Worthington, C. R.: Direct Determination of the Lamellar Structure of Peripheral Nerve Structure at low Resolution (17 Å). Biophysical J. 14, 363 (1974)

    CAS  Google Scholar 

  14. Worthington, C. R., McIntosh, T. J.: Direct Determination of the Lamellar Structure of Peripheral Nerve Myelin at moderate Resolution. Biophysical J. 14, 703 (1974)

    CAS  Google Scholar 

  15. Blaurock, A. E., Wilkins, M. H. F.: Structure of Frog-Photoreceptor Membranes. Nature 223, 906 (1969)

    Article  CAS  Google Scholar 

  16. Chabre, M.: X-Ray Diffraction Studies of Retinal Rods. I. Structure of the Disc Membrane, Effect of Illumination. II. Light Effect on the Osmotic Properties. BBA 382, 322 (1975)

    CAS  Google Scholar 

  17. Makowski, L., Caspar, D. L. D., Phillips, W. C., Goodenough, D. A.: Gap Junction Structures. II. Analysis of the X-Ray Diffraction Data. The J. of Cell Biol. 74, 629 (1977)

    Article  CAS  Google Scholar 

  18. Blaurock, A. E., Stoeckenius, W., Oesterhelt, D., Scherphof, G. L.: Structure of the Cell Envelope of Halobacterium Halobium. The J. of Cell Biol. 71. 1 (1976)

    Article  CAS  Google Scholar 

  19. Blaurock, A. E., Wober, W.: Structure of the Wall of Halobacterium halobium Gas Vesicles. J. Mol. Biol. 106, 871 (1976)

    Article  CAS  Google Scholar 

  20. Blaurock, A. E., King, G. I.: Asymetric Structure of the Purple Membrane. Science 196, 1101 (1977)

    Article  CAS  Google Scholar 

  21. Sadler, D. M., Lefort-Tran, M., Pouphile, M.: Structure of Photosynthetic Membranes of Euglena using X-Ray Diffraction. BBA 298, 620 (1973)

    CAS  Google Scholar 

  22. Sayre, D.: Some Implications of a Theorem due to Shannon. Acta Cryst. 5, 843 (1952)

    Article  Google Scholar 

  23. Moody, M. F.: Structure Determination of Membranes in Swollen Lamellar Systems. Biophys. J. 14, 697 (1974)

    CAS  Google Scholar 

  24. Worthington, C. R., King, G. I., McIntosh, T. J.: Direct Structure Determination of Multilayered Membrane-Type Systems Which Contain Fluid Layers. Biophys. J. 13, 480 (1973)

    CAS  Google Scholar 

  25. Lesslauer, W., Cain, J., Blasie, J. K.: On the Location of 1-Anilino-8-Naphtalene-Sulfonate in Lipid Model Systems. An X-Ray Diffraction Study. BBA 241, 547 (1971)

    CAS  Google Scholar 

  26. Lesslauer, W.: X-Ray Diffraction from Fatty-Acid Multilayers. Significance of Intensity Data in Low-Angle Diffraction. Acta Cryst. B 30, 1927 (1974)

    Google Scholar 

  27. Lesslauer, W.: X-Ray Diffraction from Fatty-Acid Multilayers. Angular Width of Reflections from Systems with Few Unit Cells. Acta Cryst. B 30, 1932 (1974)

    Google Scholar 

  28. Mahler, P. H.: Direkte Bestimmung des Elektronendichteprofils von Cadmium-di-Stearat unter besonderer Berücksichtigung der Messfehlerempfindlichkeit des Auswerteverfahrens. Diplomarbeit, Institut für Biophysik & Strahlenbiol. der Universität Freiburg i. Br. (1977)

    Google Scholar 

  29. Blaurock, A. E., Stoeckenius, W.: Structure of the Purple Membrane. Nature 233, 153 (1971)

    Google Scholar 

  30. Porod, G.: Die Röntgenkleinwinkelstreuung von dicht gepackten kolloiden Systemen. Kolloid Zeitschrift 124, 83 (1951)

    Article  CAS  Google Scholar 

  31. Ewald, P. P.: X-Ray Diffraction by Finite and Imperfect Crystal Lattices. Proc. Phys. Soc. (London) 52, 167 (1940)

    Article  CAS  Google Scholar 

  32. Hosemann, R., Bagchi, S. N.: Direct analysis of diffraction by matter. Amsterdam: North-Holland Publishing Company, 1962. a) Chap. I; b) Chap. II § 1; c) Chap. IV § 2; d) Chap. VII § 9

    Google Scholar 

  33. Pape, E. H.: A New Deconvolution Method for Evaluating Electron Density Distributions from Small Angle Scattering Diagrams. Biophys. J. 14, 284–294 (1974)

    CAS  Google Scholar 

  34. Kreutz, W., Menke, W.: Strukturuntersuchungen an Plastiden. III. Z. f. Naturforschung 17 b, 675 (1962)

    Google Scholar 

  35. Kreutz, W.: Strukturuntersuchungen an Plastiden. VI. Z. f. Naturforschung 19 b, 441(1964)

    Google Scholar 

  36. Kreutz, W.: X-Ray Structure Research on the Photosynthetic Membrane, in: Advances in Botanical Research. R. D. Preston (ed.). London and New York: Academic Press, Vol. 3, p. 53–168 (1970)

    Google Scholar 

  37. Schwartz, S., Cain, J. E., Dratz, E. A., Blasie, J. K.: An Analysis of Lamellar X-Ray Diffraction from Disordered Membrane Multilayers with Application to Data from Retinal Rod outer Segments. Biophys. J. 15, 1201–1233 (1975)

    CAS  Google Scholar 

  38. Pape, E. H., Klott, K., Kreutz, W.: The Determination of the Electron Density Profile of the Human Erythrocyte Ghost Membrane by Small-Angle X-Ray Diffraction. Biophys. J. 19, 141–161 (1977)

    CAS  Google Scholar 

  39. Kreutz, W., Pape, E. H.: Evaluation of X-ray diffraction patterns of biomembrane systems, in: Summer institute on the physics of biological membranes. Colbow, K. (ed.). Vancouver, B. C., Canada: Simon Fraser University (1974)

    Google Scholar 

  40. Blaurock, A. E., Nelander, J. C.: Disorder in Nerve Myelin: Analysis of the Diffuse X-Ray Scattering. J. Mol. Biol. 103, 421 (1976)

    Article  CAS  Google Scholar 

  41. Nelander, J. C., Blaurock, A. E.: Disorder in Nerve Myelin: Phasing the Higher Order Reflexions by Means of the Diffuse Scatter. J. Mol. Biol. 118, 497 (1978)

    Article  CAS  Google Scholar 

  42. Bonart, R.: Parakristalline Schichtgitter in verstrickten Linearpolymeren. I. Die Querstruktur. Kolloid-Zeitschrift & Zeitschrift für Polymere 194, 97 (1964)

    Article  CAS  Google Scholar 

  43. Gbordzoe, M. K., Kreutz, W.: Direct X-Ray Determination of the Electron-Density Profile of the Nerve Myelin Membrane, with Paracrystalline Lattice Distortions Taken into Account. J. Appl. Cryst. 11, 489 (1978)

    Article  CAS  Google Scholar 

  44. Herbette, L., Marquardt, J., Scarpa, A., Blasie, J. K.: A Direct Analysis of Lamellar X-Ray Diffraction from Hydrated Oriented Multilayers of Fully Functional Sarcoplasmic Reticulum. Biophys. J. 20, 245 (1977)

    Article  CAS  Google Scholar 

  45. Cain, J. E.: Lattice and Substitution Disorder in Oriented Membrane Systems, Structure of the Chromatophore Membrane by X-Ray Diffraction. Federation Proceedings 33, 1241 (1974)

    Google Scholar 

  46. Blasie, J. K., Erecinska, M., Samuels, S., Leigh, J. S.: The Structure of a Cytochrome Oxidase-Lipid Model Membrane. BBA 501, 33 (1978)

    Article  CAS  Google Scholar 

  47. Hodapp, N., Kreutz, W.: To be published

    Google Scholar 

  48. Müller-Klieser, Kreutz, W.: On the Cross-Section Structure of the Mitochondrial Cristae-Membrane as Revealed by X-Ray Diffraction. Z. f. Naturforschung 31 c, 612 (1976)

    Google Scholar 

  49. Papoulis, A.: Systems and transforms with applications in optics. Toronto-New York: MacGraw-Hill Book Company 1968. a) Chap. II § 1; b) Chap. II § 3; c) Chap. II § 2; d) Chap. II § 2.

    Google Scholar 

  50. Papoulis, A.: Probability, random variables and stochastic processes. Toronto-New York: McGraw-Hill Book Company 1965, Chaps. III and IV

    Google Scholar 

  51. Deas, H. D.: The Diffraction of X-Rays by a Random Assemblage of Molecules Having Partial Alignment. Acta Cryst. 5, 542 (1952) a) Sec. 4

    Article  Google Scholar 

  52. Papoulis, A.: The fourier integral and its applications. Toronto, New York: McGraw-Hill Book Company 1962

    Google Scholar 

  53. Marquardt, D. W.: An Algorithm for Least-Squares Estimation of Nonlinear Parameters. Journal Soc. Indust. and Applied Mathematics 2, 431 (1963)

    Article  Google Scholar 

  54. Bevington, P. R.: Data reduction and error analysis for the physical sciences. Toronto, New York: McGraw-Hill Book Company 1969, Chap. 11

    Google Scholar 

  55. Blaurock, A. E.: Disorder is Characteristic of Nerve Myelin. BBA 510, 11 (1978)

    CAS  Google Scholar 

  56. Magnus, W., Oberhettinger, F., Soni, R. P.: Formulas and theorems for the special functions of mathematical physics. Berlin, Heidelberg, New York: Springer 1966, Chap. 9.2.3.

    Google Scholar 

  57. Bracewell, R.: The fourier Transform and its applications. Toronto, New York: McGraw-Hill Book Company 1965, Chap. 12

    Google Scholar 

  58. Marquardt, D. W., Baumeister, T., Sheldon, J. A., Stanley, R. M.: Least Squares Estimation of Nonlinear Parameters. Engineering Department E. I. du Pont de Nemours & Co., Inc. Wilmington, Delaware

    Google Scholar 

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  1. Institut für Biophysik und Strahlenbiologie, der Universität Freiburg i. Br., Albertstr. 23, D-7800, Freiburg, Germany

    Wolfram Welte & Werner Kreutz

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  1. Wolfram Welte
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  2. Werner Kreutz
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Welte, W., Kreutz, W. (1979). A general theory for the evaluation of X-ray diagrams of biomembranes and other lamellar systems. In: Physical Chemistry. Advances in Polymer Science, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09199-8_4

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  • DOI: https://doi.org/10.1007/3-540-09199-8_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09199-8

  • Online ISBN: 978-3-540-35395-9

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