Abstract
An iterative Fourier method is applied to solving and refining the electron density profile projected into the line perpendicular to a membrane surface. Solutions to the continuous X-ray scattering pattern derived from swelling of multilayer systems or from membrane dispersions can be obtained by this technique. The method deals directly with the observed structure factors and does not rely on deconvolution of the Patterson function. We used this method previously to derive the electron density profile for acetylcholine receptor membranes (Ross et al., 1977). The present paper is an analysis of the theoretical basis for the procedure. In addition, the technique is tested on artificially generated continuous-scattering data, on the data for frog sciatic nerve myelin derived from swelling experiments by Worthington and McIntosh (1974), and on the data for purple membrane (Blaurock and Stoeckenius, 1971). Although the method applies to asymmetric membranes, the special case of centrosymmetric profiles is also shown to be solvable by the same technique. The limitations of the method and the boundary conditions that limit the degeneracy of the solution are analyzed.
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Selected References
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- Blaurock A. E., King G. I. Asymmetric structure of the purple membrane. Science. 1977 Jun 3;196(4294):1101–1104. doi: 10.1126/science.870970. [DOI] [PubMed] [Google Scholar]
- Blaurock A. E. Myelin x-ray patterns reconciled. Biophys J. 1976 May;16(5):491–501. doi: 10.1016/S0006-3495(76)85704-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Blaurock A. E., Stoeckenius W. Structure of the purple membrane. Nat New Biol. 1971 Sep 29;233(39):152–155. doi: 10.1038/newbio233152a0. [DOI] [PubMed] [Google Scholar]
- Blaurock A. E. Structure of the nerve myelin membrane: proof of the low-resolution profile. J Mol Biol. 1971 Feb 28;56(1):35–52. doi: 10.1016/0022-2836(71)90082-9. [DOI] [PubMed] [Google Scholar]
- Blaurock A. E. The structure of a lipid-cytochrome c membrane. Biophys J. 1973 Mar;13(3):290–298. doi: 10.1016/S0006-3495(73)85986-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Blaurock A. E., Worthington C. R. Low-angle x-ray diffraction patterns from a variety of myelinated nerves. Biochim Biophys Acta. 1969 Apr;173(3):419–426. doi: 10.1016/0005-2736(69)90006-6. [DOI] [PubMed] [Google Scholar]
- Burge R. E., Draper J. C. The structure of the cell wall of the Gram-negative bacterium Proteus vulgaris. 3. A lipopolysaccharide "unit membrane". J Mol Biol. 1967 Sep 14;28(2):205–210. doi: 10.1016/s0022-2836(67)80003-2. [DOI] [PubMed] [Google Scholar]
- Caspar D. L., Kirschner D. A. Myelin membrane structure at 10 A resolution. Nat New Biol. 1971 May 12;231(19):46–52. doi: 10.1038/newbio231046a0. [DOI] [PubMed] [Google Scholar]
- Duguid J. R., Raftery M. A. Fractionation and partial characterization of membrane particles from Torpedo californica electroplax. Biochemistry. 1973 Sep 11;12(19):3593–3597. doi: 10.1021/bi00743a003. [DOI] [PubMed] [Google Scholar]
- Engelman D. M. Lipid bilayer structure in the membrane of Mycoplasma laidlawii. J Mol Biol. 1971 May 28;58(1):153–165. doi: 10.1016/0022-2836(71)90238-5. [DOI] [PubMed] [Google Scholar]
- FINEAN J. B., BURGE R. E. THE DETERMINATION OF THE FOURIER TRANSFORM OF THE MYELIN LAYER FROM A STUDY OF SWELLING PHENOMENA. J Mol Biol. 1963 Dec;7:672–682. doi: 10.1016/s0022-2836(63)80115-1. [DOI] [PubMed] [Google Scholar]
- Henderson R. The structure of the purple membrane from Halobacterium hallobium: analysis of the X-ray diffraction pattern. J Mol Biol. 1975 Apr 5;93(2):123–138. doi: 10.1016/0022-2836(75)90123-0. [DOI] [PubMed] [Google Scholar]
- Lesslauer W., Blasie J. K. Direct determination of the structure of barium stearate multilayers by x-ray diffraction. Biophys J. 1972 Feb;12(2):175–190. doi: 10.1016/S0006-3495(72)86078-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Lesslauer W., Cain J., Blasie J. K. On the location of I-anilino-8-naphthalene-sulfonate in lipid model systems. An x-ray diffraction study. Biochim Biophys Acta. 1971 Aug 13;241(2):547–566. doi: 10.1016/0005-2736(71)90054-x. [DOI] [PubMed] [Google Scholar]
- Levine Y. K., Wilkins M. H. Structure of oriented lipid bilayers. Nat New Biol. 1971 Mar 17;230(11):69–72. doi: 10.1038/newbio230069a0. [DOI] [PubMed] [Google Scholar]
- Luzzati V., Tardieu A., Taupin D. A pattern-recognition approach to the phase problem: application to the X-ray diffraction study of biological membranes and model systems. J Mol Biol. 1972 Feb 28;64(1):269–286. doi: 10.1016/0022-2836(72)90335-x. [DOI] [PubMed] [Google Scholar]
- MOODY M. F. X-RAY DIFFRACTION PATTERN OF NERVE MYELIN: A METHOD FOR DETERMINING THE PHASES. Science. 1963 Nov 29;142(3596):1173–1174. doi: 10.1126/science.142.3596.1173. [DOI] [PubMed] [Google Scholar]
- Moody M. F. Letter: Structure determination of membranes in swollen lamellar systems. Biophys J. 1974 Sep;14(9):697–702. doi: 10.1016/S0006-3495(74)85945-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- ROBERTSON J. D. Structural alterations in nerve fibers produced by hypotonic and hypertonic solutions. J Biophys Biochem Cytol. 1958 Jul 25;4(4):349–364. doi: 10.1083/jcb.4.4.349. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Ross M. J., Klymkowsky M. W., Agard D. A., Stroud R. M. Structural studies of a membrane-bound acetylcholine receptor from Torpedo californica. J Mol Biol. 1977 Nov;116(4):635–659. doi: 10.1016/0022-2836(77)90264-9. [DOI] [PubMed] [Google Scholar]
- Wilkins M. H., Blaurock A. E., Engelman D. M. Bilayer structure in membranes. Nat New Biol. 1971 Mar 17;230(11):72–76. doi: 10.1038/newbio230072a0. [DOI] [PubMed] [Google Scholar]
- Worthington C. R., King G. I., McIntosh T. J. Direct structure determination of multilayered membrane-type systems which contain fluid layers. Biophys J. 1973 May;13(5):480–494. doi: 10.1016/S0006-3495(73)86001-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Worthington C. R., Liu S. C. Structure of sarcoplasmic reticulum membranes at low resolution (17A). Arch Biochem Biophys. 1973 Aug;157(2):573–579. doi: 10.1016/0003-9861(73)90676-0. [DOI] [PubMed] [Google Scholar]
- Worthington C. R., McIntosh T. J. Direct determination of the lamellar structure of peripheral nerve myelin at moderate resolution (7A). Biophys J. 1974 Oct;14(10):703–729. doi: 10.1016/S0006-3495(74)85946-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
