Fiber diffraction

Fiber diffraction is an important simplification of the general scattering technique in which molecular structure is determined from scattering data (usually of X-rays, electrons or neutrons). In fiber diffraction the scattering pattern does not change, as the sample is rotated about a unique axis (the fiber axis). Such uniaxial symmetry is frequent with filaments or fibers consisting of biological or man-made macromolecules, respectively. In crystallography fiber symmetry is an aggravation of quantitative data analysis, because reflexions are smeared and may overlap in the fiber diffraction pattern. In scattering fiber symmetry of the scattering pattern is considered a simplification.

2 instead of 3 co-ordinate directions suffice to describe the fiber diffraction pattern. The ideal fiber pattern exhibits 4-quadrant symmetry. In the ideal pattern the fiber axis is called the meridian, the perpendicular axis is the equator. Because of the fiber symmetry, many more reflections than in single-crystal diffraction show up in a (photographic) pattern. In fiber patterns these many reflections clearly appear arranged along lines (layer lines) running (almost) parallel to the equator. Thus, in fiber diffraction the layer line concept of crystallography becomes palpable.

In crystallography artificial fiber diffraction patterns are generated by rotating a single crystal about an axis (rotating crystal method).

Non-ideal fiber patterns do not show 4-quadrant symmetry. The reason is that the fiber axis and the incident beam (X-rays, electrons, neutrons) cannot be perfectly oriented perpendicular to each other. The corresponding geometric distortion has been extensively studied by Michael Polanyi introducing the concept of "Polanyi's sphere" (German: "Lagenkugel") intersecting Ewald's sphere. Later Rosalind Franklin and Raymond Gosling have presented an approximative solution. Thus, distorted two-dimensional fiber patterns recorded on flat film or detector are beneficially mapped on the representative plane of the fiber (i.e. on the central section of the cylinder in reciprocal space). This mapping is frequently called "Fraser correction". The digital Fraser correction is an iterative method that starts from the Franklin approximation. It eliminates fiber tilt, unwarps the detector image, and corrects the scattering intensity.

Historical role

Fiber diffraction data led to several important advances in the development of structural biology, e.g., the original models of the α-helix and the Watson-Crick model of double-stranded DNA.

References

*Polanyi M (1921) "Das Röntgen-Faserdiagramm (Erste Mitteilung)". "Z. Physik", 7, 149-180

*Polanyi M, Weissenberg K (1923) "Das Röntgen-Faserdiagramm (Zweite Mitteilung)". "Z. Physik", 9, 123-130

*Franklin RE, Gosling RG (1953) "The Structure of Sodium Thymonucleate Fibres. II. The Cylindrically Symmetrical Patterson Function". "Acta Cryst.", 6, 678-685

*Fraser RDB, Macrae TP, Miller A, Rowlands RJ (1976). "Digital Processing of Fibre Diffraction Patterns". "J. Appl. Cryst.", 9, 81-94.

*Millane RP, Arnott S (1985) "Digital Processing of X-Ray Diffraction Patterns from Oriented Fibers". "J. Macromol. Sci. Phys.", B24, 193-227

*Bian W, Wang H, McCullogh I, Stubbs G (2006). "WCEN: a computer program for initial processing of fiber diffractionpatterns". "J. Appl. Cryst.", 39, 752-756.

*Rajkumar G, AL-Khayat H, Eakins F, He A, Knupp C, Squire J (2005) [http://www.small-angle.ac.uk/fdr/2005/html/pdf/print/11.pdf "FibreFix — A New Integrated CCP13 Software Package"] ,"Fibre Diffraction Rev.", 13, 11-18
*Cochran W, Crick FHC, and Vand V (1952). "The Structure of Synthetic Polypeptides. I. The Transform of Atoms on a Helix". "Acta Cryst.", 5, 581-586.

*Warren BE (1990) "X-Ray Diffraction". Dover, New York

*Alexander LE (1979) "X-Ray Diffraction Methods in Polymer Science", Wiley, New York

*Klug HP, Alexander LE (1974) "X-Ray Diffraction Procedures For Polycrystalline and Amorphous Materials", 2nd ed, Wiley, New York

External links

* [http://www.small-angle.ac.uk/fdr/index.htm Fibre Diffraction Review] — Publications of the CCP13 Fibre Diffraction Software Project
* [http://www.small-angle.ac.uk/small-angle/Software/FibreFix.html FibreFix] — Windows software for the analysis of fiber patterns
* [http://fibernet.vanderbilt.edu/software/wcen WCEN] — Software (Linux, Mac, Windows) for the analysis of fiber patterns
* [http://www.mpimf-heidelberg.mpg.de/~holmes/fibre/branden.html Fiber Diffraction] — an introduction provided by Prof. K.C. Holmes, Max Planck Institute for Medical Research, Heidelberg.