Diffraction fiber

Many important biological substances do not form crystals. Among these are most membrane proteins and fibrous materials like collagen, DNA, filamentous viruses, and muscle fibers. Some membrane proteins can be crystallized in matrices of lipid and studied by X-ray diffraction (Chapter 3, Section III.D), or they can be incorporated into lipid films (which are in essence two-dimensional crystals) and studied by electron diffraction. I will discuss electron diffraction later in this chapter. Here I will examine diffraction by fibers. 

Like crystals, fibers are composed of molecules in an ordered form. When irradiated by an X-ray beam perpendicular to the fiber axis, fibers produce distinctive diffraction patterns that reveal their dimensions at the molecular level. Because many fibrous materials are polymeric and of known chemical composition and sequence, their molecular dimensions are sometimes all that is needed to build a feasible model of their structure. 

Some materials (for example, certain muscle proteins) form fibers spontaneously or are naturally found in fibrous form. Many other polymeric substances, like DNA, can be induced into fibers by pulling them from an amorphous gel with tweezers or a glass rod. For data collection, the fiber is simply suspended between a well-collimated X-ray source and a detector, such as film (Fig. 9.1). 

A simple and frequently occurring structural element in fibrous materials is the helix. 1 will use the relationship between the dimensions of simple helices and that of their diffraction patterns to illustrate how diffraction can reveal structural information. As a further simplification, 1 will assume that the helix axis is parallel to the fiber axis. As in all diffraction methods, the diffraction pattern is a Fourier transform of the object in the X-ray beam, averaged over all the orientations present in the sample. In the case of fibers, this means that the transform is averaged cylindrically, around the molecular axis parallel to the fiber axis. 

Compare helix (a) with (b), in which the helix has the same radius, but a longer pitch P (peak-to-peak distance). Note that the layer lines for (b) are more closely spaced. The layer-line spacing is inversely proportional to the helix pitch. The relationship is identical to that in crystals between lattice spacing and unit-cell dimensions [(Eq. (4.10)]. So precise measurement of layer-line spacing allows determination of helix pitch. 

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Fiberboard boxes Fiber bonding resins Fiber boxes Fiber braiding Fiber can packaging Fiber diffraction... 

Some oligonucleotides adopt an A-form helical stmcture (Fig. 2a) (5). The average stmctural parameters have been found consistent with the fiber diffraction model, but, as for B-form DNA, considerable variation is apparent among iadividual base pairs. 

Polymer or Fiber Diffraction. Polymers and fibers are often ordered ia one or two dimensions but not ordered ia the second or third dimension. The resulting diffraction patterns have broad diffuse diffraction maxima. The abiHty to coUect two dimensional images makes it possible to coUect and analyze polymer and fiber diffraction patterns. 

Early diffraction photographs of such DNA fibers taken by Rosalind Franklin and Maurice Wilkins in London and interpreted by James Watson and Francis Crick in Cambridge revealed two types of DNA structures A-DNA and B-DNA. The B-DNA form is obtained when DNA is fully hydrated as it is in vivo. A-DNA is obtained under dehydrated nonphysiological conditions. Improvements in the methods for the chemical synthesis of DNA have recently made it possible to study crystals of short DNA molecules of any selected sequence. These studies have essentially confirmed the refined fiber diffraction models for A- and B-DNA and in addition have given details of small structural variations for different DNA sequences. Furthermore, a new structural form of DNA, called Z-DNA, has been discovered. 

The F-actin helix has 13 molecules of G-actin in six turns of the helix, repeating every 360 A. Oriented gels of actin fibers yield x-ray fiber diffraction patterns to about 6 A resolution. Knowing the atomic structure of G-actin it was possible for the group of Ken Holmes to determine its orientation in the F-actin fiber, and thus arrive at an atomic model of the actin filament that best accounted for the fiber diffraction pattern. 

The structure of biopolymers can be studied using fiber diffraction... 

The occurrence of the mesophase in the fiber is confirmed by x-ray diffraction examination. The occurrence of three equatorial reflections 010, 110, and 100, the absence of layer and meridional reflections, and the manifestation of the intensity maximum of diffusively scattered radiation at 20 = 19 in the fiber diffraction pattern are the criterion for the presence of the mesophase. The... 

Five articles on polysaccharide helices solved prior to 1979 have appeared in the volumes published between 1967 and 1982.2-6 The first was a review on X-ray fiber diffraction and its application to cellulose, chitin, amylose, and related structures, and the rest were bibliographic accounts. Since then, X-ray structures of several new polysaccharides composed of simple to complex repeating units have been successfully determined, thanks to technological advances in fiber-diffraction techniques, the availability of fast and powerful computers, and the development of sophisticated software. Also, some old models have been either re-... 

A fiber-diffraction pattern is recorded on a flat-film camera in which the fiber-to-photographic film distance is typically in the range of 3 to 4 cm. During exposure to X-rays, the specimen chamber is continuously flushed with a slow and steady stream of helium gas that has been bubbled through a saturated salt solution so that (a) the fiber is maintained at a constant desired r.h. and (b) fogging of the photographic film from air scattering is reduced. 

The third category, shown in Fig. 2d, results when all of the long molecules or microcrystallites are aligned along the fiber axis, but they aggregate with little lateral ordering. This assembly, called an oriented fiber, diffracts to produce a series of layer lines that are perpendicular to the fiber axis. The intensity is nonuni-... 

In contrast to single-crystal work, a fiber-diffraction pattern contains much fewer reflections going up to about 3 A resolution. This is a major drawback and it arises either as a result of accidental overlap of reflections that have the same / value and the same Bragg angle 0, or because of systematic superposition of hkl and its counterparts (-h-kl, h-kl, and -hkl, as in an orthorhombic system, for example). Sometimes, two or more adjacent reflections might be too close to separate analytically. Under such circumstances, these reflections have to be considered individually in structure-factor calculation and compounded properly for comparison with the observed composite reflection. Unobserved reflections that are too weak to see are assigned threshold values, based on the lowest measured intensities. Nevertheless, the number of available X-ray data is far fewer than the number of atomic coordinates in a repeat of the helix. Thus, X-ray data alone is inadequate to solve a fiber structure. 

The Pn conformation of poly-L-proline (PP) or collagen in the solid state could be identified from X-ray fiber diffraction results (Cowan and McGavin, 1955). Persistence of this basic structure in solution was inferred from the resemblance between the CD spectra of solutions and films of the polypeptide. The CD spectra of the charged forms of PGA and PL closely resemble that of Pn (compare Fig. IB, 1C, and ID) however, these spectra differ significantly from those of PP peptides at high temperature or in the presence of high concentration of salts... 

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