Diffraction pattern protein crystallography

The notion of a common core structure has been further supported by synchrotron X-ray fiber diffraction patterns of several amyloid fibrils the patterns show common reflections in addition to those at 4.7 and 10 A (Sunde et al., 1997). Although these data give some insight into the arrangement of the amyloid fibril core, the exact molecular structure and organization of the proteins making up this common core have yet to be uniquely defined. The inherently noncrystalline, insoluble nature of the fibrils makes their structures difficult to study via traditional techniques of X-ray crystallography and solution NMR. An impressive breadth of biochemical and biophysical techniques has therefore been employed to illuminate additional features of amyloid fibril structure. 

In crystallography, heavy atom derivatives are required to solve the phase problem before electron density maps can be obtained from the diffraction patterns. In nmr, paramagnetic probes are required to provide structural parameters from the nmr spectrum. In other forms of spectroscopy a metal atom itself is often studied. Now many proteins contain metal atoms, but even these metal atoms may not be suitable for crystallographic or spectroscopic purposes. Thus isomorphous substitution has become of major importance in the study of proteins. Isomorphous substitution refers to the replacement of a given metal atom by another metal that has more convenient properties for physical study, or to the insertion of a series of metal atoms into a protein that in its natural state does not contain a metal. In each case it is hoped that the substitution is such that the structural and/or chemical properties are not significantly perturbed. 

The techniques of X-ray crystallography are well known. The method has been applied to proteins of molecular weight in excess of 100,000, but the difficulties in signal-to-noise ratios and in resolution of the diffraction patterns increase considerably as the molecular weight increases (cf. nmr below). In fact, the procedures and results of X-ray diffraction studies of proteins differ considerably from those of small... 

Early protein crystallographers, proceeding by analogy with studies of other crystalline substances, examined dried protein crystals and obtained no diffraction patterns. Thus X-ray diffraction did not appear to be a promising tool for analyzing proteins. In 1934, J. D. Bernal and Dorothy Crowfoot (later Hodgkin) measured diffraction from pepsin crystals still in the mother liquor. Bernal and Crowfoot recorded sharp diffraction patterns, with reflections out to distances in reciprocal space that correspond in real space to the distances between atoms. The announcement of their success was, in effect, a birth announcement for protein crystallography. 

Equation (5.15) describes one structure factor in terms of diffractive contributions from all atoms in the unit cell. Equation (5.16) describes one structure factor in terms of diffractive contributions from all volume elements of electron density in the unit cell. These equations suggest that we can calculate all of the structure factors either from an atomic model of the protein or from an electron density function. In short, if we know the structure, we can calculate the diffraction pattern, including the phases of all reflections. This computation, of course, appears to go in just the opposite direction that the crystallographer desires. It turns out, however, that computing structure factors from a model of the unit cell (back-transforming the model) is an essential part of crystallography, for several reasons. 

The possibility of viewing both the image and the diffraction pattern is unique to electron crystallography and, in favorable cases, can allow phases to be determined directly. For an ordered array (a 2-D crystal) of proteins in a lipid membrane, the direct image is, even at the highest magnification, a featureless... 

Protein structure The three-dimensional structure of a protein can be determined almost to the determination atomic level by the techniques of X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy. In X-ray crystallography a crystal of the protein to be visualized is exposed to a beam of X-rays and the resulting diffraction pattern caused as the X-rays encounter the protein crystal is recorded on photographic film. The intensities of the diffraction maxima (the darkness of the spots on the film) are then used to mathematically construct the three-dimensional image of the protein crystal. NMR spectroscopy can be used to determine the three-dimensional structures of small (up to approximately 30 kDa) proteins in aqueous solution. 

X-ray crystallography is a technique determining the three-dimensional arrangement of atoms in a protein from the diffraction pattern of X-rays, passing through a crystal of the protein or an other molecule. 

This might seem of scant use in protein crystallography, since we have no centric space groups. Crystals of biological macromolecules, as previously pointed out, cannot possess inversion symmetry. Sets of centric reflections frequently do occur in the diffraction patterns of macromolecular crystals, however, because certain projections of most unit cells contain a center of symmetry. The correlate of a centric projection, or centric plane in real space, is a plane of centric reflections in reciprocal space. A simple example is a monoclinic unit cell of space group P2. The two asymmetric units have the same hand, as they are related by pure rotation, and for every atom in one at xj, yj, Zj there is an equivalent atom in the other at —Xj, yj, —zj. If we project the contents of the unit cell on to a plane perpendicular to the y axis, namely the xz plane, by setting y = 0 for all atoms, however, then in that... 

The classical method for solving the phase problem in macromolecular crystal structures, known as isomorphous replacement, dates back to the earliest days of protein crystallography.10,16 The concept is simple enough we introduce into the protein crystal an atom or atoms heavy enough to affect the diffraction pattern measurably. We aim to figure out first where those atoms are (the heavy atom substructure) by subtracting away the protein component, and then bootstrap — use the phases based on the heavy atom substructure to solve — the structure of the protein. 

A EXPERIMENTAL FIGURE 3-38 X-ray crystallography provides diffraction data from which the three-dimensional structure of a protein can be determined, (a) Basic components of an x-ray crystallographic determination. When a narrow beam of x-rays strikes a crystal, part of it passes straight through and the rest is scattered (diffracted) in various directions. The intensity of the diffracted waves is recorded on an x-ray film or with a solid-state electronic detector, (b) X-ray diffraction pattern for a topoisomerase crystal collected on a solid-state detector. From complex analyses of patterns like this one, the location of every atom in a protein can be determined. [Part (a) adapted from L. Stryer, 1995, Biochemistry, 4th ed., W. H. Freeman and Company, p. 64 part (b) courtesy of J. Berger.]... 

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