Protein crystallography, electron density

The three-dimensional structure of protein molecules can be experimentally determined by two different methods, x-ray crystallography and NMR. The interaction of x-rays with electrons in molecules arranged in a crystal is used to obtain an electron-density map of the molecule, which can be interpreted in terms of an atomic model. Recent technical advances, such as powerful computers including graphics work stations, electronic area detectors, and... 

Once a suitable crystal is obtained and the X-ray diffraction data are collected, the calculation of the electron density map from the data has to overcome a hurdle inherent to X-ray analysis. The X-rays scattered by the electrons in the protein crystal are defined by their amplitudes and phases, but only the amplitude can be calculated from the intensity of the diffraction spot. Different methods have been developed in order to obtain the phase information. Two approaches, commonly applied in protein crystallography, should be mentioned here. In case the structure of a homologous protein or of a major component in a protein complex is already known, the phases can be obtained by molecular replacement. The other possibility requires further experimentation, since crystals and diffraction data of heavy atom derivatives of the native crystals are also needed. Heavy atoms may be introduced by covalent attachment to cystein residues of the protein prior to crystallization, by soaking of heavy metal salts into the crystal, or by incorporation of heavy atoms in amino acids (e.g., Se-methionine) prior to bacterial synthesis of the recombinant protein. Determination of the phases corresponding to the strongly scattering heavy atoms allows successive determination of all phases. This method is called isomorphous replacement. 

Structures of actual enzyme-substrate complexes are generally difficult to determine, because the reaction occurs too quickly, but techniques now available occasionally enable study of these complexes [53]. Protein X-ray crystallography has several limitations, for example, it often gives little or no information about the positions of protons (because of the low electron density of hydrogen atoms) in a particular protein. This can cause prob-... 

In summary, there are three important generalizations about error estimation in protein crystallography. The first is that the level of information varies enormously as a function primarily of resolution, but also of sequence knowledge and extent of refinement. The second generalization is that no single item of information is completely immune from possible error. If the electron density map is available or indicators such as temperature factors are known from refinement, then it is possible to tell which parameters are most at risk. The third important generalization is that errors occur at a very low absolute rate 95% of the reported information is completely accurate, and it represents a detailed and objective storehouse of knowledge with which all other studies of proteins must be reconciled. 

In protein crystallography we assume that all electron density is real, and does not have an imaginary component. In reciprocal space this observation is known as Friedel s law, which states that a structure factor F(h) and its Friedel mate F(—h) have equal amplitudes, but opposite phases. The correspondence of these two assumptions follows straight from Fourier theory and, in consequence, explicitly constraining all electron density to be real is entirely equivalent to introducing Nadditional equalities of... 

Any high-throughput system for protein crystallography requires efficient processes for converting measured diffraction images into experimental electron density maps and structures. Chapters 6 to IT and T 3 cover the various approaches to data analysis in considerable depth. 

Tsuruta, H., et al. (1998). Imaging RNA and dynamic protein segments with low-resolution virus crystallography experimental design, data processing and imph-cations of electron density maps. /. Mol. Biol. 284, 1439-1452. 

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. 

Crystal structure of a protein molecule can also be determined by x-ray crystallography. Purified protein is crystallized either by batch methods or vapor diffusion. X-rays are directed at a crystal of protein. The rays are scattered depending on the electron densities in different positions of a protein. Images are translated onto electron density maps and then analyzed computationally to construct a model of the protein. It is especially important for structure-based drug designs. 

Although protein crystallography has traditionally been used to give only a static picture of protein structure, it is also a powerful technique for studying the mobility of every residue in a protein chain. This is because, in addition to locating the positions of atoms from their electron density, it is also possible to measure their mean square displacement from the smearing out of the electron density. 

The primary data of protein crystallography yield a three-dimensional electron-density map, which must be interpreted in terms of a three-dimensional model of all atom positions in the protein. Such modeling is usually done by computer graphics. 

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. 

Occasionally, portions of the known sequence of a protein are never found in the electron-density maps, presumably because the region is highly disordered or in motion, and thus invisible on the time scale of crystallography. It is not at all uncommon for residues at termini, especially the N terminus, to be missing from a model. Discussions of these structure-specific problems are included in a thorough refinement paper, as well as in PDB header information. 

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