Crystals electron density maps

Y308->S FNR with or without the addition ofNADP can be crystallized as isomorphous crystals. Electron-density maps shows a strong density for a complete NADP, confirming that NADP is a copurified ligand. Karplus and coworkers also concluded that Tyr-308 affects the thermodynamics of nicotinamide binding, but does not appear to play an active role in influencing the conformation or reactivity of the bound nicotinamide. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Figure 12.3 Two-dimensional crystals of the protein bacteriorhodopsin were used to pioneer three-dimensional high-resolution structure determination from electron micrographs. An electron density map to 7 A resolution (a) was obtained and interpreted in terms of seven transmembrane helices (b).

The amplitudes and the phases of the diffraction data from the protein crystals are used to calculate an electron-density map of the repeating unit of the crystal. This map then has to be interpreted as a polypeptide chain with a particular amino acid sequence. The interpretation of the electron-density map is complicated by several limitations of the data. First of all, the map itself contains errors, mainly due to errors in the phase angles. In addition, the quality of the map depends on the resolution of the diffraction data, which in turn depends on how well-ordered the crystals are. This directly influences the image that can be produced. The resolution is measured in A... 

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... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

Two helices are packed antiparallel in the orthorhombic unit cell. Association of the helices occurs through a series of periodic carboxylate potassium water - carboxylate interactions. An axial projection of the unit-cell contents (Fig. 23b) shows that the helices and guest molecules are closely packed. This is the first crystal structure of a polysaccharide in which all the guest molecules in the unit cell, consistent with the measured fiber density, have been experimentally located from difference electron-density maps. The final / -value is 0.26 for 54 reflections, of which 43 are observed, and it is based on normal scattering factors.15... 

Molecular replacement is where the phases of a known structure are used to determine the structure of a protein that may be identical but crystallized in a different space group or may adopt essentially the same structure (e.g., a homologous protein). Essentially, the calculations find the rotation and translation of the molecule that work with the phases to produce an interpretable electron density map. 

Once the crystals have been soaked in compound, rapid X-ray data are collected sufficient to allow the generation of an electron density map. The difference in density between empty unsoaked crystals and those where a... 

At a certain stage in the refinement, the electron density map is interpreted using a model representation of the charge density distribution to extract the atomic coordinates. A commonly used scattering formalism is the independent-atom model (IAM), in which the total charge density in the crystal is approximated by the superposition... 

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. 

The result is the electron density map of the protein crystal. The final task for the crystallographer is to build the appropriate protein model, i. e., putting amino acid for amino acid into the electron density. Routinely the theoretical amplitudes and phases are calculated from the model and compared to the experimental data in order to check the correctness of model building. The positions of the protein backbone and the amino acid side chains are well defined by X-ray structures at a... 

For molecules of molecular weight above 20,000 g/mol, X-ray diffraction remains the only experimental approach available to obtain detailed and reliable three-dimensional atomic models. The major steps of the method include the obtention of large and well-ordered crystals, their exposure to X-rays and collection of diffraction data and the phasing of these data to obtain by Fourier analysis a three-dimensional view (or map) of the electron density of the molecule. Finally a three-dimensional atomic model of the protein is fitted like a hand in a glove within this map, using a kit containing all the available biochemical and spectroscopic information (Table 6.2). The reliability of the final atomic model is of course dependent on the qnality of the electron density map. This qnality depends on the number of X-ray data per atom and on the resolution and accnracy of these data, which in turn are highly dependent on the size and quality of the crystals. 

Interpretation of the electron density maps showed that the large subunit could not be modelled beyond His536 (Fig. 6.10), that is fifteen amino acids short of the 551 residues predicted by the nucleotide sequence (Table 6.2). At about the same time, the cleavage of this fifteen-residue stretch, which is performed by a specific protease, was reported to be an obligatory step for the maturation of the enzyme (Menon et al. 1993). It is also of interest to note that in all [NiFe] hydrogenase crystal structures this buried C-terminal histidine is ligated to a metal atom which is either a magnesium or an iron (see above). 

More than half of the volume of the crystals is taken up by liquid of crystallization, which mainly fills the spaces between molecules and shows up as flat, featureless regions in the electron density map. The rest of the map contains regions of high electron density. The boundaries between these two types of regions mark the outlines of the molecules. There are relatively few contacts between neighbouring molecules. 

Comparison of forms of atomic fragments limited by the zero flux surfaces in ESP and electron density (Fig. 7) displays the role of different factors in the formation of the crystal structure. So in crystals with NaCl-type structure the exchange and correlation of electrons decrease the size of the cation and enlarge the size of the anion which leads to the structureforming interactions anion-anion in the (001) plane of the electron density maps. In ESP-maps the big cations and small anions are seen. 

Several steps were needed to determine the structure of the core particle to higher resolution (Fig. Id). The X-ray phases of the low-resolution models were insufficient to extend the structure to higher resolution, since the resolution of the early models of the NCP was severely limited by disorder in the crystals. The disorder was presumed to derive from both the random sequences of the DNA and from heterogeneity of the histone proteins caused by variability in post-translational modification of the native proteins. One strategy for developing an atomic position model of the NCP was to develop a high-resolution structure of the histone core. This structure could then be used with molecular replacement techniques to determine the histone core within the NCP and subsequently identify the DNA in difference Fourier electron density maps. 

The crystallization and structural determination of the histone octamer was first reported in 1984 [34], However, the overall dimensions of the 3.3 A structure [15] did not appear to fit within the known X-ray structures of the nucleosome core particle [12,13], In an elegant analysis [16], re-examination of the original phasing of the histone octamer data revealed misplacement of the heavy atom site by 2.7 A. The structure was resolved, after which it was possible to build molecular models of the individual histones into the 3.1 A resolution electron density map of the histone core of the nucleosome [17]. Figure 2 shows the first atomic resolution model of the core histone octamer. Several additional publications followed in which the histone octamer structure formed the basis for constructing models of the NCP [17-21],... 

The crystal structures of two ferulic acid complexes of HRP C have been solved, one with resting state enzyme (to 2.0 A resolution) and the other with the cyanide-ligated enzyme (to 1.45 A resolution) 195). These represent a major achievement for the crystallography of peroxidase complexes. The binary complex is heterogenous, according to the 2Fo-Fc omit difference electron density map of the active site. The disordered density observed has been interpreted in terms of three... 

The volume properties of crystalline mixtures must be related to the crystal chemical properties of the various cations that occupy the nonequivalent lattice sites in variable proportions. This is particularly true for olivines, in which the relatively rigid [Si04] groups are isolated by Ml and M2 sites with distorted octahedral symmetry. To link the various interionic distances to the properties of cations, the concept of ionic radius is insufficient it is preferable to adopt the concept of crystal radius (Tosi, 1964 see section 1.9). This concept, as we have already noted, is associated with the radial extension of the ion in conjunction with its neighboring atoms. Experimental electron density maps for olivines (Fujino et al., 1981) delineate well-defined minima (cf figure 1.7) marking the maximum radial extension (rn, ,x) of the neighboring ions ... 

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