Atomic electron-density mapping

On the other hand the polarization of electron density map unsaturated carbonyl compounds makes their p carbon atoms rather electrophilic Some chemical conse quences of this enhanced electrophilicity are described m the following section... 

Step 11. At this point a computer program refines the atomic parameters of the atoms that were assigned labels. The atomic parameters consist of the three position parameters x,j, and for each atom. Also one or six atomic displacement parameters that describe how the atom is "smeared" (due to thermal motion or disorder) are refined for each atom. The atomic parameters are varied so that the calculated reflection intensities are made to be as nearly equal as possible to the observed intensities. During this process, estimated phase angles are obtained for all of the reflections whose intensities were measured. A new three-dimensional electron density map is calculated using these calculated phase angles and the observed intensities. There is less false detail in this map than in the first map. 

These stmctures tend to have a lot of disorder. It is rare that any hydrogens can be observed in the final electron density maps. In fact, many groups of atoms (water molecules and some side chains) may be so disordered that it is usually difficult to determine positions for these groups. 

Figure 18.11 Electron-density maps at different resolution show more detail at higher resolution, (a) At low resolution (5.0 A) individual groups of atoms are not resolved, and only the rodlike feature of an

Figure 18.12 The electron-density map is interpreted by fitting into it pieces of a polypeptide chain with known stereochemistry such as peptide groups and phenyl rings. The electron density (blue) is displayed on a graphics screen in combination with a part of the polypeptide chain (red) in an arbitrary orientation (a). The units of the polypeptide chain can then be rotated and translated relative to the electron density until a good fit is obtained (b). Notice that individual atoms are not resolved in such electron densities, there are instead lumps of density corresponding to groups of atoms. [Adapted from A. Jones Methods Enzym. (eds. H.W. Wyckoff, C.H. Hirs, and S.N. Timasheff) 115B 162, New York Academic Press, 1985.]...

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. 

The structure was refined by block-diagonal least squares in which carbon and oxygen atoms were modeled with isotropic and then anisotropic thermal parameters. Although many of the hydrogen atom positions were available from difference electron density maps, they were all placed in ideal locations. Final refinement with all hydrogen atoms fixed converged at crystallographic residuals of R=0.061 and R =0.075. 

A search for intermolecular bonds resulted in one possible hydrogen bond between hydroxyl 013 and lactone carbonyl Ol. The distance between 01 and 013 is 2.85 A, a value well within the range expected for OH-O hydrogen bonds (25). The hydrogen atom position for hydroxyl 013 was chosen to be along the 013-01 vector. The hydrogen position was not evident in the difference electron density map, presumably due to problems modeling the 013 position. 

PbTX-1 also cx)ntains the intermolecular hydrogen bond between hydroxyl 013 and carbonyl 01 already discussed. Only for dihydro PbTX-1 was it possible to locate an 012 hydroxyl hydrogen atom position from difference electron density maps. In that structure a peak appeared at 1.1 A from 012 and 2.1 A from symmetry related 05. 

Once an electron density map has become available, atoms may be fitted into the map by means of computer graphics to give an initial structural model of the protein. The quality of the electron density map and structural model may be improved through iterative structural refinement but will ultimately be limited by the resolution of the diffraction data. At low resolution, electron density maps have very few detailed features (Fig. 6), and tracing the protein chain can be rather difficult without some knowledge of the protein structure. At better than 3.0 A resolution, amino acid side chains can be recognized with the help of protein sequence information, while at better than 2.5 A resolution solvent molecules can be observed and added to the structural model with some confidence. As the resolution improves to better than 2.0 A resolution, fitting of individual atoms may be possible, and most of the... 

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... 

Application. Anomalous X-ray diffraction (AXRD), anomalous wide-angle X-ray scattering (AWAXS), and anomalous small-angle X-ray scattering (ASAXS) are scattering methods which are selective to chemical elements. The contrast of the selected element with respect to the other atoms in the material is enhanced. The phase problem of normal X-ray scattering can be resolved, and electron density maps can be computed. 

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 intrazeolite cations necessary to balance the negative charge on the framework aluminum atoms are poorly shielded and as a result high electric (electrostatic) fields on the order of 1-10 V/nm are found in their vicinity. The magnitudes of the electric fields can be calculated from measured effects on the vibrational frequencies or intensities of IR bands of small diatomics such as CO or N2.24 They can also be determined from difference electron density maps determined by X-ray diffraction methods.25 These high electric fields can dramatically influence the stabilities of transition states with significant charge separations. 

Figure 13 shows the electron density map at 2 A resolution for one of the a-helices in staphylococcal nuclease. Bumps for the carbonyl oxygens are clearly visible they point toward the C-terminal end of the helix, and are tipped very slightly outward away from the helix axis. At the top, in the last turn of the helix, there is a carbonyl tipped still further outward and hydrogen-bonded to a solvent molecule (marked with an asterisk). Side chain atoms or waters frequently bond to free backbone positions in the first or last turn of a helix, and hydrogen bonds with water are even more favorable for carbonyls than for NH groups (see Section II,H). 

Chemists often focus on the energetic, geometric, and spectroscopic properties of molecules. However, since the electron density exists in ordinary three-dimensional space, electron density maps of molecules can be used as tools to unearth a wealth of information about the molecule. This information includes, but is not limited to, a molecule s magnetic properties, per-atom electron population, and bond types. 

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. 

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