Resolution density maps

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).

Deisenhofer, J., et al. X-ray structure analysis of a membrane protein complex. Electron density map at 3 A resolution and a model of the chromophores of the photosynthetic reaction center from Rhodopseudomonas viridis. f. Mol. Biol. 180 385-398, 1984. 

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... 

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

Because IPES maps the densities of unoccupied states, it is related to other techniques that do the same (e.g. STS and SXAPS). When used in conjunction with a technique that maps the densities of occupied surface states, e.g. UPS or ELS, a continuous spectrum of state density from occupied to unoccupied can be obtained. Just as in UPS, in which angular resolution enables elucidation of the three-dimensional occupied band structure, so in IPES angular resolution enables mapping of the three-dimensional unoccupied band structure. This version is called KRIPES (i. e. K-re-solved IPES). 

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. 

S. Israel, R. Saravanan, N. Srinivasam, R. K. Rajaram, High resolution electron density mapping for LiF and NaF. J. Phys. Chem. Solids 64 (2003) 43. 

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... 

All three proteins were analyzed at 3.0 A resolution. Experiments were performed on a portion of the relative density map containing an entire connected protein. In order to discern effects of topological features just outside the boundaries of this volume, our analysis was extended 5.0 A outside the boundaries on all sides of this volume. 

Recently, a systematic experimental study has clearly proved the effect on a gaseous medium of both ASE and picosecond pedestal prior to the arrival of the ultrashort intense laser pulse [26]. The study has been based on sequences of electron density maps obtained from optical interferograms with femtosecond resolution and has been supported by numerical simulation of the ionization of the medium. 

Figure 3.9 Stereoview of 2 F0bs - Fcaic electron density maps at 2-A resolution for (A) Pox and (B) PN. (C) Stereoview of the Fobs - Fobs (reduced minus oxidized) electron density maps showing differences in the vicinity of the P cluster. (Reprinted with permission from Figure 3 of Peters, J. W. Stowell, M. H. B. Soltis, S. M. Finnegan, M. G. Johnson, M. K. Rees, D. C. Biochemistry, 1997, 36, 1181-1187. Copyright 1997, American Chemical Society.)...

Hill, E., Tsernoglou, D., Webb, L., Banaszak, L. Polypeptide conformation of cytoplasmic malate dehydrogenase from an electron density map at 3.0 A resolution. J. Mol. Biol. 72, 577-591 (1972). 

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. 

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). 

Fig. 13. Stereo drawing of one contour level in the electron density map at 2 A resolution for the residue 54-68 helix in staphylococcal nuclease. Carbonyl groups point up, in the C-terminal direction of the chain the asterisk denotes a solvent peak bound to a carbonyl oxygen in the last turn. Side chains on the left (including a phenylalanine and a methionine) are in the hydrophobic interior, while those on the right (including an ordered lysine) are exposed to solvent.

In high-resolution X-ray structures of proteins it is usual for a small number of solvent molecules to appear fairly clearly as peaks in the electron density map (see Fig. 13). Now that various refinement techniques are being applied to many protein structures, determination of water positions is usually a part of the process. In only a few cases,... 

Six-fold averaged electron density map of the catalytic site of D. gigas [NiEe] hydrogenase in the as-prepared oxidised form at 0.25 nm resolution... 

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. 

Figure 6.7 A stereoview of the electron density map of the catalytic site of the D.vulgaris [NiFe] hydrogenase in a reduced form at 0.14nm resolution (Higuchi et al. 1999b). 

Normal horse haemoglobin is a mixture of two distinct haemoglobins which arc present in approximately equal proportions. The nature of the chemical difference between the two components seems to reside in a single peptide. Crystallographically the two components appear to be identical and no differences can be ob.serv ed in the intensities of the X-ray reflections (36). At a resolution of 5.5 A the electron density maps of the two components should be identical. Horse oxy haemoglobin ciystallized... 

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