Electron density map interpretation

Eortier, S., Chiverton, A., Glasgow, J. and Leherte, L. (1997). Critical-point analysis in protein electron-density map interpretation. Method Enzymol. Ill, 131-157. 

How is an electron density map interpreted In the case of a conventional small molecule compound, where the electron density map is computed at or near atomic resolution, atoms appear as distinct, well-separated peaks in the map. Chemical constraints, such as reasonable bond lengths and angles, are then applied to the distribution of atoms, and based on the relative peak heights, geometry, and distances of separation, the structure of the molecule deduced. Since there is no explicit information specifying which atoms are directly bonded, connectivity must be implied. In most instances the interpretation is unambiguous and the structure clear. 

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. 

In general, the advantages of using an automated method may be comparable to those of SA refinement in X-ray crystallography [68], where many of the operations necessary to refine a structure can be done automatically and the remaining manual interventions are easier because the SA refinement usually results in a more easily interpreted electron density map. Automated methods are usually used in combination with manual assignment. However, fully automated assignment of the NOEs is possible (see Eig. 7) [69]. 

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... 

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... 

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. 

Greer J. Three dimensional pattern recognition an approach to automated interpretation of electron density maps of proteins. / Mol Biol 1974 82 279-301. 

Leherte, L., Fortier, S., Glasgow, J. and Allen, F.H. (1994) Molecular scene analysis application of a topological approach to the automated interpretation of protein electron-density maps, Acta Cryst., D50, 155-166 and references therein. 

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... 

The mathematical pictures called "electron density maps" are used to determine molecular structures and the energy level diagrams are used to determine the energies of bond formation and to interpret spectroscopy data. 

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). 

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... 

Determination of electron density maps for the u-quartz polymorph establishes that the charge transfer between silicon and oxygen is not complete and that a residual charge of +1.0 ( 0.1) electron units (e.u.) remains localized on silicon, whereas a charge of —0.5 ( 0.1) e.u. is localized on each oxygen atom. The interpretation of this fact in terms of the bond ionicity is not as univocal as it may appear at first glance. 

The electron density map (p(xyz)) can then be interpreted in terms of a three-dimensional atomic model. 

Morris, R. J., Perrakis, A., and Lamzin, V. S. (2003). ARP/wARP and automatic interpretation of protein electron density maps. Method Enzymol. 374, 229-244. 

Model building is an interpretation of the currently available electron density. Refinement is the adjustment of the built model to fit better to the experimental data. A crucial point here is that a density map computed from the refined model is generally better than the map obtained from the same model before the refinement. This then allows for an even better model to be built. Thus, refinement is needed to improve the outcome of model building by generating a better electron density map and model building is needed to provide a model in the first place and to provide stereochemical restraints for the subsequent refinement to proceed smoothly. This viewpoint merges these two steps into one model optimization process. 

Below we briefly describe the crystallographic software pipelines using AutoRickshaw as an example, with its flexibility and the ability to decide on the path to be taken dependent on the outcome of a previous step. On one hand, AutoRickshaw has features and general steps, which are also shared by many other pipelines. On the other hand, AutoRickshaw is perhaps the first software pipeline which aims not at the delivery of a fully built, refined, and validated model but rather at fast evaluation of the quality of the X-ray data in terms of interpretability of the obtained electron density map. 

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