Electron density maps quality

Ultimately the question of electron density map quality is answered by whether we can trace a single polypeptide or polynucleotide chain through the density in a manner consistent with the known amino acid or nucleotide sequence. In doing so, we consider the agreement between amino acid side chains and the density assigned to them, whether selenium atoms in a map experimentally determined by single (SAD) or multiple anomalous dispersion... 

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... 

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... 

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. 

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. 

The degree of accuracy that is attained depends on both the quality of the data and the resolution. At low resolution, 4 to 6 A (0.4 to 0.6 nm), the electron density map reveals little more in most cases than the overall shape of the molecule. At 3.5 A, it is often possible to follow the course of the polypeptide backbone, but there may be ambiguities. At 3.0 A, it is possible in favorable cases to begin to resolve the amino acid side chains and, with some uncertainty, to fit the sequence to the electron density. At 2.5 A, the positions of atoms often can be fitted with accuracy of 0.4 A. To locate atoms to 0.2 A, a resolution of about 1.9 A and very well ordered crystals are necessary. 

Here, we review how the development of SAXS as a structural technique is driven by advances in computer algorithms that allow to reconstruct low-resolution electron density maps ab initio from scattering profiles. In addition, we delineate how these low-resolution models can be used in free energy electrostatics calculations. Finally, we discuss how one can exploit the hierarchical nature of RNA folding by combining the low resolution, global information provided by SAXS with local information on RNA structure, from either experiments or state-of-the-art RNA structure prediction algorithms, to further increase the resolution and quality of models obtained from SAXS. 

At this stage, assuming that the nominal resolution is 4 A or better, the electron density map should be of sufficient quality to interpret readily the course of the polypeptide chain and rapidly build a model, usually for the icosahederal asymmetric unit. Conventional crystallographic refinement techniques are then employed to refine the model against the observed data. 

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