Electron density maps producing

For many years it was believed that hydrogen atoms could not be seen" in the electron density maps produced by X-ray diffraction. The reason for this is that the atomic X-ray scattering power is proportional to the square of the atomic number. This statement was generally, but not invariably, true until the demise of film-recording methods in the mid-1960 s and the advent of the computer-controlled X-ray diffractometers which could provide very accurate X-ray diffraction intensities. 

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... 

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. 

We will now consider how to simulate this method of image formation in the X-ray diffraction experiment where we have to use a mathematical replacement for the objective lens. The studies by Porter are of great importance because they show how the Bragg reflections give the amplitude components of a Fourier series representing the electron density in the crystal (the electron-density map). In effect, Fourier analysis takes place in the diffraction experiment, so that the scattering of X rays by the electron density in the crystal produces Bragg reflections, each with a different amplitude F hkl) and relative phase Qhkl-... 

Methods for treating isomorphous replacement data, in practice, are mathematical in nature, employ probability and statistics to deduce the best possible phases hia for each Ff,ki, and assign to that phase some measure of its precision. In the Fourier syntheses used to produce electron density maps, the individual terms are then weighted with their likelihood of being accurate or according to their precision. 

If, on the other hand, the electron density map calculated at some resolution r is somehow improved in quality in real space, then if it is transformed to produce structure factors, phases at somewhat higher resolution, r + Ar, can be computed that do have some measure of validity. Improvement of an electron density map thus allows gradual extension of phases in reciprocal space to higher resolution, and ultimately to an electron density map of sufficient quality and detail that a model can be constructed. This is another example of those bootstrap, incremental procedures so common to X-ray crystallography. 

Prior to the advent of computer graphics systems, electron density maps were, in actuality, produced as described above. Each section was printed on paper as a field of numbers, each... 

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