The resolution of an electron-density map

FIGURE 9.9. The resolution of a protein crystal structure in terms of the data measured. The higher the value of 0 to which the data are measured, the higher the resolution of the data. 

FIGURE 9.10. Different resolutions of the same structure. These diagrams were obtained by only including terms that diffract to the quoted resolution. 

FIGURE 9.11. Fit of a protein molecule to a graphics system output (o-xylose iso-merase). (a) 4 A resolution, and (b) 1.7 A resolution. Note that the fit of the model, drawn by lines, is better at the higher resolution. (Courtesy H. L. Carrell). 

When small crystal structures are studied, all Bragg reflection data are used, and relative phase angles are derived by one of the methods described in Chapter 8, and electron-density maps are calculated to the maximum possible resolution that the wavelength of the X rays permit. On the other hand, because isomorphous replacement methods are used to obtain relative phase angles for macromolecular structures, it is usual to calculate electron-density maps at low resolution initially, and to increase the resolution as more phases from isomorphous replacement data become available. Traditionally the structure determination is divided into three resolution shells that correspond to the minima of the radial distribution of intensities.  

FIGURE 9.12. Series-termination errors, (a) A normal atomic scattering factor curve and (b) the atomic peak obtained by Fourier transformation, (c) A truncated atomic scattering factor curve, such as that used for data that are measured to a lower sin 6/ value than advisable. The missing portion of the scattering curve is indicated, (d) The atomic peak obtained by Fourier transformation. Note the ripples caused by loss of the missing portion of the atomic scattering curve. 

---