Phase angle, isomorphous replacement methods

The isomorphous replacement method requires attachment of heavy atoms to protein molecules in the crystal. In this method, atoms of high atomic number are attached to the protein, and the coordinates of these heavy atoms in the unit cell are determined. The X-ray diffraction pattern of both the native protein and its heavy atom derivative(s) are determined. Application of the so-called Patterson function determines the heavy atom coordinates. Following the refinement of heavy atom parameters, the calculation of protein phase angles proceeds. In the final step the electron density of the protein is calculated. 

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. ... 

The most demanding element of macromolecular crystallography (except, perhaps, for dealing with macromolecules that resist crystallization) is the so-called phase problem, that of determining the phase angle ahkl for each reflection. In the remainder of this chapter, I will discuss some of the common methods for overcoming this obstacle. These include the heavy-atom method (also called isomorphous replacement), anomalous scattering (also called anomalous dispersion), and molecular replacement. Each of these techniques yield only estimates of phases, which must be improved before an interpretable electron-density map can be obtained. In addition, these techniques usually yield estimates for a limited number of the phases, so phase determination must be extended to include as many reflections as possible. In Chapter 7,1 will discuss methods of phase improvement and phase extension, which ultimately result in accurate phases and an interpretable electron-density map. 

FIGURE 8.23. Calculation of phase angles for a centrosymmetric crystal by the method of isomorphous replacement. Two isomorphous crystals have structure amplitudes I El I and T2. The replaceable atom M hcis calculated structure factors M = Ml -M2. From these it is possible to deduce relative phases (signs) for Fi and F2- In each ca.se the vector from Fi to F2 must be the same as the vector Fmi—Fm2-... 

Heavy-atom derivative of a protein The product of soaking a solution of the salt of a metal of high atomic number into a crystal of a protein. If the heavy-atom derivative is to be of use in structure determination, the heavy atom must be substituted in only one or two ordered positions per asymmetric unit. Then the method of isomorphous replacement can be used to determine the relative phase angles of the Bragg reflections. 

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