The use of heavy atom derivatives is just one way to obtain a set of starting phases for the calculation of electron density maps. If coordinates of a homologous protein are known, it is possible to avoid the use of heavy atom derivatives. This involves some rather complex calculations but the principal steps are shown in Fig. 2.6. The success of the method appears to be related to the degree of conformational homology between the unknown protein and the known probe molecule.
The computational steps in crystal structure determination by molecular replacement require two sets of information: (1) the coordinates of the atoms in the probe molecule, and (2) an X-ray diffraction data set from crystals of the unknown protein.
The protocol for obtaining a set of phases for an unknown protein by molecular replacement is as follows:
1. Measure X-ray data from crystals of the native protein.
2. Compare the Patterson function of the unknown protein with that of a known
protein to obtain a rotational transformation, placing the probe molecule in the correct orientation in the unknown unit cell; see Fig. 2.6. Remember, to calculate the Patterson function of a known crystalline structure, no phase information is needed. The relationship is similar to that described in Eq. (2.7) for a difference Patterson. Replace Puvw with Puvw, and Fhkl with Fhkl(calc) in Eq. (2.7). The Patterson function of the probe molecule in molecular replacement is obtained from the calculated structure factors, which in turn were obtained from the coordinates of the known structure. The Patterson function of the unknown is calculated from the observed structure amplitudes, which in turn were measured from a crystal of the unknown molecule. The three-dimensional Patterson function of the probe molecule is rotated until maximum overlap is observed between it and the Patterson from the unknown crystal. This formulation is called a rotation function. It is a time-consuming calculation even on fast computers. If it works, the orientation (but not the position) of the known protein in the unknown unit cell is determined.
3. Now find the correct translational position of the properly oriented probe molecule in the unknown unit cell. This can be done by trial and error. Structure factors are calculated at different increments on a three-dimensional grid, using the atomic coordinates of the correctly oriented probe molecule. The calculated |F(probe)| values are compared with the |F(obs)| values until a good correlation is found.
4. Calculate a set of test phases, (test, hkl), using the oriented and translated coordinates of the probe molecule in the unknown unit cell. The amplitudes for the unknown crystal, Fhkl(obs) are combined with the aforementioned phases to produce a trial electron density map.
Source: LEONARD J. BANASZAK. Foundations of Structural Biology. New York: Academic press
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