Use of heavy atom isomorphous derivatives

For most proteins, the phase information is obtained from isomorphous heavy atom derivatives. A heavy atom (e.g., Hg, U or Pt), introduced into the protein, scatters more than the light atoms (C,N,0) of the protein and is used as a marker atom. 

The structure factor of the native protein may be represented by a vector Fp and described in terms of its magnitude Fp and phase p for a particular reflection. Introduction of the heavy atom leads to a change in intensity. The corresponding structure factor is FpH with magnitude Fp and phase ap . Both the magnitudes, Fp and FpH, can be measured experimentally from the intensities of the native protein and protein plus heavy atom, respectively. Fp is related to Fp by the vector addition of Fh which is the contribution of the heavy atom to the structure factor (Fig. 6a). 

The positions of the heavy atoms can be determined from experimental measurements 

Because of the ambiguity in the cos term, there are two possible values for ap (Fig. 6b). The ambiguity can be resolved by a second heavy atom derivative. For some reflections, two derivatives may be sufficient to solve the phase problem. In general, more than two derivatives and/or the use of anomalous data are required, because of the effects of errors in the measurements on the phase determination. 

---