The accurate determination of the position and shape of heavy-atom replacement groups in proteins

Green, Ingrain & Perutz (1954) introduced the method of isomorphous replacement with heavy atoms to the X-ray analysis of the centro-symmetric zone of horse haemoglobin. In order to determine the phase angle of general reflections multiple isomorphous replacement has to be used, involving the preparation of a series of isomorphous compounds each bearing one or more heavy atoms placed on different sites (Kendrew et al., 1958). The 'heavy atoms' in proteins may often consist of sizeable organic residues to which one or more heavy atoms are attached, producing irregular 'lumps' on an electron-density map. Patterson coefficients ([FHeavy I --IFl)e can be used to determine the position of the heavy atoms in centrosymmetric projections. However, for non-centrosymmetric crystals there exists the problem of determining the position of one atom relative to another without a fixed symmetry element as origin. The first solution of this problem is due to Harker (1956) who considers trial-and-error techniques based on selected reflections. Bragg (1958) suggested a method of fitting sinusoidal curves to the envelope of the differences plotted as a function of sin 0, which can then be shown to correspond to the structure-factor graph of the heavy-atom content of the unit cell. Perutz (1956) proposed two correlation functions, later modified and improved by Blow (1958), which depend on calculating certain Fourier summations from which the heavyatom positions can be deduced. The great advantage of the Perutz-Blow approach is that an overall picture of the cell is obtained, so that subsidiary sites can be discovered. The present paper deals with another Fourier technique which is believed to possess the advantage of giving less background effect, thus leaving no doubt in placing the atomic centre within about 0.4 A from data with 6A resolution.