132 J. C. KENDREW [9 



position in the cell. We conclude that the iron atom of the haem group must 

 be somewhere on the surface of a sphere with centre at the heavy-atom posi- 

 tion and radius of some 6 A. We have thus succeeded in approximately 

 locating the haem group with respect to the axes of the unit cell. 



At the other extreme from the specific haem-group reagents are some 

 ions for which, the evidence suggests, combination is interstitial rather than 

 truly chemical; that is to say, the ion lodges in a convenient niche on the 

 protein surface or perhaps in a 'cosy corner' between two neighbouring 

 protein molecules. In such cases the ion may combine specifically with only 

 one particular crystal form, any other form (prepared by different methods, 

 and having the myoglobin molecules packed together in a different manner) 

 either giving no combination at all, or else perhaps combination at several 

 different sites. In general it will be evident that we are very ignorant of the 

 way in which the heavy groups we use are attached to the protein. In most 

 cases it might be quite laborious to discover by conventional chemical 

 methods what mechanism is involved, and it is interesting that we are at 

 present able to locate the heavy atoms far more easily by X-rays than by 

 chemical methods, and this with certainty although the structure of the 

 protein as a whole is still unknown. Even dynamic effects may be observed. 

 Thus on prolonged irradiation of a crystal of the PCMBS complex with 

 X-rays the mercury atom migrates from its normal position in the unit cell 

 to another one, which turns out (in projection at least) to be identical with 

 the site occupied by the heavy atom in the silver and gold complexes! — 

 the difference-Fourier projection calculated from the amplitudes before and 

 after irradiation is found to contain a region of negative electron density 

 at the former site and a positive peak at the latter. All in all, methods for 

 attaching heavy groups to proteins might well repay study by conventional 

 chemical techniques, and certainly protein crystallographers would be glad 

 to have them investigated in the expectation that analogous and perhaps 

 better reagents might be discovered. 



THREE-DIMENSIONAL METHODS 



In this final section we shall consider what is involved in making a Fourier 

 synthesis of a protein crystal in three dimensions. All the reflexions whose 

 spacing exceeds the resolution required must be included as terms of such 

 a synthesis, and a large majority of them will have general phases. Their 

 amplitudes, together with the corresponding amplitudes from a crystal con- 

 taining a heavy atom in a known position in the unit cell, are measured by 

 the usual techniques. Now if we wished to predict the change in the ampli- 

 tude of a reflexion of general phase which would be caused by a heavy 

 atom at a particular site in the unit cell, it would be necessary lo treat the 

 amplitude due to the protein and that due to the heavy atom as vectors, 

 and calculate iheir resultant by means of a vector diagram. Thus Fig. 5 {a) 

 shows how the protein reflexion (with amplitude |Fp| and phase <f>^ and 



