9] CRYSTALLOGRAPHY OF MYOGLOBIN 127 



MYOGLOBIN AND THE ISOMORPHOUS 

 REPLACEMENT METHOD IN TWO DIMENSIONS 



Let us assume that an isomorphous heavy-atom derivative of crystaUine 

 myoglobin has been prepared, containing, for example, one mole of mercuri- 

 iodide ion per mole of protein. This implies that one mercuri-iodide group 

 is specifically attached to a single site on each myoglobin molecule, and 

 that the resulting complex has crystalhzed in precisely the same arrange- 

 ment as normal unsubstituted myoglobin, the cell dimensions and packing 

 arrangement of the molecules remaining unchanged. We shall return later 

 to the question how such derivatives can be prepared, and assume for the 

 moment simply that it has been done. 



Owing to the presence of the Hgl4-^ group the intensities of all the re- 

 flexions in the X-ray pattern will be changed. Even as weighty an ion as 

 mercuri-iodide is very small compared with the whole protein molecule, 

 however, and at first sight one might guess that the changes in the diff'racted 

 intensities would be too small to be measured. It was Perutz's contribution 

 to realize, in the course of his studies of haemoglobin, that the changes will 

 in reality be very pronounced, in consequence of the low average intensity 

 of the reflexions from a unit cell so uniformly filled with matter as is that 

 of a protein ; the average contribution of a single specifically-situated mer- 

 cury atom is actually about one quarter of the average contribution of the 

 myoglobin molecule as a whole. 



The first step in the analysis is to measure the intensities of all the real 

 reflexions before and after the attachment of mercuri-iodide. The square 

 roots of these intensities are the moduli of the amphtudes, | F | and | F' | . 

 From them are calculated the so-called 'difference intensities' (|Fl — |F'|),2 

 and these are used as terms of a Fourier synthesis. A Fourier synthesis using 

 the intensities instead of the amplitudes of the reflexions from a crystal is 

 known as a vector synthesis, and Patterson showed many years ago that 

 its physical significance is to give a representation of all the interatomic 

 vectors in the structure, transferred to a common origin without regard to 

 the absolute co-ordinates of the atoms at which each vector terminates. If 

 there are n atoms per unit cell there are «^ interatomic vectors, so the result- 

 ing vector map is usually hopelessly confused if the structure is as complex 

 as that of a protein. By the subtractive procedure we have just outlined, 

 however, we virtually cancel out all the atoms of the protein and leave in 

 effect an empty unit cell containing only the heavy atoms; the vector syn- 

 thesis simply shows the vectors between these atoms (together with a high 

 peak at the origin representing vectors of zero length between each atom 

 and itself). The result is shown in Fig. 1. The origin is in the centre; the 

 unit cell contains two myoglobin molecules related by a screw dyad axis 

 of symmetry, and consequently two mercury atoms A and B. The vectors 

 AB and BA between these atoms are symmetrically disposed about the 



