M. F. PERUTZ 



six nearest neighbours and the interstices between the cylinders are 

 rilled with liquid. 



Of necessity only a very small part of the total diffraction pattern 

 from haemoglobin was used for the studies just described (i.e. the 

 reflexions from sets of planes parallel to the principal crystal axes) 

 while the remainder had to be disregarded for lack of any method of 

 interpretation. It was obviously desirable to prepare a three-dimen- 

 sional Patterson synthesis which was intrinsically much more likely to 

 lend itself to reasoned interpretation than the two-dimensional pro- 

 jections which had been employed in the earlier work, yet for a small 

 research team this seemed a vast and very risky enterprise. Had 

 haemoglobin not been one of the favourable structure types mentioned 

 before — and we had little evidence to suggest that it was — the meaning 

 of the vector structure might have been impossible to decipher. If I 

 decided nevertheless to take the chance, it was partly because the 

 stakes seemed to make it worth while, and partly because youthful 

 enthusiasm made me underestimate the years of soul-destroying 

 routine work which lay ahead. 



The Three-dimensional Patterson Synthesis — The physical principles 

 underlying this method are described by Kendrew and Perutz (p. 161). 

 In practice, the intensities of about 20,000 diffracted rays had to be 

 recorded, indexed, measured, corrected and tabulated. In the work 

 of indexing the reflexions and measuring their intensities, the longest 

 stage of all, I was helped by Miss Edna Davidson and Miss Joy 

 Boyes- Watson. After allowance had been made for overlapping and 

 symmetry I was left with about 7,000 relative intensities which were 

 to be the coefficients of the terms of the Fourier summation. Each 

 intensity formed the amplitude of a three-dimensional wave giving a 

 sinusoidal variation of vector density through the unit cell. In theory, 

 28,000 such waves, each of different amplitude, wave-length and 

 orientation, would have had to be summed for each of 54,000 points 

 in the unit cell. Actually this labour can be much reduced by making 

 use of the symmetry properties of cosine functions, but even so a 

 calculation of this magnitude is beyond the patience even of a crystal- 

 lographer. It was done for me by the Scientific Computing Service 

 using punched card calculating machines, and did not take more than 

 one person's working time for about four months. 



The results of the three-dimensional synthesis were plotted in the 

 form of contour maps, each of which gives the distribution of vector 

 density in a section through the unit cell. The sections are parallel 

 to the plane containing the X and Z axes (see Figure 2) and extend 

 over the whole of c and one quarter of a. Altogether 31 sections 

 were plotted, at intervals of just over 1 A, starting from the origin 



138 



