J. C. KENDREW and M. F. PERUTZ 



the unit cell and the vector structure derived from it. Such cases were 

 actually met with in the analyses of haemoglobin and myoglobin 

 described elsewhere in this volume. It will help us to understand the 

 Patterson syntheses of these two substances, if we consider the com- 

 paratively simple example of a crystal consisting of parallel straight 

 chain hydrocarbons (Figure 10). The picture on the left shows just 

 two such hydrocarbon chains, with lines joining different pairs of 

 atoms drawn in different colours. The equivalent vector structure is 

 drawn on the right. According to definition this should contain a high 

 peak at the origin (shown at the centre of the picture) surrounded by 

 a series of smaller peaks. Each of these peaks should be at the end of 

 a vector from the origin, corresponding to a line joining two atoms in 

 the hydrocarbon chains. The first four peaks around the origin, drawn 

 in black, correspond to the bonds between neighbouring atoms in the 

 hydrocarbon chains which are also drawn in black. The four yellow 

 peaks which are all on a line passing through the origin correspond to 

 the yellow lines joining pairs of next but nearest atoms along the 

 chains. Similarly the four blue peaks originate from the pairs of atoms 

 joined by blue lines. All the peaks which correspond to lines joining 

 atoms within any one chain form a row, with a pattern which repeats 

 at the same intervals along the row as does the pattern of carbon atoms 

 along the molecular chains. 



Consider now the lines joining pairs of atoms situated in neighbouring 

 chains. A few of these lines are drawn in the diagram in red ; they 

 are numbered to make the correlation with their vector equivalent 

 more obvious. The red vectors are drawn radiating from the origin 

 towards the right. In order not to confuse the diagram only a very 

 few of the inter-chain vectors are drawn, but the ones that appear 

 should enable the reader to visualize the way in which the other red 

 peaks arose. It is seen that these inter-chain vectors produce another 

 row of vector peaks which is parallel to the first row and spaced at a 

 distance equal to that between a pair of hydrocarbons in the crystal 

 structure. There is one such row on each side of the origin and, if the 

 unit cell of the crystal structure contained not just two but several 

 hydrocarbon chains side by side, the central row of vector peaks 

 through the origin would be flanked on either side by several vector 

 rows. Suppose in space each hydrocarbon chain were surrounded by 

 six neighbouring ones, then the origin in the vector structure would be 

 surrounded by six rows of vector peaks. The vector structure in this 

 case would therefore reveal the direction of the chains with respect to 

 the crystal axes, the repeat distance of the atomic pattern along the 

 chains, the distance between neighbouring chains and their relative 

 arrangement. This information would be sufficient to allow the crystal 



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