J. C. KENDREW and M. F. PERUTZ 



structure to be solved. The haemoglobin molecule has a structure of 

 this kind, though more complex than the example just given. 



Similarly a layer structure in the crystal will give rise to a vector 

 structure showing a layer of high vector density passing through the 

 origin, and other layers at equal distances on each side of the origin. 

 From the orientation of the vector layers and the distances between 

 them, the corresponding data for the molecular layers can then be 

 deduced. This was the type of structure met with in myoglobin. 



Of course it is possible (just as in the case of electron density) to 

 calculate vector densities either in three dimensions, or in projection 

 in two dimensions on to a plane, or in projection in one dimension on 

 to a line. It is to be noted that the labour that has to be spent to obtain 

 these different forms of vector maps is related in an inverse proportion 

 to the ease with which they can be interpreted. For a vector pro- 

 jection on to a line only the reflexions from one set of lattice planes 

 are required ; the computation can be done in half an hour, but 

 rarely provides much useful information. A two-dimensional pro- 

 jection needs the reflexions from all the sets of lattice planes which 

 are parallel to one crystal axis and may take a few days to compute. 

 Such projections may be extremely useful in favourable cases (e.g. 

 myoglobin), but often cannot be interpreted because peaks at different 

 levels above the plane of projection overlap. In the case of macro- 

 molecules complete calculations of vector density in three dimensions 

 have only been made possible by the introduction of punched card 

 calculating machines. Since such three-dimensional syntheses make 

 use of all the reflexions in the entire diffraction pattern, they provide 

 the maximum of direct information which that pattern can give. This 

 was the reason why such syntheses were computed for horse haemo- 

 globin and also for insulin (Crowfoot, Private Communication). 



In x-ray studies of crystalline proteins the relative phases of the 

 reflexions are generally unknown, and it is only the Patterson synthesis 

 which allows the wealth of data contained in the diffraction pattern 

 to be translated into a form which is at least potentially capable of 

 interpretation in terms of molecular structure. It often happens, of 

 course, that the unit cell contains several protein molecules in different 

 orientation, which makes it impossible to decipher the vector structure. 

 Fortunately, in the two analyses described in this volume this was not 

 so ; both vector structures revealed relatively simple systems of parallel 

 rods or layers which could be interpreted in terms of polypeptide chains. 



A more detailed treatment of the principles and practice of x-ray 

 crystallography may be found in various monographs : those by 

 R. W. James 4 , W. L. Bragg 5 and C. W. Bunn 6 are especially recom- 

 mended (in increasing order of completeness). 



178 



