128 J. C. KENDREW [9 



origin, and their positions, together with the known symmetry properties 

 of the crystal, enable us to locate the heavy atoms in the structure, at least 

 as far as their x and z co-ordinates are concerned (the projection shown is 

 made along the y axis, and is the only one which can be calculated from real 

 reflexions in the monoclinic space group to which this crystal belongs). 



« 10 



^ a 



Fig. 1. (a) Difference- vector synthesis of the mercuri-iodide complex of myoglobin 

 (type A, y projection), {b) Schematic representation of vectors between heavy groups, 

 (c) Positions of mercuri-iodide groups in the unit cell. The unit cell contains two myo- 

 globin molecules and therefore two mercuri-iodide groups. 



The next step is to compute the contributions — positive or negative — 

 which a heavy atom in the position assigned would make to each reflexion. 

 The signs of these contributions, which are calculated in a straightforward 

 and unambiguous manner, make it possible to allot signs to the protein 

 reflexions by inspection. For if a protein reflexion is positive and the con- 

 tribution of the heavy atom is likewise positive, the resultant is a stronger 

 reflexion; the reflexion is also strengthened if a negative heavy atom con- 

 tribution is added to a negative protein term ; on the other hand a positive 

 heavy atom contribution together with a negative protein contribution, or 

 vice versa, leads to a weakening of the reflexion. 



The amplitudes of the protein reflexions having been measured and their 

 signs determined, the way is clear to compute a Fourier synthesis, which is 

 a representation of the electron density in the unit cell projected along the 

 y axis. Fig. 2 shows the result. It is computed with a resolution of 6 Â. : 

 we are, however, projecting some 31 Â, thickness of protein and mother 

 liquor onto each point (31 Â. is the length of the y axis along which the 

 projection is made). It is hardly surprising, therefore, that the various fea- 

 tures of the structure overlie one another in such confusion that in the 

 resulting projection nothing can be disentangled. Increasing the resolution 

 does not help at all; the same projection computed with a resolution of 

 4 Â. is almost identical and quite as unintelligible. Of the correctness of the 

 projection there is no doubt: for the whole process of sign determination 

 can be repeated with a different isomorphous substitution in the same unit 

 cell, using, for example, a gold atom which attaches itself to a different 



