Vector Maps and Heavy Atoms in Crystal Analysis and the Insulin Structure

Abstract

CONSIDERABLE discussion has recently been devoted to the use of vector maps in crystal analysis¹ based on the Patterson method². Although much use has been made of this method in the insulin structure^1,3 the complexity of the problem and the inadequacy of the existing X-ray data to yield a solution in terms of atomic positions do not appear to have been sufficiently emphasized. It is quite obvious that fifty-nine relative measurements of amplitude cannot define a structure consisting of several thousand atoms. So far as these measurements go, the structure is effectively a continuous distribution of scattering matter, and every arbitrary assignment of phase constants to the amplitudes will yield a solution. As individual atoms cannot appear in any of these solutions, there does not seem to be any rigid criterion in favour of one any more than another. The Patterson maps, which summarize the X-ray measurements, do not remove this ambiguity because, for a similar reason, we do not know what meaning to attach to the peaks in these maps. The suggestion that certain concentrations of atoms in the molecule can be treated as point scattering sources does not seem to constitute even a reasonable approximation. As no large gaps between the atoms are likely, it may also be very difficult to distinguish between regions of high and low density which are due to real features in the structure, and those which are due to unavoidable deficiencies in the series representing it.