Pictorial Pattern Recognition and the Phase Problem of X-ray Crystallography

The availability of interactive, three-dimensional, computer graphics systems coupled to powerful digital computers encourages the development of algorithms adapted to this environment. Pictorial pattern recognition techniques make possible a number of approaches to X-ray structure determination based on molecular model building, i.e. the use of chemical information to frame “structural hypotheses” which can computationally be tested and refined by reference to the experimental data. Application of standard pattern recognition algorithms is hindered by the fact that the cross-correlation between a model and the correct structure cannot be computed because of a fundamental incompleteness in the measured data. However, it is possible to compute an upper bound to such a cross-correlation. A simple example demonstrates that this information can be the basis of a technique for structure determination that can make effective use of an interactive graphics system. Model building by cross-correlations has intrinsic advantages over usual crystallographic techniques based on the autocorrelation or Patterson function, especially for large structures. This is significant, for crystallography of biological macromolecules has been and will continue to be a field of intense interest.