Updating direct methods VI. The extended use of the information contained in the Patterson map

In the previous articles in this series, it was shown how the use of the Patterson map as a priori information significantly improves the estimation of triplet invariants and makes possible the ab initio solution of macromolecular structures with data resolutions up to 2.2 Å, provided that heavy atoms are present in the unit cell. For the above estimation, the position and intensity of the most representative Patterson peaks were used. No effort towards Patterson deconvolution is necessary. Triplet invariants, however, depend not only on individual Patterson peaks, but also on pairs of interatomic vectors that start or converge on the same atom. Such pairs presuppose the presence of a third interatomic vector, and therefore in this article we legitimately speak of Patterson peak triples. The new mathematical formulation allows their algebra to be described: the informative contribution coming from them has been incorporated into the technique of joint probability distribution functions, and the result is a concentration factor that significantly improves the estimation of triplet invariants. Experimental tests on proteins and nucleic acids show that structural complexity and non-atomic resolution are no longer an unsurpassable obstacle for crystal structure solution.