On the application of phase relationships to complex structures. XXXIII. The problems with large structures and low resolution

A conventional direct method, using the Sayre equation as a basis, has been shown to be capable of solving a small protein with data of 3.0 Å resolution or better. An analysis of the Sayre equation, with data of various resolutions and with different lower limits of |E| for the contributors in the summation, shows that its effectiveness for phasing is independent of structural complexity but does decline as the resolution becomes worse. It is suggested that a practicable lower limit for the application of conventional direct methods is about 3.5 Å. For large macromolecular structures the number of contributors to the summation in the Sayre equation becomes too large to handle and it is suggested that real-space methods should be used instead.