Direct-space methods in phase extension and phase determination. II. Developments of low-density elimination

The low-density elimination method for phase extension and refinement [Shiono & Woolfson (1992). Acta Cryst. A48, 451-456] has been improved by substituting a smoother density-modification procedure for the original sharp cut-off function. In addition, better criteria have been found for limiting the number of refinement cycles, which gives a better final result for much less work. The effectiveness of the process has been illustrated by phase refinement for a protein with high-resolution (1.17 A) data containing 808 independent non-H atoms plus 83 water molecules in the asymmetric unit; the unweighted mean-phase error was reduced from 74 to 39.3 degrees. Phase extension and refinement was also demonstrated for pig 2Zn insulin starting with multiple isomorphous replacement (MIR) phases at 1.9 A and extending out to 1.5 A. There was a significant improvement of phases and the final map had a correlation coefficient of 0.540.

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 A 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 A. 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.

On the application of phase relationships to complex structures. XXXII. A small protein at low resolution

The direct-methods program SAYTAN is applied to data at various restricted resolutions for a small protein. It is shown that useful sets of phases can be obtained even down to 3 A resolution. Conventional figures of merit are not very discriminating for the phase sets developed, but modified figures of merit seem capable of selecting the better phase sets, at least for those generated from 2 A or higher resolution data.