Direct-space methods in phase extension and phase refinement. VI. PERP (phase extension and refinement program).

Several techniques for extending and refining phases for macromolecular structures have been incorporated into a program package PERP. In addition to previously employed techniques such as solvent flattening and histogram matching, PERP includes a new way of applying the Sayre equation [Refaat, Tate & Woolfson (1995). Acta Cryst. D51, 1036-1040], low-density elimination [Shiono & Woolfson (1992). Acta Cryst. A48, 451-456] and two double-histogram methods [Refaat, Tate & Woolfson (1996). Acta Cryst. D52, 252-256]. PERP is an easy-to-use package controlled by keywords and provided with default parameters that usually give near-optimum results. Examples are given of refinement, and also extension and refinement, for six known protein structures with a variety of characteristics. In each case PERP gives a very satisfactory outcome as measured by improvements in the mean-phase-error and conventional map-correlation coefficient. The main conclusion is that the several methods used in sequence give more effective extension and refinement than using any single method alone.

Direct-space methods in phase extension and phase refinement. IV. The double-histogram method.

In the conventional histogram-matching technique for phase extension and refinement for proteins a simple one-to-one transformation is made in the protein region to modify calculated density so that it will have some target histogram in addition to solvent flattening. This work describes an investigation where the density modification takes into account not only the current calculated density at a grid point but also some characteristic of the environment of the grid point within some distance R. This characteristic can be one of the local maximum density, the local minimum density or the local variance of density. The grid points are divided into ten groups, each containing the same number of grid points, for ten different ranges of value of the local characteristic. The ten groups are modified to give different histograms, each corresponding to that obtained under the same circumstances from a structure similar to the one under investigation. This process is referred to as the double-histogram matching method. Other processes which have been investigated are the weighting of structure factors when calculating maps with estimated phases and also the use of a factor to dampen the change of density and so control the refinement process. Two protein structures were used in numerical trials, RNApl [Bezborodova, Ermekbaeva, Shlyapnikov, Polyakov & Bezborodov (1988). Biokhimiya, 53, 965-973] and 2-Zn insulin [Baker, Blundell, Cutfield, Cutfield, Dodson, Dodson, Hodgkin, Hubbard, lsaacs, Reynolds, Sakabe, Sakabe & Vijayan (1988). Philos. Trans. R. Soc. London Ser. B, 319, 456--469]. Comparison of the proposed procedures with the normal histogram-matching technique without structure-factor weighting or damping gives mean phase errors reduced by up to 10 degrees with map correlation coefficients improved by as much as 0.14. Compared to the normal histogram used with weighting of structure factors and damping, the improvement due to the use of the double-histogram method is usually of order 4 degrees in mean phase error and an increase of 0.06-0.08 in the map correlation coefficient. It is concluded that the most reliable results are found with the local-maximum condition and with R in the range 0.5-0.6 A.

Direct-space methods in phase extension and phase determination. III. Phase refinement using Sayre's equation.

An algorithm is described for refining a set of phases to agree with the Sayre equation. All operations are carried out using Fourier transforms with modest computer-store requirements even for very large systems. The procedure is tested with two moderate-sized proteins, one containing heavy atoms, and is found to give good refinement with data at more than atomic resolution (1.17 A) and useful, if less good, refinement when the data resolution is lower (1.5 A). It is concluded that at atomic resolution, or slightly below, the Sayre equation still has something to offer both for phase refinement and phase extension, especially if used cautiously with weighted multiple isomorphous replacement phases acting as a constraint on the phase changes. Even when the Sayre equation on its own refines phases badly, or not at all, it may still make an important contribution in conjunction with other real-space refinement procedures.

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.