DIRECT-SPACE METHODS IN PHASE EXTENSION AND PHASE REFINEMENT .4. THE DOUBLE-HISTOGRAM METHOD

In the conventional histogram-matching technique for phase extension a nd refinement for proteins a simple one-to-one transformation is made in the protein region to modify calculated density so that it will hav e some target histogram in addition to solvent flattening. This work d escribes an investigation where the density modification takes into ac count 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 densit y, the local minimum density or the local variance of density. The gri d points are divided into ten groups, each containing the same number of grid points, for ten different ranges of value of the local charact eristic. The ten groups are modified to give different histograms, eac h corresponding to that obtained under the same circumstances from a s tructure similar to the one under investigation. This process is refer red to as the double-histogram matching method. Other processes which have been investigated are the weighting of structure factors when cal culating maps with estimated phases and also the use of a factor to da mpen the change of density and so control the refinement process. Two protein structures were used in numerical trials, RNAp1 [Bezborodova, Ermekbaeva, Shlyapnikov, Polyakov & Bezborodov (1988). Biokhimiya, 53, 965-973] and 2-Zn insulin [Baker, Blundell, Cutfield, Cutfield, Dodso n, Dodson, Hodgkin, Hubbard, Isaacs, Reynolds, Sakabe, Sakabe & Vijaya n (1988). Philos. Trans. R. Sec. London Ser. B, 319, 456-469]. Compari son of the proposed procedures with the normal histogram-matching tech nique without structure-factor weighting or damping gives mean phase e rrors reduced by up to 10 degrees with map correlation coefficients im proved 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 m ean phase error and an increase of 0.06-0.08 in the map correlation co efficient. It is concluded that the most reliable results are found wi th the local-maximum condition and with R in the range 0.5-0.6 Angstro m.