Peter Main

Miscellaneous algorithms for density modification.

Various algorithms are described, developed for the dm density modification package, which have not been described elsewhere. Methods are described for the following problems: determination of the absolute scale and overall temperature factor of a data set, by a method which is less dependent on data resolution than Wilson statistics; an efficient interpolation algorithm for averaging and its application to refinement of averaging operators; a method for the automatic determination of averaging masks.

Phase combination and cross validation in iterated density-modification calculations.

A variety of density-modification techniques are now available for improving electron-density maps in accordance with known chemical information. This modification must, however, always be constrained by consistency with the experimental data. This is conventionally achieved by alternating cycles of map modification in real space with recombination with the experimental data in reciprocal space. The phase recombination is based upon the assumption that the density-modified map may be treated as a partial model of the structure which contains information independent of the experimentally derived phases. This assumption is shown to be incorrect, and an alternative procedure is investigated which as a side effect allows calculation of a free R factor.

Improvement of Macromolecular Electron-Density Maps by the Simultaneous Application of Real and Reciprocal Space Constraints

A general scheme for the improvement of electron-density maps is described which combines information from real and reciprocal space. The use of Sayres equation, solvent flattening and histogram matching within this scheme has been described previously [Main (1990). Acta Cryst. A46, 372-377]. Non-crystallographic symmetry averaging, the use of a partial structure and constraints on individual structure factors have now been added. A computer program, SQUASH, is described which applies all these constraints simultaneously. Its application to the maps of several structures has been successful, particularly so when non-crystallographic symmetry is present. Uninterpretable maps have been improved to the point where a significant amount of the structure can be recognized. Applying the constraints simultaneously is more powerful than applying them all in series.

Histogram matching as a new density modification technique for phase refinement and extension of protein molecules

A new density modification technique - histogram matching - is being developed with encouraging results. Its application to the known structure of pig 2Zn insulin refines the 6500 1.9 A MIR phases from a mean error of 60° to one of 46°. With these refined phases as a starting point for phase extension to 1.5 A, the mean error for the final 13 000 phases is 46°. The original 1.9 A phases continue to refine during the phase extension to a final mean error of 40°. A comparison is made with similar calculations already published.

COMBINING CONSTRAINTS FOR ELECTRON-DENSITY MODIFICATION

Publisher Summary An integrated procedure, known as SQUASH, that combines the constraints from the correct electron-density distribution, solvent flatness, correct local density shape, and equal molecules has been demonstrated to be a powerful method for macromolecular phase refinement and extension. This chapter describes progress in density modification using SQUASH. The crystallographic phase problem is indeterminate given only the structure–factor amplitudes. It is only through the knowledge of the chemical or physical properties of the electron density that the phases can be retrieved. The characteristic features of electron density can often be expressed as mathematical constraints on the phases. The phasing power of a constraint depends on the number of density points affected and the magnitudes of changes imposed on the electron density. It also depends on the physical nature and accuracy of the constraint and on how rigorously the constraint is applied. The phasing power also increases with the number of independent constraints employed.

X-ray structure of 3′,5′-diacetyl-2′-deoxy-2′-fluorouridine: A pyrimidine nucleoside in the syn conformation

The X-ray structure analysis of 3′,5′-diacetyl-2′-deoxy-2′-fluorouridine is reported. The title compound crystallized from water in the monoclinic space group P21 with cell constants a = 10.874 A, b = 7.379 A, c = 9.971 A, β = 111.41°. The structure was solved by direct methods and refined to a discrepancy index R = 0.039. Contrary to most of the pyrimidine nucleosides the orientation of the nucleobase with respect to the sugar is syn and the conformation about the C(4′)—C(5′) bond is trans—gauche. The ribose exhibits a C(3′)-endo—C(4′)-exo twist conformation and despite the fluoro substitution, bond angles and distances compare well with averaged data for unmodified C(3′)-endo puckered riboses. There are close contacts between the 3′- and 5′-acetate groups which are orientated roughly parallel to each other. The NMR results by Blandin, M., Tran—Dinh, S., Catlin, J.C. and Guschlbauer, W. (1974) Biochim. Biophys. Acta 361, 249–256 (preceding paper), suggest that the conformations in the crystal and in solution are similar.

DM/DMMULTI software for phase improvement by density modification

The DM/DMMULTI software for phase improvement by density modification is described. Keywords: DM/DMMULTI; density modification; phase improvement

The use of wavelet transforms in low-resolution phase extension

A method to extend low-resolution phases has been developed using histogram matching not only of the electron density itself but also of histograms obtained from the different levels of detail provided by the wavelet transform of the electron density. It is shown that the method can extend phases from 10 A to around 6-7 A on a wide range of trial structures differing in size, space group and solvent content. This level of phase extension can improve the electron-density map from little more than a molecular envelope to one in which secondary structure can often be identified.

Programs and program systems in wide use

Macromolecular programs and program systems in wide use are described. The chapter covers PHASES; DM/DMMULTI, software for phase improvement by density modification; the structure-determination language of the Crystallography & NMR System; the TNT refinement package; the ARP/wARP suite for automated construction and refinement of protein models; validation of protein-structure coordinates with PROCHECK; MolScript; MAGE, PROBE and kinemages; XDS; and macromolecular applications of SHELX.

Wavelet analysis of electron-density maps

The wavelet transform is a powerful technique in signal processing and image analysis and it is shown here that wavelet analysis of low-resolution electron-density maps has the potential to increase their resolution. Like Fourier analysis, wavelet analysis expresses the image (electron density) in terms of a set of orthogonal functions. In the case of the Fourier transform, these functions are sines and cosines and each one contributes to the whole of the image. In contrast, the wavelet functions (simply called wavelets) can be quite localized and may only contribute to a small part of the image. This gives control over the amount of detail added to the map as the resolution increases. The mathematical details are outlined and an algorithm which achieves a resolution increase from 10 to 7 A using a knowledge of the wavelet-coefficient histograms, electron-density histogram and the observed structure amplitudes is described. These histograms are calculated from the electron density of known structures, but it seems likely that the histograms can be predicted, just as electron-density histograms are at high resolution. The results show that the wavelet coefficients contain the information necessary to increase the resolution of electron-density maps.