Abstract
A method for improving crystallographic phases is presented that is based on the preferential occurrence of certain local patterns of electron density in macromolecular electron-density maps. The method focuses on the relationship between the value of electron density at a point in the map and the pattern of density surrounding this point. Patterns of density that can be superimposed by rotation about the central point are considered equivalent. Standard templates are created from experimental or model electron-density maps by clustering and averaging local patterns of electron density. The clustering is based on correlation coefficients after rotation to maximize the correlation. Experimental or model maps are also used to create histograms relating the value of electron density at the central point to the correlation coefficient of the density surrounding this point with each member of the set of standard patterns. These histograms are then used to estimate the electron density at each point in a new experimental electron-density map using the pattern of electron density at points surrounding that point and the correlation coefficient of this density to each of the set of standard templates, again after rotation to maximize the correlation. The method is strengthened by excluding any information from the point in question from both the templates and the local pattern of density in the calculation. A function based on the origin of the Patterson function is used to remove information about the electron density at the point in question from nearby electron density. This allows an estimation of the electron density at each point in a map, using only information from other points in the process. The resulting estimates of electron density are shown to have errors that are nearly independent of the errors in the original map using model data and templates calculated at a resolution of 2.6 A. Owing to this independence of errors, information from the new map can be combined in a simple fashion with information from the original map to create an improved map. An iterative phase-improvement process using this approach and other applications of the image-reconstruction method are described and applied to experimental data at resolutions ranging from 2.4 to 2.8 A.
Highlights
Electron-density maps corresponding to macromolecules such as proteins have features that differ in fundamental ways from those found in maps calculated with random phases
D59, 1688±1701 research papers relatively featureless solvent and large regions containing of polypeptide chains, while a map calculated with random phases has similaructuations in density everywhere (Bricogne, 1974)
This has been extensively used in histogram matching and related methods for phase improvement (Harrison, 1988; Lunin, 1988; Zhang & Main, 1990; Zhang et al, 1997; Goldstein & Zhang, 1998; Nieh & Zhang, 1999; Cowtan, 1999)
Summary
Electron-density maps corresponding to macromolecules such as proteins have features that differ in fundamental ways from those found in maps calculated with random phases. Owing to the regularity of macromolecules on a local scale, their electron-density maps have local features that are distinctive and very different from those of maps calculated from random phases (Lunin, 2000; Urzhumtsev et al, 2000; Main & Wilson, 2000; Wilson & Main, 2000; Colovos et al, 2000) This property has been used to evaluate the quality of electron-density maps and to improve phases at low resolution. We recently developed a method for density modi®cation that consisted of the identi®cation of the locations of helical or other highly regular features in an electron-density map, followed by statistical density modi®cation using an idealized version of this density as theexpected' electron density nearby (Terwilliger, 2001) This method was shown to yield some phase improvement, but suffered the serious disadvantage that after an initial cycle the features that were initially identi®ed became greatly accentuated and few new features could be found. This recoveredimage' of the electron density has many uses, including phase improvement and evaluation of map quality
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