Open AccessStatistical density modification using local pattern matching
Author(s) -
Terwilliger Thomas C.
Publication year - 2003
Publication title -
acta crystallographica section d
Language(s) - English
Resource type - Journals
ISSN - 1399-0047
DOI - 10.1107/s0907444903015142
Subject(s) - electron density , histogram , point (geometry) , correlation coefficient , electron , rotation (mathematics) , correlation function (quantum field theory) , probability density function , statistical physics , physics , mathematics , geometry , statistics , computer science , artificial intelligence , spectral density , quantum mechanics , image (mathematics)
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 Å. 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 Å.