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. 2003 Oct;59(Pt 10):1688-701.
doi: 10.1107/s0907444903015142. Epub 2003 Sep 19.

Statistical density modification using local pattern matching

Thomas C Terwilliger  1
Affiliations

Statistical density modification using local pattern matching

Thomas C Terwilliger. Acta Crystallogr D Biol Crystallogr. 2003 Oct.

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.

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Figures

Figure 1
Figure 1
Outline of procedure for density modification using local patterns.
Figure 2
Figure 2
Creating the local modified density function g x(Δx). (a) Density in the IF5A electron-density map is shown with contours at 1.5σ. The atomic model used to calculate the map is shown and the central point (‘x’) is marked with an asterisk. (b) Modified local density g x(Δx) calculated using (5) corresponding to the map in (a) is shown. All electron-density maps were created with MAPMAN (Kleywegt & Jones, 1996 ▶) and O version 8.0 (Jones et al., 1991 ▶).
Figure 3
Figure 3
Predictive power of templates. (a) Correlation of the recovered density function with true density for the IF5A map (open circles) and for the randomized IF5A map (closed triangles). The correlation of ρest calculated from (9) with model density ρ is plotted as a function of the number of templates used. For the open circles, the templates were derived from the IF5A map, the histograms from β-catenin and red fluorescent protein maps and the model density and recovered density were from the IF5A map. For the closed triangles, phases were randomized for all three maps before carrying out the calculations. (b) As in (a), except that the local density was not adjusted to remove information about the density at the central point, so that g x(Δx) = ρ(x + Δx).
Figure 4
Figure 4
Templates of local density calculated at a resolution of 2.6 Å. The templates are arranged in order of decreasing contribution to the information about the density at the central point. The sections shown are 8 × 8 Å; only the spherical region 4 Å in diameter at the center of each figure is used in the pattern-matching process. Contours at +1.5σ (a) and −1.5σ (b, templates in the same orientation as in a) are shown.
Figure 5
Figure 5
Template matching using model electron density with errors based on the structure of gene 5 protein at a resolution of 2.6 Å. (a) Model map with Gaussian phase errors adjusted to yield a correlation to the perfect map of 0.81. (b) Estimated electron density reconstructed from the map in (a). (c) Density in (b) after smoothing with a spherical smoothing function with a radius of 1.5 Å. (d) Map calculated with model structure-factor amplitudes and with phases estimated using statistical density modification based on the reconstructed density in (c). All contours are at 0.8σ.
Figure 6
Figure 6
Template-matching using gene 5 protein MAD data. As in Fig. 5 ▶, but using experimental MAD data instead of model data.
Figure 7
Figure 7
Phase improvement using template matching on gene 5 protein MAD data. (a) SOLVE electron-density map for gene 5 protein. (b) Electron-density map calculated using observed structure-factor amplitudes and combined phases. The combined phases consisted of the SOLVE phase estimates combined with the phases estimated using statistical density modification based on the reconstructed density shown in Fig. 6 ▶(b). (c) RESOLVE electron-density map after one cycle of statistical density modification starting with the map shown in (b). All contours are at 0.8σ.
Figure 8
Figure 8
Phase improvement using template matching on nusA SAD data. (a) RESOLVE electron-density map for nusA protein calculated without pattern matching. (b), (c) and (d) Electron-density maps after one, three and five cycles of density modification including pattern matching, respectively. All contours are at 1.5σ.
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