Introduction

Zhang, K. Y. J.; Cowtan, K. D.; Main, P.

doi:10.1107/97809553602060000687

International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

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International Tables for Crystallography (2006). Vol. F. ch. 15.1, p. 314 | 1 | 2 |

Section 15.1.2.2.1. Introduction

K. Y. J. Zhang,^a K. D. Cowtan^b ^* and P. Main^c

^a Division of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA,^bDepartment of Chemistry, University of York, York YO1 5DD, England, and ^cDepartment of Physics, University of York, York YO1 5DD, England
Correspondence e-mail: cowtan+email@ysbl.york.ac.uk

15.1.2.2.1. Introduction

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Histogram matching is a standard technique in image processing. It is aimed at bringing the density distribution of an image to an ideal distribution, thereby improving the image quality. The first attempt at modifying the electron-density distribution was that by Hoppe & Gassman (1968), who proposed the `3–2' rule. The electron density was first normalized to a maximum of 1 and modified by imposing positivity. Subsequently, the electron density was modified by $[\rho_{\rm mod} = 3\rho^{2} - 2\rho^{3}]$ . Podjarny & Yonath (1977) used the skewness of the density histogram as a measure of quality of the modified map. Harrison (1988) used a Gaussian function as the ideal histogram in his histogram-specification method for protein phase refinement and extension. The choice of the Gaussian function as the ideal electron-density distribution was based on theoretical arguments instead of experimental evaluation. The Gaussian function was also made independent of resolution. Lunin (1988) used the electron-density distribution to retrieve the values of low-angle structure factors whose amplitudes had not been measured during an X-ray experiment. The electron-density distribution was thought to be structure specific and was derived from a homologous structure. Moreover, the histogram was derived from the entire unit cell, including both the protein and the solvent. Zhang & Main (1988) systematically examined the electron-density histogram of several proteins and found that the ideal density histogram is dependent on resolution, the overall temperature factor and the phase error. It is, however, independent of structural conformation. The sensitivity to phase error suggests that the density histogram could be used for phase improvement. The structural conformation independence made it possible to predict the ideal histogram for unknown structures.

References

Harrison, R. W. (1988). Histogram specification as a method of density modification. J. Appl. Cryst. 21, 949–952.Google Scholar

Hoppe, W. & Gassmann, J. (1968). Phase correction, a new method to solve partially known structures. Acta Cryst. B24, 97–107.Google Scholar

Lunin, V. Yu. (1988). Use of the information on electron density distribution in macromolecules. Acta Cryst. A44, 144–150.Google Scholar

Podjarny, A. D. & Yonath, A. (1977). Use of matrix direct methods for low-resolution phase extension for tRNA. Acta Cryst. A33, 655–661.Google Scholar

Zhang, K. Y. J. & Main, P. (1988). Histogram matching as a density modification technique for phase refinement and extension of protein molecules. In Improving protein phases, edited by S. Bailey, E. Dodson & S. Phillips. Report DL/SCI/R26, pp. 57–64. Warrington: Daresbury Laboratory.Google Scholar

International Tables for Crystallography (2006). Vol. F. ch. 15.1, p. 314