Covariance and correlation estimation in electron-density maps

Acta Crystallographica. Section A, Foundations of Crystallography
Angela AltomareRosanna Rizzi

Abstract

Quite recently two papers have been published [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218; Giacovazzo et al. (2011). Acta Cryst. A67, 368-382] which calculate the variance in any point of an electron-density map at any stage of the phasing process. The main aim of the papers was to associate a standard deviation to each pixel of the map, in order to obtain a better estimate of the map reliability. This paper deals with the covariance estimate between points of an electron-density map in any space group, centrosymmetric or non-centrosymmetric, no matter the correlation between the model and target structures. The aim is as follows: to verify if the electron density in one point of the map is amplified or depressed as an effect of the electron density in one or more other points of the map. High values of the covariances are usually connected with undesired features of the map. The phases are the primitive random variables of our probabilistic model; the covariance changes with the quality of the model and therefore with the quality of the phases. The conclusive formulas show that the covariance is also influenced by the Patterson map. Uncertainty on measurements may influence the covariance, particularly in the final ...Continue Reading

References

Apr 21, 2010·Acta Crystallographica. Section A, Foundations of Crystallography·Maria Cristina BurlaGiampiero Polidori
Apr 5, 2011·Acta Crystallographica. Section D, Biological Crystallography·Henry van den BedemAshley M Deacon
Apr 14, 2011·Acta Crystallographica. Section A, Foundations of Crystallography·Carmelo Giacovazzo, Annamaria Mazzone
Apr 14, 2011·Acta Crystallographica. Section A, Foundations of Crystallography·Maria Cristina BurlaDritan Siliqi
Jun 23, 2011·Acta Crystallographica. Section A, Foundations of Crystallography·Carmelo GiacovazzoGiuliana Comunale

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