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Crystals, X-rays and ProteinsComprehensive Protein Crystallography$
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Dennis Sherwood and Jon Cooper

Print publication date: 2010

Print ISBN-13: 9780199559046

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199559046.001.0001

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The phase problem and the Patterson function

The phase problem and the Patterson function

(p.431) 12 The phase problem and the Patterson function
Crystals, X-rays and Proteins

Dennis Sherwood

Jon Cooper

Oxford University Press

This chapter demonstrates that the experimental observable in diffraction analysis is the intensity of each diffraction spot which provides only the amplitude of the corresponding structure factor and not its phase — the fundamental phase problem in crystallography. To obtain an image of the molecule forming a crystal we need to calculate a Fourier transform, which requires that we know both the amplitude and phase of each structure factor. Nevertheless, very important information can be derived by calculating a ‘phase-less’ Fourier transform of the intensities alone, which is known as the Patterson function. Although this function is inherently more complex than an electron density map since it displays all inter-atomic vectors, certain sections of the Patterson function, known as Harker sections, can yield information on the positions of the most electron-rich atoms within the crystal. The Patterson function is exploited in most methods of the solving the phase problem for proteins and simple rules for the interpretation of a Patterson function are derived.

Keywords:   Fourier transform, Patterson function, Harker lines, Harker sections, Patterson map symmetry, Patterson maps

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