Protein Crystallography: A Concise Guide by Eaton E. Lattman;Patrick J. Loll

By Eaton E. Lattman;Patrick J. Loll

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C ∆ 2 can also be written (A + iB)(A – iB), where A – iB is called the complex conjugate of C, often written C *. The polar coordinate expression for C is Ce ia, where C is the amplitude (vector length) and a is the phase (the angle the vector makes with the x axis). C * is Ce–ia. This notation is particularly suitable for crystallography, because we measure amplitude and phase separately. When we measure the intensity of a reflection we are measuring ∆F ∆2, where F = Fe ia. The missing phase that cannot be measured directly in the crystallographic experiment is a.

Instead, the crystal must be moved into di√erent orientations to allow all the reflections to be observed. In the early twentieth century, the father-and-son team of William and William Lawrence Bragg developed a simple, semiquantitative model to explain di√raction from three-dimensional crystals. In the Bragg model the crystal contains families of equally spaced parallel planes running in di√erent directions. 1. The Bragg plane families are named by three integers, h, k, and l, called Miller indices.

Crystallography Made Crystal Clear, 2nd edition, by Gale Rhodes (Academic Press, New York, 2003) is a clear and well-constructed paperback. Good figures; gentle math. Outline of Crystallography for Biologists by David Blow (Oxford University Press, Oxford, 2002) is written by one of the creators of protein crystallography. Makes extensive use of the convolution operation to explain many crystallographic points. This is a powerful tool, but it comes with a learning curve. Wonderful physical insights.

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