Theory of X-ray Diffraction by a Crystal

Abstract

The best way to learn protein X-ray diffraction is by practical work in the laboratory. However, it would be very unsatisfying to perform the experiments without understanding why they have to be done in such and such a way. Moreover, at several stages in the determination of protein structures, it is necessary to decide what the next step should be. For instance, after growing suitable crystals and soaking these crystals in solutions of heavy atom reagents, applying the isomorphous replacement method, how do you obtain the positions of the heavy atoms in the unit cell and, if you do have them, how do you proceed? Questions such as these can be answered only if you have some knowledge of the theoretical background of protein X-ray crystallography. This is presented in this chapter. A slow path will be followed, and a student with a minimal background in mathematics but the desire to understand protein X-ray crystallography should be able to work through the chapter. A working knowledge of differentiation and integration is required. If you further accept that an X-ray beam can be regarded as a wave that travels as a cosine function and if you know what a vector is, you have a good start. Derivations and explanations that are not absolutely necessary to follow the text are set off within rules; these can be skipped, if you want.