Most of the information that we have on protein structure comes from x-ray crystallography. We'll briefly discuss some of the mathematics involved these steps. The basic structure of a crystal is that of a lattice. The symmetry of the lattice has the crystallographic restriction . The simplest rule of diffraction is Braggs law .
Fourier analysis arises because the electron density function is periodic .
Even for analyzing real valued functions, it is very convenient to use Fourier sums in complex form. The electron density function is a periodic function of three variables. Fourier sums for functions of three variables are similar to those for one variable. The basic mathematical problem in x-ray crystallography is to find the arguments of the complex Fourier coefficients. This is called the phase problem .