Phase Problem in X-ray Crystallography, and Its Solution

X-ray diffraction provides one of the most important tools for examining the three-dimensional (3D) structure of biological macromolecules. The physics of diffraction requires that in order to resolve features of atomic structure it is necessary to employ radiation with a wavelength of the order of atomic spacing or smaller. Xrays have suitable wavelength, and interact with the electrons of the atoms. However, the interaction between X-rays and electrons is weak, and such energetic radiation causes ionization of the constituent atoms of the molecule, damaging the molecule under study. Therefore it is necessary to examine a vast number of molecules simultaneously: This is achieved by using a crystal containing many copies of a molecule in a regular lattice. When a crystal is exposed to X-rays, the radiation is scattered to form a diffraction pattern. The X-rays are scattered from every point in the crystal, with a strength in proportion to the concentration of electrons at that point. All the X-rays scattered along any particular direction interfere with each other, giving rise to detailed features in the diffraction pattern that depend on the arrangement of atoms in the crystal.Analysis of thediffractionpatternmay therefore allow the arrangement of atoms to be deduced. The intensity of the radiation scattered in any particular direction from the crystal depends on whether X-rays scattered along that direction interfere constructively or destructively. This in turn depends on the position and spacing of electron density features (in particular atoms) within the crystal. Examples of constructive interference, leading to strong scattering along a particular direction, and of destructive interference, leading to weak scattering, are shown in Figure 1. The crystal, by its nature, contains a regular lattice of identical molecules, and thus every feature of the electron density will be repeated at regular intervals. The basic repeating unit from which the crystal is constructed is called the unit cell. It is convenient to define crystal axes a, b and c defining the unit cell in three dimensions. Scattering along directions reflecting the lattice repeat will be reinforced by every repeat of the unit cell, and will be strong; scattering along all other directions will be weak. As a result, the full diffraction pattern of the crystal is a pattern of spots, forming a three-dimensional lattice with Article