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Structure Factors and Electron Density

In a typical crystallographic experiment, a crystal is subjected to a narrow beam of intense X-rays, and the diffraction pattern is observed with a detector or a sheet of film. This pattern forms a characteristic array of spots, commonly referred to as reflections. Crystallographers measure the intensity of these reflections and use the information to determine the distribution of electrons in the crystal. The result is a map of the crystal that shows the distribution of electrons at each point, which may then be interpreted to find coordinates for each atom in the crystallized molecules.

Two pieces of information are needed to create an electron density map: the amplitude of X-rays in each reflection and the phase of X-rays in each reflection. Together, this information is used to define a complex number, termed the structure factor, which is used to calculate the electron density map. In a typical experiment, the amplitudes of the structure factors are obtained by measurement of the reflection intensities. The phases, however, are more tricky to measure, and crystallographers have developed several methods to estimate them.

The traditional method for estimating phases, termed isomorphous replacement, is to add a few electron-dense atoms, such as metal ions, to the crystal, and compare the diffraction pattern with similar crystals that do not include the heavy atoms. Looking at the differences, researchers can find the location of the heavy atoms, and then estimate phases based on their locations. Molecular replacement is also commonly used to estimate phases. In this case, the researcher uses a previously-solved structure of the molecule as a starting model, and calculates phases based on it. More recently, anomalous scattering of X-rays has become a common method for determining phases. In these cases, special atoms like selenium or bromine are added to the molecules, and the wavelength of the X-rays is carefully tuned to give anomalous scattering. By looking at small differences in symmetrical reflections in the diffraction pattern, the phases may be estimated directly.

For many of the structures in the PDB, the authors have deposited the primary crystallographic data along with the atomic model that was solved using the data. These data files may be download from Structure Summary pages. The files include a list of all of the reflections that were used in the structure determination. A typical file includes the h, k, and l indices for each reflection, a measure of the amplitude or intensity of the reflection, and often a measure of the standard uncertainty (sigma) of the reflection. The file often may include other pieces of information, such as a flag to identify reflections used for free R-value calculations or other details of the experiment.

Tip: You will find selenomethionine amino acids in many recent structures of proteins. This is a common way that researchers add selenium to proteins for use in determining phases by anomalous scattering. Since the selenium is chemically similar to sulfur, we expect that the protein structure will be similar to the form with the normal methionine amino acids.


The left image shows one plane through the three-dimensional diffraction pattern of a DNA crystal. Each spot has a characteristic intensity that is related to the distribution of electrons in the crystal. For instance, the row of dark spots 10 rows above and below the center are characteristic of the stacking of bases in DNA. The right image shows the electron density derived from the diffraction pattern of PDB entry 6bna, created using the Astex Viewer. The view shows one base pair with a guanine and a bromocytosine. The blue contours enclose most of the electrons, and show the overall shape of the bases, and the yellow contours enclose only regions with high electron density, such as the electron-dense bromine atom.