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Temperature factor

Atoms vibrate around an equilibrium position, and therefore X-rays do not meet identical atoms on exactly the same position in successive unit cells. This is similar to an X-ray beam meeting a smeared atom on a fixed position, the size of the atom being larger if the thermal vibration is stronger with the effect of diminishing the scattered X-ray intensity. Therefore, the atomic scattering factor of the atoms must be multiplied by a temperature-dependent factor. In the simple case in which the components of vibration are the same in all directions, the vibration is called isotropic. The thermal parameter B is related to the mean square displacement u^2 of the atomic vibration:


For anisotropic vibration, the temperature factor is much more complicated. In this case, u^2 depends on the direction of S. However, it is common to work with isotropic temperature factors for the individual atoms. This is because of the restricted resolution and, consequently, the limited number of data. In a normal situation one is restricted to isotropic temperature factor, which give four total unknown parameters per atom: x, y, z, and B. For a protein with 2000 atoms in the asymmetric unit, 8000 unknown parameters must be determined. To obtain a reliable structure, the number of measured data (reflection intensities) should well exceed the number of parameters. Because of the restricted number of data, this condition is fulfilled for the determination of isotropic, but not anisotropic, temperature factors. Average values for B in protein structures range from as low as a few square Å to 30Å2 in well-ordered structures.Highest values are found in more or less flexible surface loops.

The temperature factor is a consequence of the dynamic disorder in the crystal caused by the temperature-dependent vibration of the atoms in the structure. Protein crystals have also static disorder (molecules, or parts of molecules, in different unit cells do not occupy exactly the same position and do not have exactly the same orientation). The effect of these two kind of disorder cannot be distinguished, unless intensity data at different temperatures are collected.
Crystallographic models with isotropic B-factors describe every atom in the structure using 5 numbers: 3 coordinates (x, y, x), occupancy (q), and B-factor. "An atom (known from chemical information to be present in the structure) spends the q fraction of time in the vicinity of (x, y, z), with the probability to find the atom at a certain distance from it falling off according to the normal distribution whose width is defined by the B-factor". A B-factor=200 corresponds to rmsd of 1.6 Å, which transforms to "atom spends 95% of time inside a sphere of 6.4 Å in diameter"

B-factors/ccp4b/Ian Tickle 06/01/09:
Whenever I see a significant difference (say > 10 Ang.^2) between the average B factor of the ligand and the average B factor of the protein atoms in the binding site I suspect that partial occupancy of the ligand is the true explanation

About high B-factors (from phenixbb):
The Wilson B is not "an average B calculated from the reflection". It is an estimate of what the B factor of your structure would be if all the individual B factors were equal to each other - and of course they are not. While it is an interesting property of a set of diffraction intensities it is not an estimate of the average of the individual B factors in your PDB file. The main difference, in effect, is that the largest B factors for atoms in your crystal are ignored in the Wilson B calculation. This omission results in the Wilson B always being lower than the mean of the individual B factors.