Modeling the Correlation between Z and B in an X-ray Crystal Structure Refinement

We have examined how the refined B-factor changes as a function of Z (the atomic number of a scatterer) at the sulfur site of the [4Fe:4S] cluster of the nitrogenase iron protein by refinement. A simple model is developed that quantitatively captures the observed relationship between Z and B, based on a Gaussian electron density distribution with a constant electron density at the position of the scatterer. From this analysis, the fractional changes in B and Z are found to be similar. The utility of B-factor refinement to potentially distinguish atom types reflects the Z dependence of X-ray atomic scattering factors; the weaker dependence of electron atomic scattering factors on Z implies that distinctions between refined values of B in an electron scattering structure will be less sensitive to the atomic identity of a scatterer than for the case with X-ray-diffraction. This behavior provides an example of the complementary information that can be extracted from different types of scattering studies.