Distribution Analysis of the Variation of B-Factors of X-ray Crystal Structures: Temperature and Structural Variations in Lysozyme

The B-factor (isotropic temperature factor) data for X-ray structures of hen egg-white lysozyme from the study of Young et al. (Young, Dewan, Nave, and Tilton J. Appl. Cryst. 1993, 26, 309-319) potentially contain information about the relative contributions of static and dynamic variation to these factors. The six structures of the protein were obtained at two widely different temperatures (100 and 298 K), with two crystal forms (monoclinic and tetragonal) and other experimental differences. In addition, the monoclinic lysozyme crystals with two molecules per asymmetric unit allow direct examination of variation between structures determined under identical conditions at both temperatures. The B-factors from these structures all have complex distribution functions as might be expected considering all of the influences that these values must reflect. The empirical cumulative distribution functions (eCDF's) of these data show that they are representative of complex, multicomponent distributions. Distribution analysis using the DANFIP procedure (Wampler, Anal. Biochemistry 1990, 186, 209-218) of the data sets reveals that they can be modeled as four to six Gaussian subpopulations, that these subpopulations do not correlate with specific atom types, specific amino acid residues or fixed locations in the structure. While they do seem to correlate with localized groupings of atoms, these grouping vary from structure to structure even within the same crystal under the same conditions. Temperature seems to have a global effect in this case, but it is clear that other factors including experimental error influence the distribution of B-factors within a given structure. This analysis also helps explain the oft observed lack of atomic level correlation between experimental B-factors and calculated mean square displacements from molecular dynamics simulations.