Analysis of temperature factor distribution in high-resolution protein structures

The temperature factors obtained from X-ray refinement of proteins at high resolution show large variations from one structure to another. However, the B-values expressed in units of standard deviation about their mean value (B'-factor) at the C alpha atoms show remarkably characteristic frequency distribution. In all of the 110 proteins examined in this study, the frequency distribution exhibited a bimodal distribution. The peaks in the B'-factor frequency distribution occur at -1.1 and 0.4 for a bin size of 0.5. The peak at lower temperature factor corresponds largely to buried residues, whereas the peak at larger value corresponds to exposed residues. The distribution could be accurately described as a superposition of two Gaussian functions. The parameters describing the distribution are therefore characteristic of protein structures. The frequency distribution for a given amino acid over all the proteins also shows a similar bimodal distribution, although the areas under the two Gaussians differ from one amino acid to another. The area under the frequency distribution curve for any interval in B'-factor represents the propensity of the amino acid to occur in that interval. This propensity is related both to the hydrophilicity/hydrophobicity of the residue and the tendency of the residue to impose a different degree of rigidity on the polypeptide chain. The frequency distribution of stretches of high B'-factors departs appreciably from that expected for a random distribution. The correlation in the B-values of sequentially proximal residues is probably responsible for the bimodal distribution.