Analysis of temperature factor distribution in high‐resolution protein structures

Abstract

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 @'-factor) at the Ccu atoms show remarkably characteristic frequency distribution. In all of the 1 I O 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.Keywords: accessibility; Gaussian functions; proteins; statistics; temperature factors Statistical analysis has formed a large component of the research efforts put forth to understand protein structure and function, due to the enormous diversity and complexity of their structures (Johnson et al., 1994). Statistical approaches have been developed to predict the secondary structure from the primary sequence (Chou & Fasman 1974; Gamier et al., 1978; Gamier, 1990) and for testing the compatibility of model tertiary folds for a given sequence of unknown structure (Bowie et al., 1991;Luthy et al., 1991Luthy et al., , 1992. A variety of statistical analyses has also been performed on conformational states of main chains and side chains (Dunbrack & Karplus, 1993), hydrogen bonding (Ippolito et al., 1990), water structure (Thanki et al., 1991), and topological features of secondary structural elements (Levitt & Chothia, 1976;Taylor & Thomton, 1983). Most of these analyses are concerned with protein structure and conformation. In contrast, much less attention has been paid to the atomic displacement parameter (Trueblood et al., 1996), B-values obtained from X-ray crystal structure analysis of proteins. The efforts in this direction have been concerned mainly with optimizing methods for prediction of antigenicity and flexibility of different polypeptide segments of a protein (Ragone et al., Reprint requests to: M.R.N. Murth...

Evaluating Free Energies of Binding and Conservation of Crystallographic Waters Using SZMAP

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