Nonlinear temperature dependence of the crystal structure of lysozyme: correlation between coordinate shifts and thermal factors

The static and dynamic structures of human lysozyme at seven different temperatures ranging from 113 to 178 K were investigated by normal-mode refinement of the cryogenic X-­ray diffraction data collected from a single crystal. Normal-mode refinement decomposes the mean-square fluctuations of protein atoms from their average position into the contributions from the internal degrees of freedom, which change the shape of the protein structure, and those from the external degrees of freedom, which generate rigid-body motions in the crystal. While at temperatures below 150 K the temperature dependence of the total mean-square fluctuations shows a small gradient similar to that predicted theoretically by normal-mode analysis, at temperatures above 150 K there is an apparent inflection in the temperature dependence with a higher gradient. The inflection in the temperature dependence at temperatures above 150 K occurs mostly in the external degrees of freedom. Possible causes for the dynamic transition are discussed with respect to the crystal packing and physicochemical properties of crystalline water.