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Full‐matrix least‐squares refinement of lysozymes and analysis of anisotropic thermal motion

Crystal structures of turkey egg lysozyme (TEL) and human lysozyme (HL) were refined by full‐matrix least‐squares method using anisotropic temperature factors. The refinement converged at the conventional R‐values of 0.104 (TEL) and 0.115 (HL) for reflections with Fo > 0 to the resolution of 1.12 Å and 1.15 Å, respectively. The estimated r.m.s. coordinate errors for protein atoms were 0.031 Å (TEL) and 0.034 Å (HL). The introduction of anisotropic temperature factors markedly reduced the R‐value but did not significantly affect the main chain coordinates. The degree of anisotropy of atomic thermal motion has strong positive correlation with the square of distance from the molecular centroid. The ratio of the radial component of thermal ellipsoid to the r.m.s. magnitude of three principal components has negative correlation with the distance from the molecular centroid, suggesting the domination of libration rather than breathing motion. The TLS model was applied to elucidate the characteristics of the rigid‐body motion. The TLS tensors were determined by the least‐squares fit to observed temperature factors. The profile of the magnitude of reproduced temperature factors by the TLS method well fitted to that of observed Beqv. However, considerable disagreement was observed in the shape and orientation of thermal ellipsoid for atoms with large temperature factors, indicating the large contribution of local motion. The upper estimate of the external motion, 67% (TEL) and 61% (HL) of Beqv, was deduced from the plot of the magnitude of TLS tensors determined for main chain atoms which were grouped into shells according to the distance from the center of libration. In the external motion, the translational portion is predominant and the contribution of libration and screw motion is relatively small. The internal motion, estimated by subtracting the upper estimate of the external motion from the observed temperature factor, is very similar between TEL and HL in spite of the difference in 54 of 130 amino acid residues and in crystal packing, being suggested to reflect the intrinsic internal motion of chicken‐type lysozymes. Proteins 30:232–243, 1998. © 1998 Wiley‐Liss, Inc.