On the use of normal modes in thermal parameter refinement: theory and application to the bovine pancreatic trypsin inhibitor

A method is presented whereby the amplitude coefficients of molecular normal modes of vibration are treated as independent variables in the treatment of thermal effects in X-ray diffraction, and applied to the bovine pancreatic trypsin inhibitor, form II (P2₁2₁2₁, a = 74.1, b = 23.4, c = 28.9 Å). It is shown that the description of molecular motion furnished by 892 isotropic temperature factors may be largely reproduced using only 19 molecular thermal parameters from which anisotropic temperature factors may be synthesised for every atom. The method shows that motions and/or disorders external to each molecule are the largest single source of apparent motion, and that the internal motions are comparable to those predicted by Levitt, Sander & Stern [J. Mol. Biol. (1985). 181, 423-427] at 300 K.