Rotation of structural water inside a protein: Calculation of the rate and vibrational entropy of activation

Water molecules buried inside a protein are often considered as an integral part of the structure and are increasingly used as NMR probes to study the dynamics of proteins (Denisov, V.; Peters, J.; Horlein, H. D.; Halle, B. Nat. Struct. Biol. 1996, 3, 505). The present calculations give new insights into the mobility of such structural water. Reaction path calculations using conjugate peak refinement (Fischer, S,; Karplus, M. Chem. Phys. Lett. 1992, 194, 252) are carried out to compute the transition state and activation energy (9.7 kcal mol(-1)) for the rotation of a water molecule buried in the protein bovine pancreatic trypsin inhibitor. These are compared to the values calculated (10-12.3 kcal mol(-1)) for the same process in ice, for which the experimental value has been determined (12.8 +/- 0.9 kcal mol(-1)). The process, which results in the interchange of the two water hydrogens, is similar in both systems. It is not a simple C2-flip of the buried water, but a complex motion involving two successive rotations around orthogonal axes. A normal-mode analysis performed on the ground and transition states of the protein enables the correction for the vibrational entropy to be included in the derivation of the rotational correlation time (45 ns) of the buried water. Vibrational frequencies up to 620 cm(-1) are found to contribute, thus requiring the inclusion of quantum effects, A fluctuation frequency of 20-50 cm(-1) along the curvilinear reaction path is derived, which leads to a vibrational entropy of activation of 8.6 cal mol(-1) K-1.