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 int egral 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 calculatio ns give new insights into the mobility of such structural water. React ion path calculations using conjugate peak refinement (Fischer, S,; Ka rplus, 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 experimenta l value has been determined (12.8 +/- 0.9 kcal mol(-1)). The process, which results in the interchange of the two water hydrogens, is simila r 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 s tates of the protein enables the correction for the vibrational entrop y 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 effec ts, A fluctuation frequency of 20-50 cm(-1) along the curvilinear reac tion path is derived, which leads to a vibrational entropy of activati on of 8.6 cal mol(-1) K-1.