Rotation of Structural Water inside a Protein: Calculation of the Rate and Vibrational Entropy of Activation
Received: September 10, 1997
Abstract:
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.
In Final Form: December 10, 1997