Dynamics of a protein and water molecules surrounding the protein: hydrogen-bonding between vibrating water molecules and a fluctuating protein

Internal and rigid-body motions of bovine pancreatic trypsin inhibitor (BPTI) and of water molecules surrounding the BPTI are studied in a vicinity of an energy minimum using a normal mode analysis proposed as the independent molecule model. Water's rigid-body motion is predominant in comparison to its internal motions. We have derived information about the relationship between the magnitude of a thermal ellipsoid of an H-bonding atom and the anisotropy of its ellipsoid, and the relationship between the magnitude of the ellipsoid and the H-bond strength. We see a relationship between vibrational frequencies (assuming rigid-body motion of the water molecules) and the H-bond strength of the water taking part in this H-bonding. Analyzing the H-bond strength, we found that a hydrogen in water is likely to H-bond to oxygen in the protein, whereas an oxygen in water has a less strong preference to H-bond to the protein. For water molecules acting as the hydrogen acceptor, strong H-bonding has longer lifetimes than weak H-bonding.