Crucial importance of translational entropy of water in pressure denaturation of proteins.

We present statistical thermodynamics of pressure denaturation of proteins, in which the three-dimensional integral equation theory is employed. It is applied to a simple model system focusing on the translational entropy of the solvent. The partial molar volume governing the pressure dependence of the structural stability of a protein is expressed for each structure in terms of the excluded volume for the solvent molecules, the solvent-accessible surface area (ASA), and a parameter related to the solvent-density profile formed near the protein surface. It is argued that the entropic effect originating from the translational movement of water molecules plays critical roles in the pressure-induced denaturation. We also show that the exceptionally small size of water molecules among dense liquids in nature is crucial for pressure denaturation. An unfolded structure, which is only moderately less compact than the native structure but has much larger ASA, is shown to turn more stable than the native one at an elevated pressure. The water entropy for the native structure is higher than that for the unfolded structure in the low-pressure region, whereas the opposite is true in the high-pressure region. Such a structure is characterized by the cleft and/or swelling and the water penetration into the interior. In another solvent whose molecular size is 1.5 times larger than that of water, however, the inversion of the stability does not occur any longer. The random coil becomes relatively more destabilized with rising pressure, irrespective of the molecular size of the solvent. These theoretical predictions are in qualitatively good agreement with the experimental observations.