Dissecting the vibrational entropy change on protein/ligand binding: Burial of a water molecule in bovine pancreatic trypsin inhibitor

Using normal-mode analysis, the vibrational entropy change on the burial of a crystallographically well-ordered water molecule in bovine pancreatic trypsin inhibitor (BPTI) is dissected. The vibrational entropy content of the complex is 13.4 cal mol(-1) K-1 higher than that of the unbound protein. A detailed analysis is performed of how the translational and rotational degrees of freedom of the isolated water molecule are transformed into vibrational modes in the complex. This process is shown to be well described by a model of the complex in which the water molecule librates in a rigid protein cage. These librational modes contribute 9.4 cal mol(-1) K-1 to the entropy change. The remaining 4 cal mol(-1) K-1 arises from increased protein flexibility due to softening of the delocalized modes, mostly in the frequency range below 50 cm(-1). The dominant librational entropy effect suggests a method by which an estimation of the vibrational contribution to ligand binding can be efficiently computed.