Internal hydration of protein cavities: studies on BPTI

In this paper, we present a theoretical method to calculate the hydration free energies of the protein cavities and clefts. This method is also used to compute the binding probabilities of buried water molecules. Our approach considers an ensemble of potential binding sites located within the protein and water molecules as ligand particles. The free energy to transfer a water molecule from the gas phase to the protein is calculated from the thermodynamic cycle. The protein is viewed as a dielectric continuum and a water molecule is embedded in it. Electrostatic contributions to the energies of bound water molecules and their interaction energies are computed from the solution of the Poisson equation. The nonpolar contribution and the binding entropy change are assumed to be the same for every bound water molecule. The obtained energies are used in the binding polynomial to calculate the constants for the hydration reactions and the hydration free energies. Calculated values are compared with available measurements for the initial steps of the hydration of BPTI (bovine pancreatic trypsin inhibitor) in the gas phase. The obtained energies are also used to calculate the population probabilities of the hydration sites and compute their titration curves. The results of the studies on BPTI demonstrate that an isolated buried water in the small protein cavity binds to the protein with a lower affinity than a cluster of three water molecules in a large protein cleft.