Application of scaled particle theory to model the hydrophobic effect: implications for molecular association and protein stability.

The energetics of alkane dissolution and partition between water and organic solvent are described in terms of the energy of cavity formation and solute-solvent interaction using scaled particle theory. Thermodynamic arguments are proposed that allow comparison of experimental measurements of the surface area with values calculated from an all-atom representation of the solute. While the surface tension relating to the accessible surface is shape dependent, it is found that for the molecular surface it is not. This model rationalizes the change in surface tension between the microscopic (20-30 cal/mol/A2) and macroscopic (70-75 cal/mol/A2) regimes without the need to invoke Flory-Huggins theory or to apply other corrections. The difference in the values arises (i) to a small extent as a result of the curvature dependence of surface tension and (ii) to a large extent due to the difference in the molecular surface derived from the experiment and that calculated from an extended all-atom model. The model suggests that the primary driving force for alkane association in water is due to the tendency of water to reduce the solute cavity surface. It is argued that to model the energetics of alkane association, the surface tension should be related to the molecular surface (rather than the accessible surface) with a surface tension near the macroscopic limit for water. This model is compared with results from theoretical simulations of the hydrophobic effect for two well-studied systems. The implications for antibody-antigen interactions and the effect of hydrophobic amino acid deletion on protein stability are discussed. The approach can be used to model the solute cavity formation energy in solution as a first step in the continuum modelling of biomolecular interactions.