Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins.

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.