Reconciling the understanding of 'hydrophobicity' with physics-based models of proteins

The idea that a 'hydrophobic energy' drives protein folding, aggregation, and binding by favoring the sequestration of bulky residues from water into the protein interior is widespread. The solvation free energies (ΔG_solv) of small nonpolar solutes increase with surface area (A), and the free energies of creating macroscopic cavities in water increase linearly with A. These observations seem to imply that there is a hydrophobic component (ΔG_hyd) of ΔG_solv that increases linearly with A, and this assumption is widely used in implicit solvent models. However, some explicit-solvent molecular dynamics studies appear to contradict these ideas. For example, one definition (ΔG_LJ) of ΔG_hyd is that it is the free energy of turning on the Lennard-Jones (LJ) interactions between the solute and solvent. However, ΔG_LJ decreases with A for alanine and glycine peptides. Here we argue that these apparent contradictions can be reconciled by defining ΔG_hyd to be a near hard core insertion energy (ΔGrep), as in the partitioning proposed by Weeks, Chandler, and Andersen. However, recent results have shown that ΔGrep is not a simple function of geometric properties of the molecule, such as A and the molecular volume, and that the free energy of turning on the attractive part of the LJ potential cannot be computed from first-order perturbation theory for proteins. The theories that have been developed from these assumptions to predict ΔG_hyd are therefore inadequate for proteins.