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 (ΔGsolv) 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 (ΔGhyd) of ΔGsolv 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 ΔGhyd 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 ΔGhyd 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 ΔGhyd are therefore inadequate for proteins.