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 ($\Delta G_{\text{solv}}$) 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 ($\Delta G_{\text{hyd}}$) of $\Delta G_{\text{solv}}$ 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 ($\Delta G_{\text{LJ}}$) of $\Delta G_{\text{hyd}}$ is that it is the free energy of turning on the Lennard–Jones (LJ) interactions between the solute and solvent. However, $\Delta G_{\text{LJ}}$ decreases with A for alanine and glycine peptides. Here we argue that these apparent contradictions can be reconciled by defining $\Delta G_{\text{hyd}}$ to be a near hard core insertion energy ($\Delta G_{\text{rep}}$), as in the partitioning proposed by Weeks, Chandler, and Andersen. However, recent results have shown that $\Delta G_{\text{rep}}$ 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 $\Delta G_{\text{hyd}}$ are therefore inadequate for proteins. (topical review)