The Hydrophobic Solvation Energies of Molecular-Scale Cavities Depend on the Detailed Structure of the Molecular Surface

Both the energy ($\Delta G_{\mathrm{vdw}}$) of inserting an uncharged molecular cavity into solution by turning on the Lennard-Jones interactions between the solute and solvent and the energy ($\Delta G_{\mathrm{rep}}$) of inserting a nearly hard cavity into solution have often been assumed to increase linearly with the solvent-accessible surface area ($A$), in analogy with the energy of forming macroscopic cavities in solution. Because these energies are assumed to increase with $A$, they have often been assumed to drive protein collapse during folding. However we have shown that for molecular-scale cavities neither of these energies are simple linear functions of $A$. Additionally, for both alanine and glycine peptides we have shown that $\Delta G_{\mathrm{vdw}}$ decreases with $A$, implying that $\Delta G_{\mathrm{vdw}}$ opposes folding for these systems. We also show that assuming that $\Delta G_{\mathrm{rep}}$ is linear in $A$ for large molecules but linear in the solvent-accessible volume ($V$) for small molecules is inconsistent with our findings. Any theory that can accurately predict $\Delta G_{\mathrm{vdw}}$ or $\Delta G_{\mathrm{rep}}$ will have to consider the details of the molecular shape rather than relying on coarse measures, such as $A$ and $V$.