Examining the Assumptions Underlying Continuum-Solvent Models

Continuum-solvent models (CSMs) have successfully predicted many quantities, including the solvation-free energies (ΔG) of small molecules, but they have not consistently succeeded at reproducing experimental binding free energies (ΔΔG), especially for protein-protein complexes. Several CSMs break ΔG into the free energy (ΔG_vdw) of inserting an uncharged molecule into solution and the free energy (ΔG_el) gained from charging. Some further divide ΔG_vdw into the free energy (ΔG_rep) of inserting a nearly hard cavity into solution and the free energy (ΔG_att) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein-protein complexes neither ΔG_rep nor ΔG_vdw was linear in the solvent-accessible area A, as assumed in many CSMs, and the corresponding components of ΔΔG were not linear in changes in A. We show that linear response theory (LRT) yielded good estimates of ΔG_att and ΔΔG_att, but estimates of ΔΔG_att obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of ΔG_el differed by more than 100 kcal/mol from the explicit solvent model's (ESM's) predictions, and its estimates of the corresponding component (ΔΔG_el) of ΔΔG differed by more than 10 kcal/mol. Finally, the Poisson-Boltzmann equation produced estimates of ΔG_el that were correlated with those from the ESM, but its estimates of ΔΔG_el were much less so. These findings may help explain why many CSMs have not been consistently successful at predicting ΔΔG for many complexes, including protein-protein complexes.