Examining the Assumptions Underlying Continuum-Solvent Models

Abstract

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 (ΔGvdw) of inserting an uncharged molecule into solution and the free energy (ΔGel) gained from charging. Some further divide ΔGvdw into the free energy (ΔGrep) of inserting a nearly hard cavity into solution and the free energy (ΔGatt) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein–protein complexes neither ΔGrep nor ΔGvdw 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 ΔGatt and ΔΔGatt, but estimates of ΔΔGatt obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of ΔGel differed by more than 100 kcal/mol from the explicit solvent model’s (ESM’s) predictions, and its estimates of the corresponding component (ΔΔGel) of ΔΔG differed by more than 10 kcal/mol. Finally, the Poisson–Boltzmann equation produced estimates of ΔGel that were correlated with those from the ESM, but its estimates of ΔΔGel 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.

Simple models for nonpolar solvation: Parameterization and testing

“…A second effect is the higher density of Lennard‐Jones centers within a protein, compared to bulk solvent, leading to a systematic contribution to binding free energies. Following this picture, and analogous to the Lennard‐Jones model, it is tempting to divide the nonpolar contributions to solvation into (a) a repulsive short‐range interaction that occurs when one forms a solute‐shaped cavity and (b) the weak, attractive dispersion interactions between the solute atoms and the solvent …”

“…Following this picture, and analogous to the Lennard-Jones model, it is tempting to divide the nonpolar contributions to solvation into (a) a repulsive short-range interaction that occurs when one forms a solute-shaped cavity and (b) the weak, attractive dispersion interactions between the solute atoms and the solvent. [1,15,16] The above Lennard-Jones-like nonpolar contribution, along with GB provide a practical basis to develop and parameterize implicit solvent models. One model that is commonly used treats the polar component with a GB term and the nonpolar components with a surface area (SA) term.…”

Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points

“…However, because implicit solvent models perform this averaging in an approximate way, the accuracies of their predictions can be difficult to evaluate. [18,[22][23][24][25][26] In a recent article, we proposed a new implicit/explicit thermodynamic cycle that takes advantage of the speed of implicit solvent simulations but is designed to give the same answer as exhaustive sampling in explicit solvent. If a conformational transition of interest occurs faster in implicit solvent or vacuum or the simulation is simply faster in an implicit solvent model because of the many fewer degrees of freedom in the system, then we can estimate the desired free energy change on this auxiliary (implicit solvent or vacuum) free energy surface and obtain the free energy difference on our target (explicit solvent) free energy surface by connecting the two free energy surfaces with focused free energy calculations.…”

Reconciling the understanding of ‘hydrophobicity’ with physics-based models of proteins

“…They concluded that these observations imply that γ rep should be greater for protein molecules than for alkanes because the average radii of curvature of proteins are larger than those of alkanes, and this conclusion would not be affected by noting that the proteins contain regions of negative curvature because such regions would also be associated with a larger γ rep in this model [6]. However, more recent studies [132, 133, 135] found that γ rep appears to decrease with A . Reconciling these findings would be difficult.…”

“…The integrand (〈∂ U att (0)/∂ λ 〉 λ ) of the integral used to compute the attractive component (Δ G att ) of the nonpolar solvation free energy as a function of λ for a barnase-barstar complex taken from a recent study [135]. …”