Solvation Thermodynamics from the Perspective of Endpoints DFT

Abstract

Solvation thermodynamics is concerned with the evaluation and physical interpretation of solvation free energies. Endpoints DFT provides a framework for computing solvation free energies by combining molecular simulations with a version of the classical density-functional theory of solutions which focuses on ω, the indirect (solvent-mediated) part of the solute-solvent potential of mean force (indirect PMF). The simulations are performed at the endpoints of a hypothetical charging process which transforms the solvent density from the pure liquid state to that of the solution state. The endpoints DFT expression for solvation free energy can be shown to be equivalent to the standard expression for which the key quantity is the direct correlation function, but it has the advantage that the indirect term ω is more focused on the change in solvent-solvent correlations with respect to the pure liquid as the solute is inserted into the solution. In this Perspective, we review recent developments of endpoints DFT, highlighting a series of papers we have written together beginning in 2017. We emphasize the importance of dimensionality reduction as the key to the evaluation of endpoints DFT expressions and present a recently developed, spatially resolved version of the theory. The role of interfacial water at certain positions which stabilize or destabilize a solute in solution can be analyzed with the spatially resolved version, and it is of considerable interest to investigate how changes in solvation affect protein-ligand binding and conformational landscapes from an endpoints DFT perspective. Endpoints DFT can also be employed in materials science; an example involving the rational design strategy for polymer membrane separation is described. The endpoints DFT method is a scheme to evaluate the solvation free energy by introducing approximations to integrate the classical density functional over a charging parameter. We have further proposed a new functional which captures the correct dependence of the indirect PMF ω at both endpoints of the charging process, and we review how it might be employed in future work.

Figure 1:

ΔΔG_predict based on eq 25 versus ΔΔG_DDM using double decoupling method from 12 congeneric ligand pairs. The displaed water molecules are located at binding sites on the surface of coagulation factor Xa (FXa), Streptavidin, and the mouse major urinary protein (MUP). Reprinted (adapted) with permission from Ref.[37]. Copyright (2018) American Chemical Society.

Figure 2:

Correlations of the total free energy of hydration of alanine dipeptide against the partial contribution from the excluded-volume and first-shell regions of C₁, N₁, C₂, C₃, and N₂ atomic sites and that from the excluded-volume to second-shell regions. A single point in the right panel corresponds to a single conformation of alanine dipeptide shown in the left panel. With the linear regression against the total sum, the slope is 0.54 and 0.75 for the sums to the first and second shells, respectively, with correlation coefficients of 0.99 and 1.00.

Figure 3:

Polymers examined in Ref.[53], and the correlation plot between the computed and experimental free energies Δμ of water dissolution. The dashed line in the right figure stands for the least-square fit of the computed Δμ to the experimental, and its slope is 1.0 with an intercept of 0.5 kcal/mol.