Affine-response model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies

Abstract

Two mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquid-vapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use free-energy perturbation molecular-dynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solute-solvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular "linear response" model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewise-linear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicit-solvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewise-linear response (due to the steric contribution).

Gradient models in molecular biophysics: progress, challenges, opportunities

“…The potential-of-mean-force (PMF) interpretation of continuum models provides the critical bridge allowing modelers to focus exclusively on the solvent response; extensive molecular dynamics simulations can then employ reasonably simple models of solutes in order to investigate deviations from expected continuum behavior [22]. Experiments are reality, of course, and simulations are only theory; to first order, however, today we are in a situation in which the major weaknesses in our continuum theories can be identified using higher-level theory (e.g.…”

“…Molecular dynamics studies do indicate the presence of nonlinear saturation effects at the level of individual water molecules. However, our own experience with testing solvent models against MD simulations [22], suggests to us that for the purpose of computing biomolecule solvation free energies, nonlinear response is often less relevant than nonlocal response. Recently Pettitt et al have introduced a fast electrostatic model based on tabulated solvent charge densities around protein chemical groups, achieving exceptional accuracy, while nevertheless employing a superposition principle that essentially imposes linearity [136].…”

“…In this review we survey theories based on nonlocal dielectric response in the solvent, which Dogonadze and Kornyshev proposed almost forty years ago [14], and which Kornyshev has refined and championed even to the present day, over a broad range of physical and application-driven questions [15]. Evidence for the existence of nonlocal solvent response is overwhelming, ranging from single-molecule computational studies [16, 17] to several forms of experimental studies [18, 19], and in between there have been many “computational experiments” involving atomistic simulations with large numbers of water molecules [20–22]. A recent review by structural biologists highlighted progress in measuring nonlocal effects in molecular biology [23].…”

Understanding the scale of the single ion free energy: A critical test of the tetra-phenyl arsonium and tetra-phenyl borate assumption

“…For instance, understanding the charge hyrdation a) Electronic mail: t.duignan@uq.edu.au b) Electronic mail: marcel.baer@pnnl.gov c) Electronic mail: chris.mundy@pnnl.gov asymmetry (CHA) has been the subject of significant research. [8][9][10] The CHA describes the preference for water to solvate an anion over a cation of similar size. Because we do not know what the correct values for the single ion solvation free energies are, the CHA remains elusive.…”

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

“…In our recent study of ion solvation using molecular dynamics, we found that in an uncharged quasi-spherical solute representing a small molecule, the electrostatic potential due to solvent structure was on the order of 10 kcal/mol/ e 51 ; Ashbaugh has shown that this potential depends non-monotonically on the ion radius for small ions 52 , though the magnitude of variation is small compared to the overall magnitude. This “static potential” contributes linearly to the electrostatic solvation free energy, so that instead of the usual linear-response model in which $\mathrm{normal\Delta }{G}^{\mathit{\text{solv}}}false(qfalse)=\frac{1}{2}{q}^{T}Lq$ where L is the usual reaction-potential operator, we have instead an affine-response model $\mathrm{normal\Delta }{G}^{\mathit{\text{solv}}}false(qfalse)=\frac{1}{2}{q}^{T}Lq+{\varphi }^{\text{static},T}q$.…”