Generalising the mean spherical approximation as a multiscale, nonlinear boundary condition at the solute–solvent interface

Abstract

In this paper, we extend the familiar continuum electrostatic model to incorporate finite-size effects in the solvation layer, by perturbing the usual macroscopic interface condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale solvation-layer interface condition (SLIC/MSA). We show that SLIC/MSA reproduces MSA predictions for Born ions in a variety of polar solvents, including water as well as other protic and aprotic solvents. Importantly, the SLIC/MSA model predicts not only solvation free energies accurately but also solvation entropies, which standard continuum electrostatic models fail to predict. The SLIC/MSA model depends only on the normal electric field at the dielectric boundary, similar to our recent development of a SLIC model for charge-sign hydration asymmetry, and the reformulation of the MSA as an effective boundary condition enables its straightforward application to complex molecules such as proteins, whereas traditionally it is primarily a bulk theory. This work also opens the possibility for other electrolyte models to be incorporated into fast implicit-solvent models of biomolecular electrostatics.

Solvation thermodynamics of neutral and charged solutes using the solvation‐layer interface condition continuum dielectric model

“…In this work, we have demonstrated that a simple implicit-solvent model, composed of the traditional surface-area-dependent nonpolar model plus the modified continuum dielectric model SLIC for the electrostatics, predicts solvation free energies and entropies with surprising accuracy for both neutral and charged small molecules. This result represents the joining of two previous studies of SLIC, one on solvation thermodynamics for spherical ions [36,45] and one on the solvation free energies of complex polyatomic solutes [26,35] . We note that our model does not explicitly account for either hydrogen bonding or other solvent structure [63,64] , and reproduces solvation thermodynamics in both hydrogen-bonding and non-hydrogen-bonding solvents [36] .…”

“…As the charging free energy from λ = 0 to λ = δ is very small compared to the charging free energy over the remaining interval, the charging integral can be approximated as the integral from λ = δ to λ = 1, allowing the use of the familiar linear-response expression. Readers interested in further details are referred to earlier work [26,35,36,44,45] . A critical assessment of these approximations is a subject of ongoing work.…”

“…This enhanced model of solvation electrostatics incorporates both the static potential created by solvent structure around the (uncharged) solute van der Waals cavity, and charge-hydration asymmetry, using a modified boundary condition at the solute interface. We have shown that these two relatively minor changes offer a multitude of benefits for accurate computation of solvation electrostatics [35,36,45] . First, we have shown that this model gives accurate charging free energies while using standard MD radii (R min /2, subject to a single uniform scaling factor for all atom types) [26] .…”

“…Second, the new model is more accurate in predicting how solute charging free energies change during protonation or deprotonation [26] , and (again, by design) SLIC achieves this accuracy without needing charge-dependent radii, which are sometimes claimed to be required [48] . Third, SLIC provides a new interpretation for the success of the mean-spherical approximation (MSA) in predicting the solvation thermodynamics of Born ions: one can use the MSA Born energy to derive a temperature-dependent nonlinear perturbation to the familiar macroscopic boundary condition [45] . Fourth, whereas traditional models are only accurate in predicting total molecular charging free energies, SLIC accurately predicts the charging free energies of individual atoms as well as whole molecules [35] .…”

Predicting solvation free energies and thermodynamics in polar solvents and mixtures using a solvation-layer interface condition

“…This suggests an alternative approach in which a physically meaningful, effective modification should be employed in the interface condition, rather than changing the interface directly (via the atom radii). 24,26,27,45 The asymmetric response can be described as a combination of two distinct different mechanisms. 24 The first one, as it was described above, is the steric asymmetry and the other one is the electrostatic interface potential that persists even if the solute is uncharged.…”