Modeling Charge-Sign Asymmetric Solvation Free Energies With Nonlinear Boundary Conditions

TL;DR

This paper introduces a nonlinear boundary condition in linear Poisson theory to accurately model charge-sign asymmetric hydration free energies, simplifying calculations and extending existing solvers.

Contribution

The authors develop a nonlinear boundary condition that captures charge-sign asymmetry in solvation free energies within a linear Poisson framework, validated against MD data.

Findings

Accurately reproduces MD hydration asymmetries for ions and amino acids.

Justifies linear response expressions for charging free energies.

Easily extendable to other continuum-electrostatic solvers.

Abstract

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [J. Phys. Chem. B, v. 112:2408, 2008]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.