Extending the Solvation-Layer Interface Condition Continum Electrostatic Model to a Linearized Poisson–Boltzmann Solvent

Abstract

We extend the linearized Poisson-Boltzmann (LPB) continuum electrostatic model for molecular solvation to address charge-hydration asymmetry. Our new solvation-layer interface condition (SLIC)/LPB corrects for first-shell response by perturbing the traditional continuum-theory interface conditions at the protein-solvent and the Stern-layer interfaces. We also present a GPU-accelerated treecode implementation capable of simulating large proteins, and our results demonstrate that the new model exhibits significant accuracy improvements over traditional LPB models, while reducing the number of fitting parameters from dozens (atomic radii) to just five parameters, which have physical meanings related to first-shell water behavior at an uncharged interface. In particular, atom radii in the SLIC model are not optimized but uniformly scaled from their Lennard-Jones radii. Compared to explicit-solvent free-energy calculations of individual atoms in small molecules, SLIC/LPB is significantly more accurate than standard parametrizations (RMS error 0.55 kcal/mol for SLIC, compared to RMS error of 3.05 kcal/mol for standard LPB). On parametrizing the electrostatic model with a simple nonpolar component for total molecular solvation free energies, our model predicts octanol/water transfer free energies with an RMS error 1.07 kcal/mol. A more detailed assessment illustrates that standard continuum electrostatic models reproduce total charging free energies via a compensation of significant errors in atomic self-energies; this finding offers a window into improving the accuracy of Generalized-Born theories and other coarse-grained models. Most remarkably, the SLIC model also reproduces positive charging free energies for atoms in hydrophobic groups, whereas standard PB models are unable to generate positive charging free energies regardless of the parametrized radii. The GPU-accelerated solver is freely available online, as is a MATLAB implementation.

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

“…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 . 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 . Fifth, when combined with even a simple solvent‐accessible‐surface‐area (SASA)‐proportional treatment of the nonpolar component of solvation, SLIC is able to predict water‐octanol transfer free energies with an accuracy approaching that of explicit‐solvent MD .…”

“…Presently, computing the spatially varying φ static ( r ) requires expensive explicit‐solvent simulations or other slow theory, so we have instead adopted a simpler model in which the static potential is constant (uniform) throughout the solute φ static ( r ) = φ static . Depending on the application, the constant should be obtained by either parameterization against experiment , or by explicitly calculating the field at a particular point in an uncharged solute .…”

“…Three facts are important to note about the static potential field. First, because it is generated by a charge distribution purely outside the solute volume, the static field must be a harmonic function (satisfy the Laplace equation) inside the solute . Second, solute geometry and solvent packing effects give rise to a nonconstant‐static potential field at the boundary (see ).…”

“…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 . 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) .…”

“…That is, the model recovers the correct electrostatic solvation free energy even if one inverts the sign of the charge distribution, without needing to change the atom radii. This property was the original goal of the SLIC model, and it dramatically reduces the number of free parameters in the electrostatic model, from dozens (atomic radii for different atom types) to just five (which depend purely on the solvent) . Beyond the practical advantage of simplifying parameterization procedures, the SLIC model's reduced number of free parameters mean that the model can be parameterized for solvents for which very few reference data are available .…”