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.

Keywords:

• Implicit solvent model
• continuum dielectric
• Poisson–Boltzmann
• multiscale
• nonlinear boundary condition
• solvation-layer interface condition
• boundary integral equation
• mean spherical approximation
• MSA

Acknowledgments

This work was supported in part by the National Institute of General Medical Sciences of the National Institutes of Health under award number R21GM102642. The content is solely the responsibility of the authors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Institute of General Medical Sciences of the National Institutes of Health [grant number R21GM102642].