Treating ion distribution with Gaussian-based smooth dielectric function in DelPhi.

The standard treatment of ions in the framework of the Poisson-Boltzmann equation relies on molecular surfaces, which are commonly constructed along with the Stern layer. The molecular surface determines where ions can be present. In the Gaussian-based smooth dielectric function in DelPhi, smooth boundaries between the solute and solvent take the place of molecular surface. Therefore, this invokes the question of how to model mobile ions in the water phase without a definite solute-solvent boundary. This article reports a natural extension of the Gaussian-based smooth dielectric function approach that treats mobile ions via Boltzmann distribution with an added desolvation penalty. Thus, ion concentration near macromolecules is governed by the local electrostatic potential and the desolvation penalty (from being partially desolvated). The approach is tested against the experimental salt dependence of binding free energy on 7 protein-protein complexes and 12 DNA-protein complexes, resulting in Pearson correlations of 0.95 and 0.88, respectively.