Influence of nonlinear electrostatics on transfer energies between liquid phases: Charge burial is far less expensive than Born model

The widely used Born model describes the electrostatic response of continuous media using static dielectric constants. However, when applied to a liquid environment, a comparison of Born model predictions with experimental values (e.g., transfer free energies and pKa shifts) found that agreement is only achieved by using physically unrealistic dielectric constants for proteins, lipids, etc., and/or equally unrealistic atomic radii. This leads to questions concerning the physical origins for this failure of the Born model. We partially resolve this question by applying the Langevin-Debye (LD) model of a continuous distribution of point, polarizable dipoles, a model that contains an added dependence of the electrostatic response on the solvent's optical dielectric constant and both gas- and liquid-phase dipole moments, features absent in the Born model to which the LD model reduces for weak fields. The LD model is applied to simple representations of three biologically relevant systems: (i) globular proteins, (ii) lipid bilayers, and (iii) membrane proteins. The linear Born treatment greatly overestimates both the self-energy and the transfer free energy from water to hydrophobic environments (e.g., a protein interior). By using the experimental dielectric constant, the energy cost of charge burial in either globular or membrane proteins of the Born model is reduced by almost 50% with the nonlinear theory as is the pKa shift, and the shifts agree well with experimental trends.