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 pK a 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.Langevin-Debye model ͉ pKa shifts ͉ orientational polarization ͉ dielectric saturation and screening T he interaction of molecules and ions with various solvents is of importance in many physical, chemical, and biological systems. For example, electrostatics strongly influence enzyme catalysis, electron transfer, proton transport, ion channels, photo-activation, and ligand binding (1). Macroscopic dielectric continuum models are frequently invoked to describe solvation, especially in large biological systems where computations (using molecular mechanics, molecular dynamics, quantum mechanics, or combinations thereof) with explicit solvent molecules become prohibitive for many systems of physical interest. Although continuum models neglect certain microscopic details, the hope is to reduce the errors sufficiently by correctly describing the physics (2). Unfortunately, serious limitations have long been evident with one of the most popular models, the Born model (and the equivalent use of the Poisson equation), in which the solvent is characterized solely by the static dielectric constant. For example, Sandberg and Edholm concluded that the Born model introduces errors as large as 1,000 KJ/mol when used to predict the hydration energies of multivalent ions (3). The Born model is also frequently applied in evaluating the transfer free energy of ionizable groups between water and hydrophobic media, such as proteins and lipids, thereby predicting the pK a shift of a buried ionizable group. Multiple experiments and theoretical predictions agree tha...
