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

Abstract

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...

Charges in the hydrophobic interior of proteins

“…Calculations based on MD simulations have also shown that the dielectric properties inside a protein can be comparable to the values of ε app listed in Table 1 (21-23). More recently, Freed and coworkers have pointed out that high apparent dielectric constants inside proteins can also result when dielectric saturation effects for the reference state (i.e., a model Glu in water) are ignored in the calculations (24). A rigorous computational study of the dielectric effects that determine the ionization properties of the internal Glu residues in SNase is underway in our laboratory.…”

Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization

“…[17,34], our calculation shows that "ðrÞ has a sigmoidal shape as a function of the distance from the ion because of the dielectric saturation near the ion [35]. Because the primary contribution to the solvation energy arises from the local dielectric function near the ion, which is much reduced from the bulk value, the solvation energy is higher (less negative) than that predicted by the Born expression.…”

“…The Born model has the virtue of being simple and intuitive in capturing the essential qualitative physics of solvation. However, quantitatively, the Born expression is known to be a poor description of the solvation of small ions [11], even in a one-component uniform liquid, because of the dielectric saturation (due to saturated dipole orientation) [15][16][17] near the ion. In a spatially inhomogeneous liquid or mixture, there is the additional effect of local density or composition response to the electric field of the ion.…”

Communication: Free-energy analysis of hydration effect on protein with explicit solvent: Equilibrium fluctuation of cytochrome c

“…The linear-response treatment was motivated on the basis of continuum electrostatics, 11,12 and the role of the dielectric saturation was recently examined within the framework of continuum solvent model. 38,39 Our study employs an explicit-solvent model, and the effect of dielectric saturation is naturally incorporated if it exists. According to Fig.…”