Calculation of Dielectric Constants near Polyelectrolytes in Solution

Abstract

The recent application of numerical Poisson−Boltzmann methods to the determination of the electrostatic potential and counterion distributions around polyelectrolytes such as DNA has prompted the determination of accurate solvent dielectric constants. The previous assumption for proteins of using a constant value of about 80 for the solvating environment appears inadequate when dealing with the much higher potential gradients and local ion concentrations of charged polyelectrolytes in solution. Approximations using lower dielectric values near 30 at the surface and increasing away to a bulk value of 78.5 have been incorporated into modern finite-difference Poisson−Boltzmann techniques and have led to more reasonable estimates of counterion distributions. However, choosing this dielectric constant “field” has been more a matter of guessing than scientific analysis. To put these techniques on a firmer foundation, we present a simple calculational procedure for determining dielectric constants near the surface of macromolecules and lipid membranes. To demonstrate the soundness of the calculation, we compare calculated dielectric constants near the surface of DNA with data from recent experiments measuring this quantity in both the major and minor grooves of B-form DNA. This procedure can be useful for proteins as well and may be particularly applicable in solvent pockets where strong potential gradients lead to the electrostatic guiding of ions or ligands toward specific binding sites.

Divalent cations and the electrostatic potential around DNA: Monte Carlo and Poisson-Boltzmann calculations

“…Yang et al 30 analyzed the dielectric response seen in a molecular dynamics simulation of triplex DNA in ionic solution and decomposed it into contributions from sugars, bases, phosphate groups, ions, and water. Our own studies 31,32 of the variability of the dielectric response in the environment near B-DNA have also indicated a substantial lowering from the pure water value of 78.5.…”

Continuum molecular electrostatics, salt effects, and counterion binding—A review of the Poisson–Boltzmann theory and its modifications

“…One could imagine parameterizing the results of quantum calculations for a set of model binding sites and transferring them to larger systems. Yet another improvement of the PB model which does not require a lot of computational cost is to include various dielectric constants 26,49 around the molecule which is especially important e.g. for systems immersed in membrane environment.…”

Dielectric saturation of water in a membrane protein channel

“…The reduced cluster size might result in a lowering of the relative permittivity of the same order of magnitude as that due to dielectric saturation effects. 18,19 The goal of the present study is then to show how the dielectric properties of water play a significant role in the electrostatic interactions determining the function of membrane protein channels. In a large number of studies aimed to the evaluation of electrostatic energies in proteins the discussion has focused on the protein dielectric environment, [20][21][22] while little attention has been paid to the properties of the surrounding water.…”