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

Abstract

This work is a review of the Poisson–Boltzmann (PB) continuum electrostatics theory and its modifications, with a focus on salt effects and counterion binding. The PB model is one of the mesoscopic theories that describes the electrostatic potential and equilibrium distribution of mobile ions around molecules in solution. It serves as a tool to characterize electrostatic properties of molecules, counterion association, electrostatic contributions to solvation, and molecular binding free energies. We focus on general formulations which can be applied to large molecules of arbitrary shape in all‐atomic representation, including highly charged biomolecules such as nucleic acids. These molecules present a challenge for theoretical description, because the conventional PB model may become insufficient in those cases. We discuss the conventional PB equation, the corresponding functionals of the electrostatic free energy, including a connection to DFT, simple empirical extensions to this model accounting for finite size of ions, the modified PB theory including ionic correlations and fluctuations, the cell model, and supplementary methods allowing to incorporate site‐bound ions in the PB calculations. © 2007 Wiley Periodicals, Inc. Biopolymers 89: 93–113, 2008.This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com

Correlation effects, image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

“…Also, we show the form of the free energy, which is not much different from that of [43]. Furthermore, we are able to recast it in a more conventional form [8] and are so able to discuss the physics of each term. In the next section (Sect.…”

“…We call W (r 1 , r 2 ) a fluctuating potential. However, this fluctuating potential is quite different from the one given in reference [8]. Here, the latter was only defined for point charges, which we denote by φ f (q, r, r ).…”

“…By correctly identifying entropic and electrostatic energy components, it is possible to write the free energy, in the limit Ξ → 0, in a more conventional form [8] …”

“…The unmodified PB equation for a uniformly charged cylinder may be inadequate in describing the interaction for a variety of reasons. Correlation effects [1][2][3][4][5][6][7][8][9][10][11], image charge effects [1,5,8,10,12,13], solvent effects [12,[14][15][16][17][18][19], and structure of charged groups at the macro-ion surface [1,12,[19][20][21][22] may all play an important role. Though, the relative degree of each of these effects is likely to depend on the particular properties of the type of macro-ion under consideration, most importantly its shape, charge density and surface charge distribution of fixed charged groups.…”

“…Here, we show how quantities like the average electric field due to the ions and fixed charges, as well as the effective interaction (fluctuating potential) between two (infinitesimal) test charges in solution, may be calculated from the partition function. We also discuss how the more traditional Kirkwood hierarchy [8] is obtained from the model.…”