Continuum molecular electrostatics, salt effects, and counterion binding--a review of the Poisson-Boltzmann theory and its modifications.

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.