Molecular Mean-Field Theory of Ionic Solutions: a Poisson-Nernst-Planck-Bikerman Model

Abstract

We have developed a molecular mean-field theory -- fourth-order Poisson-Nernst-Planck-Bikerman theory -- for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely, Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

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• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• Maxwell Equations without a Polarization Field using a paradigm from biophysics
• Local Structure-Preserving Relaxation Method for Charged Systems on Unstructured Meshes
• Linear-Scaling Selected Inversion based on Hierarchical Interpolative Factorization for Self Green's Function for Modified Poisson-Boltzmann Equation in Two Dimensions
• Differential Capacitance of Electric Double Layers: A Poisson-Bikerman Formula
• Field model for complex ionic fluids: analytical properties and numerical investigation
• Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations
• Computational modeling of biological nanopores