A continuum-molecular theory --- Poisson-Nernst-Planck-Fermi theory --- has been developed in recent years for simulating ionic flows in biological ion channels under physiological or experimental conditions by treating ions and water of any size as non-uniform hard spheres with interstitial voids, polarization of water, and correlations of ions. The theory can also be used to study thermodynamic and electric properties of electrolyte solutions that are essential components in batteries, fuel cells, nanopores, porous media, geothermal brines, the oceanic system etc. The theory can compute electric and steric potentials from all atoms in a protein and all ions and water molecules in channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium. The PNPF model has been verified with the experimental data of L-type calcium channel, gramicidin A channel, and sodium/calcium exchanger with real structures from Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer capacitor and ion activities in aqueous electrolyte solutions.

REFERENCES
J.-L. Liu, H.-j. Hsieh, and B. Eisenberg, Poisson-Fermi modeling of the ion exchange mechanism of the sodium/calcium exchanger, J. Phys. Chem. B 120, 2658-2669 (2016)
J.-L. Liu and B. Eisenberg, Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels, Phys. Rev. E 92, 012711 (2015)
J.-L. Liu and B. Eisenberg, Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels, J. Chem. Phys. 141, 22D532 (2014)
J.-L. Liu and B. Eisenberg, Correlated ions in a calcium channel model: A Poisson-Fermi theory, J. Phys. Chem. B 117, 12051-12058 (2013)
J.-L. Liu, Numerical methods for the Poisson-Fermi equation in electrolytes, J. Comp. Phys. 247, 88-99 (2013)