Nonlocal Dielectric Continuum Models and Finite Element Solvers for Protein Electrostatics

Calculation of electrostatics for a protein in a solution of multiple ionic species is a fundamental task in the fields of structural biology, computational biochemistry, biophysics, and mathematical biology. The Poisson-Boltzmann equation (PBE) is one commonly used dielectric continuum model for such a calculation. However, it may not work properly near a highly charged biomolecular surface due to ignoring either polarization correlation among water molecules or ion size effect. To account for polarization correlation of water molecules, the nonlocal dielectric continuum modeling approach was proposed about 40 years ago and has been greatly improved in the last decade, in part due to our work. In this talk, I will present our nonlocal dielectric theory and introduce our nonlocal PBE model and related finite element solvers. I also will discuss the close relationships between a nonlocal dielectric model and a Poisson-Fermi model, which was developed twenty years ago to account for far field correlations and ion size effects. This study has led to our nonlocal Poisson-Fermi double-layer model for a solution of multiple ionic species with distinct ion sizes. Numerical results produced from this double-layer model will be reported to demonstrate the necessity of considering nonuniform ion sizes for a dielectric continuum model.