Charge regulation and electrostatic interactions for a spherical particle in a cylindrical pore

Previous theoretical analyses of electrostatic interactions for proteins in porous media have assumed that the protein (and pore) surface maintains either constant charge or constant potential during the interaction; however, the actual surface charge is determined by the extent of the surface ionization and binding reactions, both of which are altered when the protein enters the pore due to the change in the local ionic environment caused by the distortion of the electrical potential field. Theoretical calculations for the electrostatic potential are performed for a spherical particle in a cylindrical pore, accounting for this charge regulation phenomenon using a linearized form of the charge regulation boundary condition. The equilibrium partition coefficient in the pore is then evaluated from the free energy of interaction. Specific calculations are provided for the protein bovine serum albumin, with the charge regulation parameters evaluated from a model for the detailed protein charge characteristics. Model predictions are compared with experimental data for the bovine serum albumin sieving coefficient at different pH and ionic strength. These results provide important insights into the effects of charge regulation on the magnitude of the electrostatic interactions between charged proteins and charged pores.