Effect of protein adsorption and ionic strength on the equilibrium partition coefficient of ionizable macromolecules in charged nanopores

Recent experimental data on the diffusive transport of globular protein molecules through nanopores (D similar to 20 nm), covered with chemisorbed self-assembled monolayers (SAMs) of carboxylic acid functional groups (Ku, J.-R.; Stroeve, P. Langmuir 2004, 20, 2030), show a strong increase in flux around the isoelectric point of the protein molecule at 10 mM ionic strength (on-off behavior), but not at 100 mM. To understand these observations we calculated the equilibrium partition coefficient (distribution coefficient) of a spherical protein molecule in a nanopore consisting of ionizable carboxylic acid groups as a function of ionic strength, pH, charge and size of the protein and the pore wall. When transport is diffusion-controlled, the flux of macromolecules through porous media is directly proportional to the equilibrium partition coefficient. To calculate the charge on the pore wall, the ionizable character of the carboxylic acid groups is incorporated as well as protein adsorption. At values sufficiently above the isoelectric point of the protein, pI, protein adsorption is zero. However, with decreasing pH, adsorption strongly increases. Therefore, the pore is negatively charged at sufficiently high pH (just as the protein molecule) and positively charged at sufficiently low pH (just as the protein molecule). Consequently, the equilibrium partition coefficient of additional, thus nonadsorbing, protein molecules is strongly pH-dependent with a maximum at pH around pI. The predicted influence of ionic strength on the peak width of the equilibrium partition coefficient is in qualitative agreement with the experiments, suggesting that electrostatic interactions and especially protein adsorption are important determinants of protein transport through charged nanopores.