Effect of charge regulation on steric mass-action equilibrium for the ion-exchange adsorption of proteins

A thermodynamic formalism is developed for incorporating the effects of charge regulation on the ion-exchange adsorption of proteins under mass-overloaded conditions as described by the steric mass-action (SMA) isotherm. To accomplish this, the pH titration behavior of a protein and the associated adsorption equilibrium of the various charged forms of a protein are incorporated into a model which also accounts for the steric hindrance of salt counterions caused by protein adsorption. For the case where the protein is dilute, the new model reduces to the protein adsorption model described recently by the authors which accounts for charge regulation. Similarly, the new model reduces to the steric mass-action isotherm developed by Brooks and Cramer which applies to mass-overloaded conditions for the case where charge regulation is ignored so that the protein has a fixed charge. Calculations using the new model were found to agree with experimental data for the adsorption of bovine serum albumin (BSA) on an anion-exchange column packing when using reasonable physical properties. The new model was also used to develop an improved theoretical criterion for determining the conditions required for an adsorbed species to displace a protein in displacement chromatography when the pH is near the protein pI.