Thermodynamic modeling of protein retention in mixed-mode chromatography: An extended model for isocratic and dual gradient elution chromatography.

An extended model is developed to describe protein retention in mixed-mode chromatography based on thermodynamic principles. Special features are the incorporation of pH dependence of the ionic interaction on a mixed-mode resin and the addition of a water term into the model which enables one to describe the total number of water molecules released at the hydrophobic interfaces upon protein-ligand binding. Examples are presented on how to determine the model parameters using isocratic elution chromatography. Four mixed-mode anion-exchanger prototype resins with different surface chemistries and ligand densities were tested using isocratic elution of two monoclonal antibodies at different pH values (7-10) and encompassed a wide range of NaCl concentrations (0-5M). U-shape mixed-mode retention curves were observed for all four resins. By taking into account of the deprotonation and protonation of the weak cationic functional groups in these mixed-mode anion-exchanger prototype resins, conditions which favor protein-ligand binding via mixed-mode strong cationic ligands as well as conditions which favor protein-ligand binding via both mixed-mode strong cationic ligands and non-hydrophobic weak cationic ligands were identified. The changes in the retention curves with pH, salt, protein, and ligand can be described very well by the extended model using meaningful thermodynamic parameters like Gibbs energy, number of ionic and hydrophobic interactions, total number of released water molecules as well as modulator interaction constant. Furthermore, the fitted model parameters based on isocratic elution data can also be used to predict protein retention in dual salt-pH gradient elution chromatography.