Parameter-by-parameter method for steric mass action model of ion exchange chromatography: Theoretical considerations and experimental verification

Ion exchange chromatography (IEC) is one of the most widely-used techniques for protein separation and has been characterized by mechanistic models. However, the time-consuming and cumbersome model calibration hinders the application of mechanistic models for process development. A new methodology called "parameter-by-parameter method (PbP)" was proposed with mechanistic derivations of the steric mass action (SMA) model of IEC. The protocol includes four steps: (1) first linear regression (LR1) for characteristic charge; (2) second linear regression (LR2) for equilibrium coefficient; (3) linear approximation (LA) for shielding factor; (4) inverse method (IM) for kinetic coefficient. Four SMA parameters could be one-by-one determined in sequence, reducing the number of unknown parameters per species from four to one, and predicting almost consistent retention. Numerical single-component experiments were investigated firstly, and the PbP method showed excellent agreement between experiments and simulations. The effects of loadings on the PbP and Yamamoto methods were compared. It was found that the PbP method had higher accuracy and robustness than the Yamamoto method. Moreover, a five-experiment strategy was suggested to implement the PbP method, which is straightforward to reduce the cost of calibration experiments. Finally, a real-world multi-component separation was challenged and further confirmed the feasibility of the PbP method. In general, the proposed method can not only reliably estimate the SMA parameters with comprehensive physical understanding but also accurately predict retention over a wide range of loading conditions.