Parameter-by-parameter method for steric mass action model of ion exchange chromatography: Simplified estimation for steric shielding factor

Mechanistic models play a crucial role in the process development and optimization of ion-exchange chromatography (IEC). Recent researches in steric mass action (SMA) model have heightened the need for better estimation of nonlinear parameter, steric shielding factor σ. In this work, a straightforward approach combination of simplified linear approximation (SLA) and inverse method (IM) was proposed to initialize and further determine σ, respectively. An existed, unique, and positive σ can be derived from SLA. Compared with linear approximation (LA) developed in our previous study, σ of the multi-component system can be calculated easily without solving the complex system of linear equations, leading to a time complexity reduction from O(n3) to O(n). The proposed method was verified first in numerical experiments about the separation of three charge variants. The calculated σ was more reasonable than that of LA, and the error of elution profiles with the parameters estimated by SLA+IM was only one-sixth of that by LA in numerical experiments. Moreover, the error accumulation effect could also be reduced. The proposed method was further confirmed in real-world experiments about the separation of monomer-dimer mixtures of monoclonal antibody. The results gave a lower error and better physical understanding compared to LA. In conclusion, SLA+IM developed in the present work provides a novel and straightforward way to determine σ. This simplification would help to save the effort of calibration experiments and accelerate the process development for the multi-component IEC separation.