An accelerated approach for mechanistic model based prediction of linear gradient elution ion-exchange chromatography of proteins

On the apparent dispersion coefficient of the equilibrium dispersion model: An asymptotic analysis

To model chromatography, researchers have developed several approaches. These cover a broad range of applications and, depending on the assumptions adopted, have different levels of accuracy. In general, the most suitable modelling approach is the simplest that can describe a process with the desired accuracy. A model that often meets this criterion is the equilibrium dispersion model (EDM). This features one mass balance equation per analyte, including an axial dispersion term, and assumes the analyte concentrations in the mobile and stationary phases to be in local equilibrium. To account for the finite mass transfer rate between the phases, the model employs an apparent dispersion coefficient. Two expressions are available for this coefficient, one being used much more frequently than the other. In this paper, we aimed to clarify which one should be favoured. A desirable feature of simple models is that they can be derived from more general ones with appropriate physical assumptions and rigorous mathematical methods. Thus, to answer our research question, we derived the EDM from the more general pore diffusion model (POR), using an asymptotic method. The expression obtained for the apparent dispersion coefficient does agree with one of the two reported in the literature - the less frequently used. To test the validity of this expression, we simulated elution profiles using the two versions of the EDM and compared the results against those from the POR model. The simulations were conducted in the range where the POR and EDM models should be essentially equivalent, their results confirming the outcome of the asymptotic analysis. This work offers a solid theoretical grounding for the EDM, clarifies which formulation of the model is correct, and provides usable applicability conditions for the model.

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.