Modeling multi-component separation in hydrophobic interaction chromatography with improved parameter-by-parameter estimation method

Abstract

Mechanistic models are powerful tools for chromatographic process development and optimization. However, hydrophobic interaction chromatography (HIC) mechanistic models lack an effective and logical parameter estimation method, especially for multi-component system. In this study, a parameter-by-parameter method for multi-component system (called as mPbP-HIC) was derived based on the retention mechanism to estimate the six parameters of the Mollerup isotherm for HIC. The linear parameters ($k_{s,i}$ and $k_{\text{eq},i}$) and nonlinear parameters ($n_i$ and $q_{\text{max},i}$) of the isotherm can be estimated by the linear regression (LR) and the linear approximation (LA) steps, respectively. The remaining two parameters ($k_{p,i}$ and $k_{\text{kin},i}$) are obtained by the inverse method (IM). The proposed method was verified with a two-component model system. The results showed that the model could accurately predict the protein elution at a loading of 10 g/L. However, the elution curve fitting was unsatisfactory for high loadings (12 g/L and 14 g/L), which is mainly attributed to the demanding experimental conditions of the LA step and the potential large estimation error of the parameter $q_{\text{max}}$. Therefore, the inverse method was introduced to further calibrate the parameter $q_{\text{max}}$, thereby reducing the estimation error and improving the curve fitting. Moreover, the simplified linear approximation (SLA) was proposed by reasonable assumption, which provides the initial guess of $q_{\text{max}}$ without solving any complex matrix and avoids the problem of matrix unsolvable. In the improved mPbP-HIC method, $q_{\text{max}}$ would be initialized by the SLA and finally determined by the inverse method, and this strategy was named as SLA+IM. The experimental validation showed that the improved mPbP-HIC method has a better curve fitting, and the use of SLA+IM reduces the error accumulation effect. In process optimization, the parameters estimated by the improved mPbP-HIC method provided the model with excellent predictive ability and reasonable extrapolation. In conclusion, the SLA+IM strategy makes the improved mPbP-HIC method more rational and can be easily applied to the practical separation of protein mixture, which would accelerate the process development for HIC in downstream of biopharmaceuticals.