Hybrid model development for parameter estimation and process optimization of hydrophobic interaction chromatography

Hydrophobic Interaction Chromatography (HIC) is often employed as a polishing step to remove aggregates for the purification of therapeutic proteins in the biopharmaceutical industry. To accelerate the process development and save the costs of performing time- and resource-intensive experiments, advanced model-based process design and optimization are necessary. Due to the unclear adsorption mechanism of the salt-dependent interaction between the protein and resin, the development of an accurate mechanistic model to describe the complex HIC behavior is challenging. In this work, an isotherm derived from Wang et al. is modified by adding three extra parameters together with an equilibrium dispersive model to represent the HIC process. To reduce the development effort of isotherm equations and extract missing information from the available data, a hybrid model is constructed by combining a simple and well-known multi-component Langmuir isotherm (MCL) with a neural network (NN). It is observed that the structure of the hybrid model is of critical importance to the accuracy of the developed model. During parameter estimation, a regularization strategy is incorporated to prevent overfitting. Furthermore, the impact of NN structures and regularization rates are comprehensively investigated. One of the interesting findings was that a simple NN with one hidden layer with two nodes and sigmoid as the activation function, significantly outperforms the mechanistic model, with a 62% improvement in accuracy in calibration and 31.4% in validation. To ensure the generalizability of the developed hybrid model, an in-silico dataset is generated using the mechanistic model to test the extrapolation capability of the hybrid model. Process optimization is also carried out to find the optimal operating conditions under product quality constraints using the developed hybrid model.