(493d) Physics-Informed Neural Network for Modeling Hydrophobic Interaction Chromatography Process with Unknown Isotherm and Limited Experimental Data

Hydrophobic interaction chromatography (HIC) is a widely used technique in the biopharmaceutical industry for purifying target proteins [1]. It involves binding proteins to a hydrophobic resin under high salt conditions, which promotes hydrophobic interactions. Proteins are then eluted by gradually reducing the salt concentration, allowing them to be separated based on their degree of hydrophobicity. HIC is valued for its gentle conditions that preserve protein activity, making it essential in the biopharmaceutical industry for protein purification [2]. In this research, we investigate the use of a dynamic 3-component HIC system to separate a target protein from two impurities.

Traditionally, mechanistic models based on differential equations for mass balance and adsorption isotherms have been used to model HIC processes [3-5]. However, achieving accurate HIC isotherm models presents challenges, primarily because the HIC efficiency depends significantly on the salt concentration in the mobile phase. The complexity of salt-dependent protein-ligand interactions, which are still unclear, complicates the development of precise mathematical representations of HIC isotherms [6-8]. Furthermore, the accuracy of HIC isotherm models relies on fitting numerous parameters, necessitating extensive and laborious data collection [9]. This data-intensive requirement makes the modeling process both time-consuming and challenging, as each experiment must be meticulously planned and executed to capture the nuanced effects of variable salt concentrations on protein adsorption behavior.

To address these challenges, we propose a machine-learning approach using a Physics-Informed Neural Network (PINN) [10] to model the studied HIC process. The PINN model is based on a feedforward neural network structure and learns the dynamics of the HIC process from both the mass balance equations and a limited dataset collected from only 5 HIC experiments. Unlike mechanistic models, the PINN does not require the exact isotherm model to capture the HIC dynamics, and it can learn from a relatively small amount of data since it can also learn from the mass balance.

Furthermore, we have equipped the PINN with a Lorentzian function feature layer [11] right after the input layer, to significantly enhance PINN's capacity to discern and learn the intricate patterns of concentration profiles of different components in the HIC process, thereby improving the model's performance. By testing the PINN model on unseen data, we demonstrate its ability to accurately predict the elution curves of the studied HIC process.

The proposed PINN-based approach provides a promising method to reduce the time and labor required for understanding and optimizing HIC processes. This technique can be particularly beneficial in situations where obtaining a large dataset is challenging, or when the exact isotherm models are not available. The successful application of this PINN model to the studied HIC process suggests its potential for broader applications in the modeling and optimization of various chromatographic systems in the biopharmaceutical industry.

References

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