Modeling the Gibbs–Donnan effect during ultrafiltration and diafiltration processes using the Poisson–Boltzmann theory in combination with a basic Stern model

The Gibbs–Donnan effect is a well-known phenomenon causing ions to be distributed unevenly across semi-permeable membranes that are permeable to ions but not to larger macromolecules such as proteins. In protein ultrafiltration and diafiltration (UF/DF) processes, this effect often leads to discrepancies between the pH and excipient concentrations in the final drug substance and in the DF buffer. In this work, a model describing the retentate and permeate composition throughout combined UF/DF processes is introduced. The model accounts for volume exclusion effects and electrostatic interactions between ions and the protein based on the Poisson–Boltzmann theory in combination with a basic Stern model. Advantages and limitations of the proposed model were analyzed using UF/DF experiments with multiple diafiltration buffers and proteins. A comparison between simulated and experimental permeate data showed good agreement for low to moderate Donnan potentials but model limitations for high Donnan potentials at protein concentration larger 100 gL-1. In contrast, simulated retentate data showed good agreement for both low and high Donnan potentials and for protein concentrations up to 190 gL-1. It was demonstrated that in this high protein concentration regime, the applied basic Stern model provides more accurate predictions compared to previous theories based on the Poisson–Boltzmann theory alone. This makes the model a valuable tool to describe discrepancies between pH and excipient concentrations in the final drug substance and DF buffer for highly concentrated protein formulations. As model predictions are based solely on structural information on the protein and the composition of the DF buffer, the model is particularly beneficial at an early stage in process development to streamline process development and improve process understanding.