Designing scalable ultrafiltration/diafiltration process of monoclonal antibodies via mathematical modeling by coupling mass balances and Poisson-Boltzmann equation.

Ultrafiltration/diafiltration (UF/DF) operations are employed for achieving the desired therapeutic monoclonal antibody (mAb) formulations. Due to electrostatic interactions between the charged proteins, solute ions, and uncharged excipients, the final pH and concentration values are not always equal to those in the DF buffer. At high protein concentrations, typical for industrial formulations, this effect becomes predominant. To account for challenges occurring in industrial environments, a robust mathematical framework enabling the prediction of pH and concentration profiles throughout the UF/DF process is provided. The proposed mechanistic model combines a macroscopic mass balance approach with a molecular approach based on a Poisson-Boltzmann equation dealing with electrostatic interactions and accounting for protein exclusion volume effect. The mathematical model was validated with experimental data of two commercially relevant mAbs obtained from an industrial UF/DF process using scalable laboratory equipment. The robustness and flexibility of the model were tested by using proteins with different isoelectric points and net charges. The latter was determined via a titration curve, enabling realistic protein charge-pH evaluation. In addition, the model was tested for different DF buffer types containing both monovalent and polyvalent ions, with various types of uncharged excipients. The model generality enables its implementation for the UF/DF processes of other protein varieties.