Dynamic Control to Maximize the Performance of Protein A Resin in Antibody Extraction

Abstract

Antibody therapies are critical in treating various diseases such as cancer and autoimmune diseases. Affinity chromatography is the most expensive and necessary step in the purification of antibodies. Therefore, optimizing this step is critical to maintaining downstream operations and minimizing costs. This work uses an accurate sigmoidal model to represent the resin process condition. Unfortunately, variations in antibody concentrations and the inherent process uncertainties in biological systems make the process optimization task challenging. Therefore, we capture the uncertainties of the process via utilization of the Ito processes. After several candidate Ito processes were tested, the Brownian motion with drift was found to be most suitable for capturing the uncertainties. Thus, the deterministic ordinary differential equation model based on the method of moments is then modified into a stochastic model, which can be optimized via the stochastic optimal control strategy. Pontryagin’s maximum principle is implemented and solved for the objective function of maximizing the theoretical plate number. Successful control via flow rate adjustments led to higher antibody extraction compared to fixed flow rates, which was also confirmed experimentally. Improvements in the affinity chromatography capacity for antibodies allow for less resin use and therefore smaller systems.