A distributed-parameter observer for estimating the distribution of concentrations in a tubular protein refolding reactor

• Real time concentration monitoring in tubular protein refolding process. • Combines inline and at-line measurements to estimate states and model parameters. • Using of extended Kalman filter for estimation of concentration distribution. • Model order reduction for state estimation with a distributed-parameter model. • Comparison to open-loop simulation for assessing the observer’s performance. Inclusion bodies formed during recombinant protein expression in Escherichia coli serve as a high-yield source of target proteins but require refolding to regain their native structure. Continuous refolding processes, such as tubular refolding, provide advantages over batch and fed-batch methods by enabling precise control of key process variables like concentration, temperature and refolding time. In this contribution, a real-time monitoring framework based on an extended Kalman filter configuration is presented. This filter configuration enables accurate, dynamic concentration distribution estimation by fusing continuous inline measurements of refolded protein with periodic at-line measurements of aggregated species. The combination of both measurements enhances observer precision and ensures consistent product quality. To further improve the estimation, the observer scheme is augmented to simultaneously estimate reaction rates during operation. For determining the optimal sensor locations, the impact of the measurement positions along the tube on the accuracy of the state estimates is studied. The model-based extended Kalman filter utilizes a partial differential equation model that captures the protein refolding kinetics within a tubular reactor. Coupled with a reduced-order model, real-time capable and feasible state correction is possible. This hybrid monitoring strategy improves refolding efficiency, yield, and scalability for large-scale protein production applications. Using a simulated reality, the observer methodology is validated and compared to an open-loop simulation of the refolding process.