This paper provides an overview of nonlinear state estimation techniques along with a discussion on the challenges and opportunities for future work in the field. Emphasis is given on Bayesian methods such as moving horizon estimation (MHE) and extended Kalman filter (EKF). A discussion on Bayesian, deterministic, and hybrid methods is provided and examples of each of these methods are listed. An approach for nonlinear state estimation design is included to guide the selection of the nonlinear estimator by the user/practitioner. Some of the current challenges in the field are discussed involving covariance estimation, uncertainty quantification, time-scale multiplicity, bioprocess monitoring, and online implementation. A case study in which MHE and EKF are applied to a batch reactor system is addressed to highlight the challenges of these technologies in terms of performance and computational time. This case study is followed by some possible opportunities for state estimation in the future including the incorporation of more efficient optimization techniques and development of heuristics to streamline the further adoption of MHE.

Background: Penicillin G acylase (PGA) is used industrially to catalyze the hydrolysis of penicillin G to obtain 6-aminopenicillanic acid. In Escherichia coli, the most-studied microorganism for PGA production, this enzyme accumulates in the periplasmic cell space, and temperature plays an important role in the correct synthesis of its subunits. Results: This work investigates the influence of medium composition, cultivation strategy, and temperature on PGA production by recombinant E. coli cells. Shake flask cultures carried out using induction temperatures ranging from 18 to 28°C revealed that the specific enzyme activity achieved at 20°C (3000 IU gDCW^-1) was 6-fold higher than the value obtained at 28°C. Auto-induction and high cell density fed-batch bioreactor cultures were performed using the selected induction temperature, with both defined and complex media, and IPTG and lactose as inducers. Final biomass concentrations of 100 and 120 gDCW L^-1, and maximum enzyme productivities of 7800 and 5556 IU L^-1 h^-1, were achieved for high cell density cultures using complex and defined media, respectively. Conclusions: To the best of our knowledge, the volumetric enzyme activity and productivity values achieved using the complex medium are the highest ever reported for PGA production using E. coli. Overall PGA recovery yields of 64 and 72% after purification were achieved for crude extracts obtained from cells cultivated in defined and complex media, respectively. The complex medium was the most cost-effective for PGA production, and could be used in both high cell density and straightforward auto-induction protocols.