# Metabolic Reaction Network-Based Model Predictive Control of Bioprocesses
## 4 Conclusions  
One of the current limitations in online bioprocess control is the use of macroscopic models (that only account for substrate, biomass, and product mass balances), as the available process knowledge on the relevant underlying intracellular mechanisms is not fully exploited and as such opportunities are missed towards an optimal bioprocess operation. In this article, a procedure for metabolic network-based model predictive control has been presented, by combining online flux estimation and bioprocess control using metabolic network models. This procedure firstly uses moving horizon estimation (MHE) to estimate the states and fluxes from the available measurements and subsequently solves a model predictive control (MPC) problem to determine the optimal control strategy for the studied bioprocess. To illustrate the performance of this procedure, a case study combining a CSTR bioreactor model with a metabolic network model has been implemented. Three different model structures (a constant, a linear, and a nonlinear model) have been compared, clearly indicating that the linear flux model outperforms the nonlinear Haag flux model and the constant flux model. The true model is, as expected, outperforming the other models. In addition, the influence of the horizon lengths and sampling frequency on the MPC tracking performance has been studied. While an increase of the prediction horizon length was expected to reduce the tracking error, such observation could only be made for the true model. An increase in sampling frequency (or reduction in sampling time) was expected to reduce the tracking error, but this observation could only be made for the true model and for the linear model. Figure 12: Absolute values of the absolute tracking error divided by the number of measurements for the four states for different sampling times with \(H=H_{e}=H_{p}=4\) h.  
In future work, the presented procedure will be applied to the online control of bioprocesses involving large-scale metabolic networks. In addition, uncertainty will be accounted for during the MPC routine. Furthermore, the presented metabolic network-based model predictive control procedure can also be combined with high-throughput biological datasets [26; 27] and advanced metabolomics techniques as e.g., low-frequency NMR, to improve the metabolic model predictions and process monitoring capabilities [8; 27]. One of the current limitations of metabolic network models and methods as metabolic flux analysis is the inherent pseudo-steady state assumption. This assumption is not always valid, certainly not at timescales of multiple scales due to shifting from exponential growth phase to stationary phase. The authors of [28] proposed a hybrid modeling approach, combining machine learning with metabolic network modeling which provided accurate predictions for amino acid consumption rates in Chinese Hamster Ovary Cells. Such hybrid models could also be used in the proposed metabolic network-based MPC procedure. Conceptualization, P.N., D.V., S.B., F.L. and J.V.I. ; methodology, P.N. and D.V. ; software, P.N., D.V. and S.B. ; validation, P.N. and S.B. ; formal analysis, P.N. ; investigation, P.N. and D.V. ; resources, F.L. and J.V.I. ; data curation, P.N. ; writing--original draft preparation, P.N. ; writing--review and editing, P.N., S.B., F.L. and J.V.I. ; visualization, P.N. and S.B. ; supervision, F.L. and J.V.I. ; project administration, F.L. and J.V.I. ; funding acquisition, F.L. and J.V.I. All authors have read and agreed to the published version of the manuscript.