Online moving horizon estimation of fluxes in metabolic reaction networks

• A novel methodology for online moving horizon metabolic flux estimation is presented.
• A linear flux model is seen to be performing better than a nonlinear flux model.
• The influence of the estimated parameter noise on the estimates is substantial.
• The chosen stoichiometric matrix null space basis hardly influences the results.
• The method performs well for a realistic medium-scale case study for E. coli.

Using online state and parameter estimation, concentrations and fluxes in bioprocesses can be estimated for use in monitoring, optimization and control applications. Existing methodologies, however, either ignore the dynamic nature of the problem, or focus on the extracellular concentration states and pay less attention to accurate flux estimates. These estimates are useful for online monitoring of the flux state of an organism, or for developing novel flux-based strategies for online control of bioreactors.In this contribution, the dynamic metabolic flux analysis model structure is combined with two kinetic flux models: a linear flux model and a nonlinear, more mechanistic flux model. The parameters of these models are estimated online through a moving horizon estimation strategy. The resulting algorithm is illustrated on two simulated case studies: a small-scale network, to assess the influence of important algorithm parameters on the final estimates, and a medium-scale network for Escherichia coli, to empirically test the performance of the methodology in a more realistic situation.An important parameter in this estimation strategy is the chosen noise level on the estimated parameters. This choice is not trivial, but is observed to have a significant influence on the resulting estimates. Furthermore, also the effect of the choice of the null space basis for the stoichiometric matrix of the metabolic reaction network was assessed. In the small-scale case study, it was found that a linear flux model with a specific parameter noise level was performing well for both state and flux estimation. The influence of the choice of the null space basis matrix on the estimation performance was much lower. The resulting scenario was evaluated in the medium-scale case study and found to be performing very well also in that case.