Propagation of measurement accuracy to biomass soft-sensor estimation and control quality

In biopharmaceutical process development and manufacturing, the online measurement of biomass and derived specific turnover rates is a central task to physiologically monitor and control the process. However, hard-type sensors such as dielectric spectroscopy, broth fluorescence, or permittivity measurement harbor various disadvantages. Therefore, soft-sensors, which use measurements of the off-gas stream and substrate feed to reconcile turnover rates and provide an online estimate of the biomass formation, are smart alternatives. For the reconciliation procedure, mass and energy balances are used together with accuracy estimations of measured conversion rates, which were so far arbitrarily chosen and static over the entire process. In this contribution, we present a novel strategy within the soft-sensor framework (named adaptive soft-sensor) to propagate uncertainties from measurements to conversion rates and demonstrate the benefits: For industrially relevant conditions, hereby the error of the resulting estimated biomass formation rate and specific substrate consumption rate could be decreased by 43 and 64 %, respectively, compared to traditional soft-sensor approaches. Moreover, we present a generic workflow to determine the required raw signal accuracy to obtain predefined accuracies of soft-sensor estimations. Thereby, appropriate measurement devices and maintenance intervals can be selected. Furthermore, using this workflow, we demonstrate that the estimation accuracy of the soft-sensor can be additionally and substantially increased. Electronic supplementary material The online version of this article (doi:10.1007/s00216-016-9711-9) contains supplementary material, which is available to authorized users.


Main mechanistic assumptions and equations
The main mechanistic assumptions behind data generation and soft-sensor are the same. Substrate, ammonia and oxygen is converted to biomass and carbon dioxide. As the amounts of products in biopharmaceutical processes are in the ranges of some milligrams per liter, the formed product can be neglected.
Main input signal into the model are the stoichiometry of the substrate (C 6 H 12 O 6 ) and the concentration (0.400 g mL -1 ) and feed rate of the substrate. The stoichiometry of the organism was taken from literature [1].
The feed rate at time point t during the not induced fed-batch phase was calculated in form as follows. After the induction phase, the feed rate was kept constant (relevance shown in Figure 1 of the main document). t is the time (h), µ the feed exponent (h -1 ) and F 0 the feed rate (mL) at fed-batch start which was calculated Where X is the total amount of biomass in the reactor (g), M X the C-normalized molecular weight of the biomass (g c-mol -1 ), Y X/S the biomass substrate yield (c-mol c-mol -1 ), c S the feed concentration (g mL -1 ) and M S the C-normalized molecular weight of the substrate (g c-mol -1 ).
As there is no substrate accumulation and no outflow of substrate during the fed-batch phase, the complete inflow of substrate is immediately consumed, resulting in a substrate uptake rate r S (cmol h -1 ) which is only dependent on the feed rate and the concentration of the feed.
It should be mentioned here, that all rates where the flow direction shoes into the cell or where a species is consumed, were defined to be negative (r S , OUR), while rates leading to an accumulation or formation of a species were defined to be positive (r X , CER).
The biomass formation rate r X (c-mol h -1 ) was calculated by using a fixed biomass/substrate yield in the exponential fed-batch phase, and a decreasing biomass/substrate yield in the induction phase.
The consumption of oxygen per formed amount of biomass Y O2/X (mol c-mol -1 ) was calculated by setting up the electron balance. γ S , γ S and γ O2 are the degrees of reduction based on one c-mole of substrate and biomass (c-mol -1 ), or one mole of oxygen (mol -1 ), respectively. The degrees of reduction were calculated by setting up γ N = -3, γ C = 4, γ H = 1 and γ O = -2 [2]. As γ for CO 2 , NH 3 and H 2 O according to the previous definition is 0, the degree of reduction in the system sum should not change over time.
When setting r X to 1 and and r S to 1/Y X/S , r O2 corresponds to Y O2/X and can be calculated according to the following equation: Using Y O2/X , the oxygen uptake rate OUR (mol h -1 ) now can be simply calculated.
For the calculation of the carbon dioxide evolution rate CER (mol h -1 ) it was assumed that the whole carbon flux goes into the biomass or leaves the reactor as carbon dioxide. When neglecting product formation and extracellular metabolites, the carbon balance can be stated as follows. All sum formulas are normalized to one carbon, resulting in the following equation: As the accumulation of carbon dioxide in the reactor can be neglected, the carbon dioxide evolution rate was calculated as follows: In the last step, the used oxygen and the produced carbon dioxide are added and subtracted from the inlet air and oxygen, considering water stripping and assuming the whole gas phase as ideal gas. The oxygen fraction in the air (y O2, Air ) is 0.2095, the oxygen fraction of the oxygen supply tank 0.9800 (y O2, O2 ). The volumetric inflow of oxygen O 2, in (L h -1 ) is calculated as follows: The volumetric oxygen outflow F O2, out (L h -1 ) is Similar for carbon dioxide F CO2, out (L h -1 ) In the final step, the total outflow is calculated and the detected values X CO2, out and X O2, out (%) are generated. The value y O2, wet represents the oxygen content of the exhaust gas without microbial activity. It is an important value to estimate the water stripping effect and described in detail elsewhere [3]. First the total outflow of air F Air, out has to be calculated.
In the end, the volumetric percentage fraction of oxygen and carbon dioxide can be calculated as follows: