Error propagation from prime variables into specific rates and metabolic fluxes for mammalian cells in perfusion culture

Error propagation from prime variables into specific rates and metabolic fluxes was quantified for high-concentration CHO cell perfusion cultivation. Prime variable errors were first determined from repeated measurements and ranged from 4.8 to 12.2%. Errors in nutrient uptake and metabolite/product formation rates for 5-15% error in prime variables ranged from 8-22%. The specific growth rate, however, was characterized by higher uncertainty as 15% errors in the bioreactor and harvest cell concentration resulted in 37.8% error. Metabolic fluxes were estimated for 12 experimental conditions, each of 10 day duration, during 120-day perfusion cultivation and were used to determine error propagation from specific rates into metabolic fluxes. Errors of the greater metabolic fluxes (those related to glycolysis, lactate production, TCA cycle and oxidative phosphorylation) were similar in magnitude to those of the related greater specific rates (glucose, lactate, oxygen and CO(2) rates) and were insensitive to errors of the lesser specific rates (amino acid catabolism and biosynthesis rates). Errors of the lesser metabolic fluxes (those related to amino acid metabolism), however, were extremely sensitive to errors of the greater specific rates to the extent that they were no longer representative of cellular metabolism and were much less affected by errors in the lesser specific rates. We show that the relationship between specific rate and metabolic flux error could be accurately described by normalized sensitivity coefficients, which were readily calculated once metabolic fluxes were estimated. Their ease of calculation, along with their ability to accurately describe the specific rate-metabolic flux error relationship, makes them a necessary component of metabolic flux analysis.