Inlet gas: uses single-point inlet values above. Biomass, temperature, and pressure also shared.
| Parameter | Value | Unit |
|---|
| Organism | Substrate | RQ | Metabolic State |
|---|---|---|---|
| E. coli | Glucose (aerobic) | 1.00 | Oxidative |
| E. coli | Glucose (overflow) | 1.1–1.5 | Acetate production |
| S. cerevisiae | Glucose (aerobic) | 1.00 | Oxidative |
| S. cerevisiae | Glucose (Crabtree) | 2.0–10+ | Ethanol fermentation |
| P. pastoris | Methanol | 0.66 | Methanol oxidation |
| P. pastoris | Glycerol | 0.86 | Glycerol oxidation |
| CHO cells | Glucose + glutamine | 0.9–1.1 | Mixed metabolism |
| Lipid oxidation | Fatty acids | 0.70 | Beta-oxidation |
OUR is calculated using the inert gas (N₂) balance method. Since nitrogen is neither consumed nor produced in aerobic fermentation, it serves as an internal standard for determining the outlet gas flow rate. First, calculate the N₂ fractions: yN2,in = 1 − yO2,in − yCO2,in and yN2,out = 1 − yO2,out − yCO2,out. The outlet flow is Fout = Fin × (yN2,in / yN2,out). Then OUR = (Fin × yO2,in − Fout × yO2,out) / VL, converted to mmol/L/h using the ideal gas molar volume at STP (22.414 L/mol).
RQ = CER / OUR indicates which metabolic pathways are active. RQ ≈ 1.0 means balanced oxidative glucose metabolism. RQ < 0.7 indicates fat or methanol oxidation (Pichia on methanol gives RQ ≈ 0.66). RQ > 1.0 suggests overflow metabolism — acetate production in E. coli or ethanol production in yeast (Crabtree effect). RQ is used as a real-time control signal: in RQ-stat feeding strategies, the feed rate is adjusted to maintain RQ near the target value, preventing overflow metabolism while maximising growth rate.
OUR (Oxygen Uptake Rate) is the actual oxygen consumed by the culture, measured from off-gas analysis. OTR (Oxygen Transfer Rate) is the rate at which oxygen transfers from gas bubbles to the liquid, defined as kLa × (C* − CL). At steady state, OUR = OTR and dissolved oxygen remains constant. OTRmax = kLa × C* represents the maximum oxygen supply capacity of your bioreactor. When OUR approaches OTRmax, dissolved oxygen drops toward zero and the culture becomes oxygen-limited.
The total gas flow rate changes across the bioreactor whenever RQ ≠ 1. If more O₂ is consumed than CO₂ produced (RQ < 1), the total outlet flow is lower than the inlet. If you assume equal flow rates, OUR and CER calculations can have 5–15% errors. The N₂ balance corrects for this: since N₂ is inert, Fout = Fin × yN2,in / yN2,out. This is the standard method in bioprocess engineering textbooks and is implemented in most commercial off-gas analysis software (BlueSens, Infors eve, Eppendorf BioCommand).
E. coli growing fully aerobically on glucose has RQ ≈ 1.0, reflecting the stoichiometry of complete oxidation: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O. When growth rate exceeds the capacity for full oxidation (the critical growth rate µcrit ≈ 0.3–0.4 h⁻¹), acetate overflow begins and RQ rises above 1.0. An RQ of 1.1–1.2 is an early warning; above 1.3 indicates significant overflow. In fed-batch fermentation, monitoring RQ and reducing feed rate when RQ > 1.05–1.10 is a proven strategy for minimising acetate accumulation.
Outlet gas from a bioreactor is saturated with water vapor at the culture temperature. The water vapor pressure is calculated using the Antoine equation: log₁₀(PH₂O) = 8.07131 − 1730.63 / (233.426 + T), where T is in °C and P in mmHg. At 37°C, PH₂O ≈ 47 mmHg, so about 6.2% of outlet gas is water vapor. If your analyzer reads wet-basis compositions, the dry-basis correction is: ydry = ywet / (1 − yH₂O). Most modern off-gas analyzers (BlueSens, Servomex) include a condenser and measure on a dry basis, but you should check your instrument documentation.