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Drybench Bioreactor.
Fed-batch bioreactor simulator, E. coli preset
When dissolved oxygen runs out in an E. coli fed-batch run, and what would rescue it within your vessel's limits: rpm, vvm, oxygen enrichment, then the feed.
per hour
Change it to simulate this run again in your browser. Every other value is the preset's.
- Oxygen runs out
- 12.3h
- Without rescue. The culture would take up more oxygen than the simulated vessel can transfer.
- Rescue
- 900 rpm, 2 vvm, 40 % O₂, feed capped at μ 0.105
- Within the limits you enter; ignores cooling capacity.
- With rescue: lowest DO
- 30.0% air saturation
The run
- With rescue
- Without rescue
Show the data
| Time (h) | Dissolved oxygen (% air saturation): With rescue | Dissolved oxygen (% air saturation): Without rescue | Event |
|---|---|---|---|
| 0.00 | 100.0 | 100.0 | Flag 1 starts: Outside this model: fast glucose uptake |
| 0.96 | 93.7 | 93.7 | |
| 1.92 | 88.7 | 88.7 | |
| 3.00 | 78.1 | 78.1 | |
| 3.96 | 60.7 | 60.7 | |
| 4.66 | 41.1 | 41.1 | Flag 1 ends: Outside this model: fast glucose uptake |
| 5.00 | 100.0 | 100.0 | |
| 6.00 | 71.6 | 71.6 | |
| 6.96 | 65.6 | 65.6 | |
| 7.92 | 58.5 | 58.5 | |
| 9.00 | 48.7 | 48.7 | |
| 9.96 | 38.1 | 38.1 | |
| 10.59 | 30.0 | 30.0 | Flag 2 starts: Unverified: Van 't Riet's range |
| 10.59 | 30.0 | 30.0 | Rescue step 1: 900 rpm |
| 10.92 | 49.0 | 25.3 | |
| 12.00 | 37.2 | 8.0 | |
| 12.32 | – | 2.2 | Flag 3 starts: Outside this model: oxygen-limited |
| 12.32 | – | 2.2 | Oxygen runs out |
| 12.56 | 30.0 | – | Flag 2 ends: Unverified: Van 't Riet's range |
| 12.56 | 30.0 | – | Flag 2 starts: Unverified: Van 't Riet's range |
| 12.56 | 30.0 | – | Rescue step 2: 2 vvm |
| 12.96 | 47.0 | – | |
| 13.92 | 36.4 | – | |
| 14.43 | 30.0 | – | Rescue step 3: 40 % O₂ |
| 15.00 | 112.9 | – | |
| 15.96 | 97.7 | – | |
| 16.92 | 79.8 | – | |
| 18.00 | 56.0 | – | |
| 18.96 | 31.2 | – | |
| 19.00 | 30.0 | – | Rescue step 4: feed capped at μ 0.105 |
| 19.92 | 80.5 | – | |
| 21.00 | 69.5 | – | |
| 21.96 | 59.1 | – | |
| 22.92 | 48.1 | – | |
| 24.00 | 34.8 | – |
Where this run leaves the model
- Flag 1: Outside this model until 4.7 h: E. coli makes acetate when it takes up glucose fast, even with oxygen present, which this model does not simulate. Here glucose uptake is 0.8 g per g of dry biomass per hour or more, the rate at which E. coli MG1655 began to make acetate in chemostats (Vemuri et al. 2006).
- Flag 2: With rescue: Van 't Riet's range decides this run's range verdict from 10.6 to 12.6 h and from 12.6 h. Unverified: not yet checked against Van 't Riet 1979; the range was compared only with a scanned copy, so treat the verdict as unconfirmed.
- Flag 3: Without rescue: Outside this model from 12.3 h: when oxygen limits growth, E. coli ferments part of its glucose, which this model does not simulate. Here the simulated vessel cannot supply the oxygen the culture needs.
The rescue
- Raise the agitation to 900 rpm at 10.6 h (kLa 637 per hour, extrapolated): the vessel's limit
- Raise the gas flow to 2 vvm at 12.6 h (kLa 842 per hour, extrapolated): the vessel's limit
- Enrich the inlet gas to 40 percent O₂ at 14.4 h: the vessel's limit
- Cap the feed at μ 0.105 per hour from 19.0 h
With these steps dissolved oxygen stays at or above the setpoint to the end of the run.
Within the limits you enter; ignores cooling capacity.
The rescue cascade stays within the agitation, gas-flow and oxygen-enrichment limits you enter, and ignores cooling capacity, vessel pressure and gas-safety limits. Oxygen enrichment near flammable solvents or vapours is a fire and explosion hazard. Do not run a vessel from these outputs without your own engineering review.
Every value and where it comes from
| Parameter | Value | Source |
|---|---|---|
| Maximum specific growth rate, μmax | 0.61 per hour | CitedHaverkorn van Rijsewijk et al. 2011Table 1: 0.61 ± 0.01 per hour, wild-type BW25113 in batch on glucose (M9, 37 °C)Reported range 0.54 to 1.23 per hour (Kovárová-Kovar and Egli 1998, Table 2, the 37 °C rows; strains and methods at 37 °C on glucose) |
| Substrate affinity, Ks | 0.000033 g/L | CitedKovárová et al. 1996, as quoted by Kovárová-Kovar and Egli 1998abstract: about 33 µg/L at every temperature from 17.4 to 40 °C (ML30, glucose-limited chemostats)Reported range 0.000033 to 0.00716 g/L (Kovárová-Kovar and Egli 1998, Table 2, the 37 °C rows; strains and methods at 37 °C on glucose) |
| Substrate inhibition, Ki | none | Model choiceMonod: no substrate inhibition |
| True yield of biomass on substrate, Y | 0.422 g/g | Cited, convertedNanchen et al. 2006Table 1: MG1655, glucose-limited chemostats, 37 °C; 76 ± 3 g dry weight per mol glucose ÷ 180.156 g/molReported range 0.422 to 0.572 g/g (Nanchen et al. 2006, Table 1; the strains listed there, 76 to 103 g/mol) |
| Maintenance, ms | 0.0667 g/g/h | Cited, convertedNanchen et al. 2006Table 1: MG1655, glucose-limited chemostats, 37 °C; 0.37 ± 0.09 mmol glucose/g/h × 0.180156 g/mmolReported range 0.0198 to 0.0685 g/g/h (Nanchen et al. 2006, Table 1; the strains listed there, 0.11 to 0.38 mmol/g/h) |
| Oxygen affinity, Ko | 0.00387 mg/L | Cited, convertedStolper et al. 2010Results: Ks for growth 121 ± 20 nM O₂ (K-12, on glycerol, 37 °C); 121 nM × 31.998 g/molReported range 0.000096 to 0.0064 mg/L (Stolper et al. 2010, Discussion; 3 to 200 nM, the Km of the cytochrome bd and bo oxidases quoted there) |
| Substrate | glucose | Setting |
| Biomass carbon fraction | 0.4738 g C per g dry weight | CitedFolsom and Carlson 2015Table 2: glucose-limited chemostats, D 0.1 to 0.4 per hour, mean 47.38 ± 0.74 percent (MG1655)Reported range 0.4706 to 0.4769 g C per g dry weight (Folsom and Carlson 2015, Table 2; the four glucose-limited dilution rates) |
| Biomass degree of reduction, γX | 4.17 per C-mol | Cited, convertedFolsom and Carlson 2015Table 2: glucose-limited chemostats, mean formula CH1.725N0.23O0.4325; 4 + H − 2·O − 3·N, ammonium the nitrogen source (the table's own degree of reduction, 4.86, counts nitrogen at oxidation state 0)Reported range 4.14 to 4.2 per C-mol (Folsom and Carlson 2015, Table 2; the four glucose-limited dilution rates' formulas) |
| Growth-associated product, α | 0 g/g | Model choiceproduct off |
| Non-growth-associated product, β | 0 g/g/h | Model choiceproduct off |
| Starting biomass, X0 | 0.1 g/L | Setting |
| Starting substrate, S0 | 4 g/L | Setting |
| Starting volume, V0 | 7 L | Setting |
| Mode | fed-batch | Setting |
| Feed law | exponential | Setting |
| Feed starts at | 5 h | Setting |
| Substrate in the feed, Sf | 500 g/L | Setting |
| Set growth rate, μset | 0.2 per hour | Setting |
| The pump's limit, Fmax | 0.3 L/h | Setting |
| Working volume limit, Vmax | 10 L | Setting |
| Feed stops at | none | Setting |
| Temperature | 37 °C | Setting |
| Headspace pressure | 1 atm, absolute | Setting |
| Inlet O₂ | 20.95 % of the dry gas | Setting |
| Gas flow | 1 vvm | Setting |
| Agitation | 600 rpm | Setting |
| kLa from | value | Setting |
| kLa at these settings | 400 per hour | Setting |
| DO setpoint | 30 % air saturation | Setting |
| Vessel diameter, T | 0.22 m | Setting |
| Impeller diameter, D | 0.088 m | Setting |
| Rushton impellers | 1 | Setting |
| Broth, for the correlation | coalescing | Setting |
| Agitation limit | 900 rpm | Setting |
| Gas flow limit | 2 vvm | Setting |
| Inlet O₂ limit | 40 % | Setting |
| Gas-flow basis | actual | Model choiceLegacy vvm is actual dry-gas volume at reactor temperature and pressure, per current liquid volume. |
| Feed dissolved oxygen | 0 mg/L | Model choiceDefault feed is deoxygenated; change to the measured feed dissolved oxygen. |
Mass balance
Over the run, carbon closes within 10⁻⁷ and electrons within 10⁻⁷ of what went in, as a fraction of it: the substrate fed and taken up against the biomass, product, CO₂ and what the feed and draw-off carry.
Verification
This preset's run is one of the 33 scenarios the engine is checked against SciPy's Radau on (2026-10-07), and its golden run holds this published version still. The verification page lists the fixtures, their hashes and the tolerances.
Preset e-coli-fed-batch@1; model 2.0.0; solver 1.1.0. Computed when this page was built; the app recomputes it in your browser.
Draft until the independent bioprocess reviewer signs the equations, the presets and the fixtures (Q-19).
Limits
- Teaching and estimation model, not a validated process model.
- The rescue cascade stays within the agitation, gas-flow and oxygen-enrichment limits you enter, and ignores cooling capacity, vessel pressure and gas-safety limits. Oxygen enrichment near flammable solvents or vapours is a fire and explosion hazard. Do not run a vessel from these outputs without your own engineering review.
- Presets combine literature values and operating choices from multiple conditions; they are teaching scenarios, not validated strain/process parameter sets. Quantitative process use requires measured parameters and specialist validation.
- Literature growth-fitted Ks is not interchangeable with the uptake Ks used here. Without product/inhibition and with excess oxygen, growth half-saturation is Ks × (1 + 2Yms/μmax). Presets are not silently transformed without refitting.
- Nominal Rushton Np=5 assumes standard baffled turbulent geometry (Re above 10⁴, Kaiser et al. 2017); the app does not compute Reynolds number or broth rheology. Vessel geometry, multiple impellers and real-broth transfer need measurement.
- An unstructured uptake/Monod model with mixed literature parameters has not been quantitatively validated for a given strain or process. Reported parameter ranges do not establish predictive uncertainty for these composite presets.
- The Crabtree effect is not modelled; the S. cerevisiae preset stays glucose-limited, and a run that leaves glucose limitation or runs short of oxygen is flagged.
- The acetate onset is MG1655's; other strains differ.
- CHO and other sparged mammalian cultures are not modelled for oxygen limitation.
- The DO setpoint is a process margin, not a kinetic threshold.
- The gas phase is taken at steady state (no hold-up). Feed oxygen enters dC/dt through (Fin/V)(Cfeed−C); zero feed DO is the default. The chart shows oxygen in the liquid; a DO probe's reading lags it by the probe's response time, which is not modelled.
- Excursions past a limit that last less than about 3 minutes are not flagged: the model leaves out the gas phase's hold-up and the DO probe's response, which act over about a minute.
- Gas flow has an explicit actual or reference basis, including reference temperature and absolute pressure. The same ideal dry-inlet-gas conversion supplies molar flow, superficial velocity and gassed power. Gas-flow humidification and hydrostatic expansion are not modelled; freshwater solubility includes its water-vapour correction, but broth salinity and composition require measurement. Vvm is per current liquid volume; flow rises during feeding while kLa is held between aeration changes.
- Van 't Riet's empirical correlation supplies no validated prediction interval for your vessel or broth. Yawalkar et al. 2002 report substantial deviations for some conditions; use measured kLa when available.
- Real broths fall anywhere between the coalescing form used by default and the non-coalescing form; enter a measured kLa if you have one.
- The presets' 10 L vessel sits at the lower edge of the tank sizes Hughmark's correlation was fitted on (0.21 to 3.33 m).
- kLa is taken at the volume where the aeration is set, at the start or at a rescue step, and held as the volume grows.
- The product is biomass-equivalent for substrate yield, carbon fraction and degree of reduction. Product-enabled OUR, CER and RQ are approximate for chemically different products.
- When uptake falls below maintenance, nothing grows and nothing decays: death and endogenous decay are not modelled.
- The CO₂ evolution rate is the CO₂ produced: dissolved CO₂ and bicarbonate are not modelled.
- No heat transfer, pH control, parameter fitting or Monte Carlo.
- Scale-up assumes geometrically similar vessels with the same impellers, Np and gas flow per volume; constant P/V holds ungassed power, so gassed P/V differs between scales. It ignores cooling, mixing time and shear. Every kLa is the correlation's, flagged outside its fitted range, with no prediction interval.
- The yield check refuses only what the carbon and electron balances forbid; a feasible yield is not thereby a likely one.
- The model's feed law; pump calibration, line dead volume and feed density at temperature are yours to check.
- A complex medium is context; the model simulates one declared substrate; delivery is not verified.
- Matched by exact compound identity against a short ruled list; names are not read; glucose monohydrate is converted to anhydrous glucose by formula mass, assuming the exact monohydrate.
- An apparent ln(response) slope over your window; not the model's μmax; no OD-to-biomass conversion; no interval.
- Elapsed time from a declared event is not physiological equivalence; responses are not converted or overlaid on one axis; a simulation reference is context only.
- Estimates one parameter, conditional on every other value as entered; a wrong fixed value biases it without warning.
- Needs measured biomass as mass concentration and measured substrate; optical density alone is refused.
- No confidence interval; a profile is a numerical diagnostic.
- Values marked “Unverified” have not yet been checked against their sources; each is checked, or removed, before this app leaves preview.
- A link carries the preset and every parameter you changed, never results; a run you keep stays in this browser. No account needed.
- No offline use: the pages are served by the site, and nothing is installed.
A simulation, not a forecast. Every output follows from the model equations and the parameters you entered. It is a teaching and estimation model, not a validated process model, and not a prediction for any real strain, vessel or process.
Open in the appThe app shows the run in full, with its flags, and every value you can change.