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Drybench Bioreactor.
Pichia methanol fed-batch simulation
A Pichia methanol fed-batch with Haldane kinetics: growth, methanol, the feed and dissolved oxygen, each value with its source or labelled illustrative.
per hour
Change it to simulate this run again in your browser. Every other value is the preset's.
- Oxygen runs out
- Not within the run
- Lowest DO
- 40.6% air saturation
- Biomass at 24 h
- 24.6g/L
- Peak OUR
- 81.3mmol/L/h
The run
Show the data
| Time (h) | Dissolved oxygen (% air saturation) | Biomass (g/L) | Substrate (g/L) | Feed rate (L/h) | Event |
|---|---|---|---|---|---|
| 0.00 | 100.0 | 10 | 0 | 0.00886 | |
| 0.96 | 80.1 | 10.2 | 0.449 | 0.00921 | |
| 1.92 | 75.8 | 10.5 | 0.565 | 0.00957 | |
| 3.00 | 73.6 | 11 | 0.604 | 0.00999 | |
| 3.96 | 72.3 | 11.4 | 0.614 | 0.0104 | |
| 4.92 | 71.2 | 11.8 | 0.616 | 0.0108 | |
| 6.00 | 69.9 | 12.4 | 0.616 | 0.0113 | |
| 6.96 | 68.8 | 12.8 | 0.616 | 0.0117 | |
| 7.92 | 67.6 | 13.3 | 0.615 | 0.0122 | |
| 9.00 | 66.2 | 13.9 | 0.615 | 0.0127 | |
| 9.96 | 65.0 | 14.4 | 0.614 | 0.0132 | |
| 10.92 | 63.6 | 15 | 0.613 | 0.0137 | |
| 12.00 | 62.1 | 15.6 | 0.613 | 0.0143 | |
| 12.96 | 60.7 | 16.2 | 0.612 | 0.0149 | |
| 13.92 | 59.3 | 16.8 | 0.612 | 0.0155 | |
| 15.00 | 57.6 | 17.5 | 0.611 | 0.0161 | |
| 15.96 | 56.0 | 18.2 | 0.611 | 0.0168 | |
| 16.92 | 54.4 | 18.8 | 0.61 | 0.0174 | |
| 18.00 | 52.5 | 19.6 | 0.61 | 0.0182 | |
| 18.96 | 50.7 | 20.4 | 0.61 | 0.0189 | |
| 19.92 | 48.9 | 21.1 | 0.609 | 0.0197 | |
| 21.00 | 46.8 | 22 | 0.609 | 0.0205 | |
| 21.96 | 44.9 | 22.8 | 0.609 | 0.0213 | |
| 22.92 | 42.9 | 23.6 | 0.608 | 0.0222 | |
| 24.00 | 40.6 | 24.6 | 0.608 | 0.0231 |
Where this run leaves the model
This run stays inside the model and the correlations' ranges.
With these kinetics growth tops out at 0.08 per hour (at 3.6 g/L methanol); wild-type X-33 grew at 0.10 per hour at 25 °C and washed out at 0.13 (Tomàs-Gamisans et al. 2018). The preset's feed (0.04 per hour) sits below both.
Growth kinetics (μmax, Ks, Ki): a recombinant strain in fed-batch (Zhang et al. 2000), as quoted by Cos et al. 2006, temperature not stated in the source read; yield, maintenance and composition: wild-type X-33 in methanol-limited chemostats at 25 °C (Tomàs-Gamisans et al. 2018).
Maintenance at both ends of its range
The data do not resolve maintenance, so the run is shown at both ends of its range, with everything else as the preset sets it.
| Maintenance (g/g/h) | Biomass at the end (g/L) | Lowest DO (% air saturation) | Peak OUR (mmol/L/h) | DO below the setpoint |
|---|---|---|---|---|
| 0 | 24.6 | 42.8 | 78.3 | never |
| 0.021 | 24.4 | 25.5 | 101.6 | from 22.3 h |
Every value and where it comes from
| Parameter | Value | Source |
|---|---|---|
| Maximum specific growth rate, μmax | 0.146 per hour | CitedZhang et al. 2000, as quoted by Cos et al. 2006the Haldane fitReported range 0.087 to 0.146 per hour (Cos et al. 2006, Table 2; the two Haldane fits tabulated there (refs. [36] and [37])) |
| Substrate affinity, Ks | 1.5 g/L | CitedZhang et al. 2000, as quoted by Cos et al. 2006the Haldane fitReported range 1.35 to 1.5 g/L (Cos et al. 2006, Table 2; the two Haldane fits tabulated there (refs. [36] and [37])) |
| Substrate inhibition, Ki | 8.86 g/L | CitedZhang et al. 2000, as quoted by Cos et al. 2006the Haldane fitReported range 7.08 to 8.86 g/L (Cos et al. 2006, Table 2; the two Haldane fits tabulated there (refs. [36] and [37])) |
| True yield of biomass on substrate, Y | 0.411 g/g | Our fitTomàs-Gamisans et al. 2018Table 1: methanol, qS at the measured growth rates μexp 0.035, 0.049, 0.065, 0.084 and 0.099 per hour; least-squares line qS = μ/Y + ms through the five points (unweighted): slope 2.4305 g/g, intercept 0.0027 g/g/hReported range 0.37 to 0.46 g/g (Tomàs-Gamisans et al. 2018, Table 1; two standard errors of the fit) |
| Maintenance, ms | 0.0027 g/g/h | Our fitTomàs-Gamisans et al. 2018Table 1: methanol, qS at the measured growth rates μexp 0.035, 0.049, 0.065, 0.084 and 0.099 per hour; least-squares line qS = μ/Y + ms through the five points (unweighted): slope 2.4305 g/g, intercept 0.0027 g/g/hReported range 0 to 0.021 g/g/h (Tomàs-Gamisans et al. 2018, Table 1; two standard errors of the fit, cut at zero; Dietzsch et al. 2011's MutS value, 0.016, lies inside it)Our fit of Pirt's line to the five chemostats of Tomàs-Gamisans et al. 2018 (Table 1); the data do not resolve maintenance. Dietzsch's MutS value, 0.016, lies inside this range. |
| Oxygen affinity, Ko | 0.01 mg/L | Illustrativeno source read gives Pichia's oxygen affinity; set at the order of E. coli's measured value (Stolper et al. 2010, 121 nM, 0.004 mg/L), rounded upReported range 0.001 to 0.1 mg/L (Stolper et al. 2010, Results; the tenfold test's span)Illustrative: not a measured value. Changing it tenfold either way does not change biomass, DO, OUR, the time oxygen runs out or the rescue steps at the precision shown (see the verification page). |
| Substrate | methanol | Setting |
| Biomass carbon fraction | 0.4228 g C per g dry weight | CitedTomàs-Gamisans et al. 2018Table 2: methanol, the weighted average, 42.28 ± 0.53 percent (X-33, 25 °C)Reported range 0.418 to 0.432 g C per g dry weight (Tomàs-Gamisans et al. 2018, Table 2; the three methanol dilution rates) |
| Biomass degree of reduction, γX | 3.999 per C-mol | Cited, convertedTomàs-Gamisans et al. 2018Table 2: methanol, the weighted average, C 42.28, H 6.43, N 10.06, O 33.83 percent; CH1.812N0.204O0.601 per C-mol, 4 + H − 2·O − 3·N, ammonium the nitrogen source |
| 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 | 10 g/L | Setting |
| Starting substrate, S0 | 0 g/L | Setting |
| Starting volume, V0 | 7 L | Setting |
| Mode | fed-batch | Setting |
| Feed law | exponential | Setting |
| Feed starts at | 0 h | Setting |
| Substrate in the feed, Sf | 790 g/L | Setting |
| Set growth rate, μset | 0.04 per hour | Setting |
| The pump's limit, Fmax | 0.1 L/h | Setting |
| Working volume limit, Vmax | 10 L | Setting |
| Feed stops at | none | Setting |
| Temperature | 25 °C | Setting |
| Headspace pressure | 1 atm, absolute | Setting |
| Inlet O₂ | 20.95 % of the dry gas | Setting |
| Gas flow | 1 vvm | Setting |
| Agitation | 800 rpm | Setting |
| kLa from | value | Setting |
| kLa at these settings | 700 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 10⁻⁸ and electrons within 10⁻⁸ 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 pichia-aox1@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.