Monod Fed Batch Growth and Substrate Model Simulator
Run the existing E. coli fed-batch teaching preset and inspect how substrate supply, biomass and oxygen demand interact. Its literature-based parameters are explicitly a composite of several strains and experiments. The curves are model outputs for the stated assumptions, not a validated prediction for one production strain or a mammalian culture.
The cited preset uses a 24-hour horizon, 37 °C, 7 L starting volume in a 10 L vessel and a batch phase followed by exponential feed. Its parameter table distinguishes cited biology, conversions, model choices and operating settings. The growth-rate source is BW25113, glucose affinity ML30, and several yield, maintenance and composition inputs MG1655; they are not one experimentally measured strain profile.
Follow the balances before interpreting the curve
The classical Monod relationship describes saturating growth with a limiting substrate. This engine instead applies the saturating factors to substrate uptake, allocates maintenance and derives growth from the remaining budget. Its uptake half-saturation constant is a concentration, while maximum growth is a rate. Literature growth-fitted affinity values are therefore being reused under an explicit modelling assumption. Oxygen also limits uptake, so substrate availability alone does not determine growth.
The fed-batch liquid volume changes with feed. A concentration can flatten because of dilution even while total biomass increases. Follow substrate amount, biomass concentration and vessel volume together. The model also accounts for maintenance and its declared uptake relationships, so supplied carbon is not assumed to become new biomass with perfect efficiency.
Interpret the feed target as an operating assumption
An exponential feed is designed around a chosen growth-rate target and the model inputs. It does not guarantee that the organism achieves that target. Oxygen availability, substrate accumulation, maximum flow and vessel capacity can constrain the simulated trajectory. The timing of the feed transition and the initial substrate pool therefore matter as much as the final curve shape.
The preset separates literature-derived biological parameters from operating settings such as starting volume and feed concentration. Changing an operating setting is a scenario calculation; it is not new evidence about the organism. Preserve the preset version and each override so that a comparison between runs has a clear, reproducible cause.
Use parameter provenance to judge transferability
The cited values come from several E. coli strains and experimental regimes. A convenient composite can teach balance behaviour while remaining unsuitable for direct process prediction. Examine the original strain, medium, temperature and measurement basis of an input before transferring it. A precise numerical value does not remove uncertainty caused by applying it outside its experimental context.
The independent numerical fixtures test whether the equations and solver behave as specified. They do not prove that those equations describe every reactor. Validation against suitable measurements is a separate task. Keep solver correctness, parameter evidence and biological adequacy distinct when explaining what a simulation can support.
Equations and variables
Substrate uptake with Monod and oxygen factors
qS = (μmax/Y + ms) × S/(Ks + S) × C/(Ko + C)
- qS, ms
- Specific substrate uptake and maintenance requirement (g substrate g biomass⁻¹ h⁻¹)
- μmax
- Maximum growth rate (h⁻¹)
- Y
- Biomass yield on substrate (g g⁻¹)
- S, Ks
- Substrate concentration and uptake half-saturation constant (g L⁻¹)
- C, Ko
- Dissolved oxygen and oxygen half-saturation constant (mg L⁻¹)
Product-free growth after maintenance
μ = Y × max(0, qS − ms)
- μ
- Growth rate for this product-off preset (h⁻¹)
- Y, qS, ms
- Yield, substrate uptake and maintenance as defined above
Fed-batch biomass concentration balance
dX/dt = μX − (F/V)X
- X
- Biomass concentration (g L⁻¹)
- F
- Feed flow into the vessel (L h⁻¹)
- V
- Liquid volume (L)
- μ
- Modelled specific growth rate (h⁻¹)
Scope and limitations
- The preset combines literature values across strains and conditions. It is a reproducible teaching model, not a validated strain-specific process model.
- The preset selects Monod kinetics without substrate inhibition. Optional Haldane inhibition is a different assumption and requires an appropriate inhibition constant.
- The engine applies literature growth-fitted Ks values to substrate uptake, then allocates maintenance before growth. This modelling choice changes the growth half-saturation behaviour. No validated mammalian-cell biology or endogenous decay is claimed.
Sources and provenance
- Bioreactor model methods and independent verificationOriginal reference calculations; see source notices
Model outputs are simulations, not observations from a reactor.
- Haverkorn van Rijsewijk et al.: E. coli flux and growth measurementsCited method/data facts; existing preset attribution
- Kovárová et al.: glucose-limited E. coli ML30 growthCited parameter; existing preset read scope is abstract
- Nanchen et al.: E. coli continuous-culture fluxesCited parameter facts; existing preset attribution
Technical questions
Why does biomass concentration depend on feed volume?
Feed changes both the amount of biomass supported and the liquid volume used to express its concentration. The dilution term appears in the concentration balance even when no culture is removed. Inspect total amount and concentration separately when interpreting a rising-volume fed batch.
Does Monod kinetics include substrate inhibition?
The Monod form used by this preset saturates with increasing substrate and has no inhibitory term. The optional Haldane form adds S squared divided by an inhibition constant to the denominator. Selecting that form changes the model and requires an appropriate parameter, not just a new chart label.
Can this preset predict my production strain?
It provides a transparent starting model with cited and declared inputs. Its composite parameters and simplified mechanisms have not been calibrated to your strain, medium, vessel and process. Compare against suitable observations and inspect the model limitations before drawing process-specific conclusions.
Connected workflows
- Oxygen transfer and uptake modelling
Inspect the oxygen-transfer constraints that can limit growth.
- Viable-cell seeding volumes
Compare a cell-amount balance with a dynamic growth model.
- Protein A280 concentration calculation
Connect simulated production questions to explicit protein amount measurements.
- Haldane Substrate Inhibition and Growth Kinetics Model
Compare Monod uptake with the substrate-inhibited Haldane model on the Pichia preset.
- Exponential Fed-Batch Feed Rate and Growth Simulator
Follow the exponential feed law that holds a constant specific growth rate.