When microbial growth depends on more than one essential substrate (e.g., carbon source and nitrogen source), the overall growth rate can be limited by the substrate that imposes the most severe restriction. This model represents such scenarios by assuming the specific growth rate (μ) relative to the maximum (\(\mu_{\max}\)) is determined by the *minimum* of the individual Monod terms for each substrate.
The equation is:
μ / μmax = min [ (cs,1 / (cs,1 + Ks,1)) , (cs,2 / (cs,2 + Ks,2)) ]
Where:
- μ: Specific growth rate (units typically h⁻¹).
- μmax: Maximum specific growth rate (same units as μ).
- cs,1, cs,2: Concentrations of limiting substrates 1 and 2 (units e.g., g/L, mg/L).
- Ks,1, Ks,2: Monod constants for substrates 1 and 2 (same units as corresponding cs).
This model is often applied when substrates are non-substitutable (e.g., one is a carbon source, the other a nitrogen source). Ensure consistent units between cs,i and Ks,i for each substrate.
| Species | Substrate | Ks (mg l⁻¹) |
|---|---|---|
| Aerobacter aerogenes | Glucose | 8 |
| Aspergillus oryzae | Glucose | 5 |
| Escherichia coli | Glucose | 4 |
| Klebsiella aerogenes | Glucose | 9 |
| Klebsiella aerogenes | Glycerol | 9 |
| Klebsiella oxytoca | Glucose | 10 |
| Klebsiella oxytoca | Arabinose | 50 |
| Klebsiella oxytoca | Fructose | 10 |
| Penicillium chrysogenum | Glucose | 4 |
| Saccharomyces cerevisiae | Glucose | 180 |