The Monod model is a widely used mathematical model to describe the relationship between the specific growth rate (μ) of a microorganism and the concentration of a limiting substrate (cs). It assumes that at low substrate concentrations, the growth rate is proportional to cs, while at high concentrations, the rate approaches a maximum value (μmax).
The Monod equation is:
μ = μmax * (cs / (cs + Ks))
Where:
- μ: Specific growth rate (units typically h⁻¹).
- μmax: Maximum specific growth rate (same units as μ).
- cs: Concentration of the limiting substrate (units e.g., g/L, mg/L, mol/L).
- Ks: Monod constant or saturation constant (same units as cs). It represents the substrate concentration at which the specific growth rate is half of the maximum (μ = 0.5 * μmax).
Ensure that the units for cs and Ks are consistent.
| 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 |