Product Inhibition Kinetics Calculator (μ)

The theoretical maximum specific growth rate in the absence of product inhibition.
The current concentration of the limiting substrate. Units must match Ks.
Saturation constant; substrate concentration at which μ ≈ 0.5 * μmax (without inhibition). Units must match cs.
The current concentration of the inhibitory product. Units must match Ki.
Product inhibition constant; characterizes the extent of inhibition by the product. Units must match p.

Calculation Explanation

Metabolic products generated during fermentation can inhibit microbial growth. This model extends the basic Monod equation to account for inhibition by a product concentration (\(p\)). A product inhibition constant (\(K_i\)) quantifies the inhibitory effect.

The equation for product inhibition kinetics is:
μ = μmax * (cs / (cs + Ks)) * (1 / (1 + p / Ki))

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).
- Ks: Monod constant or saturation constant (same units as cs).
- p: Concentration of the inhibitory product (units e.g., g/L, mg/L).
- Ki: Product inhibition constant (same units as p). A smaller Ki value indicates stronger inhibition at lower product concentrations.

Ensure that the units for cs and Ks are consistent, and the units for p and Ki are consistent.

Reference Data (Ks)

Table 6.1 Typical Ks values for different microbial cells growing on different sugars
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