Table 3:

Example of kinetic models for substrate inhibition

Source	Equations
Haldane (Andrews, 1968)	$\mu =\frac{{\mu }_{\text{max}}}{\left(1+\frac{{\text{K}}_{\text{S}}}{\text{S}}\right)\left(1+\frac{\text{S}}{{\text{K}}_{\text{i},\text{S}}}\right)}$
Aiba et al. (1968)	$\mu ={\mu }_{\text{max}}\frac{\text{S}}{\text{S}+{\text{K}}_{\text{S}}}{\text{e}}^{\frac{-\text{S}}{{\text{K}}_{\text{i},\text{S}}}}$
Tessier (Edwards, 1970)	$\mu ={\mu }_{\text{max}}({\text{e}}^{\frac{-\text{S}}{{\text{K}}_{\text{i},\text{S}}}}-{\text{e}}^{\frac{-\text{S}}{{\text{K}}_{\text{i},\text{S}}}})$

μ = specific growth rate (h⁻¹), μ_max = maximum specific growth rate (h⁻¹), K_s = half-saturation constant (mg/L), S= substrate concentration (mg/L), K_i= inhibition constant (mg/L)