This calculator estimates the maximal specific growth rate (μmax) based on thermodynamic principles, derived by equating the maximal rate of catabolic Gibbs energy production to the Gibbs energy required for growth and maintenance under maximal growth conditions.
The formula used is (Eq. 3.9 from Heijnen):
μmax = [ 3 * (-ΔGCAT / γd - 4.5) / (1 / Ymaxgx) ] * exp[ - (69000 / R) * ( (1 / T) - (1 / 298) ) ]
Where:
- μmax: Maximal specific growth rate (h⁻¹).
- 3: Maximal electron transport rate at 298 K (mol e⁻ C-mol⁻¹ X h⁻¹).
- (-ΔGCAT / γd): Catabolic Gibbs energy release per transferred mole of electrons (kJ/mol e⁻).
- 4.5: Maintenance energy rate at 298 K (kJ C-mol⁻¹ X h⁻¹).
- 1/Ymaxgx: Minimum Gibbs energy for growth per unit biomass (kJ C-mol⁻¹ X).
- T: Temperature (Kelvin).
- 69000: Activation energy-like term (J/mol).
- R: Ideal gas constant (8.314 J/mol·K).
- 298: Reference temperature (Kelvin).
This equation provides reasonable estimates for μmax across various microorganisms, linking growth kinetics directly to the underlying bioenergetics and temperature.