Re-interpretation of the logistic equation for batch microbial growth in relation to Monod kinetics

Lett Appl Microbiol. 2009 Apr;48(4):398-401. doi: 10.1111/j.1472-765X.2008.02537.x. Epub 2009 Jan 23.


Aims: To determine the underlying substrate utilization mechanism in the logistic equation for batch microbial growth by revealing the relationship between the logistic and Monod kinetics. Also, to determine the logistic rate constant in terms of Monod kinetic constants.

Methods and results: The logistic equation used to describe batch microbial growth was related to the Monod kinetics and found to be first-order in terms of the substrate and biomass concentrations. The logistic equation constant was also related to the Monod kinetic constants. Similarly, the substrate utilization kinetic equations were derived by using the logistic growth equation and related to the Monod kinetics.

Conclusion: It is revaled that the logistic growth equation is a special form of the Monod growth kinetics when substrate limitation is first-order with respect to the substrate concentration. The logistic rate constant (k) is directly proportional to the maximum specific growth rate constant (mu(m)) and initial substrate concentration (S(0)) and also inversely related to the saturation constant (K(s)).

Significance and impact of the study: The semi-empirical logistic equation can be used instead of Monod kinetics at low substrate concentrations to describe batch microbial growth using the relationship between the logistic rate constant and the Monod kinetic constants.

MeSH terms

  • Bacteria / growth & development*
  • Bacteria / metabolism
  • Bacteriological Techniques / methods
  • Biomass
  • Bioreactors
  • Culture Media
  • Kinetics
  • Logistic Models*


  • Culture Media