title: Re-interpretation of the logistic equation for batch microbial growth in relation to Monod kinetics.
abstract: OBJECTIVE
  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.
  
  
  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.
  
  
  CONCLUSIONS
  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)).
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Environmental Engineering, Dokuz Eylul University, Buca, Izmir, Turkey. fikret.kargi@deu.edu.tr
authors.forename: F
authors.initials: F
authors.lastname: Kargi
mesh_terms: D001419:Bacteria / Q000254:growth & development* / Q000378:metabolism; D001431:Bacteriological Techniques / Q000379:methods; D018533:Biomass; D019149:Bioreactors; D003470:Culture Media; D007700:Kinetics; D016015:Logistic Models
chemical_list: D003470:Culture Media