Analysis of the logistic function model: derivation and applications specific to batch cultured microorganisms

Mathematical models are useful for describing microbial growth, both in natural ecosystems and under research conditions. To this end, a rate expression that accounted for depletion of nutrients was used to derive the logistic function model for batch cultures. Statistical analysis was used to demonstrate the suitability of this model for growth curve data. Two linear forms of the model and two procedures for calculating growth rate constants were derived to facilitate statistical evaluation of growth curves. The procedures for calculating growth rate constants were found to be useful for calculation of growth rate constants at each time point, or for estimating growth rate constants from early growth curve data. The utility of the logistic function model and its alternative forms is discussed with respect to planning experiments, analyzing growth curves for the effects of factors other than nutrient limitation, and developing more complete descriptions of cell proliferation.