Logistic Equations Effectively Model Mammalian Cell Batch and Fed-Batch Kinetics by Logically Constraining the Fit

Abstract

A four-parameter logistic equation was used to fit batch and fed-batch time profiles of viable cell density in order to estimate net growth rates from the inoculation through the cell death phase. Reduced three-parameter forms were used for nutrient uptake and metabolite/product formation rate calculations. These logistic equations constrained the fits to expected general concentration trends, either increasing followed by decreasing (four-parameter) or monotonic (three-parameter). The applicability of this approach was first verified for Chinese hamster ovary (CHO) cells cultivated in 15-L batch bioreactors. Cell density, metabolite, and nutrient concentrations were monitored over time and used to estimate the logistic parameters by nonlinear least squares. The logistic models fit the experimental data well, supporting the validity of this approach. Further evidence to this effect was obtained by applying the technique to three previously published batch studies for baby hamster kidney (BHK) and hybridoma cells in bioreactors ranging from 100 mL to 300 L. In 27 of the 30 batch data sets examined, the logistic models provided a statistically superior description of the experimental data than polynomial fitting. Two fed-batch experiments with hybridoma and CHO cells in benchtop bioreactors were also examined, and the logistic fits provided good representations of the experimental data in all 25 data sets. From a computational standpoint, this approach was simpler than classical approaches involving Monod-type kinetics. Since the logistic equations were analytically differentiable, specific rates could be readily estimated. Overall, the advantages of the logistic modeling approach should make it an attractive option for effectively estimating specific rates from batch and fed-batch cultures.