An unsteady, unstructured, unsegregated and based on first principles mathematical model has been proposed to describe IPTG (isopropyl-β-d-tiogalactopiranoside) transport in induced fed-batch cultures of E. coli M15 ΔglyA [pQEαβrham] [pREP4] producing rhamnulose 1-phosphate aldolase (RhuA). The model predicts extracellular and intracellular IPTG concentration. Experimental extracellular IPTG concentrations under different operational conditions were obtained by HPLC–MS analysis. These experimental data were used to fit the parameters of the model. The model was also able to predict the experimental behavior of two different E. coli strains producing fuculose 1-phosphate aldolase (FucA). IPTG transport to cells was the contribution of three processes: a diffusion process, and two active processes (one non-specific and another specific).
Calleja, D., Fernández-castañé, A., Pasini, M., De Mas, C., & López-santín, J. (2014). Quantitative modeling of inducer transport in fed-batch cultures of Escherichia coli. Biochemical Engineering Journal, 91, 210-219. https://doi.org/10.1016/j.bej.2014.08.017