Modelling and simulation of cell growth dynamics, substrate consumption, and lactic acid production kinetics of Lactococcus lactis

Lactococcus lactis species have been and still are extensively investigated due to their significant commercial importance. Current scientific research focuses on strains utilized in food industry, due to their multiple uses in food and beverages fabrication. Biomass of Lactococcus lactis is of great interest as well as the end products of its metabolism such as lactic acid and nisin. However their production is constantly challenged due to end product inhibition occurring during intensive propagation of the coccus in reactor systems. To successfully predict the behavior of the culture, the approach of combining mathematics with biology, ergo the development of an unstructured mathematical model, was taken. Although Luedeking and Piret is the model that has been extensively used to demonstrate growth in end-product inhibition cultures, its applicability is limited due to its dependance on the specific growth and product coefficients, particularly related to the culturing conditions used. To overcome these hurdles, a combination of the non competitive single product end inhibition Taylor and Hinselwood models was used, with the significance of this model laying in the fact that it offers a feasible alternative to the commonly used model of Luedeking and Piret for describing fermentation kinetics governed by end-product inhibitions. The fitting with the experimental values, in batch mode, was tested in terms of the coefficient of determination (R²), having values 0.97 ～ 0.99 and suggesting a very good fitting with the experimental data. The model was further developed to achieve theoretical predictions of volumetric cell productivity in continuous and fed-batch mode of substrate feed in different culturring systems.