Modeling the batch bacteriocin production system by lactic acid bacteria by using modified three-dimensional Lotka–Volterra equations

• A model that relates culture pH, biomass and nisin production was developed.
• The model was based on three-dimensional predator–prey Lotka–Volterra systems.
• The model successfully described other bacteriocin production systems.

Different batch cultures of Lactococcus lactis CECT 539, a nisin-producing strain, were carried out in culture media prepared with whey and mussel processing wastes. From these cultures, a reasonable system of differential equations, similar to the three-dimensional Lotka–Volterra two predators-one prey model, was set up to describe, for the first time, the relationship between the absolute rates of growth, pH drop and nisin production.Thus, the nisin production system was described as a three-species (pH, biomass and nisin) ecosystem. In this case, both nisin and biomass production were considered as two pH-dependent species that compete for the nitrogen source. Excellent agreement (R2 values ≥0.9885) resulted between model predictions and the experimental data, and significant values for all the model parameters were obtained. The developed model was demonstrated (R2 values ≥0.9874) for five batch cultivations of the strains L. lactis CECT 539 in MRS broth and Lactobacillus sakei LB 706 (sakacin A producer), Pediococcus acidilactici LB42-923 (pediocin AcH producer), L. lactis ATCC 11454 (nisin producer) and Leuconostoc carnosum Lm1 (leuconocin Lcm1 producer) in TGE broth. These results suggest that the batch bacteriocin production system in these culture media can be successfully described by using the Lotka–Volterra approach.