Abstract
Nisin, an antibacterial compound produced by Lactococcus lactis strains, has been approved by the US Food and Drug Administration to be used as a safe food additive to control the growth of undesirable pathogenic bacteria. Nisin is commonly described as a pH-dependent primary metabolite since its production depends on growth and culture pH evolution. However, the relationships between bacteriocin synthesis (BT), biomass production (X), culture pH, and the consumption of the limiting nutrient (total nitrogen: TN) have not been described until now. Therefore, this study aims to develop a competitive four-dimensional Lotka–Volterra-like Equation (predator-prey system) to describe these complex relationships in three series of batch fermentations with L. lactis CECT 539 in diluted whey (DW)-based media. The developed four-dimensional predator-prey system accurately described each individual culture, providing a good description of the relationships between pH, TN, X, and BT, higher values for R2 and F-ratios, lower values (<10%) for the mean relative percentage deviation modulus, with bias and accuracy factor values approximately equal to one. The mathematical analysis of the developed equation showed the existence of one asymptotically stable equilibrium point, and the phase’s diagram obtained did not show the closed elliptic trajectories observed in biological predator-prey systems.
Highlights
Nisin, a bacteriocin produced by Lactococcus lactis strains, has a wide antibacterial activity against food spoilage and pathogenic bacteria
Different mathematical models have been commonly used to describe the kinetics of growth (e.g., Verhulst, Gompertz, Richards, Bertalanffy, Weibull, and Monod) and bacteriocin synthesis by lactic acid bacteria (LAB) in batch fermentations [2,3,4,5,6,7,8]
The main contribution of this paper is the development and mathematical analysis, for the first time, of a four-dimensional predator-prey system for an accurate description of the batch nisin production system by L. lactis Corobllreoctthio. n (CECT) 539 in different series of fermentation in diluted whey (DW) media supplemented with different concentrations of glucose (DW-G cultures), total sugars and phosphorous (DW-TS-TP cultures), or MRS broth nutrients (DW-MRS cultures)
Summary
A bacteriocin produced by Lactococcus lactis strains, has a wide antibacterial activity against food spoilage and pathogenic bacteria. For high nisin production at low cost, it is necessary to know the relationship between the main culture variables, which could be elucidated with the use of appropriate mathematical models This could allow proper monitoring and control of these bioprocesses [2]. Different mathematical models have been commonly used to describe the kinetics of growth (e.g., Verhulst, Gompertz, Richards, Bertalanffy, Weibull, and Monod) and bacteriocin synthesis (e.g., unmodified and modified forms of the Luedeking–Piret model) by lactic acid bacteria (LAB) in batch fermentations [2,3,4,5,6,7,8] These models do not always provide an accurate or reasonable description of the bacteriocin production system
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