Evaluation and Mathematical Analysis of a Four-Dimensional Lotka&ndash;Volterra-like Equation Designed to Describe the Batch Nisin Production System

Giménez-Palomares, Fernando; Fernández de Córdoba, Pedro; Mejuto, Juan C.; Bendaña-Jácome, Ricardo J.; Pérez-Guerra, Nelson

doi:10.3390/math10050677

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Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System

Fernando Giménez-Palomares

¹,

Pedro Fernández de Córdoba

Juan C. Mejuto

^2,*

Ricardo J. Bendaña-Jácome

³ and

Nelson Pérez-Guerra

^4,*

Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain

Department of Physical Chemistry, Faculty of Science, University of Vigo, 32004 Ourense, Spain

Department of Engineering, Materials, Structural Mechanics and Construction, Faculty of Sciences, University of Vigo, Ourense Campus, As Lagoas, s/n, 32004 Ourense, Spain

⁴

Department of Analytical and Food Chemistry, Faculty of Sciences, University of Vigo, Ourense Campus, As Lagoas, s/n, 32004 Ourense, Spain

Authors to whom correspondence should be addressed.

Academic Editors: Theodore E. Simos, Charampos Tsitouras and Christopher Goodrich

Mathematics 2022, 10(5), 677; https://doi.org/10.3390/math10050677

Received: 30 December 2021 / Revised: 10 February 2022 / Accepted: 16 February 2022 / Published: 22 February 2022

(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)

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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. View Full-Text

Keywords: nisin; asymptotically stable equilibrium point; batch fermentation; four-dimensional predator-prey system; mathematical analysis

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MDPI and ACS Style

Giménez-Palomares, F.; Fernández de Córdoba, P.; Mejuto, J.C.; Bendaña-Jácome, R.J.; Pérez-Guerra, N. Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System. Mathematics 2022, 10, 677. https://doi.org/10.3390/math10050677

AMA Style

Giménez-Palomares F, Fernández de Córdoba P, Mejuto JC, Bendaña-Jácome RJ, Pérez-Guerra N. Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System. Mathematics. 2022; 10(5):677. https://doi.org/10.3390/math10050677

Chicago/Turabian Style

Giménez-Palomares, Fernando, Pedro Fernández de Córdoba, Juan C. Mejuto, Ricardo J. Bendaña-Jácome, and Nelson Pérez-Guerra. 2022. "Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System" Mathematics 10, no. 5: 677. https://doi.org/10.3390/math10050677

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Evaluation and Mathematical Analysis of a Four-Dimensional Lotka–Volterra-like Equation Designed to Describe the Batch Nisin Production System

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