Modeling the effects of pH variation and bacteriocin synthesis on bacterial growth

Abstract

Bacteriocin secretion and the modification of extracellular pH are some competitive adaptations that bacteria have acquired to persist against adverse environmental conditions. Thus, its permanence in a microbial network is determined by the adaptation that the bacterium has, therefore, directly affecting the rate of bacterial growth and its population balance. In this regard, it should be noted that bacterial secretion plays an important role in bacterial control, both intra and inter-specific, by modifying the amount of bacteria in equilibrium, while the pH determines the maximum rate of bacterial growth and the effectiveness and degradation of bacteriocins release. From the point of view of mathematical modeling, these attributes favor extending the logistic growth model as a base system for bacterial growth by incorporating a bacteriocin-bacteria association term. On the other hand, bacteriocin secretion and pH variation are based on the Luedeking-Piret function, where pH levels influence each mathematical term of bacterial growth and bacteriocin concentration. Taking all of this into account, the ordinary differential equation model emerges, which, through Lyapunov’s theory, demonstrates the stability and absence of chaos in the proposed model, while the simulations confirm it. The modeling proposed in this work has the capacity to replicate diverse scenarios of great interest, such as microbial contamination in medical supplies and the food industry.