Modeling of the competitive growth of Listeria monocytogenes and Lactococcus lactis in vegetable broth

Abstract

Current mathematical models used by food microbiologists do not address the issue of competitive growth in mixed cultures of bacteria. We developed a mathematical model which consists of a system of nonlinear differential equations describing the growth of competing bacterial cell cultures. In this model, bacterial cell growth is limited by the accumulation of protonated lactic acid and decreasing pH. In our experimental system, pure and mixed cultures of Lactococcus lactis and Listeria monocytogenes were grown in a vegetable broth medium. Predictions of the model indicate that pH is the primary factor that limits the growth of L. monocytogenes in competition with a strain of L. lactis which does not produce the bacteriocin nisin. The model also predicts the values of parameters that affect the growth and death of the competing populations. Further development of this model will incorporate the effects of additional inhibitors, such as bacteriocins, and may aid in the selection of lactic acid bacterium cultures for use in competitive inhibition of pathogens in minimally processed foods.

FIG. 1

Observed and predicted results for the model. The observed data are indicated by symbols, and the predicted data are indicated by lines. The observed concentrations of L. lactis (•) and L. monocytogenes (■) (in log CFU per milliliter) are shown in the top panels, while the pH values (⧫), protonated lactic acid concentrations (in millimoles per liter) (▴), and malic acid concentrations (in millimoles per liter) (▾) are shown in the bottom panels. The same x axis is used for each pair of top and bottom panels.

FIG. 2

Limiting lower pH allowing the growth of L. monocytogenes. The mean values from five independent determinations of growth rate at each pH value are shown (○). The regression line for the entire data set (solid line) and the 95% confidence limits for the regression line (dashed lines) are also shown.

FIG. 3

Limiting protonated acid concentration for the growth of L. monocytogenes. The mean values from five independent determinations of growth rate for each concentration of protonated acid are shown (○). The regression line for the entire data set (solid line) and the 95% confidence limits for the regression line (dashed lines) are also shown.

FIG. 4

Limiting protonated acid concentration for the growth of L. lactis. The mean values from five independent determinations of growth rate for each concentration of protonated acid are shown (○). The regression line for the entire data set (solid line) and the 95% confidence limits (dashed lines) for the regression line are also shown.