Use of the Gompertz equation to model non-linear survival curves and predict temperature,pH, and sodium chloride effects for Listeria monocytogenes Scott A

Numerous examples of non-linear survival curves, plotted as log surviving cells vs. time, for bacteria exposed to heat have been reported. Factors which may affect the shape of a survival curve and the heat resistance of bacteria include temperature, pH, and NaCl concentration. Many studies have examined the effect of these factors individually, but little information exists on the combined effects. The objective of this study was to mathematically model non-linear survival curves to account for these factors and their interactions simultaneously.

Heat resistance of Listeria monocytogenes (L. monocytogenes) was determined in 0.1M KH$\sb 2$PO$\sb 4$ buffer and in infant formula at three temperatures (50, 55, and 60 C), three pH levels (5, 6, and 7), and three NaCl concentrations (0, 2, 4%). Survival curves were fit using linear regression, non-linear regression with a modified logistic equation, and non-linear regression with a modified Gompertz equation.

The Gompertz equation was the preferred model since it fit survival curves which were linear, those which displayed an initial lag region followed by a linear region, and those which were sigmoidal. The Gompertz equation generated parameter estimates for three regression coefficients. Parameter estimates were used to describe the lag region, death rate, and the tailing region of a survival curve. These estimates were also used to predict single and interactive effects of temperature, pH, NaCl, and time on the log surviving fraction (LSF) of bacteria.

Many interactions significantly (p $<$.05) affected the LSF in KH$\sb 2$PO$\sb 4$ buffer and in infant formula. Generally, increased pH or NaCl concentration lead to an increased (p $<$.05) LSF, whereas, increased time or temperature lead to a decreased (p $<$.05) LSF. All multiple factor interactions significantly (P $<$.05) affected the LSF. These interactions differed depending on the heating medium and the region of the survival curve. Correlation of observed LSF vs. predicted LSF from the Gompertz model were good in KH$\sb 2$PO$\sb 4$ buffer (R$\sp 2$ =.89) and infant formula (R$\sp 2$ =.92).

This study has demonstrated that the Gompertz equation and non-linear regression can be used as an effective means to predict survival curve shape and response to heat of L. monocytogenes in many different environmental conditions.