Modeling the Variability of Single-Cell Lag Times for Listeria innocua Populations after Sublethal and Lethal Heat Treatments

Optical density measurements were used to estimate the effect of heat treatments on the single-cell lag times ofListeria innocua fitted to a shifted gamma distribution. The single-cell lag time was subdivided into repair time (the shift of the distribution assumed to be uniform for all cells) and adjustment time (varying randomly from cell to cell). After heat treatments in which all of the cells recovered (sublethal), the repair time and the mean and the variance of the single-cell adjustment time increased with the severity of the treatment. When the heat treatments resulted in a loss of viability (lethal), the repair time of the survivors increased with the decimal reduction of the cell numbers independently of the temperature, while the mean and variance of the single-cell adjustment times remained the same irrespective of the heat treatment. Based on these observations and modeling of the effect of time and temperature of the heat treatment, we propose that the severity of a heat treatment can be characterized by the repair time of the cells whether the heat treatment is lethal or not, an extension of theF value concept for sublethal heat treatments. In addition, the repair time could be interpreted as the extent or degree of injury with a multiple-hit lethality model. Another implication of these results is that the distribution of the time for cells to reach unacceptable numbers in food is not affected by the time-temperature combination resulting in a given decimal reduction.