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

Abstract

Optical density measurements were used to estimate the effect of heat treatments on the single-cell lag times of Listeria 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 the F 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 timetemperature combination resulting in a given decimal reduction.Heat treatment is a method of preservation widely used in the food industry (24). Relatively mild thermal treatments below 100°C are sufficient to kill vegetative cells of food-borne pathogens or spoilage organisms, while inactivation of bacterial spores in nonacid foods requires much higher process temperatures, typically 121°C or more. In early studies to develop processes for the safe production of canned foods, the concept of thermal death point was used, this being defined as the length of time at different temperatures needed to destroy a definite concentration of spores under defined conditions (3). The work of Esty and Meyer (8) demonstrated a linear relationship between heating temperature and the logarithm of the time needed to inactivate suspensions containing 60 billion spores of proteolytic Clostridium botulinum. This work, often cited as the first example of a predictive model, led to the standard for canned food sterilization being based on a reduction of the spore population by a factor of 10 12 . Studies on the kinetics of thermal inactivation established that the concentration of viable vegetative cells or spores decreases more or less exponentially with time of heating such that a plot of the logarithm of the viable cell concentration versus time yields a straight line (3, 6). The assumption of a logarithmic order of death underlies thermal process calculations based on D and z values, where D is the time needed for a 10-fold reduction in viable numbers and z is the temperature change needed to bring about a 10-fo...

Analysis of the Variability in the Number of Viable Bacteria after Mild Heat Treatment of Food

“…In addition, other studies of the effects of heat treatments and other stresses on the variability of cell responses have focused on the lag time. Regarding the coefficient of variation of the lag time, some authors have reported that it is not affected by the intensity of the heat treatment (14) while others have found a general increase after heat treatments and other stresses (6,11). Therefore, the heterogeneity of the surviving population may also be reflected by greater variability in the repair time needed for the survivors to start dividing.…”

“…Stochastic models for the growth of populations have been developed based on the experimentally measured distributions for the lag times of single cells and spores (13,14,18,19,26). In those models, the distribution of the initial number of cells was assumed to be independent of the heat treatment or previous stress.…”

“…Under this assumption, variations in the growth rate are assumed to be caused by lack of control over the environmental conditions. Recently, distributions of the length of the lag phase among the surviving cells after different stresses have been measured (6,9,14,18). Usually, the distribution of the initial number of cells in a food product is assumed to be independent of previous processing and storage conditions.…”

Controlling Listeria monocytogenes in ready-to-eat foods: Working towards global scientific consensus and harmonization – Recommendations for improved prevention and control

“…1e100 CFU g À1 to measure the potential for growth and the impact of microbial competition, but numbers need to be sufficient so that they are above the detection level throughout the length of the study. Low inocula of several different L. monocytogenes strains should be used in challenge studies to account for variability in results, e.g., the duration of the lag phase (Beaufort et al, 2008;Métris, George, Mackey, & Baranyi, 2008). To allay concerns over exceeding a regulatory limit of 100 CFU g À1 , the challenge testing should never be carried out with levels above 50e100 CFU g À1 .…”

Combining Individual-Based Modeling and Food Microenvironment Descriptions To Predict the Growth of Listeria monocytogenes on Smear Soft Cheese

“…For several years, it has been accepted that the accurate prediction of the behavior of food-borne pathogens contaminating food with a few cells requires a single-cell approach, taking into account the variability of individual cell lag times, since this variability will strongly influence the lag phase duration of the bacterial population (9)(10)(11)(12)(13). More recently, studies also emphasized the need to take into account the single-cell growth probability when assessing the behavior of these food-borne bacteria (14)(15)(16)(17).…”