Modeling the Effect of Abrupt Acid and Osmotic Shifts within the Growth Region and across Growth Boundaries on Adaptation and Growth of Listeria monocytogenes

This study aims to model the effects of acid and osmotic shifts on the intermediate lag time of Listeria monocytogenes at 10°C in a growth medium. The model was developed from data from a previous study (C. I. A. Belessi, Y. Le Marc, S. I. Merkouri, A. S. Gounadaki, S. Schvartzman, K. Jordan, E. H. Drosinos, and P. N. Skandamis, submitted for publication) on the effects of osmotic and pH shifts on the kinetics of L. monocytogenes. The predictive ability of the model was assessed on new data in milk. The effects of shifts were modeled through the dependence of the parameter h₀ (“work to be done” prior to growth) induced on the magnitude of the shift and/or the stringency of the new environmental conditions. For shifts across the boundary, the lag time was found to be affected by the length of time for which the microorganisms were kept at growth-inhibiting conditions. The predicted concentrations of L. monocytogenes in milk were overestimated when the effects of this shift were not taken into account. The model proved to be suitable to describe the effects of osmotic and acid shifts observed both within the growth domain and across the growth boundaries of L. monocytogenes.The lag phase of a microorganism is usually seen as a period of transition from an initial physiological state to the state of balanced growth. The duration of the lag phase, denoted by lag in what follows, depends on the amount of work to be carried out by the cells prior to exponential growth and the rate at which this work is undertaken (6, 13). According to Baranyi and Roberts (2), the “work to be done” is proportional to h₀, the product of the lag time and the rate at which the work is carried out. Robinson et al. (13) pointed out that there is no direct way to measure this rate, and it is often assumed that it is equal to the specific growth rate characteristic of the growth conditions (2). Some authors use the relative lag time (RLT) (7, 8) as a replacement for the “work to be done” h₀ parameter. In fact the two concepts appear to be very similar, RLT and h₀ being proportional to each other.The transient phase following inoculation is commonly called the initial lag phase. Many authors (6, 7, 14, 17) observed that subsequent abrupt changes in the environmental conditions (temperature, pH, and water activity a_w]) during the growth phase were able to induce a so-called “intermediate” lag phase. In other words, abrupt changes cause extra “work to be done” that cells have to perform before reinitiating their growth. Most of the studies on intermediate lag times have focused on abrupt thermal changes. For example, some authors have proposed models for the effects of temperature shifts on the lag time of Escherichia coli (14) and Lactobacillus plantarum (17). Using the data of Whiting and Bagi (15), for Listeria monocytogenes, Delignette-Muller et al. (3) highlighted a linear relationship between the “work to be done” and the magnitude and direction of the temperature shifts. Less attention has been given to the effects of acid and osmotic shifts, although such shifts pose a higher energetic burden to the cells than temperature shifts, especially around the growth boundaries (C. I. A. Belessi, Y. Le Marc, S. I. Merkouri, A. S. Gounadaki, S. Schvartzman, K. Jordan, E. H. Drosinos, and P. N. Skandamis, submitted for publication). Generally, the “work to be done” increases with the magnitude of the shifts applied (3, 7) and the cells in exponential phase are more sensitive to abrupt shifts than those in stationary phase (7). Muñoz-Cuevas et al. (9) proposed a model for the lag time of L. monocytogenes induced by temperature and water activity downshifts within the growth region. For osmotic shifts, the authors found that the “work to be done” was related not only to the magnitude of the shift and but also to the level of the environmental factors (temperature and water activity) after the shift.In most of the available modeling packages, predictions in dynamic environments are based on the assumption that when the environmental conditions change, the specific growth rate changes instantaneously relative to the new conditions. The intermediate lag times caused by abrupt changes in the environmental conditions are commonly neglected in the models. Besides, the models usually ignore the effects of shifts across the growth boundary and the duration of the period the cells spend above the growth/no-growth boundary on the physiological state of the cells. However, such abrupt shifts are important, as they may occur for example during fermentation and ripening of dairy products (10, 11) or during cross-contamination (e.g., when L. monocytogenes is accidently transferred to a different environment). The aim of this work was to develop a model to describe the effects of such abrupt shifts (within the growth range or across the growth boundary) on the possibly induced intermediate lag time of L. monocytogenes. The analysis here is based on the data from a previous study (Belessi et al., submitted) on the effects of acid and osmotic shifts on the kinetics of L. monocytogenes at 10°C. We also used new data in milk to explore the possibility of integrating the proposed approach in a generic growth model.