Modeling the lag period and exponential growth of Listeria monocytogenes under conditions of fluctuating temperature and water activity values

Abstract

The dynamic model for the growth of a bacterial population described by Baranyi and Roberts (J. Baranyi and T. A. Roberts, Int. J. Food Microbiol. 23:277-294, 1994) was applied to model the lag period and exponential growth of Listeria monocytogenes under conditions of fluctuating temperature and water activity (a(w)) values. To model the duration of the lag phase, the dependence of the parameter h(0), which quantifies the amount of work done during the lag period, on the previous and current environmental conditions was determined experimentally. This parameter depended not only on the magnitude of the change between the previous and current environmental conditions but also on the current growth conditions. In an exponentially growing population, any change in the environment requiring a certain amount of work to adapt to the new conditions initiated a lag period that lasted until that work was finished. Observations for several scenarios in which exponential growth was halted by a sudden change in the temperature and/or a(w) were in good agreement with predictions. When a population already in a lag period was subjected to environmental fluctuations, the system was reset with a new lag phase. The work to be done during the new lag phase was estimated to be the workload due to the environmental change plus the unfinished workload from the uncompleted previous lag phase.

FIG. 1.

Effect of the previous and current environments on the amount of work to be done during the lag phase. h₀ depended on the magnitude of the sudden change in the a_w or temperature and also on the final temperature and a_w values. (A) Effect of an increase in the level of NaCl on h₀ at 6°C (○), 10°C (□), 15°C (▵), 28(⋄), and 37°C (×). The final level of NaCl was 10%. (B) Effect of a decrease in temperature on h₀ with 10% (○), 6% (□), 3% (▵), and 0.5% (×) NaCl. The final temperature was 6°C.

FIG. 2.

Square roots of the maximum specific growth rates (h⁻¹) (μ_max) at several temperatures and at several values for the a_w adjusted with NaCl.

FIG. 3.

Transition from exponential phase to lag phase and vice versa. Predicted (dotted lines) and observed (filled circles) bacterial concentrations at fluctuating temperatures (solid line) and a_w values (expressed as levels of NaCl by a dashed line). One of the lines for predicted values does not consider any lag phase (pred without lag). The lag phase is indicated by a thick line over the dotted line for the predicted values, and its duration was determined by the time needed to carry out work to adapt to the environmental changes (the kinetics of this work is indicated by a dashed and dotted line). The environmental changes applied to exponentially growing populations comprised (A) two successive and sudden increases in the NaCl level, (B) two successive and sudden decreases in temperature, and (C) a decrease in temperature followed by an increase in the NaCl level.

FIG. 4.

Environmental fluctuations affecting populations already in lag phase. Predicted (dotted lines) and observed (filled circles) bacterial concentrations at fluctuating temperatures (dashed line) and a_w values (expressed as levels of NaCl by a solid line). In panels A and C, one of the predicted lines does not consider any lag phase (pred without lag). The lag phase is indicated by a thick line over the dotted line for the predicted values, and its duration was determined by the time needed to carry out work to adapt to the environmental changes (the kinetics of this work is indicated by a dashed and dotted line). When an increase in temperature was applied to a population in lag phase, the workload was carried out at a higher rate according to the new temperature, shortening the lag phase (panel A, full period; panel B, first 50 h). When an increase in the NaCl level was applied to a population already in lag phase, initially, due to a decrease in temperature, the work to be done increased, starting a new, longer lag period. The bacterial cells were assumed to carry out both workloads due to temperature and to a_w simultaneously (panel C, full period; panel D, first 50 h).