A combined discrete–continuous model describing the lag phase of Listeria monocytogenes

Food microbiologists generally use continuous sigmoidal functions such as the empirical Gompertz equation to obtain the kinetic parameters specific growth rate (μ) and lag phase duration (λ) from bacterial growth curves. This approach yields reliable information on μ; however, values for λ are difficult to determine accurately due, in part, to our poor understanding of the physiological events taking place during adaptation of cells to new environments. Existing models also assume a homogeneous population of cells, thus there is a need to develop discrete event models which can account for the behavior of individual cells. Time to detection (td) values were determined for Listeria monocytogenes using an automated turbidimetric instrument, and used to calculate μ. Mean individual cell lag times (tL) were calculated as the difference between the observed td and the theoretical value estimated using μ. Variability in tL for individual cells in replicate wells was estimated using serial dilutions. A discrete stochastic model was applied to the individual cells, and combined with a deterministic population-level growth model. This discrete–continuous model incorporating tL and the variability in tL (expressed as standard deviation; S.D.L) predicted a reduced variability between wells with increased number of cells per well, in agreement with experimental findings. By combining the discrete adaptation step with a continuous growth function it was possible to generate a model which accurately described the transition from lag to exponential phase. This new model may serve as a useful tool for describing individual cell behavior, and thus increasing our knowledge of events occurring during the lag phase.