Development of a dynamic continuous-discrete-continuous model describing the lag phase of individual bacterial cells

AIMS: A previous model for adaptation and growth of individual bacterial cells was not dynamic in the lag phase, and could not be used to perform simulations of growth under non-isothermal conditions. The aim of the present study was to advance this model by adding a continuous adaptation step, prior to the discrete step, to form a continuous-discrete-continuous (CDC) model. METHODS AND RESULTS: The revised model uses four parameters: N(0), initial population; N(max), maximum population; p0, mean initial individual cell physiological state; SD(p0), standard deviation of the distribution of individual physiological states. A truncated normal distribution was used to generate tables of distributions to allow fitting of the CDC model to viable count data for Listeria monocytogenes grown at 5 degrees C to 35 degrees C. The p0 values increased with increasing SD(p0) and were, on average, greater than the corresponding population physiological states (h0); p0 and h0 were equivalent for individual cells. CONCLUSION: The CDC model has improved the ability to simulate the behaviour of individual bacterial cells by using a physiological state parameter and a distribution function to handle inter-cell variability. The stages of development of this model indicate the importance of physiological state parameters over the population lag concept, and provide a potential approach for making growth models more mechanistic by incorporating actual physiological events. SIGNIFICANCE AND IMPACT OF THE STUDY: Individual cell behaviour is important in modelling bacterial growth in foods. The CDC model provides a means of improving existing growth models, and increases the value of mathematical modelling to the food industry.