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 ce lls was not dynamic in the lag phase, and could not be used to perform simu lations of growth under non-isothermal conditions. The aim of the present s tudy was to advance this model by adding a continuous adaptation step, prio r to the discrete step, to form a continuous-discrete-continuous (CDC) mode l. Methods and Results: The revised model uses four parameters: N-0, intial po pulation; N-max, maximum population; p(0), mean initial individual cell phy siological state; SDp0, standard deviation of the distribution of individua l physiological states. A truncated normal distribution was used to generat e tables of distributions to allow fitting of the CDC model to viable count data for Listeria monocytogenes grown at 5 degreesC to 35 degreesC. The p( 0) values increased with increasing SDp0 and were, on average, greater than the corresponding population physiological states (h(0)); p(0) and h(0) we re equivalent for individual cells. Conclusions: The CDC model has improved the ability to simulate the behavio ur of individual bacterial cells by using a physiological state parameter a nd a distribution function to handle inter-cell variability. The stages of development of this model indicate the importance of physiological state pa rameters over the population lag concept, and provide a potential approach for making growth models more mechanistic by incorporating actual physiolog ical events. Significance and Impact of the Study: Individual cell behaviour is importan t 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.