Development of a global stochastic model relating the distribution of individual cell and population physiological states.

Our ability to predict the lag (lambda) prior to growth of foodborne pathogens is limited by our lack of understanding of the physiological changes taking place in the individual cell during the adaptation process. Theoretical models have been developed to describe the stochastic nature of individual cells, and probability distributions have been used to assign hypothetical values of the physiological state to individual cells (p(i)). The aim of this study is to develop a polynomial model which will link distributions of p(i) values to the physiological state of the population (h(0)), and thus to the lambda. Risk analysis software was used to simulate values of p(i) for populations of cells drawn from lognormal distributions with parameters alpha and beta, and growth curves were simulated using a modified continuous-discrete-continuous (CDC) model. Values for h(0) were then obtained for each growth curve by fitting with the heterogeneous population model (HPM). Multiple regression analysis was used to develop a polynomial function which described the subsequent h(0) value as a function of alpha and beta (R(2)=0.9957). Outputs from simulations using the polynomial model agree well with results from related stochastic models, and suggest that distributions can accurately describe the physiological state of cell populations.