C. PIN, J. BARANYI AND G. GARCÍA DE FE R NA ND O . 2000. A quadratic response surface model is presented to describe the maximum specific growth rate of Yersinia enterocolitica, at refrigeration temperatures, under modified atmospheres. The presence of CO 2 affected mainly the lag phase of the organism. The length of the lag phase increased with higher levels of CO 2 in the atmosphere, and this effect was more noticeable at low temperatures. The effect of oxygen was similar but less pronounced. The observed growth was slower with higher CO 2 . Oxygen also decreased the growth rate, but its effect was significant only when its proportion in the atmosphere was greater than about 40%. Model predictions were compared with growth rates obtained in sea food inoculated with Y. enterocolitica and packaged under modified atmospheres. Predictions were also checked to determine whether they were inside the strict interpolation region of the model.

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Cronobacter spp. have been responsible for severe infections in infants associated with consumption of powdered infant formula and follow-up formulae. Despite several risk assessments described in published studies, few approaches have considered the tremendous variability in cell response that small micropopulations or single cells can have in infant formula during storage, preparation or post process/preparation before the feeding of infants. Stochastic approaches can better describe microbial single cell response than deterministic models as we prove in this study. A large variability of lag phase was observed in single cell and micropopulations of ≤50 cells. This variability increased as the heat shock increased and growth temperature decreased. Obviously, variability of growth of individual Cronobacter sakazakii cell is affected by inoculum size, growth temperature and the probability of cells able to grow at the conditions imposed by the experimental conditions should be taken into account, especially when errors in bottle-preparation practices, such as improper holding temperatures, or manipulation, may lead to growth of the pathogen to a critical cell level. The mean probability of illness from initial inoculum size of 1 cell was below 0.2 in all the cases and for inoculum size of 50 cells the mean probability of illness, in most of the cases, was above 0.7.

Many articles dealing with individual cell lag phase determination assume that growth, when observed, comes from one cell. This assumption is not in agreement with the Poisson distribution, which uses the probability of growth in a sample to predict how many samples contain one, two, or some other number of cells. This article analyses and compares different approaches to improve the accuracy of lag phase estimation of individual cells and micropopulations. It argues that if the highest initial load, as predicted by the Poisson distribution, is assigned to the sample with the shortest lag phase, the second highest to the sample with the second shortest lag phase and so on, the resulting lag phase distributions would be more accurate. This study also proposes the use of a robust test, permutation test, to compare lag phase distributions obtained in different situations.

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