Modelling the influence of the inoculation level on the growth/no growth interface of Listeria monocytogenes as a function of pH, aw and acetic acid.

This research is an extension of previous work reported in Gysemans et al. [Gysemans, K.P.M., Bernaerts, K., Geeraerd, A.H., Vermeulen, A., Debevere, J., Devlieghere, F., Van Impe, J.F., 2007. Exploring the performance of logistic regression model types on growth/no growth data of Listeria monocytogenes. International Journal of Food Microbiology 114, 316-331.] in which the growth/no growth interface of Listeria monocytogenes was modelled as a function of water activity (a(w)), pH and undissociated acetic acid percentage (UAc). The major difference with the previous work is that in the present research the influence of the cell density (N) is also considered during the modelling process. New experimental data were therefore collected as a function of a wide range of cell densities up until the level of the individual cell. Prior to the development of model that incorporates N, the expected inadequacy of the high cell density growth/no growth model developed in Gysemans et al. (2007) on the new cell density dependent data was illustrated. Inadequacy of the model at lower cell densities was expected since the data showed a significant reduction of the growth probability as N decreased. For the development of a model that incorporates the effect of N, a square-root type logistic regression model was proposed and evaluated. The model predicts a strong influence of the cell density with an increase in the growth probability if the cell count increased. The onset of this increase is dependent on the intrinsic factors of the medium (pH, a(w), and acetic acid concentration). The model also suggests that it is unlikely that a larger population has a higher chance to start growing just because the chance on a strong cell is higher in a larger population. It seems that the bacteria influence each other's growth.

Exploring the performance of logistic regression model types on growth/no growth data of Listeria monocytogenes.

Several model types have already been developed to describe the boundary between growth and no growth conditions. In this article two types were thoroughly studied and compared, namely (i) the ordinary (linear) logistic regression model, i.e., with a polynomial on the right-hand side of the model equation (type I) and (ii) the (nonlinear) logistic regression model derived from a square root-type kinetic model (type II). The examination was carried out on the basis of the data described in Vermeulen et al. [Vermeulen, A., Gysemans, K.P.M., Bernaerts, K., Geeraerd, A.H., Van Impe, J.F., Debevere, J., Devlieghere, F., 2006-this issue. Influence of pH, water activity and acetic acid concentration on Listeria monocytogenes at 7 degrees C: data collection for the development of a growth/no growth model. International Journal of Food Microbiology. .]. These data sets consist of growth/no growth data for Listeria monocytogenes as a function of water activity (0.960-0.990), pH (5.0-6.0) and acetic acid percentage (0-0.8% (w/w)), both for a monoculture and a mixed strain culture. Numerous replicates, namely twenty, were performed at closely spaced conditions. In this way detailed information was obtained about the position of the interface and the transition zone between growth and no growth. The main questions investigated were (i) which model type performs best on the monoculture and the mixed strain data, (ii) are there differences between the growth/no growth interfaces of monocultures and mixed strain cultures, (iii) which parameter estimation approach works best for the type II models, and (iv) how sensitive is the performance of these models to the values of their nonlinear-appearing parameters. The results showed that both type I and II models performed well on the monoculture data with respect to goodness-of-fit and predictive power. The type I models were, however, more sensitive to anomalous data points. The situation was different for the mixed strain culture. In that case, the type II models could not describe the curvature in the growth/no growth interface which was reversed to the typical curvatures found for monocultures. This unusual curvature may originate from the fact that (i) an interface of a mixed strain culture can result from the superposition of the interfaces of the individual strains, or that (ii) only a narrow range of the growth/no growth interface was studied (the local trend can be different from the trend over a wider range). It was also observed that the best type II models were obtained with the flexible nonlinear logistic regression, although reasonably good models were obtained with the less flexible linear logistic regression with the nonlinear-appearing parameters fixed at experimentally determined values. Finally, it was found that for some of the nonlinear-appearing parameters, deviations from their experimentally determined values did not influence the model fit. This was probably caused by the fact that only a limited part of the growth/no growth interface was studied.

Influence of pH, water activity and acetic acid concentration on Listeria monocytogenes at 7 degrees C: data collection for the development of a growth/no growth model.

Growth/no growth models can be used to determine the chance that microorganisms will grow in specific environmental conditions. As a consequence, these models are of interest in the assessment of the safety of foods which can be contaminated with food pathogens. In this paper, growth/no growth data for Listeria monocytogenes (in a monoculture and in a mixed strain culture) are presented. The data were gathered at 7 degrees C in Nutrient Broth with different combinations of environmental factors pH (5.0-6.0, six levels), water activity (0.960-0.990, six levels) and acetic acid concentration (0-0.8% (w/w), five levels). This combination of environmental factors for the development of a growth/no growth model was based on the characteristics of sauces and mayonnaise based salads. The strains used were chosen from screening experiments in which the pH, water activity and acetic acid resistance of 26 L. monocytogenes strains (LFMFP culture collection) was determined at 30 degrees C in Brain Heart Infusion broth. The screening showed that most L. monocytogenes strains were not able to grow at a(w)<0.930, pH<4.3 or a total acetic acid concentration >0.4% (w/w). Among these strains, the ones chosen were the most resistant to one of these factors in the hope that, if the resulting model predicted no growth at certain conditions for those more resistant strains, then these predictions would also be valid for the less resistant strains. A mixed strain culture was also examined to combine the strains that were most resistant to one of the factors. A full factorial design with the selected strains was tested. The experiments were performed in microtiter plates and the growth was followed by optical density measurements at 380 nm. The plates were inoculated with 6 log CFU/ml and twenty replicates were made for each treatment combination. These data were used (1) to determine the growth/no growth boundary and (2) to estimate the influence of the environmental conditions on the time to detection. From the monoculture and mixed strain data, the growth boundary of L. monocytogenes is shown not to be a straight cut-off but a rather narrow transition zone. The experiments also showed that in the studied region, a(w) did not have a pronounced influence on the position of the growth/no growth boundary while a low concentration of acetic acid (0.2% (w/w)) and a pH decrease from 6.0 to 5.8 was sufficient to significantly reduce the possibility of growth. The determination of the time to detection showed a significant increase at the combinations of environmental conditions near the 'no growth zone'. For example, at 0.2% (w/w) acetic acid, there was an increase from +/-10 days to 30 days by lowering pH from 5.8 to 5.6 at a(w) values of 0.985 and 0.979, while at pH 5.4 less than 50% growth occurred for all a(w) values.

Optimal experiment design for cardinal values estimation: guidelines for data collection.

Optimal experiment design for parameter estimation (OED/PE) is an interesting technique for modelling practices when aiming for maximum parameter estimation accuracy. Nowadays, experimental designs for secondary modelling within the field of predictive microbiology are mostly arbitrary or based on factorial design. The latter type of design is common practice in response surface modelling approaches. A number of levels of the factor(s) under study are selected and all possible treatment combinations are performed. It is however not always clear which levels and treatment combinations are most relevant. An answer to this question can be obtained from optimal experiment design for-in this particular case-parameter estimation. This technique is based on the extremisation of a scalar function of the Fisher information matrix. The type of scalar function determines the final focus of the optimised design. In this paper, optimal experiment designs are computed for the cardinal temperature model with inflection point (CTMI) and the cardinal pH model (CPM). A model output sensitivity analysis (depicting the sensitivity of the model output to a small change in the model parameters) yields a first indication of relevant temperature or pH treatments. Performed designs are: D-optimal design aiming for a maximum global parameter estimation accuracy (by minimising the determinant of the Fisher information matrix), and E-optimal design improving the confidence in the most uncertain model parameter (by maximising the smallest eigenvalue of the Fisher information matrix). Although lowering the information content of a set of experiments, boundary values on the design region need to be imposed during optimisation to exclude unworkable experiments and partly account for incorrect nominal parameter values. Opposed to the frequently applied equidistant or arbitrary treatment placement, optimal design results show that typically four informative temperature or pH levels are selected and replicate experiments are to be performed at these points. Informative experiments are typically placed at points with an extreme model output sensitivity.