Predicting B. cereus growth and cereulide production in dairy mix.

This study aims to quantify growth and cereulide production by Bacillus cereus and their potential correlation in an intermediate dairy wet-mix. Systematic experiments were carried out using the emetic reference strain F4810/72 in the suboptimal range of temperature of 12 °C to 20 °C. Growth and cereulide kinetic parameters were estimated and the three parameters (i) time to first cereulide quantification (tcer), (ii) maximum specific growth rates (µmax) and (iii) cereulide production rates (k) were modelled as a function of temperature. As temperature increased, growth lag time and tcer were shorter while microbial increase and cereulide production happened earlier, and at higher rates. Maximum concentration of cells and maximum cereulide concentration proved to be temperature-independent, reaching the average values of 7.9 ± 0.3 log10(CFU/mL) and 2.6 ± 0.2 log10(ng.g-1) respectively. Moreover, the time to reach the widely used threshold of 5 log10CFU/mL (t5log) was tested against tcer, and this suggested that this threshold can be used with increased confidence at lower temperatures to assure toxin is not quantified in this matrix. The average tcer were equal to 314 h, 118 h, 73 h and 45 h for 12 °C, 15 °C, 18 °C and 20 °C respectively. A validation study was performed using independent data sets obtained with the same strain in other dairy matrices. The microbial growth models presented good predictive power even when extrapolated beyond the temperature range of construction. Nevertheless, the models proposed for prediction of toxin production over time presented limitations, especially for food matrices that deviate significantly from the original matrix for which the model was developed, making cereulide predictions less accurate. Our findings suggest that similar modelling approaches can be used to predict growth, time to first cereulide quantification as well as cereulide formation over time for a specific matrix, but that matrix-extrapolations are more suitable for growth than for cereulide.

Corrigendum: Modeling Bacillus cereus Growth and Cereulide Formation in Cereal-, Dairy-, Meat-, Vegetable-Based Food and Culture Medium.

[This corrects the article DOI: 10.3389/fmicb.2021.639546.].

The effect of pH on the growth rate of Bacillus cereus sensu lato: Quantifying strain variability and modelling the combined effects of temperature and pH.

In this study, the effect of pH, alone or in combination with temperature, on the maximum growth rate (µmax) of B. cereus sensu lato was investigated. In phase 1, the effect of pH at 30 °C was studied for 16 mesophilic strains and 2 psychrotrophic strains of Bacillus cereus sensu lato. The µmax vs. pH relationship was found to show a similar pattern for all the strains. Several pH models from literature were evaluated and the best performing 'growth rate vs. pH' model selected. A stochastic model was then developed to predict the maximum specific growth rate of mesophilic B. cereus at 30 °C as a function of pH, the intra-species variability being incorporated via considering the model parameters (e.g. pHmin) randomly distributed. The predicted maximum specific growth rates were acceptably close to independent published data. In phase 2, the combined effects of temperature and pH were studied. Growth rates were also generated at 15, 20 and 40 °C for a selection of strains and the pH model was fitted at each temperature. Interestingly, the results showed that the estimates for the pHmin parameter for mesophilic strains were lower at 20-30 °C than near the optimum temperature (40 °C), suggesting that experiments for the determination of this parameter should be conducted at lower-than-optimum temperatures. New equations were proposed for the relationship between temperature and the minimum pH-values, which were also consistent with the experimental growth boundaries. The parameters defining this equation quantify the minimum temperature for growth observed experimentally, the temperature of maximum enzyme stability and the maximum temperature for growth. Deviations from the Gamma hypothesis (multiplicative effects of environmental factors on the maximum specific growth rate) were observed near the growth limits, especially at 40 °C. To improve model performance, two approaches, one based on a minimum pH-term (doi: https://doi.org/10.3389/fmicb.2019.01510) and one based on an interaction term (doi: http://dx.doi.org/10.1016/S0168-1605(01)00640-7) were evaluated.

A stochastic approach for modelling the effects of temperature on the growth rate of Bacillus cereus sensu lato.

A stochastic model that predicts the maximum specific growth rate (µmax) of Bacillus cereus sensu lato as a function of temperature was developed. The model integrates the intra-species variability by incorporating distributions of cardinal parameters (Tmin, Topt, Tmax) in the model. Growth rate data were generated for 22 strains, covering 5 major phylogenetic groups of B. cereus, and their cardinal temperatures identified. Published growth rate data were also incorporated in the model fitting, resulting in a set of 33 strains. Based on their cardinal temperatures, we identified clusters of Bacillus cereus strains that show similar response to temperature and these clusters were considered separately in the stochastic model. Interestingly, the µopt values for psychrotrophic strains were found to be significantly lower than those obtained for mesophilic strains. The model developed within this work takes into account some correlations existing between parameters (µopt, Tmin, Topt, Tmax). In particular, the relationship highlighted between the b-slope of the Ratkowsky model and Tmin (doi: https://doi.org/10.3389/fmicb.2017.01890) was adapted to the case of the popular Cardinal Temperature Model. This resulted in a reduced model in which µopt is replaced by a function of Tmin, Topt and 2 strain-independent parameters. A correlation between the Tmin parameter and the experimental minimal growth temperature was also highlighted and integrated in the model for improved predictions near the temperature growth limits. Compared to the classical approach, the model developed in this study leads to improved predictions for temperatures around Tmin and more realistic tails for the predicted distributions of µmax. It can be useful for describing the variability of the Bacillus cereus Group in Quantitative Microbial Risk Assessment (QMRA). An example of application of the stochastic model to Reconstituted Infant Formulae (RIF) was proposed.

Modeling Bacillus cereus Growth and Cereulide Formation in Cereal-, Dairy-, Meat-, Vegetable-Based Food and Culture Medium.

This study describes the simultaneous Bacillus cereus growth and cereulide formation, in culture medium and cereal-, dairy-, meat-, and vegetable-based food matrices. First, bacterial growth experiments were carried out under a wide range of temperatures (from 9 to 45°C), using the emetic reference strain F4810/72, in the above-mentioned matrices. Then, the generated data were put in a modeling framework where the response variable was a vector of two components: the concentration of B. cereus and that of its toxin, cereulide. Both were considered time-, temperature- and matrix-dependent. The modeling was carried out in a series of steps: the parameters fitted in one step became the response variable of the following step. Using the square root link function, the maximum specific growth rate of the organism and the time to the appearance of quantifiable cereulide were modeled against temperature by cardinal parameters models (CPM), for each matrix. Finally, a validation study was carried out on an independent data set obtained in the same matrices and using various Bacillus cereus strains. Results showed that both growth and toxin-formation depended on the food matrix and on the environment but not in the same way. Thus, the matrix (culture medium), where the highest growth rate of B. cereus was observed, was not the medium where the shortest time to quantifiable cereulide occurred. While the cereal-based matrix generated the smallest growth rates (0.41-times smaller than culture medium did), quantifiable cereulide appeared in it at earlier times compared to the other tested matrices. In fact, three groups of matrices could be distinguished based on their ability to support cereulide formation (1) the cereal-based matrix (highest), (2) the culture medium and the dairy-based matrix (intermediate), and (3) the meat- and vegetable-based matrices (lowest). This ranking between the matrices is quite different from that based on their suitability to the growth of the organism. Our models can be used in HACCP studies, to improve shelf-life predictions and, generally, microbiological food safety assessments of products for which B. cereus is the main concern.

Optimization of turbidity experiments to estimate the probability of growth for individual bacterial cells.

Using turbidity measurements to quantify bacterial growth is a common and well-established practice in microbiology. Automated devices offering high throughput analyses have largely contributed to the increase of its use. A main difficulty of this method is that it detects growth only at late exponential phase, making turbidity measurements limited for studies focussing on low cell numbers. This work proposes an improved estimator for the probability of growth of individual cells using turbidity-based measurements, when the initial number of cells is low and random. We modify the currently used estimator for the expected cell number per well, a Poisson-parameter, and show that an optimal scenario is when ca 20% of the wells do not become turbid, resulting in improved accuracy and precision.

From Culture-Medium-Based Models to Applications to Food: Predicting the Growth of B. cereus in Reconstituted Infant Formulae.

Predictive models of the growth of foodborne organisms are commonly based on data generated in laboratory medium. It is a crucial question how to apply the predictions to realistic food scenarios. A simple approach is to assume that the bias factor, i.e., the ratio between the maximum specific growth rate in culture medium and the food in question is constant in the region of interest of the studied environmental variables. In this study, we investigate the validity of this assumption using two well-known link functions, the square-root and the natural logarithm, both having advantageous properties when modeling the variation of the maximum specific growth rate with temperature. The main difference between the two approaches appears in terms of the respective residuals as the temperature decreases to its minimum. The model organism was Bacillus cereus. Three strains (B594, B596, and F4810/72) were grown in Reconstituted Infant Formulae, while one of them (F4810/72) was grown also in culture medium to calculate the bias factor. Their growth parameters were estimated using viable count measurements at temperatures ranging from 12 to 25°C. We utilized the fact that, if the bias factor is independent of the temperature, then the minimum growth temperature parameter of the square-root model of Ratkowsky et al. (1982) is the same for culture medium and food. We concluded, supported also by mathematical analysis, that the Ratkowsky model works well but its rearrangement for the natural logarithm of the specific growth rate is more appropriate for practical regression. On the other hand, when analyzing mixed culture data, available in the ComBase database, we observed a trend different from the one generated by pure cultures. This suggests that the identity of the strains dominating the growth of mixed cultures depends on the temperature. Such analysis can increase the accuracy of predictive models, based on culture medium, to food scenarios, bringing significant saving for the food industry.

Rethinking Tertiary Models: Relationships between Growth Parameters of Bacillus cereus Strains.

The maximum specific growth rates of 12 strains, pair-wise belonging to six groups of Bacillus cereus sensu lato, were fitted against temperature by a reparametrized version of the model of Ratkowsky et al. (1983). This way, the interpretation of the new parameter set was similar to that of the cardinal-values-model of Rosso and Robinson (2001), both models including the minimum, optimum and maximum temperatures for growth as well as a fourth parameter scaling along the dependent variable. The modularity of the reparametrized version of the Ratkowsky model was utilized to show a so-far undetected relationship between this scaling parameter and the cardinal temperatures, which linked even distant (e.g., mesophilic and psychotropic) strains of B. cereus. We propose that the name "tertiary modeling" should be used for investigations like ours, as logically derived from the concepts of "primary" and "secondary" modeling. Such tertiary models may reveal biological relationships between kinetic parameters within a group of strains. It can also be used to create an overarching predictive model for mixed cultures, when different strains grow together but independently of each other.

The use of predictive models to optimize risk of decisions.

The purpose of this paper is to set up a mathematical framework that risk assessors and regulators could use to quantify the "riskiness" of a particular recommendation (choice/decision). The mathematical theory introduced here can be used for decision support systems. We point out that efficient use of predictive models in decision making for food microbiology needs to consider three major points: (1) the uncertainty and variability of the used information based on which the decision is to be made; (2) the validity of the predictive models aiding the assessor; and (3) the cost generated by the difference between the a-priory choice and the a-posteriori outcome.