Modeling the growth kinetics of Bacillus cereus as a function of temperature, pH, sodium lactate and sodium chloride concentrations

A Novel Approach to Predict the Growth of Staphylococcus aureus on Rice Cake

This study aimed to investigate the growth kinetics of Staphylococcus aureus on rice cake and to determine the shelf life based on the probability model of the increase in S. aureus contamination on rice cake. Secondary models were developed based on the growth parameters derived from the Baranyi model at constant temperatures (15, 25, 35, and 45°C). External validation was then conducted using additional data under experimental conditions not used in development of the models to verify the performance and reliability of the developed model through different goodness-of-fit indices. Furthermore, the growth of S. aureus on rice cake under dynamic temperature was obtained with the root mean square error (RMSE) of 0.218 and the 90.9% acceptable prediction rate. In addition, probability models of the 1-, 2-, 3-, and 4-log increases of S. aureus on rice cake were also developed from the data, which could provide the probability and the time to a certain log increase. The results of validation demonstrated that the developed predictive model and the obtained growth parameters could be used for evaluating the growth behavior of S. aureus on rice cake under different conditions, and qualified to supply sufficient information for microbiological risk assessment studies of S. aureus on rice cake in Korea.

Modeling the growth of Listeria monocytogenes in mold-ripened cheeses

This study presents possible applications of predictive microbiology to model the safety of mold-ripened cheeses with respect to bacteria of the species Listeria monocytogenes during (1) the ripening of Camembert cheese, (2) cold storage of Camembert cheese at temperatures ranging from 3 to 15°C, and (3) cold storage of blue cheese at temperatures ranging from 3 to 15°C. The primary models used in this study, such as the Baranyi model and modified Gompertz function, were fitted to growth curves. The Baranyi model yielded the most accurate goodness of fit and the growth rates generated by this model were used for secondary modeling (Ratkowsky simple square root and polynomial models). The polynomial model more accurately predicted the influence of temperature on the growth rate, reaching the adjusted coefficients of multiple determination 0.97 and 0.92 for Camembert and blue cheese, respectively. The observed growth rates of L. monocytogenes in mold-ripened cheeses were compared with simulations run with the Pathogen Modeling Program (PMP 7.0, USDA, Wyndmoor, PA) and ComBase Predictor (Institute of Food Research, Norwich, UK). However, the latter predictions proved to be consistently overestimated and contained a significant error level. In addition, a validation process using independent data generated in dairy products from the ComBase database (www.combase.cc) was performed. In conclusion, it was found that L. monocytogenes grows much faster in Camembert than in blue cheese. Both the Baranyi and Gompertz models described this phenomenon accurately, although the Baranyi model contained a smaller error. Secondary modeling and further validation of the generated models highlighted the issue of usability and applicability of predictive models in the food processing industry by elaborating models targeted at a specific product or a group of similar products.

Alternative approach to modeling bacterial lag time, using logistic regression as a function of time, temperature, pH, and sodium chloride concentration

The objective of this study was to develop a probabilistic model to predict the end of lag time (λ) during the growth of Bacillus cereus vegetative cells as a function of temperature, pH, and salt concentration using logistic regression. The developed λ model was subsequently combined with a logistic differential equation to simulate bacterial numbers over time. To develop a novel model for λ, we determined whether bacterial growth had begun, i.e., whether λ had ended, at each time point during the growth kinetics. The growth of B. cereus was evaluated by optical density (OD) measurements in culture media for various pHs (5.5 ∼ 7.0) and salt concentrations (0.5 ∼ 2.0%) at static temperatures (10 ∼ 20°C). The probability of the end of λ was modeled using dichotomous judgments obtained at each OD measurement point concerning whether a significant increase had been observed. The probability of the end of λ was described as a function of time, temperature, pH, and salt concentration and showed a high goodness of fit. The λ model was validated with independent data sets of B. cereus growth in culture media and foods, indicating acceptable performance. Furthermore, the λ model, in combination with a logistic differential equation, enabled a simulation of the population of B. cereus in various foods over time at static and/or fluctuating temperatures with high accuracy. Thus, this newly developed modeling procedure enables the description of λ using observable environmental parameters without any conceptual assumptions and the simulation of bacterial numbers over time with the use of a logistic differential equation.

Growth characteristics and development of a predictive model for Bacillus cereus in fresh wet noodles with added ethanol and thiamine

Response surface methodology was used to determine growth characteristics and to develop a predictive model to describe specific growth rates of Bacillus cereus in wet noodles containing a combination of ethanol (0 to 2% [vol/wt]) and vitamin B(1) (0 to 2 g/liter). B. cereus F4810/72, which produces an emetic toxin, was used in this study. The noodles containing B. cereus were incubated at 10°C. The growth curves were fitted to the modified Gompertz equation using nonlinear regression, and the growth rate values from the curves were used to establish the predictive model using a response surface methodology quadratic polynomial equation as a function of concentrations of ethanol and vitamin B(1). The model was shown to fit the data very well (r(2) = 0.9505 to 0.9991) and could be used to accurately predict growth rates. The quadratic polynomial model was validated, and the predicted growth rate values were in good agreement with the experimental values. The polynomial model was found to be an appropriate secondary model for growth rate (GR) and lag time (LT) based on the correlation of determination (r(2) = 0.9899 for GR, 0.9782 for LT), bias factor (B(f) = 1.006 for GR, 0.992 for LT), and accuracy factor (A(f) = 1.024 for GR, 1.011 for LT). Thus, this model holds great promise for use in predicting the growth of B. cereus in fresh wet noodles using only the bacterial concentration, an important contribution to the manufacturing of safe products.

A response surface model to describe the effect of temperature and pH on the growth of Bacillus cereus in cooked rice

This study was performed to develop a predictive model for the growth rate of Bacillus cereus in cooked rice. A response surface methodology (RSM) was used with a combination of storage temperature (10 to 40 degrees C) and pH value (5.4 to 6.8). The growth curves generated under different conditions were fitted using a modified Gompertz equation, and the relationship of the growth rate to the growth curves was modeled using an RSM quadratic polynomial equation. The predictive model was significant (P < 0.01), and the predicted values of the growth parameters obtained using the model equations were in close agreement with experimental values (R2 = 0.9864). The RSM evaluation for describing the growth rate of B. cereus involved both a bias factor (Bf) and an accuracy factor (Af). Both the Bf value (1.006) and the Af value (1.011) approached 1.0 and were within acceptable ranges. Therefore, the adequacy of the predictive model for B. cereus in cooked rice was verified by the validation data.