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 (lambda) during the growth of Bacillus cereus vegetative cells as a function of temperature, pH, and salt concentration using logistic regression. The developed lambda model was subsequently combined with a logistic differential equation to simulate bacterial numbers over time. To develop a novel model for lambda, we determined whether bacterial growth had begun, i.e., whether lambda 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 similar to 7.0) and salt concentrations (0.5 similar to 2.0%) at static temperatures (10 similar to 20 degrees C). The probability of the end of lambda 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 lambda was described as a function of time, temperature, pH, and salt concentration and showed a high goodness of fit. The lambda model was validated with independent data sets of B. cereus growth in culture media and foods, indicating acceptable performance. Furthermore, the lambda 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 lambda using observable environmental parameters without any conceptual assumptions and the simulation of bacterial numbers over time with the use of a logistic differential equation.