Transforming kinetic model into a stochastic inactivation model: Statistical evaluation of stochastic inactivation of individual cells in a bacterial population

Deterministic Approach and Monte Carlo Simulation to Predict Listeria monocytogenes Time to Grow on Refrigerated Ham: A Study Supporting Risk-based Decisions for Consumers' Health

This study assessed the growth of Listeria monocytogenes in ready-to-eat (RTE) ham during storage under conditions simulating domestic practices with the intention to offer support in the elaboration of food safety policies that should better protect consumers against food poisoning at home. RTE ham, artificially contaminated at either medium (10²-10³ CFU/g) or high (10⁴-10⁵ CFU/g) concentration, was stored at both isothermal (4℃ in a refrigerator able to maintain a relatively constant temperature and 5℃ and 7℃ in a refrigerator with fluctuating temperature) and dynamic (5℃ and 7℃ with intermittent exposure to ambient temperature, e.g. 25℃) conditions. Under isothermal conditions, the increasing storage temperature determined a significantly increased (p < 0.05) capacity of L. monocytogenes to grow. The kinetic growth parameters were derived by fitting the Baranyi and Roberts model to the experimental data and, based on the maximum specific growth rates, it was estimated the temperature dependence of L. monocytogenes growth in RTE ham. At medium contamination level, sanitary risk time calculation revealed that, unlike storage at 5℃ and 7℃, storage at 4℃ of the RTE ham extends the time period during which the product is safe for consumption by ∼40 and 52%, respectively. However, the real temperature fluctuations included in the Monte Carlo simulations at low L. monocytogenes counts (1, 5 and 10 CFU/g) have shortened the safety margins. Stochastic models also proved to be useful tools for describing the pathogen's behavior when refrigeration of the RTE ham alternates with periods of ham being kept at room temperature, considered dynamic conditions of growth.

The COM-Poisson Process for Stochastic Modeling of Osmotic Inactivation Dynamics of Listeria monocytogenes

Controlling harmful microorganisms, such as Listeria monocytogenes, can require reliable inactivation steps, including those providing conditions (e.g., using high salt content) in which the pathogen could be progressively inactivated. Exposure to osmotic stress could result, however, in variation in the number of survivors, which needs to be carefully considered through appropriate dispersion measures for its impact on intervention practices. Variation in the experimental observations is due to uncertainty and biological variability in the microbial response. The Poisson distribution is suitable for modeling the variation of equi-dispersed count data when the naturally occurring randomness in bacterial numbers it is assumed. However, violation of equi-dispersion is quite often evident, leading to over-dispersion, i.e., non-randomness. This article proposes a statistical modeling approach for describing variation in osmotic inactivation of L. monocytogenes Scott A at different initial cell levels. The change of survivors over inactivation time was described as an exponential function in both the Poisson and in the Conway-Maxwell Poisson (COM-Poisson) processes, with the latter dealing with over-dispersion through a dispersion parameter. This parameter was modeled to describe the occurrence of non-randomness in the population distribution, even the one emerging with the osmotic treatment. The results revealed that the contribution of randomness to the total variance was dominant only on the lower-count survivors, while at higher counts the non-randomness contribution to the variance was shown to increase the total variance above the Poisson distribution. When the inactivation model was compared with random numbers generated in computer simulation, a good concordance between the experimental and the modeled data was obtained in the COM-Poisson process.

Bayesian Generalized Linear Model for Simulating Bacterial Inactivation/Growth Considering Variability and Uncertainty

Conventional regression analysis using the least-squares method has been applied to describe bacterial behavior logarithmically. However, only the normal distribution is used as the error distribution in the least-squares method, and the variability and uncertainty related to bacterial behavior are not considered. In this paper, we propose Bayesian statistical modeling based on a generalized linear model (GLM) that considers variability and uncertainty while fitting the model to colony count data. We investigated the inactivation kinetic data of Bacillus simplex with an initial cell count of 10⁵ and the growth kinetic data of Listeria monocytogenes with an initial cell count of 10⁴. The residual of the GLM was described using a Poisson distribution for the initial cell number and inactivation process and using a negative binomial distribution for the cell number variation during growth. The model parameters could be obtained considering the uncertainty by Bayesian inference. The Bayesian GLM successfully described the results of over 50 replications of bacterial inactivation with average of initial cell numbers of 10¹, 10², and 10³ and growth with average of initial cell numbers of 10^–1, 10⁰, and 10¹. The accuracy of the developed model revealed that more than 90% of the observed cell numbers except for growth with initial cell numbers of 10¹ were within the 95% prediction interval. In addition, parameter uncertainty could be expressed as an arbitrary probability distribution. The analysis procedures can be consistently applied to the simulation process through fitting. The Bayesian inference method based on the GLM clearly explains the variability and uncertainty in bacterial population behavior, which can serve as useful information for risk assessment related to food borne pathogens.

Application of growth rate from kinetic model to calculate stochastic growth of a bacteria population at low contamination level

Traditional predictive microbiology is not suited for cell growth predictions for low-level contamination, where individual cell heterogeneity becomes apparent. Accordingly, we simulated a stochastic birth process of bacteria population using kinetic parameters. We predicted the variation in behavior of Salmonella enterica serovar Typhimurium cells at low inoculum density. The modeled cells were grown in tryptic soy broth at 25 °C. Kinetic growth parameters were first determined empirically for an initial cell number of 10⁴ cells. Monte Carlo simulation based on the growth kinetics and Poisson distribution for different initial cell numbers predicted the results of 50 replicate growth experiments with the initial cell number of 1, 10, and 64 cells. Indeed, measured behavior of 85% cells fell within the 95% prediction area of the simulation. The calculations link the kinetic and stochastic birth process with Poisson distribution. The developed model can be used to calculate the probability distribution of population size for exposure assessment and for the evaluation of a probability that a pathogen would exceed critical contamination level during food storage.