Calculating stochastic inactivation of individual cells in a bacterial population using variability in individual cell inactivation time and initial cell number

The probability of bacterial spores surviving a thermal process: The 12D myth and other issues with its quantitative assessment

The concepts of "D-value," "thermal death time" and "commercial sterility," innovative and useful at their inception, are based on untenable assumptions, notably that the log-linear isothermal inactivation model has universal applicability, that extrapolation over several orders of magnitude below the detection level is permissible, and that total microbial inactivation is theoretically impossible. Almost all commonly observed inactivation patterns, the log-linear is just a special case, can be described by both deterministic and fully stochastic models, examples of which are given. Unlike the deterministic, the stochastic models predict either complete elimination of the targeted cells or spores in realistic finite time, or residual survival. In most cases, the published survival data do not contain enough information to establish which actually happens. The microbial safety of thermally processed foods can be compromised not only by under-processing but also by a variety of mishaps whose occurrence probabilities are unrelated to the inactivation kinetics. Moreover, the available sampling plans to detect microbial contamination in sterilized containers through incubation alone are insensitive to levels of potential safety concerns. In principle, many of these issues could be resolved by developing new dramatically improved detection methods and/or verifiable methods to predict very low levels of microbial survival.

Is skipping the definition of primary and secondary models possible? Prediction of Escherichia coli O157 growth by machine learning

To predict bacterial population behavior in food, statistical models with specific function form have been applied in the field of predictive microbiology. Modelers need to consider the linear or non-linear relationship between the response and explanatory variables in the statistical modeling approach. In the present study, we focused on machine learning methods to skip definition of primary and secondary structure model. Support vector regression, extremely randomized trees regression, and Gaussian process regression were used to predict population growth of Escherichia coli O157 at 15 and 25 °C without defining the primary and secondary models. Furthermore, the support vector regression model was applied to predict small population of bacteria cells with probability theory. The model performance of the machine learning models were nearly equal to that of the current statistical models. Machine learning models have a potential for predicting bacterial population behavior.

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.

Synergistic Effects of Butyl Para-Hydroxybenzoate and Mild Heating on Foodborne Pathogenic Bacteria

ABSTRACT

Although high-temperature heat treatments can efficiently reduce pathogen levels, they also affect the quality and nutritional profile of foods and increase the cost of processing. The food additive butyl para-hydroxybenzoate (BPB) was investigated for its potential to synergistically enhance thermal microbial inactivation at mild heating temperatures (54 to 58°C). Four foodborne pathogenic bacteria, Cronobacter sakazakii, Salmonella enterica Typhimurium, attenuated Escherichia coli O157:H7, and Listeria monocytogenes, were cultured to early stationary phase and then subjected to mild heating at 58, 55, 57, and 54°C, respectively, in a model food matrix (brain heart infusion [BHI]) containing low concentrations of BPB (≤125 ppm). The temperature used with each bacterium was selected based on the temperature that would yield an approximately 1- to 3-log reduction over 15 min of heating in BHI without BPB in a submerged coil system. The inclusion of BPB at ≤125 ppm resulted in significant enhancement of thermal inactivation, achieving 5- to >6-log reductions of the gram-negative strains with D-values of <100 s. A 3- to 4-log reduction of L. monocytogenes was achieved with a similar treatment. No significant microbial inactivation was noted in the absence of mild heating for the same time period. This study provides additional proof of concept that low-temperature inactivation of foodborne pathogens can be realized by synergistic enhancement of thermal inactivation by additives that affect microbial cell membranes.

HIGHLIGHTS

Modeling Salmonella spp. inactivation in chicken meat subjected to isothermal and non-isothermal temperature profiles

Salmonella genus has foodborne pathogen species commonly involved in many outbreaks related to the consumption of chicken meat. Many studies have aimed to model bacterial inactivation as a function of the temperature. Due to the large heterogeneity of the results, a unified description of Salmonella spp. inactivation behavior is hard to establish. In the current study, by evaluating the root mean square errors, mean absolute deviation, and Akaike and Bayesian information criteria, the double Weibull model was considered the most accurate primary model to fit 61 datasets of Salmonella inactivation in chicken meat. Results can be interpreted as if the bacterial population is divided into two subpopulations consisting of one more resistant (2.3% of the total population) and one more sensitive to thermal stress (97.7% of the total population). The thermal sensitivity of the bacteria depends on the fat content of the chicken meat. From an adapted version of the Bigelow secondary model including both temperature and fat content, 90% of the Salmonella population can be inactivated after heating at 60 °C of chicken breast, thigh muscles, wings, and skin during approximately 2.5, 5.0, 9.5, and 57.4 min, respectively. The resulting model was applied to four different non-isothermal temperature profiles regarding Salmonella growth in chicken meat. Model performance for the non-isothermal profiles was evaluated by the acceptable prediction zone concept. Results showed that >80% of the predictions fell in the acceptable prediction zone when the temperature changes smoothly at temperature rates lower than 20 °C/min. Results obtained can be used in risk assessment models regarding contamination with Salmonella spp. in chicken parts with different fat contents.

Variability in microbial inactivation: From deterministic Bigelow model to probability distribution of single cell inactivation times

Phenotypic heterogeneity seems to be an important component leading to biological individuality and is of great importance in the case of microbial inactivation. Bacterial cells are characterized by their own resistance to stresses. This inherent stochasticity is reflected in microbial survival curve which, in this context, can be considered as cumulative probability distribution of lethal events. The objective of the present study was to present an overview on the assessment and quantification of variability in microbial inactivation originating from single cells and discuss this heterogeneity in the context of predicting microbial behavior and Risk assessment studies. The detailed knowledge of the distribution of the single cells' inactivation times can be the basis for stochastic inactivation models which, in turn, may be employed in a risk - based food safety approach.

Describing the Individual Spore Variability and the Parameter Uncertainty in Bacterial Survival Kinetics Model by Using Second-Order Monte Carlo Simulation

The objective of this study was to separately describe the fitting uncertainty and the variability of individual cell in bacterial survival kinetics during isothermal and non-isothermal thermal processing. The model describing bacterial survival behavior and its uncertainties and variabilities during non-isothermal inactivation was developed from survival kinetic data for Bacillus simplex spores under fifteen isothermal conditions. The fitting uncertainties in the parameters used in the primary Weibull model was described by using the bootstrap method. The variability of individual cells in thermotolerance and the true randomness in the number of dead cells were described by using the Markov chain Monte Carlo (MCMC) method. A second-order Monte Carlo (2DMC) model was developed by combining both the uncertainties and variabilities. The 2DMC model was compared with reduction behavior under three non-isothermal profiles for model validation. The bacterial death estimations were validated using experimentally observed surviving bacterial count data. The fitting uncertainties in the primary Weibull model parameters, the individual thermotolerance heterogeneity, and the true randomness of inactivated spore counts were successfully described under all the iso-thermal conditions. Furthermore, the 2DMC model successfully described the variances in the surviving bacterial counts during thermal inactivation for all three non-isothermal profiles. As a template for risk-based process designs, the proposed 2DMC simulation approach, which considers both uncertainty and variability, can facilitate the selection of appropriate thermal processing conditions ensuring both food safety and quality.

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

Kinetic models performing point estimation are effective in predicting the bacterial behavior. However, the large variation of bacterial behavior appearing in a small number of cells, i.e. equal or less than 10² cells, cannot be expressed by point estimation. We aimed to predict the variation of Escherichia coli O157:H7 behavior during inactivation in acidified tryptone soy broth (pH3.0) through Monte Carlo simulation and evaluated the accuracy of the developed model. Weibullian fitted parameters were estimated from the kinetic survival data of E. coli O157:H7 with an initial cell number of 10⁵. A Monte Carlo simulation (100 replication) based on the obtained Weibullian parameters and the Poisson distribution of initial cell numbers successfully predicted the results of 50 replications of bacterial inactivation with initial cell numbers of 10¹, 10², and 10³ cells. The accuracy of the simulation revealed that more than 83% of the observed survivors were within predicted range in all condition. 90% of the distribution in survivors with initial cells less than 100 is equivalent to a Poisson distribution. This calculation transforms the traditional microbial kinetic model into probabilistic model, which can handle bacteria number as discrete probability distribution. The probabilistic approach would utilize traditional kinetic model towards exposure assessment.

Describing Uncertainty in Salmonella Thermal Inactivation Using Bayesian Statistical Modeling

Uncertainty analysis is the process of identifying limitations in scientific knowledge and evaluating their implications for scientific conclusions. In the context of microbial risk assessment, the uncertainty in the predicted microbial behavior can be an important component of the overall uncertainty. Conventional deterministic modeling approaches which provide point estimates of the pathogen's levels cannot quantify the uncertainty around the predictions. The objective of this study was to use Bayesian statistical modeling for describing uncertainty in predicted microbial thermal inactivation of Salmonella enterica Typhimurium DT104. A set of thermal inactivation data in broth with water activity adjusted to 0.75 at 9 different temperature conditions obtained from the ComBase database (www.combase.cc) was used. A log-linear microbial inactivation was used as a primary model while for secondary modeling, a linear relation between the logarithm of inactivation rate and temperature was assumed. For comparison, data were fitted with a two-step and a global Bayesian regression. Posterior distributions of model's parameters were used to predict Salmonella thermal inactivation. The combination of the joint posterior distributions of model's parameters allowed the prediction of cell density over time, total reduction time and inactivation rate as probability distributions at different time and temperature conditions. For example, for the time required to eliminate a Salmonella population of about 107 CFU/ml at 65°C, the model predicted a time distribution with a median of 0.40 min and 5th and 95th percentiles of 0.24 and 0.60 min, respectively. The validation of the model showed that it can describe successfully uncertainty in predicted thermal inactivation with most observed data being within the 95% prediction intervals of the model. The global regression approach resulted in less uncertain predictions compared to the two-step regression. The developed model could be used to quantify uncertainty in thermal inactivation in risk-based processing design as well as in risk assessment studies.