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.

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.

Prediction of population behavior of Listeria monocytogenes in food using machine learning and a microbial growth and survival database.

In predictive microbiology, statistical models are employed to predict bacterial population behavior in food using environmental factors such as temperature, pH, and water activity. As the amount and complexity of data increase, handling all data with high-dimensional variables becomes a difficult task. We propose a data mining approach to predict bacterial behavior using a database of microbial responses to food environments. Listeria monocytogenes, which is one of pathogens, population growth and inactivation data under 1,007 environmental conditions, including five food categories (beef, culture medium, pork, seafood, and vegetables) and temperatures ranging from 0 to 25 °C, were obtained from the ComBase database ( www.combase.cc ). We used eXtreme gradient boosting tree, a machine learning algorithm, to predict bacterial population behavior from eight explanatory variables: 'time', 'temperature', 'pH', 'water activity', 'initial cell counts', 'whether the viable count is initial cell number', and two types of categories regarding food. The root mean square error of the observed and predicted values was approximately 1.0 log CFU regardless of food category, and this suggests the possibility of predicting viable bacterial counts in various foods. The data mining approach examined here will enable the prediction of bacterial population behavior in food by identifying hidden patterns within a large amount of data.

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.