Modeling growth limits of Bacillus spp. spores by using deep-learning algorithm

Growth/no growth boundary models for Bacillus spores that accounted for the effects of environmental pH, water activity (aw), acetic acid, lactic acid, bacterial strain, and storage period were developed using conventional logistic regression and machine learning algorithms. Growth in tryptic soy broth at 317 conditions comprising nine levels of pH (4.0-6.5), six levels of aw (0.85-1.00), six levels of acetic acid concentrations (0-0.8%), and five levels of lactic acid concentrations (0-0.8%) was examined to confirm growth limit conditions. All models developed using logistic regression, neural network, and deep learning on the basis of obtained datasets successfully described growth/no growth boundaries of three Bacillus species. Although the logistic regression model failed to describe growth limits under some conditions, neural network and deep learning approaches enabled to determine them in such cases. The developed models were evaluated by independent experimental data of growth in tryptic soy broth and in clam soup. The deep learning model enabled better prediction of independent data with smaller probabilistic variability values than those of the logistic regression and neural network models. The deep learning procedure can be utilized for growth boundary modeling to control bacterial growth safely and flexibly.