One- and Two-Step Kinetic Data Analysis Applied for Single and Co-Culture Growth of Staphylococcus aureus, Escherichia coli, and Lactic Acid Bacteria in Milk

Modelling growth of Bacillus cereus in paneer by one-step parameter estimation

Bacillus cereus phylogenetic group III and IV strains are commonly associated with food products and cause toxin mediated foodborne diseases. These pathogenic strains have been identified from milk and dairy products, such as reconstituted infant formula and several cheeses. Paneer is a fresh, soft cheese originating from India that is prone to foodborne pathogen contamination, such as by Bacillus cereus. However, there are no reported studies of B. cereus toxin formation in paneer or predictive models quantifying growth of the pathogen in paneer under different environmental conditions. This study assessed enterotoxin-producing potential of B. cereus group III and IV strains, isolated from dairy farm environments, in fresh paneer. Growth of a four-strain cocktail of toxin-producing B. cereus strains was measured in freshly prepared paneer incubated at 5-55 °C and modelled using a one-step parameter estimation combined with bootstrap re-sampling to generate confidence intervals for model parameters. The pathogen grew in paneer between 10 and 50 °C and the developed model fit the observed data well (R² = 0.972, RMSE = 0.321 log₁₀ CFU/g). The cardinal parameters for B. cereus growth in paneer along with the 95% confidence intervals were: μ_opt 0.812 log₁₀ CFU/g/h (0.742, 0.917); T_opt is 44.177 °C (43.16, 45.49); T_min is 4.405 °C (3.973, 4.829); T_max is 50.676 °C (50.367, 51.144). The model developed can be used in food safety management plans and risk assessments to improve safety of paneer while also adding to limited information on B. cereus growth kinetics in dairy products.

Development of a New Modelling Approach and Performance Evaluation of Meta-heuristic Optimization Algorithms for the Prediction of Kinetic Growth Parameters for Pseudomonas spp. in Fish

The main aim of the current work was to build up a new mathematical modelling approach in predictive food microbiology field for the prediction of growth kinetics of microorganisms. For this purpose, the bacterial growth data of Pseudomonas spp. in whole fish (gilt-head seabream) subjected to isothermal and non-isothermal storage temperatures were collected from previously published growth curves. Maximum specific growth rate (1/h) and lag phase duration (h) were described as a function of storage temperature using the direct two-step, direct one-step and inverse dynamic modelling approaches based on various meta-heuristic optimization algorithms. The fitting capability of the modelling approaches and employed optimization algorithms was separately compared, and the one-step modelling approach for the direct methods and the Bayesian optimization method for the used algorithms provided the best goodness of fit results. These two were then further processed in validation step. The inverse dynamic modelling approach based on the Bayesian optimization algorithm yielded satisfactorily statistical indexes (1.02 > Bias factor > 1.09 and 1.07 > Accuracy factor > 1.13), which indicates it can be reliably used as an alternative way of describing the growth behaviour of Pseudomonas spp. in fish in a fast and efficient manner with minimum labour effort.

A Study and Modeling of Bifidobacterium and Bacillus Coculture Continuous Fermentation under Distal Intestine Simulated Conditions

The diversity and the stability of the microbial community are associated with microecological interactions between its members. Antagonism is one type of interaction, which particularly determines the benefits that probiotics bring to host health by suppressing opportunistic pathogens and microbial contaminants in food. Mathematical models allow for quantitatively predicting intrapopulation relationships. The aim of this study was to create predictive models for bacterial contamination outcomes depending on the probiotic antagonism and prebiotic concentration. This should allow an improvement in the screening of synbiotic composition for preventing gut microbial infections. The functional model (fermentation) was based on a three-stage continuous system, and the distal colon section (N₂, pH 6.8, flow rate 0.04 h^–1) was simulated. The strains Bifidobacterium adolescentis ATCC 15703 and Bacillus cereus ATCC 9634 were chosen as the model probiotic and pathogen. Oligofructose Orafti P95 (OF) was used as the prebiotic at concentrations of 2, 5, 7, 10, 12, and 15 g/L of the medium. In the first stage, the system was inoculated with Bifidobacterium, and a dynamic equilibrium (Bifidobacterium count, lactic, and acetic acids) was achieved. Then, the system was contaminated with a 3-day Bacillus suspension (spores). The microbial count, as well as the concentration of acids and residual carbohydrates, was measured. A Bacillus monoculture was studied as a control. The stationary count of Bacillus in monoculture was markedly higher. An increase (up to 8 h) in the lag phase was observed for higher prebiotic concentrations. The specific growth rate in the exponential phase varied at different OF concentrations. Thus, the OF concentration influenced two key events of bacterial infection, which together determine when the maximal pathogen count will be reached. The mathematical models were developed, and their accuracies were acceptable for Bifidobacterium (relative errors ranging from 1.00% to 2.58%) and Bacillus (relative errors ranging from 0.74% to 2.78%) count prediction.