Comparing experimental design schemes in predictive food microbiology: Optimal parameter estimation of secondary models

Optimal experimental design (OED) for the growth rate of microbial populations. Are they really more "optimal" than uniform designs?

Secondary growth models from predictive microbiology can describe how the growth rate of microbial populations varies with environmental conditions. Because these models are built based on time and resource consuming experiments, model-based Optimal Experimental Design (OED) can be of interest to reduce the experimental load. In this study, we identify optimal experimental designs for two common models (full Ratkowsky and Cardinal Parameters Model (CPM)) for a different number of experiments (10-30). Calculations are also done fixing one or more model parameters, observing that this decision strongly affects the layout of the OED. Using in silico experiments, we conclude that OEDs are more informative than conventional (equidistant) designs with the same number of experiments. However, OEDs cluster the experiments near the growth limits (Xmin and Xmax) resulting in impractical designs with aggregated experimental runs ~10 times longer than conventional designs. To mitigate this, we propose a novel optimality criterion (i.e., the objective function) that accounts for the aggregated time. The novel criterion provides a reduction in parameter uncertainty with respect to the conventional design, without an increase in the experimental load. These results underline that an OED is only based on information theory (Fisher information), so the results can be impractical when actual experimental limitations are considered. The study also emphasizes that most OED schemes identify where to measure, but do not give an indication on how many experiments should be made. In this sense, numerical simulations can estimate the parameter uncertainty that would be obtained for a particular experimental design (OED or not). These results and methodologies (available in Open Code) can guide the design of future experiments for the development of secondary growth models.

The Most Probable Curve method - A robust approach to estimate kinetic models from low plate count data resulting in reduced uncertainty

A novel method is proposed for fitting microbial inactivation models to data on liquid media: the Most Probable Curve (MPC) method. It is a multilevel model that makes a separation between the "true" microbial concentration according to the model, the "actual" concentration in the media considering chance, and the actual counts on the plate. It is based on the assumptions that stress resistance is homogeneous within a microbial population, and that there is no aggregation of microbial cells. Under these assumptions, the number of colonies in/on a plate follows a Poisson distribution with expected value depending on the proposed kinetic model, the number of dilutions and the plated volume. The novel method is compared against (non)linear regression based on a normal likelihood distribution (traditional method), Poisson regression and gamma-Poisson regression using data on the inactivation of Listeria monocytogenes. The conclusion is that the traditional method has limitations when the data includes plates with low (or zero) cell counts, which can be mitigated using more complex (discrete) likelihoods. However, Poisson regression uses an unrealistic likelihood function, making it unsuitable for survivor curves with several log-reductions. Gamma-Poisson regression uses a more realistic likelihood function, even though it is based mostly on empirical hypotheses. We conclude that the MPC method can be used reliably, especially when the data includes plates with low or zero counts. Furthermore, it generates a more realistic description of uncertainty, integrating the contribution of the plating error and reducing the uncertainty of the primary model parameters. Consequently, although it increases modelling complexity, the MPC method can be of great interest in predictive microbiology, especially in studies focused on variability analysis.

Development of predictive models evaluating the spoilage-delaying effect of a bioprotective culture on different yeast species in yogurt

Yeast spoilage of fermented dairy products causes challenges for the dairy industry, including economic losses due to wasted product. Food cultures with bioprotective effects are becoming more widely used to help ensure product quality throughout product shelf life. To assist the dairy industry when evaluating product quality throughout shelf life and the effect of bioprotective cultures, we aimed to build stochastic models that provide reliable predictions of yeast spoilage in yogurt with and without bioprotective culture. Growth characterizations of Debaryomyces hansenii, Yarrowia lipolytica, Saccharomyces cerevisiae, and Kluyveromyces marxianus at storage temperatures of 7, 12, and 16°C during a 30-d storage period were conducted in yogurt with and without a bioprotective culture containing Lacticaseibacillus rhamnosus strains. The kinetic growth parameters were calculated using the Buchanan growth model, and these parameters were used as baseline values in Monte Carlo models to translate the yeast growth into spoilage levels. The models were developed using 100,000 simulations and they predicted yeast spoilage levels in yogurt by the 4 yeast types. Each modeled yogurt batch was set to be contaminated with yeast at a concentration drawn from a normal distribution with a mean of 1 log₁₀ cfu/mL and standard deviation of 1 log₁₀ cfu/mL and stored for 30 d at a temperature drawn from a normal distribution with a mean of 6.1°C and a standard deviation of 2.8°C. Considering a spoilage level of 5 log₁₀ cfu/mL, the predicted number of spoiled samples was reduced 3-fold during the first 10 d and by 2-fold at the end of shelf life when a bioprotective culture was added to the yogurt. The models were evaluated by sensitivity analyses, where the main effect factors were maximum yeast population, storage temperature, and yeast strain. The models were validated by comparing the model output to actual observed spoilage data from a European dairy using the bioprotective culture. When the model prediction, based on a mixture of the 4 specific yeast strains, was compared with spoilage data from the European dairy, the observed effect of bioprotective cultures was considerably higher than predicted, potentially influenced by the presence of contaminating strains more sensitive to a bioprotective culture than those characterized here. The developed Monte Carlo models can predict yeast spoilage levels in yogurt at specific production settings and how this may be affected by various parameters and addition of bioprotective cultures.