Guidelines for the design of (optimal) isothermal inactivation experiments

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.

Dynamic Thermal Treatments in Green Coconut Water Induce Dynamic Stress Adaptation of Listeria innocua That Increases Its Thermal Resistance

The global coconut water market is projected to grow in the upcoming years, attributed to its numerous health benefits. However, due to its susceptibility to microbial contamination and the limitations of non-thermal decontamination methods, thermal treatments remain the primary approach to ensure the shelf-life stability and the microbiological safety of the product. In this study, the thermal inactivation of Listeria innocua, a Listeria monocytogenes surrogate, was evaluated in coconut water and in tryptone soy broth (TSB) under both isothermal (50-60 °C) and dynamic conditions (from 30 to 60 °C, with temperature increases of 0.5, 1 and 5 °C/min). Mathematical models were used to analyse the inactivation data. The Geeraerd model effectively described the thermal inactivation of L. innocua in both TSB and coconut water under isothermal conditions, with close agreement between experimental data and model fits. Parameter estimates and analysis revealed that acidified TSB is a suitable surrogate medium for studying the thermal inactivation of L. innocua in coconut water, despite minor differences observed in the shoulder length of inactivation curves, likely attributed to the media composition. The models fitted to the data obtained at isothermal conditions fail to predict L. innocua responses under dynamic conditions. This is attributed to the stress acclimation phenomenon that takes place under dynamic conditions, where bacterial cells adapt to initial sub-lethal treatment stages, leading to increased thermal resistance. Fitting the Bigelow model directly to dynamic data with fixed z-values reveals a three-fold increase in D-values with lower heating rates, supporting the role of stress acclimation. The findings of this study aid in designing pasteurization treatments targeting L. innocua in coconut water and enable the establishment of safe, mild heat treatments for refrigerated, high-quality coconut water.

Disentangling the contributions of initial heterogeneities and dynamic stress adaptation to nonlinearities in bacterial survival curves

The deviations from log-linearity that are often observed in bacterial survivor curves can be explained using different arguments, both biological and experimental. In this study, we used Bacillus subtilis as a model organism to demonstrate that the generally accepted vitalistic arguments (initial heterogeneities in the stress resistance of the cells in the population) may fail to describe microbial inactivation in some situations. In this sense, we showed how dynamic stress acclimation during an isothermal treatment provides an alternative explanation for survivor curves with an upwards curvature. We also provided an innovative experimental approach based on preadaptation experiments to evaluate which hypothesis is more suitable for the bacterial response. Furthermore, we used our experimental results to define bounds for the possible stress acclimation that may take place during dynamic treatments, concluding that the magnitude of stress acclimation may be larger for dynamic treatments than for isothermal experiments. We also evaluated the contribution of the SigB general stress response system to heat resistance by comparing the heat survival of wt and the ΔsigB mutant. Both strains survived better in 51, 52.5 and 55 °C when cells were pre-adapted at 48 °C than non-pre-adapted cells. However, ΔsigB was less resistant to heat than wt due to the missing SigB general stress system. Although these conclusions were based on B. subtilis as a model organism, this study can be the first step towards the development of a novel methodology able to estimate dynamic effects using only isothermal experiments. This would improve the models developed within the predictive microbiology community, improving our ability to predict microbial inactivation during industrial treatments, which are most often dynamic.

The importance of what we cannot observe: Experimental limitations as a source of bias for meta-regression models in predictive microbiology

Meta-regression models have gained in popularity during the last years as a way to create more generic models for Microbial Risk Assessments that also include variability. However, as with most meta-analyses and empirical models, systematic biases in the data can result in inaccurate models. In this article, we define experimental bias as a type of selection bias due to the practical limitations of microbial inactivation experiments. Conditions with extremely high D-values (i.e. slow inactivation) need very long experimental runs to cause significant reductions. On the other hand, when the D-value is extremely low, not enough data points can be gathered before the microbial population is below the detection limit. Consequently, experimental designs favour conditions within a practical experimental range, introducing a selection bias in the D-values. We demonstrate the impact of experimental bias in meta-regression models using numerical simulations. Models fitted to data with experimental bias overestimated the z-value and underestimated variability. We propose a rapid heuristic method to identify experimental bias in datasets, and we propose truncated regression to mitigate its impact in meta-regression models. Both methods were validated using simulated data. Thereafter the procedures were tested by building a meta-regression model for actual data for the inactivation of Bacillus cereus spores. We concluded that the dataset included experimental bias, and that it would cause an overestimation of the microbial resistance at high temperatures (>120 °C) for classical meta-regression models. This effect was mitigated when the model was built using truncated regression. In conclusion, we demonstrate that experimental bias could potentially result in inaccurate models for predictive microbiology. Therefore, checking for experimental bias should be a routine step in meta-regression modelling, and be included in guidelines on data analysis for meta-regression.

Multiobjective Optimization of a Frying Process Balancing Acrylamide Formation and Quality: Solution Analysis and Uncertainty Propagation

In this study, we performed multi-objective model-based optimization of a potato-frying process balancing between acrylamide production and a quality parameter (yellowness). Solution analysis revealed that, for most of the Pareto solutions, acrylamide levels exceeded the EFSA recommendation. Almost equivalent optimal solutions were found for moderate processing conditions (low temperatures and/or processing times) and the propagation of the uncertainty of the acrylamide production model parameters led to Pareto fronts with notable differences from the one obtained using the nominal parameters, especially in the ranges of high values of acrylamide production and yellowness. These results can help to identify processing conditions to achieve the desired acrylamide/yellowness balance and design more robust processes allowing for the enhancement of flexibility when equivalent optimal solutions can be retrieved.

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.

Dynamics of Microbial Inactivation and Acrylamide Production in High-Temperature Heat Treatments

In food processes, optimizing processing parameters is crucial to ensure food safety, maximize food quality, and minimize the formation of potentially toxigenic compounds. This research focuses on the simultaneous impacts that severe heat treatments applied to food may have on the formation of harmful chemicals and on microbiological safety. The case studies analysed consider the appearance/synthesis of acrylamide after a sterilization heat treatment for two different foods: pureed potato and prune juice, using Geobacillus stearothermophilus as an indicator. It presents two contradictory situations: on the one hand, the application of a high-temperature treatment to a low acid food with G. stearothermophilus spores causes their inactivation, reaching food safety and stability from a microbiological point of view. On the other hand, high temperatures favour the appearance of acrylamide. In this way, the two objectives (microbiological safety and acrylamide production) are opposed. In this work, we analyse the effects of high-temperature thermal treatments (isothermal conditions between 120 and 135 °C) in food from two perspectives: microbiological safety/stability and acrylamide production. After analysing both objectives simultaneously, it is concluded that, contrary to what is expected, heat treatments at higher temperatures result in lower acrylamide production for the same level of microbial inactivation. This is due to the different dynamics and sensitivities of the processes at high temperatures. These results, as well as the presented methodology, can be a basis of analysis for decision makers to design heat treatments that ensure food safety while minimizing the amount of acrylamide (or other harmful substances) produced.

Impact of Heating Rates on Alicyclobacillus acidoterrestris Heat Resistance under Non-Isothermal Treatments and Use of Mathematical Modelling to Optimize Orange Juice Processing

Alicyclobacillus acidoterrestris is a spoilage microorganism responsible for relevant product and economic losses in the beverage and juice industry. Spores of this microorganism can survive industrial heat treatments and cause spoilage during posterior storage. Therefore, an effective design of processing treatments requires an accurate understanding of the heat resistance of this microorganism. Considering that industrial treatments are dynamic; this understanding must include how the heat resistance of the microorganism is affected by the heating rate during the heating and cooling phases. The main objective of this study was to establish the effect of heating rates and complex thermal treatments on the inactivation kinetics of A. acidoterrestris. Isothermal experiments between 90 and 105 °C were carried out in a Mastia thermoresistometer, as well as four different dynamic treatments. Although most of the inactivation takes place during the holding phase, our results indicate the relevance of the heating phase for the effectiveness of the treatment. The thermal resistance of A. acidoterrestris is affected by the heating rate during the heating phase. Specifically, higher heating rates resulted in an increased microbial inactivation with respect to the one predicted based on isothermal experiments. These results provide novel information regarding the heat response of this microorganism, which can be valuable for the design of effective heat treatments to improve product safety and stability. Moreover, it highlights the need to incorporate experimental data based on dynamic treatments in process design, as heating rates can have a very significant effect on the thermal resistance of microorganisms.