Quantitative microbial spoilage risk assessment caused by fungi in sports drinks through multilevel modelling.

The risk of fungal spoilage of sports drinks produced in the beverage industry was assessed using quantitative microbial spoilage risk assessment (QMSRA). The most relevant pathway was the contamination of the bottles during packaging by mould spores in the air. Mould spores' concentration was estimated by longitudinal sampling for 6 years (936 samples) in different production areas and seasons. This data was analysed using a multilevel model that separates the natural variability in spore concentration (as a function of sampling year, season, and area) and the uncertainty of the sampling method. Then, the expected fungal contamination per bottle was estimated by Monte Carlo simulation, considering their settling velocity and the time and exposure area. The product's shelf life was estimated through the inoculation of bottles with mould spores, following the determination of the probability of visual spoilage as a function of storage time at 20 and 30 °C using logistic regression. The Monte Carlo model estimated low expected spore contamination in the product (1.7 × 10-6 CFU/bottle). Nonetheless, the risk of spoilage is still relevant due to the large production volume and because, as observed experimentally, even a single spore has a high spoilage potential. The applicability of the QMSRA during daily production was made possible through the simplification of the model under the hypothesis that no bottle will be contaminated by more than one spore. This simplification allows the calculation of a two-dimensional performance objective that combines the spore concentration in the air and the exposure time, defining "acceptable combinations" according to an acceptable level of spoilage (ALOS; the proportion of spoiled bottles). The implementation of the model at the operational level was done through the representation of the simplified model as a two-dimensional diagram that defines acceptable and unacceptable areas. The innovative methodology employed here for defining and simplifying QMSRA models can be a blueprint for future studies aiming to quantify the risk of spoilage of other beverages with a similar scope.

Human health risk-benefit assessment of fish and other seafood: a scoping review.

Fish and other seafood are important sources of nutrients, but they are also sources of chemical contaminants that may cause adverse health effects. This article aimed to identify existing risk-benefit assessments (RBA) of fish, shellfish, and other seafood, compare methodologies, discuss differences and commonalities in findings, and identify limitations and ways forward for future studies. We conducted a scoping review of the scientific literature of studies in all languages published from 2000 through April 2019. We identified 106 RBA of fish and other seafood across Europe, Asia, North America, Africa, and at the global level. Studies were heterogeneous in terms of types of fish and other seafood considered, beneficial and adverse compounds assessed, and overall methodology. Collected data showed that a diet consisting of a variety of lean and fatty fish and other seafood is recommended for the overall population and that women of childbearing age and children should limit the consumption of fish and other seafood types that have a high likelihood of contamination. Our review emphasizes the need for evidence-based, up-to-date, and harmonized approaches in RBA in general.

Evaluation of Multicriteria Decision Analysis Algorithms in Food Safety: A Case Study on Emerging Zoonoses Prioritization.

Decision making in food safety is a complex process that involves several criteria of different nature like the expected reduction in the number of illnesses, the potential economic or health-related cost, or even the environmental impact of a given policy or intervention. Several multicriteria decision analysis (MCDA) algorithms are currently used, mostly individually, in food safety to rank different options in a multifactorial environment. However, the selection of the MCDA algorithm is a decision problem on its own because different methods calculate different rankings. The aim of this study was to compare the impact of different uncertainty sources on the rankings of MCDA problems in the context of food safety. For that purpose, a previously published data set on emerging zoonoses in the Netherlands was used to compare different MCDA algorithms: MMOORA, TOPSIS, VIKOR, WASPAS, and ELECTRE III. The rankings were calculated with and without considering uncertainty (using fuzzy sets), to assess the importance of this factor. The rankings obtained differed between algorithms, emphasizing that the selection of the MCDA method had a relevant impact in the rankings. Furthermore, considering uncertainty in the ranking had a high influence on the results. Both factors were more relevant than the weights associated with each criterion in this case study. A hierarchical clustering method was suggested to aggregate results obtained by the different algorithms. This complementary step seems to be a promising way to decrease extreme difference among algorithms and could provide a strong added value in the decision-making process.

Mathematical modelling of the stress resistance induced in Listeria monocytogenes during dynamic, mild heat treatments.

Modelling of stress acclimation induced by thermal inactivation of Listeria monocytogenes under dynamic conditions is analyzed in this work. A mathematical model that separates the effect of the instantaneous temperature from the one of stress acclimation, was used. The model was trained using isothermal inactivation experiments, and one biphasic dynamic treatment with a heating rate of 1 °C/min and a holding phase of 60 °C. These experiments were performed in laboratory media (Tryptic Soy Broth; TSB). The model parameters estimated through these experiments (D55=12.87±0.82min, z=4.58±0.04°C, a=0.11±0.01min-1, E=0.50±0.01°C and c=1.23±0.03) were successfully used to predict the microbial inactivation for another seven inactivation profiles, with and without a holding phase. Moreover, similar experiments were performed using milk as heating media, obtaining a good agreement between the model predictions and the empirical observations. The results of this study are compatible with the hypothesis that L. monocytogenes is able to develop a physiological response during dynamic treatments that increases its thermal resistance. Also, that the model used can be used to predict microbial inactivation of this microorganism taking into consideration stress acclimation.

Effect of storage conditions in the response of Listeria monocytogenes in a fresh purple vegetable smoothie compared with an acidified TSB medium.

In this study, growth and/or inactivation of Listeria monocytogenes 4032 at different inoculum levels in a vegetable smoothie with purple colour, (previously heat stabilised at 95 °C for 3 min) was evaluated. Growth/inactivation was compared with acidified TSB medium at the same pH level with HCl. Samples were stored at different temperatures (5, 10, 15 and 25 °C). All the smoothies stored at 15 and 25 °C showed growth up to 7.5-8.0 log CFU/mL and at 10 °C growth was only observed at the highest inoculum level. Growth was only observed at 25 °C in acidified TSB. In the case of the smoothies inoculated and stored at 5 °C, L. monocytogenes was not able to grow but survived for a long period of time, whereas at the lower inocula at 10 °C they presented a slow inactivation for an extended time. Acidified TSB inoculated and stored showed inactivation at 5, 10 and 15 °C. Best inactivation modelling alternatives are proposed. The differences between the smoothie and TSB medium about growth or survival in this study, even at relatively low pH values, were due to the favorable nutritional composition of the smoothie compared to a laboratory medium. Results in this study can allow to design safe conditions for smoothie production.

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.

Development of novel natto using legumes produced in Europe.

Natto is a traditional Japanese fermented product consisting of cooked soybeans fermented with Bacillus subtilis var. natto. We assessed three different B. subtilis strains and investigated their impact on product quality aspects, such as microbial quality, textural quality (poly-γ-glutamate strand formation), free amino acids (FAA), and volatile organic compounds (VOCs), but also the vitamin K1, K2 and B1 content, and presence of nattokinase. Using Bayesian contrast analysis, we conclude that the quality attributes were influenced by both the substrate and strain used, without significant differences in bacterial growth between strain or substrate. Overall, all the tested European legumes, except for brown beans, are adequate substrates to produce natto, with comparable or higher qualities compared to the traditional soy. Out of all the tested legumes, red lentils were the most optimal fermentation substrate. They were fermented most consistently, with high concentrations of vitamin K2, VOCs, FAA.

Systematic risk ranking of microbiological hazards in infant foods.

Ensuring food safety, particularly for vulnerable groups, like infants and young children, requires identifying and prioritizing potential hazards in food chains. We previously developed a web-based decision support system (DSS) to identify specific microbiological hazards (MHs) in infant and toddler foods through a structured five-step process. This study takes the framework further by introducing systematic risk ranking (RR) steps to rank MH risks with seven criteria: process survival, recontamination, growth opportunity, meal preparation, hazard-food association evidence, food consumption habits of infants and toddlers in the EU, and MH severity. Each criterion is given a semi-quantitative or quantitative score or risk value, contributing to the final MH risk calculation via three aggregation methods: semi-quantitative risk scoring, semi-quantitative risk value, and outranking multi-criteria decision analysis (MCDA). To validate the criteria and ranking approaches, we conducted a case study to rank MH risks in infant formula, compared the results of the three risk ranking methods, and additionally evaluated the ranking results against expert opinions to ensure their accuracy. The results showed strong agreement among the three methods, consistently ranking Salmonella non-Typhi and Cronobacter spp. and Shiga-toxin-producing Escherichia coli as the top MH risks in infant formulae, with minor deviations. When MHs were ranked after an initial hazard identification step, all three methods produced nearly identical MH rankings, reinforcing the reliability of the ranking steps and the selected criteria. Notably, the risk value and MCDA methods provided more informative MH rankings compared to the risk scoring method. The risk value and risk scoring methods were implemented into an online tool, called the MIcrobiological hazards risk RAnking decision support system (Mira-DSS), available at https://foodmicrobiologywur.shinyapps.io/MIcrobial_hazards_RAnking/. In conclusion, our framework enables the ranking of MH risks, facilitating intervention comparisons and resource allocations to mitigate MH risks in infant foods, with potential applicability to broader food categories.

A secondary model for the effect of pH on the variability in growth fitness of Listeria innocua strains.

Variability in microbial growth is a keystone of modern Quantitative Microbiological Risk Assessment (QMRA). However, there are still significant knowledge gaps on how to model variability, with the most common assumption being that variability is constant. This is implemented by an error term (with constant variance) added on top of the secondary growth model (for the square root of the growth rate). However, this may go against microbial ecology principles, where differences in growth fitness among bacterial strains would be more prominent in the vicinity of the growth limits than at optimal growth conditions. This study coins the term "secondary models for variability", evaluating whether they should be considered in QMRA instead of the constant strain variability hypothesis. For this, 21 strains of Listeria innocua were used as case study, estimating their growth rate by the two-fold dilution method at pH between 5 and 10. Estimates of between-strain variability and experimental uncertainty were obtained for each pH using mixed-effects models, showing the lowest variability at optimal growth conditions, increasing towards the growth limits. Nonetheless, the experimental uncertainty also increased towards the extremes, evidencing the need to analyze both sources of variance independently. A secondary model was thus proposed, relating strain variability and pH conditions. Although the modelling approach certainly has some limitations that would need further experimental validation, it is an important step towards improving the description of variability in QMRA, being the first model of this type in the field.

Training in modern statistical methodologies and software tools for the definition and analysis of (stochastic) quantitative microbial risk assessment models with a comparison between the Hungarian and Spanish food supply chains.

Human pathogenic Salmonella enterica strains have been infecting people since historical times. The original human pathogens, typhoid Salmonella strains (e.g. S. Typhi) played a huge role in the previous centuries but nowadays in the developed world the number of cases or outbreaks caused by these serotypes deceased due to the development of personal and public hygiene. Nowadays in these regions the animal-borne zoonotic serotypes (e.g. S. Enteritidis) became more important because of their high prevalence in intensive animal husbandry. But these bacteria can also appear in fruits and vegetables. The fellow joined the scientific work of the Polytechnic University of Cartagena, Spain about the safety of plant-based products, where he could gain experience in microbiological laboratory exercises and theoretical calculations of statistics and modelling. The activities in the laboratory were part of the research lines already established at the host institution, being based on the protocols they have already implemented. Nonetheless, the fellow had the opportunity to design his own experiment, do the experimental work required and analysed the data within the context of a qualitative microbiological risk assessment. The main focus was on the heat resistance of two strains of zoonotic Salmonella spp. at different temperatures. Experiments were done using a reference strain and an extremely resistant variant to evaluate this rare phenotype. The experiments were executed using a Mastia thermoresistometer, a device patented by the host institution that provides more control when studying thermal treatments than traditional methods. The data was analysed using the principles of predictive microbiology, using the D-value as an estimate of heat resistance that provides insight into the bacterial behaviour. For this, the fellow used the bioinactivation software, developed within the host group. Through the work and results the fellow learned the principles of quantitative microbiological risk assessment (QMRA) and predictive microbiology, which was the aim for the EU-FORA programme.

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.

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 Potential of Essential Oils from Active Packaging to Reduce Ethylene Biosynthesis in Plant Products. Part 2: Fruits (Blueberries and Blackberries).

Plant essential oils (EOs) have an important ability to inhibit ethylene biosynthesis. Nevertheless, the effects of EOs on the key components of ethylene biosynthesis (l-aminocyclopropane-1-carboxylic (ACC) oxidase activity, ACC synthase activity, and ACC content) have not yet been thoroughly studied. Accordingly, this study focused on the effects of emitted EOs from active packaging (EO doses from 100 to 1000 mg m-2) on the key components of ethylene biosynthesis of blueberries and blackberries under several storage temperatures. Anise EO and lemon EO active packaging induced the greatest inhibitory effects (60-76%) on the ethylene production of blueberries and blackberries, respectively, even at high storage temperatures (22 °C). In terms of EO doses, active packaging with 1000 mg m-2 of anise EO or lemon EO led to the highest reduction of ethylene production, respectively. At 22 °C, the investigated EO active packing reduced the activities of ACC synthase and ACC oxidase up to 50%. In order to minimise ethylene biosynthesis in blueberries and blackberries when they are stored even under improper temperature scenarios at high temperatures, this EO active packaging is a natural and efficient technological solution.

Differences Due to Sex and Sweetener on the Bioavailability of (Poly)phenols in Urine Samples: A Machine Learning Approach.

Metabolic diseases have been related to the overdrinking of high-sugar content beverages. As a result, the demand for alternative formulations based on plant-based ingredients with health-promoting properties has increased during the last few years. Nonetheless, the design and production of effective formulations requires understanding the bioavailability of these compounds. For this purpose, a two-month longitudinal trial with 140 volunteers was conducted to measure the beneficial effects of a maqui-citrus beverage, rich in (poly)phenols. From data obtained by quantifying metabolites present in urine samples, biostatistical and machine learning (data imputation, feature selection, and clustering) methods were applied to assess whether a volunteer's sex and the sweetener added to the beverage (sucrose, sucralose, or stevia) affected the bioavailability of (poly)phenol metabolites. Several metabolites have been described as being differentially influenced: 3,4-dihydroxyphenylacetic acid and naringenin with its derivatives were positively influenced by stevia and men, while eriodictyol sulfate and homoeridictyol glucunoride concentrations were enhanced with stevia and women. By examining groups of volunteers created by clustering analysis, patterns in metabolites' bioavailability distribution as a function of sex and/or sweeteners (or even due to an uncontrolled factor) were also discovered. These results underline the potential of stevia as a (poly)phenol bioavailability enhancer. Furthermore, they also evidence sex affects the bioavailability of (poly)phenols, pointing at a sex-dependent metabolic pathway regulation.

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.

Application of High Hydrostatic Pressure in fresh purple smoothie: Microbial inactivation kinetic modelling and qualitative studies.

The inactivation kinetics of Listeria monocytogenes during High Hydrostatic Pressure (HHP) treatments was studied in a purple smoothie based of fresh fruit and vegetables. Pressure intensity studied was 300, 350, 400 and 450 MPa. Untreated samples were used as control. Furthermore, the effects on quality attributes (sensory, total soluble solids content, colour, titratable acidity, pH, vitamin C and total phenolics content) were also monitored. Microbial inactivation was modelled as a function of the HHP intensity using the Geeraerd model. Shoulder and tail effects were observed only for the 300 MPa pressure assayed, supporting a multiple hit kinetic inactivation of critical factors. Increasing the HHP intensity resulted in a faster inactivation with tailing. A strong positive correlation was observed between the pressure level and the inactivation rate (k). Hence, a linear model was used to describe the relationship between both variables. Nevertheless, further data are required to confirm this secondary model. Quality was mostly unaffected by the HHP treatments, except for the vitamin C content, which reported reductions of 26 and 21% after 300 and 350 MPa, respectively. In conclusion, HHP can be a viable technology for processing fruit and vegetable-based smoothies to preserve quality and safety. A pressure of 400 MPa is advisable to ensure an efficient microbial inactivation with the best sensory and nutritional quality retention.

The Potential of Essential Oils from Active Packaging to Reduce Ethylene Biosynthesis in Plant Products. Part 1: Vegetables (Broccoli and Tomato).

Essential oils (EOs) extracted from plants have a high potential to reduce ethylene biosynthesis, although their effects have not been deeply studied yet on the key components of the ethylene biosynthesis pathway: l-aminocyclopropane-1-carboxylic (ACC) oxidase activity, ACC synthase activity, and ACC content. Hence, the present study aimed to elucidate the effects of released EOs from active packaging (with different EO doses ranging from 100 to 1000 mg m-2) on the ethylene biosynthesis key components of broccoli and tomato under different storage temperature scenarios. The largest ethylene inhibitory effects on broccoli and tomatoes were demonstrated by grapefruit EO and thyme essential EO (up to 63%), respectively, which were more pronounced at higher temperatures. Regarding EO doses, active packaging with a thyme EO dose of 1000 mg m-2 resulted in the strongest reduction (33-38%) of ethylene production in tomatoes. For broccoli, identical results were shown with a lower grapefruit EO dose of 500 mg m-2. The studied EO-active packaging decreased ACC synthase and ACC oxidase activities by 40-50% at 22 °C. Therefore, this EO-active packaging is a natural and effective technology to reduce ethylene biosynthesis in broccoli and tomatoes when they are stored, even in unsuitable scenarios at high temperatures.

Shelf life estimation of refrigerated vacuum packed beef accounting for uncertainty.

This study estimates the shelf life of vacuum packed beef meat (three muscles: striploin (longissimus thoracis et lumborum, LTL), tenderloin (psoas major, PM) and outside chuck (trapezius thoracis, TT)) at refrigeration temperatures (0 °C-10 °C) based on modelling the growth of two relevant groups of spoilage microorganisms: lactic acid bacteria (LAB) and Enterobacteriaceae. The growth models were developed combining a two-step and a one-step approach. The primary modelling was used to identify the parameters affecting the growth kinetics, guiding the definition of secondary growth models. For LAB, the secondary model included the effect of temperature and initial pH on the specific growth rate. On the other hand, the model for Enterobacteriaceae incorporated the effect of temperature on the specific growth rate and the lag phase; as well as the effect of the initial pH on the specific growth rate, the lag phase and the initial microbial count. We did not observe any significant effect of the type of muscle on the growth kinetics. Once the equations were defined, the models were fitted to the complete dataset using a one-step approach. Model validation was carried out by cross-validation, mitigating the impact of an arbitrary division between training and validation sets. The models were used to estimate the shelf life of the product, based on the maximum admissible microbial concentration (7 log CFU/g for LAB, 5 log CFU/g for Enterobacteriaceae). Although LAB was the dominant microbiota, in several cases, both LAB and Enterobacteriaceae reached the critical concentration practically at the same time. Furthermore, in some scenarios, the end of shelf life would be determined by Enterobacteriaceae, pointing at the potential importance of non-dominant microorganisms for product spoilage. These results can aid in the implementation of effective control measures in the meat processing industry.

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.

Different model hypotheses are needed to account for qualitative variability in the response of two strains of Salmonella spp. under dynamic conditions.

In this article, the thermal inactivation of two Salmonella strains (Salmonella Enteritidis CECT4300 and Salmonella Senftenberg CECT4565) was studied under both isothermal and dynamic conditions. We observed large differences between these two strains, with S. Senftenberg being much more resistant than S. Enteritidis. Under isothermal conditions, S. Senftenberg had non-linear survivor curves, whereas the response of S. Enteritidis was log-linear. Therefore, weibullian inactivation models were used to describe the response of S. Senftenberg, with the Mafart model being the more suitable one. For S. Enteritidis, the Bigelow (log-linear) inactivation model was successful at describing the isothermal response. Under dynamic conditions, a combination of the Peleg and Mafart models (secondary model of Mafart; t* of Peleg) fitted to the isothermal data could predict the response of S. Senftenberg to the dynamic treatments tested (heating rates between 0.5 and 10 °C/min). This was not the case for S. Enteritidis, where the model predictions based on isothermal data underestimated the microbial concentrations. Therefore, a dynamic model that considers stress acclimation to one of the dynamic profiles was fitted, using the remaining profiles as validation. In light of this, besides its quantitative impact, variability between strains of bacterial species can also cause qualitative differences in microbial inactivation. This is demonstrated by S. Enteritidis being able to develop stress acclimation where S. Senftenbenberg could not. This has important implications for the development of microbial inactivation models to support process design, as every industrial treatment is dynamic. Consequently, it is crucial to consider different model hypotheses, and how they affect the model predictions both under isothermal and dynamic conditions.