Development and application of predictive models for fungal growth as tools to improve quality control in yogurt production

Advancements in Predictive Microbiology: Integrating New Technologies for Efficient Food Safety Models

Predictive microbiology is a rapidly evolving field that has gained significant interest over the years due to its diverse application in food safety. Predictive models are widely used in food microbiology to estimate the growth of microorganisms in food products. These models represent the dynamic interactions between intrinsic and extrinsic food factors as mathematical equations and then apply these data to predict shelf life, spoilage, and microbial risk assessment. Due to their ability to predict the microbial risk, these tools are also integrated into hazard analysis critical control point (HACCP) protocols. However, like most new technologies, several limitations have been linked to their use. Predictive models have been found incapable of modeling the intricate microbial interactions in food colonized by different bacteria populations under dynamic environmental conditions. To address this issue, researchers are integrating several new technologies into predictive models to improve efficiency and accuracy. Increasingly, newer technologies such as whole genome sequencing (WGS), metagenomics, artificial intelligence, and machine learning are being rapidly adopted into newer-generation models. This has facilitated the development of devices based on robotics, the Internet of Things, and time-temperature indicators that are being incorporated into food processing both domestically and industrially globally. This study reviewed current research on predictive models, limitations, challenges, and newer technologies being integrated into developing more efficient models. Machine learning algorithms commonly employed in predictive modeling are discussed with emphasis on their application in research and industry and their advantages over traditional models.

Characterisation of the surface growth of Mucor circinelloides in cheese agar media using predictive mathematical models

The main objective of this work was to characterise the mycelial growth of Mucor circinelloides, one of the fungal contaminants that appear frequently in the artisan cheese production environment. The study uses primary Baranyi and Huang models to compare their parameters and predict M. circinelloides on cheese-based medium (CBA) under diverse environmental conditions (temperature range from 6 to 37 °C and 0 and 1 % NaCl concentration). However, the Baranyi model consistently estimated longer lag phases and higher surface growth rates (sgr) than the Huang model; both models showed adequate best-fit performance (exactly with the mean coefficient of determination R2 = (0.993 ± 0.020 × 10-1). The groups of primary growth parameters were analysed against temperature using the cardinal model (CM) with the following main outputs. The optimal surface growth rates (sgropt) on CBA were 6.8 and 6.5 mm/d calculated with the Baranyi and Huang models, respectively. They were reduced by approximately 46 % on the surface of the agar medium when 1 % NaCl was added. Topt was estimated in a very narrow range of 32.1-32.5 °C from both primary sgr data sets (0 % and 1 % NaCl). Similarly, Tmax values of 37.2 °C and 37.3 °C were estimated for the Baranyi and Huang models, respectively; however, they decreased at 2 °C in CBA with 1 % NaCl (Tmax = 35.1 °C). The application of CM for sgr provided an estimation of the parameter Tmin with negative values that are considered only as a theoretical output. The results provide insight into the modelling and prediction of fungi growth as a function of time and salt concentration, including the times to detect visible mycelial growth of Mucor circinelloides. The mere quantification of this phenomenon can be useful for practice. Adjusting the frequency of the cheese surface washing step with a salt solution at the early stage of ripening properly can prevent the growth of not only fast fungal growers.

Intraspecific variability in cardinal growth temperatures and water activities within a large diversity of Penicillium roqueforti strains

Different strains of a given fungal species may display heterogeneous growth behavior in response to environmental factors. In predictive mycology, the consideration of such variability during data collection could improve the robustness of predictive models. Among food-borne fungi, Penicillium roqueforti is a major food spoiler species which is also used as a ripening culture for blue cheese manufacturing. In the present study, we investigated the intraspecific variability of cardinal temperatures and water activities (a_w), namely, minimal (T_min and a_wmin), optimal (T_opt and a_wopt) and maximal (T_max) temperatures and/or a_w estimated with the cardinal model for radial growth, of 29 Penicillium roqueforti strains belonging to 3 genetically distinct populations. The mean values of cardinal temperatures and a_w for radial growth varied significantly across the tested strains, except for T_max which was constant. In addition, the relationship between the intraspecific variability of the biological response to temperature and a_w and putative genetic populations (based on microsatellite markers) within the selected P. roqueforti strains was investigated. Even though no clear relationship was identified between growth parameters and ecological characteristics, PCA confirmed that certain strains had marginal growth response to temperature or a_w. Overall, the present data support the idea that a better knowledge of the response to abiotic factors such as temperature and a_w at an intraspecific level would be useful to model fungal growth in predictive mycology approaches.

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.

Modelling the Radial Growth of Geotrichum candidum: Effects of Temperature and Water Activity

Modelling the growth of microorganisms in relation to environmental factors provides quantitative knowledge that can be used to predict their behaviour in foods. For this reason, the effects of temperature and water activity (a_w) adjusted with NaCl on the surface growth of two isolates and one culture strain of Geotrichum candidum were studied. A dataset of growth parameters obtained from almost 600 growth curves was employed for secondary modelling with cardinal models (CMs). The theoretical minimal temperature resulting from the modelling of the mycelium proliferation rate ranged from −5.2 to −0.4 °C. Optimal and maximal temperatures were calculated and found to have narrow ranges of 25.4 to 28.0 °C and 34.2 to 37.6 °C, respectively. Cardinal a_w values associated with radial growth (a_wmin from 0.948–0.960 and a_wopt from 0.992–0.993) confirmed the salt sensitivity of the species. Model goodness-of-fit was evaluated by the coefficient of determination R², which ranged from 0.954 to 0.985, and RMSE, which ranged from 0.28 to 0.42. Substantially higher variability accompanied the lag time for growth modelling than the radial growth rate modelling despite the square root transformation of the reciprocal lag phase data (R² = 0.685 to 0.808). Nevertheless, the findings demonstrate that the outputs of growth modelling can be applied to the quantitative evaluation of the roles of G. candidum in fresh cheese spoilage as well as the ripening of Camembert-type cheeses or various artisanal cheeses. Along with validation, the interactions with lactic acid bacteria can be included to improve the predictions of G. candidum in the future.

Sensitivity of Molds From Spoiled Dairy Products Towards Bioprotective Lactic Acid Bacteria Cultures

Fungal spoilage of dairy products is a major concern due to food waste and economical losses, some fungal metabolites may furthermore have adverse effects on human health. The use of lactic acid bacteria (LAB) is emerging as a potential clean label alternative to chemical preservatives. Here, our aim was to characterize the growth potential at three storage temperatures (5, 16, and 25°C) of a panel of molds (four Mucor and nine Penicillium strains) isolated from dairy products, then investigate the susceptibility of the molds toward 12 LAB cultures. Fungal cell growth and morphology in malt extract broth was monitored using oCelloScope at 25°C for 24 h. Mucor plumbeus 01180036 was the fastest growing and Penicillium roqueforti ISI4 (P. roqueforti ISI4) the slowest of the tested molds. On yogurt-agar plates, all molds grew at 5, 16, and 25°C in a temperature-dependent manner with Mucor strains growing faster than Penicillium strains regardless of temperature. The sensitivity toward 12 LAB cultures was tested using high-throughput overlay method and here all the molds except P. roqueforti ISI4 were strongly inhibited. The antifungal action of these LAB was confirmed when spotting mold spores on agar plates containing live cells of the LAB strains. However, if cells were removed from the fermentates, the inhibitory effects decreased markedly. The antifungal effects of volatiles tested in a plate-on-plate system without direct contact between mold and LAB culture media were modest. Some LAB binary combinations improved the antifungal activity against the growth of several molds beyond that of single cultures in yogurt serum. The role of competitive exclusion due to manganese depletion was examined as a possible antifungal mechanism for six Penicillium and two Mucor strains. It was shown that this mechanism was a major inhibition factor for the molds tested apart from the non-inhibited P. roqueforti ISI4 since addition of manganese with increasing concentrations of up to 0.1 mM resulted in partly or fully restored mold growth in yogurt. These findings help to understand the parameters influencing the mold spoilage of dairy products and the interactions between the contaminating strains, substrate, and bioprotective LAB cultures.

[Atypical spoilage microorganisms in Argentinean yogurts: Gas-producing molds and bacteria of the genus Gluconobacter]

Microbial food alterations lead to unfit products for consumption, and their discarding, to significant economic losses for the food industry. During storage, fresh foods offer available niches for the survival and growth of undesirable microorganisms. In dairy products, data regarding spoilage and/or pathogenic bacteria is better documented than those for molds and yeasts. Dairy products are less susceptible to mold's contamination than products such as fruits and vegetables, due to their refrigerated storage; their elaboration from heat-treated milk and, for fermented ones, the dominant microbiota that acidifies the medium. However, even cheeses and yogurts may be susceptible to mold contamination. Atypical cases of yogurt samples containing spoilage microorganisms not previously reported (molds producing gas and bacteria of the genus Gluconobacter) in Argentinean fermented milks are presented here. For yogurt, in particular, the "classic" altering organisms were always being yeasts, and in other countries, molds belonging to the genus Aspergillus.

Staphylococcus aureus 2064 growth as affected by temperature and reduced water activity

Based on 247 growth data, the growth of S. aureus 2064 in dependence on temperatures (8-50°C) and a^w values (0.999-0.83) was described. Optimal values of a_wat all studied temperatures were determined by using Gibson model. Its compatibility was confirmed by several statistical indices, e.g. root mean square errors (RMSE 0.003-0.138), standard errors of prediction (%SEP 0.6-17.5). Cardinal values for S. aureus growth (T_min=7.7°C, T_opt=40.6°C, T_max=46.7°C, a_wmin=0.808, a_wopt=0.994, μ_opt=1.97 1/h) were determined by using CM model with indices RMSE=0.071, SEP=17.5%. Our findings can provide relevant growth information that can be used in S. aureus exposure assessment or in validation of other data regarding the growth of this opportunistic pathogen in foods.

Modelling the growth of pear postharvest fungal isolates at different temperatures

The effect of temperature on the mycelium growth kinetics of four postharvest fungal isolates (i.e., Penicillium expansum, Alternaria alternata, Botrytis cinerea and Rhizopus stolonifer) was assessed. A cardinal model with inflection (CMI) was used to describe the effect of the temperature on the growth rate (μ) and the lag time (λ) of each isolate. Cardinal temperature values such as T_min, T_max and T_opt were estimated and isolates were sorted according to their growth rate and lag time duration. Additionally, model validation was performed on a medium prepared from mashed pear pulp and on artificially wound-inoculated pear fruits. P. expansum was shown to be the most psychotrophic fungus with the lowest estimated T_min = -8.78. Model validation on pear pulp agar showed growth rate over-prediction in the case of R. stolonifer and B. cinerea but a good correlation in the case of P. expansum and A. alternata. In vivo experiments on pear fruits showed discrepancies from the synthetic and the simulated counterparts for all the fungi with the only exception of P. expansum.

Assessment of intraspecies variability in fungal growth initiation of Aspergillus flavus and aflatoxin B1 production under static and changing temperature levels using different initial conidial inoculum levels

Intraspecies variability in fungal growth and mycotoxin production has important implications for food safety. Using the Bioscreen C we have examined spectrophotometrically intraspecies variability of A. flavus using 10 isolates under different environments, including temperature shifts, in terms of growth and aflatoxin B₁ (AFB₁) production. Five high and five low AFB₁ producers were examined. The study was conducted at 5 isothermal conditions (from 15 to 37 °C) and 4 dynamic scenarios (between 15 and 30 °C). The experiments were carried out in a semisolid YES medium at 0.92 a_w and two inoculum levels, 10² and 10³ spores/mL. The Time to Detection (TTD) of growth initiation was determined and modelled as a function of temperature through a polynomial equation and the model was used to predict TTD under temperature upshifts conditions using a novel approach. The results obtained in this study have shown that a model can be developed to describe the effect of temperature upshifts on the TTD for all the studied isolates and inoculum levels. Isolate variability increased as the growth conditions became more stressful and with a lower inoculum level. Inoculum level affected the intraspecies variability but not the repeatability of the experiments. In dynamic conditions, isolate responses depended both on the temperature shift and, predominantly, the final temperature level. AFB₁ production was highly variable among the isolates and greatly depended on temperature (optimum temperature at 30-35 °C) and inoculum levels, with often higher production with lower inoculum. This suggests that, from an ecological point of view, the potential isolate variability and interaction with dynamic conditions should be taken into account in developing strategies to control growth and predicting mycotoxin risks by mycotoxigenic fungi.

Quantitative microbiological risk assessment in food industry: Theory and practical application

The objective of this article is to bring scientific background as well as practical hints and tips to guide risk assessors and modelers who want to develop a quantitative Microbiological Risk Assessment (MRA) in an industrial context. MRA aims at determining the public health risk associated with biological hazards in a food. Its implementation in industry enables to compare the efficiency of different risk reduction measures, and more precisely different operational settings, by predicting their effect on the final model output. The first stage in MRA is to clearly define the purpose and scope with stakeholders, risk assessors and modelers. Then, a probabilistic model is developed; this includes schematically three important phases. Firstly, the model structure has to be defined, i.e. the connections between different operational processing steps. An important step in food industry is the thermal processing leading to microbial inactivation. Growth of heat-treated surviving microorganisms and/or post-process contamination during storage phase is also important to take into account. Secondly, mathematical equations are determined to estimate the change of microbial load after each processing step. This phase includes the construction of model inputs by collecting data or eliciting experts. Finally, the model outputs are obtained by simulation procedures, they have to be interpreted and communicated to targeted stakeholders. In this latter phase, tools such as what-if scenarios provide an essential added value. These different MRA phases are illustrated through two examples covering important issues in industry. The first one covers process optimization in a food safety context, the second one covers shelf-life determination in a food quality context. Although both contexts required the same methodology, they do not have the same endpoint: up to the human health in the foie gras case-study illustrating here a safety application, up to the food portion in the brioche case-study illustrating here a quality application.

Diversity and Control of Spoilage Fungi in Dairy Products: An Update

Fungi are common contaminants of dairy products, which provide a favorable niche for their growth. They are responsible for visible or non-visible defects, such as off-odor and -flavor, and lead to significant food waste and losses as well as important economic losses. Control of fungal spoilage is a major concern for industrials and scientists that are looking for efficient solutions to prevent and/or limit fungal spoilage in dairy products. Several traditional methods also called traditional hurdle technologies are implemented and combined to prevent and control such contaminations. Prevention methods include good manufacturing and hygiene practices, air filtration, and decontamination systems, while control methods include inactivation treatments, temperature control, and modified atmosphere packaging. However, despite technology advances in existing preservation methods, fungal spoilage is still an issue for dairy manufacturers and in recent years, new (bio) preservation technologies are being developed such as the use of bioprotective cultures. This review summarizes our current knowledge on the diversity of spoilage fungi in dairy products and the traditional and (potentially) new hurdle technologies to control their occurrence in dairy foods.

Growth Modeling of Aspergillus niger Strains Isolated from Citrus Fruit as a Function of Temperature on a Synthetic Medium from Lime (Citrus latifolia T.) Pericarp

Molds are responsible for postharvest spoilage of citrus fruits. The objective of this study was to evaluate the effect of temperature on growth rate and the time to visible growth of Aspergillus niger strains isolated from citrus fruits. The growth of these strains was studied on agar lime medium (AL) at different temperatures, and growth rate was estimated using the Baranyi and Roberts model (Int. J. Food Microbiol. 23:277-294, 1994). The Rosso et al. cardinal model with inflexion (L. Rosso, J. R. Lobry, S. Bajard, and J. P. Flandrois, J. Theor. Biol. 162:447-463, 1993) was used as a secondary model to describe the effect of temperature on growth rate and the lag phase. We hypothesized that the same model could be used to calculate the time for the mycelium to become visible (t_v) by substituting the lag phase (1/λ and 1/λ_opt) with the time to visible colony (1/t_v-opt and 1/t_v), respectively, in the Rosso et al.

MODEL

High variability was observed at suboptimal conditions. Extremes of temperature of growth for A. niger seem to have a normal variability. For the growth rate and time t_v, the model was satisfactorily compared with results of previous studies. An external validation was performed in lime fruits; the bias and accuracy factors were 1.3 and 1.5, respectively, for growth rate and 0.24 and 3.72, respectively, for the appearance time. The discrepancy may be due to the influence of external factors. A. niger grows significantly more slowly on lime fruit than in culture medium, probably because the nutrients are more easily available in medium than in fruits, where the peel consistency may be a physical barrier. These findings will help researchers understand the postharvest behavior of mold on lime fruits, host-pathogen interactions, and environmental conditions infecting fruit and also help them develop guidelines for future work in the field of predictive mycology to improve models for control of postharvest fungi.

Single vs multiple-spore inoculum effect on growth kinetic parameters and modeled probabilities of growth and aflatoxin B1 production of Aspergillus flavus on pistachio extract agar

The objective of the present study was to assess the differences in modeled growth/AFB1 production probability and kinetic growth parameters for Aspergillus flavus inoculated as single spores or in a concentrated inoculation point (~500 spores). The experiment was carried out at 25°C and at two water activities (0.85 and 0.87) on pistachio extract agar (3%). Binary data obtained from growth and AFB1 studies were modeled using linear logistic regression analysis. The radial growth curve for each colony was fitted to a linear model for the estimation of the lag phase for growth and the mycelial growth rate. In general, radial growth rate and lag phase for growth were not normally distributed and both of them were affected by the inoculation type, with the lag phase for growth being more affected. Changing from the multiple spore to the single spore inoculation led to a delay of approximately 3-5days on the lag phase and higher growth rates for the multiple spore experiment were found. The same trend was observed on the probability models, with lower predicted probabilities when colonies came up from single spores, for both growth and AFB1 production probabilities. Comparing both types of models, it was concluded that a clear overestimation of the lag phase for growth occurred using the linear model, but only in the multiple spore experiment. Multiple spore inoculum gave very similar estimated time to reach some set probabilities (t10, t50 and t100) for growth or AFB1 production due to the abruptness of the logistic curve developed. The observed differences suggest that inoculum concentration greatly affects the outcome of the predictive models, the estimated times to growth/AFB1 production being much earlier for the concentrated inoculum than for a single spore colony (up to 9days). Thus the number of spores used to generate data in predictive mycology experiments should be carefully controlled in order to predict as accurately as possible the fungal behavior in a foodstuff.

Modelling the effect of temperature, water activity and carbon dioxide on the growth of Aspergillus niger and Alternaria alternata isolated from fresh date fruit

AIMS

To quantify and model the combined effects of temperature (T) (10-40°C), water activity (a_w ) (0·993-0·818) and CO₂ concentration (9·4-55·1%, v/v) on the growth rate of Aspergillus niger and Alternaria alternata that cause spoilage during the storage and packaging of dates.

METHODS AND RESULTS

The effects of environmental factors were studied using the γ-concept. Cardinal models were used to quantify the effect of studied environmental factors on the growth rates. Firstly, the cardinal parameters were estimated independently from experiments carried out on potato dextrose agar using a monofactorial design. Secondly, model performance evaluation was conducted on pasteurized date paste. The boundary between growth and no-growth was predicted using a deterministic approach. Aspergillus niger displayed a faster growth rate and higher tolerance to low a_w than Al. alternata, which in turn proved more resistant to CO₂ concentration. Minimal cardinal parameters of T and a_w were lower than those reported in the literature.

CONCLUSIONS

The combination of the a_w and CO₂ effects significantly affected As. niger and Al. alternata growth. The γ-concept model overestimated growth rates, however, it is optimistic and provides somewhat conservative predictions.

SIGNIFICANCE AND IMPACT OF THE STUDY

The developed model provides a decision support tool for the choice of the date fruit conservation mode (refrigeration, drying, modified atmospheric packaging or their combination) using T, a_w and CO₂ as environmental factors.

Quantifying the effect of water activity and storage temperature on single spore lag times of three moulds isolated from spoiled bakery products

The inhibitory effect of water activity (a_w) and storage temperature on single spore lag times of Aspergillus niger, Eurotium repens (Aspergillus pseudoglaucus) and Penicillium corylophilum strains isolated from spoiled bakery products, was quantified. A full factorial design was set up for each strain. Data were collected at levels of a_w varying from 0.80 to 0.98 and temperature from 15 to 35°C. Experiments were performed on malt agar, at pH5.5. When growth was observed, ca 20 individual growth kinetics per condition were recorded up to 35days. Radius of the colony vs time was then fitted with the Buchanan primary model. For each experimental condition, a lag time variability was observed, it was characterized by its mean, standard deviation (sd) and 5^th percentile, after a Normal distribution fit. As the environmental conditions became stressful (e.g. storage temperature and a_w lower), mean and sd of single spore lag time distribution increased, indicating longer lag times and higher variability. The relationship between mean and sd followed a monotonous but not linear pattern, identical whatever the species. Next, secondary models were deployed to estimate the cardinal values (minimal, optimal and maximal temperatures, minimal water activity where no growth is observed anymore) for the three species. That enabled to confirm the observation made based on raw data analysis: concerning the temperature effect, A. niger behaviour was significantly different from E. repens and P. corylophilum: T_opt of 37.4°C (standard deviation 1.4°C) instead of 27.1°C (1.4°C) and 25.2°C (1.2°C), respectively. Concerning the a_w effect, from the three mould species, E. repens was the species able to grow at the lowest a_w (aw_min estimated to 0.74 (0.02)). Finally, results obtained with single spores were compared to findings from a previous study carried out at the population level (Dagnas et al., 2014). For short lag times (≤5days), there was no difference between lag time of the population (ca 2000 spores inoculated in one spot) and mean (nor 5^th percentile) of single spore lag time distribution. In contrast, when lag time was longer, i.e. under more stressful conditions, there was a discrepancy between individual and population lag times (population lag times shorter than 5^th percentiles of single spore lag time distribution), confirming a stochastic process. Finally, the temperature cardinal values estimated with single spores were found to be similar to those obtained at the population level, whatever the species. All these findings will be used to describe better mould spore lag time variability and then to predict more accurately bakery product shelf-life.

Description of Aspergillus flavus growth under the influence of different factors (water activity, incubation temperature, protein and fat concentration, pH, and cinnamon essential oil concentration) by kinetic, probability of growth, and time-to-detection models

A Box-Behnken design was used to determine the effect of protein concentration (0, 5, or 10g of casein/100g), fat (0, 3, or 6g of corn oil/100g), a_w (0.900, 0.945, or 0.990), pH (3.5, 5.0, or 6.5), concentration of cinnamon essential oil (CEO, 0, 200, or 400μL/kg) and incubation temperature (15, 25, or 35°C) on the growth of Aspergillus flavus during 50days of incubation. Mold response under the evaluated conditions was modeled by the modified Gompertz equation, logistic regression, and time-to-detection model. The obtained polynomial regression models allow the significant coefficients (p<0.05) for linear, quadratic and interaction effects for the Gompertz equation's parameters to be identified, which adequately described (R²>0.967) the studied mold responses. After 50days of incubation, every tested model system was classified according to the observed response as 1 (growth) or 0 (no growth), then a binary logistic regression was utilized to model A. flavus growth interface, allowing to predict the probability of mold growth under selected combinations of tested factors. The time-to-detection model was utilized to estimate the time at which A. flavus visible growth begins. Water activity, temperature, and CEO concentration were the most important factors affecting fungal growth. It was observed that there is a range of possible combinations that may induce growth, such that incubation conditions and the amount of essential oil necessary for fungal growth inhibition strongly depend on protein and fat concentrations as well as on the pH of studied model systems. The probabilistic model and the time-to-detection models constitute another option to determine appropriate storage/processing conditions and accurately predict the probability and/or the time at which A. flavus growth occurs.

Modeling red cabbage seed extract effect on Penicillium corylophilum: Relationship between germination time, individual and population lag time

The inhibitory effect of a red cabbage seed extract on germination time, individual (single spore) and population lag time of Penicillium corylophilum was studied. First, to compare the biological variability of single spore germination and lag times under stressful conditions, data were collected at levels of red cabbage seed extract varying from 0 to 10 mg/g (150 spores observed in each trial of germination, ca 50 spores in each individual lag experiment). Experiments were performed on malt agar at 25 °C, pH 5.2, aw 0.99. The data, without any transformation, were statistically analyzed; several probability distribution functions were used to fit the cumulated germination times and the individual lag times of spores. In both cases, the best fit was obtained with the Normal distribution. In parallel, lag times at the population level (ca 2000 spores per trial) were collected for the same range of plant extract. Not surprisingly, the difference between individual and population lag times could be explained by a stochastic process. More interestingly, it was shown that under stressful conditions, the population lag time did not correspond to the time required for germination of 95% of spores, but to a much longer time. Finally, it was deduced from the statistical analysis, completed by microscopic observations, that the plant extract affected mainly the hyphal elongation (and then the lag time) and not the germination. Next, secondary models were developed to quantify the effect of red cabbage seed extract on the median of germination times, individual and population lag times. The Minimum Inhibitory Concentrations (MICs) were estimated. It was shown that the red cabbage seed extract MIC for P. corylophilum lag time did not depend on the inoculum load. Application of the secondary models allowed us to conclude that under the conditions of our experiment, the addition of 10 mg/g of red cabbage seed extract enabled extension of lag time to two weeks.

Quantifying Effect of Lactic, Acetic, and Propionic Acids on Growth of Molds Isolated from Spoiled Bakery Products

The combined effect of undissociated lactic acid (0 to 180 mmol/liter), acetic acid (0 to 60 mmol/liter), and propionic acid (0 to 12 mmol/liter) on growth of the molds Aspergillus niger, Penicillium corylophilum, and Eurotium repens was quantified at pH 3.8 and 25°C on malt extract agar acid medium. The impact of these acids on lag time for growth (λ) was quantified through a gamma model based on the MIC. The impact of these acids on radial growth rate (μ) was analyzed statistically through polynomial regression. Concerning λ, propionic acid exhibited a stronger inhibitory effect (MIC of 8 to 20 mmol/liter depending on the mold species) than did acetic acid (MIC of 23 to 72 mmol/liter). The lactic acid effect was null on E. repens and inhibitory on A. niger and P. corylophilum. These results were validated using independent sets of data for the three acids at pH 3.8 but for only acetic and propionic acids at pH 4.5. Concerning μ, the effect of acetic and propionic acids was slightly inhibitory for A. niger and P. corylophilum but was not significant for E. repens. In contrast, lactic acid promoted radial growth of all three molds. The gamma terms developed here for these acids will be incorporated in a predictive model for temperature, water activity, and acid. More generally, results for μ and λ will be used to identify and evaluate solutions for controlling bakery product spoilage.

Effect of inoculum size and water activity on the time to visible growth of Penicillium chrysogenum colony

In order to assess the effect of the inoculum size on the time to visible growth for Penicillium chrysogenum, the correlation described by González et al. (González, H.H.L., Resnik, S.L., Vaamonde, G., 1987. Influence of inoculum size on growth rate and lag phase of fungi isolate from Argentine corn. International Journal of Food Microbiology 4, 111-117) was compared to the model introduced by Gougouli et al. (Gougouli, M., Kalantzi, K., Beletsiotis, E., Koutsoumanis, K.P., 2011. Development and application of predictive models for fungal growth as tools to improve quality control in yogurt production. Food Microbiology 28, 1453-1462). Based on the regression coefficient, the latter model performed better than the former one to fit the data obtained for P. chrysogenum grown on Potato Dextrose Agar at 25 °C. Inoculum sizes in the range 10(1)-10(5) spores were tested at 0.930, 0.950, 0.970, and 0.995 aw. By extrapolation of the straight line, the model of Gougouli et al. (2011) provided accurate estimations of the time to visible growth for a single spore inoculum, tvg (N=1). In order to avoid experiments at reduced water activities, the influence of water activity on the model parameters, and on the ratio tvg (N=1) over the germination time was assessed.

Predicting and preventing mold spoilage of food products

This article is a review of how to quantify mold spoilage and consequently shelf life of a food product. Mold spoilage results from having a product contaminated with fungal spores that germinate and form a visible mycelium before the end of the shelf life. The spoilage can be then expressed as the combination of the probability of having a product contaminated and the probability of mold growth (germination and proliferation) up to a visible mycelium before the end of the shelf life. For products packed before being distributed to the retailers, the probability of having a product contaminated is a function of factors strictly linked to the factory design, process, and environment. The in-factory fungal contamination of a product might be controlled by good manufacturing hygiene practices and reduced by particular processing practices such as an adequate air-renewal system. To determine the probability of mold growth, both germination and mycelium proliferation can be mathematically described by primary models. When mold contamination on the product is scarce, the spores are spread on the product and more than a few spores are unlikely to be found at the same spot. In such a case, models applicable for a single spore should be used. Secondary models can be used to describe the effect of intrinsic and extrinsic factors on either the germination or proliferation of molds. Several polynomial models and gamma-type models quantifying the effect of water activity and temperature on mold growth are available. To a lesser extent, the effect of pH, ethanol, heat treatment, addition of preservatives, and modified atmospheres on mold growth also have been quantified. However, mold species variability has not yet been properly addressed, and only a few secondary models have been validated for food products. Once the probability of having mold spoilage is calculated for various shelf lives and product formulations, the model can be implemented as part of a risk management decision tool.

Relation between germination and mycelium growth of individual fungal spores

The relation between germination time and lag time of mycelium growth of individual spores was studied by combining microscopic and macroscopic techniques. The radial growth of a large number (100-200) of Penicillium expansum and Aspergillus niger mycelia originating from single spores was monitored macroscopically at isothermal conditions ranging from 0 to 30°C and 10 to 41.5°C, respectively. The radial growth curve for each mycelium was fitted to a linear model for the estimation of mycelium lag time. The results showed that the lag time varied significantly among single spores. The cumulative frequency distributions of the lag times were fitted to the modified Gompertz model and compared with the respective distributions for the germination time, which were obtained microscopically. The distributions of the measured mycelium lag time were found to be similar to the germination time distributions under the same conditions but shifted in time with the lag times showing a significant delay compared to germination times. A numerical comparison was also performed based on the distribution parameters λ(m) and λ(g), which indicate the time required from the spores to start the germination process and the completion of the lag phase, respectively. The relative differences %(λ(m)-λ(g))/λ(m) were not found to be significantly affected by temperatures tested with mean values of 72.5±5.1 and 60.7±2.1 for P. expansum for A. niger, respectively. In order to investigate the source of the above difference, a time-lapse microscopy method was developed providing videos with the behavior of single fungal spore from germination until mycelium formation. The distances of the apexes of the first germ tubes that emerged from the swollen spore were measured in each frame of the videos and these data were expressed as a function of time. The results showed that in the early hyphal development, the measured radii appear to increase exponentially, until a certain time, where growth becomes linear. The two phases of hyphal development can explain the difference between germination and lag time. Since the lag time is estimated from the extrapolation of the regression line of the linear part of the graph only, its value is significantly higher than the germination time, t(G). The relation of germination and lag time was further investigated by comparing their temperature dependence using the Cardinal Model with Inflection. The estimated values of the cardinal parameters (T(min), T(opt), and T(max)) for 1/λ(g) were found to be very close to the respective values for 1/λ(m), indicating similar temperature dependence between them.