Staphylococcus aureus is one of the pathogens most commonly involved in foodborne outbreaks, being characterised as a high-level priority II pathogen (WHO, 2017). From 2009 to 2021, staphylococcal toxins were responsible for 2.1% of foodborne outbreaks in the United States, affecting 4,412 individuals, resulting in 199 hospitalisations and two deaths (CDC, 2021). In Brazil, Staphylococcus aureus was the second most frequent pathogen in food between 2013 and 2022, accounting for 9.7% of waterborne and foodborne disease outbreaks (Brasil, 2023). Milk and dairy products are often associated with foodborne infections and intoxications (De Buyser et al., Reference De Buyser, Dufour, Maire and Lafarge2001; Johler et al., Reference Johler, Weder, Bridy, Huguenin, Robert, Hummerjohann and Stephan2015; Keba et al., Reference Keba, Rolon, Tamene, Dessie, Vipham, Kovac and Zewdu2020), representing 6.7% of foods incriminated in outbreaks in Brazil (Brasil, 2023).
The prevalence of S. aureus in milk and dairy products is a public health concern. A study conducted between 1992 and 2021 investigated the presence of S. aureus in these products. The prevalence in raw milk, dairy products and pasteurized milk was 33.4%, 16.8% and 11.1%, respectively (Zhang et al., Reference Zhang, Wang, Jin, Li, Zhang, Shi and Zhao2022). Staphylococcus aureus can multiply and produce enterotoxins (SE) in these foods. The main staphylococcal enterotoxins involved in foodborne outbreaks are Staphylococcal enterotoxin A (SEA), SED, SEC, SEB and SEE, in descending order of occurrence. They are heat resistant, maintaining their stability at 121°C for 28 minutes (Anderson et al., Reference Anderson, Beelman and Doores1996). This is a concern for products such as Minas Frescal cheese, as SEs remain stable even after heat treatments, like pasteurization and ultra-high temperature.
Furthermore, Minas Frescal cheese is a fresh food, high-moisture and its production involves extensive handling, which facilitates the prevalence, growth and production of enterotoxins by S. aureus (da S Cândido et al., Reference da S Cândido, Silva, Matos, Do N Silva, Camargo, Cobo Zanella, Mores Rall and Cirone Silva2020). The detection of enterotoxigenic S. aureus in Minas Frescal cheese has been frequently reported (Arcuri et al., Reference Arcuri, Ângelo, Martins Guimarã Es, Talon, De Fatima Borges, Leroy, Loiseau, Lange, De Andrade and Montet2010; Martin et al., Reference Martin, de O Silva, Fonseca, Morales, Silva, Miquelluti and Porto2016; Silva et al., Reference Silva, Carvalho, Andretta and Nero2021). Therefore, it is essential to control the growth of S. aureus in cheeses to prevent the production of enterotoxins that cause outbreaks.
The incidence of S. aureus and consequent enterotoxin production can be reduced through effective food safety control measures. To achieve this, it is essential to know the dynamics of enterotoxin production of this microorganism under the conditions to which the food may be exposed during its production and storage. The mathematical model is a promising approach to understanding and controlling microbial growth and allows for a detailed analysis of the underlying mechanisms. Several predictive models that can predict S. aureus growth and SEA production have been previously proposed (Fujikawa and Morozumi, Reference Fujikawa and Morozumi2006; Tango et al., Reference Tango, Akkermans, Hussain, Khan, Van Impe, Jin and Oh2018; Valík et al., Reference Valík, Ačai and Medveďová2018; Yu et al., Reference Yu, Song, Kim, Lee, Choi, Lee and Paik2020). However, these models can predict where there is microbial growth or toxin production, without predictions about the conditions under which they inhibit or reduce this behaviour. The secondary logistic regression model is an advanced method that predicts the probability of microbial growth or metabolite production in response to combinations of factors such as temperature, pH and preservatives (Morassi et al., Reference Morassi, Silva, Furtado, Freire, Santos, Chaves, Granato, Silva, Peña and Sant'Ana2022; da Silva et al., Reference da Silva, Fernandes, de Jesus Pimentel-filho, de Andrade, Alves, Eller and Peña2022; Oladeinde et al., Reference Oladeinde, Awosile, Woyda, Abdo, Endale, Strickland, Lawrence, Cudnik, House and Cook2023). This approach may be interesting given that there are no reports in the literature of the implementation of probabilistic models for SEA production under the influence of Minas Frescal cheese production and storage conditions.
This study aimed to develop a probabilistic logistic regression model of SEA production by S. aureus with different combinations of temperature, pH, sodium chloride (NaCl) concentrations, initial S. aureus concentration and time.
Material and methods
Strain and inoculum preparation
For the experiment, a strain of S. aureus ATCC 13,565, producer of SEA, was used. The strain was activated in 10 mL of brain heart infusion (BHI) broth (Oxoid Ltd., Basingstoke, UK) and incubated at 35°C for 24 h. Inoculum standardization was performed by reading the optical density (OD) in a spectrophotometer (Kazuaki IL-227) at 600 nm, where the absorbance was adjusted to 0.100, equivalent to approximately 8 log CFU/mL as previously determined by calibration curves. After adjustment, serial decimal dilutions were prepared in 0.85% saline solution (w/v) to obtain an inoculum with approximately 0 log CFU/mL, 3 log CFU/mL or 5 log CFU/mL, which were used in the growth and enterotoxin detection assays. To confirm the concentrations, S. aureus was diluted in a 0.85% (w/v) saline solution, plated on BHI agar in triplicate using the microdroplet technique and incubated at 35°C for 18 h. Colonies were counted and the results were expressed in log CFU/mL.
Experimental design
The culture medium used was BHI broth prepared according to the manufacturer's instructions. The growth and enterotoxin production of S. aureus were tested with different combinations of five factors, namely temperature (10°C, 15°C and 25°C), pH (5.3, 5.5, 6.0, 6.5 and 6.7), NaCl (0.8%, 1.0%, 1.5%, 2.0% and 2.2%), S. aureus concentration (0 log, 3 log and 5 log CFU/mL) and time (0, 24, 48, 72, 96, 120, 144 and 240 h), with three replications for each combination. For pH adjustments, solutions of hydrochloric acid (HCl) and sodium hydroxide (NaOH) at a concentration of 1 mol/L were used. Saline concentrations were obtained by adding appropriate amounts of NaCl to the medium. After adjusting the pH and NaCl with the solutions mentioned above, the culture media were sterilised at 121°C for 15 minutes. To assess the S. aureus count and enterotoxin production capacity, tubes containing BHI medium adjusted to the specified pH and NaCl concentrations, with the three S. aureus concentrations, representing different contamination levels, were incubated at different temperatures (10°C, 15°C and 25°C) for up to 144 h for 15°C and 25°C and up to 240 h for 10°C. The tested values are within the range of conditions to which S. aureus may be exposed during the processing and storage of Minas Frescal cheese. The selection of temperature, pH and sodium chloride concentration was based on a previous study conducted by our research group (Silva et al., Reference Silva, Carvalho, Andretta and Nero2021), which evaluated commercial samples of this product, as well as data reported by Nunes and Caldas (Reference Nunes and Caldas2017). The temperature of 25°C was included as “inadequate storage temperature”, considering that clandestine production and sale of cheeses are common in some Brazilian states. The time intervals were selected based on the maximum refrigerated shelf life of the product after opening, as commonly used in other studies (Silva et al., Reference Silva, Dos Santos, Silva, Silva, Machado and Garcia2019; De Oliveira Souza et al., Reference De Oliveira Souza, Brasileiro, De Carvalho, Da Silva, Nero and De Aguiar Ferreira2012). Every 24 h, aliquots were collected from each experiment for toxin detection and simultaneous microbial concentration evaluation. The growth of S. aureus was monitored to determine the concentration of the microorganism at the time of SEA production in each situation studied. For S. aureus enumeration, each sample was diluted in a 0.85% (w/v) saline solution, plated on BHI agar in triplicate using the microdroplet technique and incubated at 35°C for 18 h. Colonies were counted and the results were expressed in log CFU/mL. The experiment was done in three repeats in triplicate.
Enterotoxin detection
Samples were subjected to an enzyme-linked fluorescent assay (ELFA) for the detection of SEA from S. aureus ATCC 13,565. Samples in culture medium were centrifuged at 5000 × g for 15 minutes and 500 µL aliquots of the resulting supernatant were placed in a well of the VIDAS® Staphylococcal Enterotoxins (SET2) Kit and examined using the ELFA reader at 450 nm, MiniVIDAS (MiniVIDAS bioMérieux, Inc., France). As for the milk and cheese samples that were used in the validation tests described below, they were extracted according to the Biomérieux® extraction protocol for dairy products. Samples with TV (Test Value) titres <0.13 were considered negative for the presence of enterotoxin, while those with VT titres >0.13 were considered positive. VT is the ratio between the relative fluorescence of the standard and the relative fluorescence of the sample.
Mathematical model of SEA production
The results were monitored by collecting samples every 24 h for up to 240 h to determine the presence or absence of SEA production. The matrices generated by combinations of the studied factors (temperature, pH, NaCl concentration, initial S. aureus concentration and time) and the enterotoxin production responses obtained by the ELFA method in MiniVidas (coded as 0 [no-enterotoxin production] and 1 [enterotoxin production]) were fitted to the probabilistic logistic regression model below, using SPSS Statistics 25.0 software.
\begin{equation}P\left( x \right) = {\text{ }}\frac{{{e^{\left| {\beta 0 + {{\sum}}\beta ixi} \right|}}}}{{1 + {\text{ }}{e^{\left| {\beta 0 + {{\sum}}\beta ixi} \right|}}}}\end{equation}P(x) is the dependent variable and represents the probability (0–1) of enterotoxin production/no production by S. aureus 13565; β0 is the intercept (baseline log-odds of enterotoxin production), and βi represents the coefficient of each independent variable xi (temperature, pH, NaCl concentration, initial contamination level, and time). Samples with VT equal to or greater than 0.13 were classified as enterotoxin producers (1) and those below 0.13 as no-enterotoxin producers (0). The model was fitted using the stepwise selection procedure, in which predictors were added based on statistical significance (P < 0.05) assessed by the Wald test. This procedure allowed for the identification of the most relevant variables and interaction terms influencing SEA production. Regression coefficients were estimated using the maximum likelihood estimation (MLE) method. The final model included linear, quadratic and interaction terms that significantly contributed to the prediction. The general logit model necessary for the linearization of the model used is represented by Eq. 2.
\begin{align}
Logit\left( P \right) &= Ln\left( {\frac{P}{{1 - P}}} \right) = {\beta _0} + \beta_1time + \beta_2T + \beta_3pH + NaCl\nonumber\\
& \quad + \beta_5inculum + \beta_6time^2 + \beta_7T^2 + \beta_8pH^2 + \beta_9NaC{l_2} \nonumber\\
& \quad+ \beta_10inculum^2 + \beta_{11}time * T + \beta_8time * pH \nonumber\\
& \quad+ \beta_9time * NaCl + \beta_{10}time * inculum + \beta_{10}T * pH \nonumber\\
& \quad+ \beta_{11}T * NaCl + \beta_{12}T * inculum + \beta_{13}pH * NaCl \nonumber\\
& \quad+ \beta_{14}pH * inculum \nonumber\\
\end{align}where: P = probability (0 – 1) of enterotoxin production/no-production by S. aureus 13,565; β0–β14 are adjustable coefficients; T, temperature; pH, pH value; NaCl, the concentration of sodium chloride; inoculum, the initial concentration of S. aureus.
The performance of the model was evaluated using the Nagerlkerke R2 test, Hosmer–Lemeshow test and agreement percentage. The probabilities of SEA production by S. aureus under the studied conditions were also calculated using Eq. 2. Furthermore, critical time predictions in the enterotoxin production were performed at probability levels of 0.1, 0.5 and 0.9 by substituting the logit probability value (P) into the model described in Eq. 2 and calculating the time, maintaining all other independent variables constant. All figures and probability curves were generated using SigmaPlot version 13.0 (Systat Software Inc., San Jose, CA, USA).
Experimental validation of the model
The model was validated for its predictive performance against different combinations not tested during model construction, in a culture medium and in a food matrix. For food matrix validation, milk and cheese were used, with pH, temperature and NaCl values within the studied range.
For culture medium validation, eight untested combinations were employed, which were not used during the data collection for model development (pH = 5.7 and 6.3; T = 12°C and 20°C; NaCl = 1.2% and 1.8%) S. aureus at concentrations of 0, 3 and 5 log CFU/mL for each combination and incubation for 144 h (Table 3).
For food validation, ultrapasteurised (UHT) milk and Minas Frescal cheese were used in different combinations (Table 3). Volumes of 500 mL UHT milk were placed in sterile 1000-mL bottles, inoculated with S. aureus at concentrations of 0, 3 and 5 log CFU/mL, pH fixed at 6.6 and incubated at temperatures of 12°C and 20°C for 144 h. The cheeses were manufactured at a laboratory scale according to the methodology described by Van Tassell et al. (Reference Van Tassell, Ibarra-Sánchez, Takhar, Amaya-Llano and Miller2015) with adaptations (Supplementary File). Every 24 h, aliquots of the milk and cheeses incubated were collected for toxin detection and simultaneous evaluation of microbial concentration.
The probability values obtained in the generated model were compared with those obtained in validation. In the data analysis, predicted probability values above 0.5 were classified as enterotoxin production (1), while those below 0.5 were classified as no-enterotoxin production (0). Based on these results, the percentages of agreement were determined to evaluate the difference in the probability of SEA production between predicted and observed data.
Results and discussion
Staphylococcus aureus growth and SEA production under simulated cheese conditions
The conditions found in Minas Frescal cheese were replicated to assess the influence of factors on the growth of S. aureus ATCC 13,565 and its ability to produce SEA (Supplementary Fig. S1). The growth of S. aureus was monitored for 144 h for samples at 15°C and 25°C and for 240 h for samples at 10°C, as at this temperature, they had not yet reached the logarithmic (log) growth phase, during which the production of enterotoxin A occurs. This delayed growth at 10°C can be attributed to reduced membrane fluidity, which affects ATP synthesis, DNA replication, nutrient transport and protein biosynthesis, prolonging the lag phase and delaying exponential growth (Phadtare, Reference Phadtare2004; Shivaji and Prakash, Reference Shivaji and Prakash2010; Yang et al., Reference Yang, Xie, Cheng, Zhang, Zhao and Qian2020). Additionally, the combined effect of low temperature, acidic pH and salt concentrations can produce a synergistic stress effect, further limiting microbial kinetics, as previously reported for S. aureus under similar conditions (Rosengren et al., Reference Rosengren, Lindblad and Lindqvist2013).
Among the evaluated conditions, the population density found varied from 8.27 to 9.36 log CFU/mL at 25°C and from 3.90 to 8.27 log CFU/mL at 15°C. At 10°C, with an inoculum concentration of 0 log CFU/mL remained below the detection limit (<1.0 log CFU/mL) throughout the incubation period, while for the other studied inoculum concentrations, a maximum population of 7.79 log CFU/mL was observed.
When starting with the initial concentration of 5 and 3 log CFU/mL, the S. aureus strain studied reached the logarithmic growth phase in all evaluated conditions at 15°C and 25°C. However, at 10°C and an initial concentration of 3 log CFU/mL, the bacteria only reached the logarithmic phase under optimal pH conditions (6.0–6.7), regardless of the NaCl concentration and remained in the lag phase at an initial concentration of 0 log CFU/mL. This indicates the influence of the initial concentration, temperature and pH on the growth of S. aureus. Similar behaviour was observed by other authors (Alomar et al., Reference Alomar, Lebert and Montel2008; Valero et al., Reference Valero, Pérez-Rodríguez, Carrasco, Fuentes-Alventosa, García-Gimeno and Zurera2009). The lower the temperature and the initial contamination level, the longer the lag phase and the longer it takes to reach the logarithmic phase, where the production of SEA occurs (Chen et al., Reference Chen, Song, Xu and Zhang2018; Daughtry et al., Reference Daughtry, Davey and King1997; Tremaine et al., Reference Tremaine, Brockman and Betley1993).
In the first 24 h, S. aureus produced SEA in all samples at 25°C, regardless of the initial inoculum level. At 15°C, production occurred progressively, reaching 100% in all conditions at 144 h of incubation. The temperature of 10°C prevented the SEA production for up to 72 h and after 240 h of storage at 10°C, SEA was produced in all samples inoculated with 5 log CFU/mL, in 30% of the samples with 3 log CFU/mL, and at 0 log CFU/mL, S. aureus still had not produced SEA (Table 1). The average shelf life of Minas Frescal cheese is 30 days and it should be maintained at temperatures of up to 8°C. Silva et al. (Reference Silva, Carvalho, Andretta and Nero2021) found that Minas Frescal cheese was stored at excessive temperatures between 9°C and 12°C on market shelves. According to the findings of this study, if there is an initial contamination level of 5 log CFU/mL in the product, stored at 10°C, S. aureus can multiply and produce SEA after 72 h of storage.
Staphylococcal enterotoxin A production responses (%) at combinations of time, temperature and initial S. aureus concentration
Therefore, it is essential to control the initial contamination level and keep the cheese under refrigeration temperatures of up to 8°C to ensure its safety during its shelf life (Brasil, 1997).
Mathematical model of staphylococcal enterotoxin A production
The use of S. aureus growth models in culture media and foods of animal origin is well established (Araújo et al., Reference Araújo, de O Arruda, Duarte, Sousa, da C Lima, Conceiçaõ, Schaffner and Souza2017; Elahi and Fujikawa, Reference Elahi and Fujikawa2019a; Valero et al., Reference Valero, Pérez-Rodríguez, Carrasco, Fuentes-Alventosa, García-Gimeno and Zurera2009). However, the application of probability models to predict the production of enterotoxins by S. aureus under variable conditions in cheeses of importance in Brazil needs further exploration. Based on the conditions found in Minas Frescal cheese from retail sale (Silva et al., Reference Silva, Carvalho, Andretta and Nero2021), a logistic regression model was built to predict the influence of these factors on the production of SEA by S. aureus. The estimated parameters with standard error for the model are shown in Table 2. The parameters that significantly influenced the production of enterotoxins (P ≤ 0.05) were selected by the backward stepwise method to create the model. The mathematical equation generated is represented by Eq. 3.
\begin{align}Logit{\text{ }}\left( P \right) &= Ln{\text{ }}\left( {\frac{P}{{1 - P}}} \right) = 70.5030 - 0.2347{\text{*}}time + 2.9965{\text{*}}T \nonumber\\
&\quad- 34.1153{\text{*}}pH + 1.0328{\text{*}}inoculum - 0.0696{\text{ *}}T2 \nonumber\\
&\quad+ 2.7729{\text{*}}pH2 + 0.0146{\text{*}}time*T + 0.0106{\text{*}}time{\text{*}}pH \nonumber\\
&\quad+ 0.0188{\text{*}}time*inoculum - {\text{ }}0.0485{\text{*}}T*inoculum \nonumber\\
\end{align}Parameters obtained and the respective adjustment indices of the prediction model of staphylococcal enterotoxin A production/no production
The production of SEA by S. aureus was influenced by time, temperature, pH, inoculum concentration and their interactions (P < 0.05), but not by NaCl concentration. This result could be attributed to the NaCl range used in this study. Nunes and Caldas (Reference Nunes and Caldas2017) and Elahi and Fujikawa (Reference Elahi and Fujikawa2019a), when using broader NaCl ranges (0.64% to 4.6% and 0.5%–20%, respectively), observed a greater influence of salt on growth and enterotoxin production responses by S. aureus. However, as the present study aimed to investigate real situations observed in cheese, these values were within the range of NaCl found (Silva et al., Reference Silva, Carvalho, Andretta and Nero2021).
In a parametric model, the Wald test can be used to define the importance of each independent variable on the dependent variable (Wang and Guo, Reference Wang and Guo2001). Thus, the combinations of time and temperature or initial concentration had the most significant influence on SEA, followed by the linear factors time and temperature (Table 2), consistent with the results found by Hedberg et al. (Reference Hedberg, Palazzi-Churas, Radke, Selman and Tauxe2008) and Babic et al. (Reference Babic, Pajić, Radinović, Boboš, Bulajić, Nikolić and Velebit2019), but differ from the results found by Ding et al. (Reference Ding, Yu, Hwang, Dong, Chen, Ye and Liu2016).
According to the model of Eq. 3, higher pH and longer time result in greater chances of S. aureus producing SEA. However, the influence of pH was more pronounced at 15°C and an initial inoculum concentration of 3 log CFU/mL, where SEA production was observed within 24 h only in samples with pH 6.5 and 6.7. Other factors, such as time, temperature and inoculum concentration, demonstrated a more significant impact on SEA production, corroborating the results of the Wald test, where the combination of time and pH was the factor that had the least impact on the responses. In the study conducted by Ding et al. (Reference Ding, Yu, Hwang, Dong, Chen, Ye and Liu2016), pH only affected SEA production when combined with temperature and water activity. According to Genigeorgis (Reference Genigeorgis1989), the ideal pH for the enterotoxin production is between 7 and 8.
The logistic regression model showed good performance in predicting microbial behaviour in food (Koseki et al., Reference Koseki, Mizuno and Yamamoto2007; Huang et al., Reference Huang, Jia and Hwang2022; Morassi et al., Reference Morassi, Silva, Furtado, Freire, Santos, Chaves, Granato, Silva, Peña and Sant'Ana2022). The model obtained demonstrated good statistical fit to the data using Nagelkerke R2, Hosmer and Lemeshow test and % predicted correctly. The Nagelkerke R2 exceeded 0.90% and 94.40% of the data were correctly predicted. The Hosmer and Lemeshow test, which assesses whether there is a significant difference between observed and predicted data, yielded a P > 0.05, indicating no significant difference between the obtained and predicted results (Table 2). This indicates that the model is adequate to describe the production of SEA by S. aureus in response to the evaluated factors.
The predicted probabilities of SEA production by the model ranged from 0% under conditions at 10°C to 100% at 15°C and 25°C during the 240 h of incubation. For 25°C, in all conditions, probabilities above 90% were observed at 24 h. The lowest probabilities (2%–3%) for 15°C were noted at initial concentrations of 0 and 3 log CFU/mL, pH 6, 1.5% and 2.2% of NaCl, while at 10°C, all conditions with initial concentrations of 0 log CFU/mL showed a zero probability at 24 h (Fig. 1A). These results may be attributed to the fact that at 24 h, the bacteria are still in the lag phase at low temperatures and in the log phase at 25°C. Probabilities above 95% at 10°C were observed from 144 h, with initial concentrations of 3 log CFU/mL, pH 6.5 and 6.7 and 1% and 1.5% of NaCl (Fig. 1C). With increasing temperature and initial S. aureus concentration, there was an increase in the probability of SEA production.
Probability responses of enterotoxin (●) production/no-enterotoxin production (о) of S. aureus ATCC 13,565 as a function of pH 5.5, inoculum concentration and storage temperatures at (A) 24 h, (B) 72 h, (C) 144 h, and (D) 240 h. To the right the first line represents 0.1. The second 0.5. And the third 0.9 of probability.
Probabilities above 0.5 were considered as SEA production, while those below 0.5 indicated no-SEA production (Fig. 1). An increase in probability with a consequent expansion in the region of production and a reduction in the region of no-production of SEA can be observed as time and temperature progress. For scenarios at 10°C and 0 log CFU/mL of S. aureus, there was no SEA production even after 240 h (Fig. 1D). Minas Frescal cheese, especially when informally produced, is often at room temperature or sold without refrigeration. In this study, 25°C was the best temperature for SEA production and 10°C exhibited the most inhibitory effect among the factors evaluated. Previously, studies have documented production of staphylococcal enterotoxins at refrigeration temperatures of 10°C (Elahi and Fujikawa, Reference Elahi and Fujikawa2019b; Tsutsuura et al., Reference Tsutsuura, Shimamura and Murata2013). Therefore, it is essential to store the cheeses at adequate refrigeration temperatures.
Different concentration levels of S. aureus were tested to simulate low and high initial contamination in Minas Frescal cheese. Figure 1 shows that the higher the initial inoculum concentration, the smaller the region of no-enterotoxin production (P < 0.5) and the greater the probability of enterotoxin production. According to the Food and Drug Administration (FDA), enterotoxin production begins at 5 log CFU/mL. In this study, for most conditions, SEA could only be detected when the S. aureus concentration reached this level, as observed by Mohammadi and Hanifian (Reference Mohammadi and Hanifian2015) and Cai et al. (Reference Cai, Pei, Zhang, Liu, Lu, Li, Dong, Wang, Zhu and Ji2023). In the model conducted by Hu et al. (Reference Hu, Lin, Chen and Yan2018) in cooked chicken, SEA was produced only when the concentration of S. aureus reached 6 log CFU/mL. Therefore, the production of enterotoxins is not only associated with the inoculum (Al-Nabulsi et al., Reference Al-Nabulsi, Osaili, Sawalha, Olaimat, Albiss, Mehyar, Ayyash and Holley2020). Other factors, such as temperature, the food matrix and competing cultures, influence enterotoxin production. In this study, the Wald test showed that other factors, such as time, temperature and their modifications, had a greater influence on the SEA responses.
The probabilistic model developed in this study (Equation 3) can be used to define critical limits for enterotoxin production, considering the variables involved in the manufacture of Minas Frescal cheese. Among the factors evaluated, time had a significant influence on the likelihood of enterotoxin formation. Therefore, critical times for enterotoxin production were predicted at different probability levels (Table 3). Conservative probability levels are commonly applied when a high level of microbiological safety is required. At P = 0.05, under all conditions involving storage at 20°C, the predicted critical time for enterotoxin production was less than 1 h. This highlights the considerable risk associated with storing the product at elevated temperatures, even for short periods. On the other hand, the combination of low storage temperature and low initial contamination delayed enterotoxin production beyond the maximum time evaluated in this study (>240 h), indicating enhanced safety under such conditions.
Critical time predicted with P = 0.1, P = 0.5 and P = 0.9 of the enterotoxin A production by S. aureus ATCC 13,565 at environmental conditions
<0 values below the studied range.
>240 values above the studied range.
In the present study, different combinations of the conditions in BHI broth, Minas Frescal cheese and UHT milk were used to validate the model. The probability responses for SEA production observed during 144 h of storage were compared with predicted responses from the developed model (Table 4). Of the 72 conditions tested in BHI, 88% were correctly classified by the model. The model overestimated SEA production in 7% (fail-safe) and underestimated it in 5% (fail-dangerous). Fail-safe situations, in which the model predicted SEA production but no enterotoxin was detected experimentally, occurred under the following conditions: an initial S. aureus concentration of 3 log CFU/mL, 144 h of incubation at 12°C, pH 5.7 and 1.8% NaCl; and at 0 log CFU/mL with 24 h of storage at 20°C, pH values of 5.7 and 6.3 and NaCl concentrations of 1.2% and 1.8%. In contrast, fail-dangerous scenarios, where the model failed to predict enterotoxin production that was observed, involved 12°C, pH values of 5.7 and 6.3, NaCl concentrations of 1.2% and 1.8%, 72 h of incubation with an initial S. aureus level of 3 log CFU/mL and 144 h of incubation with 0 log CFU/mL of inoculum. This result is expected for models developed in culture media, as they contain nutrients that provide ideal conditions for the development of microorganisms, resulting in models with fail-safe variations (Te Giffel and Zwietering, Reference Te Giffel and Zwietering1999).
Validation responses in BHI, Minas Frescal cheese and UHT milk of the enterotoxin A production by S. aureus ATCC 13,565 at environmental conditions
* Obs.: The value “1” in validation assays was assigned when enterotoxin production was observed (i.e., samples with VT equal to or greater than 0.13). The value “0” was assigned when enterotoxin production was not observed (samples with VT below than 0.13).
** Pred.: Predicted values were obtained by inserting in the generated models, the same pH, temperature, time, inoculum and NaCl values employed in the validation experiments.
The behaviour of microorganisms in culture media under the influence of environmental factors may differ in food matrices. Studies conducted with logistic regression models were validated in culture media (Elahi and Fujikawa, Reference Elahi and Fujikawa2019a; Tabanelli et al., Reference Tabanelli, Montanari, Patrignani, Siroli, Lanciotti and Gardini2014; Moraes et al., Reference Moraes, Cruz, Souza, Oliveira, Alvarenga, Peña, Sant'Ana and Magnani2018). Therefore, when using models developed in culture media, it is first necessary, in addition to validation in culture media, to prove their use through validation in food to confirm the applicability of the model to practical situations (Arroyo-López et al., Reference Arroyo-López, Bautista Gallego, Valero, García-Gimeno and Garrido Fernández2014; Silva et al., Reference Silva, Baranyi, Carciofi and Ellouze2017). In this study, validation in UHT milk and Minas fresh cheese showed agreement with the observed data of 78% and 83%, respectively. These results confirm the applicability of the developed model to predict SEA production responses by S. aureus in Minas Frescal cheese.
Conclusion
This study demonstrated that temperature, pH, time and the initial S. aureus concentration significantly influenced the SEA production responses, while NaCl concentration had no significant effect within the tested range. At 25°C, S. aureus produced SEA under all tested conditions within the first 24 h of storage, while at 10°C, S. aureus growth was delayed and SEA production was inhibited at low initial contamination levels. The logistic regression model, developed based on the tested combinations of environmental factors, demonstrated good predictive performance, with a high statistical fit (Nagelkerke R2 > 0.90 and 94.4% correct predictions). Validation in Minas Frescal cheese and UHT milk confirmed the applicability of the model, with accuracies of 83% and 78%, respectively. The results reinforce the importance of controlling and including the initial contamination level in the models and maintaining strict temperature control during storage, as SEA production was delayed or absent at lower temperatures and inoculum levels. The model proved to be an important tool for estimating SEA production risk in Minas Frescal cheese and may contribute to microbial risk assessment and management strategies in the dairy industry. Future research should be proposed to assess the SEA concentration under different environmental conditions and in diverse food matrices.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/S002202992510160X.
Acknowledgements
This study was financed by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES, Brasília, DF, Brazil – financial code 001), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, Brasília, DF, Brazil) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG, Belo Horizonte, MG, Brazil). bioMérieux supported the study by providing the kit VIDAS.
Competing interests
The authors have not stated any conflicts of interest.
