Food processing and preservation faces challenges such as nutrient conservation or the search for alternatives to chemical synthetic preservatives, which can preserve food quality, prevent microbial deterioration, and control enzymatic and chemical degradation. These new alternatives have focused on ensuring food safety but also providing a product with excellent sensory and nutritional quality (Hossain et al., 2016; Ngnitcho et al., 2017). On the other hand, traditional conservation products and sanitizers used in the food industry have been used for a long time, and have gradually acquired resistance (Davidson and Harrison, 2002). The combination of factors that affect microbial growth in foods can lead to less severe treatments that have a lesser effect on the nutrimental and sensory properties of food products. The combination of preservation factors is known as hurdle or barrier technologies, and have been successfully used in food processing to increase the product's shelf life (Khan et al., 2017; Ngnitcho et al., 2017).

Among the antimicrobial compounds suggested for use in hurdle technologies, spices are recognized for their biological properties, including antimicrobial, and antioxidant activities. These biological properties have been attributed to the complexity of their chemical or structural composition, and the functional groups present in their major active compounds (Rivera-Calo et al., 2015). Among species, essential oils used in food processing are thyme, basil, cinnamon, mint, tea tree, and eucalyptus, which are recognized for their functional groups and lipophilic properties (Hossain et al., 2016). The addition of these secondary metabolites has been evaluated in meat food, seafood, daily food, and fruits, vegetables, cereals whit promising results (Perricone et al., 2015; Possas et al., 2017).

One of the most studied essential oil is Oregano's that include carvacrol and thymol as bioactive components, as well as minor concentration of other terpenes and aromatic compounds, recognized as GRAS, while not exceeding 50 mg/kg (Marinelli et al., 2018; Navarro-Cruz et al., 2018). Extraction of Oregano essential oil (OEO) can be done using different parts of the plant, including leaf, stem, or root (Rivera-Calo et al., 2015). Worldwide, there are close to 40 different plant species known as oregano, with differences in the proportion of thymol and carvacrol in the essential oil; also, there are differences in the composition of a particular oregano species. In Mexico, Lippia berlandieri (also identified as Lippia graveolens) is the most common oregano spice found, but other species such as Poliomintha longiflora or Lippia palmeri have also been studied (Ortega-Nieblas et al., 2011; Cid-Pérez et al., 2016).

OEO has been reported with antifungal and antimicrobial effects under several conditions, both in the laboratory in vitro experiments and while added to food products (Witkowska et al., 2014; Hossain et al., 2016; Cid-Pérez et al., 2019). When added to food products, is necessary to consider that the antimicrobial effect of essential oils can be modified by intrinsic factors such as the presence of lipid, proteins, carbohydrates, salt content or the pH of the food matrix, regardless of the deteriorative of pathogenic microorganism that is intended to be controlled or eliminated (García-Díez et al., 2017). Also, the extrinsic factors such as storage temperature and relative humidity can affect the food safety of the stored products (Gutierrez et al., 2008).

The understanding of the microbial growth in food is essential to evaluate the efficacy of preservation methods and can provide a base for the preparation of high-quality products (McMeekin et al., 2002). The use of experimental designs and prediction models can provide a preliminary assessment of a food product processing or formulation, by giving a quantitative measure of the interaction of hurdle factors on the microbiota present in a food system (Gutierrez et al., 2009). Predictive microbiology studies the microbial responses to environmental factors, expressed in mathematical equations that can predict the behavior of microorganisms under new conditions (Akkermans et al., 2018; Ochoa-Velasco et al., 2018).

In order to evaluate the effect of food composition on the antifungal activity of Mexican oregano, this work was aimed to use predictive models to evaluate the combined effect of pH, percentage of protein, and concentration of Mexican OEO (Lippia berlandieri Schauer and Poliomintha longiflora Gray), on the growth of food-related fungi, Penicillium expansum and Aspergillus ochraceus.

The contamination of molds in food represents a risk to the consumer since they can produce allergenic metabolites such as aflatoxins, ochratoxins A, fumonisins, trichothecenes, and zearalenones. Mycotoxins are the cause of autoimmune, teratogenic, cancerogenic, and mutagenic health problems (Hossain et al., 2016). OEO has demonstrated its fungicidal effect alone, as part of edible films or encapsulated to keep their biological properties, for food preservation, to extend the shelf life (Avila-Sosa et al., 2010; Cid-Pérez et al., 2016; Ribeiro-Santos et al., 2017). The general mechanism of action of essential oils, include morphological alterations in the cell membrane of pathogenic microorganisms (Tang et al., 2018). However, it is essential to understand the effect of food components or properties, such as pH, on the antimicrobial effect of the essential oil.

Predictive microbiology has been used to explain the antifungal mechanisms of natural antimicrobials. Weibull‘s distribution model has been used to study the viability of P. expansum spores places in contact with betel leaf essential oil. The authors noted that spore survival decreases while treatment times increased. Spore inactivation is due to the loss of cell membrane integrity, since the essential oil penetrates inside the cell, and interferes with the enzymatic activities of cell wall synthesis (Basak and Guha, 2017). The use of predictive models does not always provide information for the interaction of the variables studied. Possas et al. (2017) used the primary models of Baranyi and Weibull to evaluate the growth and survival of Salmonella on meat products, applying thyme essential oil with thymol as the main component (60%), and carvacrol in lower concentration (3.8%). Although the Weibull model has high flexibility to adapt to too many types of data, the results were not sufficient to model them.

Extrinsic food factors such as temperature and relative humidity, or intrinsic factors such as water activity, are among the most important factors that affect fungal growth in foods (Avila-Sosa Sanchez et al., 2015). However, the effect of other food properties or intrinsic factors are not extensively reported. The interaction of pH and protein content was tested on the fungicidal effect of Mexican oregano essential oils. We expected to have a synergistic effect, or that the pH and protein concentration were not negatively affecting the antifungal effect of the OEO. In most cases, the predictive models that were statistically significant, linearly included protein and OEO, with no effect of interaction among the two factors. The growth rate (V_m) was not affected by the different compositions of the media, except for A. ochraceous in the presence of OEO with high proportion of thymol, were a combination of linear and quadratic effects of the essential oil and pH, as well as the lineal interaction of both factors were included in the model (Equation 8). The complexity of the model does not allow for a maximum prediction response. P. expansum lag time was also explained by a regression model that included a quadratic effect of the essential oil and a lineal effect of pH (Equation 6). The non-linear effect of essential oil concentrations on fungal growth has been previously reported, where higher or lower concentrations of OEO promoted fungal growth (Portillo-Ruiz et al., 2005).

The effect of pH and food ingredients has also been monitored for the antilisterial effect of Origanum vulgare essential oil on the lag phase and maximum growth of Listeria monocytogenes. OEO was more effective at pH 5.0; lower pH values increased the lag phase and reduced maximum growth. An acidic pH increases the OEO hydrophobicity, also increasing the dissolution of the membrane lipids, with the consequent interference with cellular functionality (Albuquerque et al., 2006; Rivera-Calo et al., 2015; Navarro-Cruz et al., 2018). The effect of pH is also related to the type of acid used to adjust the media, since organic acids are also mild antimicrobials. Propionic acid is used as a food preservative due to its fungicidal ability. It has been reported that a concentration of 0.20%, propionic acid reduces the growth rate of Aspergillus spp, Geotrichum spp, Mucor spp, Penicillium spp, and Scopulariosis spp by up to 50% (Khan et al., 2017). The concentrations of pH used in this report were from mildly acidic to neutral, and two models, there was no interaction with the OEO fungicidal capacity. It can be considered that the citric acid that was used to adjust the pH values does not affect the fungicidal action of OEO.

The hydrophobic components of essential oils are absorbed in the protein matrix and the lipid fraction of a food product, leaving essential oils less available to act, as reported for Listeria monocytogenes, where the presence of these components promoted the bacterial growth (Gutierrez et al., 2008). On the other hand, food nutrients can be helpful for bacterial cell recovery. When different essential oils (oregano and thyme) were combined, an additive antimicrobial effect on the bacteria was observed. When NaCl (5 g/100 mL) was added to the media added with starch, water activity decreased, and microbial counts were also reduced (Perricone et al., 2015; Cattelan et al., 2018). When OEO (carvacrol 65.1%) and NaCl were evaluated separately on the growth of Escherichia coli, the effect observed suggested the use of the essential oil with salt reduction in the food products, considering the health problem caused by a high salt intake (Witkowska et al., 2014). This synergistic phenomenon has also been reported for oregano oil (Origanum vulgare) and thyme (Thymus vulgaris), when evaluated against Aspergillus flavus, Aspergillus parasiticus, and Penicillium chysogenus (Hossain et al., 2016). The authors found the lowest values of minimum fungicidal concentration in this system when compared with other oils derived from basil, cinnamon, eucalyptus, tangerine, mint, and tea tree. The combination of essential oils halted colonial growth and its maximum growth rate. The lag phase was extended by the antifungal effect, as obtained by the modified Gompertz model (Witkowska et al., 2014). Another alternative to potentiate the effect of essential oils, is the combination with peptides or proteins produced by specific lactic bacteria, including bacteriocins such as nisin V at 500–1,000 UI/g (derived from Lactococcus lactis), pediocin (derived from Pediococcus acidilactici), or enterocine A (Abdollahzadeh et al., 2014; Field et al., 2015; Ghrairi and Hani, 2015).

In order to increase the effectiveness of essential oils when incorporated into a food matrix, several strategies have been proposed. One strategy is the microencapsulation and nano emulsification of essential oils (Estrada-Cano et al., 2017; Dávila-Rodríguez et al., 2019). Another strategy is the preparation of packing materials, such as the edible coats and films formed with chitosan, carboxymethylcellulose, or starch and added with essential oils. Both strategies aim to distribute essential oils evenly and reduce interaction with food ingredients (Paparella et al., 2016; Basak and Guha, 2017; Navarro-Cruz et al., 2018; Ochoa-Velasco et al., 2018).

The composition of the three Mexican oregano essential oils varied on their proportion of thymol and carvacrol; the difference was also observed in the growth of the molds studied. A. ochraceus was more sensible to the presence of OEO and higher concentrations of protein than P. expansum. The predominant effect was the added effect of protein content and concentration of OEO on the maximum fungal growth, with a lineal effect and no interaction among the two variables. Lag time was also affected by protein content, although the predictive models did not have statistical significance. The growth rate was not affected by the three variables studied.

The development of predictive models can provide information on the growth or inactivation of microorganism present in food, under various conditions. Also, it can help on the determination of the detrimental or synergistic effect of a particular food additive, such as essential oils bioactivities, in interaction with food components or food properties. The interactions among components of a food matrix can be very complex, and quantitative measurements of these interactions are useful on the determination of the final preservation effect in the food product. On the other hand, the variable chemical composition of essential oils will also affect their antifungal capacity. Even more, the response of fungal isolates even from the same fungal genera and species can vary, and the isolates will be differentially affected by the antifungal compounds. Further studies are needed to propose general trends on the interaction of food components, food characteristics, and natural food antimicrobials. These mathematical tools are useful for food industries to determine the food safety risk of processed food products. Scientific research in predictive microbiology can finally enrich databases for the development of software (tertiary models) that supporting food safety from processing to the table.

The datasets generated for this study are available on request to the corresponding author.

Experimental design: AL-G, AL-M, and GN-M. Experimentation: AL-G. Methods: RÁ-S, AL-G, and AL-M. Supervision: RÁ-S, and NG-M. Statistical analysis: RÁ-S, NG-M, and GN-M. Manuscript draft: AL-G. Final manuscript: GN-M. All author: read and approved the final manuscript.