A model to predict the fate of Listeria monocytogenes in different cheese types – A major role for undissociated lactic acid in addition to pH, water activity, and temperature

Undissociated lactic acid has been shown to play a major role in complete growth inhibition of Listeria monocytogenes in Gouda cheese. In addition, low water activity conditions may contribute to growth inhibition. In the current study, it was assessed whether the major factors that inhibit growth of L. monocytogenes in Gouda cheese are the factors that determine growth in other types of ready-to-eat cheese as well. Various types of cheeses were selected, some of which had been associated with listeriosis, while others had not. Based on the composition of the different cheese types, the concentrations of undissociated lactic acid were calculated for each type. The ability to support growth of L. monocytogenes was predicted using the Gamma model, based on literature data on total lactic acid content, moisture content, fat content, pH, Aw, and temperature, and optimal growth rates in milk at 30–37 C. In addition, the actual specific growth rates of L. monocytogenes in the various cheeses were calculated based on available experimental growth data. In 9 out of the 10 RTE cheeses reviewed, the undissociated lactic acid concentrations and aw determined growth/no growth of L. monocytogenes. No growth was correctly predicted for feta, Cheddar and Gouda, and growth was correctly predicted for ricotta, queso fresco, Camembert, high-moisture mozzarella, cottage and blue cheese. Growth of L. monocytogenes was not observed in practice upon inoculation of Emmental, whereas growth in this cheese type was predicted when including the above mentioned factors in the models. Other factors, presumably acetic and propionic acid, are thought to be important to inhibit growth of the pathogen in Emmental. The results from our study show that for cheeses in which lactic acid is a main acid, our model based on undissociated lactic acid, temperature, pH and aw gives a good prediction of potential outgrowth of L. monocytogenes. Implications for L. monocytogenes legislation are discussed per type of RTE cheese reviewed.


Introduction
Most cheeses are intended to be ready-to-eat (RTE) products and do not undergo a heating step prior to consumption. RTE cheeses can be manufactured from pasteurized milk or from raw milk. Various RTE cheeses, such as Latin-style, blue-veined, and mould cheeses have been linked to cases of listeriosis (Jackson et al., 2018), a disease caused by Listeria monocytogenes (Swaminathan and Gerner-Smidt, 2007). L. monocytogenes may be present at low concentrations in raw milk (Table 1) and RTE cheeses manufactured from raw milk may therefore pose a risk (Jackson et al., 2018). It is unlikely that L. monocytogenes survives pasteurization of the cheese milk (den Besten and Zwietering, 2012). Yet, this pathogen can survive in highly acidic, salty and lowtemperature environments (ICMSF, 1996), it can form biofilms (Borucki et al., 2003;Cossart et al., 2003;Carpentier and Cerf, 2011) and it may be persistent in the RTE cheese processing environment. Contamination of finished products must be prevented, especially as the product does not undergo a heat treatment prior to consumption.
EU regulation EC 2073/2005 lays down certain process hygiene criteria to indicate the correct functioning of the production process (European Commission, 2005). The regulation also lays down food safety criteria for relevant foodborne bacteria, their toxins and metabolites in specific foods. The given criteria define the acceptability of a product placed on the market. Specific criteria for L. monocytogenes apply to RTE foods, including RTE cheeses. Under all circumstances, it is important to avoid potential contamination of the product with this pathogen. This relates to ingredients and post-processing contamination. Products other than those intended for infants and for special medical purposes are categorized based on the ability of the food product to support (category 1.2) or not support (category 1.3) growth of L. monocytogenes. Food products with pH ≤ 4.4 or with a w ≤ 0.92 and food products with pH < 5.0 and a w ≤ 0.94 are automatically considered as a food product belonging to category 1.3. Other food products may also belong to this category, subject to scientific evidence. An overview of the European food safety criteria for L. monocytogenes in RTE foods is presented in Fig. 1, including the sampling plan and stage at which each criterion applies per category. The US has a zero-tolerance approach for all RTE foods, with absence in 25 g; the FDA states that absence in 25 g needs to be demonstrated in two 25 g samples compiled from two 125 g samples (FDA). While a 'zero-tolerance' applies to RTE foods in the USA, it may be valuable to know whether the product supports growth or not, as part of a risk based approach (Farber et al., 2021).
Various authorities have classified different cheese types according to their potential risk related to listeriosis. The classification of cheese by the Food and Drug Administration (FDA) in the USA is based on the moisture on whole cheese content (moisture%) (FDA, 2003). Based on cluster analysis of predicted per serving and per annum relative ranking, consumption of soft unripened cheese (e.g. cottage, ricotta) is considered of high risk, soft ripened cheese (brie, Camembert, feta, mozzarella) and semi-soft cheese (blue) of moderate risk, and hard cheese (Cheddar, parmesan) of very low risk for listeriosis.
Listeriosis cases have never been linked with Gouda cheeses made from pasteurized milk. Gouda cheese, having a moisture% of 39 to 53% (van den Berg et al., 2004) is classified as a semi-soft cheese according to the FDA definition. With a pH > 5.0 and a w > 0.94, Gouda is not automatically classified as a cheese that does not support growth of L. monocytogenes based on criteria mentioned in EC 2073(European Commission, 2005. For Gouda cheese, it was demonstrated by challenge tests that it does not support growth of L. monocytogenes (Northolt et al., 1988;Wemmenhove et al., 2013 and. Undissociated lactic acid was established as the key parameter inhibiting this growth during initial ripening, together with a w and pH (Wemmenhove et al., 2016a and. Upon prolonged ripening periods and in cheese rind, low water activity conditions can lead to full growth inhibition of L. monocytogenes (Wemmenhove et al., 2016b). The aim of this study was to establish whether undissociated lactic acid, together with pH and a w also determine the fate of L. monocytogenes in cheeses other than Gouda. A literature review was performed to investigate associations of certain cheeses with listeriosis cases or absence thereof. Based on this overview, four cheese types were identified with links to listeriosis cases, while for six cheeses no links were established. Based on the compositions of Gouda cheese and nine other cheeses (i.e., blue, Camembert, Cheddar, cottage, Emmental, feta, highmoisture mozzarella, queso fresco, ricotta), undissociated lactic acid concentrations were calculated and growth / no growth predictions were made based on the Gamma model for these 10 cheeses at a reference temperature of 10 • C. In addition, actual specific growth rates in these other cheeses were calculated by extracting growth data based on published experimental studies and adjusted to the same reference temperature. These growth rates, based on practical observations, were subsequently compared with the growth rates as calculated with the model, to verify the predictions.

Physicochemical properties of cheeses
Data on physicochemical properties (e.g. total lactic acid content, moisture content, fat content, pH, a w ) and storage temperature were obtained for 10 cheeses, namely, blue, Camembert, Cheddar, cottage, Emmental, feta, Gouda, mozzarella (high-moisture), queso fresco, and ricotta. Data were extracted from cheese handbooks and scientific literature (Supplementary Table A.1). The concentration of undissociated lactic acid in the different cheeses was calculated using Eq. 6.12 from Wemmenhove et al. (2018).

Prediction of specific growth rates based on cheese composition
Optimal growth rates (μ opt ) for L. monocytogenes were extracted from Combase based on specific growth rates in milk at 30-37 • C; the values used were 1.69 h − 1 (maximum value) and 0.73 h − 1 (average value).

Actual specific growth rates of L. monocytogenes in different cheeses based on reported growth
Actual specific growth rates μ of L. monocytogenes in different cheeses were calculated based on data available in published challenge studies. Data were obtained through a literature search (searching Scopus and Web of Science for: monocytogenes AND cheese AND (Blue OR Camembert OR Cheddar OR Cottage OR Emmental OR Feta OR Gouda OR Mozzarella OR Queso Fresco OR Ricotta OR Swiss), sorted on relevance) and Combase (search on www.combase.cc for Listeria monocytogenes AND cheese, data from all scientific article records were incorporated for each of the 10 cheese types).
The μ 10 • C values were calculated for each type of cheese using ∆logN•ln(10) t , with Δlog N as the log concentration of L. monocytogenes at the end of sampling minus the log concentration after pressing, and with t as the time between the end of sampling and after pressing. The predicted specific growth rates (μ 10 • C values) were extracted from Combase (www.combase.cc) when searching for growth rates of L. monocytogenes in milk at 30-37 • C. The μ 10 • C values were based on Gamma factors for undissociated lactic acid, a w , temperature and pH calculated according to Zwietering et al. (1996) and Te Giffel and Zwietering (1999), and a MIC of undissociated lactic acid for L. monocytogenes of 6.35 mM according to Aryani et al. (2015). Average conditions were chosen for undissociated lactic acid, a w and pH (according to Table 2). The temperature was normalized to 10 • C by use of the square-root function of McMeekin et al. (1993): (T− Tmin) 2 , with T min = − 1.5 • C and T ref = 10 • C and μ T as the specific growth rate at temperature T. The application of the square-root function by McMeekin et al. (1993) for temperature is only validated for positive actual specific growth rates. Similar to the positive actual specific growth rates, the negative growth rates were also normalized to 10 • C, using this function.

Cheeses associated with listeriosis
An overview was made of cheeses actually linked with listeriosis. Data were obtained through a literature search (searching Google, EFSA reports, CDC reports, Scopus and Web of Science for: listeriosis AND cheese, or 'Listeria', 'outbreak' and 'cheese', sorted on relevance, first 300 hits) for the years 1983-2019.

Undissociated lactate and a w of 10 types of cheeses
The values of undissociated lactic acid, pH, a w and storage temperatures of 10 different cheese types, namely, blue, Camembert, Cheddar, cottage, Emmental, feta, Gouda, mozzarella (high-moisture), queso fresco, and ricotta, are listed in Supplementary Table A.1 and the average values are presented in Table 2. These data show that high concentrations of undissociated lactic acid are found in Cheddar, feta and Gouda, even higher than the MIC of 6.35 mM required to fully inhibit growth of L. monocytogenes (Aryani et al., 2015). Cottage, queso fresco, and ricotta contain very low concentrations of undissociated lactic acid and the a w of the latter cheeses is high. In blue cheese, the concentration of undissociated lactic acid is <6.35 mM, but the a w value (0.925) approximates the growth limit of L. monocytogenes. In Camembert, high-moisture mozzarella, and Emmental, the average concentration of undissociated lactic acid is 1.01, 3.09 and 2.80 mM and the a w is 0.965, 0.940 and 0.970, but these values do not approximate the growth limits of L. monocytogenes.

Prediction of growth of L. monocytogenes in 10 types of cheeses
In addition to physicochemical properties, Table 2 displays predicted specific growth rates of L. monocytogenes per cheese type, which are calculated based on the physicochemical properties of the various cheese types and optimal growth rates in milk of L. monocytogenes, as obtained from Combase which contains an overview of studies on growth of L. monocytogenes in milk. For Cheddar, feta and Gouda, full growth inhibition is predicted (based on undissociated lactic acid). The highest growth of L. monocytogenes is predicted for ricotta and queso fresco, and some growth is predicted in blue, Camembert, high-moisture mozzarella and Emmental.

Growth of L. monocytogenes in cheeses based on published challenge studies
Supplementary Table A.2 displays specific growth rates of L. monocytogenes in and on 10 cheese types, as extracted from challenge studies that have been published previously. The reported challenge studies were performed at different storage temperatures. As low storage temperature in itself may be a growth-limiting factor, results of the different challenge studies cannot be compared directly. To adjust for the effect of temperature on growth inhibition of L. monocytogenes, the challenge data were normalized to a storage temperature of 10 • C. Fig. 2 shows the actual and predicted specific growth rates whilst normalizing to a storage temperature of 10 • C. In the cheeses blue, Camembert, cottage, high-moisture mozzarella, queso fresco, ricotta and Emmental, growth of L. monocytogenes was predicted, which is in line with results from challenge tests (Supplementary Table A.2), except for Emmental for which growth was only predicted but not observed. In feta and Gouda, no growth of L. monocytogenes was observed nor predicted. In Cheddar, no growth was predicted and in most cases growth was not observed in most reported challenge tests. Two data points showed growth, but in these cases, no information on cheese characteristics were given (see discussion section). Overall, correct prediction of growth or no growth of L. monocytogenes was obtained for 9 out of 10 cheese types. Table 3 consists of an overview of listeriosis outbreaks that were linked with RTE cheeses. Mainly soft cheeses (e.g. queso fresco, ricotta, mould-ripened cheese) have been linked with listeriosis. Those soft cheeses were all able to support growth of L. monocytogenes, according to challenge studies published previously (Fig. 2). For the hard cheeses linked with listeriosis (mature cheese, Pave du Nord), it was not reported whether the cheese milk was raw or pasteurized.

Discussion
Similar to Gouda cheese, the same four factors (i.e., undissociated lactic acid, temperature, pH and a w ) were found to be important for growth inhibition of L. monocytogenes in/on other types of RTE cheeses.
For 9 out of 10 cheese types, correct predictions of growth / no growth were obtained when including the factors undissociated lactic acid, temperature, pH and a w in the prediction. Outgrowth of L. monocytogenes was correctly predicted for ricotta, queso fresco, Camembert, high-moisture mozzarella, cottage and blue). No growth was correctly predicted for feta, Cheddar and Gouda, except for two data points based on one study by Cui et al. (2016) who reported growth of L. monocytogenes on the surface of commercial Cheddar cheese; in that study, however, acid content, pH, and salt content were not specified, nor did they report on possible growth of moulds, which may lead to a rise in pH and consequently a reduction in concentrations of undissociated acid. Our results show the importance of undissociated lactic acid, temperature, pH and a w for cheese in general.
In Fig. 2, our predictions are indicated with an arrow. More elaborate predictions of the growth rate were not performed, as undissociated lactic acid is a critical model factor, but the amount of obtained data on total lactic acid content was limited for many of the studied cheeses (Supplementary Table A.1). Per cheese type analyzed, there is a large variation in the actual specific growth rates. Part of the variation could be caused by physicochemical properties of the cheese that may differ between productions and may alter during cheese production and storage (Supplementary Table A.1). Another part of the variation could be due to variation in properties of L. monocytogenes strains that were used in the challenge tests (e.g. variation in growth rates results from Combase data, and acid sensitivity as described by Wemmenhove et al. (2016a)).
The model predictions are based on Gamma factors for undissociated lactic acid, pH, a w and temperature. The Gamma factor for undissociated lactic acid was calculated based on values extracted from literature for total lactic acid content, moisture content, fat content and pH. Fat in a cheese with equal dry matter only minimally affects the concentration of undissociated lactic acid, as can be deduced from Equation [6.12] in Table 2 Average values for total lactic acid content, moisture content, fat content, pH, a w , temperature (T), the calculated undissociated lactic acid and the resulting Gamma factors, calculated from these average values and from the formulas in Supplementary  The Gamma factors are displayed in italics. In addition to the predicted specific growth rate μ, the growth rate μ 10 • C was calculated as described in paragraph 2.3. Wemmenhove et al. (2018). This minimal effect of fat content on the fate of L. monocytogenes was confirmed by an additional study, showing that the fate of L. monocytogenes in model Gouda cheeses with a normal fat content of 48% w/w fat in dry matter was the same as that of a low fat content of 30% w/w fat in dry matter that had a similar acidification curve (results not shown). Leong et al. (2014) and Mehta and Tatini (1994) also did not report differences in the fate of L. monocytogenes in normal-fat versus low-fat cheese. Less inhibition of growth of L. monocytogenes is only expected in low-fat cheese with an increased moisture content, because such cheese will have a lower concentration of undissociated lactic acid (Wemmenhove et al., 2018) and the a w will be higher (Wemmenhove et al., 2014). In low-salt cheese, the a w is increased and this may result in less growth inhibition of L. monocytogenes due to a w . In most cheeses analyzed in Table 2, a w is not the primary inhibiting factor. In blue cheese, however, a w is the primary growth-inhibiting factor; for such a cheese, lowering of the salt content may result in less growth inhibition. The factors undissociated lactic acid, temperature, pH and a w do not fully explain why growth of L. monocytogenes is inhibited in practice upon inoculation in cheese milk used to make Emmental or inoculation on the surface of Emmental. In the challenge studies of Buazzi et al. (1992) and Bachmann and Spahr (1995), L. monocytogenes was inoculated into the milk, that was then curded and subjected to 2 min at 65 • C and 45 min at 53 • C. In the other challenge studies with Emmental (Genigeorgis et al., 1991;Leong et al., 2014), L. monocytogenes did not undergo a heating process, but the pathogen was inactivated. Acetic acid, propionic acid and free fatty acids are anticipated to be important factors for inhibition of growth of L. monocytogenes in Emmental, in addition to storage temperature, pH and a w . Inhibition of growth of L. monocytogenes by acetic and propionic acid has been described (Wemmenhove et al., 2016a), and inhibition of L. monocytogenes by free fatty acids has also been reported (Wemmenhove et al., 2018). Currently, no model is available to predict growth in cheese based on undissociated acetic acid and propionic acid, or combinations thereof, or of these acids in combination with undissociated lactic acid in cheese.
The actual specific growth rates (normalized at 10 • C) of L. monocytogenes in and on high-moisture mozzarella that have been reported are considerably higher than the predicted growth rates at 10 • C. The reason for the large deviation between actual and predicted specific growth rates may result from relatively large variations in the concentration of undissociated lactic acid in this type of mozzarella, with reported pH values varying between 4.9 and 6.2 for this type of cheese (Supplementary Table A  monocytogenes for 10 different RTE cheese types at 10 • C, to validate the importance of the factors undissociated lactic acid, a w and pH on growth inhibition. The actual growth rates of L. monocytogenes were extracted from 58 challenge studies (n = 308 for 10 cheese types, data described in Supplementary Table A.2) and were compared to predicted growth rates (Table 2). Per cheese type, the squares display the growth rates for L. monocytogenes after artificial contamination of the surface or crust, and the triangles display the growth after artificial contamination of the cheese curd or milk. The μ 10 • C values calculated with μ opt = 1.69 h − 1 (maximum) are indicated with black arrows, and those calculated with μ opt = 0.73 h − 1 (average) are indicated with grey arrows. A detailed description of the calculation of the actual and predicted specific growth rates is displayed in paragraphs 2.2 and 2.3 of the Materials and Methods section.
concentrations of undissociated lactic acid in mozzarella (0-2.37 mM; when predictions are based on such lactic acid concentrations, no deviation between actual and predicted rates existed).
We reviewed undissociated lactic acid as a key parameter for growth inhibition of L. monocytogenes in many types of cheese. Therefore, it seems justified that RTE cheeses are classified based on their undissociated lactic acid concentration, and not only on pH and a w . For cheeses such as Emmental, other inhibitory factors need further substantiation. The importance of undissociated lactic acid is underlined by the calculated Gamma factors for 10 cheese types using a MIC of undissociated lactic acid for L. monocytogenes of 6.35 mM and average values for total lactic acid content, moisture content, fat content, pH, a w and temperature (Table 2). This calculation showed that in three out of 10 cheese types (namely, feta, Cheddar and Gouda), the Gamma factor for undissociated lactic acid is 0, implying that undissociated lactic acid alone fully inhibits growth of L. monocytogenes in these three cheese types.
In Table 4, a suggested categorization according to EU regulation EC 2073/2005 for 10 RTE cheese types is presented. The categorization is based on whether or not the consumption of the cheese was associated with identified cases of listeriosis in the past, and whether or not growth rates extracted from challenge studies and those predicted based on growth-inhibiting factors were positive or not. Ricotta, queso fresco, Camembert, high-moisture mozzarella, cottage and blue cheese were all linked to listeriosis (Table 3) and at the same time able to support growth of L. monocytogenes (Fig. 2). The data presented lend support to categorization of Gouda, feta and Cheddar as a category 1.3 food with levels not exceeding 100 colony forming units per gram (cfu/g) in five samples (n = 5) for products placed on the market during their shelf-life. Feta has an average pH of 4.65 and a total lactic acid content of 14 g per kg cheese; the undissociated lactic acid concentration is thus calculated to be 29.8 mM ( Table 2). Cheddar has an average pH of 5.2 and a total lactic acid content of 15.0 g per kg cheese, resulting in an undissociated lactic acid concentration of 13.9 mM (Table 2). In all challenge studies with Cheddar and feta, no growth of L. monocytogenes was observed (Fig. 2), except for the study by Cui et al. (2016). The concentrations of undissociated lactic acid in the cheeses in their study are unknown, as acid content, pH, and salt content were not specified and there may have been mould growth (resulting in pH increase) as a commercial product was used. For high-moisture mozzarella, growth was observed and predicted, therefore categorization as a 1.2 food is suggested, especially in high-moisture mozzarella-type cheeses with pH >5.18 (then <6.35 mM undissociated lactic acid is calculated). For category 1.2 foods, the following food safety criteria apply: The cheeses queso fresco and Camembert can be categorized as category 1.2 foods, requiring absence of L. monocytogenes in 25 g (n = 5) before the food has left the immediate control of the food business operator, who has produced it. In queso fresco and Camembert, average pH values are 6.36 and 6.06 and average total lactic acid contents are 1.0 and 10.0 g per kg cheese, respectively, corresponding with undissociated lactic acid concentrations of 0.09 mM and 1.01 mM, respectively. As the calculated concentrations of undissociated lactic acid are much lower than the average and maximum MICs of 5.11 and 6.35 mM, respectively, for L. monocytogenes (Wemmenhove et al., 2016a), it is unlikely that undissociated lactic acid is an Table 3 Overview of listeriosis outbreaks in 1983-2019 that were related to consumption of cheese. Compiled from EFSA reports (Eurosurveillance), CDC reports, Google and a general search in Web of Science and Scopus (keywords 'listeriosis' and 'cheese', or 'Listeria', 'outbreak' and 'cheese', sorted on relevance, first 300 hits).
(   Classification of different types of cheese, with regards to food safety criteria. Classification is based on the association with listeriosis in the past (+ when linked), the minimum and maximum value for ∆logN•ln(10) t as calculated from data from challenge studies (+ when positive values were obtained; +/− when sometimes positive values andwhen no positive values were obtained for ∆logN•ln(10) t ) and the predicted specific growth rates (μ) using the Gamma model with average values of the individual factors undissociated lactic acid, temperature (T), pH and a w in the cheese as listed in Table 2, without including a lag time and μ opt = 1.69 h − 1 and 0.73 h − 1 (equaling the maximum and average optimum growth rates for L. monocytogenes in milk as extracted from Combase (www.combase.cc) when searching for growth rates of L. monocytogenes in milk at 30-37 • C, and a MIC of undissociated lactic acid for L. monocytogenes of 6.35 mM according to Aryani et al. (2015).

Type of cheese
Cheese category and risk ranking according to FDA Associated with identified cases of listeriosis in the past (based on * +/− , because 2 out of 45 specific growth rates obtained from literature were positive. On the surface of commercial Cheddar, 2 positive growth rates were obtained by Cui et al. (2016), but the validity of these data is questionable, as no data on pH, a w or possible mould growth were available.
important growth-inhibiting factor in these cheeses. In practice, queso fresco and Camembert cheeses have been linked with listeriosis cases on several occasions (Table 3), and growth of L. monocytogenes was supported in challenge studies that were performed with these cheeses. When a food is categorized as an RTE food product able to support growth of L. monocytogenes, stringent control measures, supplemented with sampling for verification, need to be in place. In such cheeses, heat treatment of the raw milk becomes an even more important factor to reduce the risk of contamination with L. monocytogenes. Pasteurization is an effective measure to reduce the risk of contamination of cheese products with L. monocytogenes via raw milk. A minimal heat treatment of 15 s at 72 • C leads to an average reduction of 10.4 log cfu/g based on an average D value and by 2.7 log cfu/g based on a 95% upper confidence interval for the D value (den Besten and Zwietering, 2012).
In the case of cottage cheese, sorbic acid may be added which inhibits growth of L. monocytogenes (Østergaard et al., 2014; Østergaard et al., 2015). Those additional hurdles and storage regimes are very cheese-specific and not included in our model. Undissociated lactic acid has been shown to play a major role in the inhibition of growth of L. monocytogenes in various cheeses. In the cheeses Cheddar, feta and Gouda, undissociated lactic acid is expected to lead to full growth inhibition. A low water activity, such as in blue cheese, can be an additional critical factor for growth, and can inhibit growth of L. monocytogenes together with temperature and pH. In cheeses associated previously to listeriosis such as Camembert, ricotta and cottage cheese, there is insufficient undissociated lactic acid for full growth inhibition, and therefore additional factors for growth inhibition are required.
To safeguard the safety of cheeses with respect to L. monocytogenes, critical control points such as pasteurization must be validated and verified, post-processing contamination prevented, and product composition and storage conditions designed so that levels do not exceed specified limits. The presented model will be a valuable tool to assess potential outgrowth of the pathogen in cheeses that contain lactic acid as the main acid.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.