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Modelling the probability of Listeria monocytogenes growing in cheese

Commercial cheese correctly manufactured with pasteurised milk and lactic starter cultures has a well deserved reputation as a nutritious and safe product. However, under certain circumstances cheese may support the growth of food poisoning bacteria or serve as a ‘vehicle’ for their transmission.

Four pathogens are of particular significance, *Listeria monocytogenes*, *Salmonella* species, enteropathogenic *Escherichia coli* and *Staphylococcus aureus*. *Listeria monocytogenes,* the causal agent of listeriosis, is arguably the most significant of this group.

*L. monocytogenes i*s particularly significant since it can grow / survive for long periods in cheese and cause serious illness leading to death; the death rate arising from listeriosis can exceed 30%. It can also induce abortion in humans and its ability to cross the placenta, and access the brain makes it a particularly dangerous pathogen.

This article provides an introduction to the binary and ordinal logistic regression models developed by Bolton and Frank (1999) for predicting the probability of *L. monocytogenes* growing in cheese after 42 days storage at 10°C.

**Characteristics of ***Listeria monocytogenes*

*L. monocytogenes* is a Gram-positive, non-sporing bacterium that can grow in high salt environments (up to 10 % sodium chloride), and over a wide pH (5.0-9.6) and temperature range (< 3° – 45°C); it can grow aerobically and microaerophilically ( Bajard *et al., *1996; Pearson and Marth, 1990).

While the organism is relatively sensitive to heat there has been considerable debate regarding its sensitivity to pasteurisation. While D _{71-72°C } values have generally been reported as < 4s, a D_{72}_{°C }value of 4.6 ± 0.5 s has been reported (Bunning *et al.,* 1992) for heat-shocked cells. Assuming a D_{72°C }value of 5s and raw milk containing 1000 (a high value) CFU / ml, pasteurisation at 72°C for 15s would be predicted to result in around 1 CFU / ml surviving (see http://www.dairyscience.info/newcalculators/listeria-d.asp) emphasising the critical importance of ensuring only low concentrations of this pathogen in raw milk.

**Concentration of ***Listeria monocytogenes *in raw milk

Precise information on the concentration of this pathogen in raw milk is not available. Generally it would appear that the concentration is usually <10 CFU / ml but higher concentrations of the order of 10^{3 }CFU/ml and above have been reported.

Bemrah *et al. *(1998) have simulated the distribution of *L. monocytogenes* in milk prior to cheesemaking; values ranging from 0 to 32.68 CFU / ml with a mean of 1.29 and a median of 0.32 CFU /ml were calculated. The probability of milk being contaminated was estimated to be 67%.

Poorly made silage has been reported to contain around 10^{7 }CFU / g and may be a significant source of *L. monocytogenes *on some farms (Wilesmith and Gitter (1986). Mastitis due to *L. monocytogenes *has also been reported and infected animals can produce milk containing around 10^{6 }CFU / ml.* *

* ***Growth and survival of ***Listeria monocytogenes* in cheese

Mexican-style soft fresh cheeses (similar to those involved in the listeriosis outbreak in 1985) are characterised by relatively high pH values, mean pH 5.8, with a mean salt in moisture of 3.61%. Lactic starter cultures are generally not used and acidification is achieved using organic acids such as lactic, citric or acetic. It is now known that these conditions provide an excellent growth medium for *L. monocytogenes.*

While some food borne pathogens are inhibited by the growth of the lactic acid bacteria used as starters the experimental data do not consistently support their antimicrobial activity against *L. monocytogenes.* Nevertheless there is some evidence to suggest that lactic cultures can at least inhibit the growth of the pathogen.

Slow growth to potentially high cell densities can be expected if *L. monocytogenes *is present in soft cheeses such as Brie, Camembert, Feta and Cottage cheese.

Slight growth of *L. monocytogenes *can be expected in correctly manufactured Cheddar cheese of normal compositional quality followed by a slow decline over many months.

**Minimum infective dose**

Precise information is not available. Normal healthy individuals are presumed to be fairly resistant but individuals with compromised or weak immune systems including those with cancer, the elderly, newborn, pregnant women, HIV sufferers and organ recipients are particularly susceptible. Concentrations between 10^{2} and 10^{3} CFU/ml or even lower may be sufficient to cause listeriosis in susceptible individuals.

**Permitted concentration of ***Listeria monocytogenes* in food

Current EC regulations (Regulation(EC) No 2073/2005) permit 100 CFU/g of *L. monocytogenes* in ready to eat food regardless of whether the pathogen can grow in the food. This is somewhat contentious in that some scientists argue that there is significant inherent risk in having this concentration of pathogen in any product that supports its growth.

**Overview of cheese borne listeriosis**

Cheese has been implicated in a number of major outbreaks of listeriosis in Europe and North America. An outbreak in California in 1985 was shown to be due to the consumption of Mexican-style fresh cheese (Linnan *et al*., 1988). There were some 86 cases of listeriosis; many involved mothers and their young children. At least twenty nine deaths occurred (33.7% mortality). Following investigation of the outbreak it has been suggested that the producers of the cheese may have mixed raw and pasteurised milk or that post pasteurisation contamination may have caused the problem (Silliker, 1986).

Between 1983 and 1987, Switzerland experienced a long-lasting outbreak of listeriosis, 122 cases, due to the contamination of a locally produced soft cheese, 31 were fatal (25.4% mortality, Billie *et al*., 2006).

Two major outbreaks linked to the consumption of Brie de Meaux (Goulet *et al*., 1995) and soft cheeses (RNSP, 1997) have been reported in France.

Tome cheese was implicated in a further outbreak of listeriosis in Switzerland in 2005. Within a period of 7 weeks, 10 cases of listeriosis were diagnosed; four of the cases were in men and six were in women (two of which were pregnant). Three patients died (42.9 % mortality) and both pregnancies ended in septic abortion. *L. monocytogenes* at 32 000 CFU / g was found in the cheese. Microbiological studies revealed that the factory environment was extensively contaminated with *L.* *monocytogenes *(Billie *et al.,* 2006).

Fretz *et al* (2010) reported an outbreak of listeriosis in Austria and Germany due to the consumption of ‘Quargel’ cheese. The outbreak accounted for 14 cases in 2009, including four deaths.The cheese product was voluntarily withdrawn from the market on 23 January 2010. The outbreak was identified by molecular typing.

Following confirmation that a *L. monocytogenes* 1/2a isolate from the production plant was indistinguishable from the outbreak strain by genotyping Quargel cheese products were sampled at the production plant. The authors reported that investigations on January 13 yielded three different strains of* **L. monocytogenes* 1/2a, including the outbreak strain, in numbers < 100 CFU/g per gram. However cheese sampled later (18 January 2010) yielded greater than 100 CFU/g *L. monocytogenes*.

Growth / no-growth models for predicting the growth of *Listeria monocytogenes* in Mexican-style fresh cheese after 42 days storage at at 10°C.

Bolton and Frank (1999) used binary and ordinal logistic regression to model the behaviour of *L. monocytogenes *in a cheese-based model system over a range of pH, salt and moisture content. Two models were developed, a binary regression and an ordinal logistic regression model. The binary regression model can be used to predict the probability of growth or no growth of *L. monocytogenes.* The ordinal logistic regression model can also be used to assess the probability of growth, but will also predict the probability of death or stasis (no growth) occurring within the range of data inputs used to formulate the model.

**Binary logistic regression model:** The binary logistic regression model can be described using equation 1.

Equation 1, Logit (P) =-13.609 + 2.8859(pH)-0.405 (%S/M), where pH represents the pH of the cheese, P is the probability of growth occurring and S/M is the concentration of sodium chloride in the cheese moisture; note Bolton and Frank (1999) use an equivalent term 'brine' rather than S/M.

Logit (P) is a mathematical abbreviation for ln [P/ (1-P)]. The values in equation 1 can easily be calculated using an Excel spreadsheet. Some students find difficulty in simplifying the logit expression and an explanation of how to do this is provided below assuming that logit =-5.664.

If Ln (P/1-P) = -5.664 (equation 1), what is the value of P?

Convert both sides of the equation to exponents of the base e.

Then e ^{ln (P/1-P) }_{=} e ^{-5.664}

Since the base of a logarithm and the base of an exponent are the same, equation (1) can be rewritten to give:

(P/1-P)= e ^{-5.664}

Taking e as 2.72,

e ^{-5.664 }= 0.0034

Then (p/1-P) =0.0034

Simplifying

P = 0.0034

1-p 1

P= 0.0034-0.0034p

1.0034p=0.0034

P= 0.0034/1.0034

=0.0034 or 0.3%

**Ordinal regression model:** The ordinal logistic regression model (Bolton and Frank, 1999) can be described using equations 2 and 3.

The probability of *L. monocytogenes *growth occurring is given by equation 2.

Equation 2, Logit (θ_{1}) =-13.291 + 2.672(pH)-0.376 (%S/M), where pH represents the pH of the cheese, θ_{1} is the probability of growth occurring and S/M is the concentration of sodium chloride in the cheese moisture; note Bolton and Frank (1999) use an equivalent term 'brine' rather than S/M.

The probability of *L. monocytogenes *growth occurring or *L. monocytogenes* survival is given by equation 3.

Equation 3, Logit (θ_{2}) =-11.591 + 2.672(pH)-0.376 (%S/M), where pH represents the pH of the cheese, θ_{2} is the probability of growth occurring and S/M is the concentration of sodium chloride in the cheese moisture; note Bolton and Frank (1999) use an equivalent term 'brine' rather than S/M.

The probability of growth occurring is given by Logit (θ_{1}), the probability of stasis by Logit (θ_{2})-Logit (θ_{1}) and the probability of death occurring by 100-Logit (θ_{2})._{ }

Logit (θ_{1}) and Logit (θ_{2}) are mathematical abbreviations as described and solved for ln [P/ (1-P)] above.

**Observations on the models**

Bolton and Frank (1999) reported that the binary model correctly predicted growth in 87% of trials. The ordinal logistic model had a 84.3% concordance with observed experimental responses.

Salt/moisture and pH conditions calculated to give 5% probability of growth with the binary model did not allow growth of *L. monocytogenes *under experimental conditions. Salt/moisture and pH conditions calculated to give 50% growth were found to allow the growth of *L. monocytogenes * in 66% of trials.

Judgement is required to set the position or value of the growth-no-growth interface by selecting a particular value of P, θ_{1,} or θ_{2} , the probability that growth will occur e.g. a P value of 10% may be appropriate for the binary model.

During validation, Bolton and Frank (1999) found that the model also worked with cheeses other than Mexican-style fresh cheese and suggested that it may have value with cheeses that have pH and salt in moisture values within the range used for model development.

The models were validated using a temperature of 10°C; the antimicrobial effects of acid and salt on *L. monocytogenes* are temperature dependent and increase with temperature. Since the antimicrobial effects of acidity are decreased at low temperatures caution should be used in using the model at storage temperatures significantly less than 10°C.

The models were not designed to account for the anti-listerial activity of lactic starter cultures.

Explore the binary logistic regression model **Explore the ordinal logistic regression model **

**Literature cited**

Bajard, S., Rosso, L., Fardel, G. and Flandrois, J. P. (1996). The particular behaviour of *Listeria monocytogenes* under sub-optimal conditions. Int. J. Food Microbiol. 29:201–211.

Bille *et al*. (2006). Outbreak of human listeriosis associated with tomme cheese in northwest Switzerland. Eurosurveillance, 11, Issue 6. Available from: http://www.eurosurveillance.org/ViewArticle.aspx?ArticleId=633.

Bunning, V. K., Crawford, R. G, Tierney, J. T. and Peeler, J. T. (1992). Thermotolerance of Heat-Shocked Listeria monocytogenes in Milk Exposed to High-Temperature, Short-Time Pasteurization. Appl. and Environ. Microbiol., 58: 2096-2098.

Bolton, L.F. and Frank, J.E. (1999). Defining the growth/no-growth interface for *Listeria monocytogenes* in Mexican-style cheese based on salt, pH and moisture content. J. Food Prot. 62, 601-609.

Fretz R., Sagel, U., Ruppitsch W., Pietzka, A.T., Stöger, A., Huhulescu, S., Heuberger, S., Pichler, J., Much, P., Pfaff, G., Stark, K., Prager, R., Flieger, A., Feenstra O., Allerberger, F. (2010) Listeriosis outbreak caused by acid curd cheese ‘Quargel’, Austria and Germany 2009. Euro Surveill. 15(5):pii=19477. Available online: http://www.eurosurveillance.org/ViewArticle.aspx?ArticleId=19477 .

Goulet, V., Jacquet, C., Vaillant, V., Rebiere, I., Mouret, E., Lorente, C., Maillot, E., Stainer, F., Rocourt, J. (1995). Listeriosis from consumption of raw-milk cheese. Lancet 345, 1581-1582.

Linnan, M.J., Mascola, L., Dong Lou, X., Goulet, V., May, S., Salminen, C., Hird, D.W., Yonekura, L.M., Hayes, P., Weaver, R., Audurier, A., Plikaytis, B.D., Fannin, S.L., Kleks, A., Broome, C.V., (1988). Epidemic listeriosis associated with Mexican-style cheese. N. Engl. J. Med. 319, 823-828.

Pearson, L. J. and Marth, E. H. (1990). *Listeria monocytogenes-*Threat to a Safe Food Supply: A Review. J. Dairy Sci. 73:912-928.

RNSP (1997). Epidémie de listériose 1997, Rapport du Reseau National de Santé Publique, France. Available from: http://www.invs.sante.fr/publications/listeriose/ .

Silliker, J. H. (1986). *Listeria monocytogenes. *Food Technol. 40(8):24.

Wilesmith, J.W. and Gitter, M., (1986). Epidemiology of ovine listeriosis in Great Britain. Vet. Rec. 119, 467-470.

**How to cite this article**

Mullan, W.M.A. (2009).
[On-line]. Available from: __https://www.dairyscience.info/food-model/178-listeria-model.html .__ Accessed: 17 September, 2019.
Updated 21 February 2010.