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Modelling in food technology

Models in food technology, at the simplest level, are equations showing the relationship between two or more variables.  Dunn (1986) defined a mathematical model of a process as a 'system of equations whose solution, given specified input data, is representative of the response to a corresponding set of inputs'.

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Predicting the safety of products preserved using acetic acid

Commercially, cold-filled acidic pickles, sauces (e.g. salad cream, mayonnaise) and food dressings are preserved, and their microbiological safety assured, by the use of acetic acid, salt (NaCl) and sugar. This article provides an overview of a major preservation model and access to the model to enable the effect of sauce components and pH to be investigated.

The Comite´ des Industries des Mayonnaises et Sauces Condimentaires de la Communaute´ Économique Européenne (CIMSCEE) has provided guidance on a safety value, Σs, for a microbiologically safe product preserved using acetic acid (Anonymous, 1993). A safe product has been defined as one which is so formulated that when an inoculum of viable cells of  Escherichia coli is  added to the product this is reduced by 3 log cycles in less than 72 h. Products exhibiting this level of antibacterial activity have a CIMSCEE safety value (Σs) of greater than 63.

Σs is calculated using equation 1.

Equation 1.  Σs =15.75 (1 - ɑ) (total acetic acid %) + 3.08 (salt %) + (hexose %) + 0.5 (disaccharide %) + 40 (4-pH). 

The value (1 - ɑ) represents the proportion of acetic acid which is undissociated, this is dependent on a number of factors but principally on the pH of the aqueous phase of the product; using the pKa (4.76 at 25°C) for acetic acid and the pH of the aqueous phase, (1 - ɑ) can be calculated using the Henderson–Hasselbalch equation, equation 2, where pKa is the negative logarithm of the ionization constant (K) of an acid, this is the pH of the solution in which half of the acid molecules are ionised. Note that the pKa value is not an absolute one; it will vary with the ionic strength of a solution so salt addition for example will change the value. 

Equation 2. equation2

 Equation 2 can be simplified and rearranged to give:

(1 - ɑ) = 1/ (10pH-pKa +1) and

  (1 - ɑ) can then be calculated using e.g. an Excel spreadsheet.  Using Excel, the data can be entered as


=1/ (10^ (pH- pKa) +1)

where pH and pKa are replaced with their numerical values or appropriate spreadsheet cell references. This is also shown in the Excel graphic.

Using this formula the (1 - ɑ) values at say pH 3, and 5 can be calculated as 0.983 and 0.365 respectively. This means that at pH 3, 98 % of the acetic acid is undissociated compared with only 37 % at pH 5 (values have been rounded).

 Using equation 1 a technologist can adjust the formulation of cold-filled acidic pickles, sauces and food dressings to obtain a desired CIMSCEE value by varying e.g. the concentration of acetic acid (which will also affect the pH), salt and sugar in the product.

The CIMSCEE model is based on the work of Tuynenberg Muys (1971).

Mechanism of antimicrobial activity of  acetic acid

While acetic acid will decrease the pH and that in itself is inhibitory the general mechanism behind the inhibitory effect is considered to be associated with the undissociated acid. As pH decreases the proportion of acetic acid in its undissociated form increases; at pH 7 <1% is in this form increasing to some 98% at pH 3. 

The undissociated acid is understood to readily pass through the cell wall of microorganisms and in the relatively high pH of the cytoplasm, dissociates into hydrogen and acetate ions. The accumulation of hydrogen ions results in the internal pH of the cytoplasm dropping, damaging essential enzyme systems and ultimately causing cell death. The acetate anion may also exert antimicrobial effects.

Casey and Condon (2002) have shown that adding NaCl to broth containing E. coli  and acetic acid results in the pH of the cytoplasm of E. coli increasing; this may be the explanation for the acid protective effect experienced when salt is added to an acidic food product.

Limitations of the CIMSCEE model

 Food spoilage

The CIMSCEE model has several limitations; these are largely concerned with the design of Tuynenberg Muys (1971) original studies e.g. Tuynenberg Muys (1971) conducted his work at 20°C and hence this model cannot be easily applied to food stored at refrigerated tempertures.

Products with Σs values >63 are generally regarded as microbiologically stable at ambient temperatures. However, if they had been contaminated with the mould Moniliella acetoabutans, which can tolerate high concentrations of acetic acid, they will spoil; Moniliella acetoabutans can utilise acetic acid as a carbon source. Control is at the production level where this mould must be eliminated from the environment.

 Food safety

Modern commercially produced acidic sauces and dressings produced using acetic acid are not high-risk vehicles for food poisoning and  have a good safety history. However, there has been at least one outbreak of Escherichia coli O157:H7 associated with mayonnaise and mayonnaise based dressings (Weagant et al. 1994). This along with observations by several researchers that E. coli under certain circumstances can persist for significant periods in products produced using acetic acid has led to a number of investigations of the survival of  E. coli in these products and indirectly on the utility of the CIMSCEE safety value for assuring consumer safety.

These studies have identified that the model may give false-positives (survival predicted when experimental data showed death) when tests are undertaken at temperatures of 30°C (Chapman et. al., 2006). More importantly work has identified that Escherichia coli including VTEC strains can survive for days and in some cases many weeks when  mayonnaise is  held at low temperatures.

 It is clear that the absence of a temperature dependant variable is a weakness in this model; the antimicrobial effects of acetic and similar organic acids tend to increase with temperature.

 Other work has revealed that the CIMSCEE model gave false negatives (predicted death when survival occurred) when particular salt and or sucrose combinations were tested e.g. when the salt concentration was > 2.5% and/or when the sucrose concentration was > 4%, resulting in the suggestion that the model fails to take interactions between salt and sucrose into account (Chapman et. al., 2006).  Note the protective effects of salt and / or sugar for E. coli exposed to low pH have been found by others (Casey and Condon; 2002; McKellar et. al., 2002).

 Literature Cited

Anonymous (1993). Code for the production of microbiologically safe and stable emulsifed and non-emulsifed sauces containing acetic acid (The CIMSCEE code. In Shelf Life of Foods-Guidelines for its Determination and Prediction, pp. 49-51, London, Institute of Food Science and Technology.
Casey, P. G., and Condon, S. (2002). Sodium chloride decreases the bactericidal effect of acid pH on Escherichia coli O157:H45. Int. J. Food Microbiol. 76:199–206.
Chapman, B., Jensen, N.,  Ross, T. and Cole, M. (2006). Salt, alone or in combination with sucrose, can improve the survival of Escherichia coli O157 (SERL 2) in model acidic sauces. Appl. Environ. Microbiol. 72, 5165–5172.
McKellar, R. C., Lu, X.  and Delaquis, P. J. (2002). A probability model describing the interface between survival and death of Escherichia coli O157:H7 in a mayonnaise model system. Food Microbiol. 19, 235–247.
Tuynenburg Muys, G. (1971). Microbial safety in emulsions. Process Biochem. 6:25-28.
Weagant, S. D., Bryant, J. L. and Bark, D. H. (1994) Survival of Escherichia coli O157:H7 in mayonnaise and mayonnaise-based sauces at room and refrigerated temperatures. J. Food Prot. 57, 629-631.

 Evaluate the model

 
How to cite this article

Mullan, W.M.A. (2009) . [On-line]. Available from: http://www.dairyscience.info/index.php/food-model.html . Accessed: 24 April, 2014. Updated 2013.

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 aureusListeria monocytogenes, the causal agent of listeriosis, is arguably the most significant of this group.

L. monocytogenes is 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 D72°C value of 4.6 ± 0.5 s has been reported (Bunning et al., 1992) for heat-shocked cells.  Assuming a D72°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.

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