The presence of L. monocytogenes in cooked meat products is often due to post heat-treatment recontamination. Processing lines with equipment that is difficult to clean properly (Nesbakken et al., 1996) plays a significant role in the contamination of meat products with L. monocytogenes (Wenger and Salvat). Effective cleaning and the implementation of HACCP-systems might contribute making the products free from pathogenic bacteria, but these steps are not always sufficient.

For products that are consumed without additional heat treatment, such as sliced meat products, the safety of the product can be enhanced by adding substances that act like hurdles to the growth of L. monocytogenes. Such hurdles are, for example, pH-lowering substances, sodium chloride and different organic compounds. Salt of organic acids that are described in the literature as effective against bacterial growth are, for example, sodium lactate and sodium acetate (de; Chen; Schlyter; Qvist and Wederquist et al., 1994).

When formulating hurdles for meat products and other foods, mathematical models that predict the bacterial growth under various combinations of inhibitory factors are very useful. The number of effective combinations to be experimentally verified in inoculation studies may be reduced using predictive modelling. When developing models, a significant amount of growth data must be collected. Since viable count measurements are time-consuming, a more convenient method for collecting the growth data may be required. An alternative method for the collection of growth data is absorbance measurement (for example McMeekin; Dalgaard; Dalgaard and Neumeyer). However, when developing a model based upon absorbance measurements, the relationship between growth when measured as viable count and growth when measured as absorbance must be established, since growth rates calculated from absorbance data may differ from those calculated from viable count data ( Dalgaard et al., 1994).

Models for L. monocytogenes and Listeria innocua have been published (for example Cole; Duh; Houtsma; Fern; McClure and Membr), and the commercially available Food MicroModel, (Food MicroModel Ltd., Leatherhead, UK) includes two growth models for L. monocytogenes. These models include one or more of the factors temperature, pH, sodium chloride, sodium lactate and sodium nitrite. The present paper describes a mathematical model for predicting the growth of L. monocytogenes at different levels of pH, sodium chloride, sodium lactate and sodium acetate, at 9°C and in a medium supplemented with 70 ppm sodium nitrite. Collection of the growth data was done using absorbance measurements in broth cultures and the absorbance measurement was evaluated. The model was compared to the Food MicroModel, and validated against the growth of L. monocytogenes in a meat product.

2. MATERIAL AND METHODS

2.1. Strains

A cocktail of L. monocytogenes 167 (serotype 4b), L. monocytogenes 187 (serotype 4b) and L. monocytogenes 2230/92r (serotype 1) was used in the experiments. L. monocytogenes 167 was isolated from a knife in a meat production plant; L. monocytogenes 187 from a cooked sausage and strain L. monocytogenes 2230/92 from a second type of cooked sausage implicated in a listeriosis outbreak in Norway. L. monocytogenes 2230/92r was a rifampicin resistant mutant of 2230/92. Stock cultures of each strain were prepared by centrifuging (5000 rpm, 4°C, 15 min) a 20 h culture in BHI-broth incubated at 37°C, (subcultured twice for 24 h each at 37°C). The pellets were resuspended in BHI-broth with 10% glycerol and kept in aliquots at −80°C.

2.2. Inoculum

From each stock culture, 40 l of the glycerol suspension was cultured in 10 ml of BHI broth (28°C, 24 h), 100 l of each culture was subsequently transferred to 10 ml of BHI broth and subcultured (28°C, 24 h). A cocktail (1:1:1) of the strains was used as the inoculum. The inoculation level was 10⁷ cfu/ml (1%, v/v).

2.3. Medium

The basal medium contained 2.0% tryptose (Oxoid L47), 0.2% D-glucose (BDH 10117), 0.05% sodium ascorbate (Kebo 1.8601) and 70 ppm sodium nitrite (Fluka 71759). The pH was adjusted with phosphate buffer (combinations of 0.2 M disodium hydrogenphosphate, Fluka 71644 and 0.2 M sodium dihydrogenphosphate, Merck 6346). Appropriate amounts of sodium chloride (Sigma S3014), sodium lactate (Sigma L7022) and sodium acetate (Fluka 71180) were added.

2.4. Growth measurements

The inoculated medium was incubated in microtiter plates with 400 l of culture in each well. The wells were covered with 50 l of paraffin. Uninoculated controls were used in parallel to check the sterility of the medium.

2.4.1. Absorbance measurement

The growth was followed by absorbance measurements in Bioscreen C using the Biolink software (Labsystems Corp. Helsinki, Finland). The measurements were performed at wavelengths of 450–580 nm (wide band).

2.4.2. Viable count measurement

Samples were taken from the wells, diluted and pour-plated in BHI agar. The agar plates were incubated at 29°C for 3 days.

2.5. Calculation of the maximum specific growth rate

Absorbance values were transformed to log_e (absorbance). The transformation factor log_e was calculated from a Box–Cox transformation and Bartlett’s test of homogeneity of variances (Sokal and Rohlf, 1981). Viable count data were transformed to log₁₀ (colony forming units, cfu). Values of maximum specific growth rate (_max) were calculated by fitting the growth curves with the equation described by Baranyi (Baranyi and Roberts, 1994), using the DMFit program and the default value m=1 (IFR Reading Laboratory, UK).

2.6. Evaluation of absorbance measurements

Values of absorbance and viable count were determined for a dilution series of a log phase culture of the L. monocytogenes cocktail grown at 25°C for 24 h in basal medium at pH 6.2 and supplemented with 2.5% sodium chloride and 1% glucose. The viable count data, expressed as log₁₀ cfu, were plotted against the absorbance data to establish the detection level of the instrument.

The linearity of the absorbance measurements was studied by calculating the relationship between the absorbance of different dilutions of the inoculum in the medium using analyses of variance (Systat Inc., Evanston, IL USA). The relationship between the absorbance measurements and the viable counts was calculated using the Pearson correlation matrix (Systat Inc).

The relationship between the values of _max obtained from viable count and absorbance measurements was evaluated in basal medium at pH 6.5, supplemented with a total of five combinations of sodium chloride (1.0 and 4.0%), sodium lactate (0 and 5%) and sodium acetate (0 and 0.6%). The inoculated medium was incubated at 9°C for 30 days. Absorbance and viable count measurements were made on duplicate samples during the incubation period, and the _max-values were calculated.

The effect of the inoculum level (10¹–10⁷ cfu/ml) on the _max was determined in basal medium at pH 6.2, supplemented with 2.5% sodium chloride and 2.5% sodium lactate. The absorbance was measured on duplicate cultures during anaerobic incubation at 25°C for 4 days.

2.7. Modelling

The effect of different levels of the factors pH, sodium chloride, sodium lactate and sodium acetate on the growth of L. monocytogenes was studied in the basal medium at 9°C for 30 days. The levels of the different factors studied are given in Fig. 1. The basal medium, having 17 combinations of pH and sodium chloride, was inoculated and appropriate levels of sodium lactate and sodium acetate were subsequently added.

 

 

Fig. 1. Values of variables applied for the development of the model of the growth rate of L. monocytogenes. In total, 56 combinations were studied. The figure illustrates the levels of (circle) sodium lactate and (triangle) sodium acetate at pH (a) 5.5, (b) 6.0, (c) 6.2, (d) 6.4 and (e) 6.5.

 

The fractional factorial design used was developed using the statistics program Modde (Umetri Umeå, Sweden). In total, 95 absorbance curves were obtained, whereof 39 were duplicates. For each curve, the _max was calculated, as described above. A Response Surface Model (RSM), consisting of two Central Composite Faced Centred designs (CCF) with 28 experiments each, was developed using Multi Linear Regression.

The model applied was:

(1)
_max=constant+k₁*pH+k₂*NaCl+k₃*lactate+k₄*acetate+
k₅*pH*pH+k₆*NaCl*NaCl+k₇*lactate*lactate+k₈*acetate*acetate+
k₉*pH*NaCl+k₁₀*pH*lactate+k₁₁*pH*acetate+k₁₂*NaCl*lactate+
k₁₃*NaCl*acetate+k₁₄*lactate*acetate

3.3. Validation of the model

The developed model was compared to the Food MicroModel (FMM), which is based on viable count measurements. The relationship between the _max predicted from the two models is shown in Fig. 5; the _maxabs-values were transferred to _maxvc using Eq. (4). The bias factor was 0.84 and the accuracy factor 1.20. Thus, the developed model showed a slight underprediction of the growth rates, when compared to the Food MicroModel, and the predictions were, on average, 16% below the ones of the FMM. The predictions of the models were, on average, within 20% of the ones of the FMM. The correlation between the predictions from the two models was, however, good, with a correlation coefficient of 0.91.

 

 

Fig. 5. Maximum specific growth rates of L. monocytogenes predicted from the developed model versus those predicted from the Food MicroModel.

 

The developed model was also validated against the growth of L. monocytogenes in a cooked meat product. Fig. 6 shows the relationship between the values of _max predicted using the developed model and the _max calculated from the growth of L. monocytogenes, measured as viable count, in the product. It can be seen that the predicted values of _max were lower than the values of _max, observed in the product. The bias factor was 0.84, the accuracy factor 1.26 and the correlation coefficient 0.98.

 

 

Fig. 6. Maximum specific growth rates of L. monocytogenes predicted from the developed model versus those observed in an emulsion-type sausage stored vacuum-packed at 9°C.

 

4. DISCUSSION

Absorbance measurements were, in the present study, demonstrated to be a reliable, precise and convenient method of collecting the growth data. Using the Bioscreen, data points were gathered continuously and the growth curve fitting was based upon a large number of data points. Some possible drawbacks using absorbance measurements are: the non-linearity of absorbance measurements, the high detection level, and the possible displacement of the absorbance growth curve towards the late exponential growth phase, as opposed to the viable count growth curve (Dalgaard and McMeekin). In the present study, the absorbance measurements were linear in the absorbance interval studied. Dalgaard et al. (1994) found, in their study, that the absorbance response was non-linear and concluded that the non linearity seems to be related to the spectrophotometer, rather than the growth medium or the bacterial strain.

When studying bacterial growth from viable count measurements, the inoculum level is usually between 10¹–10³ cfu/ml. In the present study, the inoculum level used was equal to the detection level, i.e. about 10⁷ cfu/ml. This high inoculum level did not, however, affect the maximum specific growth rate of L. monocytogenes; an inoculum level between 10¹ and 10⁷ cfu/ml provided the same growth rate. Furthermore, there was a linear relationship between the values of the maximum specific growth rates derived from the absorbance, and the ones derived from the viable count measurements. Dalgaard et al. (1997) and Neumeyer et al. (1997) also found in their studies, that turbidimetric data could be used instead of viable count measurements for growth rate estimations. The conclusion is that absorbance measurements may be used for model development, a conclusion that is in accordance with Begot and Dalgaard and Neumeyer et al. (1997).

A drawback using absorbance measurements is that the high detection level makes it difficult to measure the lag time. Knowledge of the lag time is important when predicting the risk for bacterial growth during storage of meat products. In the estimation of product safety the lagtime should therefore be included.

The developed model demonstrated a high correlation with predictions from the Food MicroModel. Predicted values using the developed model were, however, lower than the ones predicted using the Food MicroModel. An underprediction was also obtained in comparison to the growth observed in four vacuum-packed, sliced emulsion-type sausages with different combinations of pH, NaCl and Na-lactate levels (Blom et al., 1997). The sliced emulsion-type sausage used in the validation contained NaCl supplemented with NaNO₃, providing an initial concentration of 50 ppm; after cooking, the analysed level of free NaNO₃ was 5 ppm. The observed underprediction could be due to a lower nitrite level in the product (5 ppm), compared to the growth medium (70 ppm) used when developing the model. Nitrite is reported to inhibit the growth of L. monocytogenes. In smoked salmon, the addition of 190–200 ppm NaNO₃ inhibited the growth of L. monocytogenes at 5°C (Pelroy et al., 1994). Using a bacteriological medium, 200 ppm NaNO₃ totally inhibited the growth of L. monocytogenes (5°C, pH 6.0, 0.5 or 4.5% NaCl), while at levels between 0 and 100 ppm the growth rates were similar (Buchanan et al., 1989). It is not known whether it is the reacted nitrite or the free nitrite in a meat product that has an inhibitory effect on L. monocytogenes.

The growth of L. monocytogenes was significantly affected by the single factors pH, NaCl, Na-lactate and Na-acetate. This has also been reported by others (Buchanan; Cole; Schlyter; Wederquist et al., 1994 and Fern). The combined effect of lactate and acetate is also demonstrated to have an antilisterial effect. A combination of ≥0.1% diacetate and 2.5% lactate is reported to inhibit the growth of L. monocytogenes in turkey slurries, held at 4°C (Schlyter et al., 1993). In the present study, all interactions were statistically significant to the growth rate of L. monocytogenes. This opens up a large number of combinations that are conceivable for testing in real products. Using the developed model, various combinations may be tested by the computer before doing extensive inoculation studies on real products. This approach was applied in a study where the addition of lactate and acetate was successfully used to control the growth of L. monocytogenes in two cooked meat products during cold storage (Blom et al., 1997).

5. CONCLUSIONS

In conclusion, absorbance data were used for developing a model that included four factors (pH, NaCl, Na-lactate and Na-acetate). Comparison to the Food MicroModel, and observations on inoculated sausage showed, however, a slight underprediction for the maximum specific growth rates of L. monocytogenes.

ACKNOWLEDGEMENTS

The invaluable technical assistance of Mrs Britt Arvidsson is acknowledged. Predictions were made using the Food MicroModel Version 1, and are presented with the permission of Food MicroModel Ltd, Randalls Road, Leatherhead, Surrey KT22 7RY, UK. Financial support was obtained from Norway Meat Cooperative, the Norwegian Research Council, Norway and the Scan Group, Sweden.

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