A probability model describing the interface between survival and death of Escherichia coli O157:H7 in a mayonnaise model system

Food Microbiology, 2002, 19, 235^247 Available online at http://www.idealibrary.com on

doi:10.1006/fmic.2001.0449

ORIGINAL ARTICLE

A probability model describing the interface between survival and death of Escherichia coli O157:H7 in a mayonnaise model system R. C. McKellar1; *, X. Lu1 and P. J. Delaquis2

A probability model was developed to describe the in£uence of temperature (10^301C) and factors characterizing the composition of mayonnaise (salt [0?5^16?5%], pH [3?5^6?0], acetic acid [0^4%] and sucrose [0^8%]) on the survival of Escherichia coli O157:H7 in tryptic soy broth. pH was adjusted independently by the use of HCl or NaOH. Logistic polynomial regression with a total of 1820 factor combinations was used to describe the in£uence of main, quadratic, and cross-product e¡ects of the environmental factors. The model successfully predicted survival or death in 1772 (97?4%) of the samples; of those incorrectly predicted, 28 were false-positive (survival predicted where death occurred) and 20 were false-negative (death predicted where survival occurred). The concordance index was 99?4% and the disconcordance index was 0?6%, indicating a good ¢t of the model to the observed data. The model was validated using survival data from experimental mayonnaise inoculated with E. coli O157:H7. Of 30 combinations of acetic acid, salt and sucrose tested, survival/death was incorrectly predicted by the model in only six cases and, of these, only one prediction was not ‘fail-safe’. This prediction was attributed to the in£uence of quadratic e¡ects in the model, and to attempts to make predictions outside the boundary of experimental conditions. The results suggest that the probability model developed here can be usefully applied to predictions of E. coli O157:H7 survival in mayonnaise. Crown Copyright # 2002 Published by Elsevier Science Ltd. All rights reserved.

Introduction Current methods for the manufacture of commercial mayonnaise rely on the use of pasteurized eggs to minimize the hazard posed by Salmonella. Products manufactured from unpasteurized eggs must have a pH
4?1, an acetic acid level in the aqueous phase of *Corresponding author: E-mail: mckellarr@em. agr.ca Contribution number S069 from the Food Research Program 0740 -0020/02/2^30235 +13 $35.00/0

1?4%, and be held for a period of 72 h before being shipped (Zhao and Doyle 1994, Raghubeer et al. 1995). In spite of these precautions, an outbreak of Escherichia coli O157:H7 was associated with mayonnaise and mayonnaisebased dressings (Weagant et al. 1994). In this and other studies (Raghubeer et al. 1995, Erickson et al. 1995) O157:H7 did not survive in mayonnaise under conditions (251C for 72 h) normally associated with the storage and distribution of mayonnaise. In contrast, other workers have shown that O157:H7 can survive in mayonnaise for up to 17 days at 201C (Zhao

Crown Copyright r 2002 Published by Elsevier Science Ltd. All rights reserved.

Received: 9 November 2001 1 Food Research Program, Agriculture and Agri-Food Canada, 93 Stone Road West, Guelph, Ontario, Canada N1G 5C9 2 Paci¢c Agri-Food Research Centre, Agriculture and AgriFood Canada, Summerland, British Columbia, Canada V0H1Z0

236 R. C. McKellar et al.

and Doyle 1994, Hathcox et al. 1995). Extended survival in mayonnaise has also been observed at refrigeration temperatures (Weagant et al. 1994, Zhao and Doyle 1994, Hathcox et al. 1995). These studies were performed in mayonnaise consisting of di¡erent formulations and under a wide range of storage temperatures. It is therefore di⁄cult to establish conditions clearly which would be expected to limit the survival of O157:H7. In addition, there is considerable potential for cross-contamination during the preparation of mayonnaise-based salads containing meat products. The observation that O157:H7 can grow at 211C in beef salad containing 40% mayonnaise emphasizes the potential hazard associated with recontamination of mayonnaise-based products with foodborne pathogens (Abdul-Raouf et al. 1993). Hence, a model which accurately predicts the behaviour of E. coli in mayonnaise or mayonnaise-based products is highly desirable. Kinetic models for bacterial growth/no growth have successfully predicted the behaviour of foodborne pathogens in many foods. Some of these models performed poorly when they were used to estimate conditions which approach those which limit growth (Sutherland et al. 1995, Neumeyer et al. 1997). It has been suggested that the distinction between traditional probability and kinetic models is closing, and that a combined approach incorporating aspects of each would be more appropriate for modelling the interface between growth and death (Ross and McMeekin 1994). Ratkowsky and Ross (1995) have proposed a probability model based on logistic regression, and this approach has been used with a modi¢ed square root model to describe the in£uence of temperature, pH, aw and nitrite on the probability of growth. This approach was extended to the study of E. coli and the in£uences of temperature, pH, lactic acid and aw on growth (Presser et al. 1998). It would be useful to have a probability model which could predict survival/death of E. coli O157:H7 in mayonnaise; however, there are no reports on the use of logistic regression to model survival/death of a foodborne pathogen. Therefore, the purpose of the present study was to develop a probability model to describe the in£uence of temperature,

pH, salt, sucrose and acetic acid on the survival of E. coli O157:H7.

Materials and Methods Strains and culture conditions The following strains of Escherichia coli O157:H7 were described previously (McKellar and Knight 1999): C7927, C9490, 380 -94, EC940340 and EC920283. Stock cultures were prepared in tryptic soy broth (TSB; Difco Laboratories, Detroit, Michigan, USA) plus 15% w/v glycerol (BDH Inc.,Toronto, Ontario, Canada), and were frozen in 0?3 -ml aliquots in cryovials at 801C. Strains were subcultured from frozen stock twice in TSB for 24 h at 371C prior to use. A cocktail of the ¢ve strains was prepared by ¢rst culturing each separately in 5 ml of TSB at 301C for 24 h to stationary phase, then mixing the strains in equal proportions.

Development of survival model Media preparation. TSB was prepared with sucrose, salt and acetic acid, and the pH was adjusted with HCl or NaOH.The resulting solutions were ¢lter-sterilized using 0?45m Nalgene ¢lter units (Nalge Company, Rochester, New York, USA).

Experimental design. A fractional factorial experimental design with ¢ve factors was used in this study. The factors examined were temperature (10, 15, 20, 25, 301C), acetic acid (0, 0?5, 1, 1?5, 2, 2?5, 3, 4%), salt (0?5, 1?5, 2?5, 3?5, 4?5, 8?5, 12?5, 16?5%), sucrose (0, 4, 8%) and pH (3?5, 4, 4?5, 5, 5?5, 6?0), with a total of 1820 treatment combinations being tested. Data were collected with ¢ve replicates at each treatment combination. The inital experimental design was intended to explore the survival/death interface, and additional combinations of conditions were added as it became more di⁄cult to achieve the necessary log reduction in viable cell numbers (e.g. when salt and/or sucrose concentrations were high).

Survival experiments. The cocktail of strains (50 ml) was inoculated into ¢ve replicate

Survival and death of E. coli O157:H7 in a mayonnoise model 237

volumes of 5 ml of test media to produce starting populations of approximately 107 cfu ml1 , and incubated at the appropriate temperature for 72 h. Tubes were observed visually for growth, and non-growing samples were further diluted 100 fold into fresh standard TSB and incubated for a further 72 h at 371C. The continued absence of growth was taken as an indication of a 45?7 log reduction in viable cell numbers under the initial test conditions. Probability of survival (de¢ned as o5?7 log reduction in 72 h) was scored from 0 to 1, representing the proportion of the ¢ve replicates to demonstrate survival.

Model development. A logistic regression model was constructed based on the approach of Ratkowsky and Ross (1995) with the exception that these authors, along with others (Presser et al. 1998, Bolton and Frank 1999; Jenkins et al. 2000, LopezMalo et al. 2000), had developed models for the probability of growth. The model was of the form shown in equation 1:   P LogitðPÞ ¼ Ln ¼f ð1Þ 1P where P is the survival probability to be modelled, and f is de¢ned as in equation 2: f ¼ b0 þ b1 F1 þ . . . þ b5 F5 þ b12 F1 F2 þ . . . þ b45 F4 F5 þ b11 F12 þ . . . þ b55 F52 ð2Þ where bi and bij represent parameters to be ¢t, and Fi represents the ¢ve explanatory factors (temperature, undissociated acetic acid [UA], salt, sucrose and pH). In this model, all factors are considered as continuous variables. In place of the total acetic acid concentration, UA was used as a factor in the analysis, and was calculated using the Henderson^Hasselbach equation: ½Acetic acid ð3Þ 1 þ 10pHpKa where the acetic acid concentration is a percentage (v/v) and the pKa for acetic acid is 4?76. The model is an example of a generalized linear regression model with binomial error, logistic link function and linear predictor which consists of the main e¡ects, two-way interactions and quadratic e¡ects of ¢ve factors. The resulting model was implemented in AnaUA ¼

lyticas (Lumina Decision Systems, Los Gatos, California, USA) for the purpose of simulating conditions for validation of the model in mayonnaise.

Validation experiments Mayonnaise preparation. Mayonnaise was prepared according to a recipe representative of commercial formulations consisting of 80% w/w oil, 10% w/w whole egg and 10% w/w other constituents (vinegar, water, salt and sucrose). For experimental purposes, the portion of ingredients comprising the aqueous phase of the emulsion was set at 18?91% based on whole egg composition of 10?9% total lipids (Powrie and Nakai 1986). Formulations containing 0?5% salt and 0% sucrose were prepared with 1, 2, 3 and 4% acetic acid in the aqueous phase for survival studies at 5, 10, 15, 20, 25 and 301C. Formulations containing 4?5% salt and 8% sucrose were prepared with 2 and 3% acetic acid for survival studies at 20, 25, and 301C. An emulsion could not be maintained in mayonnaise containing 4?5% salt, 8% sucrose and 4% acetic acid, and this combination was not tested. Liquid whole egg was prepared fresh daily by blending six large size commercial eggs. Each formulation of mayonnaise was prepared by combining whole egg with distilled water, acetic acid, sodium chloride and sucrose. The ingredients were maintained at a cool temperature using an ice bath. Commercially available 100% canola oil (Canola Harvest, Lethbridge AB, Canada) was slowly added with constant mixing using a 280 -W hand-held blender (Braun Canada Ltd, Mississauga, Ontario, Canada) at high speed. The pH was measured using a Corning Model 140 pH meter and batches of mayonnaise were divided into several 25 -g samples which were sealed tightly and equilibrated overnight at the appropriate storage temperatures.

In£uence of acetic acid on pH. Mayonnaise was prepared according to the basic formulation given above. Additional constituents included 0?8% sucrose, 0?5% salt and 6?7% water. Twenty batches were prepared containing acetic acid in concentrations ranging from

238 R. C. McKellar et al.

0 to 0?8% (calculated concentrations of 0^4?2% in the aqueous phase). Controls were also done with acetic acid added to TSB. The resulting pH values were measured with a glass electrode.

Inoculation and microbiological analysis. The contents of one cryovial of each of the ¢ve strains of E. coli O157:H7 described above were transferred to TSB and incubated overnight at 371C. Cells were concentrated by centrifugation at 3220 g for 15 min using the Eppendorf 5810 centrifuge (Eppendorf, Hamburg, Germany). The supernatant was removed and the cells suspended in sterile distilled water. Mayonnaise samples (25 g) were immediately inoculated with 0?25 ml of cell suspension, blended for 30 s using the Stomacher Lab Blender Model 400 (Seward Medical, London, UK), and replaced at the appropriate storage temperature. Cell density of the inoculum preparation was determined at the start and the end of the procedure by preparing serial dilutions in 0?1% Bacto Peptone (Difco) and spread plating in duplicate on tryptic soy yeast extract agar [TSAYE: TSB supplemented with 5g l1 yeast extract (Oxoid, Basingstoke, UK) and 15 g l1 agar agar (BDH)]. Plates were incubated for 48 h at 371C. Inoculum levels in mayonnaise samples were established by calculation. Residual levels of E. coli O157:H7 in mayonnaise were determined after 72 h storage by diluting duplicate 25 g samples in 225 ml TSB, blending for 1 min, preparing serial dilutions in 0?1% Bacto Peptone and spread plating in duplicate on TSAYE. One ml of the initial 101 dilution was surface spread to give a resolution of 101 cfu g1. In addition, the initial 101 dilution was incubated for 72 h at 371C before being streaked onto TSAYE and MacConkey agar (Difco) to detect o101 cfu g1 by enrichment. Con¢rmation of colonies presumptively counted as E. coli O157:H7 was carried out by determining lactose fermentation on MacConkey agar followed by serological identi¢cation using E. coli O157 Test Kit (Oxoid). Several representative colonies were con¢rmed for each sample. All results were reported as log10 cfu 25 g1.

Statistical analysis The logistic model (equation 1) was derived using the SAS PROC LOGISTIC (SAS Institute Incorporated, Cary, North Carolina, USA), a procedure for ¢tting a logistic regression model. Automatic variable selection option with forward selection method was used to choose the most signi¢cant e¡ects (Po0?10). Fitting of a two-phase exponential decay function data showing the e¡ect of added acetic acid on pH in TSB and mayonnaise was performed using PrismTM (GraphPad Software, Inc., San Diego, California, USA).

Results A logistic model was derived using a total of 1820 treatment combinations; the parameter values are given in Table 1. With a probability of survival of Po0?5 taken as the cuto¡ point for death, a total of 1523 (83?7%) combinations of experimental conditions permitted survival over 72 h.The model successfully predicted survival or death in 1772 (97?4%) of the samples; of those incorrectly predicted, 28 were false-positive (survival predicted where death occurred) and 20 were false-negative (death predicted where survival occurred). A concordance index described by PROC LOGISTIC was used to assess the model performance. In this procedure, an event response was de¢ned as the response having an ordered value of 1 and a non-event response was de¢ned as the response having an ordered value of 2. A pair of observations with di¡erent responses is said to be concordant (discordant) if the observation with the response that has the larger ordered value has the lower (higher) predicted event probability. If a pair of observations with di¡erent responses is neither concordant nor discordant, it is a tie. The results showed that the degree of agreement between the probabilities predicted by the ¢tted model and all observations was 99?6% concordant and 0?6% discordant. This indicates a good ¢t of the model to the observed data. Figure 1 shows the relationship between model predictions and the experimental data. The survival/death interface with P = 0?5 (50%

Survival and death of E. coli O157:H7 in a mayonnoise model 239

Table 1. Parameter estimates for logistic regression model Coe⁄cient Intercept Sucrose UA pH Salt Temperature UA2 Temperature2 Salt2 Sucrose2 UA  pH Temperature  Salt Temperature  Sucrose pH  Sucrose UA  Sucrose

Degrees of freedom

Estimate

Standard error

Chi-square

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0?084 1?23 16?6 3?01 0?500 0?808 0?270 0?036 0?112 0?058 2?98 0?026 0?034 0?163 0?169

2?947 0?2577 1?359 0?6992 0?1198 0?0987 0?0947 0?0025 0?0076 0?0110 0?3314 0?0038 0?0071 0?0911 0?0437

0?0008 22?77 149?97 18?59 17?40 66?90 8?129 208?22 215?37 27?81 80?91 47?45 22?63 3?218 14?94

P 0?9773 0?0001 0?0001 0?0001 0?0001 0?0001 0?0044 0?0001 0?0001 0?0001 0?0001 0?0001 0?0001 0?0728 0?0001

UA, undissociated acetic acid calculated using the Henderson^Hesselbach equation.

probability of survival) is indicated by the solid lines; the broken and dashed lines represent predictions at P = 0?1 (more conservative) and P = 0?9 (less conservative), respectively. The pH interface as in£uenced by temperature with salt at 0?5% and acetic acid at 3% occurs at between 3?5 and 4?0 for 10 to 201C, increasing to 4?5 at 301C (Fig. 1a). The interface between P = 0?1 and P = 0?9 was abrupt over the whole temperature range. The in£uence of salt on the pH interface was also explored at 3% acetic acid using data from 301C (Fig. 1b). The interface, which was between 4?5 and 5?0 at 0?5% salt, was reduced slightly to between 4?0 and 4?5 at 1?0% salt and, similarly to the temperature pro¢le, the interface was abrupt over the entire range of salt concentrations. When the in£uence of acetic acid concentration was examined, some marked di¡erences were noted (Fig. 1c). At acetic acid concentrations of
0?5%, survival occurred at pH 3?5, the lowest pH tested. At 1^2% acetic acid, the interface was at pH 4?0^4?5, and at 3 and 4% acetic acid, it was at 4?5^5?0. In contrast to the temperature- and salt-dependent interfaces, the interface with acetic acid was broader at lower as compared to higher concentrations of acid (Fig. 1c). In addition, at 1^1?5% acetic acid, there were two incidents of partial survival (survival in 1^4 of the ¢ve replicates), which was probably responsible for the broad inter-

face seen in Fig. 1c. Generally, all ¢ve replicates show either all survival or all death. Partial survival was found in only 56 of the 1820 experimental conditions tested. The predictive ability of the model was compared with predictions made by a model developed at Unilever Research Laboratory by G. Tuynenburg Muys (Muys 1971). This model was part of the code for the production of microbiologically safe and stable emulsi¢ed and nonemulsi¢ed sauces containing acetic acid (known as the CIMSCEE code) which was developed for the European Sauces Trade Association (Anonymous 1993). The model is of the form: y ¼ 15 75UA þ 3 08  Salt þ 0 5  Sucrose þ 40ð4  pHÞ

ð4Þ

where UA is the undissociated acetic acid. If the value of y exceeds 63, pathogens are considered not to survive (assumed to be equivalent to Po0?5). This model correctly predicted 1587 (87?2%) of the experimental samples, with 106 false-positives and 127 false-negatives. For the purpose of simulating conditions which might exist in mayonnaise, it was important to consider that pH is not usually adjusted independently, but is a function of the added acetic acid. Experiments were performed in which acetic acid was added to TSB and mayonnaise, and the resulting pH related back to the

240 R. C. McKellar et al.

Figure 2. In£uence of acetic acid concentration on the pH of TSB (*) and whole egg mayonnaise (*).

the mayonnaise (r2 = 0?9989) data (Fig. 2). The pH of mayonnaise was subsequently calculated from the amount of added acetic acid using the following equation: pH ¼ 3 532 þ 1 173 e0:4301 AA þ 3 099

Figure 1. Survival/death interface for pH as in£uenced by a temperature (salt 0?5%; acetic acid 3%); b salt (temperature 301C; acetic acid 3%); c acetic acid (temperature 301C; salt 0?5%). Survival in all ¢ve replicates (*); death in all ¢ve replicates (*); survival in 1^4 replicates (&). P0?1 (broken line); P0?5 (solid line); P0?9 (dashed line). added acid. Non-linear regression revealed that a two-phase exponential decay function gave the best ¢t to the TSB (r2 = 0?9948) and

e5 594 AA ð5Þ where AA is the concentration of acetic acid. A simulation model was constructed in Analyticas using equations 1, 2, 3 and 5. In routine simulations, it was necessary to account for the fact that, while a wide range of factor levels were included in the design, not all combinations were tested. Baranyi et al. (1996) have pointed out that interpolation should be limited to the region of the combinations tested, termed the ‘minimum convex polyhedron’ (MCP), or ‘convex hull’ of the experimental design. The MCP will always be smaller or equal to the nominal variable space. In addition to restricting factors to within the nominal variable space, additional restrictions on pH and salt were calculated as described by Baranyi et al. (1996) and are given in equations 6 and 7: 3 5opHo6  1 875  Sucrose

ð6Þ

0 5oSalto16 5  0 5  Sucrose or ð7Þ 0 5oSalto16 5  4 8  ðpH  3 5Þ Thus the model will not make predictions for high pH when sucrose is added, and limits the salt concentration to o12?5% at either high pH or with added sucrose.

Survival and death of E. coli O157:H7 in a mayonnoise model 241

Example simulations with added acetic acid (2^4%) and increasing levels of either salt (0?5^ 4?5%) or sucrose (0^8%) are shown in Figs 3 and 4, respectively. In all simulations, the pH was controlled by the addition of acetic acid. Decreasing the incubation temperature generally resulted in increased survival under all conditions. At 2 and 3% acetic acid, increasing salt above 0?5% resulted in a predicted probability of survival of 1?0 at 25 and 201C, respectively (Figs 3a and b). At 4% acetic acid (Fig. 3c), maximum survival was not predicted at any temperature tested. In addition, a quadratic e¡ect was noted at the highest acetic acid level tested. Similar results were found with increasing concentrations of sucrose (Fig. 4). Maximum survival was attained at 25 and 201C with added sucrose at 2 and 3% acetic acid (Figs 4a and b). Survival with added sucrose was improved at 4% acetic acid, reaching close to 1?0 at 8% added sucrose (Fig. 4c). The model was validated in mayonnaise at minimum salt (0?5%) and with no added sucrose, and the conditions are given in Table 2. Mean log reductions are taken from duplicate treatments in each of two replicate experiments. For validation, the MCP was not considered, and the model was allowed to predict outside the experimental boundaries to search out weaknesses in predictive ability. In particular, survival was tested at 51C, a condition not included in the model building. In general, the model correctly predicted survival or death in mayonnaise (Table 2). Only four combinations of conditions led to incorrect predictions and, of these, only one could be considered ‘fail-dangerous’. At 2% acetic acid and 251C, a high probability of survival was indicated, while actual log reduction was 6?55. In 3% acetic acid at 20 and 151C, survival was also less than predicted by the model (6?73 and 6?02 log reductions, respectively). At 4% acetic acid at 51C, a medium probability of survival (0?01oPo0?99) was predicted by the model (Table 2). Actual log reduction was only 3?31, thus this was considered to be a ‘faildangerous’ prediction. Simulations were performed using 4% acetic acid at 51C (open circles in Fig. 5), and the results suggest that the prediction of survival under these conditions may have been due to quadratic e¡ects of

Figure 3. Simulated probability of survival in a 2%, b 3%, and c 4% acetic acid with salt at 0?5% (*), 1?5% (*), 2?5% (&), 3?5% (&), and 4?5% (~).

the model at o101C. If this quadratic e¡ect had not been predicted by the model, the actual predicted probability of survival would have been closer to 1?0, more in line with the experimental ¢ndings. Figure 5 also shows that the addition of 8% sucrose, either alone or in combination with 4?5% salt, removed the predicted quadratic e¡ect, and the model then predicted survival at 4101C. Di⁄culties encountered in

242 R. C. McKellar et al.

however, both were ‘fail-safe’. High probabilities of survival were predicted for 2% acetic acid at 251C and for 3% acetic acid at 201C; experimental log reductions were 5?72 and 5?75, respectively.

Discussion

Figure 4. Simulated probability of survival in a 2%, b 3%, and c 4% acetic acid with sucrose at 0?0% (*), 1?0% (*), 2?0% (&), 4?0% (&), and 8?0% (~).

manufacturing mayonnaise with 4% acetic acid and high salt and sucrose precluded further validation studies under these conditions. Validation experiments were carried out using 2 and 3% acetic acid, with 4?5% salt and 8% sucrose (Table 3). Of the six combinations studied, two gave incorrect predictions;

In the present study, a model for predicting the probability of survival of E. coli O157:H7 in mayonnaise with high accuracy was developed. Ratkowsky and Ross (1995) were the ¢rst to suggest that kinetic models for growth could be adapted to model binary growth/no growth data, thus providing a model for the probability of growth under de¢ned conditions. Since then, this approach has been used to model growth/ no growth for: E. coli as a function of temperature, pH, lactic acid and aw (Presser et al. 1998) or temperature and aw (Salter et al. 2000); Listeria monocytogenes in Mexican-style cheese (Bolton and Frank 1999); Zygosaccharomyces bailii in high-acid foods (Jenkins et al. 2000, LopezMalo and Palou 2000); and Saccharomyces cerevisiae under the e¡ects of aw , pH and sorbate (LopezMalo et al. 2000).This is the ¢rst reported logistic model de¢ning the survival/ death interface of a foodborne pathogen. The model was able to predict experimental results with 97?4% accuracy. This was as good as or better than predictions of growth or no growth made by other logistic regression models such as 87?7% for L. monocytogenes in cheese (Bolton and Frank 1999), 97?3% for E. coli and lactic acid (Presser et al. 1998), and 92?86% for S. cerevisiae with sorbate (LopezMalo et al. 2000). Interestingly, the CIMSCEE model also makes accurate (87?2%) predictions, even though this model does not take temperature into account. The CIMSCEE model was designed to provide the European Sauces Trade Association with a code for the production of microbiologically safe and stable emulsi¢ed and non-emulsi¢ed sauces containing acetic acid. Temperature is an important factor in the logistic regression model, and has been shown to have a signi¢cant e¡ect on survival of E. coli O157:H7 exposed to acetic acid in mayonnaise (Weagant et al. 1994, Zhao and Doyle 1994, Hathcox et al. 1995, Raghubeer

Survival and death of E. coli O157:H7 in a mayonnoise model 243

Table 2. Validation of a probability of survival model in mayonnaise (0?5% salt; 0% sucrose) Acetic acid (%)

Temp. (1C)

pH

Probability of survival

Mean log reduction (n = 4)

s.d.

Correct prediction

Correct replicates (n = 4)

30 25 20 15 10 5 30 25 20 15 10 5 30 25 20 15 10 5 30 25 20 15 10 5

4?33

High High High High High High Low High High High High High Low Low High High High High Low Low Low Medium Medium Medium

3?38 1?61 1?27 0?29 0?27 0?22 7?57 6?55 4?41 2?00 0?80 0?41 9?37 7?90 6?73 6?02 4?85 1?60 8?77 9?37 7?57 6?97 7?07 3?31

0?64 0?83 1?21 0?21 0?20 0?27 1?23 0?80 1?62 0?12 0?11 0?14 0?06 1?74 0?26 0?65 1?48 0?21 1?23 0?06 1?17 0?06 2?82 1?51

Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes No No Yes Yes Yes Yes Yes Yes Yes No

4 4 4 4 4 4 4 1 3 4 4 4 4 4 0 2 3 4 4 4 4 4 3 0

1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4

4?07

3?88

3?77

Fail-safe

Yes

Yes Yes

No

Results are the means of two replicates from each of two independent trials. A high (P40?99) and low (P40?01) probability of survival means o5?7 and 45?7 log reduction in viability, respectively, at the indicated temperature in 72 h. A medium probability of survival (0?01oPo0?99) is scored correct when the experimental value is 45?7 log reduction. A fail-safe prediction is one in which, when the model predicts incorrectly, it errs on the side of safety.

Table 3. Validation of a probability of survival model in mayonnaise (4?5% salt; 8% sucrose) Acetic acid (%) 2 2 2 3 3 3

Temp. (1C)

pH

Probability of survival

Mean log reduction (n = 4)

s.d.

Correct prediction

Correct replicates

30 25 20 30 25 20

3?95

Medium High High Low Medium High

7?02 5?72 3?81 7?02 7?02 5?75

0?04 0?83 0?40 0?04 0?04 1?08

Yes No Yes Yes Yes No

4 2 4 4 4 2

3?86

Fail-safe

Yes

Yes

A high (P40?99) and low (P40?01) probablity of survival means o5?7 and 45?7 log reduction in viability, respectively, at the indicated temperature in 72 h. A medium probability of survival (0?01oPo0?99) is scored correct when the experimental value is 45?7 log reduction. A fail-safe prediction is one in which, when the model predicts incorrectly, it errs on the side of safety.

et al. 1995). Examination of the CIMSCEE predictions revealed that temperature e¡ects were responsible for some of the model failures; false-positives (survival predicted when experimental data showed death) tended to occur when the treatment temperature was 301C. It

was further noted that CIMSCEE gave falsenegatives (predicted death when survival occurred) when salt was 42?5% and/or sucrose was 44%, suggesting that the model fails to take interactions between salt and sucrose into account.

244 R. C. McKellar et al.

Figure 5. Simulated probability of survival in 4% acetic acid with 0?5% salt/0% sucrose (*), 0?5% salt/8% sucrose (*), or 4?5% salt/8% sucrose (&) as a function of temperature. The original study suggesting the use of probability modelling of the growth/no growth interface (Ratkowsky and Ross 1995) used data which was obtained from work by Zaika et al. (1992), who measured growth after only 24 h. In a later study (Presser et al. 1998), a longer growth period of up to 51 days was used to ensure that growth (if it occurred at all) would be detected. In the present study, a similar limit to the survival/death probability model was that a maximum time of 72 -h incubation was imposed. The 72 h hold time used here was taken from the US regulations for commercial mayonnaise made with unpasteurized eggs (US Food and Drug Administration 1990), which had been based on earlier work on Staphylococcus and Salmonella undertaken by Wetherington and Fabian (1950). It is important to emphasize, however, that E. coli O157:H7 can survive in mayonnaise under conditions which would be expected to preclude survival of Salmonella (Zhao and Doyle 1994, Hathcox et al. 1995). Early examination of the regression analysis revealed that the use of undissociated acetic acid as an independent variable instead of the total acid concentration gave improved models (data not shown). This is a reasonable observation, as it has been clearly demonstrated that the undissociated form of organic acids is the e¡ective molecule (ICMSF 1980). Results of validation experiments indicated that the survival model correctly predicted sur-

vival in mayonnaise in most cases.With one exception, failures were considered to be ‘failsafe’, that is, survival was predicted whereas no survival was actually found. This was due to the fact that, generally, E. coli were more sensitive in mayonnaise than in TSB. This may have been due in part to the presence of antimicrobial agents such as lysozyme in whole eggs. Other workers have speculated on the synergistic e¡ects of lysozyme and acetic acid in mayonnaise on survival of foodborne pathogens (Glass and Doyle 1991, Raghubeer et al. 1995), and it has been suggested that other components of mayonnaise, such as type of oil and spices, can also in£uence pathogen survival (Radford et al. 1991, Radford and Board 1993). The single ‘fail-dangerous’ (false-negative) prediction in mayonnaise may be explained in several ways. The model was constructed o make predictions down to 101C only; predictions below that should only be made with extreme caution. The prediction of survival was also in£uenced by the quadratic e¡ects of the polynomial function as seen in Fig. 4. If this e¡ect is discounted, the probability of survival would be considerably higher. As this prediction was actually a medium probability of survival, it is possible always to obtain ‘fail-safe’ predictions by only selecting conditions which give a low probability of survival. Some ‘fail-dangerous’ predictions were also made when the model predictions were compared with the experimental data used to build the model. These were found generally under the following experimental conditions: 25^ 301C; salt 40?5%; pH
4?0. It was interesting to note that false-positives were found over the same ranges. A further examination revealed that both false-positive and false-negative predictions corresponded to probabilities of close to 0?5, which was used as the cuto¡ point. Thus, it was not possible to make accurate predictions close to the arbitrary boundary of survival/death. It is generally accepted that predictions from a polynomial model cannot be made by extrapolation beyond the range of experimentally tested conditions. Baranyi et al. (1996)have further shown that interpolation is only accep-

Survival and death of E. coli O157:H7 in a mayonnoise model 245

table within the MCP, which is usually smaller than the nominal variable space. This prevents extrapolation to combinations of variables which, while still within the nominal variable space, were not actually experimentally tested. For example, in the present study, we extended the range of acetic acid concentrations tested up to 4% in combination with high salt or sucrose, but only examined responses at pH values
5?0. Thus, incorporation of MCP calculations into the model precludes predictions at higher pH values (see equations 6 and 7). The model was constructed to pH as an independent factor, which generated terms for main and cross-product e¡ects of pH with UA and sucrose. In the preparation of mayonnaise, pH is controlled solely by the addition of acetic acid, and the subsequent pH was found to follow a biphasic exponential decay function. Xiong et al. (2000) have also shown a similar relationship between pH and acetic acid concentration in mayonnaise, and have further demonstrated the in£uence of mayonnaise composition on pH. In this study, whole egg mayonnaise was used, and there was no further examination of the e¡ect of mayonnaise composition. These workers have also shown that addition of salt had a small (ca. 0?1 pH units for 4?5% salt) but significant e¡ect on pH, but this was not taken into account in the present model. Sucrose did not signi¢cantly in£uence the pH (Xiong et al. 2000). In the ¢nal model, the function linking pH to the concentration of added acetic acid was incorporated to allow predictions of survival in mayonnaise. It is always di⁄cult to compare survival data from various published studies, due to the use of diverse protocols, and particularly to the use of a wide variety of mayonnaise formulations. Our results show that, in general, O157:H7 strains were more sensitive in our mayonnaise than in other reported studies. At the same temperatures and usually slightly higher pH values, we achieved greater degrees of inactivation than other studies. Some speci¢c comparisons follow. Erickson et al. (1995) challenged various commercial mayonnaises with E. coli O157:H7 and stored them at 251C. Extensive (47-log) inacti-

vation within 3 days was found in products with pH o3?6. Weagant et al. (1994) also examined the survival of O157:H7 strains in commercial mayonnaise at pH 3?65 and found 46 -log reduction in 72 h at 251C. In our study, a 49 log reduction was found at pH 3 77 at 251C. Hathcox et al. (1995) examined the survival of O157:H7 in real mayonnaise (pH 3?86 -3?97) and found 1?5 -log and 3 -log reductions in 72 h at 20 and 301C, respectively. Our comparable results show a 6?73 and 9?37-log reduction at pH 3?88 at those two temperatures. Raghubeer et al. (1995) reported a 46 -log reduction of several O157:H7 strains within 96 h at 221C in commercial mayonnaise with pH
4?1. In our study, 46 -log reduction was observed with as little as 2% acetic acid at 251C with a ¢nal pH of 4?07. In the present study, we used increments of pH (0?5 units) and similar increments of the other environmental factors (temperature: 51C; acetic acid: 1%; salt: 1%; sucrose: 2%) to construct the probability model. We observed a total of only 56 conditions (3?08%) in which a fraction of the 5 replicate samples showed survival. Generally, either none of the replicates showed survival, or they all did, suggesting an abrupt shift from survival to death. It is possible that the increments we selected were not su⁄ciently narrow to completely de¢ne the interface. Some evidence has accumulated to suggest that this interface may be quite abrupt regardless of the increments selected. In studies of the in£uence of lactic acid on E. coli, the interface between growth and no growth as controlled by pH was found to be very abrupt; under most experimental conditions, all of the replicates either grew or did not grow (Presser et al. 1998). In that study, pH increments of 0?1 were used in model construction, and 4 replicate cultures were tested with the expectation that at the interface some fraction of the replicates would show growth. In fact, there were few examples of conditions giving other than complete growth or no growth (Presser et al. 1998).These authors suggest that, for practical applications, it may not be necessary to calculate probabilities; the interface could be de¢ned at a selected level of probability (Presser et al. 1998). Our observations tend to support this view.

246 R. C. McKellar et al.

Acknowledgements The authors would like to thank A. Hawke, K. Stanich, K. Knight and M. Smith for their excellent technical assistance, and W. H. Ross for help with the logistic modelling.

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