Modelling inactivation of Listeria monocytogenes by pulsed electric fields in media of different pH

International Journal of Food Microbiology 103 (2005) 199 – 206 www.elsevier.com/locate/ijfoodmicro

Modelling inactivation of Listeria monocytogenes by pulsed electric fields in media of different pH ´ lvarez, S. Condo´n, J. RasoT N. Go´mez, D. Garcı´a, I. A Tecnologı´a de los Alimentos, Facultad de Veterinaria, Universidad de Zaragoza, Miguel Servet 177, 50.013 Zaragoza, Spain Received 19 January 2004; received in revised form 6 September 2004; accepted 25 November 2004

Abstract A study of the effect of square-wave pulsed electric fields (PEF) on the inactivation of Listeria monocytogenes in McIlvaine buffer of different pH (3.5–7.0) was conducted. L. monocytoges was more PEF sensitive at higher electric field strengths (E) and in media of low pH. A treatment at 28 kV/cm for 400 As that inactivated 1.5, 2.3 and 3.0 Log 10 cycles at pH 7.0, 6.5 and 5.0 respectively destroyed almost 6.0 Log 10 cycles at pH 3.5. The general shape of survival curves of L. monocytogenes PEF treated at different pH was convex/concave upwards. A mathematical model based on the Weibull distribution accurately described these survival curves. At each pH, the shape parameter (n value) did not depend on E. The relationship between n value of the Weibull model and the pH of the treatment medium was described by the Gompertz equation. A multiple linear regression model using three predictor variables (E, E 2, pH 2) related the Log 10 of the scale paramenter (b value) of the Weibull model with E and pH of the treatment medium. A tertiary model developed using McIlvaine buffer as treatment medium predicted satisfactorily the inactivation of L. monocytogenes in apple juice. D 2005 Elsevier B.V. All rights reserved. Keywords: Pulsed electric fields; Inactivation; L. monocytogenes; pH; Mathematical modelling

1. Introduction Listeria monocytogenes is a gram-positive, nonsporeforming, facultatively anaerobic, psychrotrophic microorganism that in the past few decades has emerged as a foodborne pathogen of major signifi-

T Corresponding author. Tel.: +34 976 76 15 81; fax: +34 976 76 15 90. E-mail address: [email protected] (J. Raso). 0168-1605/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ijfoodmicro.2004.11.033

cance. The ability of these bacteria to grow over a wide temperature range in acidic environments, as well as in the absence of or at very low amounts of O2 enables it to multiply in many environments. In addition, when L. monocytogenes is unable to multiply in conditions such as low pH or high concentrations of NaCl it may be able to survive for a prolonged period of time. Although most cases of human listeriosis appear to be sporadic, L. monocytogenes has become a serious public health concern because of its high mortality rate (Farber and Peterkin, 2000).

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In recent years there is an increasing consumer demand for high quality minimally processed foods. The supply of these products to the market with a safety level comparable to conventional foods is a primary challenge for the food industry. In order to reduce the impact of severe heat treatments which guarantees food safety but that produces negative effects on sensory and nutritional properties of foods, considerable efforts have been directed towards the development of novel nonthermal processes such as pulsed electric fields (Ho and Mittal, 2000). The main advantage of this technology is that it can inactivate vegetative forms of microorganisms at lower temperatures as compared to conventional thermal processing (Raso et al., 2000). Microbial inactivation by PEF has been intensively investigated in recent years. In these studies it has been demonstrated that microbial inactivation by PEF is influenced by many factors (Wouters et al., 2001). These factors can be classified into: process parameters, treatment medium characteristics and microbial characteristics. The medium in which microorganisms are treated can strongly influence the PEF resistance of microorganisms. The pH of the treatment medium is an important environmental factor influencing the microbial PEF sensitivity. Several studies on the effect of pH on microbial resistance to PEF have demonstrated that the influence of pH depends on the microorganism investigated. Some bacteria are more PEF resistant at neutral than at acidic pH (Vega-Mercado et al., ´ lvarez et al., 2002) 1996; Wouters et al., 1999; A others are more PEF resistant at acidic pH ´ lvarez et al., 2000; Garcı´a (Jeantet et al., 1999; A et al., 2003) and pH did not influence the PEF ´ lvarez et al., sensitivity of Yersinia enterocolitica (A 2003b). Predictive microbiology is a tool that can provide a way to study the influence of various environmental factors on microbial inactivation or growth and to evaluate their effect quantitatively. Several different primary mathematical models have been used to describe the kinetics of microbial inactivation by PEF considering only the electric field strengths and treatment time. Hu¨lsheger et al. (1981) developed a mathematical expression to model the microbial decline assuming a double

logarithmic relation between the survival fraction and the treatment time. Microbial inactivation by PEF has also been described by using a model based on the Fermi’s equation (Peleg, 1995), the first order kinetics model (Martin-Belloso et al., 1997; Reina et al., 1998) and the log-logistic model (Raso et al., 2000). Recently an equation based on the Weibull distribution has been the mathematical approach mostly used to model microbial inactivation by PEF (Rodrigo et al., ´ lvarez et al., 2003a,b,c). The main 2001, 2003; A advantages of the model based on the Weibull distribution are its simplicity and its capability of modeling survival curves that are linear and those that contain shoulder or tailing regions (Peleg and Cole, 1998). Several primary models have been used to describe the kinetics of microbial inactivation by PEF, however equations describing how the parameters of the primary model change with changes in environmental factors such as pH have not been developed. The objective of this investigation was to develop a predictive model to describe the influence of the intensity of the electric field strength and the pH of the treatment medium on the inactivation of L. monocytogenes by PEF and to validate the model in apple juice.

2. Material and methods 2.1. Microorganisms and growth conditions The strain of L. monocytogenes (CECT 4031, ATCC 15313) used in this investigation was supplied by the Spanish Type Culture Collection. It was maintained on slants of Tryptic Soy Agar (Biolife, Milan, Italy) with 0.6% Yeast Extract (Biolife) (TSAYE) added. A broth subculture was prepared by inoculating a test tube containing 5 ml of Tryptic Soy Broth (Biolife) with 0.6% Yeast Extract (TSBYE) with a single colony from a plate of TSAYE, followed by inoculation at 37 8C for 24 h. Flasks containing 50 ml of sterile TSBYE were inoculated with this subculture to a final concentration of 10 6 cells/ml. The culture was incubated under

N. Go´mez et al. / International Journal of Food Microbiology 103 (2005) 199–206

agitation at 35 8C until the stationary growth phase was reached, 24 h. 2.2. Pulsed electric fields equipment The PEF equipment used in this investigation has been previously described (Heinz et al., 1999). High electric fields pulses were produced by discharging a 2 AF capacitor (Maxwell, San Diego, CA, USA) via an IGBT switch (Behlke, HTS 101-80-FI, Frankfurt, Germany) into a treatment chamber. A function generator (Tektronix, AGF 320, Wilsonville, OR, USA) delivered the on-time signal to the switch. The capacitor was charged using a high voltage direct current power supply (FUG, HCK 2500M 35000, Rosenhein, Germany). Microorganisms were treated in a parallel-electrode treatment chamber of 0.5 ml (electrode distance: 0.25 cm; area: 2.01 cm 2). The circuit configuration generated squared waveform pulses of different widths at different electric field strengths and frequencies. 2.3. Microbial inactivation experiments Before treatment, microorganisms were centrifuged at 6000
g for 5 min at room temperature and resuspended in citrate–phosphate McIlvaine buffer of different pH (3.5, 5.0, 6.5 and 7.0) (Dawson et al., 1974) which concentration was adjusted to an electrical conductivity of 2 mS/cm. The microbial suspension (0.5 ml) at a concentration of 10 9 CFU/ml was placed into the treatment chamber with a sterile syringe. Cumulative treatment times ranged from 10 As to 1000 As and electric field strengths were set at 15, 19, 22, 25 and 28 kV/cm. Pulse frequency of 1 Hz and pulse width of 2 As were used. Previously it was demonstrated that the interval between pulses did not have effect on lethality (Raso et al., 2000). The maximum number of pulses applied was 500. Under these conditions, the final temperature of the treatment media was always below 35 8C (Raso et al., 2000). After treatment, appropriate serial dilutions were prepared in TSBYE and plated into TSAYE. Colonies were counted after incubation at 37 8C for 48 h with an improved image analyser automatic counter (Protos, Analytical Measuring Systems, Cambridge, UK) as previously described (Condo´n et al., 1996).

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2.4. Curve fitting A mathematical model based on the Weibull distribution was used to fit the survival curves (log 10 of the survival fraction vs. treatment time) of L. monocytogenes. If the microbial PEF resistance follows a Weibull distribution, the survival function will be ( van Boekel, 2002):   n 1 t log10 S ðt Þ ¼  ð1Þ 2:303 b where t is the treatment time and b and n are the scale and shape parameters, respectively. The b value represents the time necessary to inactivate the first 0.434 log 10 cycles of the population. The n parameter accounts for upward concavity of a survival curve (nb1), a linear survival curve (n=1), and downward concavity (nN1). The estimated values of b and n in Eq. (1) were computed by the Solver function of the Excel 5.0 package (Microsoft, Seattle, WA) and the GraphPad PRISMR (Graph Software, San Diego, CA). The relationship between the estimated n values at each pH investigated and the electric field strength was modelled by the Gompertz function. A quadratic polynomial (response surface) model was generated by multiple regression analysis to model the effect of pH and electric field strength on the estimated b values using the software Statgraphics Plus 5.1 (Statistical Graphics, USA). 2.5. Model validation The tertiary model developed was validated in apple juice (pH 3.7). For the validation study the following experiments were performed: 50, 150, 300 and 500 As at 15 kV/cm; 10, 20, 100, 200, 400, 600 and 1000 As at 19 kV/cm; 10, 20, 100, 200 and 400 As at 22 kV/cm; 10, 20, 100, 200 and 400 As at 25 kV/cm and 10, 20, 100, 200 and 400 As at 28 kV/cm. Bias and accuracy factors were used as a quantitative way to measure the performance of the different models (Ross, 1996). The bias factor indicates by how much, on average, the predictions differ the observed data: When the bias factor is N1 the model overpredicts and when the bias factor is b1 the model underpredicts. The accuracy factor indicates by how much, on average, the predictions differ from the observed data.

N. Go´mez et al. / International Journal of Food Microbiology 103 (2005) 199–206

0 -1

Log10 survival fraction

Fig. 1 illustrates as an example the influence of pH on microbial inactivation of L. monocytogenes by pulsed electric fields treatments. This figure shows the survival curves of L. monocytogenes in McIlvaine buffer of pH 7.0, 6.5, 5.0 and 3.5 at the lowest (15 kV/ cm) medium (22 kV/cm) and the highest (28 kV/cm) electric field strengths investigated. At all pH investigated treatments at electric field strengths lower than 15 kV/cm scarcely affected viability of L. monocytogenes cells. At all electric field strengths investigated L. monocytogenes was more sensitive to PEF in media of low pH. For example a treatment at 28 kV/cm for 400 As that inactivated 1.5, 2.3 and 3.0 Log 10 cycles at pH 7.0, 6.5 and 5.0 respectively destroyed almost 6.0 Log 10 cycles at pH 3.5. Reina et al. (1998) and Fleischman et al. (2004) also demonstrated that L. monocytogenes is very resistant to PEF in media of neutral pH at treatment temperatures below 35 8C. Shape of the survival curves changed depending on the pH of the treatment medium. Survival curves in McIlvaine buffer of pH 7.0 and 6.5 were close to linear or slightly upwardly concaved. However, at lower pH survival curves were concave upwards; the microbial inactivation was faster at the first moments of the treatment, and then progressively declined. Similar results were obtained at the other electric field strengths investigated. The general shape of survival curves of L. monocytogenes at different pH were similar to other survival curves obtained in our laboratory with other microorganisms (Raso et al., ´ lvarez et al., 2003a,b,c). Concave upwards 2000; A survival curves have also been obtained by others authors working with batch or continuous PEF apparatus (Jayaram et al., 1992; Sensoy et al., 1997; Ohshima et al., 2002; Rodrigo et al., 2003). Different authors have investigated the influence of pH on microbial resistance to PEF. However, neither the influence of this factor on the shape of the survival curves has been investigated nor its effect on microbial resistance has been quantified. Survival curves obtained by plotting the Log 10 of the survival fraction against the treatment time at different field strengths and pH were fitted to Eq. (1). The estimated parameters b and n obtained are shown in Table 1. RMSE and R 2 of the fits range from 0.028 to 0.232 and from 0.95 to 0.99 respectively. The time

A

-2 -3 -4 -5 -6 -7 0

200

400

600

800

1000

Treatment time (µs)

B 0

Log10 survival fraction

3. Results and discussion

-1 -2 -3 -4 -5 -6 -7 0

200

400

600

800

1000

Treatment time (µs)

C Log10 survival fraction

202

0 -1 -2 -3 -4 -5 -6 -7 0

200

400

600

800

1000

Treatment time (µs) Fig. 1. Survival curves of L. monocytogenes treated at 15 kV/cm (A), 22 kV/cm (B) and 28 kV/cm (C) in media of different pH: pH 7.0 (o), pH 6.5 (z), pH 5 (4) and pH 3.5 (n). Treatment time represents the cumulative times of pulses of a width of 2 As at a frequency of 1 Hz. Error bars correspond to confidence limits (95%).

N. Go´mez et al. / International Journal of Food Microbiology 103 (2005) 199–206

203

Table 1 b and n values from the fitting of the mathematical model based on the Weibull distribution to the survival curves of Listeria monocytogenes treated by PEF in media of different pH pH

kV/cm

b (CL 95%)a

n (CL 95%)a

R2

7.0

15 19 22 25 28 15 19 22 25 28 15 19 22 25 28 15 19 22 25 28

2101.00 843.80 439.70 111.40 76.35 2514.00 359.00 94.41 57.24 31.19 108.20 14.13 9.44 4.31 2.67 17.64 5.01 1.83 0.95 0.40

0.85 0.88 0.88 0.62 0.76 0.57 0.60 0.58 0.61 0.64 0.36 0.37 0.40 0.39 0.39 0.34 0.39 0.42 0.43 0.38

0.98 0.97 0.99 0.98 0.99 0.97 0.97 0.99 0.99 0.98 0.95 0.97 0.99 0.99 0.98 0.96 0.97 0.99 0.99 0.99

6.5

5.0

3.5

a b c

(1697.00–2505.00) (712.50–975.00) (357.80–521.60) (67.51–155.30) (39.89–112.80) (1253.00–3776.00) (277.00–440.00) (56.18–132.60) (32.61–81.87) (7.65–54.73) (41.46–174.9) (0.56–27.69) (0.38–19.27) (2.12–6.51) (0.75–6.10) (3.47–38.76) (1.49–11.51) (0.27–3.39) (0.31–1.59) (0.06–0.73)

(0.56–1.13) (0.67–1.09) (0.75–1.02) (0.52–0.72) (0.63–0.88) (0.38–0.75) (0.43–0.76) (0.46–0.71) (0.51–0.72) (0.48–0.80) (0.23–0.49) (0.27–0.47) (0.30–0.50) (0.35–0.43) (0.30–0.49) (0.22–0.46) (0.28–0.50) (0.36–0.48) (0.38–0.48) (0.04–0.43)

b

RMSEc 0.028 0.051 0.045 0.096 0.119 0.010 0.044 0.069 0.083 0.193 0.069 0.110 0.118 0.070 0.232 0.119 0.189 0.150 0.107 0.115

CL 95%: confidence limit. R 2: determination coefficient. RMSE: root mean square error.

to reduce 0.434 Log 10 cycles the population of L. monocytogenes (b value) was shorter at higher field strengths and at lower pH. The variability of the shape factor (n value) with the electric field strength and pH was studied by means of an analysis of variance. The b values corresponding to the survival curves obtained at 15 kV/cm at pH 7.0 and 6.5 were not considered in the variance analysis because the time to reduce 0.434 Log 10 cycles the population of L. monocytogenes was longer that the highest treatment time investigated (1000 As). The n values were not influenced by the electric field strength at each pH investigated (PN0.05). However, the pH of the treatment medium affected the n value which decreased from a mean of 0.80 to a mean of 0.39 when the pH of the treatment medium decreased from 7.0 to 3.5. The n values were always lower than 1 and smaller in more acidic media (pH 5.0 and 3.5) reflecting that at higher pH the shape of the survival curves was closer to a straight line. According to the principle of parsimony, models should contain as few parameters as possible (Ratkowsky, 1993). Since at a given pH there were no significant differences between the n values for the

different electric field strength, survival curves were refitted with n set at their mean values in order to reduce the number of parameters of the model based on the Weibull distribution. The RMSE and R 2 of the fits by setting n at their mean value did not change substantially (Table 2). Therefore, at the four pH investigated it was possible to reduce the number of parameters of the Weibull equation. Equations describing how the parameters of the primary model change with changes in environmental or other factors correspond to the secondary level of modelling. The relationship between the n parameter and the pH of the treatment medium was described by the Gomperzt equation (Fig. 2). Eq. (2) shows the relationship obtained (RMSE=0.003, R 2=0.99): n ¼ 0:38 þ 63:33
ee

ð0:25xpHþ3:37Þ

ð2Þ

where pH is the pH of the treatment medium. The relationship between the b value, electric field strength (E) and pH of treatment medium was described by a multiple linear regression with the decimal logarithm of b as the dependent variable. In a

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Table 2 b values from the fitting of Eq. (1) with the n value set at its mean value for each pH to the survival curves of Listeria monocytogenes treated by PEF in media of different pH kV/cm

b (CL 95%)a

n (mean value)

R2

7.0

19 22 25 28 19 22 25 28 15 19 22 25 28 15 19 22 25 28

786.54 (697.00–876.20) 380.66 (352.80–412.50) 186.06 (168.30–203.80) 85.52 (79.43–91.60) 363.17 (312.90–413.40) 102.10 (90.05–114.10) 57.39 (51.77–60.99) 26.57 (22.74–30.40) 116.17 (83.08–149.20) 16.17 (12.68–19.51) 7.68 (6.20–9.07) 4.15 (3.81–4.45) 2.30 (1.88–2.70) 27.66 (19.55–35.77) 5.16 (4.02–6.29) 1.20 (1.06–0.34) 0.54 (0.47–0.62) 0.50 (0.45–0.55)

0.79

0.98 0.99 0.99 0.99 0.97 0.98 0.99 0.98 0.95 0.97 0.99 0.99 0.98 0.96 0.97 0.99 0.99 0.99

6.5

5.0

3.5

a b c

0.61

0.38

0.39

b

RMSEc 0.044 0.069 0.083 0.193 0.044 0.069 0.083 0.193 0.070 0.112 0.121 0.072 0.234 0.131 0.189 0.194 0.161 0.123

CL 95%: confidence limit. R 2: determination coefficient. RMSE: root mean square error.

3

Log (b)

pH

4

2 1 0

7 6

5

-1 15

17

19

4

21

23

25

27

E

29

3

pH

Fig. 3. Relationship between the Log 10 of b value, electric field strength (E) and pH of treatment medium.

cally not significant ( PN0.01) and in order to simplify the model these were removed from the model. The multiple regression equation for the log 10b value (Eq. (3)) yielded a R 2 value of 0.99: Log b ¼ 4:82  0:37
E þ 0:0056
E2 þ 0:63
pH2

first approach, they were considered as possible independent variables of the polynomial regression equation: pH, E, pH
E, pH 2, and E 2. The independent variables pH and pH
E were statisti1.00

ð3Þ

The response surface graph constructed from the secondary model is shown in Fig. 3. This figure shows that the b value decreases as electric field strength increased and pH decreased. Eqs. (2) and (3) were introduced in Eq. (1) to obtain the corresponding tertiary model. To improve

Estimated data (Log N/N 0)

-7

n value

0.75

0.50

0.25

-6 -5 -4 -3 -2 -1

0.00 3

4

5

6

7

pH Fig. 2. Relationship between the n parameter and the pH of the treatment medium. Line corresponds to the fit of Eq. (2) to experimental values. Error bars correspond to confidence limits (95%).

0 0

-1

-2

-3

-4

-5

-6

-7

Observed data (Log N/N0) Fig. 4. Plot of the observed values in McIlvaine buffer of different pH vs. estimated values for the tertiary model. Response surface was predicted by Eq. (3).

N. Go´mez et al. / International Journal of Food Microbiology 103 (2005) 199–206

Log10 S ðt Þ 1 ¼  2:303  0:38þ0:79
eeð0:97pH6:60Þ t
ð4Þ 2 2 104:5250:354
Eþ0:0052
E þ0:067
pH

A plot of the observed and estimated data is given in Fig. 4. The difference between a point of the graph and the line of equivalence is a measure of the inaccuracy of the corresponding estimation. This inaccuracy can be quantified by the accuracy factor (A f) that averages the distance between each point and the line of equivalence as a measure of how close on average estimations are to observations. Based on the accuracy factor calculated, the estimations were, on average, a factor of 1.28 different from the observed values. The bias factor answers the question whether, on average, the observed values lie above or below the line of equivalence and, if so, how much. According to the bias factor calculated (1.03) we can conclude that the model fits well the inactivation of L. monocytogenes in McIlvaine buffer of different pH. To ensure that a model is sufficiently accurate for its intended use it is important to validate the model for the specific food. Although the internal validation of the model with the data used to develop it indicated that quality of the model developed was good, foods may have additional factors that affect microbial inactivation that are not included in the model. To check the predictive capability of the model the resistance of L. monocytogenes to PEF was studied in apple juice and results obtained were compared with the values estimated by the model. To calculate the estimated values the actual pH of the apple juice (pH=3.7) was used. In Fig. 5, the predictions are compared with the values obtained experimentally. The bias and accuracy factor calculated 1.02 and 1.14 indicated that the model predicts accurately the inactivation of L. monocytogenes in apple juice.

-7

Estimated data (Log N/N0)

the estimates of the parameters of the tertiary model all survival curves obtained in this investigation were fitted to this new equation. This analysis improves the precision of the estimated parameters because it avoids possible errors made through the estimation of intermediate parameters and because all raw data are used to estimate the parameters. Eq. (4) corresponds to the final tertiary model obtained after the fit (RMSE=0.22, R 2=0.98)

205

-6 -5 -4 -3 -2 -1 0 0

-1

-2

-3

-4

-5

-6

-7

Observed data (Log N/N0) Fig. 5. Plot of the observed values in apple juice vs. predicted values for the tertiary model. 15 kV/cm (.), 19 kV/cm (z), 22 kV/cm ( S ), 25 kV/cm (E) and 28 kV/cm (n).

From the results obtained in this investigation it can be concluded that the pH of the treatment medium influences the PEF resistance of L. monocytogenes and the shape of the survival curves. A tertiary model based on the Weibull distribution developed in McIlvaine buffer of different pH predicted satisfactory the inactivation of L. monocytogenes in apple juice.

Acknowledgements This study was carried out within the AGL20001222 project. N.G. gratefully acknowledged the financial support for her doctoral studies from the bMinisterio de Ciencia y Tecnologı´aQ.

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