Predictive Modeling for Growth of Non- and Cold-adapted Listeria monocytogenes on Fresh-cut Cantaloupe at Different Storage Temperatures Yoon-Ki Hong, Won Byong Yoon, Lihan Huang, and Hyun-Gyun Yuk
The aim of this study was to determine the growth kinetics of Listeria monocytogenes, with and without cold-adaption, on fresh-cut cantaloupe under different storage temperatures. Fresh-cut samples, spot inoculated with a 4-strain cocktail of L. monocytogenes (3.2 log CFU/g), were exposed to constant storage temperatures held at 10, 15, 20, 25, or 30 °C. All growth curves of L. monocytogenes were fitted to the Baranyi, modified Gompertz, and Huang models. Regardless of conditions under which cells grew, the time needed to reach 5 log CFU/g decreased with the elevated storage temperature. Experimental results showed that there were no significant differences (P > 0.05) in the maximum growth rate k (log CFU/g h−1 ) and lag phase duration λ (h) between the cultures of L. monocytogenes with or without previous cold-adaption treatments. No distinct difference was observed in the growth pattern among 3 primary models at various storage temperatures. The growth curves of secondary modeling were fitted on an Arrhenius-type model for describing the relationship between k and temperature of the L. monocytogenes on fresh-cut cantaloupe from 10 to 30 °C. The root mean square error values of secondary models for non- and cold-adapted cells were 0.018, 0.021, and 0.024, and 0.039, 0.026, and 0.017 at the modified Gompertz, Baranyi, and Huang model, respectively, indicating that these 3 models presented the good statistical fit. This study may provide valuable information to predict the growth of L. monocytogenes on fresh-cut cantaloupes at different storage conditions. Abstract:
M: Food Microbiology & Safety
Keywords: cold-adaptation, fresh-cut cantaloupe, Listeria monocytogenes, predictive modeling
Listeriosis has occurred and increased along with the increased demand of fresh and fresh-cut fruits and vegetables. This study was conducted to predict the growth of non- and cold-adapted L. monocytogenes on fresh-cut cantaloupe at different temperature using mathematical model. These results can be helpful for risk assessments of L. monocytogenes in fresh-cut cantaloupe. This study provides valuable information to food handlers to choose proper storage temperatures for extending the shelf-life of fresh-cut cantaloupe.
Practical Application:
Introduction Listeria monocytogenes presents a major food safety concern due to listeriosis that has a high mortality rate (Bennion and others 2008). This bacterium is Gram-positive psychrotrophic foodborne pathogen that can grow at refrigerated temperatures (ICMSF 1996; Gr¨undling and others 2004). Listeriosis is commonly linked to deli meats, cheeses, and unpasteurized milk; however, the transmission vehicles have recently changed due to an increase in the number of Listeria infections associated with fresh and fresh-cut fruits and vegetables such as cabbage, celery, lettuce, and strawberry (Schlech 1996; Sapers and Doyle 2009; Vandamm and others 2013). Cantaloupe (Cucumis melo var. reticulatus), an orange-fleshed melon, is one of the most popular tropical fruits worldwide since MS 20131307 Submitted 9/14/2013, Accepted 3/10/2014. Authors Hong and Yoon are with Dept. of Food Science and Biotechnology, College of Agriculture and Life Sciences, Kangwon Natl. Univ., Chuncheon, Gangwondo 200-701, South Korea. Author Huang is with Eastern Regional Research Center, Agricultural Research Service, U.S. Dept. of Agriculture, 600 E. Mermaid Lane, Wyndmoor, PA 19038, U.S.A. Author Yuk is with Food Science and Technology Programme, Dept. of Chemistry, Natl. Univ. of Singapore, 3 Science Drives 3, 117544, Singapore. Direct inquiries to author Yuk (E-mail: [email protected]).
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the fruit is delicious and rich in vitamin A, vitamin C, and potassium (Pe˜nuela 2012). In general, cantaloupes grow on vines on the ground in a trailing and scrambling manner (FAO 2011), and the inner flesh of the fruit is rich in sugars and low in acidity (pH 6.7), which is a favorable condition for growth of foodborne pathogens (Gil and others 2006). In addition, pathogenic bacteria from contaminated soil and irrigation water may be harbored on rough outer rind of the fruit (Mahmoud and others 2008), and easily transferred into the flesh when the fruit is cut (Ukuku and Fett 2002; Selma and other 2008). For these reasons, cantaloupes have been implicated in many foodborne bacterial infections involving consumption of fresh-cut products contaminated with Escherichia coli O157:H7, Salmonella spp., and L. monocytogenes (Mohle-Boetani and others 1999; CDC 2002, 2007, 2008, 2011a, 2011b; Mahmoud and others 2008; FDA 2009; Olaimat and Holley 2012). In 2011, a multistate outbreak of L. monocytogenes infection linking to whole cantaloupe was in the United States. This outbreak caused a total 147 cases and 33 deaths (CDC 2012). Since cantaloupe generally serves as fresh-cut form at food establishments without additional treatment, storage condition plays an important role in preventing listeriosis. Previous research R C 2014 Institute of Food Technologists
doi: 10.1111/1750-3841.12468 Further reproduction without permission is prohibited
Modeling of L. monocytogenes on cantaloupe . . . genes serovar 1/2b (ATCC BAA-839; human outbreak), L. monocytogenes serovar 1 (ATCC 19111; poultry outbreak), and L. monocytogenes serovar 4b (ATCC 13932; Spinal fluid of child outbreak), purchased from the American Type Culture Collection (ATCC; Manassas, Va., U.S.A.) were selected in this study. Frozen cultures were activated in 10 mL trypticase soy broth (TSB; Oxoid, Basingstoke, Hampshire, U.K.). All cultures were adapted to resist 200 μg/mL nalidixic acid (Sigma-Aldrich, St. Louis, Mo., U.S.A.) by stepwise increment of nalidixic acid concentration after each transfer of the respective culture. After which, all media used in this study were supplemented with 200 μg/mL nalidixic acid so that the L. monocytogenes cells isolated from inoculated cantaloupes were relatively free from other background bacterial contaminants (Beuchat and Mann 2008; Strawn and Danyluk 2010). Nalidixic acid adapted L. monocytogenes were transferred daily to maintain viability. Preparation of inoculum. Prior to inoculation, each nalidixic acid adapted cell culture was inoculated into 10 mL of TSB supplemented with 200 μg/mL nalidixic acid (TSBN) and incubated at 37 °C for 24 h with 2 consecutive transfers using a loopful of the culture. The cultures were centrifuged at 3500 rpm Materials and Methods for 10 min at 4 °C, and washed 3 times by removing the superBacterial strains and culture condition. L. monocytogenes natant and suspending the cell pellet in 1 mL of 0.1% peptone waserovar 1/2b (ATCC BAA-839; human outbreak), L. monocyto- ter (PW, Oxoid). After washing, 1 mL from each L. monocytogenes
Figure 1–Comparison of modified Gompertz, Baranyi, and Huang models on the growth of NCA cell of L. monocytogenes on fresh-cut cantaloupes at diffent storage temperatures. (A) 5 °C (not fitted), (B) 10 °C, (C) 15 °C, (D) 20 °C, (E) 25 °C, and (F) 30 °C. Vol. 79, Nr. 6, 2014 r Journal of Food Science M1169
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demonstrated that L. monocytogenes is able to grow at refrigerated temperatures with long lag and generation times (Barbosa and others 1994). According to an FAO report (2011), poor temperature control is a main factor contributing to foodborne illness associated with melons, followed by pre-cut and/or mixed dish. Thus, it is crucial to understand the growth kinetics of L. monocytogenes on the fresh-cut cantaloupe under different storage temperatures. A previous study reported that freshly harvested L. monocytogenes inoculated onto fresh-cut cantaloupe can grow well at temperatures between 4 and 43 °C (Fang and others 2013). However, it remains unclear if L. monocytogenes, exposed to and adapted to low temperature, may affect its growth and multiplication in freshcut cantaloupe since bacterial adaption may occur during storage. Therefore, the objective of this study was to investigate the effect of cold adaption on the growth of L. monocytogenes in fresh-cut cantaloupe and compare its growth kinetics with freshly harvested bacterial cultures. This work also aimed to develop mathematical models that can describe the growth behaviors of L. monocytogenes in fresh-cut cantaloupe under different storage temperature conditions.
Modeling of L. monocytogenes on cantaloupe . . .
12
Primary models. All growth curves of L. monocytogenes at 10, 15, 20, 25, and 30 °C were fitted to the Baranyi, modified Gompertz, and Huang models. The growth data obtained at 5 °C were not fitted to the models since the distinctive growth was not observed. The Baranyi model (Baranyi and Roberts 1994) is defined by exp [μmax A(t )] − 1 Y(t ) = Y0 + μmax A(t ) − ln 1 + exp (Ymax − Y0 )
+ exp (−h 0 ) − exp (−μmax t − h 0 )]
6 4
B
8 6 4
2
2
0
0 0
20
40
60
80
100
Baranyi
0
20
Time(h)
12
6 4
0 0
20
Gompertz
40
60
2
80
Baranyi
100
0
log CFU/g
8 6 4 Gompertz
Huang
5
10 15 20 25 30 35 40 45 50 Time(h)
F
10
Baranyi
Gompertz
0
12
2
100
4
Huang
E
10
80
6
Time(h)
12
60
8
log CFU/g
log CFU/g
8
Baranyi
40
Huang
D
10
2
Gompertz
Time(h)
C
10
(2)
where Y(t) = ln CFU/g of cell concentration at time t, Y0 = ln(x0 ), x0 is the initial cell concentration (CFU/g), Ymax is the maximum cell concentration (ln CFU/g), μmax is the specific growth rate (ln CFU/g h−1 ), h0 = μmax λ, λ is the lag phase duration (h) at the incubation temperature, and t is the incubation/growth time (h).
10
8
(1)
1 A(t ) − ln[exp (−μmax t ) μmax
A(t ) = t +
log CFU/g
log CFU/g
populations of bacterial cells were expressed in log CFU/g of fruit. Predictive model for bacterial growth.
12
A
10
log CFU/g
M: Food Microbiology & Safety
culture was aseptically combined to produce a cocktail of 4 serovars. The bacterial suspension was diluted with 0.1% PW to obtain a final concentration of ca. 4.0 to 5.0 log CFU/mL. Freshly prepared cocktail of L. monocytogenes was designated as non-cold-adapted (NCA) cells. Cold-adaptation. To allow L. monocytogenes cells to adapt to cold temperature, the bacterial suspension prepared described above was stored at 5 °C for 5 days, according to the procedures adopted and modified from Mastronicolis and others (2006). The bacterial cultures obtained from this procedure were designated as cold-adapted (CA) cells. Storage study and enumeration. The inoculated cantaloupes were incubated under different storage temperatures (5, 10, 15, 20, 25, or 30 °C) to investigate the growth of L. monocytogenes. The samples were periodically retrieved to determine the growth of L. monocytogenes, with sampling frequencies adjusted according to the storage temperatures. To enumerate L. monocytogenes from samples, 100 mL of 0.1% PW was added to each sample and homogenized for 1 min using a stomacher (IUL Instruments, Barcelona, Spain). After which, serial dilutions were made with 0.1% PW and pour-plated into trypticase soy agar (TSA; Oxoid) supplemented with 200 μg/mL nalidixic acid (TSAN). Plates were incubated at acrobatically 37 °C for 48 h, followed by manual counting of colonies. The
Huang
0
8 6 4 2
Baranyi
Gompertz
Huang
0 0
5
10 15 20 25 30 35 40 45 50 Time(h)
0
5
10 15 20 25 30 35 40 45 50 Time(h)
Figure 2–Comparison of modified Gompertz, Baranyi, and Huang models on the growth of CA cell of L. monocytogenes on fresh-cut cantaloupes at diffent storage temperatures. (A) 5 °C (not fitted), (B) 10 °C, (C) 15 °C, (D) 20 °C, (E) 25 °C, and (F) 30 °C.
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The modified Gompertz model (Zwietering and others 1990) (P < 0.05) among the mean values were analyzed by Tukey’s HSD test. is defined by 2.718k(λ − t ) Results and Discussion y(t ) = y0 + Ce xp −exp +1 (3) Modeling of growth for a certain pathogen on foods is an essenC tial step for a microbial risk assessment, which is a structured prowhere y(t) is the log CFU/g of cell concentration at time t, y0 = cess for determining the risk associated with any hazards in foods log(x0 ), C is the asymptotic increase in population density, and k (McMeekin and others 2008). To date, many efforts in the preis the the maximum growth rate (log CFU/g h−1 ). dictive microbiology have been made by developing new growth The Huang model (Huang 2011, 2013) is defined by models or modifying the existing models for better describing microbial growth data obtained from experiments. Among them, the Y0 Ymax (4) modified Gompertz and Baranyi models (Eq. 1 and 2) have been Y(t ) = Y0 + Ymax − ln e + e − e Y0 e −μmax B(t ) well established and used in many microbial growth studies. However, the Huang model has been recently developed and applied to 1 1 + e −β(t −λ) the growth models of some foodborne pathogens in foods (Huang B(t ) = t + ln (5) β 1 + e βλ 2011, 2013). It is necessary to validate this model in different laboratories. Each model of these models has its advantages. Although where β is a constant that defines the transition from the an empirical model, the modified Gompertz model is very easy lag phase to the exponential phase of a growth curve. Huang to understand and has been extensively used in the literature. The (2013) suggested that the parameter β = 4 is suitable for Baranyi model is more complex than the modified Gompertz, analyzing bacterial growth curve in the Huang model. With but it introduced an interesting parameter h , which is basically a 0 β = 4, the Huang model can be used to analyze the growth virtual parameter and an indicator of the physiological state of the curves with lag phase up to 175 h. For this reason, β was bacterium under investigation. This parameter is used to quantify initially 25 (Huang 2011), but reduced to 4 (Huang 2013) the prior history on bacterial growth (Baranyi and Roberts 1994). without affecting the performance and curve-fitting of the In addition, it plays the role of a bridge between the history and model. the actual environment. However, h0 is a virtual parameter that Secondary model. The secondary model used in this study was an is difficult to be observed, and validated, and is sensitive to temArrhenius-type model developed by Huang and others (2011), perature shift (Delignette-Muller and others 2005). The Huang model, however, is a relatively simply model based on the funand defined by damental growth phenomenon of microorganisms in foods. This n model clearly defines the duration of lag phase and exponential G k = α (T + 273.15) exp − (6) growth rate in a single equation, and is more intuitive than the R (T + 273.15) traditional growth models such as modified Gompertz and Baranyi where R is the gas constant (8.314 J/mol·K), T is the tempera- models (Huang 2011). Thus, this study compared 2 existing modture (°C), G is the a type of kinetic energy related to bacterial els (the modified Gompertz and Baranyi models) with the Huang growth, n and α are coefficients. In this equation, k is the maxi- model in modeling the growth of NCA and cold adapted (CA) L. mum growth rate was used. In the modified Gompertz model, this monocytogenes on locally produced fresh-cut cantaloupe at various value was directly calculated from the model. For the Baranyi and storage temperatures. The growth curves of NCA and CA L. monocytogenes on freshHuang models, the specific growth rates (μmax ) in these models were converted to k by dividing μmax in Eq. (1), (2), and (4) with cut cantaloupe were fitted into the Baranyi, modified Gompertz, and Huang models at 10, 15, 20, 25 and 30 °C, respectively. The 2.303 (or ln 10). cell growth at 5 °C could not be fitted into the models since the Curve fitting. Once the growth curves were obtained, each growth did not develop into full curves (Figure 1). Under the curve was fitted to the primary models and then to secondary incubation temperatures between 10 and 30 °C, the inoculated models using nonlinear regression. The nonlinear regression was L. monocytogenes cells, with or without previous exposure to cold conducted using the Trust-Region algorithm. All curve fitting adaptation, grew rapidly on fresh-cut cantaloupe, and grew faster as was performed using Matlab Curve Fitting ToolboxTM (version the storage temperatures increased. At the initial inoculation level 3.3, Mathworks, Inc., Natick, Mass., U.S.A.) to determine the of 3.2 log CFU/g, the averaged time needed for the population parameters for each model. of NCA cells of L. monocytogenes reached to 5 log CFU/g 80, 60, Evaluation of model performance and statistical 22, 13, 8, and 7 h at 5, 10, 15, 20, 25 and 30 °C, respectively analysis. All experiments were conducted in independent tripli- (Figure 1). For CA cells, the average time to 5 log CFU/g in the cates with duplicate samples analyzed at each sampling time. The inoculated samples was 76, 62, 17, 15, 10 and 8 h at 5, 10, 15, 20, goodness-of-fit of the primary and secondary models were assessed 25 and 30 °C, respectively (Figure 2). by calculating and comparing the root mean square error (RMSE) The results obtained in this study were in agreement with the values of the models (Boonyawantang and others 2012) using previous studies, which showed that the growth of L. monocytogenes Eq. (7): on fresh produce was highly dependent on storage temperature,
revealing that an increase in storage temperature accelerates the n 2 cell growth (Koseki and Isobe 2005; Sinigaglia and others 2006; 1 [Experimental value − Model value] (7) RMSE = Wang and others 2013). For example, Wang and others (2013) Degree of freedom showed that L. monocytogenes on white cabbage stored at higher The k and λ values from each growth model were evaluated temperatures had shorter times to reach the maximum population by analysis of variance (ANOVA) and significant differences (5–8 log CFU/g). It was evident that L. monocytogenes can grow on Vol. 79, Nr. 6, 2014 r Journal of Food Science M1171
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Modeling of L. monocytogenes on cantaloupe . . .
Modeling of L. monocytogenes on cantaloupe . . . Table 1–Effects of temperature and model type on the maximum growth rate (k) and lag phase duration (λ) of NCA and CA L. monocytogenes on fresh-cut cantaloupe across all temperature conditions—ANOVA. Parameter NCA
k λ
CA
k λ
Temperature Model Residuals Temperature Model Residuals Temperature Model Residuals Temperature Model Residuals
df
Sum sq.
Mean sq.
F-value
Pr(>F)
4 2 8 4 2 8 4 2 8 4 2 8
1.190E−01 2.054E−04 1.190E−01 1.871E+03 7.535E+00 3.145E−04 8.100E−02 1.206E−04 1.409E−03 2.134E+03 2.261E+01 7.038E+01
3.000E−02 1.027E−04 3.931E−05 4.678E+02 3.767E+00 3.931E−05 2.000E−02 6.032E−05 1.761E−04 5.334E+02 1.130E+01 8.797E+00
754.436 2.612
2.438E−10 1.340E−01
45.983 0.370
1.459E−05 7.020E−01
115.148 0.342
4.190E−07 7.200E−01
60.633 1.285
5.070E−06 3.280E−01
Table 2–Effects of cell-adapted type the maximum growth rate (k) and lag phase duration (λ) of NCA and CA L. monocytogenes on fresh-cut cantaloupe at each temperature conditions—ANOVA. Parameter k
M: Food Microbiology & Safety
λ
Temperature (°C)
df
Sum sq.
Mean sq.
F-value
Pr(>F)
10 Residuals 15 Residuals 20 Residuals 25 Residuals 30 Residuals 10 Residuals 15 Residuals 20 Residuals 25 Residuals 30 Residuals
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2.228E−05 5.685E−06 1.463E−04 3.574E−05 6.740E−05 1.000E−03 1.135E−04 2.349E−04 3.659E−04 1.772E−03 3.570E+01 1.965E+01 1.334E+00 5.673E+01 2.500E−02 2.740E+00 1.767E+00 5.582E+00 1.827E+00 5.081E+00
2.228E−05 2.843E−06 1.463E−04 1.787E−05 6.740E−05 5.426E−04 1.135E−04 1.175E−04 3.659E−04 8.858E−04 3.570E+01 9.825E+00 1.334E+00 2.837E+01 2.500E−02 1.370E+00 1.767E+00 2.791E+00 1.827E+00 2.540E+00
7.838
0.107
8.189
0.103
0.124
0.758
0.966
0.429
0.413
0.586
3.633
0.196
0.047
0.848
0.019
0.904
0.633
0.510
0.719
0.486
fresh-cut cantaloupe at refrigerated temperatures, but the growth was somewhat hampered and failed to develop into full growth curves. Similarly, Sinigaglia and others (2006) reported that L. monocytogenes on fresh-cut coconut grew at 2 and 4 °C with an increase of only 1.0 to 1.5 log CFU/g during the storage for 12 days. L. innocua population also increased by 0.4 log on fresh-cut “Elegant Lady” peach at 5 °C (Alegre and others 2010). Table 1 lists the results of ANOVA of k and λ of NCA and CA for the effect of temperature and growth model. According to Table 1, there was no significant difference (P = 0.134−0.720) in k and λ values among 3 models, whereas both parameters from the each model were significantly (P = 2.44 × 10−10 to 5.07 × 10−6 ) affected by the storage temperature. In the modified Gompertz and Huang model, the λ values of NCA were gradually decreased from 35.14 to 0.00, with the storage temperature ranging from 10 to 30 °C. A similar trend was seen for λ values of CA, showing 33.22 to 0.00 between 10 and 30 °C, respectively (data not shown in Table 1). In the Baranyi model, the h0 is a dimensionless parameter quantifying the initial physiological state of the cell. In real world applications, the average h0 value is used (Huang 2010). For Baranyi model, the average h0 value for CA and NCA was 1.89 ± 1.05 and 2.44 ± 1.74 (n = 5), respectively. The k values of NCA gradually increased from 0.03 to 0.26 between 10 and 30 °C. A similar trend was seen for the k values of CA, showing 0.04
M1172 Journal of Food Science r Vol. 79, Nr. 6, 2014
to 0.22 between 10 and 30 °C. Previous study also showed that k and λ values were significantly changed at different storage temperatures (Fang and others 2013). RMSE values for NCA and CA cells ranged 0.62 to 1.83 and 0.46 to 1.53 at 10 °C, respectively, whereas the values were 0.19 to 0.70 at 25 °C. The results in Table 1 also suggest that any of the 3 primary models used in this study can be used to describe the growth of L. monocytogenes in fresh-cut cantaloupe. Similar with this study, Juneja and others (2009) reported that there was no significantly difference in describing the growth of Salmonella in raw ground beef among the Baranyi, modified Gompertz, Huang, and logistic models. Contrarily, Huang (2010) reported that the growth rates estimated from the Gompertz model were significantly higher than those from the Huang model when E. coli O157:H7 was grown in mechanically tenderized beef. When L. monocytogenes was grown in a liquid media, specific growth rates (μmax ) from the Gompertz and logistic models were markedly different from those estimated by the Baranyi model (Perni and others 2005). It is known that the bacterial growth curves including the lag to stationary phases would be required for the empirical models such as the modified Gompertz model when the models are used to predict bacterial growth, whereas Baranyi and Huang models, the mechanistic models, could be used for incomplete growth without the stationary phase (Juneja and others 2009). Although incomplete growth
Modeling of L. monocytogenes on cantaloupe . . .
0.4
k
Baranyi
Gompertz
Huang
Baranyi
Gompertz
Huang
0.2
0.1
0
0
0.4
k
5
10
15 20 Temperature(°C)
25
30
(b)
0.3
Baranyi
Gompertz
Huang
Baranyi
Gompertz
Huang
0.1
0
NCA CA
Model
α
G
n
RMSE
Gompertz Baranyi Huang Gompertz Baranyi Huang
9.377E−04 7.785E−04 9.768E−04 7.938E−04 7.785E−04 7.869E−04
2395 2379 2397 2382 2371 2374
49.57 68.28 49.87 49.59 61.69 61.92
0.018 0.021 0.024 0.039 0.026 0.017
spectively, showing that NCA cells need more energy (P < 0.05) than CA cells. Fang and others (2013) reported a higher G value (2560 J/mol) for L. monocytogenes on fresh-cut cantaloupe than that of this study, although the same food matrix was used. This might be due to the differences in primary model, bacterial stain, and cantaloupe. In the study reported by Fang and others (2013), a 3-parameter logistic model was used, and the lag phase was neglected. At 5 °C, the maximum growth rates of NCA cells calculated from the Arrhenius-type model were 8.81 × 10−4 , 2.14 × 10−4 , and 6.85 × 10−4 log CFU/g h−1 , for the modified Gompertz, Baranyi, and Huang model, respectively, while these values for CA cells were 2.88 × 10−3 , 2.04 × 10−3 , and 1.37 × 10−3 log CFU/g h−1 . The RMSE values of secondary models for NCA and CA cells were 0.018, 0.021, and 0.024, and 0.039, 0.026, and 0.017 at the modified Gompertz, Baranyi, and Huang model, respectively. It indicates that 3 models presented the good statistical fit for the data. This result also indicates that CA L. monocytogenes did not show better growth on the fresh-cut cantaloupe under the refrigerated condition.
5
10
15 20 Temperature(°C)
The growth of L. monocytogenes on fresh-cut cantaloupe was highly affected by the storage temperatures, showing the k increased with the elevated temperature. There was no significant difference in growth parameters at primary and secondary models between NCA and CA cells at different storage temperatures, indicating that CA cells did not show better growth at refrigeration temperature. In addition, there was no distinct difference in the growth pattern among 3 primary models at various storage temperatures. Thus, this study indicates that 3 primary models used in this study could be used to predict the behavior of L. monocytogenes on fresh-cut cantaloupe. These results may be helpful for risk assessments of L. monocytogenes in fresh-cut cantaloupe and this study provides valuable information to food handlers to decide a proper temperature to extend its shelf-life.
References
0.2
0
Bacterial cells
Conclusion
(a)
0.3
Table 3–Parameters for Arrhenius-type model of NCA and CA L. monocytogenes on fresh-cut cantaloupe.
25
30
Figure 3–Secondary curve fitting of L. monocytogenes using Arrhenius-type model for modified Gompertz, Baranyi, and Huang model.
Alegre I, Abadias M, Anguera M, Usall J, Vi˜nas I. 2010. Fate of Escherichia coli O157:H7, Salmonella and Listeria innocua on minimally-processed peaches under different storage conditions. Food Microbiol 27(7):862–8. Bang W, Drake MA. 2002. Resistance of cold- and starvation-stressed Vibrio vulnificus to heat and freeze-thaw exposure. J Food Prot 65(6):975–80. Baranyi J, Roberts TA. 1994. A dynamic approach to predicting bacterial growth in food. Int J Food Microbiol 23(3–4):277–94. Barbosa WB, Cabedo L, Wederquist HJ, Sofos JN, Schmidt GR. 1994. Growth variation among species and strains of Listeria in culture broth. J Food Prot 57(9):765–9. Bennion JR, Sorvillo F, Wise ME, Krishna S, Mascola L. 2008. Decreasing listeriosis mortality in the United States, 1990–2005. Clin Infect Dis 47(7):867–74. Beuchat LR, Mann DA. 2008. Survival and growth of acid-adapted and unadapted Salmonella in and on raw tomatoes as affected by variety, stage of ripeness, and storage temperature. J Food Prot 71(8):1572–9. Boonyawantang A, Mahakarnchanakul W, Rachtanapun C, Boonsupthip W. 2012. Behavior of pathogenic Vibrio parahaemolyticus in prawn in response to temperature in laboratory and factory. Food Cont 26(2):479–85. [CDC] Centers for Disease Control and Prevention. 2002. Multistate outbreaks of Salmonella serotype poona infections associated with eating cantaloupe from Mexico—United States and Canada, 2000–2002. Morb Mortal Wkly Rep 51(46):1044–7.
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curves without lag and stationary phases at some temperature conditions were observed, there was no difference among the primary models. Cold chain system for fresh fruits during transportation and storage may induce cold adaptation on foodborne pathogens on surface of the fruits, probably influencing bacterial growth and survival on fresh-cut fruits (Rodriguez-Romo and Yousef 2005). Thus, the growth parameters (k and λ) of NCA and CA cell were also compared to see if cold adaptation affects on growth of L. monocytogenes on fresh-cut cantaloupe during storage at low temperatures. The present results showed that there was no significant difference (P > 0.05) in k and λ values between NCA and CA (Table 2). Previous studies with other foodborne pathogens such as Vibrio vulnificus (Bang and Drake 2002) and Salmonella spp. (Sim and others 2013) also showed that there was no enhanced growth of CA cells compared to NCA cells at lower temperatures in broth and fresh-cut dragon fruits, respectively. However, these previous studies did not use the growth models to predict the behavior of pathogens during storage; hence it is difficult to directly compare the results. The maximum growth rates derived from the primary models were fitted to the Arrhenius-type model for describing the relationship between k and temperature in L. monocytogenes inoculated onto fresh-cut cantaloupe (Figure 3) and the model parameters were calculated based on the model (Table 3). Regardless of conditions under which the cells grew, similar G values were obtained among 3 primary models. The average G values of NCA and CA cells were calculated as 2375 and 2390 J/mol, re-
Modeling of L. monocytogenes on cantaloupe . . .
M: Food Microbiology & Safety
[CDC] Centers for Disease Control and Prevention. 2007. Salmonella Oranienburg infections associated with fruit salad served in health-care facilities—Northeastern United States and Canada, 2006. Morb Mortal Wkly Rep 56(39):1025–8. [CDC] Centers for Disease Control and Prevention. 2008. Investigation of outbreak of infections caused by Salmonella Litchfield. Atlanta, GA: Centers for Disease Control and Prevention. Available from: http://www.cdc.gov/salmonella/litchfield/. Accessed 2013 Aug 13. [CDC] Centers for Disease Control and Prevention. 2011a. Investigation update: multistate outbreak of Salmonella Panama infections linked to cantaloupe. Atlanta, GA: Centers for Disease Control and Prevention. Available from: http://www.cdc.gov/salmonella/ panama0311/062311/index.html. Accessed 2013 Aug 13. [CDC] Centers for Disease Control and Prevention. 2011b. Surveillance for foodborne disease outbreaks—United States, 2008. Atlanta, GA: Centers for Disease Control and Prevention. Available from: http://www.cdc.gov/mmwr/preview/mmwrhtml/ mm6035a3.htm?s_cid=mm60355a3_w. Accessed 2012 Nov 10. [CDC] Centers for Disease Control and Prevention. 2012. Multistate outbreak of listeriosis linked to whole cantaloupes from Jensen farms, Colorado. Listeria (Listeriosis). Atlanta, GA: Centers for Disease Control and Prevention Available from: http://www.cdc. gov/listeria/outbreaks/cantaloupes-jensen-farms/082712/index.html. Accessed 2012 Oct 10. Delignette-Muller ML, Baty F, Cornu M, Bergis H. 2005. Modelling the effect of a temperature shift on the lag phase duration of Listeria monocytogenes. Int J Food Microbiol 100(1–3):77–84. Fang T, Liu Y, Huang L. 2013. Growth kinetics of Listeria monocytogenes and spoilage microorganisms in fresh-cut cantaloupe. Food Microbiol 34(1):174–81. [FAO] Food and Agriculture Organization of the United Nations. 2011. Microbiological hazards and melons. Rome, Italy: Food and Agriculture Organization of the United Nations. Available from: ftp://ftp.fao.org/ag/agn/jemra/Microbiological_hazards_and_melons_Nov08.pdf. Accessed 2012 Nov 10. [FDA] Food and Drug Administration. 2009. Guidance for industry: guide to minimize microbial food safety hazards of melons; draft guidance. Silver Spring, MD: Dept. of Health and Human Services, Food and Drug Administration, Center for Food Safety and Applied Nutrition. Available from: http://www.fda.gov/Food/GuidanceRegulation/ GuidanceDocumentsRegulatoryInformation/ProducePlantProducts/ucm174171.htm. Accessed 2013 Aug 13. Gil MI, Aguayo E, Kader AA. 2006. Quality changes and nutrient retention in fresh-cut versus whole fruits during storage. J Agric Food Chem 54(12):4284–96. Gr¨undling A, Burrack LS, Bouwer HG, Higgins DE. 2004. Listeria monocytogenes regulates flagella motility gene expression through MogR, a transcriptional repressor required for virulence. P Natl Acad Sci USA 101(33):12318–23. Huang L. 2010. Growth kinetics of Escherichia coli O157:H7 in mechanically-tenderized beef. Int J Food Microbiol 140(1):40–8. Huang L. 2011. A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new B˘elehdr´adek-type model for evaluating the effect of temperature on growth rate. Food Microbiol 28(4):770–6. Huang L. 2013. Optimization of a new mathematical models for bacterial growth. Food Cont 32(1):283–8. Huang L, Hwang A, Phillips J. 2011. Effect of temperature on microbial growth ratemathematical analysis: the Arrhenius and Eyring-Polanyi connections. J Food Sci 76(8): E553–60. [ICMSF] Intl. Commission on Microbiological Specifications for Foods. 1996. Listeria monocytogenes. In: ICMSF editors. Microorganisms in foods 5: microbiological specifications of food pathogens. London: Blackie Academic & Professional. p 141–82. Juneja VK, Melendres MV, Huang L, Subbiah J, Thippareddi H. 2009. Mathematical modeling of growth of Salmonella in raw ground beef under isothermal conditions from 10 to 45 °C. Int J Food Microbiol 131(2–3):106–11.
M1174 Journal of Food Science r Vol. 79, Nr. 6, 2014
Koseki S, Isobe S. 2005. Growth of Listeria monocytogenes on iceberg lettuce and solid media. Int J Food Microbiol 101(2):217–25. Mahmoud BS, Vaidya NA, Corvalan CM, Linton RH. 2008. Inactivation kinetics of inoculated Escherichia coli O157:H7, Listeria monocytogenes and Salmonella poona on whole cantaloupe by chlorine dioxide gas. Food Microbiol 25(7):857–65. Mastronicolis SK, Boura A, Karaliota A, Magiatis P, Arvanitis N, Litos C, Tsakirakis A, Paraskevas P, Moustaka H, Heropoulos G. 2006. Effect of cold temperature on the composition of different lipid classes of the foodborne pathogen Listeria monocytogenes: focus on neutral lipids. Food Microbiol 23(2):184–94. McMeekin T, Bowman J, McQuestin O, Mellefont L, Ross T, Tamplin M. 2008. The future of predictive microbiology: strategic research, innovative applications and great expectations. Int J Food Microbiol 128(1):2–9. Mohle-Boetani J, Reporter R, Werner SB, Abbott S, Farrar J, Waterman SH, Vugia DJ. 1999. An outbreak of Salmonella serogroup Saphra due to cantaloupes from Mexico. J Infect Dis 180(4):1361–4. Olaimat AN, Holley RA. 2012. Factors influencing the microbial safety of fresh produce: a review. Food Microbiol 32(1):1–19. Pe˜nuela C. 2012. Florida fresh: cantaloupes. Gainesville, FL: Univ. of Florida IFAS Extension Available from: http://edis.ifas.ufl.edu/fy1101. Accessed 2013 Aug 13. Perni S, Andrew PW, Shama G. 2005. Estimating the maximum growth rate from microbial growth curves: definition is everything. Food Microbiol 22(6):491–5. Rodriguez-Romo LA, Yousef AE. 2005. Microbial adaptation and safety of produce. In: Sapers GM, Gorny JR, Yousef AE, editors. Microbiology of fruit and vegetables. Boca Raton, Fla.: CRC Press. p 95–116. Sapers GM, Doyle MP. 2009. Scope of the produce contamination problem. In: Saper GM, Solomon EB, Matthew KR, editors. The produce contamination problem: causes and solutions. California: Academic Press. p 3–19. Schlech WF. 1996. Overview of listeriosis. Food Cont 7(4–5):183–6. Selma MV, Ib´an˜ ez AM, Allende A, Cantwell M, Suslow T. 2008. Effect of gaseous ozone and hot water on microbial and sensory quality of cantaloupe and potential transference of Escherichia coli O157:H7 during cutting. Food Microbiol 25(1):162–8. Sim HL, Hong YK, Yoon WB, Yuk HG. 2013. Behavior of salmonella spp. and natural microbiota on fresh-cut dragon fruits at different storage temperatures. Int J Food Microbiol 160(3): 239–44. Sinigaglia M, Bevilacqua A, Campaniello D, D’Amato D, Corbo MR. 2006. Growth of Listeria monocytogenes in fresh-cut coconut as affected by storage conditions and inoculum size. J Food Prot 69(4):820–5. Strawn LK, Danyluk MD. 2010. Fate of Escherichia coli O157:H7 and Salmonella spp. on fresh and frozen cut mangoes and papayas. Int J Food Microbiol 138(1–2): 78–84. Ukuku DO, Fett W. 2002. Behavior of Listeria monocytogenes inoculated on cantaloupe surfaces and efficacy of washing treatments to reduce transfer from rind to fresh-cut pieces. J Food Prot 65(6):924–30. Wang J, Rahman S, Zhao XH, Forghani F, Park MS, Oh DH. 2013. Predictive models for the growth kinetics of Listeria monocytogenes on white cabbage. J Food Safety 33(1): 50–8. Vandamm JP. Li D, Harris LJ, Schaffner DW, Danyluk MD. 2013. Fate of Escherichia coli O157:H7, Listeria monocytogenes, and Salmonella on fresh-cut celery. Food Microbiol 34(1):151–7. Zwietering MH, Jongenburger I, Rombouts FM, Van’t Riet K. 1990. Modeling of the bacterial growth curve. Appl Environ Microbiol 56(6):1875–81.
The aim of this study was to determine the growth kinetics of Listeria monocytogenes, with and without cold-adaption, on fresh-cut cantaloupe under different storage temperatures. Fresh-cut samples, spot inoculated with a 4-strain cocktail of L. monocytogenes (3.2 log CFU/g), were exposed to constant storage temperatures held at 10, 15, 20, 25, or 30 °C. All growth curves of L. monocytogenes were fitted to the Baranyi, modified Gompertz, and Huang models. Regardless of conditions under which cells grew, the time needed to reach 5 log CFU/g decreased with the elevated storage temperature. Experimental results showed that there were no significant differences (P > 0.05) in the maximum growth rate k (log CFU/g h−1 ) and lag phase duration λ (h) between the cultures of L. monocytogenes with or without previous cold-adaption treatments. No distinct difference was observed in the growth pattern among 3 primary models at various storage temperatures. The growth curves of secondary modeling were fitted on an Arrhenius-type model for describing the relationship between k and temperature of the L. monocytogenes on fresh-cut cantaloupe from 10 to 30 °C. The root mean square error values of secondary models for non- and cold-adapted cells were 0.018, 0.021, and 0.024, and 0.039, 0.026, and 0.017 at the modified Gompertz, Baranyi, and Huang model, respectively, indicating that these 3 models presented the good statistical fit. This study may provide valuable information to predict the growth of L. monocytogenes on fresh-cut cantaloupes at different storage conditions. Abstract:
M: Food Microbiology & Safety
Keywords: cold-adaptation, fresh-cut cantaloupe, Listeria monocytogenes, predictive modeling
Listeriosis has occurred and increased along with the increased demand of fresh and fresh-cut fruits and vegetables. This study was conducted to predict the growth of non- and cold-adapted L. monocytogenes on fresh-cut cantaloupe at different temperature using mathematical model. These results can be helpful for risk assessments of L. monocytogenes in fresh-cut cantaloupe. This study provides valuable information to food handlers to choose proper storage temperatures for extending the shelf-life of fresh-cut cantaloupe.
Practical Application:
Introduction Listeria monocytogenes presents a major food safety concern due to listeriosis that has a high mortality rate (Bennion and others 2008). This bacterium is Gram-positive psychrotrophic foodborne pathogen that can grow at refrigerated temperatures (ICMSF 1996; Gr¨undling and others 2004). Listeriosis is commonly linked to deli meats, cheeses, and unpasteurized milk; however, the transmission vehicles have recently changed due to an increase in the number of Listeria infections associated with fresh and fresh-cut fruits and vegetables such as cabbage, celery, lettuce, and strawberry (Schlech 1996; Sapers and Doyle 2009; Vandamm and others 2013). Cantaloupe (Cucumis melo var. reticulatus), an orange-fleshed melon, is one of the most popular tropical fruits worldwide since MS 20131307 Submitted 9/14/2013, Accepted 3/10/2014. Authors Hong and Yoon are with Dept. of Food Science and Biotechnology, College of Agriculture and Life Sciences, Kangwon Natl. Univ., Chuncheon, Gangwondo 200-701, South Korea. Author Huang is with Eastern Regional Research Center, Agricultural Research Service, U.S. Dept. of Agriculture, 600 E. Mermaid Lane, Wyndmoor, PA 19038, U.S.A. Author Yuk is with Food Science and Technology Programme, Dept. of Chemistry, Natl. Univ. of Singapore, 3 Science Drives 3, 117544, Singapore. Direct inquiries to author Yuk (E-mail: [email protected]).
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the fruit is delicious and rich in vitamin A, vitamin C, and potassium (Pe˜nuela 2012). In general, cantaloupes grow on vines on the ground in a trailing and scrambling manner (FAO 2011), and the inner flesh of the fruit is rich in sugars and low in acidity (pH 6.7), which is a favorable condition for growth of foodborne pathogens (Gil and others 2006). In addition, pathogenic bacteria from contaminated soil and irrigation water may be harbored on rough outer rind of the fruit (Mahmoud and others 2008), and easily transferred into the flesh when the fruit is cut (Ukuku and Fett 2002; Selma and other 2008). For these reasons, cantaloupes have been implicated in many foodborne bacterial infections involving consumption of fresh-cut products contaminated with Escherichia coli O157:H7, Salmonella spp., and L. monocytogenes (Mohle-Boetani and others 1999; CDC 2002, 2007, 2008, 2011a, 2011b; Mahmoud and others 2008; FDA 2009; Olaimat and Holley 2012). In 2011, a multistate outbreak of L. monocytogenes infection linking to whole cantaloupe was in the United States. This outbreak caused a total 147 cases and 33 deaths (CDC 2012). Since cantaloupe generally serves as fresh-cut form at food establishments without additional treatment, storage condition plays an important role in preventing listeriosis. Previous research R C 2014 Institute of Food Technologists
doi: 10.1111/1750-3841.12468 Further reproduction without permission is prohibited
Modeling of L. monocytogenes on cantaloupe . . . genes serovar 1/2b (ATCC BAA-839; human outbreak), L. monocytogenes serovar 1 (ATCC 19111; poultry outbreak), and L. monocytogenes serovar 4b (ATCC 13932; Spinal fluid of child outbreak), purchased from the American Type Culture Collection (ATCC; Manassas, Va., U.S.A.) were selected in this study. Frozen cultures were activated in 10 mL trypticase soy broth (TSB; Oxoid, Basingstoke, Hampshire, U.K.). All cultures were adapted to resist 200 μg/mL nalidixic acid (Sigma-Aldrich, St. Louis, Mo., U.S.A.) by stepwise increment of nalidixic acid concentration after each transfer of the respective culture. After which, all media used in this study were supplemented with 200 μg/mL nalidixic acid so that the L. monocytogenes cells isolated from inoculated cantaloupes were relatively free from other background bacterial contaminants (Beuchat and Mann 2008; Strawn and Danyluk 2010). Nalidixic acid adapted L. monocytogenes were transferred daily to maintain viability. Preparation of inoculum. Prior to inoculation, each nalidixic acid adapted cell culture was inoculated into 10 mL of TSB supplemented with 200 μg/mL nalidixic acid (TSBN) and incubated at 37 °C for 24 h with 2 consecutive transfers using a loopful of the culture. The cultures were centrifuged at 3500 rpm Materials and Methods for 10 min at 4 °C, and washed 3 times by removing the superBacterial strains and culture condition. L. monocytogenes natant and suspending the cell pellet in 1 mL of 0.1% peptone waserovar 1/2b (ATCC BAA-839; human outbreak), L. monocyto- ter (PW, Oxoid). After washing, 1 mL from each L. monocytogenes
Figure 1–Comparison of modified Gompertz, Baranyi, and Huang models on the growth of NCA cell of L. monocytogenes on fresh-cut cantaloupes at diffent storage temperatures. (A) 5 °C (not fitted), (B) 10 °C, (C) 15 °C, (D) 20 °C, (E) 25 °C, and (F) 30 °C. Vol. 79, Nr. 6, 2014 r Journal of Food Science M1169
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demonstrated that L. monocytogenes is able to grow at refrigerated temperatures with long lag and generation times (Barbosa and others 1994). According to an FAO report (2011), poor temperature control is a main factor contributing to foodborne illness associated with melons, followed by pre-cut and/or mixed dish. Thus, it is crucial to understand the growth kinetics of L. monocytogenes on the fresh-cut cantaloupe under different storage temperatures. A previous study reported that freshly harvested L. monocytogenes inoculated onto fresh-cut cantaloupe can grow well at temperatures between 4 and 43 °C (Fang and others 2013). However, it remains unclear if L. monocytogenes, exposed to and adapted to low temperature, may affect its growth and multiplication in freshcut cantaloupe since bacterial adaption may occur during storage. Therefore, the objective of this study was to investigate the effect of cold adaption on the growth of L. monocytogenes in fresh-cut cantaloupe and compare its growth kinetics with freshly harvested bacterial cultures. This work also aimed to develop mathematical models that can describe the growth behaviors of L. monocytogenes in fresh-cut cantaloupe under different storage temperature conditions.
Modeling of L. monocytogenes on cantaloupe . . .
12
Primary models. All growth curves of L. monocytogenes at 10, 15, 20, 25, and 30 °C were fitted to the Baranyi, modified Gompertz, and Huang models. The growth data obtained at 5 °C were not fitted to the models since the distinctive growth was not observed. The Baranyi model (Baranyi and Roberts 1994) is defined by exp [μmax A(t )] − 1 Y(t ) = Y0 + μmax A(t ) − ln 1 + exp (Ymax − Y0 )
+ exp (−h 0 ) − exp (−μmax t − h 0 )]
6 4
B
8 6 4
2
2
0
0 0
20
40
60
80
100
Baranyi
0
20
Time(h)
12
6 4
0 0
20
Gompertz
40
60
2
80
Baranyi
100
0
log CFU/g
8 6 4 Gompertz
Huang
5
10 15 20 25 30 35 40 45 50 Time(h)
F
10
Baranyi
Gompertz
0
12
2
100
4
Huang
E
10
80
6
Time(h)
12
60
8
log CFU/g
log CFU/g
8
Baranyi
40
Huang
D
10
2
Gompertz
Time(h)
C
10
(2)
where Y(t) = ln CFU/g of cell concentration at time t, Y0 = ln(x0 ), x0 is the initial cell concentration (CFU/g), Ymax is the maximum cell concentration (ln CFU/g), μmax is the specific growth rate (ln CFU/g h−1 ), h0 = μmax λ, λ is the lag phase duration (h) at the incubation temperature, and t is the incubation/growth time (h).
10
8
(1)
1 A(t ) − ln[exp (−μmax t ) μmax
A(t ) = t +
log CFU/g
log CFU/g
populations of bacterial cells were expressed in log CFU/g of fruit. Predictive model for bacterial growth.
12
A
10
log CFU/g
M: Food Microbiology & Safety
culture was aseptically combined to produce a cocktail of 4 serovars. The bacterial suspension was diluted with 0.1% PW to obtain a final concentration of ca. 4.0 to 5.0 log CFU/mL. Freshly prepared cocktail of L. monocytogenes was designated as non-cold-adapted (NCA) cells. Cold-adaptation. To allow L. monocytogenes cells to adapt to cold temperature, the bacterial suspension prepared described above was stored at 5 °C for 5 days, according to the procedures adopted and modified from Mastronicolis and others (2006). The bacterial cultures obtained from this procedure were designated as cold-adapted (CA) cells. Storage study and enumeration. The inoculated cantaloupes were incubated under different storage temperatures (5, 10, 15, 20, 25, or 30 °C) to investigate the growth of L. monocytogenes. The samples were periodically retrieved to determine the growth of L. monocytogenes, with sampling frequencies adjusted according to the storage temperatures. To enumerate L. monocytogenes from samples, 100 mL of 0.1% PW was added to each sample and homogenized for 1 min using a stomacher (IUL Instruments, Barcelona, Spain). After which, serial dilutions were made with 0.1% PW and pour-plated into trypticase soy agar (TSA; Oxoid) supplemented with 200 μg/mL nalidixic acid (TSAN). Plates were incubated at acrobatically 37 °C for 48 h, followed by manual counting of colonies. The
Huang
0
8 6 4 2
Baranyi
Gompertz
Huang
0 0
5
10 15 20 25 30 35 40 45 50 Time(h)
0
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10 15 20 25 30 35 40 45 50 Time(h)
Figure 2–Comparison of modified Gompertz, Baranyi, and Huang models on the growth of CA cell of L. monocytogenes on fresh-cut cantaloupes at diffent storage temperatures. (A) 5 °C (not fitted), (B) 10 °C, (C) 15 °C, (D) 20 °C, (E) 25 °C, and (F) 30 °C.
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The modified Gompertz model (Zwietering and others 1990) (P < 0.05) among the mean values were analyzed by Tukey’s HSD test. is defined by 2.718k(λ − t ) Results and Discussion y(t ) = y0 + Ce xp −exp +1 (3) Modeling of growth for a certain pathogen on foods is an essenC tial step for a microbial risk assessment, which is a structured prowhere y(t) is the log CFU/g of cell concentration at time t, y0 = cess for determining the risk associated with any hazards in foods log(x0 ), C is the asymptotic increase in population density, and k (McMeekin and others 2008). To date, many efforts in the preis the the maximum growth rate (log CFU/g h−1 ). dictive microbiology have been made by developing new growth The Huang model (Huang 2011, 2013) is defined by models or modifying the existing models for better describing microbial growth data obtained from experiments. Among them, the Y0 Ymax (4) modified Gompertz and Baranyi models (Eq. 1 and 2) have been Y(t ) = Y0 + Ymax − ln e + e − e Y0 e −μmax B(t ) well established and used in many microbial growth studies. However, the Huang model has been recently developed and applied to 1 1 + e −β(t −λ) the growth models of some foodborne pathogens in foods (Huang B(t ) = t + ln (5) β 1 + e βλ 2011, 2013). It is necessary to validate this model in different laboratories. Each model of these models has its advantages. Although where β is a constant that defines the transition from the an empirical model, the modified Gompertz model is very easy lag phase to the exponential phase of a growth curve. Huang to understand and has been extensively used in the literature. The (2013) suggested that the parameter β = 4 is suitable for Baranyi model is more complex than the modified Gompertz, analyzing bacterial growth curve in the Huang model. With but it introduced an interesting parameter h , which is basically a 0 β = 4, the Huang model can be used to analyze the growth virtual parameter and an indicator of the physiological state of the curves with lag phase up to 175 h. For this reason, β was bacterium under investigation. This parameter is used to quantify initially 25 (Huang 2011), but reduced to 4 (Huang 2013) the prior history on bacterial growth (Baranyi and Roberts 1994). without affecting the performance and curve-fitting of the In addition, it plays the role of a bridge between the history and model. the actual environment. However, h0 is a virtual parameter that Secondary model. The secondary model used in this study was an is difficult to be observed, and validated, and is sensitive to temArrhenius-type model developed by Huang and others (2011), perature shift (Delignette-Muller and others 2005). The Huang model, however, is a relatively simply model based on the funand defined by damental growth phenomenon of microorganisms in foods. This n model clearly defines the duration of lag phase and exponential G k = α (T + 273.15) exp − (6) growth rate in a single equation, and is more intuitive than the R (T + 273.15) traditional growth models such as modified Gompertz and Baranyi where R is the gas constant (8.314 J/mol·K), T is the tempera- models (Huang 2011). Thus, this study compared 2 existing modture (°C), G is the a type of kinetic energy related to bacterial els (the modified Gompertz and Baranyi models) with the Huang growth, n and α are coefficients. In this equation, k is the maxi- model in modeling the growth of NCA and cold adapted (CA) L. mum growth rate was used. In the modified Gompertz model, this monocytogenes on locally produced fresh-cut cantaloupe at various value was directly calculated from the model. For the Baranyi and storage temperatures. The growth curves of NCA and CA L. monocytogenes on freshHuang models, the specific growth rates (μmax ) in these models were converted to k by dividing μmax in Eq. (1), (2), and (4) with cut cantaloupe were fitted into the Baranyi, modified Gompertz, and Huang models at 10, 15, 20, 25 and 30 °C, respectively. The 2.303 (or ln 10). cell growth at 5 °C could not be fitted into the models since the Curve fitting. Once the growth curves were obtained, each growth did not develop into full curves (Figure 1). Under the curve was fitted to the primary models and then to secondary incubation temperatures between 10 and 30 °C, the inoculated models using nonlinear regression. The nonlinear regression was L. monocytogenes cells, with or without previous exposure to cold conducted using the Trust-Region algorithm. All curve fitting adaptation, grew rapidly on fresh-cut cantaloupe, and grew faster as was performed using Matlab Curve Fitting ToolboxTM (version the storage temperatures increased. At the initial inoculation level 3.3, Mathworks, Inc., Natick, Mass., U.S.A.) to determine the of 3.2 log CFU/g, the averaged time needed for the population parameters for each model. of NCA cells of L. monocytogenes reached to 5 log CFU/g 80, 60, Evaluation of model performance and statistical 22, 13, 8, and 7 h at 5, 10, 15, 20, 25 and 30 °C, respectively analysis. All experiments were conducted in independent tripli- (Figure 1). For CA cells, the average time to 5 log CFU/g in the cates with duplicate samples analyzed at each sampling time. The inoculated samples was 76, 62, 17, 15, 10 and 8 h at 5, 10, 15, 20, goodness-of-fit of the primary and secondary models were assessed 25 and 30 °C, respectively (Figure 2). by calculating and comparing the root mean square error (RMSE) The results obtained in this study were in agreement with the values of the models (Boonyawantang and others 2012) using previous studies, which showed that the growth of L. monocytogenes Eq. (7): on fresh produce was highly dependent on storage temperature,
revealing that an increase in storage temperature accelerates the n 2 cell growth (Koseki and Isobe 2005; Sinigaglia and others 2006; 1 [Experimental value − Model value] (7) RMSE = Wang and others 2013). For example, Wang and others (2013) Degree of freedom showed that L. monocytogenes on white cabbage stored at higher The k and λ values from each growth model were evaluated temperatures had shorter times to reach the maximum population by analysis of variance (ANOVA) and significant differences (5–8 log CFU/g). It was evident that L. monocytogenes can grow on Vol. 79, Nr. 6, 2014 r Journal of Food Science M1171
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Modeling of L. monocytogenes on cantaloupe . . .
Modeling of L. monocytogenes on cantaloupe . . . Table 1–Effects of temperature and model type on the maximum growth rate (k) and lag phase duration (λ) of NCA and CA L. monocytogenes on fresh-cut cantaloupe across all temperature conditions—ANOVA. Parameter NCA
k λ
CA
k λ
Temperature Model Residuals Temperature Model Residuals Temperature Model Residuals Temperature Model Residuals
df
Sum sq.
Mean sq.
F-value
Pr(>F)
4 2 8 4 2 8 4 2 8 4 2 8
1.190E−01 2.054E−04 1.190E−01 1.871E+03 7.535E+00 3.145E−04 8.100E−02 1.206E−04 1.409E−03 2.134E+03 2.261E+01 7.038E+01
3.000E−02 1.027E−04 3.931E−05 4.678E+02 3.767E+00 3.931E−05 2.000E−02 6.032E−05 1.761E−04 5.334E+02 1.130E+01 8.797E+00
754.436 2.612
2.438E−10 1.340E−01
45.983 0.370
1.459E−05 7.020E−01
115.148 0.342
4.190E−07 7.200E−01
60.633 1.285
5.070E−06 3.280E−01
Table 2–Effects of cell-adapted type the maximum growth rate (k) and lag phase duration (λ) of NCA and CA L. monocytogenes on fresh-cut cantaloupe at each temperature conditions—ANOVA. Parameter k
M: Food Microbiology & Safety
λ
Temperature (°C)
df
Sum sq.
Mean sq.
F-value
Pr(>F)
10 Residuals 15 Residuals 20 Residuals 25 Residuals 30 Residuals 10 Residuals 15 Residuals 20 Residuals 25 Residuals 30 Residuals
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2.228E−05 5.685E−06 1.463E−04 3.574E−05 6.740E−05 1.000E−03 1.135E−04 2.349E−04 3.659E−04 1.772E−03 3.570E+01 1.965E+01 1.334E+00 5.673E+01 2.500E−02 2.740E+00 1.767E+00 5.582E+00 1.827E+00 5.081E+00
2.228E−05 2.843E−06 1.463E−04 1.787E−05 6.740E−05 5.426E−04 1.135E−04 1.175E−04 3.659E−04 8.858E−04 3.570E+01 9.825E+00 1.334E+00 2.837E+01 2.500E−02 1.370E+00 1.767E+00 2.791E+00 1.827E+00 2.540E+00
7.838
0.107
8.189
0.103
0.124
0.758
0.966
0.429
0.413
0.586
3.633
0.196
0.047
0.848
0.019
0.904
0.633
0.510
0.719
0.486
fresh-cut cantaloupe at refrigerated temperatures, but the growth was somewhat hampered and failed to develop into full growth curves. Similarly, Sinigaglia and others (2006) reported that L. monocytogenes on fresh-cut coconut grew at 2 and 4 °C with an increase of only 1.0 to 1.5 log CFU/g during the storage for 12 days. L. innocua population also increased by 0.4 log on fresh-cut “Elegant Lady” peach at 5 °C (Alegre and others 2010). Table 1 lists the results of ANOVA of k and λ of NCA and CA for the effect of temperature and growth model. According to Table 1, there was no significant difference (P = 0.134−0.720) in k and λ values among 3 models, whereas both parameters from the each model were significantly (P = 2.44 × 10−10 to 5.07 × 10−6 ) affected by the storage temperature. In the modified Gompertz and Huang model, the λ values of NCA were gradually decreased from 35.14 to 0.00, with the storage temperature ranging from 10 to 30 °C. A similar trend was seen for λ values of CA, showing 33.22 to 0.00 between 10 and 30 °C, respectively (data not shown in Table 1). In the Baranyi model, the h0 is a dimensionless parameter quantifying the initial physiological state of the cell. In real world applications, the average h0 value is used (Huang 2010). For Baranyi model, the average h0 value for CA and NCA was 1.89 ± 1.05 and 2.44 ± 1.74 (n = 5), respectively. The k values of NCA gradually increased from 0.03 to 0.26 between 10 and 30 °C. A similar trend was seen for the k values of CA, showing 0.04
M1172 Journal of Food Science r Vol. 79, Nr. 6, 2014
to 0.22 between 10 and 30 °C. Previous study also showed that k and λ values were significantly changed at different storage temperatures (Fang and others 2013). RMSE values for NCA and CA cells ranged 0.62 to 1.83 and 0.46 to 1.53 at 10 °C, respectively, whereas the values were 0.19 to 0.70 at 25 °C. The results in Table 1 also suggest that any of the 3 primary models used in this study can be used to describe the growth of L. monocytogenes in fresh-cut cantaloupe. Similar with this study, Juneja and others (2009) reported that there was no significantly difference in describing the growth of Salmonella in raw ground beef among the Baranyi, modified Gompertz, Huang, and logistic models. Contrarily, Huang (2010) reported that the growth rates estimated from the Gompertz model were significantly higher than those from the Huang model when E. coli O157:H7 was grown in mechanically tenderized beef. When L. monocytogenes was grown in a liquid media, specific growth rates (μmax ) from the Gompertz and logistic models were markedly different from those estimated by the Baranyi model (Perni and others 2005). It is known that the bacterial growth curves including the lag to stationary phases would be required for the empirical models such as the modified Gompertz model when the models are used to predict bacterial growth, whereas Baranyi and Huang models, the mechanistic models, could be used for incomplete growth without the stationary phase (Juneja and others 2009). Although incomplete growth
Modeling of L. monocytogenes on cantaloupe . . .
0.4
k
Baranyi
Gompertz
Huang
Baranyi
Gompertz
Huang
0.2
0.1
0
0
0.4
k
5
10
15 20 Temperature(°C)
25
30
(b)
0.3
Baranyi
Gompertz
Huang
Baranyi
Gompertz
Huang
0.1
0
NCA CA
Model
α
G
n
RMSE
Gompertz Baranyi Huang Gompertz Baranyi Huang
9.377E−04 7.785E−04 9.768E−04 7.938E−04 7.785E−04 7.869E−04
2395 2379 2397 2382 2371 2374
49.57 68.28 49.87 49.59 61.69 61.92
0.018 0.021 0.024 0.039 0.026 0.017
spectively, showing that NCA cells need more energy (P < 0.05) than CA cells. Fang and others (2013) reported a higher G value (2560 J/mol) for L. monocytogenes on fresh-cut cantaloupe than that of this study, although the same food matrix was used. This might be due to the differences in primary model, bacterial stain, and cantaloupe. In the study reported by Fang and others (2013), a 3-parameter logistic model was used, and the lag phase was neglected. At 5 °C, the maximum growth rates of NCA cells calculated from the Arrhenius-type model were 8.81 × 10−4 , 2.14 × 10−4 , and 6.85 × 10−4 log CFU/g h−1 , for the modified Gompertz, Baranyi, and Huang model, respectively, while these values for CA cells were 2.88 × 10−3 , 2.04 × 10−3 , and 1.37 × 10−3 log CFU/g h−1 . The RMSE values of secondary models for NCA and CA cells were 0.018, 0.021, and 0.024, and 0.039, 0.026, and 0.017 at the modified Gompertz, Baranyi, and Huang model, respectively. It indicates that 3 models presented the good statistical fit for the data. This result also indicates that CA L. monocytogenes did not show better growth on the fresh-cut cantaloupe under the refrigerated condition.
5
10
15 20 Temperature(°C)
The growth of L. monocytogenes on fresh-cut cantaloupe was highly affected by the storage temperatures, showing the k increased with the elevated temperature. There was no significant difference in growth parameters at primary and secondary models between NCA and CA cells at different storage temperatures, indicating that CA cells did not show better growth at refrigeration temperature. In addition, there was no distinct difference in the growth pattern among 3 primary models at various storage temperatures. Thus, this study indicates that 3 primary models used in this study could be used to predict the behavior of L. monocytogenes on fresh-cut cantaloupe. These results may be helpful for risk assessments of L. monocytogenes in fresh-cut cantaloupe and this study provides valuable information to food handlers to decide a proper temperature to extend its shelf-life.
References
0.2
0
Bacterial cells
Conclusion
(a)
0.3
Table 3–Parameters for Arrhenius-type model of NCA and CA L. monocytogenes on fresh-cut cantaloupe.
25
30
Figure 3–Secondary curve fitting of L. monocytogenes using Arrhenius-type model for modified Gompertz, Baranyi, and Huang model.
Alegre I, Abadias M, Anguera M, Usall J, Vi˜nas I. 2010. Fate of Escherichia coli O157:H7, Salmonella and Listeria innocua on minimally-processed peaches under different storage conditions. Food Microbiol 27(7):862–8. Bang W, Drake MA. 2002. Resistance of cold- and starvation-stressed Vibrio vulnificus to heat and freeze-thaw exposure. J Food Prot 65(6):975–80. Baranyi J, Roberts TA. 1994. A dynamic approach to predicting bacterial growth in food. Int J Food Microbiol 23(3–4):277–94. Barbosa WB, Cabedo L, Wederquist HJ, Sofos JN, Schmidt GR. 1994. Growth variation among species and strains of Listeria in culture broth. J Food Prot 57(9):765–9. Bennion JR, Sorvillo F, Wise ME, Krishna S, Mascola L. 2008. Decreasing listeriosis mortality in the United States, 1990–2005. Clin Infect Dis 47(7):867–74. Beuchat LR, Mann DA. 2008. Survival and growth of acid-adapted and unadapted Salmonella in and on raw tomatoes as affected by variety, stage of ripeness, and storage temperature. J Food Prot 71(8):1572–9. Boonyawantang A, Mahakarnchanakul W, Rachtanapun C, Boonsupthip W. 2012. Behavior of pathogenic Vibrio parahaemolyticus in prawn in response to temperature in laboratory and factory. Food Cont 26(2):479–85. [CDC] Centers for Disease Control and Prevention. 2002. Multistate outbreaks of Salmonella serotype poona infections associated with eating cantaloupe from Mexico—United States and Canada, 2000–2002. Morb Mortal Wkly Rep 51(46):1044–7.
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curves without lag and stationary phases at some temperature conditions were observed, there was no difference among the primary models. Cold chain system for fresh fruits during transportation and storage may induce cold adaptation on foodborne pathogens on surface of the fruits, probably influencing bacterial growth and survival on fresh-cut fruits (Rodriguez-Romo and Yousef 2005). Thus, the growth parameters (k and λ) of NCA and CA cell were also compared to see if cold adaptation affects on growth of L. monocytogenes on fresh-cut cantaloupe during storage at low temperatures. The present results showed that there was no significant difference (P > 0.05) in k and λ values between NCA and CA (Table 2). Previous studies with other foodborne pathogens such as Vibrio vulnificus (Bang and Drake 2002) and Salmonella spp. (Sim and others 2013) also showed that there was no enhanced growth of CA cells compared to NCA cells at lower temperatures in broth and fresh-cut dragon fruits, respectively. However, these previous studies did not use the growth models to predict the behavior of pathogens during storage; hence it is difficult to directly compare the results. The maximum growth rates derived from the primary models were fitted to the Arrhenius-type model for describing the relationship between k and temperature in L. monocytogenes inoculated onto fresh-cut cantaloupe (Figure 3) and the model parameters were calculated based on the model (Table 3). Regardless of conditions under which the cells grew, similar G values were obtained among 3 primary models. The average G values of NCA and CA cells were calculated as 2375 and 2390 J/mol, re-
Modeling of L. monocytogenes on cantaloupe . . .
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[CDC] Centers for Disease Control and Prevention. 2007. Salmonella Oranienburg infections associated with fruit salad served in health-care facilities—Northeastern United States and Canada, 2006. Morb Mortal Wkly Rep 56(39):1025–8. [CDC] Centers for Disease Control and Prevention. 2008. Investigation of outbreak of infections caused by Salmonella Litchfield. Atlanta, GA: Centers for Disease Control and Prevention. Available from: http://www.cdc.gov/salmonella/litchfield/. Accessed 2013 Aug 13. [CDC] Centers for Disease Control and Prevention. 2011a. Investigation update: multistate outbreak of Salmonella Panama infections linked to cantaloupe. Atlanta, GA: Centers for Disease Control and Prevention. Available from: http://www.cdc.gov/salmonella/ panama0311/062311/index.html. Accessed 2013 Aug 13. [CDC] Centers for Disease Control and Prevention. 2011b. Surveillance for foodborne disease outbreaks—United States, 2008. Atlanta, GA: Centers for Disease Control and Prevention. Available from: http://www.cdc.gov/mmwr/preview/mmwrhtml/ mm6035a3.htm?s_cid=mm60355a3_w. Accessed 2012 Nov 10. [CDC] Centers for Disease Control and Prevention. 2012. Multistate outbreak of listeriosis linked to whole cantaloupes from Jensen farms, Colorado. Listeria (Listeriosis). Atlanta, GA: Centers for Disease Control and Prevention Available from: http://www.cdc. gov/listeria/outbreaks/cantaloupes-jensen-farms/082712/index.html. Accessed 2012 Oct 10. Delignette-Muller ML, Baty F, Cornu M, Bergis H. 2005. Modelling the effect of a temperature shift on the lag phase duration of Listeria monocytogenes. Int J Food Microbiol 100(1–3):77–84. Fang T, Liu Y, Huang L. 2013. Growth kinetics of Listeria monocytogenes and spoilage microorganisms in fresh-cut cantaloupe. Food Microbiol 34(1):174–81. [FAO] Food and Agriculture Organization of the United Nations. 2011. Microbiological hazards and melons. Rome, Italy: Food and Agriculture Organization of the United Nations. Available from: ftp://ftp.fao.org/ag/agn/jemra/Microbiological_hazards_and_melons_Nov08.pdf. Accessed 2012 Nov 10. [FDA] Food and Drug Administration. 2009. Guidance for industry: guide to minimize microbial food safety hazards of melons; draft guidance. Silver Spring, MD: Dept. of Health and Human Services, Food and Drug Administration, Center for Food Safety and Applied Nutrition. Available from: http://www.fda.gov/Food/GuidanceRegulation/ GuidanceDocumentsRegulatoryInformation/ProducePlantProducts/ucm174171.htm. Accessed 2013 Aug 13. Gil MI, Aguayo E, Kader AA. 2006. Quality changes and nutrient retention in fresh-cut versus whole fruits during storage. J Agric Food Chem 54(12):4284–96. Gr¨undling A, Burrack LS, Bouwer HG, Higgins DE. 2004. Listeria monocytogenes regulates flagella motility gene expression through MogR, a transcriptional repressor required for virulence. P Natl Acad Sci USA 101(33):12318–23. Huang L. 2010. Growth kinetics of Escherichia coli O157:H7 in mechanically-tenderized beef. Int J Food Microbiol 140(1):40–8. Huang L. 2011. A new mechanistic growth model for simultaneous determination of lag phase duration and exponential growth rate and a new B˘elehdr´adek-type model for evaluating the effect of temperature on growth rate. Food Microbiol 28(4):770–6. Huang L. 2013. Optimization of a new mathematical models for bacterial growth. Food Cont 32(1):283–8. Huang L, Hwang A, Phillips J. 2011. Effect of temperature on microbial growth ratemathematical analysis: the Arrhenius and Eyring-Polanyi connections. J Food Sci 76(8): E553–60. [ICMSF] Intl. Commission on Microbiological Specifications for Foods. 1996. Listeria monocytogenes. In: ICMSF editors. Microorganisms in foods 5: microbiological specifications of food pathogens. London: Blackie Academic & Professional. p 141–82. Juneja VK, Melendres MV, Huang L, Subbiah J, Thippareddi H. 2009. Mathematical modeling of growth of Salmonella in raw ground beef under isothermal conditions from 10 to 45 °C. Int J Food Microbiol 131(2–3):106–11.
M1174 Journal of Food Science r Vol. 79, Nr. 6, 2014
Koseki S, Isobe S. 2005. Growth of Listeria monocytogenes on iceberg lettuce and solid media. Int J Food Microbiol 101(2):217–25. Mahmoud BS, Vaidya NA, Corvalan CM, Linton RH. 2008. Inactivation kinetics of inoculated Escherichia coli O157:H7, Listeria monocytogenes and Salmonella poona on whole cantaloupe by chlorine dioxide gas. Food Microbiol 25(7):857–65. Mastronicolis SK, Boura A, Karaliota A, Magiatis P, Arvanitis N, Litos C, Tsakirakis A, Paraskevas P, Moustaka H, Heropoulos G. 2006. Effect of cold temperature on the composition of different lipid classes of the foodborne pathogen Listeria monocytogenes: focus on neutral lipids. Food Microbiol 23(2):184–94. McMeekin T, Bowman J, McQuestin O, Mellefont L, Ross T, Tamplin M. 2008. The future of predictive microbiology: strategic research, innovative applications and great expectations. Int J Food Microbiol 128(1):2–9. Mohle-Boetani J, Reporter R, Werner SB, Abbott S, Farrar J, Waterman SH, Vugia DJ. 1999. An outbreak of Salmonella serogroup Saphra due to cantaloupes from Mexico. J Infect Dis 180(4):1361–4. Olaimat AN, Holley RA. 2012. Factors influencing the microbial safety of fresh produce: a review. Food Microbiol 32(1):1–19. Pe˜nuela C. 2012. Florida fresh: cantaloupes. Gainesville, FL: Univ. of Florida IFAS Extension Available from: http://edis.ifas.ufl.edu/fy1101. Accessed 2013 Aug 13. Perni S, Andrew PW, Shama G. 2005. Estimating the maximum growth rate from microbial growth curves: definition is everything. Food Microbiol 22(6):491–5. Rodriguez-Romo LA, Yousef AE. 2005. Microbial adaptation and safety of produce. In: Sapers GM, Gorny JR, Yousef AE, editors. Microbiology of fruit and vegetables. Boca Raton, Fla.: CRC Press. p 95–116. Sapers GM, Doyle MP. 2009. Scope of the produce contamination problem. In: Saper GM, Solomon EB, Matthew KR, editors. The produce contamination problem: causes and solutions. California: Academic Press. p 3–19. Schlech WF. 1996. Overview of listeriosis. Food Cont 7(4–5):183–6. Selma MV, Ib´an˜ ez AM, Allende A, Cantwell M, Suslow T. 2008. Effect of gaseous ozone and hot water on microbial and sensory quality of cantaloupe and potential transference of Escherichia coli O157:H7 during cutting. Food Microbiol 25(1):162–8. Sim HL, Hong YK, Yoon WB, Yuk HG. 2013. Behavior of salmonella spp. and natural microbiota on fresh-cut dragon fruits at different storage temperatures. Int J Food Microbiol 160(3): 239–44. Sinigaglia M, Bevilacqua A, Campaniello D, D’Amato D, Corbo MR. 2006. Growth of Listeria monocytogenes in fresh-cut coconut as affected by storage conditions and inoculum size. J Food Prot 69(4):820–5. Strawn LK, Danyluk MD. 2010. Fate of Escherichia coli O157:H7 and Salmonella spp. on fresh and frozen cut mangoes and papayas. Int J Food Microbiol 138(1–2): 78–84. Ukuku DO, Fett W. 2002. Behavior of Listeria monocytogenes inoculated on cantaloupe surfaces and efficacy of washing treatments to reduce transfer from rind to fresh-cut pieces. J Food Prot 65(6):924–30. Wang J, Rahman S, Zhao XH, Forghani F, Park MS, Oh DH. 2013. Predictive models for the growth kinetics of Listeria monocytogenes on white cabbage. J Food Safety 33(1): 50–8. Vandamm JP. Li D, Harris LJ, Schaffner DW, Danyluk MD. 2013. Fate of Escherichia coli O157:H7, Listeria monocytogenes, and Salmonella on fresh-cut celery. Food Microbiol 34(1):151–7. Zwietering MH, Jongenburger I, Rombouts FM, Van’t Riet K. 1990. Modeling of the bacterial growth curve. Appl Environ Microbiol 56(6):1875–81.
