Food Microbiology 40 (2014) 41e47

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Evaluating growth models of Pseudomonas spp. in seasoned prepared chicken stored at different temperatures by the principal component analysis (PCA) Miaoyun Li, Yuanhui Li, Xianqing Huang, Gaiming Zhao*, Wei Tian Henan Key Lab of Meat Processing and Quality Safety Control, College of Food Science and Technology, Henan Agricultural University, Zhengzhou 450002, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 July 2013 Received in revised form 1 October 2013 Accepted 24 November 2013 Available online 9 December 2013

The growth of Pseudomonas of pallet-packaged seasoned prepared chicken products under selected storage temperatures (5  C, 10  C, 15  C, 20  C and 25  C) has been studied in this paper. The modified Gompertz, Baranyi and Huang models were used for data fitting. Statistical criteria such as residual sum of squares, mean square error, Akaike’s information criterion, Pseudo-R2 were used to evaluate model performance. Results showed that RSS (Residual sum of squares) index contribution rate was more than 90% of the variability, which could be explained by the first principal components analyzed by the principal component analysis (PCA). The index values reported in Sichuan-style chicken skewers and chicken flesh and bones were about 94.85% and 93.345% respectively, and both the rate were better than the standard (85%). Therefore, RSS can be used as the main evaluating index to analyze and compare the difference of those three models. With the smallest average values of RSS and the biggest pseudo-R2 at most temperatures, the Baranyi model was more suitable to fit the data of Pseudomonas obtained from the two prepared chicken products than Gompertz model and Huang model. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Pseudomonas Seasoned prepared chicken meat products Kinetic model Goodness-of-fit

1. Introduction With the cold chain in food improved, prepared chicken is more and more popular due to the advantage of convenience, high protein and low fat. It has become one of the fastest growing foods recently (Nam et al., 2010; Zhang et al., 2010). Pseudomonas spp. was considered as the specific spoilage organisms of the chilled meat under different packaging conditions and storage temperatures (Jeremiah et al., 1995; Drosinos and Board, 1994, 1995; Mano et al., 2000; Li et al., 2006). Predictive models have been used to study the population dynamics of pathogenic and spoiling bacteria at various times and temperatures during the storage of food ((Ratkowsky et al., 1983; Zwietering et al., 1996; Henk et al., 1997). In recent years, several models for growth of Pseudomonas spp in raw meat have been developed (Koutsoumanis et al., 2006; Dominguez and Schaffner, 2007), which were considered to be the effort in the development of dynamic growth models of Pseudomonas in food products (Gospavic

* Corresponding author. Tel./fax: þ86 371 63558150. E-mail addresses: [email protected] (M. Li), [email protected] (G. Zhao). 0740-0020/$ e see front matter Ó 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.fm.2013.11.014

et al., 2008; Dominguez and Schaffner, 2007; Koutsoumanis et al., 2006). The modified Gompertz model is one of the empirical models, which has been studied by a number of investigators and used in the predictive microbiology software programs such as the Pathogen Modeling Programs (http://www.arserrc.gov/mfs/) and the Food Micro-model (McClure et al., 1994). The Baranyi model (Baranyi and Roberts, 1994) was used to predict microbial growth, united with an adjustment function A (t) that depended on the physiological state of the microbial cells (Dalgaard, 1995; Sutherland et al., 1995, 1997; Fernandez et al., 1997). There are also many other mathematical models that have been used to describe microbial growth in the meat industry. However, few reports could tell which model is the most appropriate one to predict the growth of microbial in prepared chicken meat. Performances of the different models were evaluated by using various statistical criteria, such as mean square error (MSE), pseudo-R2, Akaike’s and Bayesian’s information criteria (Li et al., 2013; Juneja et al., 2009). But there was no significant difference in the performances of different models, suggesting that the models were equally suitable for describing isothermal bacterial growth. Thus, no similar model has been found in the literature and it’s still uncertain which model is more accurate to fit the growth of

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Pseudomonas in spontaneously contaminated prepared chicken meat under pallet packaging. Principal component analysis (PCA) is a kind of commonly used multivariate analysis method, of which the actual application is very wide, such as population statistics, quantity geography, and molecular dynamics simulation. PCA can replace the original index that has certain correlations by resetting a set of new independents (Ekenel and Sankur, 2004). It can decrease the dimensionality of the data and pinpoint the most important factors causing variability (Schirone et al., 2011; Pintado et al., 2008). However, there are few studies to evaluate mathematical models and compare several statistical criteria by PCA. In the study, three mathematical models (modified Gompertz, Baranyi and Huang models) were used for data fitting to evaluate the growth of Pseudomonas of pallet-packaged seasoned prepared chicken meat stored at different temperatures. Statistical criteria such as residual sum of squares, mean square error, Akaike’s information criterion and Pseudo-R2 were used to evaluate model performance. And the statistical criteria among the three models were compared by PCA. Therefore, the objective was mainly to determine which model should be preferentially used in monitoring the growth of Pseudomonas of prepared chicken meat and which statistical criteria should be used to evaluate model performance.

2.3. Growth kinetics and mathematical modeling In our study, three growth models were chosen as the primary model to fit the initial data of Pseudomonas growth under a set of constant temperatures in order to obtain the primary model curves. All the model parameters related to the Pseudomonas dynamics were obtained by fitting the growth curve on the measurement data of Pseudomonas in two kinds of prepared chicken meat at selected temperatures. For convenience of comparing these models, a natural logarithm was used, which is 2.303 log10 cfu/g. The first model was the modified Gompertz model. Although this model is only an empirical model, it is a model that has been widely used in the literature (Gibson et al., 1987, 1988; Huang, 2010). A large amount of kinetic data can be derived from this model.

Y ¼ N0 þ ðNmax  N0 Þexpf  exp½  mG ðt  MÞg

In Eq. (1), Y is the natural logarithm of bacteria count at time t, ln cfu/g; N0 and Nmax are the initial and maximum values of cell concentration; mG is the relative growth rate at time t ¼ M (h1), which is the inflection point of the curve. From Eq. (1), two parameters, lag phase (l) and specific growth rate (K), can be derived according to Equations (2) and (3).

l ¼ M

2. Materials and methods 2.1. Product and sample processing The seasoned prepared chicken products were obtained from a local commercial meat plant in Henan province, China. For the chicken flesh and bones, diced chicken breast and chicken gristle was mixed with the Mexican flavored marinade for 6e18 h at 0e 8  C. For the Sichuan-style chicken skewers, diced chicken breast was also mixed with the Mexican flavored marinade for 6e18 h at 0e8  C. They were transported to the laboratory in a cooling box and cut by the sterilized knife. The cuts, around 200 g in each pallet, were then wrapped with PE cling film. All meat samples were stored under high precision low temperature incubator (Sanyo MIR 254) at 5, 10, 15, 20 and 25  C for different specify durations. Temperature was recorded every 5 min using thermographs throughout the experiment. During the storage, samples (n ¼ 5) were taken every 24, 12, 8, 6, 4 h at 5, 10, 15, 20, 25  C respectively for 96 h, and microbial counts were determined periodically. Every measurement was repeated at least 5 times. 2.2. Microbiological analysis In a sterile environment, each case (five replicates), meat samples (25 g for each) were transferred to a Stomacher-blenderbag (Lu Qiao Company, Beijing, China) and prepared by homogenizing (AES Easy Mix) for 100 s with 225 ml sterilized physiological saline solution (0.9% w/v NaCl (Dean Reagent Company, Tianjin, China). During this study, the two kinds of prepared chicken meat samples were analyzed for the number of Pseudomonas. The drop plate method (Chen et al., 2003) was used for bacterial enumeration. The culture media was CFC (Pseudomonads agar base type CM 0559 with selective supplement SR0103; Oxoid) for Pseudomonas. Each sample was conducted in duplicate Petri dishes. Then all the dry plates were transferred into a 25  C incubator and colonies were enumerated after 48 h.

(1)

K ¼

1

mG

ðNmax  N0 ÞmG e

(2)

(3)

The second growth model was the modified Huang, which was recently developed (Huang, 2008). This model is derived from the three phase (lag, exponential, and stationary) growth phenomenon under isothermal conditions. Furthermore, the growth kinetic parameters can directly be obtained from the Huang model. In the Huang model l was denoted as the duration of the lag phase, which is expressed as

Y ¼ N0 þ Nmax  lnfexpðN0 Þ þ ½expðNmax Þ  expðN0 Þexp½K  BðtÞg

(4)

where,

BðtÞ ¼ t þ

1 1 þ exp½  25ðt  lÞ ln 25 1 þ expð25lÞ

(5)

The last model was the Baranyi model (Baranyi and Roberts, 1994). Different from empirical models, the Baranyi model is a theoretical model, which is based on certain “theoretical” understandings of bacterial growth, which is written as

i h  Y ¼ N0 þ K t þ ln eKt þ eh0  eKth0 ! eKth0  eh0  ln 1 þ y e max  y0

(6)

where,

l ¼

h0 K

(7)

Y is ln cfu/g of cell concentration at time t; y0 is the initial cell concentration; ymax is the maximum cell concentration; and K is the maximum specific growth rate. The parameter h0 is simply a transformation of the initial conditions, making the curve fitting procedures more stable (Baranyi et al., 1995).

M. Li et al. / Food Microbiology 40 (2014) 41e47

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2.4. Statistical analysis All the models were fit to the experimental data by nonlinear regression using the NLIN procedure of the SAS package. The performance of models was evaluated by using a comparison of mean square error (MSE) obtained from NLIN procedure: the equation for Mean Squared Error is

Fig. 1. Fitting of the Baranyi, Huang, and Gompertz models to population of Pseudomonas in pallet-packaged Sichuan-style chicken skewers stored at 5, 10, 15, 20, and 25  C, respectively. Fig. 2. Fitting of the Baranyi, Huang, and Gompertz models to population of Pseudomonas in pallet-packaged chicken flesh and bones stored at 5, 10, 15, 20, and 25  C, respectively.

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M. Li et al. / Food Microbiology 40 (2014) 41e47

Table 1 Comparison and analysis of statistic criteria obtained from three models of Sichuanstyle chicken skewers. T ( C)

Models

RSS

MSE

AIC

Pseudo-R2

5

Baranyi Hunag Gompertz Hunag Gompertz Baranyi Baranyi Hunag Gompertz Baranyi Hunag Gompertz Baranyi Hunag Gompertz

8.3028 8.9779 8.5621 21.3761 20.2763 14.8635 5.5398 3.7694 3.0823 2.9924 2.4109 2.8888 5.4721 6.2081 6.2596

0.2684 0.2806 0.2762 0.8907 0.8448 0.6193 0.2131 0.149 0.1185 0.0965 0.0778 0.0932 0.2105 0.2388 0.2591

38.2875 35.5514 37.2111 5.1692 3.6902 5.0050 38.1772 49.7284 55.7656 74.0056 81.5682 75.2388 38.546 34.7603 34.5124

0.9620 0.9589 0.9608 0.9343 0.9377 0.9543 0.9817 0.9875 0.9898 0.9901 0.9920 0.9905 0.9839 0.9817 0.9816

10

15

20

25

MSE ¼

RSS ¼ df

P

mobserved  mpredicted

n X

ðyi  b yiÞ

(9)

i¼1

where n is the number of data points, yi is the ith observed value and ybi is the fitted value for the ith observation. An alternative comparison method for comparing models is the Akaike’s Information Criterion (AIC), based on information theory (Burnham and Annderson, 2002; Motulsky and Christopoulos, 2003). For all the experimental data, the AIC is given by:

 AIC ¼ n ln

 RSS 2ðm þ 1Þðm þ 2Þ þ 2ðm þ 1Þ þ n nm2

(10)

where RSS is the residual sum of squares, n is the number of data points and m is the number of parameters. When comparing individual AIC values, the model with the smallest AIC value is most likely to be correct (López et al., 2004; Motulsky and Christopoulos, 2003).

Table 2 Comparison and analysis of statistic criteria obtained from three models of chicken flesh and bones. T C

Model

RSS

MSE

AIC

Pseudo-R2

5

Baranyi Huang Gompertz Baranyi Huang Gompertz Baranyi Huang Gompertz Baranyi Huang Gompertz Baranyi Huang Gompertz

8.4879 8.0114 8.186 2.601 2.604 2.9576 3.8164 3.8698 4.25 1.4872 1.5629 1.8158 2.8031 2.8282 3.2244

0.207 0.2003 0.2046 0.0722 0.0723 0.0822 0.1231 0.1248 0.1371 0.048 0.0504 0.0586 0.0779 0.0786 0.0896

50.2448 52.5559 51.6935 78.9119 78.8715 74.415 65.4925 65.0061 61.7261 98.4769 96.7392 91.4898 76.2928 75.9808 71.3921

0.84056 0.84951 0.846231 0.978522 0.978497 0.975577 0.971219 0.970816 0.967949 0.98169 0.980758 0.977644 0.970805 0.970543 0.966417

10

15

20

25

Total

% of variance

Cumulative %

3.794 0.132 0.074 0

94.85 3.306 1.839 0.005

94.85 98.155 99.995 100

Pseudo  R2 ¼ 1  SSðResidualÞ=SSðTotalCorrected Þ

(8)

2

Total variance explained

The last statistical indicator used was pseudo-R2. Pseudo-R2 was used to compare the quality of nonlinear models. The higher the means of pseudo-R2 is, the better the model fits (Juneja et al., 2007). A pseudo-R2 is defined as (Schabenberger, 2005):

where RSS is the residual sum of squares, and df is the degree of freedom, df ¼ n  m, n is the number of data points and m is the number of parameters. Estimates for parameters were obtained by minimizing the residual sum of squares (RSS):

RSS ¼

Component

RSS MSE AIC R2

2

df

Table 3 Principal component analysis of four statistic criteria of Sichuan-style chicken skewers.

(11)

The model with the lowest values of all these measures was selected as the best model. To determine which model is more applicable to fit the growth data of Pseudomonas at all temperature conditions, the average values of statistics were calculated. All the four statistical criteria, i.e. residual sum of squares, mean square error, Akaike’s information criterion and Pseudo-R2, were analyzed by the principal component analysis (PCA) procedure of the SPSS 13.0 in order to find out which statistical criteria has the most significant effect on these models.

3. Results and discussion 3.1. Fitting curves of primary models Fig. 1 shows the fitting of the Baranyi, Huang, and Gompertz models to experimental growth data of Pseudomonas in palletpackaged Sichuan-style chicken skewers at 5, 10, 15, 20 and 25  C, respectively. Graphically, all models chosen in this study fit the data well, for the three models presented typical sigmoid shapes at selected temperatures except 5  C. Meanwhile, the final populations for 10, 15, 20 and 25  C were around 17 ln cfu/g, for which was only 14.64 ln cfu/g at 5  C. The time to reach the stationary phase was approximately 16, 6, 8, 4 and 3 h at 5, 10, 15, 20 and 25  C, respectively. Fig. 2 shows the fitting of the Baranyi, Huang, and Gompertz models to experimental growth data of Pseudomonas in palletpackaged chicken flesh and bones at 5, 10, 15, 20 and 25  C, respectively. Obviously, all models chosen in this study fit the data well; however, the three models presented typical sigmoid shapes at 5  C except other selected temperatures. A possible explanation for the different shape of the growth curves was that the strains of Pseudomonas in the study of prepared meat which had been marinated for 6e18 h at 0e8  C in the factory got though the lag phase, but our sampling points were later as with the growth of Pseudomonas. So the lag phase was shorter than the actual in these curves.

Table 4 Principal component analysis of four statistic criteria of chicken flesh and bones. Component

Total variance explained Total

% of variance

Cumulative %

RSS MSE AIC R2

3.734 0.246 0.02 0

93.345 6.151 0.493 0.011

93.345 99.495 99.989 100

M. Li et al. / Food Microbiology 40 (2014) 41e47

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Fig. 3. “Scree Plot” of evaluation indexes of Sichuan-style chicken skewers by Principal Component Analysis.

3.2. Which model is precise, anything in common? In this section, we examined the fit properties of three models in meat microbiology and if there is anything in common within these models for the two products, and we decided which one was more consistent for most of the tests performed based on the results. According to some typical fits of the growth data of Pseudomonas, we investigated the model that was optimal to fit the growth data of Pseudomonas obtained directly from the products and could be suitable to predict the shelf-life of raw prepared chicken in meat production. Four indices are used for model comparison. By comparing the statistical criteria (RSS, AIC, MSE and pseudo-R2) of the three models (Table 1, Table 2), the results showed that Baranyi model could give a consistently goodness of fit for most the data obtained from both the samples. Different form the previous research, Baty and Delignette-Muller (2004) compared the modified Gompertz model, the Baranyi model and the Lag-exponential model, applying 15 datasets divided from the growth of a cocktail of three Escherichia coli O157:H7 strains at diverse conditions of temperature (5e 42  C), whereas concluded that no model consistently provided the best fit for all datasets. Table 1 shows that the values of the four statistics criteria of three models were significantly different by ANOVA statistically analysis (P < 0.05). The largest value of Pseudo-R2 and minimum of RSSE, AIC, MSE belonged to Baranyi model at 5, 10, 25  C, where Pseudo-R2 was 0.962, 0.9543, 0.9839 respectively. The lowest values of the four statistics criteria belonged to the Modified Gompertz at 15  C, where Pseudo-R2 was 0.9898. However, Huang model has the largest value of Pseudo-R2 and minimum of RSS, AIC,

Fig. 4. “Scree Plot” of evaluation indexes of chicken flesh and bones by Principal Component Analysis.

Fig. 5. Comparison of RSS of three models of Sichuan-style chicken skewers.

MSE at 20  C. The result of the ANOVA analysis showed that the three models were not different significantly. Thus, we concluded that the statistic criteria of the Baranyi model were better than the other two models at most of selected temperatures. Meanwhile, Table 2 shows that the values of the four statistics criteria of three models were significantly different by ANOVA statistically analysis (P < 0.05). The largest value of Pseudo-R2 and minimum of RSS, AIC, MSE belonged to Baranyi model at 10, 15, 20,25  C except 5  C, Huang model has the largest value of Pseudo-R2 and minimum of RSS, AIC, MSE at 5  C. In general, the statistic criteria of the Baranyi model were better than other two models at selected temperatures except 5  C. The two kinds of raw prepared chicken had the same most appropriate model, i.e. Baranyi model that provided a consistently preferable goodness-of-fit for most growth data. 3.3. Principal component analysis In our work, there were four statistic criteria obtained from three models compared and analyzed. Table 3 and Table 4 showed the results of Principal component analysis (PCA) by SPSS 13.0 package. From the two tables, we found that statistic criteria RSS index contribution rate were 94.85% and 93.345% respectively, both of which exceeded 85%. Fig. 3 and Fig.4 were the “Scree Plot” of evaluation indexes by Principal Component Analysis of Sichuanstyle chicken skewers and chicken flesh and bones respectively,

Fig. 6. Comparison of RSS of three models of chicken flesh and bones.

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M. Li et al. / Food Microbiology 40 (2014) 41e47

Table 5 Parameter values of Baranyi models for the growth curves at various storage temperatures of Sichuan-style chicken skewers. T C

N0 ln (cfu/g)

Nmax ln (cfu/g)

K (1/h)

l (h)

5 10 15 20 25

7.1886 8.6433 8.2661 9.1635 8.6845

15.1120 17.1953 15.8880 16.6709 17.5171

0.0513 0.2057 0.2961 0.4385 0.6832

56.0351 5.6587 8.4421 4.3291 3.9895

and we found out that the changing rates in four evaluation indexes were very intuitive, where the first component changed to the second component quickly and the changing rate was big particularly. However, the changing rates of the second, third and the fourth were not obvious. Based on these findings, we compared the index RSS at different temperature individually. Fig. 5 and Fig. 6 compared the difference of RSS obtained under isothermal conditions at different temperatures from the two products. According to the two figures, we noticed that the Baranyi model had the minimum RSS, AIC, MSE values and the maximum pseudo-R2 value at most selected temperatures. Then it demonstrated that the Baranyi model was the best choice to describe the growth of Pseudomonas in the two prepared chicken products. 3.4. The parameters derived from Baranyi model Table 5 and Table 6 showed the estimations of initial cell number (N0 in ln cfu/g), maximum cell number (Nmax in ln cfu/g), maximum growth rate (K in hour1) and lag-phase (l in hour) which were derived from the Baranyi model for the Pseudomonas in Sichuan-style chicken skewers and chicken flesh and bones stored at selected temperatures, respectively. Due to low temperature environment and the suppressed growth, the growth rate of Pseudomonas in Sichuan-style chicken skewers was 0.0513 (1/h) at 5  C, while the growth rate under 25  C was 0.6832 (1/h) which was 13.3 times than that of 5  C. As the temperature rose, the growth rate of pseudomonas increased. On the contrary, lag-phase (l in hour) decreased gradually with temperature increased. At 5  C, the lag-phase was 16.04 h, which reduced to 3.99 h at 25  C. Meanwhile, we noticed the same results of four parameters of chicken flesh and bones from Table 4b. Li et al. (2013) showed similar results using three mathematical models to analyze the growth of Pseudomonas spp. in pallet-packaged pork stored at different temperatures. 4. Conclusions The modified Gompertz, Huang, and Baranyi models could fit the growth data of Pseudomonas of two raw prepared chicken meat in pallet packaging at different temperatures. RSS obtained from the three models was the first principal components, of which contribution rate exceeded 90%, for 94.85% and 93.345% in Sichuanstyle chicken skewers and chicken flesh and bones, respectively. It Table 6 Parameter values of Baranyi models for the growth curves at various storage temperatures of chicken flesh and bones. T C

N0 ln (cfu/g)

Nmax ln (cfu/g)

K (1/h)

l (h)

5 10 15 20 25

11.2370 12.3829 12.2002 12.9670 12.8114

13.6834 17.2118 17.6499 17.0282 17.1230

0.0792 0.1237 0.1703 0.3343 0.3473

51.5960 2.1310 3.1832 2.9776 0.7040

can be used as the main evaluating index to analyze and compare the difference models. Baranyi model, with the smallest average values of RSS and the biggest pseudo-R2 at most temperatures, is more suitable to fit the data of Pseudomonas obtained from the two prepared chicken meat than Gompertz model and Huang model, which showed an overall acceptable performance to describe the growth of Pseudomonas of prepared chicken meat under pallet packaging. This study can be used to evaluate the microbial safety of Pseudomonas under pallet-packaging.

Acknowledgements This study was funded by the National Natural Science Funds of China (grant no. 31071567) and the scientific and technological projects of national public sectors of China (grant No. 2012BAD28B02-02). The authors are grateful to the help from the Henan Key Laboratory of Meat Processing and Quality Safety Control.

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Evaluating growth models of Pseudomonas spp. in seasoned prepared chicken stored at different temperatures by the principal component analysis (PCA).

The growth of Pseudomonas of pallet-packaged seasoned prepared chicken products under selected storage temperatures (5°°C, 10°°C, 15°°C, 20°°C and 25°...
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