Use of response surface methodology to investigate the effect of food constituents on Staphylococcus aureus inactivation by high pressure and mild heat

Process Biochemistry 41 (2006) 362–369 www.elsevier.com/locate/procbio

Use of response surface methodology to investigate the effect of food constituents on Staphylococcus aureus inactivation by high pressure and mild heat Yu-Long Gao a,*, Xing-Rong Ju a, Han-Hu Jiang b a

College of Food Science and Engineering, Nanjing University of Finance and Economics, Railway North-Street No. 128, Nanjing 210003, Jiangsu Province, PR China b College of Food Science and Technology, Nanjing Agricultural University, Nanjing 210095, Jiangsu Province, PR China Received 20 March 2005; received in revised form 12 June 2005; accepted 21 June 2005

Abstract The previous experimental results for effect of high pressure and mild heat on Staphylococcus aureus in milk using response surface methodology showed that the optimum process parameters for six log-cycles reduction of S. aureus were obtained as: temperature, 34.4 8C; pressure, 329.8 MPa; pressure holding time, 15.5 min. Based on the results, response surface methodology (RSM) was employed in the present work, the effect of food main constituents like soybean protein, sucrose, bean oil and pH of the food matrix on the S. aureus inactivation by high pressure and mild heat was studied, and a quadratic predictive model for the effect of food constituents and pH of food matrix on S. aureus reduction by high pressure and mild heat was built with RSM accurately. The experimental results showed that the efficiencies of S. aureus reduction in milk and food matrix designed in the present work under the HHP treatment process parameters described above had some differences. The soybean protein (P = 0.0082), sucrose (P < 0.0001), and pH (P = 0.0429) significantly affected reduction of S. aureus, and the effect of bean oil on reduction of S. aureus was not significant (P = 0.2790). The adequacy of the predictive model equation for predicting the magnitude orders of S. aureus reduction was verified effectively by the validation data. # 2005 Elsevier Ltd. All rights reserved. Keywords: High pressure processing (HPP); Reduction of Staphylococcus aureus; Response surface methodology (RSM); Food constituents; Predictive model; Effect

1. Introduction Nowadays, consumer demands are more and more directed towards high-quality, minimally processed, nutritious and fresh-like products. Traditional thermal processing methods cause loss of desirable properties related to texture, flavor, color, and nutrient value. Food scientists and the food industry are therefore searching for novel methods that may destroy undesired microorganisms with less adverse effects on product quality. Thanks to technological progress in the engineering aspects, physical alternative such as high pressure processing (HPP) is becoming more attractive. HPP offers an alternative potential non-thermal preservation * Corresponding author. Tel.: +86 25 83493936; fax: +86 25 83495837. E-mail address: [email protected] (Y.-L. Gao). 1359-5113/$ – see front matter # 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.procbio.2005.06.023

method for pasteurization of food products. The major benefit of pressure is its immediate and uniform effect throughout different media, avoiding difficulties like nonstationary conditions typical for convection-type and conduction-type processes [1–6]. HPP treatment causes less deterioration of essential vitamins, phytochemicals, aroma compounds compared with the classical heat treatment, but microorganisms can be inactivated if the applied pressures are high enough [7,8]. Microorganisms are variable with regard to their sensitivity to HPP. Staphylococcus aureus, a Gram-positive facultative anaerobic bacterium, has the ability to grow at a wide range of temperatures and pH [9]. Staphylococcal food poisoning is one of the main food-borne infections [10]. One of the objectives of food preservation by HPP, as with commercial sterilization and pasteurization in thermal

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processing, is the destruction of spores and vegetative cells of pathogens. The previous published experimental results for effect of high pressure and mild heat on S. aureus using RSM showed that the optimum process parameters for six log-cycles reduction of S. aureus were obtained as: temperature, 34.4 8C; pressure, 329.8 MPa; pressure holding time, 15.5 min [11]. Based on the results, in this study, the influence of main nutrient composition in food on S. aureus inactivation was evaluated. Cells stressed by high pressure can resuscitate in a nutrient-rich medium [12]. A low pHvalue and a high aw-value make vegetative microbial cells more sensitive to a high pressure treatment [13,14]. As Kalchayanand showed, a nutrient-rich medium is always more protective than an aqueous buffer medium [15]. Milk and cream protect microorganism against pressure [4,16]. Therefore, S. aureus reduction by high pressure and mild heat in buffer solutions are not always applicable to food system. It is important to take into account that results of studies in buffers or laboratory media cannot be directly extrapolated to real food situations [17]. For this study, we therefore evaluated the effects of main constituents like the soybean protein, sucrose, bean oil and pH of the food matrix on the S. aureus inactivation by high pressure and mild heat, and develop a response surface model using a Central Composite Design [18,19] for predicting the magnitude of S. aureus cell reduction. This would result in a more accurate model and help the introduction of HPP technology. The development of response surface predictive model to describe the HPP inactivation of S. aureus in food matrices should be very beneficial to the application in food preservation and help construct HACCP program to maintain food safety.

2. Materials and methods 2.1. Preparation of S. aureus As 1.2465 culture Stock cultures of S. aureus As 1.2465, obtained from China General Microbiological Culture Collection Center China, were maintained on nutrient agar (Oxoid CM3, Basingstoke, UK) during 48 h at 37 8C and stored at 4 8C and subcultured every month. The purity of the cultures was evaluated microscopically. For growth, a loop of S. aureus was transferred from a nutrient agar plate to nutrient broth tubes.

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of food constituents in Table 2, the food matrix groups were prepared by adding the weighed food constituents (soybean protein, sucrose, bean oil) to a definite amount sterile physiological solution (0.85% NaCl solution), then homogenized in a homogenizer (SRH60-70, Shanghai samro homogenizer Co., Ltd., Shanghai, China). After homogenization in a homogenizer, the pH of the food matrix was adjusted (by adding 1N NaOH, or 1N HCl, or both) using a combination glass electrode connected a digital pH meter (Model 340, Corning, New York, USA) which was placed in each food matrix for continuous monitoring of pH changes. Finally these food matrix groups were sterilized at 115 8C for 15 min and kept on ice (0 8C) until required. 2.3. HPP treatment The nutrient broth culture was incubated at 37 8C for 18 h to stationary phase. The cells were harvested by centrifugation at 3000
g for 15 min, washed with sterile sodium phosphate buffer (0.1 M, pH 7.0), and resuspended in the food matrices groups prepared above, yielding a final cell population of (5.0  1.1)
109 CFU/ml. All samples were inoculated 2 h before treatment to allow cells to acclimatize to the new environment. One milliliter of un-inoculated food matrix was transferred onto nutrient agar (Oxoid CM3, Basingstoke, UK) plates and incubated at 37 8C for 72 h to ensure that the food matrix samples were sterile. Food matrix samples (5.0 ml) were transferred into sterile plastic micro test tubes, heat-sealed avoiding enclosure of air and stored on ice until they were pressurized. Pressurization of samples was carried out using a high pressure unit (volume 200 ml, 52 Institute, Baotou Neimeng, China) at 34.4 8C and 329.8 MPa for 15.5 min. The high-pressure transmission fluid used was an oil, bis (2-ethylhexyl) sebacate (Li-Dong precision machinery company, Shenzhen, China). The pressure chamber was heated/cooled to a desired level prior to pressurization with a thermostat jacket connected to a water bath. The pressure level, time and temperature of pressurization were controlled by a computer program (BTNMC for HPP Control 1.0). The pressure come-up rate was 350 MPa/min and the pressure-release time was almost immediate. The temperature increase due to adiabatic heating in the HPP chamber was less than 2 8C/ 200 MPa. Samples were placed in the pressure chamber 5 min prior to treatment to equilibrate the sample temperature level. 2.4. Determination of plate counts after treatment

2.2. Preparation of food constituents under study Soybean protein and bean oil were purchased from Shangdong Yuwang Industrial and Commercial Co., Ltd. (Yucheng, Shandong Province, China). Sucrose used was of highest available purity and purchased from Sigma. The food matrix samples were prepared in sterile physiological solution (0.85% NaCl solution). According to the proportion

Following the release of pressure viable S. aureus counts in the samples were determined immediately by serial dilution in 0.1% peptone water, plated onto nutrient agar (Oxoid CM3, Basingstoke, UK) plates, and incubated at 37 8C for 4 days prior to counting colonies to allow injured cells to form visible colonies. Three replicates were performed. Inactivation was expressed as a logarithmic

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Table 1 Code and level of variables chosen for the trials Factor

Levela

Symbols

pH Soybean protein (%) Bean oil (%) Sucrose (%)

Coded

Uncoded

2

1

0

1

2

x1 x2 x3 x4

X1 X2 X3 X4

4.00 0.00 0.00 0.25

5.50 1.25 2.50 3.50

7.00 2.50 5.00 6.75

8.50 3.75 7.50 10.00

10.00 5.00 10.00 13.25

a

x1 = (X1  7.00)/1.50; x2 = (X2  2.50)/1.25; x3 = (X3  5.00)/2.5; x4 = (X4  6.75)/3.25.

viability reduction, log(No/Nt), with Nt and N0, respectively, the final number of survivals (CFU/ml) after a treatment and the initial number of cells (CFU/ml) in the untreated sample.

becomes: Y ¼ B0 þ B1 x1 þ B2 x2 þ B3 x3 þ B4 x4 þ B12 x1 x2 þ B13 x1 x3 þ B14 x1 x4 þ B23 x2 x3 þ B24 x2 x4 þ B34 x3 x4 þ B11 x21

2.5. Methodology and design of experiments

þ B22 x22 þ B33 x23 þ B44 x24 ;

Response surface methodology (RSM), an empirical modeling technique used to estimate the relationship between a set of controllable experimental factors and observed results [20,21], is currently one of the most popular optimization technique in the field of food science because of its comprehensive theory, reasonably high efficiency and simplicity [22]. The most common experimental design used in RSM is the Central Composite Design (CCD) which has equal predictability in all directions from the center [23,24]. In addition, CCDs are optimized designs for fitting quadratic models. The number of experimental points in the CCD is sufficient to test statistical validity of the fitted model and lack-of-fit of the model [22]. The central point in CCD is replicated several times to estimate the error due to experimental or random variability. The Central Composite Design of the investigation for four independent variables to obtain the quadratic predictive model allowed for the design of a minimal number of experimental runs [25]. The four different parameters like pH of food matrix, soybean protein, bean oil and sucrose were chosen as main variables and designated as X1, X2, X3, and X4, respectively. The low, middle and high levels, of each variable were designated as 1, 0, and +1, respectively, and are given in Table 1. The variables were coded according to the Eq. (1): xi ¼ ðXi  X0 Þ=DX;

(1)

where xi = (dimensionless) coded value of the variable Xi, X0 = the value of Xi at the centre point and DX = the step change. Table 2 shows the actual design of experiments. The behavior of the system was explained by the following second degree polynomial equation: Y ¼ B0 þ

n n n X X X B i xi þ Bi j xi x j þ B j j x2j i¼1

i< j

(2)

j¼1

where Y = predicted response, it can be observed that in the present study, four variables are involved and hence n takes the value 4. Thus, by substituting the value 4 for n, Eq. (2)

(3)

where x1, x2, x3 and x4 are input variables; B0 is a constant; B1, B2, B3 and B4 are linear coefficients; B12, B13, B14, B23, B24 and B34 are cross-product coefficients; B11, B22, B33 and B44 are quadratic coefficients. Y is predicted response, which can be calculated in the light of the Eq. (4) Y ¼ logðN0 =Nt Þ;

(4)

Table 2 Central composite design arrangement and responses Trial no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Variable

Y

x1

x2

x3

x4

Observed

Predicted

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 2 2 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 2 2 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 2 2 0 0 0 0 0 0

6.50 8.01 5.85 6.71 6.19 6.85 5.82 6.41 5.90 5.29 5.85 5.79 5.88 5.79 5.66 5.89 6.89 6.97 6.71 5.69 5.90 5.78 6.41 5.49 5.94 5.89 5.82 5.92 5.55 6.33

6.73 7.54 5.88 6.73 6.29 7.02 5.58 6.35 5.91 5.68 5.84 5.65 6.02 5.71 6.08 5.81 6.61 7.15 6.52 5.77 5.92 5.65 6.57 5.22 5.91 5.91 5.91 5.91 5.91 5.91

(0.03) (0.03) (0.01) (0.05) (0.01) (0.02) (0.01) (0.08) (0.04) (0.05) (0.07) (0.09) (0.04) (0.02) (0.04) (0.01) (0.01) (0.04) (0.07) (0.06) (0.07) (0.03) (0.01) (0.03) (0.04) (0.05) (0.01) (0.03) (0.05) (0.04)

Values in parentheses are coefficients of variation of measures.

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Table 3 Analysis of variance (ANOVA) for predictive equation for reduction of S. aureus Source

Sum of squares

Degree of freedom

Mean square

F-value

Prob > F

Model Lack of fit Pure error Corrected total

7.93 1.03 0.32 9.28

14 10 5 29

0.57 0.10 0.063

16.3 1.64

0.0005 0.3054

R2Adj ¼ 0:7200;

R ¼ 0:9244;

R2 ¼ 0:8545:

the experimental data, the response variable and the test variables are related by the following second-order polynomial equation:

where Y is the inactivation parameter. For Eq. (3), a total of 30 runs are necessary to estimate the 15 coefficients of the predictive model (3). In the present investigation, Design Expert package (Version 6.0.5, Stat-ease Inc., Minneapolis, MN, USA, 2001) was used for regression analysis of the data obtained and to estimate the coefficients of the regression equation. The fit of the regression model attained was checked by the adjusted coefficient of determination ðR2Adj Þ. The statistical significance of the model was determined by the application of Fischer’s F-test. The two-dimensional graphical representation of the system behavior called the response surface was used to describe the individual and cumulative effects of the variables as well as the mutual interactions between the variables on the dependant variable.

Y ¼ 5:908 þ 0:135x1  0:186x2  0:338x4 þ 0:242x21  0:259x1 x4 þ 0:193x2 x4 þ 0:136x3 x4

(5)

A summary of the analysis of variance (ANOVA) for the selected quadratic predictive model is shown in Table 3. The correlation measure for testing the goodness of fit of the regression equation is the adjusted determination coefficient ðR2Adj Þ. The value of R2Adj (0.7200) for Eq. (5) being close to 1 indicates a high degree of correlation between the observed and predicted values. Statistical testing of the model was done in the form of analysis of variance (ANOVA) which is required to test the significance and adequacy of the model. Here the ANOVA of the regression model demonstrates that the model is highly significant, as is evident from the calculated F-value (16.3) and a very low probability value (P = 0.0005). Moreover the computed F-value is much greater than the tabulated F-value (F 0.01 (14,5) = 9.77) indicating that the treatment differences are highly significant. The model also showed statistically insignificant lack of fit, as is evident from the lower calculated F-value (1.64) than the tabular F-value F 0.05 (14,10) = 4.60 even at 0.05 level. The model was found to be adequate for prediction within the range of variables employed. The coefficient values of Eq. (5) were calculated and tested for their significance using Design Expert; and are listed in Table 4. The P-values are used as a tool to

3. Results and discussions 3.1. Predictive models of regression The values of the response (log-cycle reduction for S. aureus) obtained under the different experimental conditions are summarized in Table 2. The variability associated with test samples again, was small as indicated by the coefficients of variation measurements given in the parenthesis. The application of RSM offers, on the basis of parameter estimate, an empirical relationship between the response variable (reduction of S. aureus) and the test variables under consideration. By applying multiple regression analysis on Table 4 Test of significance for regression coefficients Model term

Coefficient estimate

Degree of freedom

S.E.

95% CI low

95% CI high

F-value

Prob > F

Intercept x1 x2 x3 x4 x21 x22 x23 x24 x1x2 x1x3 x1x4 x2x3 x2x4 x3x4

5.9083 0.1354 0.1863 0.0688 0.3388 0.2420 0.0595 0.0305 0.0030 0.0094 0.0194 0.2594 0.0356 0.1931 0.1369

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

0.122 0.061 0.061 0.061 0.061 0.057 0.057 0.057 0.057 0.075 0.075 0.075 0.075 0.075 0.075

5.65 0.00 0.32 0.20 0.47 0.12 0.06 0.15 0.13 0.15 0.18 0.42 0.12 0.03 0.02

6.17 0.27 0.06 0.06 0.21 0.36 0.18 0.09 0.12 0.17 0.14 0.10 0.20 0.35 0.30

– 4.89 9.26 1.26 30.63 17.86 1.08 0.28 0.00 0.02 0.07 11.97 0.23 6.64 3.33

– 0.0429 0.0082 0.2790 <0.0001 0.0007 0.3154 0.6018 0.9586 0.9021 0.7996 0.0035 0.6415 0.0211 0.0879

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Fig. 1. Response surface plot and its contour plot of the effect of pH and sucrose and their mutual interactions on S. aureus reduction of HPP.

check the significance of each of coefficients, which in turn may indicate the pattern of the interactions between the variables. The smaller the value of P, the more significant is the corresponding coefficient. It can be seen from this table that the linear coefficients (x1, x2, x4), one quadratic term coefficient ðx21 Þ, and cross product coefficients (x1x4, x2x4) were significant, the P-values being very small (P < 0.05). The coefficients for cross product effect of bean oil and sucrose (x3x4) may be slightly significant (P < 0.09). The other term coefficients ðx3 ; x22 ; x23 ; x24 ; x1 x2 ; x1 x3 ; x2 x3 Þ are not significant. 3.2. Response surface plot and its contuor plot showing effects of food constituents on reduction of S. aureus The graphical representations of the regression Eq. (5), called the response surfaces and the contour plots were

obtained using the Design Expert and are presented in Figs. 1–3. Fig. 1 shows the 3D response surface plot at varying pH and and sucrose concentration at fixed soybean protein concentration of 2.50 g/100 g (0 level) and bean oil concentration of 5.0 g/100 g (0 level). From Fig. 1, it can be seen that reduction for S. aureus decrease with increase in concentration of sucrose, and reduction for S. aureus is found to decrease rapidly with increase of pH at the beginning, but beyond the range of pH (5.50–6.25), reduction for S. aureus increases with increasing pH. This is the result of interactive effect between pH of food matrix and sucrose. The contour plot in Fig. 2, which gives the reduction of S. aureus as a function of soybean protein and sucrose at fixed bean oil concentration of 5.0 g/100 g (0 level) and pH of 7.0 (0 level), shows that reduction of S. aureus decrease with increasing concentration of soybean protein and sucrose.

Fig. 2. Response surface plot and its contour plot of the effect of soybean protein and sucrose and their mutual interactions on S. aureus reduction of HPP.

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Fig. 3. Response surface plot and its contour plot of the effect of sucrose and bean oil and their mutual interactions on S. aureus reduction of HPP.

Analyzing the soybean protein–sucrose plot, a significant synergistic interactional effect by protecting S. aureus As 1.2465 simultaneously is observed when soybean protein is combined with sucrose. Fig. 3 shows how reduction of S. aureus varies with sucrose and bean oil concentration at fixed pH of 7.0 (0 level) and soybean protein concentration of 2.50 g/100 g (0 level). With increase of bean oil concentration, the changes of inactivation of S. aureus were not evident. Similarly, some synergistic protective effect of sucrose in the presence of bean oil is shown in Fig. 3. These results above do indicate that S. aureus is quite sensitive to high and low pH, soybean protein and sucrose have indeed protective effect to S. aureus, and the protective effect of bean oil to S. aureus was not obvious during pressurization. This was in agreement with Raso et al. [5] who observed no protective effect of milk fat during high pressure pasteurization of milk. Gervilla et al. [26] studied inactivation of HPP treatments on S. aureus CECT 534 in ovine milk adjusted to 0, 6, and 50% fat content. They found percentage of fat (6 and 50%) did not show a progressive baroprotective effect in all pressurization conditions. These observations are in line with our results in the present paper. On comparison of the sensitivities of the microorganisms in a pH 5.3 phosphate buffer solution, cheese slurry, and Cheddar cheese, greatest sensitivity to HPP was shown in the pH 5.3 phosphate buffer by S. aureus ATCC 6538 [27]; therefore, a direct extrapolation of data for microbial inactivation by HPP obtained with buffer or physiological solutions to predict levels of inactivation in foodstuffs may give misleading results. Gu¨zel-Seydim et al. [28] investigated the ozone-induced destruction of S. aureus ATCC 27661 in the presence of fat, protein, and carbohydrate sources. They showed that the starch provided little or no protective effects compared to the buffer control, while protein and fat provided the greatest levels of protection to S.

aureus. It seems that the mechanisms of the two kinds of pasteurization processes (HPP, Ozone) have some similarities. In agreement with former studies, a nutrient-rich medium (especially a proteinaceous medium) is believed to be protective than an aqueous buffer medium [1,29]. Proteins in general seem to protect microorganisms against pressure inactivation [1,4,15]. Protective effects of sucrose against pressure inactivation were reported by Oxen and Knorr [30] and Simpson and Gilmour [31]. The effect was suggested to relate to the decrease in water activity. Water was demonstrated to be necessary for an appropriate high pressure inactivation [4,32], and resistance to pressure inhibition was shown at reduced aw-values. This effect was attributed to cell shrinkage which probably causes a thickening in the cell membrane, reducing membrane permeability and membrane fluidity [33]. In the past, the important effect of pH has been demonstrated [34,2,5]. A low food pH is a major advantage in high pressure inactivation procedures [35,36]. The effects of food constituents on pressure resistance are complicated. The influence of the food during HPP treatment and the fate of microorganism in the food after treatment determine microbiological safety and stability. The previous published study showed the magnitude orders of S. aureus cell reduction of S. aureus As 1.2465 reduction in milk and food matrices designed in the present work (Table 2) had some differences under the same HHP condition [11,37], which is due to the different content of food components in them. Therefore, the medium in which the microorganism is treated is an important determinant of the level of inactivation observed. For instance, B. stearothermophilus spore ATCC 7953 inactivation in cocoa mass is only possible in excess of a critical water content. Up to a moisture content of 10%, the spores remained unaffected. However, in excess of 10% moisture, the resistance of spores against pressure and heat was gradually reduced. By adjusting moisture content of the cocoa mass to

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Table 5 Verified results of the model equation Trial No.

Variable

Y

X1

X2

X3

X4

Observed

Predicted

1 2 3 4 5 6 7 8 9 10

4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 7.50 8.00

1.00 1.20 1.25 1.25 1.30 1.35 2.00 2.90 3.00 3.30

2.00 2.20 2.50 2.80 3.00 3.30 4.00 4.50 5.00 6.00

0.25 0.28 3.00 3.40 4.00 4.40 5.00 5.50 6.00 6.00

7.39 7.17 6.83 6.72 6.61 6.55 6.28 6.09 6.00 6.07

7.32 7.20 6.91 6.73 6.58 6.57 6.31 6.10 6.06 6.13

(0.01) (0.03) (0.05) (0.02) (0.03) (0.01) (0.07) (0.01) (0.04) (0.02)

the food matrix on the reduction of S. aureus. The soybean protein (P = 0.0082), sucrose (P < 0.0001), and pH (P = 0.0429) significantly affected reduction of S. aureus, and the effect of bean oil on reduction of S. aureus was not significant (P = 0.2790). A predictive model for reduction of S. aureus was established as a function of soybean protein, sucrose, bean oil and pH of the food matrix in food matrix environment. The adequacy of the predictive model was verified effectively by the validation data.

References

Values in parentheses are coefficients of variation of measures.

30%, the inactivation of B. stearothermophilus spores was clearly pressure and temperature dependent. These observations suggested that the spores can be effectively protected by their surrounding matrix against lethal effects of pressure and heat. By means of water addition to the medium, spore kill is enhanced [38]. It is clear that a marked advantage using response surface methodology to investigate the effect of food composition on S. aureus inactivation by high pressure and mild heat can obtain a regression equation predicting the number of S. aureus reduction after a certain temperature-high pressure treatment, and can tell which of the nutrient fractions are believed to be more important factors. The regression equation model is probably of great help in food industry. Additionally, more research is required to ascertain the precise mechanism of protective effects of food constituent on inactivation of S. aureus during HPP. 3.3. Verification of predictive model In order to validate the adequacy of the model equation (Eq. (5)), a total of 10 verification experiments were carried out at 34.4 8C and 329.8 MPa for 15.5 min under different combinations of food constituents and the results shown in Table 5. The validation data were analyzed by using the SPSS software (Version 10.0, SPSS Inc.). The correlation coefficients (R) between the experimental and predicted values are 0.9964. The results of analysis indicated that the experimental values were in good agreement with the predicted ones, and also suggested that the model of Eq. (5) was satisfactory and accurate. Although the model equation was empirical, it was quite satisfactory.

4. Conclusion Response surface methodology involving an experimental design and regression analysis was used to evaluate the effects of soybean protein, sucrose, bean oil and pH of

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