Probabilistic Models to Predict the Growth Initiation Time for Pseudomonas spp. in Processed Meats Formulated with NaCl and NaNO₂

Abstract

This study developed probabilistic models to determine the initiation time of growth of Pseudomonas spp. in combinations with NaNO₂ and NaCl concentrations during storage at different temperatures. The combination of 8 NaCl concentrations (0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, and 1.75%) and 9 NaNO₂ concentrations (0, 15, 30, 45, 60, 75, 90, 105, and 120 ppm) were prepared in a nutrient broth. The medium was placed in the wells of 96-well microtiter plates, followed by inoculation of a five-strain mixture of Pseudomonas in each well. All microtiter plates were incubated at 4, 7, 10, 12, and 15℃ for 528, 504, 504, 360 and 144 h, respectively. Growth (growth initiation; GI) or no growth was then determined by turbidity every 24 h. These growth response data were analyzed by a logistic regression to produce growth/no growth interface of Pseudomonas spp. and to calculate GI time. NaCl and NaNO₂ were significantly effective (p<0.05) on inhibiting Pseudomonas spp. growth when stored at 4-12℃. The developed model showed that at lower NaCl concentration, higher NaNO₂ level was required to inhibit Pseudomonas growth at 4-12℃. However, at 15℃, there was no significant effect of NaCl and NaNO₂. The model overestimated GI times by 58.2±17.5 to 79.4±11%. These results indicate that the probabilistic models developed in this study should be useful in calculating the GI times of Pseudomonas spp. in combination with NaCl and NaNO₂ concentrations, considering the over-prediction percentage.

Introduction

Pseudomonas spp. are psychrotrophic bacteria, and they are the main cause for milk spoilage (Reddy et al., 1969), chicken (Pittard et al., 1982), fish (Miller et al., 1973), and meat especially at chill temperatures (Nychas et al., 2008). In food, they produce special fluorescent green, yellow or bluish compounds (Brown et al., 1958). Moreover, they generate off-odors in the meats by producing prolyitc and lipolyic enzymes (Champagne et al., 1994; Sorhaug and Stepaniak, 1997). Although Pseudomonas spp. causes physicochemical changes, microbiological criteria for the bacteria are not established because they are not pathogenic bacteria.

In processed meat products, NaNO₂ plays an important role in developing of cured meat color and flavor, retarding lipid autoxidation, and preventing Clostridium botulinum germination in anaerobic condition (Pegg and Shahidi, 2006). However, NaNO₂ has the potential to produce N-nitroso compounds under acidic conditions in stomach (Sugimura, 2000). N-nitroso compounds have been found to cause carcinogenic activity in many animal models (Cassens, 1995). Hence, consumers have low acceptance level for processed meat products. Even though processed meat products formulated with low concentrations of NaNO₂ have been developed to avoid potential side effects, but the concern for microbial safety due to lowered concentrations of NaNO₂ has now increased (Sinedlar et al., 2007).

NaCl has been used to improve water-holding capacity, fat binding properties, flavor and the inhibition of microbial growth in processed meat products (Guàrdia et al., 2006; Rhee and Zipirin, 2001). However, the high level of NaCl intake is related to hypertension (Tobian et al., 1979), cardiac failure (Frolich, 1999), and stroke (Perry and Beevers, 1992). Thus, consumers are willing to have the low concentration of NaCl in processed meat products, but this low NaCl concentration may not inhibit bacterial growth. Therefore, the minimum concentrations of NaNO₂ and NaCl need to be determined to inhibit bacterial growth and also to meet consumers’ requirement. Thus, the interactive responses for these two ingredients should be considered in order to determine the minimum concentrations. The probabilistic model should be appropriate to achieve this goal. Probabilistic model using logistic regression can estimate the probabilities of bacterial growth and interface between growth and no growth of bacteria under various conditions (López-Malo et al., 2000; Tienungoon et al., 2000). This mathematical technique can be applied to estimate the GI time of foodrelated bacteria.

Most studies on the relationship between Pseudomonas spp. and NaNO₂ have focused on the antimicrobial effect of NaNO₂ on Pseudomonas spp. (Henry and Bessieres, 1984; Nicke et al., 2013), but the combination effect of NaNO₂ and NaCl on Pseudomonas spp. in processed meats has not been fully studied yet.

Therefore, the objective of this study was to develop probabilistic models to determine the GI time of Pseudomonas spp. in combinations with NaNO₂ and NaCl concentrations.

Materials and Methods

Inoculum preparation

The isolated colonies of Pseudomonas aeruginosa strains (NCCP10338, NCCP10250, and NCCP11229) and Pseudomonas fluorescens strains (KACC10326 and KACC 10323) in Cetrimide agar (Becton Dickinson and Company, USA) were cultured in a nutrient broth (NB; Becton Dickinson and Company) at 35℃ for 24 h. One hundred microliter fractions of the cultures were transferred into 10 mL NB for subculture at 35℃ for 24 h. After incubation, five strains were mixed and centrifuged at 1,912 g and 4℃ for 15 min, and cell pellet was washed twice with phosphate-buffered saline (PBS; pH 7.4; 0.2 g of KH₂PO₄, 1.5 g of Na₂HPO₄·7H₂O, 8.0 of NaCl, and 0.2 g of KCl in 1 L of distilled water). The cell suspension was diluted with PBS to 5 Log CFU/mL.

Growth/no growth response

The combination of 8 levels (0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, and 1.75%) of NaCl (Samchun pure chemical Co. Ltd., Korea) and 9 levels (0, 15, 30, 45, 60, 75, 90, 105, and 120 ppm) of NaNO₂ (Duksan pure chemicals Co. Ltd., Korea) were prepared in NB. Two hundred and twenty five microliters of the medium were placed in wells of 96-well microtiter plates, and 25 μL of inoculum was inoculated into each well. All microtiter plate wells were then incubated at 4, 7, 10, 12, and 15℃ for 528, 504, 504, 360, and 144 h, respectively. Growth (growth initiation; GI) or no growth was then determined by turbidity every 24 h. The combinations that became turbid, were considered growth, while the unturbid combination was considered no growth. The growth response was regarded as ‘1’ and no growth response was assigned as ‘0’ (Koutsoumanis et al., 2004).

Probabilistic model development

The growth response data were analyzed with the SAS version 9.2 logistic regression analysis (SAS Institute Inc., USA) to estimate the growth probabilities of Pseudomonas spp. Significant parameters were selected through a stepwise selection method (p<0.05).

Logit (P) = a₀ + a₁·NaCl + a₂·NaNO₂ + a₃·Time + a₄·NaCl² + a₅·NaNO₂ ² + a₆·Time² + a₇·NaCl·NaNO₂ + a₈·NaCl·Time + a₉·NaNO₂·Time

Where Logit (P) is an abbreviation of ln[P/(1−P)], P is the probability of growth within the range of 0 to 1, a_i is the estimates, NaCl is NaCl concentrations, NaNO₂ is NaNO₂ concentrations, and Time is storage time.

Evaluation of developed model

Observed data for Pseudomonas spp. growth were obtained from commercial frankfurters and bacon. The frankfurters and bacon were cut into 7 g and placed into plastic bags (Food Saver^®, Rollpack, Korea). The 0.1 mL portions of the inoculum were inoculated on one side of the sample surface. The inoculated samples were massaged 15 times in order to spread the bacteria and then sealed using a packager (Food Guard^®; Rollpack, Korea). The samples were then aerobically stored at 4, 7, 12, and 15℃ for 336, 312, 192, and 120 h, respectively. To quantify bacterial populations, the samples were analyzed at appropriate intervals. The 30 mL of 0.1% buffered peptone water (BPW; Becton Dickinson and Company) was added into the sample bag and homogenized using a pummeler (BagMixer®, Interscience, France) for 60 s. The homogenates were serially diluted with 0.1% BPW, and 0.1 mL of the diluents was surface-plated on Cetrimide agar. The plates were incubated at 35℃ for 24 h, and the typical colonies were manually counted to determine GI time. A growth greater than 1-log considered growth (Koutsomanis et al., 2004; Lee et al., 2013). The observed GI times were then compared to the predicted GI times of Pseudomonas spp. estimated under the developed model.

Results and Discussion

The estimates of coefficients selected from the logistic regression analysis, using an automatic variable selection option with a stepwise selection method, are shown in Table 1. The estimates were then used to produce interfaces between growth and no growth of Pseudomonas spp. at 0.1, 0.5, and 0.9 of probabilities with the combination for NaNO₂ and NaCl level for each storage temperature (Figs. 1-2). This result can also be used to determine the GI time of Pseudomonas spp. NaCl, NaNO₂, and storage time were generally significant (p<0.05) factors for inhibiting Pseudomonas spp. growth during storage at 4-12℃ (Table 1). However, NaNO₂ and NaCl did not have any significant effects on the growth of the bacteria at 15℃. Moreover, a square function for NaCl and NaNO₂ was not observed at 12 and 15℃ (Table 1).

Table 1. Estimates of the parameters selected from the logistic regression analysis by a stepwise selection method to calculate the growth probability of Pseudomonas spp. at 4-15℃.

Variable	4℃			7℃			10℃			12℃			15℃
	Estimate	SEa	p	Estimate	SE	p	Estimate	SE	p	Estimate	SE	p	Estimate	SE	p
Intercept	−19.4190	0.77	<0.001	−9.1128	0.43	<0.001	−7.0291	0.34	<0.001	10.5739	0.45	<0.001	25.3165	2.24	<0.001
NaNO2	0.00320	0.01	0.623	-0.0165	0.00	0.001	0.0180	0.01	0.001	0.00645	0.00	0.018	0.00212	0.00	0.573
NaCl	1.4815	0.36	<0.001	1.3652	0.32	<0.001	−0.0798	0.15	0.587	−0.9429	0.26	0.001	−0.4328	0.25	0.083
Time	0.1149	0.01	<0.001	0.0592	0.00	<0.001	0.0517	0.00	<0.001	0.1223	0.00	<0.001	0.4673	0.04	<0.001
NaNO22	−0.00011	0.00	0.005	0.000099	0.00	0.004	0.00024	0.00	<0.001	-	-	-	-	-	-
NaCl2	−0.8441	0.19	<0.001	−0.8103	0.16	<0.001	-	-	-	-	-	-	-	-	-
Time2	−0.00014	0.00	<0.001	−0.0006	0.00	<0.001	0.00006	0.00	<0.001	0.00023	0.00	<0.001	0.00132	0.00	<0.001
NaNO2×NaCl	−0.00689	0.00	0.003	−0.00783	0.00	0.001	−0.00535	0.00	0.009	0.00902	0.00	0.001	−0.0244	0.00	<0.001
NaNO2×Time	0.00004	0.00	0.001	-	-	-	0.00004	0.00	0.003	-	-	-	-	-	-
NaCl×Time	-	-	-	-	-	-	-	-	-	0.00333	0.00	0.017	-	-	-

^a Standard error

Fig. 1. Growth/no-growth interfaces of Pseudomonas spp. at 4℃ with respect to NaNO₂ concentration and storage time as a function of NaCl levels at growth probabilities of 0.1 (left line), 0.5 (middle line), and 0.9 (right line); no growth: ○, growth: ●, 50% growth: △.

Fig. 2. Growth/no-growth interfaces of Pseudomonas spp. at 7℃ with respect to NaNO₂ concentration and storage time as a function of NaCl levels at growth probabilities of 0.1 (left line), 0.5 (middle line), and 0.9 (right line); no growth: ○, growth: ●, 50% growth: △.

For 4 and 7℃, the antimicrobial effect of NaNO₂ on Pseudomonas spp. growth slightly increased to 1% NaCl, but the antimicrobial effect dramatically increased to 1.25% NaCl (Figs. 1 and 2). This result indicates that the obvious antimicrobial effect of NaNO₂ to inhibit Pseudomonas spp. growth can be found in high NaCl concentration (>1.25% NaCl). In addition, the combination effect of NaCl and NaNO₂ on the inhibition of Pseudomonas spp. growth was also observed at 10, 12, and 15℃ (data not shown). According to these results, it is suggested that NaCl concentration of ready-to-eat meat products should be at a certain level to have the obvious antimicrobial effect of NaNO₂ on Pseudomonas spp. growth. This is proven by the result from Fig. 3, showing that the difference of growth probability among NaNO₂ concentrations became more obvious as NaCl concentration increased. Similarly, a study by Pelroy et al. (1994) also showed that the concentration-dependent antimicrobial effect of NaNO₂ on L. monocytogenes in cold-processed salmon in high NaCl concentrations when stored at 5 and 10℃. Shahamat et al. (1980) and Buchanan et al. (1989) examined the antimicrobial effects of NaNO₂ on L. monocytogenes and suggested that the antilisterial effect is improved with NaCl and other factor such as pH, and temperature. Hence, Allaker et al. (2001) suggested that even though the specific inhibitory modes of nitrite are not well clarified, its antimicrobial effectiveness depends on several factors including salt concentration, pH, reductants, iron content, and others.

Fig. 3. Probabilities of Pseudomonas spp. at different levels of NaCl and NaNO₂ when stored at 15℃.

The concordance index was used in order to measure the goodness of fit in the developed probabilistic model. The concordance index indicated the degree of agreement between the observations and calculated probabilities. In this study, the concordance index was 94.5-98.1%, while the discordance was 1.9-5.3%, depending on the storage temperature (data not shown).

To evaluate the performance of the developed probabilistic models in this study, the model performance was assessed with the observed data. The predicted GI times calculated by the estimates of the parameters listed in Table 1 at the probability level of 0.5 were then compared to the predicted GI times (Table 2). A growth more than 1-log scale was considered ‘growth’. The developments of the growth/no growth model were compared with the observed growth data. The predicted GI times were generally overestimated when compared to the observed values by 58.2±17.5% to 79.4±11%. This result indicates that Pseudomonas spp. initiated to grow earlier in frankfurter and bacon than in broth media by 58.2-79.4%. Over-prediction percentages were 79.4±11% (4℃), 66.4±14.6% (7℃), 58.2±17.5% (12℃), and 68.2±2.1% (15℃) (Table 2). In our study, the broth media became turbid, when Pseudomonas spp. grew up to approximately 5-6 Log CFU/mL, and at the point, Pseudomonas spp. growth was determined. However, data from ready-to-eat meats were considered as “growth” if a growth greater than 1-log was observed. Because of this reason, there was a difference between the predicted data and the observed data. Therefore, decreased GI time by 58.2 to 79.4 % compared to the predicted GI time from developed probabilistic model should be applied for real processed meat products such as frankfurters and bacon.

Table 2. Comparison of observed and predicted growth initiation (GI) time of Pseudomonas spp. at various concentrations of NaCl and NaNO₂.

Temperature (℃)	Product	Conditions		Predicted GI time (h)	Observed GI time (h)	Over-prediction percentage (%)b
		NaCl (%)	NaNO2 (ppm)
4	Frankfurt A	1.4	5a	230	168	79.4±11
	Frankfurt B	1.3	0	228	168
	Bacon	1.6	26	234.6	216
7	Frankfurt A	1.4	5	186	96	66.4±14.6
	Frankfurt B	1.3	0	180	120
	Bacon	1.6	26	208	168
12	Frankfurt A	1.4	5	121	48	58.2±17.5
	Frankfurt B	1.3	0	119	72
	Bacon	1.6	26	129	96
15	Frankfurt A	1.4	5	69.6	48	68.2±2.1
	Frankfurt B	1.3	0	68.8	48
	Bacon	1.6	26	73	48

^aadded NaNO₂ level

^bPercentage (%) = (the observed data/the predicted data)×100; values are means±standard errors.

In conclusion, the probabilistic models developed in this study can be used to calculate the GI times of Pseudomonas spp. in frankfurters and bacon as a function of NaCl and NaNO₂ concentrations, considering the over-prediction percentage, and thus, the probabilistic models can be useful in controlling bacterial spoilage in the processed meats by Pseudomonas spp.