Mathematical Model for Predicting the Growth Probability of Staphylococcus aureus in Combinations of NaCl and NaNO2 under Aerobic or Evacuated Storage Conditions.

The objective of this study was to describe the growth patterns of Staphylococcus aureus in combinations of NaCl and NaNO2, using a probabilistic model. A mixture of S. aureus strains (NCCP10826, ATCC13565, ATCC14458, ATCC23235, and ATCC27664) was inoculated into nutrient broth plus NaCl (0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, and 1.75%) and NaNO2 (0, 15, 30, 45, 60, 75, 90, 105, and 120 ppm). The samples were then incubated at 4, 7, 10, 12 and 15℃ for up to 60 d under aerobic or vacuum conditions. Growth responses [growth (1) or no growth (0)] were then determined every 24 h by turbidity, and analyzed to select significant parameters (p<0.05) by a stepwise selection method, resulting in a probabilistic model. The developed models were then validated with observed growth responses. S. aureus growth was observed only under aerobic storage at 10-15℃. At 10-15℃, NaCl and NaNO2 did not inhibit S. aureus growth at less than 1.25% NaCl. Concentration dependency was observed for NaCl at more than 1.25%, but not for NaNO2. The concordance percentage between observed and predicted growth data was approximately 93.86%. This result indicates that S. aureus growth can be inhibited in vacuum packaging and even aerobic storage below 10℃. Furthermore, NaNO2 does not effectively inhibit S. aureus growth.

Introduction

Consumers consider many factors when purchasing certain foods, and their awareness of food safety is becoming more important because volumes of imported and processed foods are increasing (Choe ; Kim and Kim, 2003). Some foods contain additives, which are included to improve the quality of the product. Such additives include NaCl and NaNO2, which play a role in preservation and food safety, especially in processed meat products (Pereira ; Shapiro ). However, recently, consumers have started to express a preference for processed meat products formulated with low concentrations of NaCl and NaNO2, because of the health issues involved (Bedale ; Guàrdia ; Kim ).

The processed meat industry has tried to use substitutes for additives, especially NaNO2, and consumers are satisfied with the appearance of the products (Lee ). In processed meats, NaNO2 plays a role in color fixing and inhibiting pathogenic bacteria, such as Listeria monocytogenes, Clostridium botulinum, and Staphylococcus aureus (Hospital ; Karina ; Latham ; Tompkin ). Although NaNO2 substitutes may fix the color in processed meat products, most have no antimicrobial activity. Thus, using a NaNO2 substitute or a low concentration of NaNO2 may result in greater pathogenic bacterial growth than in conventional meat products.

S. aureus is a gram-positive enterotoxigenic bacterium (CDC, 2014). Twenty to thirty percent of people are carriers of S. aureus (Normanno ), and it can contaminate food during processing; the pathogen may produce enterotoxins at 105-106 CFU/g of S. aureus (Chiefari ; Park ). Ham can be contaminated with S. aureus during slaughter, processing, or handling (Borch ; Ingham ). Park reported that they had isolated S. aureus from 0.6% of the ham samples they examined, and Atanassova isolated the pathogen from 35.6% of smoked ham.

Therefore, we developed mathematical models to predict the growth probability of S. aureus in a combination of NaCl and low-concentration NaNO2 under both aerobic and vacuum storage conditions.

Materials and Methods

Inoculum preparation

Five S. aureus strains (NCCP10826, ATCC13565, ATCC14458, ATCC23235 and ATCC27664) were cultured in 10 mL nutrient broth (NB; Becton, Dickinson and Company, USA) at 35℃ for 24 h. The one-tenth milliliter aliquots of the cultures were subcultured in 10 mL fresh NB at 35℃ for 24 h. The subcultures were then centrifuged at 1,912 g for15 min at 4℃, and washed twice with phosphate-buffered saline (PBS, pH 7.4; 0.2 g of KH2- PO4, 1.5 g of Na2HPO4·7H2O, 8.0 g of NaCl, and 0.2 g of KCl in 1 L of distilled water). Each cell suspension of the S. aureus strains was mixed, and the mixture was serially diluted with PBS to obtain 4 Log CFU/mL.

Sample preparation and inoculation

NB was formulated with NaCl (0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, and 1.75%) and NaNO2 (0, 15, 30, 45, 60, 75, 90, 105, and 120 ppm). Two hundred five microliter of the samples were placed into each well of a 96-well microtiter plate (SPL Life Sciences Co., Ltd., Korea), and 25-μL portions of S. aureus inoculum were inoculated into the samples. The microtiter plates were sealed with paraffin film (Parafilm M®; Bemis Company Inc., USA) for aerobic storage, or placed in airtight containers with AnaeroGen packs (Oxoid Ltd., UK) for vacuum storage. The AnaeroGen packs were replaced every 24 h. The microtiter plates were stored at 4-15℃ for up to 60 d, depending on storage temperature, under aerobic or vacuum conditions. We used plain NB and NB plus S. aureus cells for the negative and positive controls, respectively.

Probabilistic model development

During storage, the growth responses for each combination (n=4) were determined by turbidity every 24 h. If a combination was turbid, it was designated as “growth (score=1)”, otherwise it was designated as “no growth (score=0)”. The growth response data were analyzed by logistic regression as follows:

where P is the probability of growth, a are estimates, NaCl is the NaCl concentration, NaNO2 is the NaNO2 concentration, Time is the storage time and Temp is the storage temperature. Among the parameters, NaNO2 and storage Time were transformed for proper application to the model. In the equation, the significance parameters (p<0.05) were selected by a stepwise selection method using SAS® (Version 9.3; SAS Institute Inc., USA). In addition, the estimates of selected parameters were used to produce growth/no growth interfaces at 0.1, 0.5 and 0.9 probability.

Minimum bactericidal concentration (MBC) test

To determine the MBC of NaCl and NaNO2 for S. aureus, the aqueous portions of the microtiter plate wells that were clear were streaked on mannitol sorbitol agar (MSA; Becton, Dickinson and Company), and the plates were incubated at 37℃ for 24 h to observe S. aureus survival by colony.

Validation of model performance with emulsion type sausage

To evaluate the performance of the developed probabilistic model, the predicted growth response from the model was compared with the observed growth response from real food. To prepare observed growth response data, emulsion-type sausages were manufactured according to the formulation given in Table 1. Each batch of the formula was mixed for 6 min using a cutter (MSK 760-II; Mado, Germany), and stored at 4℃ for 1 h. The mixtures were then filled into collagen casings (30 g per casing) using a Konti A50 automatic sausage can filler (Frey, Germany). The resulting sausages were then smoked at 75℃ for 40 min in a smokehouse (MAXI 3501; Kerres, Germany) and chilled. The vacuum-packaged smoked sausages were heated at 80℃ for 15 min and stored at 4℃ until required. The sausages (25 g) were placed in a sterilized plastic container containing S. aureus inoculum at 3 Log CFU/mL, and gently stirred for 2 min to complete inoculation. The samples were air-dried for 15 min to allow S. aureus cell attachment, and transferred to sample bags. The bags were sealed for the aerobic or vacuum-packaged experiments and stored at 10℃ for 65-70 d and 15℃ for 35-43 d, respectively. During storage, S. aureus cell counts were enumerated on MSA (Becton, Dickinson and Company). If the S. aureus cell count increased by more than 1 Log CFU/g compared with that on day 0, the result was considered to be “growth”, otherwise “no growth” was recorded (Gwak ; Koutsoumanis ).

Table 1.

Formulation of emulsion-type sausages

Ingredients (%)	No NaNO2			10 ppm NaNO2
	1.00% NaCl	1.25% NaCl	1.50% NaCl	1.00% NaCl	1.25% NaCl	1.50% NaCl
Pork meat	60	60	60	60	60	60
Pork fat	20	20	20	20	20	20
Ice	20	20	20	20	20	20
Total	100	100	100	100	100	100
NaCl	1.00	1.25	1.50	1.00	1.25	1.50
NaNO2	-	-	-	0.0029	0.00303	0.00305
Phosphate	0.03	0.03	0.03	0.03	0.03	0.03
Isolated soy protein	1.00	1.00	1.00	1.00	1.00	1.00
Mixed spice	0.50	0.50	0.50	0.50	0.50	0.50
Sugar	0.50	0.50	0.50	0.50	0.50	0.50
Potassium sorbate	0.20	0.20	0.20	0.20	0.20	0.20

Results and Discussion

In vacuum condition, S. aureus growth was not observed at any growth temperature up to 60 d, regardless of the NaCl and NaNO2 concentrations, indicating that S. aureus can be inhibited effectively in vacuum packaging, even at low concentrations of NaCl and NaNO2, and therefore, no probabilistic model was developed (data not shown). Under aerobic conditions, S. aureus growth was not observed below 10℃ up to 60 d, regardless of the NaCl and NaNO2 concentrations, but the MBC test showed that S. aureus cells were not completely destroyed. Their cell counts were just reduced or retained at all concentrations of NaCl and NaNO2 examined in this study. This result indicates that NaCl concentrations up to 1.75% and NaNO2 concentrations up to 120 ppm, and their combinations, may not be sufficient to destroy S. aureus at low temperatures, and S. aureus cells that survive below 10℃ may grow above 10℃, allowing S. aureus to produce enterotoxins. In agreement with this result, Lee reported that the Tmin (theoretical minimum growth temperature) value for S. aureus was 10.2℃ in cheese. However, Lee and Le Marc reported lower Tmin values for carbonara sauce (5.2℃) and milk (5.8℃). These results indicate that the Tmin values for S. aureus depend on the food matrix. The low temperature adaptation of S. aureus is related to the lipoamide dehydrogenase gene (lpd) in the bkd gene cluster, which causes the production of branched-chain fatty acids in phospholipids, resulting in improved membrane fluidity (Singh ; Yoon ).

S. aureus growth was observed at 10, 12 and 15℃, and the probability model was developed to describe the growth pattern using logistic regression. Significant parameters affecting S. aureus growth are presented in Table 2, and the parameters with estimates were used to produce the growth/no growth interfaces at 0.1, 0.5 and 0.9 probabilities in Figs. 1 and 2. The results in Table 2 show that S. aureus growth was affected (p<0.0001) by storage temperature, storage time, and the concentrations of NaCl and NaNO2, but no interaction effects, including for NaCl×NaNO2, were observed.

Table 2.

Estimates of the parameters selected from the logistic regression analysis by a stepwise selection method to produce the interfaces between growth and no growth of Staphylococcus aureus at desired probabilities under aerobic conditions

Variables	Estimate	SE	p-value
Interception	−38.2620	0.2078	<0.0001
Temperature	0.7171	0.0038	<0.0001
NaNO2 concentration/10	0.0951	0.0021	<0.0001
NaCl concentration	−0.9255	0.0148	<0.0001
Log (Time)	10.2063	0.0599	<0.0001

Fig. 1.

Growth/no growth interfaces of Staphylococcus aureus in nutrient broth at 10℃ with respect to NaNO2 concentration and storage time for various NaCl concentrations under aerobic conditions 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 Staphylococcus aureus in nutrient broth at 15℃ with respect to NaNO2 concentration and storage time for various NaCl concentrations under aerobic conditions at growth probabilities of 0.1 (left line), 0.5 (middle line) and 0.9 (right line); no growth: ○, growth: ●, 50% growth: △.

At 10℃, NaCl and NaNO2 did not inhibit the growth of S. aureus, as well as combination of NaCl and NaNO2 at less than 1.25% NaCl. However, interestingly, the initiation time for S. aureus growth decreased as NaNO2 concentration increased at less than 1.25% NaCl (Fig. 1). Schlag reported that the nreABC gene is involved in nitrate reduction. Therefore, the antibacterial effect of NaNO2 on S. aureus was not detected.

A NaCl concentration of more than 1.25% inhibited S. aureus growth (Fig. 1). In addition, no difference in initiation time for S. aureus growth was observed among the various NaNO2 concentrations, and the initiation times were longer than those at less than 1.25% NaCl. Even at more than 1.25% NaCl, the combination effect was not observed (Fig. 1), as shown in Table 2, and the S. aureus growth response at 0 ppm NaNO2 was similar to that at 120 ppm (Fig. 1). This result indicates that a NaCl concentration of more than 1.25% is needed to inhibit S. aureus growth, but NaNO2 is not effective in inhibiting S. aureus growth. However, Lee reported a NaCl and NaNO2 combination effect on Lactobacillus in frankfurters, and Jo reported a combination effect on Pseudomonas spp. in processed meats. These results suggest that the NaCl and NaNO2 combination effect depends on the type of foodborne bacteria. S. aureus grew better at 12℃ than at 10℃, and demonstrated a NaCl concentration-dependent growth response (Fig. 2). In addition, no obvious effect of NaNO2 on the inhibition S. aureus growth was observed (Fig. 2), which was similar to the result at 15℃ (data not shown). In agreement with these observations, a study by Bang also showed that nitrite had no effect on inhibiting S. aureus growth.

To evaluate the performance of the developed probabilistic models in this study, observed growth responses were collected from real food (emulsion-type sausages) in an additional study, and the observed growth responses from the study were compared with the predicted growth responses from developed probabilistic models. Because the predictions from the developed probabilistic models were expressed as numbers, growth was determined at more than 0.5 of growth probability (Yoon ). In addition, growth responses (growth or no growth) from the sausages were determined at 1 Log CFU/g of S. aureus growth (Gwak ; Koutsoumanis ). Comparisons between predicted and observed growth response are presented in Table 3; the observed growth responses mostly agreed with the predicted growth responses. The accordance percentage between the predicted and observed growth responses was 93.86%, indicating that the developed probabilistic model was capable of predicting the growth responses of S. aureus in emulsion-type sausages, formulated with various concentrations of NaCl and NaNO2.

Table 3.

Comparisons between observed and predicted growth responses of Staphylococcus aureus in emulsion-type sausage under aerobic conditions

Temperature (℃)	NaNO2 (ppm)	NaCl (%)	Time (h)	Observed growth response	Predicted growth response
10	0	1.00	0-1,3201)	NG	NG
			1,440	NG	G
			1,560	G	G
		1.25	0-1,320	NG	NG
			1,440	NG	NG
			1,560	G	G
		1.50	0-1,320	NG	NG
			1,440	NG	NG
			1,560	NG	G
	10	1.00	0-1,320	NG	NG
			1,440	NG	G
			1,560	G	G
			1,680	G	G
		1.25	0-1,320	NG	NG
			1,440	NG	G
			1,560	G	G
			1,680	G	G
		1.50	0-1,320	NG	NG
			1,440	NG	NG
			1,560	G	G
			1,680	G	G
15	0	1.00	0-5282)	NG	NG
			696	NG	G
			864	G	G
			1,032	G	G
		1.25	0-528	NG	NG
			696	NG	G
			864	G	G
			1,032	G	G
		1.50	0-528	NG	NG
			696	NG	G
			864	G	G
			1,032	G	G
	10	1.00	0-4803)	NG	NG
			600	NG	G
			720	G	G
			840	G	G
		1.25	0-480	NG	NG
			600	NG	NG
			720	G	G
			840	G	G
		1.50	0-480	NG	NG
			600	NG	NG
			720	G	G
			840	G	G

1)Time interval (h): 0, 120, 240, 360, 528, 696, 864, 1,080, 1,320. 2)Time interval (h): 0, 120, 240, 360, 528. 3)Time interval (h): 0, 120, 240, 360, 480.

In conclusion, the probabilistic models were appropriate for describing the growth responses of S. aureus at different concentrations of NaCl and NaNO2. Vacuum storage can inhibit S. aureus growth in emulsion-type sausages, and storage below 10℃ can inhibit S. aureus growth under aerobic storage conditions, even at low concentrations of NaCl and NaNO2. In storage above 10℃, a NaCl concentration of more than 1.25% is necessary to inhibit S. aureus growth effectively, but NaNO2 may not effectively inhibit S. aureus growth.