Probabilistic modeling of the growth of Listeria monocytogenes: effect of nisin, temperature, and strain in the presence of potassium chloride or potassium sorbate

ABSTRACT

The effects of temperature and nisin with either potassium chloride (KCl) or potassium sorbate on growth boundaries of three different Listeria monocytogenes strains in broth were studied. One ATCC7644 strain and two ready-to-eat food (RTE) isolates at different temperatures (4, 20, and 37°C) and nisin (0, 50, 100, 200, and 400 μg/mL) levels with either KCl (0, 1, 2, 3, and 4% w/v) or potassium sorbate (0, 0.05, 0.10, 0.15, and 0.20% w/v) were used. Highest and lowest growth probabilities were obtained for ATTC7644 and 120 (meat-based RTE isolate) strains, respectively with KCl and strain 137 (vegetable-based RTE isolate) was in between. However, the growth probabilities of the strains were just the opposite with the use of sorbate: strain 120 had the highest, whereas ATCC7644 strain had the lowest growth probability. Our results showed that nisin in combination with other preservatives may lead to diverse growth responses for different strains of L. monocytogenes. Validation studies performed in UHT whole milk and meat broth at 8 and 12°C and nisin levels of 25, 75, 150, and 250 μg/mL with either KCl (1.5%) or sorbate (0.125%) indicated 46% and 73% accurate predictions for milk and meat broth, respectively. Although a quick growth estimate was possible with the use of broth, we concluded that a model developed in a laboratory medium should not be extended in real food systems.

KEYWORDS:

• Logistic regression
• foodborne pathogen
• predictive microbiology
• strain variation

Introduction

Listeria monocytogenes, the pathogen responsible for the serious illness known as listeriosis, presents a formidable challenge for eradication. This is attributed to its resilience and ability to thrive and endure in adverse conditions such as low temperatures, high salt concentrations, and low pH levels.^[1] It is known that L. monocytogenes can be a threat for processed or ready-to-eat (RTE) foods, fresh and dairy products, as well as seafoods.^[2]

Predictive models, in particular probabilistic models, can be used to find the best combinations of different preservatives such as nisin, salt, and extrinsic or intrinsic parameters like temperature, pH, or water activity (a_w) for preventing the growth.^[3] Many probabilistic models based on logistic regression were proposed for growth limits of L. monocytogenes in laboratory media and food products under different conditions (temperature, pH, a_w, etc.)^[3–6] as well as other foodborne pathogens such as Escherichia coli O157:H7^[7] and Salmonella spp.^[8]

Several preservatives are used to prevent microbial growth in foods. Some of them can be used alone, whereas some can be used in conjunction with the others. Nisin, for example, is an important natural antimicrobial substance, and it is generally used in combination with organic acids and salts.^[9] Potassium sorbate is another antimicrobial preservative which is commonly used in foods. The efficacy of potassium sorbate to prevent the growth of L. monocytogenes was well documented.^[10] Sodium chloride (NaCl) is not only a preservative but also a flavor enhancer. However, there is a tendency to replace NaCl with potassium chloride (KCl) to reduce the sodium intake.^[9] Studies on preventing the growth of L. monocytogenes by use of nisin in combination with other chemicals or hurdles are abundant^[11–13]; however, modeling studies on L. monocytogenes by use of nisin with NaCl, KCl, and sorbate are scarce. Two notable examples are the works of Boziaris et al.^[9] and Şentürk et al.^[14] Therefore, the objectives of this study were to propose a probabilistic model to determine the growth limits of L. monocytogenes strains including RTE isolates at different temperatures and nisin levels with either KCl or sorbate and further try to validate the models on real food systems.

Materials and method

Experimental design for determination of growth boundaries of L. monocytogenes

A full factorial design was used to track the growth of L. monocytogenes in tryptic soy broth (TSB). Three levels of temperature (4, 20, and 37°C), five levels of potassium chloride (0, 1, 2, 3, and 4% w/v) (Product Number: 104936, Merck) or potassium sorbate (0, 0.05, 0.10, 0.15, and 0.20%) (Product Number: 105118, Merck), and five levels of nisin (0, 50, 100, 200, and 400 µg/mL) were used for three strains. Nisin stock solutions were formulated using nisaplin (2.5% nisin A, Product Number: N5764, Sigma) by incorporating either 0.020 g or 0.200 g into 10 mL of 0.02 N HCl.^[14] Three replications were performed for each combination, which resulted in 675 data points [3 temperature levels × 5 KCl levels (or 5 sorbate levels) × 5 nisin levels × 3 strains × 3 replications]. Temperature levels were selected to represent the refrigeration, ambient, and abuse temperatures. Salt, sorbate, and nisin concentrations were the ones that are generally used or allowed levels except 400 µg/mL for nisin in foods.^[15]

Preparation of broth and growth evaluation

Uninoculated samples were employed as negative controls, while broths (TSB) devoid of salt, sorbate, or nisin were inoculated with 10⁶ CFU/mL of L. monocytogenes to serve as the positive control. Microbial growth was tracked weekly by measuring optical density (OD) at 600 nm up to 8 weeks. A microplate reader with 96 wells (BioTek Elisa Reader, Biotek Inc., USA) was used for growth evaluation. The increase of 0.1 in the OD values was considered as growth.^[14,15] If the increase in OD was about 0.1 (for example 0.09 or 0.11), then growth was also verified by plate counts for those wells. If the OD increase was higher than 0.1 (for example, 0.15 or 0.20), then it was considered as growth without the plate counts.

Model development

Two models were proposed:

(1a) $\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{i}\mathrm{t}(p)=a_0+a_1.X_1+a_2.X_2+a_3.X_{3\mathrm{n}}+a_4.X_4$(1a)

(1b) $\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{i}\mathrm{t}(p)=a_0+a_1.X_1+a_2.X_2+a_3.X_3+a_4.X_4$(1b)

or

(2a) $\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{i}\mathrm{t}\left(\mathrm{p}\right)=b_0+b_1.X_1+b_2.X_2+b_3.X_3+b_4.X_4+b_5.X_1.X_2+b_6.X_1.X_3+b_7.X_1.X_4+b_8.X_2.X_3+b_9.X_2.X_4+b_{10}.X_3.X_4+b_{11}.X_1.X_2.X_3+b_{12}.X_1.X_2.X_4+b_{13}.X_1.X_3.X_4+b_{14}.X_2.X_3.X_4+b_{15}.X_1.X_2.X_3.X_4$(2a)

(2b) $\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{i}\mathrm{t}(p)=b_0+b_1.X_1+b_2.X_2+b_3.X_3+b_4.X_4+b_5.X_1.X_2+b_6.X_1.X_3+b_7.X_1.X_4\text{break}\hspace{0.17em}+b_8.X_2.X_3+b_9.X_2.X_4+b_{10}.X_3.X_4+b_{11}.X_1.X_2.X_3\hspace{0.17em}+b_{12}.X_1.X_2.X_4\text{break}+\hspace{0.17em}{b}_{13}.X_1.X_3.X_4\hspace{0.17em}+b_{14}.X_2.X_3.X_4+b_{15}.X_1.X_2.X_3.X_4,$(2b)

where p is the probability of growth in the range of 0–1 (growth = 1, no growth = 0), logit(p) = ln[p/(1–p)] a₀–a₄, b₀–b₁₅ are the coefficients of the model to be estimated, $X_1$ is the temperature (°C), $X_2$ is the nisin concentration (µg/mL), $X_3$ is the KCl concentration (% w/v), $X_{3^{\prime }}$ is the potassium sorbate concentration (% w/v), and $X_4$ is the strain of L. monocytogenes. We used strain as the main effect in the model to avoid performing logistic regression separately for each strain.

SPSS (Version 22, Chicago, IL, USA) was used for logistic regression, and goodness-of-fit models were compared by using (i) −2·ln L, with L being the likelihood in its optimum, (ii) Hosmer-Lemeshow (H-L) statistic, (iii) maximum rescaled R² statistic, and (iv) percent concordant.^[14,16] Eq (1) was the simplest possible model, whereas Eq (2) was more complex with the interaction terms. If the interaction terms were insignificant (P > .05), they were removed from the model and regression was repeated without those terms, i.e., remaining coefficients in the model were all significant (P ≤ .05).

Model validation

The developed model was validated in UHT whole milk and meat broth without any preservatives at 8 and 12°C at a KCl concentration of 1.5% (w/v) or a sorbate concentration of 0.125% (w/v) and nisin concentrations of 25, 75, 150, and 250 μg/mL. A total of 96 combinations (48 for UHT milk and 48 for meat broth) were tested with an initial inoculum of 10⁶ CFU/mL bacteria for all strains. Each combination was repeated three times, and growth was monitored by plate count in tryptic soy agar (TSA). If more than one log₁₀ increase was observed, it was considered as growth since ±0.5 log₁₀ was within the experimental error on routine plate count data.

Results and discussion

No growth was observed in negative control (0 CFU/mL), while growth was detected in positive control during storage at 20°C as expected. This indicated that our sterilization protocols were sufficient since there were no bacteria as well as preservatives in the negative control. On the other hand, in the positive control, growth was observed within 24 h where there were only bacteria (10⁶ CFU/mL) but no preservatives. As the initial inoculum of L. monocytogenes increases, the growth probability increases.^[14,17] Therefore we used 10⁶ CFU/mL as the initial inoculum. Growth responses (1: growth and 0: no growth) of three strains with the inoculum level of 10⁶ CFU/mL revealed that in general, same response (growth or no growth) was observed for all replicates; however, there were some exceptions. At 4°C, in the absence of nisin and with 2 or 3% of KCl, two out of three responses for strain 120 were no growth and the remaining one was growth, meaning that the growth probability was 33%. At 20°C, in the presence of 50 μg/mL nisin and with 0.15 or 0.20% of sorbate, one out of three responses for strain 120 was no growth and two were growth, meaning that the growth probability was 67% (results not shown). Among 675 combinations, 352 of the observations were no growth (0) and 323 of them were growth (1) for KCl trial and 346 of the observations were no growth (0) and 329 of them were growth (1) for sorbate trial.

Effect of temperature, nisin, KCl, and strain

The results of the logistic regression for temperature, nisin, KCl, and strain experiments are given in Table 1. The simple model [Eq.(1a)] had an insignificant parameter (P > .05), and therefore, the more complex model [Eq.(2a)] with interaction terms was used. Moreover, the P value for H-L statistics was 0.041, viz., P < .05 for the simple model, meaning that the model was rejected^[14,18]. On the other hand, although the complex model had 16 parameters initially [Eq.(2a)], eight of them were statistically significant (P ≤ .05) after the removal of insignificant terms, and all goodness-of-fit indices were better than those of the simple model (Table 1).

Table 1. Parameters of the models for temperature (T), nisin, KCl, and strain as the independent variables and relative statistics.

Model	Coefficient	Estimate	SE	P value
SIMPLE MODEL	Constant	1.18	0.46	0.010
	T	0.22	0.019	<0.001
	Nisin	−0.025	0.002	<0.001
	KCl	−0.078	0.099	0.431
	Strain	−1.11	0.19	<0.001
	Goodness-of-fit
	−2lnL	333.970
	HL	16.084 (P = .041)
	Maximum rescaled R^2	0.786
	Percent concordant	87.9%
COMPLEX MODEL	Constant	−5.88	1.50	<0.001
	T	1.34	0.43	0.0017
	Nisin	−0.15	0.04	<0.001
	T × nisin	0.0059	0.001	<0.001
	T × KCl	−0.14	0.045	0.0025
	T × strain	0.22	0.048	<0.001
	T × nisin × strain	−0.005	0.001	<0.001
	Nisin × KCl × strain	0.012	0.004	0.0026
	Goodness-of-fit
	−2lnL	94.047
	HL	0.216 (P = 1.000)
	Maximum rescaled R^2	0.950
	Percent concordant	96.6%

Predicted probabilities of the growth of three strains with respect to the nisin concentration at different temperatures and at a constant KCl concentration (1.5%) are shown in Figure 1. As expected, higher temperatures and lower nisin concentrations led to higher growth probabilities for each strain. It was obvious that ATCC7644 strain had the highest growth probability at a KCl concentration of 1.5%, whereas strain 120 had the lowest. This result was in agreement with our previous study with the same strains under the same conditions except that NaCl was used instead of KCl.^[14] Furthermore, as the temperature increased, differences in growth probabilities between the strains were more pronounced (Figure 1).

Figure 1. Predicted growth probabilities of Listeria monocytogenes strains with respect to nisin: black lines for ATCC7644, blue lines for 137, and red lines for 120 at different temperatures and at a constant KCl concentration (1.5%). Predictions were plotted by using the parameter values of the complex model [Eq.(2a)] given in Table 1.

Predicted probabilities of the growth of three strains with respect to temperature at different nisin concentrations and at a constant KCl concentration (1.5%) are shown in Figure 2. Similar results were observed: strain 120 had the lowest growth probability, ATCC7644 had the highest, and strain 137 was in between. At lower nisin concentrations, variations among the strains were lower; however, as the nisin concentration increased, variation was remarkable (Figure 2).

Figure 2. Predicted growth probabilities of Listeria monocytogenes strains with respect to temperature: black lines are for ATCC7644, blue lines for 137, and red lines for 120 at different nisin concentrations and at a constant KCl concentration (1.5%). Predictions were plotted by using the parameter values of the complex model [Eq.(2a)] given in Table 1.

Effect of temperature, nisin, sorbate, and strain

The simple model [Eq.(1b)] had two insignificant parameters (P > .05), and therefore, once again a more complex model [Eq.(2b)] with interaction terms was used (Table 2). After the elimination of insignificant terms and repeating the regression, the complex model had only six parameters. Predicted probabilities of the growth of three strains with respect to the nisin concentration at different temperatures and at a constant sorbate concentration (0.125%) are shown in Figure 3. Interestingly, the trend was just the opposite compared to the use of KCl: ATCC7644 had the lowest probability of growth, whereas 120 had the highest, indicating that the sorbate with nisin had a different impact on the strains than KCl. The observed differences between the growth responses of the strains to nisin-KCl and nisin-sorbate combinations may be due to the different interactions of KCl or sorbate with nisin as well as any genetic background or the nisin-resistant pattern of a strain. Our findings revealed that strain variations to nisin may be quite different in the presence of sorbate or KCl. Figure 4 shows the predicted growth probabilities with respect to temperature at different nisin concentrations and at a constant sorbate concentration (0.125%). As the temperature (Figure 3) or nisin concentration increased (Figure 4), variations between the strains were almost identical for sorbate unlike KCl (see Figures 1 and 2).

Figure 3. Predicted growth probabilities of Listeria monocytogenes strains with respect to temperature: black lines are for ATCC7644, blue lines for 137, and red lines for 120 at different nisin concentrations and at a constant sorbate concentration (0.125%). Predictions were plotted by using the parameter values of the complex model [Eq.(2b)] given in Table 2.

Figure 4. Predicted growth probabilities of Listeria monocytogenes strains with respect to temperature: black lines are for ATCC7644, blue lines for 137, and red lines for 120 at different nisin concentrations and at a constant sorbate concentration (0.125%). Predictions were plotted by using the parameter values of the complex model [Eq.(2b)] given in Table 2.

Table 2. Parameters of the models for temperature (T), nisin, sorbate, and strain as the independent variables and relative statistics.

Model	Coefficient	Estimate	SE	P value
SIMPLE MODEL	Constant	−0.047	0.508	0.926
	T	0.17	0.021	<0.001
	Nisin	−0.056	0.005	<0.001
	Sorbate	−0.033	0.031	0.298
	Strain	1.46	0.254	<0.001
	Goodness-of-fit
	−2lnL	224.897
	HL	9.148 (P = .330)
	Maximum rescaled R^2	0.868
	Percent concordant	92.1%
COMPLEX MODEL	T	0.204	0.026	<0.001
	Nisin	−0.064	0.007	<0.001
	Strain	1.55	0.23	<0.001
	Sorbate × strain	−0.069	0.027	0.0103
	Nisin × sorbate × strain	0.0011	0.00029	<0.001
	T × nisin × sorbate × strain	−0.00003	0.00001	0.0015
	Goodness-of-fit
	−2lnL	213.896
	HL	12.097 (P = .147)
	Maximum rescaled R^2	0.876
	Percent concordant	92.6%

Validation of the models

We observed 22 “accurate” predictions out of 48 combinations (46%) in milk and 35 out of 48 (73%) in meat broth for all strains (Table S1). Almost identical accurate predictions were obtained for nisin in combination with KCl (58%) and with sorbate (60%). Among the strains, the highest prediction rate was found for strain 120 (66%), the rates were obtained for 137 and ATCC7644 strains were identical (56%).

The model was developed in a laboratory medium (broth); however, validation was performed in food products, and this may be the reason for having relatively low predictions. A rapid estimation of growth limits can be possible by using the broth, but deviations from the results could be obtained in the laboratory medium compared to a real or complex food system^[19] as foods may contain many components that can positively or negatively affect the microbial growth.^[18] It should be noted that the content of whole milk (lactose, lipid, proteins, calcium, etc.) was different than that of broth. On the other hand, meat broth and TSB had structural and textural similarities, and therefore, it was not surprising to have higher predictions for meat broth than UHT milk. A probabilistic model developed for Clostridium sporogenes in nutrient broth^[15] and the validity of the growth model were examined in processed cheese analog. The results showed that the model developed was not able to predict the probability of growth of C. sporogenes in the food system.^[18]

Conclusion

The effects of temperature and nisin in the presence of either KCl or sorbate on three L. monocytogenes strains in broth were studied, and models based on logistic regression were developed. The main effects of the models were temperature, nisin, KCl, or sorbate and strain. It was observed that KCl and sorbate had different impacts on the growth probabilities of the strains. Highest growth probability was observed for the ATCC7644 strain, and the lowest was observed for strain 120 with the use of KCl. On the other hand, ATCC7644 strain had the lowest growth probability, while strain 120 had the lowest when sorbate was used. This result showed the variation in growth responses of the strains to different combinations of antimicrobial agents. Although the prediction capability of the model was higher than 70% in meat broth, it was poor (<50%) for UHT milk. Validation of the model revealed that new studies based on probabilistic models for the foodborne pathogens should be performed on food products; however, this would be cumbersome and challenging because quick OD measurements may not be possible with real food systems.

Credit authorship statement

E.Ş. contributed to methodology and writing – original draft. S.B. contributed to conceptualization, methodology, data curation, software, writing – original draft, and writing – review and editing., P.Ş. contributed to conceptualization, writing – original draft, writing – review and editing, supervision, and funding acquisition.

Acknowledgments

We thank Dr Başar Karaca for his experimental support throughout this study.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships to influence the work reported in this paper.

Data availability statement

Data will be made available on request.

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/10942912.2023.2268858