New Term to Quantify the Effect of Temperature on pHmin-Values Used in Cardinal Parameter Growth Models for Listeria monocytogenes

The aim of this study was to quantify the influence of temperature on pH_min-values of Listeria monocytogenes as used in cardinal parameter growth models and thereby improve the prediction of growth for this pathogen in food with low pH. Experimental data for L. monocytogenes growth in broth at different pH-values and at different constant temperatures were generated and used to determined pH_min-values. Additionally, pH_min-values for L. monocytogenes available from literature were collected. A new pH_min-function was developed to describe the effect of temperatures on pH_min-values obtained experimentally and from literature data. A growth and growth boundary model was developed by substituting the constant pH_min-value present in the Mejlholm and Dalgaard (2009) model (J. Food. Prot. 72, 2132–2143) by the new pH_min-function. To obtain data for low pH food, challenge tests were performed with L. monocytogenes in commercial and laboratory-produced chemically acidified cheese including glucono-delta-lactone (GDL) and in commercial cream cheese. Furthermore, literature data for growth of L. monocytogenes in products with or without GDL were collected. Evaluation of the new and expanded model by comparison of observed and predicted μ_max-values resulted in a bias factor of 1.01 and an accuracy factor of 1.48 for a total of 1,129 growth responses from challenge tests and literature data. Growth and no-growth responses of L. monocytogenes in seafood, meat, non-fermented dairy products, and fermented cream cheese were 90.3% correctly predicted with incorrect predictions being 5.3% fail-safe and 4.4% fail-dangerous. The new pH_min-function markedly extended the range of applicability of the Mejlholm and Dalgaard (2009) model from pH 5.4 to pH 4.6 and therefore the model can now support product development, reformulation or risk assessment of food with low pH including chemically acidified cheese and cream cheese.

Introduction

Cardinal parameter models (CPMs) contain parameters with biological or graphical interpretation (Rosso, 1995). CPMs to predict growth and growth boundary of Listeria monocytogenes (CPM-Lm) are popular, extensively validated and widely used in the assessment and risk management of processed and ready-to-eat foods These models include terms to quantitatively describe the growth inhibiting effect of different environmental factors and each term include at least one cardinal parameter related to growth limiting conditions e.g., for temperature (T_min), pH (pH_min), and water activity (a_wmin) (Te Giffel and Zwietering, 1999; Augustin and Carlier, 2000; Augustin et al., 2005; Zuliani et al., 2007; Mejlholm and Dalgaard, 2009; Østergaard et al., 2014; Corbion, 2017). Remarkably, available CPM-Lm include very different pH_min-values ranging from 4.3 to 5.0. This can be due to differences in the mathematical terms used to estimate pH_min-values along with different acidulants and strain variability as often suggested (Augustin et al., 2005; Aryani et al., 2015). However, the experimental conditions used to estimate pH_min-values have been little studied quantitatively, although the minimal pH-value supporting growth is known to depend on environmental conditions including temperature (Rocourt and Buchrieser, 2007).

As for other predictive food microbiology models the performance of CPM-Lm can be evaluated by comparison of predicted growth responses with observed growth in foods. Often, indices of model performance, including bias (B_f) and accuracy (A_f) factors, are used to facilitate model evaluation and to determine the range of environmental conditions where a model can be successfully validated (Ross, 1996; Augustin et al., 2005; Østergaard et al., 2014). Mejlholm et al. (2010) evaluated the performance of four of the more extensive CPM-Lm, including the effect of several environmental factors, by using 1,014 growth responses in meat, seafood, poultry and non-fermented dairy products. The model of Mejlholm and Dalgaard (2009) performed better than the other models, with B_f- and A_f- values for growth rate predictions of 1.0 and 1.5, respectively. However, the range of applicability for this model has been limited to pH-values above 5.4 as predicted growth rates at lower pH-values were too low due to a constant pH_min-value of 4.97 used in the pH-term (Mejlholm et al., 2010; Mejlholm and Dalgaard, 2015). L. monocytogenes can grow at pH values as low as 4.3–4.4 (Farber et al., 1989; ICMSF, 1996; Tienungoon et al., 2000), which is important for several types of food including products acidified with glucono-delta-lactone (GDL) and gluconic acid (GAC). El-Shenawy and Marth (1990) found growth of L. monocytogenes in milk containing GDL or GAC at pH lower than 5.0 when products were stored at 13 and 35°C. Genigeorgis et al. (1991) showed that L. monocytogenes has the potential to grow in cottage cheese with pH 4.9 to 5.1 when stored at 4, 8, or 30°C. More recently, Nyhan et al. (2018) showed that béarnaise sauce and zucchini purée with pH of 4.7 can support growth of L. monocytogenes at 30°C. To assess and manage L. monocytogenes growth in food with pH as low as 4.3–4.4 it is interesting to study the performance of predictive models. Furthermore, it remains unclear if GDL or GAC have any antimicrobial effect beyond that of lowering product pH.

The objective of the present study was to quantify the influence of temperature on pH_min-values of L. monocytogenes as used in CPMs. Firstly, the growth inhibiting effect of pH and GAC was studied at different temperatures to determine values for pH_min and the minimum inhibitory concentration (MIC) of undissociated GAC (MIC_GACu). Secondly, a new pH_min-function was developed, including the effect of temperature on pH_min-values, and this new pH_min-function was included in the growth and growth boundary model of Mejlholm and Dalgaard (2009) along with a GAC-term containing the MIC-value for undissociated GAC. Finally, the performance of the expanded model was evaluated by comparison of predicted and observed growth for L. monocytogenes. Data included new challenge test with chemically acidified cheese and cream cheese as well as available growth responses from literature.

Materials and Methods

Bacterial Strains, Pre-culture Conditions, and Inoculation

Eight strains of L. monocytogenes from milk, cheese, butter or the dairy environment were provided by Arla Foods and used as a cocktail (SLU 92, 612, LM 19, 6) or individually (ISO 570, 99714, SLU 2493, SLU 2265) to determined μ_max-values in broth and/or for inoculation of challenge tests. Each strain was transferred from storage at −80°C to Brain Heart Infusion (BHI) broth (CM1135, Oxoid, Hampshire, UK) and incubated for 24 h at 25°C. Subsequently, for broth studies all strains were pre-cultured 1 or 2 days at 8 to 20°C in BHI broth with 0.5% NaCl and pH 5.5. For challenge tests the individual strains, later used as a cocktail, were pre-cultured one or 2 days at a temperature ranging from 8 to 20°C in BHI broth with pH 5.5 and 3% NaCl or at pH 5.2 with 1% NaCl and 500 ppm lactic acid to simulate conditions encountered in chemically acidified and cream cheese as used in the present study. Pre-cultures were grown to a relative increase in absorbance (540 nm) of 0.05 to 0.2 (Novaspec II, Pharmacia Biotech, Allerød, Denmark) equivalent to late exponential phase-beginning stationary phase. The L. monocytogenes cocktail of strains (Lm-mix) were obtained by mixing equal volumes of individual pre-cultured strains. For Lm-mix and pre-cultures of individual strains the cell concentration was determined by direct phase contrast microscopy prior to dilution and subsequent inoculation of experiments.

Cardinal Parameter Values for pH and Gluconic Acid

The effect of pH and GAC concentrations on μ_max-values of L. monocytogenes were determined at different temperatures. For each condition, growth of Lm-mix or individual strains was determined in duplicate by automated absorbance measurements at 540 nm (BioScreen C, Labsystems, Helsinki, Finland). Detection times defined as the incubation time necessary to observe an increase in absorbance of 0.05 from the lowest absorbance measured in the beginning of incubation; was determined for each absorbance growth curve. μ_max-values of Lm-mix and individual strains were determined from absorbance detection times for serially diluted inoculation levels of 10², 10³, 10⁴, 10⁵, and 10⁶ cfu/ml as previously described (Dalgaard and Koutsoumanis, 2001).

The effect of 17 pH-values from 4.4 to 6.8 on μ_max-values were determined separately at different temperatures (5, 8, 10, 15, 20, 25, 35, and 37°C) by using BHI broth adjusted to the desired pH values with HCl, autoclaved (121°C, 15 min.) and pH readjusted if necessary. A total of 221 μ_max-values, all above zero h⁻¹, were determined experimentally in BHI-broth. Seventeen pH_min-values were estimated by fitting Equation (1) to square root transformed μ_max-values from broth experiments obtained for the studied pH range at different constant temperatures.

$\begin{array}{ll}\sqrt{{\mu }_{max}}=\sqrt{{\mu }_{ref-1\left({*}^{\circ }\text{C}\right)}·\left(1-10^{\left(p{H}_{min}-pH\right)}\right)}& (1)\end{array}$

where μ_max is the maximum specific growth rate (h⁻¹) and μ_ref−1(^*°C) is the fitted reference maximum specific growth rate for each studied temperature. Additionally, 44 pH_min-values (obtained in broth adjusted to different pH-values with HCl or H₂SO₄) were extracted from literature and used to model the effect of storage temperature on pH_min-values of L. monocytogenes (George et al., 1988; Ryser and Marth, 1988; Farber et al., 1989; Petran and Zottola, 1989; Duffy et al., 1994; Brocklehurst et al., 1995; Koutsoumanis et al., 2004a; Aryani et al., 2015).

The effect of 54 GAC (D-gluconic acid sodium salt, G9005 Sigma-Aldrich, St. Louis, USA) concentrations [0–26.7% (w/v)] on μ_max-values were determined separately at different temperatures (8, 20, and 25°C) in BHI broth adjusted with HCl to pH 5.5 after addition of the organic acid and again after autoclaving (121°C, 15 min.) the broth if necessary. In total 144 μ_max-values, all above 0 h⁻¹, were determined experimentally in BHI-broth. Cardinal parameter value for undissociated gluconic acid (MIC_GACU) was determined from concentrations of undissociated GAC calculated by using Equation (2) with a pK_a-value of 3.7 (Quitmann et al., 2014). The cardinal parameter values (MIC_GACU and T_min) were estimated by fitting Equation (3) to the 144 square root transformed μ_max-values.

$\begin{array}{ll}Undissociatedorganicacid(mM)=\frac{Organicacid(mM)}{1+10^{pH-pka}}& (2)\end{array}$

$\begin{array}{ll}\sqrt{{\mu }_{max}}=\sqrt{{\mu }_{ref-3}·{\left(\frac{T-T_{min}}{T_{ref}-T_{min}}\right)}^2·{\left({1-\left(\frac{\left[GA{C}_U\right]}{MI{C}_{UGAC}}\right)}^{n1}\right)}^{n2}}& (3)\end{array}$

where T is the temperature (°C), T_min is the theoretical minimum temperature that prevents growth. A constant T_min –value of −2.83°C was used and this parameter was not fitted (see Supplementary Table 2). [GAC_U] is the concentrations (mM) of undissociated gluconic acid and MIC_{U GAC} is the fitted MIC value (mM) of undissociated GAC that prevent growth of L. monocytogenes. In Equation (3), n1 was set to 1 or 0.5 and n2 was set to 1 or 2 (Dalgaard, 2009) in order to describe data most appropriately and this was determined from root mean square error (RMSE) values.

Challenge Tests With Chemically Acidified Cheese and Cream Cheese

A total of 20 challenge tests were performed to generate L. monocytogenes growth data in GDL chemically acidified cheese (n = 12) and cream cheese (n = 8) for model evaluation (see section Evaluation of New pHmin-Function, GAC-Term and Models).

Chemically Acidified Cheese and Cream Cheese

Chemically acidified cheese was prepared from five different batches of ultra-filtrated milk concentrate (UF-conc.) provided by Arla Foods and containing 40% dry matter. Cheese was prepared in batches of 2,000 g of UF-conc. by adding different volumes of a glucono-delta-lactone solution (GDL 54%, Roquette^®, Lestrem, France) and 36 ml of rennet solution (3.3% Hannilase^® XP 200 NB, Chr. Hansen, Hørsholm, Denmark). For four batches of UF-conc. the salt concentration was adjusted by adding 3.5 or 5% NaCl (Merck, Kenilworth, US). In total, 11 laboratory-produced and one commercial chemically acidified cheese, with variation in salt, pH and added amount of GDL solution were studied in challenge tests (Table 1). Additionally, four batches of two types of cream cheese were purchased from a supermarket and were used in eight challenge tests (Table 2).

TABLE 1

Table 1. Data obtained from challenge tests performed with chemically acidified cheese inoculated with L. monocytogenes.

TABLE 2

Table 2. Storage conditions and product characteristics for challenge tests with cream cheese.

Inoculation and Microbiological Analysis

Growth of L. monocytogenes in chemically acidified cheese and cream cheese was determined in 20 challenge tests including a total of 60 curves with growth or no-growth responses at constant and dynamic storage temperature (Tables 1, 2). Chemically acidified cheese and cream cheese were inoculated with 0.1% (v/w) of Lm-mix appropriately diluted in chilled saline water (0.85% NaCl) to obtain an initial concentration in the range of 1 to 3.5 log (cfu/g). Inoculation of chemically acidified cheese was performed in each batch of UF-conc. following addition of GDL solution. After the chemically acidified cheese was set it was packaged into 50 ± 1 g cheese containers and stored at 4.4–25.4°C during 10–30 days depending on the storage temperature (Table 1). Thirty three individual packages of cream cheese (150 g) were combined to form a 5,000 g sample which was then inoculated, re-packaged into 50 ± 1 g cheese containers and stored at 4.5–22.0°C during 30 days (Table 2). Storage temperature during challenge tests was regularly recorded by data loggers (TinytagPlus, Gemini Data Loggers Ltd, Chichester, UK). Six to 12 times during storage samplings were performed to quantify growth responses. At each sampling a container with 50 ± 1 g of cheese was analyzed and then discarded. Ten grams of cheese were diluted 10-fold with chilled physiological saline (PS, 0.85% NaCl and 0.10% Bacto-peptone) and subsequently homogenized for 30 s at normal speed in a Stomacher 400 (Seward Medical, London, UK). Ten-fold dilutions were performed with chilled PS. Aerobic viable counts (AVC) for chemically acidified cheese were enumerated by surface plating on standard plate count agar (CM0463, Oxoid, Hampshire, UK) and incubation at 25°C for 24 h. For cream cheese viable counts of lactic acid bacteria (LAB) were determined by double layer pour plating in nitrite actidione polymyxin (NAP) agar (pH 6.2) with incubation at 25°C for 72 h (Davidson and Cronin, 1973). Viable counts of L. monocytogenes were determined for both types of cheeses by surface plating on PALCAM agar base (CM0877, Oxoid, Hampshire, UK) with PALCAM selective supplement (SR0150, Oxoid, Hampshire, UK) and incubation at 37°C for 48 h.

Product Characteristics

pH was measured directly in the cheese with a PHC10801 puncture combination probe (Hach, Brønshøj, Denmark) at all times of sampling for microbiological analysis Other product characteristics of cheeses were determined by analysis of three packages (50 ± 1 g) for each treatment at the start of the challenge test. NaCl was quantified by automated potentiometric titration (785 DMP Titrino, Metrohm, Hesisau, Switzerland) and a_w was measured by a water activity meter (Aqua Lab model CX-2, Decagon devices Inc., Pullman, US). The concentration of lactic, acetic, citric, and gluconic acid was determined by HPLC using external standards for identification and quantification (Dalgaard and Jørgensen, 2000; Østergaard et al., 2014). Concentrations of undissociated organic acids in the products were calculated from Equation (2), using pKa values of 4.76, 3.13, 3.86, and 3.7 for acetic, citric, lactic, and gluconic acid, respectively, together with the pH and concentrations (mM) of organic acids in the water phase of foods. To determine water phase concentrations of organic acids, the dry matter content was determined by oven drying at 105°C for 24 ± 2 h. Due to the hydrophilic nature of the studied acetic, citric, lactic and gluconic acids more than 95% of their undissociated forms was assumed to be present in the water phase and partitioning between water and lipid phases of chesses was not quantified (Brocklehurst and Wilson, 2000; Mejlholm and Dalgaard, 2015; Wemmenhove et al., 2018).

Primary Growth Model

The integrated and log transformed logistic model with lag-time (four parameter model) or without lag-time (three parameter model) (Equation 4; Rosso et al., 1996) was fitted to all individual growth curves of L. monocytogenes obtained in challenge tests at constant temperature. Fitted parameter values for lag time (t_lag, h), maximum specific growth rate (μ_max, h⁻¹) initial cell concentration (N₀, cfu/g), and maximum population density (N_max, cfu/g) were determined for each growth curve and data was reported as average ± standard deviation for each treatment (Table 1). An F-test was used to determine if the lag time was significant.

$\begin{array}{ll}\begin{array}{lll}log\left(N_t\right)=log\left(N_0\right)& & ift<t_{lag}\\ log\left(N_t\right)=log\left(\frac{N_{max}}{1+\left(\left(\frac{N_{max}}{N_0}\right)-1\right)·exp\left(-{\mu }_{max}·\left(t-t_{lag}\right)\right)}\right)& & ift\ge t_{lag}\end{array}& (4)\end{array}$

where t is the storage time (h) and N_t is the cell concentration (cfu/g) at time t. Other parameters were described above.

Growth Data of L. monocytogenes From Literature

A total of 170 growth responses of L. monocytogenes in milk, meat products and other foods at different temperatures were collected from literature. Growth of L. monocytogenes was described using the growth parameters t_lag (h), μ_max (h⁻¹), N₀ (log cfu/g), and N_max (log cfu/g) obtained by fitting growth data from graphs with Equation (4). Published growth rates available in tables were adjusted by multiplying them with a correction factor. The logistic model with delay was used as the reference model; therefore, the maximum specific growth rates estimated with the Baranyi model (Baranyi and Roberts, 1994) were multiplied by 0.97 (Augustin et al., 2005). For 60 of the 170 growth responses collected from literature one or more of the relevant product characteristics were not reported (Table 3). In 21 experiments the pH of milkshake and fresh pork were assumed to be 6.7 and 6.2, respectively. For 33 and 27 experiments with meat products 0.7% water phase lactic acid and 50 ppm nitrite were assumed to be present, respectively.

TABLE 3

Table 3. Storage conditions and product characteristics in experiments (n= 170) used for evaluation of the model.

Evaluation of New pH_min-Function, GAC-Term and Models

The new pH_min-function and GAC-term were evaluated by comparison of predicted and observed growth responses. We used this approached to establish if the expanded model of Mejlholm and Dalgaard (2009) including the new pH_min-function and GAC-term (see section Expanded Model for Growth of L. monocytogenes in Different Foods) could predict growth of L. monocytogenes as determined in the present study for chemically acidified cheese and cream cheese with pH from 4.6 to 5.5 (n = 20; Tables 1, 2) as well as for a broad range of data from literature (n = 1,129; Table 6).

For predicted and observed μ_max-values the calculated B_f- and A_f-values were evaluated as previously suggested with 0.95 < B_f < 1.11 indicating good model performance, B_f of 1.11–1.43 or 0.87–0.95 corresponding to acceptable model performance and B_f < 0.87 or > 1.43 reflecting unacceptable model performance (Ross, 1996; Ross et al., 2000; Mejlholm et al., 2010). A_f-values above 1.5 was used to indicate an incomplete model or systematic deviation between observed and predicted μ_max-values (Mejlholm and Dalgaard, 2013).

Predicted and observed growth and no-growth responses were assessed by calculating the percentage of all samples that were correctly predicted. Incorrect predictions were described as fail-safe (growth predicted when no growth was observed) or fail-dangerous (no growth predicted when growth was observed). The ψ-value was calculated for all predicted growth responses to indicate if they were close to the growth boundary of L. monocytogenes (ψ = 1.0) or well into the growth (ψ < 1) or no-growth (ψ > 1) regions. For chilled products with shelf-life of more than 5 weeks, product formulations resulting in a ψ-value > 2 has been recommended (Dalgaard and Mejlholm, 2019). Graphs with predicted and observed growth in challenge tests performed with chemically acidified cheese at dynamic storage temperature were used to assess these data.

Statistical Analysis and Curve Fitting

Model parameters and standard errors were estimated by using GraphPad PRISM (version 8, GraphPad Software, San Diego, CA, USA). F-tests to determine significant lag times were performed using Microsoft Excel 2010 (Microsoft Corp., Redmond, WA, USA).

Results

Cardinal Parameter Values for pH and Gluconic Acid

Temperature had a marked effect on pH_min-values determined by fitting Equation (1) to μ_max-values of Lm-mix or of individual strains grown in BHI broth (Figure 1). pH_min-values on average decreased from 4.9 at 5°C to 4.3 at 15–20°C and then increased to 4.7 at 37°C (Figure 1). The cardinal parameter value for GAC i.e., the MIC-value of undissociated GAC (MIC_{U GAC}) was 26.4 ± 1.1 mM as determined at 8, 20, and 25°C by using Equation (3) with n1 and n2 equal to 1.

FIGURE 1

Figure 1. Cardinal parameter values (pH_min) at different temperatures for a cocktail of L. monocytogenes strains [SLU 92, 612, LM19, 6, ()] and individual strains [ISO570 (), 99714 (), SLU 2493 (), SLU 2265 ()].

New Cardinal Parameter pH_min-Function for L. monocytogenes

Equation (5) was used to describe the observed effect of storage temperature on pH_min-values of L. monocytogenes.

$\begin{array}{ll}\begin{array}{ll}p{H}_{minT}=p{H}_{min0}-T*\left(\frac{\left(p{H}_{min0}-p{H}_{minR}\right)}{T_R}\right)& 0\le T<T_R\\ p{H}_{minT}=p{H}_{minR}+\left(T-T_R\right)*\left(\frac{\left(p{H}_{min37}-p{H}_{minR}\right)}{\left(37-T_R\right)}\right)& T_R<T<37°C\end{array}& (5)\end{array}$

where T_R is the temperature (°C) corresponding to the lowest pH_min-value; T is the storage temperature (°C); pH_minT is the estimated pH_min–value at T (°C); pH_min0 and pH_min37 are, respectively, the estimated pH_min–value at 0°C and 37°C; pH_minR is the pH_min–value at T_R (°C) (Figure 2). The parameter values (Table 4) were estimated by fitting Equation (5) to pH_min-values for Lm-mix, individual stains and literature data (Figure 2).

FIGURE 2

Figure 2. Observed and fitted pH_min-values from the present study and from literature. Data for L. monocytogenes cocktail of the strains [SLU92, 612, LM19, 6, ()] and individual strains [ISO570 (), 99714 (), SLU 2493 (), SLU 2265 ()] from the present study. Data from Aryani et al. (2015) (○), Brocklehurst et al. (1995) (), Duffy et al. (1994) (▴), Farber et al. (1989) (), George et al. (1988) (l), Koutsoumanis et al. (2004a) (), Petran and Zottola (1989) (), and Ryser and Marth (1988) (▾). Solid line (—) and dashed line (−−−) represent, respectively, the fitted model and confidence interval (95%).

TABLE 4

Table 4. Fitted parameter values for new pH_min-function.

Expanded Model for Growth of L. monocytogenes in Different Foods

The model of Mejlholm and Dalgaard (2009) was expanded by substituting the constant pH_min-value of 4.97 in the existing CPM-Lm by the new pH_min-function (Equation 5) (Model 1). Model 1 was further expanded by adding a GAC-term including the MIC_{U GAC}–value determined in the present study (Equation 3) (Model 2). As for the model of Mejlholm and Dalgaard (2009) the effect of interaction between environmental parameters (ξ) in model 1 and model 2 was taken into account by using the Le Marc approach (Le Marc et al., 2002; Mejlholm and Dalgaard, 2009) (Supplementary Tables 1–3).

Challenge Tests With Chemically Acidified Cheese and Cream Cheese

The chemically acidified cheese produced in the laboratory (Batch 1, 3, 4, and 5; Table 1) had pH of 4.7–5.5, water phase salt content of 3.82–11.7% and gluconic acid in the water phase of 2.44–4.46% (w/v). Commercially available chemical acidified cheese had pH 4.6 ± 0.1, water phase salt of 4.43 ± 0.28% and gluconic acid in the water phase of 4.52 ± 1.09% (Table 1). Commercial cream cheese had pH of 4.7–5.1, water phase salt content of 1.79–2.07%, lactic, acetic, and citric acid in the water phase of 3,102–10,930 ppm, 980–1,808 ppm and 618–5,121 ppm, respectively.

L. monocytogenes grew in the studied chemically acidified cheese with pH-values of 4.6–5.5 (Table 1). However, L. monocytogenes did not grow in challenge test 4 with chemically acidified cheese performed at 14.0°C due to a high water phase salt concentration (11.7 ± 0.0%) in that product. Nevertheless, growth of L. monocytogenes was observed in challenge test 1 with chemically acidified cheese where the product had low pH (4.8 ± 0.2) and relatively high water phase salt (7.24 ± 0.06%) (Table 1). L. monocytogenes did not grow in any challenge test performed with cream cheese (Table 2).

Evaluation of Predictive Models for L. monocytogenes

For chemically acidified cheese and cream cheeses the original model of Mejlholm and Dalgaard (2009) predicted no-growth in 15 out of the 17 challenge tests at constant temperatures resulting in a high percentage (35%) of fail-dangerous predictions (Table 5). For the two challenge tests with pH 5.2 and 5.5 where growth was both predicted (ψ of 0.2 and 0.3) and observed the model significantly underestimated growth rates of L. monocytogenes as shown by a B_f value of 0.51 (Table 6). However, growth rates of L. monocytogenes in chemically acidified cheese were accurately predicted by model 1, including the new pH_min-function (Equation 5), as shown by B_f- and A_f-values of 1.03 and 1.26 (n = 9; Table 6). Model 1 predicted growth in 9 out of the 17 challenge tests resulting in 100% correct predictions of growth and no-growth (Table 5). For challenge test with cream cheese, model 1 correctly predicted no-growth and ψ-values of 1.5 to >10 were determined showing that most of the studied products were far from the growth boundary (ψ-values of 1).

TABLE 5

Table 5. Comparison of observed and predicted maximum specific growth rate (μ_max-values) of L. monocytogenes for experimental data^a.

TABLE 6

Table 6. Comparison of observed and predicted growth of L. monocytogenes obtained from experimental and literature data (n = 1,129).

Model 2, developed in the present study and including the new pH_min-function (Equation 5) as well as a GAC-term, significantly underestimated growth rates of L. monocytogenes in chemically acidified cheese as shown by a B_f-value of 0.26 (n = 8, Table 6). The model predicted growth in 8 out of the 17 experiments resulting in 90% correct and 10% fail-dangerous predictions (Table 5). These results for evaluation of model 1 and model 2 suggest GAC, beyond lowering the pH, has no inhibiting effect on growth of L. monocytogenes. Inclusion of the gluconic acid MIC-term in model 2 decreased model performance and consequently this term is not needed to correctly predict growth of L. monocytogenes in the studied chemically acidified cheese. Further evaluation of model 1 and model 2 was performed with μ_max-data obtained from the literature. The Mejlholm and Dalgaard (2009) model slightly underestimated growth rates of L. monocytogenes in dairy and meat products as shown by B_f-values of 0.79 and 0.85, respectively (Table 6). For these products without GAC, similar B_f-values were obtained with model 1 and 2 indicating that growth can be accurately predicted with both models (Table 6). However, exclusively model 1 was able to accurately predict growth in chemically acidified cheese with low pH as shown above (Table 5). Importantly, model 1 predicted growth of L. monocytogenes in meat, seafood, poultry and non-fermented dairy products (n = 707) with good precision and resulted in B_f-/A_f-values of 1.02/1.50 (Table 6). Model 1 and the Mejlholm and Dalgaard (2009) model were further evaluated with a data set composed by experimental and literature data (n = 1,129, Table 6). B_f− and A_f-values for model 1 were of 1.01 and 1.48, whereas values of 0.98 and 1.50 were obtained with the Mejlholm and Dalgaard (2009) model. Model 1 predicted growth/no-growth responses correctly for 90.3% of the growth responses with the incorrect predictions distributed as 5.3% fail-safe and 4.4% fail-dangerous, resulting in a better performance compared with either of the other two models (Table 6). Model predictions were fail-safe or correct for the two challenge tests with chemically acidified cheese stored at dynamic temperature. An N_max-value of 6.8 log cfu/g was used for these predictions as this value was observed in products with similar characteristics (Table 1, Figure 3). For zucchini purée and béarnaise sauce, with low pH and storage at 30°C, model 1 had an acceptable B_f−value of 1.26 but the A_f-values of 1.56 and 38% fail-safe prediction indicated unacceptable precision of the model (Table 7).

FIGURE 3

Figure 3. Comparison of observed (□) and predicted (-) growth of L. monocytogenes at dynamic storage temperature. Chemically acidified cheese was studied at 4.4–25.4°C (A; CT 11) and 5.2–25.3°C (B; CT 12). Temperature profiles are shown as gray lines. Solid lines represent the predicted growth by model 1 with N_max of 6.8 log cfu/g.

TABLE 7

Table 7. Observed and predicted growth of L. monocytogenes with data from Nyhan et al. (2018).

Discussion

The present study quantified the effect of temperature on pH_min-values for L. monocytogenes and included this effect (Equation 5) in an extensive growth and growth boundary model that was subsequently successfully validated for pH values as low as 4.6 (Supplementary Tables 1, 2). This expanded model (Model 1, section Expanded Model for Growth of L. monocytogenes in Different Foods) including the effect of both general product characteristics (temperature, NaCl/aw, pH) and product specific ingredients (organic acids and other preserving factors) provides new options to predict L. monocytogenes growth responses. These predictions are useful in the assessment and management of L. monocytogenes growth for processed and ready-to-eat foods including non-fermented dairy products and cream cheese with pH of 4.6 or above. Based on the performed model evaluation, the range of applicability for model 1 in foods includes storage temperatures from 2 to 35°C, pH between 4.6 and 7.7 and water phase salt concentrations as low as 0% with the range of the other environmental factors as reported previously (Mejlholm et al., 2010; Mejlholm and Dalgaard, 2015).

The successfully validated model 1 can be used to assess L. monocytogenes growth in chemically acidified cheeses and cream cheeses depending on storage conditions and product characteristics. As an example, if a chemically acidified cheese (pH 4.6 and 4.4% water phase NaCl) is contaminated with 1 L. monocytogenes/g after pasteurization (e.g., while adding GDL) and subsequently chill stored at 5°C then the product will not support growth. However, if the product is stored at 25°C a critical concentration of 100 cfu/g (CA, 2011; EC, 2011; ANZ, 2018) will be exceeded after <2 days. Model 1 predicts that a formulation with 0.21% lactic acid in the water phase will prevent growth of L. monocytogenes for that product also at 25°C (ψ of 2.5). As another example the model can be used to predict growth/no-growth-conditions for cream cheese at 5°C with pH 5.2, 1.9% water phase NaCl, water phase organic acids concentrations of 0.20% (lactic), 0.10% (acetic), and 0.10% (citric). If the product is contaminated with 1 cfu/g then growth of L. monocytogenes will not be supported (ψ of 2.1); however if the same contaminated product is stored at 25°C then the critical cell concentration will be exceeded in 2.5 days (ψ of 0.4). Model 1 predicted that a cream cheese reformulated with lower pH (5.0) and increased concentrations in the water phase of lactic acid (0.45%) and acetic acid (0.15%) will prevent growth of L. monocytogenes at 25°C (ψ of 2.4).

The observed effect of temperature on pH_min-values for L. monocytogenes (Figure 1) are in agreement with previous studies based on broth acidified with hydrochloric acid. Koutsoumanis et al. (2004a) found that the minimum pH supporting growth of L. monocytogenes at 4 and 10°C was 4.96, while at 15 and 30°C it was 4.45. Farber et al. (1989) determined pH of 5.0 to 5.4 needed to prevent L. monocytogenes growth at 4°C whereas at 30°C lower pH-values of 4.3 to 4.7 were required. For a_w of 0.990, 0% lactic acid and temperatures of 4, 15, and 30°C the model of Tienungoon et al. (2000) predicted pH-growth-limits of L. monocytogenes to be 5.38, 4.40, and 4.38. These data are in agreement with the present study, where the effect of temperature on pH_min-values was quantified with markedly more data. Furthermore, the new model 1 includes more environmental factors than the model of Tienungoon et al. (2000) and therefore has wider application e.g., for product formulation or documentation of food safety.

The effect of temperature on pH_min-values for L. monocytogenes as quantified in the present study (Figure 1) has been important to accurately predict growth and growth boundary of this pathogen in food with low pH (Tables 5, 6). Temperature may have a similar effect on other microorganisms than L. monocytogenes as indicated by growth data for e.g., Escherichia coli (Salter et al., 2000; McKellar and Lu, 2001), Salmonella (Koutsoumanis et al., 2004b) and Staphylococcus aureus (Valero et al., 2009). It seems interesting in future studies to evaluate if CPMs with temperature dependent pH_min-function could be valuable to predict growth and growth boundary responses of other microorganisms as well as to obtain more information on why a minimum pH_min-value is observed at a temperature markedly below the optimum temperature for growth for L. monocytogenes.

The performed experiments with chemically acidified cheese highlighted an important limitation of the Mejlholm and Dalgaard (2009) model to accurately predict growth of L. monocytogenes in foods with low pH (Tables 5, 6). This limitation is due to a constant pH_min-value for L. monocytogenes of 4.97 and consequently, no-growth is predicted below that pH-value, irrespective of the storage temperature. Model 1, with a new pH_min-function (Equation 5), did not have this limitation and showed good model performance for products with pH as low 4.6 (Table 6).

The acceptable B_f-value but high A_f-value of model 1 for zucchini purée and béarnaise sauce (B_f- and A_f-values of 1.26 and 1.56; Table 7) could be due to inhibiting compounds in some of these products that were not included in model 1. In fact, some of the treatments studied by Nyhan et al. (2018) included propionic acid. It was therefore investigated if including a propionic acid term and MIC value from Le Marc et al. (2002) could improve the performance of model 1. Addition of the Le Marc et al. (2002) propionic acid term and MIC value improved performance of the expanded model 1 (B_f- and A_f-values of 1.14 and 1.49; Table 7), however, further evaluation of the expanded model containing a propionic acid term is necessary for vegetable products and sauces due to a high percentage of fail-safe predictions (38%; Table 7).

Despite the inhibitory effect of GAC observed in broth, with MIC_{U GAC} of 26.4 ± 1.1 mM (Section Cardinal Parameter Values for pH and Gluconic Acid), comparison of predicted and observed L. monocytogenes growth in foods (Table 6) showed no need to include a GAC-term in the developed growth and growth boundary model (Model 1, section Expanded Model for Growth of L. monocytogenes in Different Foods). This result is not in contradiction with available data although an antimicrobial effect of GDL and GAC against L. monocytogenes has been reported by several studies. For instance, Juncher et al. (2000) found a recipe for saveloys with 2.0% lactate and 0.25% GDL to prevent growth of L. monocytogenes. The addition of GDL reduced product pH from 6.37 to 6.08 resulting in an increase of undissociated lactic acid from 1.2 to 2.3 mM. Similarly, Qvist et al. (1994) found bologna-type sausage with 2% lactate and 0.5% GDL prevented growth of L. monocytogenes at 5 and 10°C during 28 days of storage. Product pH was reduced from 6.6 to 6.0 by 0.5% GDL and this resulted in an increase of undissociated lactic acid from 0.7 to 2.8 mM. El-Shenawy and Marth (1990) suggested that using GAC or GDL at concentrations high enough to coagulate milk for cottage cheese production should contribute to control L. monocytogenes during the manufacturing process. For these examples, the L. monocytogenes growth inhibition can be explained by the combined effect of product pH, undissociated lactic acid and other product characteristics rather than by the suggested effect of GAC or GDL as shown in the present study for different foods by using model 1.

In conclusion, the present study quantified and modeled the effect of temperature used to estimate pH_min-values of L. monocytogenes and showed the importance of this effect for accurate prediction of growth in low pH foods. The new model can support product development, reformulation or risk assessment of a wide range of foods including meat, seafood and different dairy products (milk, cream, desserts, chemically acidified cheese, and cream cheese). The new model can be included in predictive microbiology application software such as the Food Spoilage and Safety Predictor (FSSP http://fssp.food.dtu.dk/) to facilitate its use by the industry and food safety authorities.

Data Availability

All datasets generated for this study are included in the manuscript.

Author Contributions

The literature review was conducted by VM-R and EG. Research objectives were defined by VM-R, and the specific research questions was developed by VM-R, EG, and PD. Data was analyzed by VM-R, and results were interpreted by VM-R and PD. Expansion of the model was by VM-R. The tables, figures, and manuscript were created by VM-R. All authors revised and approved the manuscript.

Conflict of Interest Statement

EG is employed by Arla Foods.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The Danish Dairy Research Foundation funded the present study as part of the project Predictive food microbiology tool for risk assessment and documentation of food safety.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmicb.2019.01510/full#supplementary-material

References

ANZ (2018). Standard 1.6.1. Australia New Zealand Food Standards Code - Standard 1.6.1 - Microbiological Limits for Food. Available online at: https://www.legislation.gov.au/Series/F2015L00411/Compilations (accessed January 19, 2019).

Google Scholar

Aryani, D. C., den Besten, H. M. W., Hazeleger, W. C., and Zwietering, M. H. (2015). Quantifying strain variability in modeling growth of Listeria monocytogenes. Int. J. Food Microbiol. 208, 19–29. doi: 10.1016/j.ijfoodmicro.2015.05.006

PubMed Abstract | CrossRef Full Text | Google Scholar

Augustin, J. C., and Carlier, V. (2000). Modelling the growth rate of Listeria monocytogenes with a multiplicative type model including interactions between environmental factors. Int. J. Food Microbiol. 56, 53–70. doi: 10.1016/S0168-1605(00)00224-5

PubMed Abstract | CrossRef Full Text | Google Scholar

Augustin, J. C., Zuliani, V., Cornu, M., and Guillier, L. (2005). Growth rate and growth probability of Listeria monocytogenes in dairy, meat and seafood products in suboptimal conditions. J. Appl. Microbiol. 99, 1019–1042. doi: 10.1111/j.1365-2672.2005.02710.x

PubMed Abstract | CrossRef Full Text | Google Scholar

Baranyi, J., and Roberts, T. A. (1994). A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23, 277–294. doi: 10.1016/0168-1605(94)90157-0

PubMed Abstract | CrossRef Full Text | Google Scholar

Barmpalia, I. M., Koutsoumanis, K. P., Geornaras, I., Belk, K. E., Scanga, J. A., Kendall, P. A., et al. (2005). Effect of antimicrobials as ingredients of pork bologna for Listeria monocytogenes control during storage at 4 or 10°C. Food Microbiol. 22, 205–211. doi: 10.1016/j.fm.2004.08.003

CrossRef Full Text | Google Scholar

Brocklehurst, T. F., Parker, M. L., Gunning, P. A., Coleman, H. P., and Robins, M. M. (1995). Growth of food-borne pathogenic bacteria in oil-in-water emulsions: II-effect of emulsion structure on growth parameters and form of growth. J. Appl. Bacteriol. 78, 609–615. doi: 10.1111/j.1365-2672.1995.tb03106.x

PubMed Abstract | CrossRef Full Text | Google Scholar

Brocklehurst, T. F., and Wilson, P. D. G. (2000). The role of lipids in controlling microbial growth. Grasas y Aceites 51, 66–73. doi: 10.3989/gya.2000.v51.i1-2.408

CrossRef Full Text | Google Scholar

CA (2011). FD-FSNP 0071. Policy on Listeria monocytogenes in Ready-to-Eat Foods. Bureau of microbial hazards, Food Directorate, Canada. Available online at: http://www.food-label-compliance.com/Sites/5/Downloads/Listeria-monocytogenes-Policy-Health-Canada-040111-Apr-2011.pdf (accessed January 19, 2019).

Google Scholar

Corbion (2017). Corbion^® Listeria Control Model. Available online at: https://clcm.corbion.com/ (accessed September 07, 2018).

Google Scholar

Dalgaard, P. (2009). Modelling of microbial growth. Bull. Int. Dairy Feder. 433, 45–60.

Google Scholar

Dalgaard, P., and Jørgensen, L. V. (2000). Cooked and brined shrimps packed in a modified atmosphere have a shelf-life of >7 months at 0°C, but spoil in 4-6 days at 25°C. Int. J. Food Sci. Technol. 35, 431–442. doi: 10.1046/j.1365-2621.2000.00402.x

CrossRef Full Text | Google Scholar

Dalgaard, P., and Koutsoumanis, K. (2001). Comparison of maximum specific growth rates and lag times estimated from absorbance and viable count data by different mathematical models. J. Microbiol. Methods 43, 183–196. doi: 10.1016/S0167-7012(00)00219-0

PubMed Abstract | CrossRef Full Text | Google Scholar

Dalgaard, P., and Mejlholm, O. (2019). “Modelling growth of Listeria and lactic acid bacteria in food environments,” in Foodborne Bacterial Pathogenes, ed A. Bridier (New York, NY: Springer), 1918, 247–264.

Google Scholar

Daminelli, P., Dalzini, E., Cosciani-Cunico, E., Finazzi, G., D'Amico, S., and Losio, M. N. (2014). Prediction of the maximal growth rate of Listeria monocytogenes in sliced mortadella by the square root type model. Ital. J. Food Sci. 26, 261–267.

Google Scholar

Davidson, C. M., and Cronin, F. (1973). Medium for the selective enumeration of lactic acid bacteria from foods. Appl. Microbiol. 26, 439–440.

PubMed Abstract | Google Scholar

Duffy, L. L., Vanderlinde, P. B., and Grau, F. H. (1994). Growth of Listeria monocytogenes on vacuum-packed cooked meats: effects of pH, aw, nitrite and ascorbate. Int. J. Food Microbiol. 23, 377–390. doi: 10.1016/0168-1605(94)90164-3

PubMed Abstract | CrossRef Full Text | Google Scholar

EC (2011). Commission Regulation (EC) No. 1129/2011 of the 11 November 2011 Amending Annex II to Regulation (EC) No. 1333/2008 of the European Parliament and of the Council by Establishing a Union List of Food Additives.

Google Scholar

El-Shenawy, M. A., and Marth, E. H. (1990). Behaviour of Listeria monocytogenes in the presence of gluconis acid and during preparation of cottage cheese curd using gluconic acid. J. Dairy Sci. 73, 1429–1438. doi: 10.3168/jds.S0022-0302(90)78807-8

CrossRef Full Text | Google Scholar

Farber, J. M., Sanders, G. W., Dunfield, S., and Prescott, R. (1989). The effect of various acidulants on the growth of Listeria monocytogenes. Lett. Appl. Microbiol. 9, 181–183. doi: 10.1111/j.1472-765X.1989.tb00319.x

CrossRef Full Text | Google Scholar

Genigeorgis, C., Carniciu, M., Dutulescu, D., and Farver, T. B. (1991). Growth and survival of Listeria monocytogenes in market cheeses stored at 4 to 30°C. J. Food Prot. 54, 662–668. doi: 10.4315/0362-028X-54.9.662

PubMed Abstract | CrossRef Full Text | Google Scholar

George, S. M., Lund, B. M., and Brocklehurst, T. F. (1988). The effect of pH and temperature on initiation of growth of Listeria monocytogenes. Lett. Appl. Microbiol. 6, 153–156. doi: 10.1111/j.1472-765X.1988.tb01237.x

CrossRef Full Text | Google Scholar

ICMSF (1996). “Listeria monocytogenes,” in Microorganisms in Foods 5: Characteristics of Microbial Pathogens, eds T. A. Roberts, A. C. Baird-Parker, and R. B. Tompkin (London: Blackie Academic and Professional), 141–182.

Google Scholar

Juncher, D., Vestergaard, C. S., Søltoft-Jensen, J., Weber, C. J., Bertelsen, G., and Skibsted, L. H. (2000). Effects of chemical hurdles on microbiological and oxidative stability of a cooked cured emulsion type meat product. Meat Sci. 55, 483–491. doi: 10.1016/S0309-1740(00)00011-5

PubMed Abstract | CrossRef Full Text | Google Scholar

Koutsoumanis, K. P., Kendall, P. A., and Sofos, J. N. (2004a). A comparative study on growth limits of Listeria monocytogenes as affected by temperature, pH and a_w when grown in suspension or on a solid surface. Food Microbiol. 21, 415–422. doi: 10.1016/j.fm.2003.11.003

CrossRef Full Text | Google Scholar

Koutsoumanis, K. P., Kendall, P. A., and Sofos, J. N. (2004b). Modeling the boundaries of growth of Salmonella Typhimurium in broth as a function of temperature, water activity and pH. J. Food Prot. 67, 53–59. doi: 10.4315/0362-028X-67.1.53

PubMed Abstract | CrossRef Full Text | Google Scholar

Le Marc, Y., Huchet, V., Bourgeois, C. M., Guyonnet, J. P., Mafart, P., and Thuault, D. (2002). Modelling the growth kinetics of Listeria as a function of temperature, pH and organic acid concentration. Int. J. Food Microbiol. 73, 219–237. doi: 10.1016/S0168-1605(01)00640-7

PubMed Abstract | CrossRef Full Text | Google Scholar

Lianou, A., Moschonas, G., Nychas, G. E., and Panagou, E. Z. (2018). Growth of Listeria monocytogenes in pasteurized vanilla cream pudding as affected by storage temperature and the presence of cinnamon extract. Food Res. Int. 106, 1114–1122. doi: 10.1016/j.foodres.2017.11.027

PubMed Abstract | CrossRef Full Text | Google Scholar

Lobacz, A., and Kowalik, J. (2015). A predictive model for Listeria monocytogenes in UHT dairy products with various fat content during cold storage. J. Food Saf. 35, 119–127. doi: 10.1111/jfs.12163

CrossRef Full Text | Google Scholar

Luo, K., Hong, S.-S., Wang, J., Chung, M. J., and Deog-Hwan, O. (2015). Development of predictive models for the growth kinetics of Listeria monocytogenes on fresh pork under different storage temperatures. J. Food Prot. 78, 921–926. doi: 10.4315/0362-028X.JFP-14-428

PubMed Abstract | CrossRef Full Text | Google Scholar

McKellar, R., and Lu, X. (2001). A probability of growth model for Escherichia coli O157:H7 as a function of temperature, pH, acetic acid and salt. J. Food Prot. 64, 1922–1928. doi: 10.4315/0362-028X-64.12.1922

PubMed Abstract | CrossRef Full Text | Google Scholar

Mejlholm, O., and Dalgaard, P. (2009). Development and validation of an extensive growth and growth boundary model for Listeria monocytogenes in lightly preserved and ready-to-eat shrimp. J. Food Prot. 72, 2132–2143. doi: 10.4315/0362-028X-72.10.2132

PubMed Abstract | CrossRef Full Text | Google Scholar

Mejlholm, O., and Dalgaard, P. (2013). Development and validation of an extensive growth and growth boundary model for psychrotolerant Lactobacillus spp. in seafood and meat products. Int. J. Food Microbiol. 167, 244–260. doi: 10.1016/j.ijfoodmicro.2013.09.013

PubMed Abstract | CrossRef Full Text | Google Scholar

Mejlholm, O., and Dalgaard, P. (2015). Modelling and predicting the simultaneous growth of Listeria monocytogenes and psychrotolerant lactic acid bacteria in processed seafood and mayonnaise-based seafood salads. Food Microbiol. 46, 1–14. doi: 10.1016/j.fm.2014.07.005

PubMed Abstract | CrossRef Full Text | Google Scholar

Mejlholm, O., Gunvig, A., Borggaard, C., Blom-Hanssen, J., Mellefont, L., Ross, T., et al. (2010). Predicting growth rates and growth boundary of Listeria monocytogenes- an international validation study with focus on processed and ready-to-eat meat and seafood. Int. J. Food Microbiol. 141, 137–150. doi: 10.1016/j.ijfoodmicro.2010.04.026

PubMed Abstract | CrossRef Full Text | Google Scholar

Nyhan, L., Begley, M., Mutel, A., Qu, Y., Johnson, N., and Callanan, M. (2018). Predicting the combinatorial effects of water activity, pH, and organic acids on Listeria growth in media and complex food matrices. Food Microbiol. 74, 75–85. doi: 10.1016/j.fm.2018.03.002

PubMed Abstract | CrossRef Full Text | Google Scholar

Østergaard, N. B., Eklöw, A., and Dalgaard, P. (2014). Modelling the effect of lactic acid bacteria from starter- and aroma culture on growth of Listeria monocytogenes in cottage cheese. Int. J. Food Microbiol. 188, 15–25. doi: 10.1016/j.ijfoodmicro.2014.07.012

PubMed Abstract | CrossRef Full Text | Google Scholar

Petran, R. L., and Zottola, E. A. (1989). A study of factors affecting growth and recovery of Listeria monocytogenes Scott A. J. Food Sci. 54, 458–460. doi: 10.1111/j.1365-2621.1989.tb03105.x

CrossRef Full Text | Google Scholar

Quitmann, H., Fan, R., and Czermak, P. (2014). “Acidic organic compounds in beverage, food and feed production,” in Biotechnology of Food and Feed Additives, eds H. Zorn and P. Czermak (New York, NY: Springer), 91–142.

Google Scholar

Qvist, S., Sehested, K., and Zeuthen, P. (1994). Growth suppression of Listeria monocytogenes in a meat product. Int. J. Food Microbiol. 24, 283–293. doi: 10.1016/0168-1605(94)90126-0

PubMed Abstract | CrossRef Full Text | Google Scholar

Resnik, S. L., and Cherife, J. (1988). Proposed theoretical water activity values at various temperatures for selected solutions to be used as reference sources in the range of microbial growth. J. Food Prot. 51, 419–423.

PubMed Abstract | Google Scholar

Rocourt, J., and Buchrieser, C. (2007). “The genus Listeria and Listeria monocytogenes,” in Listeria, Listeriosis, and Food Safety, eds E. T. Ryser and E. H. Marth (Boca Raton, FL: CRC Press, 1–20.

Google Scholar

Ross, T. (1996). Indices for performance evaluation of predictive models in food microbiology. J. Appl. Bacteriol. 81, 501–508. doi: 10.1111/j.1365-2672.1996.tb03539.x

PubMed Abstract | CrossRef Full Text | Google Scholar

Ross, T., Dalgaard, P., and Tienungoon, S. (2000). Predictive modelling of the growth and survival of Listeria in fishery products. Int. J. Food Microbiol. 62, 231–245. doi: 10.1016/S0168-1605(00)00340-8

PubMed Abstract | CrossRef Full Text | Google Scholar

Rosso, L. (1995). Modélisation et Microbiologie Prévissionnelle: Élaboration d'un nouvel outil pour l'Agro-alimentaire (Ph.D. thesis). Université Claude Bernard, Lyon, France.

Google Scholar

Rosso, L., Bajard, S., Flandrois, J. P., Lahellec, C., Fournaud, J., and Veit, P. (1996). Differential growth of Listeria monocytogenes at 4 and 8°C: consequences for the shelf life of chilled products. J. Food Prot. 59, 944–949. doi: 10.4315/0362-028X-59.9.944

PubMed Abstract | CrossRef Full Text | Google Scholar

Ryser, E. T., and Marth, E. H. (1988). Growth of Listeria monocytogenes at different pH values in un cultured whey or whey cultured with Penicillium camemberti. Can. J. Microbiol. 34, 730–734. doi: 10.1139/m88-124

PubMed Abstract | CrossRef Full Text | Google Scholar

Salazar, J. K., Bathija, V. M., Carstens, C. K., Narula, S. S., Shazer, A., Stewart, D., et al. (2018). Listeria monocytogenes growth kinetics in milkshakes made from naturally and artificially contaminated ice cream. Front. Microbiol. 9:62. doi: 10.3389/fmicb.2018.00062

PubMed Abstract | CrossRef Full Text | Google Scholar

Salter, M. A., Ratkowsky, D. A., Ross, T., and McMeekin, T. A. (2000). Modelling the combined temperature and salt (NaCl) limits for growth of a pathogenic Escherichia coli strain using nonlinear logistic regression. Int. J. Food Microbiol. 61, 159–167. doi: 10.1016/S0168-1605(00)00352-4

PubMed Abstract | CrossRef Full Text | Google Scholar

Taormina, P. J., and Dorsa, W. J. (2010). Survival and death of Listeria monocytogenes on cooked bacon at three storage temperatures. Food Microbiol. 27, 667–671. doi: 10.1016/j.fm.2010.02.006

PubMed Abstract | CrossRef Full Text | Google Scholar

Te Giffel, M. C., and Zwietering, M. H. (1999). Validation of predictive models describing the growth of Listeria monocytogenes. Int. J. Food Microbiol. 46, 135–149. doi: 10.1016/S0168-1605(98)00189-5

PubMed Abstract | CrossRef Full Text | Google Scholar

Tienungoon, S., Ratkowsky, D. A., McMeekin, T. A., and Ross, T. (2000). Growth limits of Listeria monocytogenes as a function of temperature, pH, NaCl, and lactic acid. Appl. Environ. Microbiol. 66, 4979–4987. doi: 10.1128/AEM.66.11.4979-4987.2000

PubMed Abstract | CrossRef Full Text | Google Scholar

Valero, A., Pérez-Rodríguez, F., Carrasco, E., Fuentes-Alventosa, J. M., García-Gimeno, R. M., and Zurera, G. (2009). Modelling the growth boundaries of Staphylococcus aureus: effect of temperature, pH and water activity. Int. J. Food Microbiol. 133, 186–194. doi: 10.1016/j.ijfoodmicro.2009.05.023

PubMed Abstract | CrossRef Full Text | Google Scholar

Wemmenhove, E., van Valenberg, H. J. F., van Hooijdonk, A. C. M., Wells-Bennik, M. H. J., and Zwietering, M. H. (2018). Factors that inhibit growth of Listeria monocytogenes in nature-ripened Gouda cheese: a major role for undissociated lactic acid. Food Control 84, 413–418. doi: 10.1016/j.foodcont.2017.08.028

CrossRef Full Text | Google Scholar

Zuliani, V., Lebert, I., Augustin, J. C., Garry, P., Vendeuvre, J. L., and Lebert, A. (2007). Modelling the behaviour of Listeria monocytogenes in ground pork as a function of pH, water activity, nature and concentration of organic acid salts. J. Appl. Microbiol. 103, 536–550. doi: 10.1111/j.1365-2672.2007.03283.x

PubMed Abstract | CrossRef Full Text | Google Scholar