Quantifying Variability in Growth and Thermal Inactivation Kinetics of Lactobacillus plantarum

ABSTRACT

The presence and growth of spoilage organisms in food might affect the shelf life. In this study, the effects of experimental, reproduction, and strain variabilities were quantified with respect to growth and thermal inactivation using 20 Lactobacillus plantarum strains. Also, the effect of growth history on thermal resistance was quantified. The strain variability in μ_max was similar (P > 0.05) to reproduction variability as a function of pH, a_w, and temperature, while being around half of the reproduction variability (P < 0.05) as a function of undissociated lactic acid concentration [HLa]. The cardinal growth parameters were estimated for the L. plantarum strains, and the pH_min was between 3.2 and 3.5, the a_w,min was between 0.936 and 0.953, the [HLa_max], at pH 4.5, was between 29 and 38 mM, and the T_min was between 3.4 and 8.3°C. The average D values ranged from 0.80 min to 19 min at 55°C, 0.22 to 3.9 min at 58°C, 3.1 to 45 s at 60°C, and 1.8 to 19 s at 63°C. In contrast to growth, the strain variability in thermal resistance was on average six times higher than the reproduction variability and more than ten times higher than the experimental variability. The strain variability was also 1.8 times higher (P < 0.05) than the effect of growth history. The combined effects of strain variability and growth history on D value explained all of the variability as found in the literature, although with bias. Based on an illustrative milk-processing chain, strain variability caused ∼2-log₁₀ differences in growth between the most and least robust strains and >10-log₁₀ differences after thermal treatment.

IMPORTANCE Accurate control and realistic prediction of shelf life is complicated by the natural diversity among microbial strains, and limited information on microbiological variability is available for spoilage microorganisms. Therefore, the objectives of the present study were to quantify strain variability, reproduction (biological) variability, and experimental variability with respect to the growth and thermal inactivation kinetics of Lactobacillus plantarum and to quantify the variability in thermal resistance attributed to growth history. The quantitative knowledge obtained on experimental, reproduction, and strain variabilities can be used to improve experimental designs and to adequately select strains for challenge growth and inactivation tests. Moreover, the integration of strain variability in prediction of microbial growth and inactivation kinetics will result in more realistic predictions of L. plantarum dynamics along the food production chain.

INTRODUCTION

Spoilage microorganisms are of interest for the food industry since their presence and growth in food products might cause decay and might contribute to undesired food product loss. Lactic acid bacteria are an important group of spoilage microorganisms and are abundant in the environment. They can be found in diverse niches (1) and are commonly isolated from plant and plant material (2), soil (3), silage (4), meat (5), vegetables (6), and milk (7). Since they are natural contaminants of raw food ingredients, controlling their presence and growth to the level spoilage is perceived is critical to ensure the shelf life of food products.

Accurate control and realistic prediction of shelf life is, however, complicated by the natural diversity among strains. Recently, strain variability in the growth and thermal resistance of Listeria monocytogenes was quantified (8, 9). The impact of strain variability on growth and thermal resistance was also reported for other pathogens such as, Salmonella enterica (10–12), Staphylococcus aureus (13, 14), Bacillus cereus (15), and Escherichia coli (16–18). Although strain variability in growth and thermal inactivation kinetics has been reported for pathogens, limited information is available for spoilage microorganisms (19–23). To extend the knowledge of variability in growth and thermal resistance of spoilage microorganisms, Lactobacillus plantarum was chosen as a model species not only because it is often found as contaminant in different food products (24–31) but also based on the availability of growth and thermal inactivation data in literature (22, 23, 32–34) to benchmark microbiological variability. Although high diversity in genomic and phenotypic levels of L. plantarum have been reported (1, 35, 36), none of the studies focused on the quantification of strain variability in growth and thermal resistance. Therefore, the objectives of the present study were to quantify strain variability, reproduction (biological) variability, and experimental variability with respect to the growth and thermal inactivation kinetics of L. plantarum and to quantify the variability in thermal resistance attributed to growth history. Strain variability was defined as the difference between strains from the same species (8), reproduction variability was defined as the difference between independent reproductions of the same strain (within strain variability) (8), and experimental variability was defined as the difference between duplicate measurements conducted using the same culture (8). The quantification of variability factors for growth kinetics was focused on the maximum specific growth rate (μ_max). Although, lag phase is also an important parameter in growth kinetics, it is generically difficult to define representatively and to determine accurately using a practical contamination scenario and therefore was not considered in this study. Quantitative knowledge of variability in growth and thermal resistance will allow researchers to better characterize this species and to better predict the behavior of this spoilage organism in food products.

MATERIALS AND METHODS

Growth experiments. (i) Culture preparation.

Twenty strains of L. plantarum were used in the present study (Table 1). Stock cultures were stored at −80°C in 70% De Man, Rogosa, and Sharpe (MRS) broth (Merck/Millipore) supplemented with 30% (vol/vol) glycerol (Sigma-Aldrich, Germany). From the stock, L. plantarum strains were grown on an MRS agar plate made from MRS broth and bacteriological agar (1.5% [wt/wt]; Oxoid, England) and incubated under microaerobic conditions for 48 h at 30°C. Then, one colony was inoculated in a 30-ml tube containing 10 ml MRS broth, which was incubated for 24 h at 30°C. A second culture was then made by transferring 0.5% (vol/vol) of the first overnight culture to 100 ml of MRS broth, followed by incubation for 24 h at 30°C. The working culture was prepared from this second overnight culture according to a procedure previously described (8, 37). Briefly, the culture was transferred to 50-ml centrifuge tubes and centrifuged for 15 min for strains FBR02, FBR06, FBR30, and SF2A35B and for 2 min for the other strains at 15,557 × g (Centrifuge 5804 R; Eppendorf). Longer centrifugation times were needed for the former four strains because they produced slimy extracellular polymeric substances, which influenced sedimentation. The supernatant was discarded, and the pellet was resuspended in 2 ml of peptone physiological salt (PPS; Tritium Microbiologie B.V., Netherlands). Then, 1 ml of the pooled suspension of two pellets was diluted in PPS to obtain an optical density at 600 nm (OD₆₀₀) of 0.5 (Spectrophotometer Novospec II; Pharmacia Biotech) or ∼10⁸ CFU/ml. This standardized working culture was used for further experiments.

TABLE 1.

Twenty L. plantarum strains and their sources

(ii) Preparation of media.

Eight pH values, namely, 7.0, 6.0, 5.0, 4.0, 3.6, 3.5, 3.4, and 3.3, were selected to test the effect of pH on the maximum specific growth rate (μ_max) of L. plantarum. For each experiment, the MRS broth was buffered using 100 mM sodium phosphate buffer (1 M Na₂HPO₄ and 1 M NaH₂PO₄ [both from Merck KGaA, Darmstadt, Germany]). Because only the effect of pH was considered, 1 M sulfuric acid (Riedel-de Haën, Seelze, Germany) (8) was used to adjust the pH of the medium. After pH adjustment, the medium was filter sterilized (Steritop; Millipore, Billerica, MA) before use.

Six different concentrations of sodium chloride (NaCl; AnalaR Normapur; VWR International, Leuven, Belgium), namely, 2, 4, 6, 8, 9, and 10% (wt/vol), were added to MRS broth containing 20 g/liter d(+)-glucose, and the broth was autoclaved. The corresponding a_w values of the NaCl-adjusted MRS broth and plain MRS broth (0% added NaCl) were measured using a Novasina water activity meter (Labmaster a_w; Novasina, Lachen, Switzerland) set at 30°C. The a_w values of the medium after autoclaving were 0.993, 0.982, 0.970, 0.958, 0.948, 0.942, and 0.937 for the initial NaCl concentrations of 0, 2, 4, 6, 8, 9, and 10% (wt/vol), respectively.

Five concentrations (2.5, 5, 10, 20, and 30 mM) of dl-lactic acid 85% (Sigma-Aldrich) in its undissociated form at pH 4.5 were used. The preparation of the medium adjusted with lactic acid was done as previously described (8, 38). Briefly, the ratio between the dissociated and undissociated forms of lactic acid at set pH was calculated using the Henderson-Hasselbalch equation:

$$\text{pH}=\text{p}{\text{K}}_{\text{a}}+\text{log}\frac{[{\text{A}}^{-}]}{[\text{HA}]}$$ (1)

where pH is the preset pH (pH 4.5) of the medium using sulfuric acid as acidulant, pK_a is the acid dissociation constant (pK_a of lactic acid 3.86), [A⁻] is the concentration of anions, and [HA] is the concentration of the undissociated acid. The conjugated salt of lactic acid used here was potassium lactate (Corbion, Gorinchem, The Netherlands). Since the addition of lactic acid and its salt influence the water activity, the use of a lower pH (4.5 instead of 5.7) was preferred to reduce the amount of salt in the medium for the same concentration of undissociated lactic acid.

For the effect of temperature (T), the growth experiments were conducted at seven temperature points, namely, 30, 25, 20, 18, 12, 10, and 7°C in plain MRS medium (pH 5.7, a_w of 0.993). The Bioscreen C was placed in a room with ambient temperature of approximately 20°C for the experiments at 30, 25, 20, and 18°C. The Bioscreen C was placed in a cold room with an ambient temperature of 7°C for experiments at 10 and 12°C and in a cold room with an ambient temperature of 4°C for the experiments at 7°C. The temperature of the Bioscreen C chamber was recorded at every sampling time and was stable at the set temperature.

(iii) Estimating μ_max as function of pH, a_w, undissociated lactic acid concentration ([HLa]), and temperature.

The growth experiments were performed according to a previously described procedure (8). Briefly, the standardized culture was diluted 10,000-fold in each pH-, a_w-, and [HLa]-adjusted MRS broth and in plain MRS broth for the temperature experiment, aiming for an initial cell concentration of ∼10⁴ CFU/ml for the highest concentration of the four sequential 2-fold dilutions. The diluted suspension was spiral plated (Eddy Jet; IUL Instruments) onto MRS agar plates in duplicate to determine the initial concentration (N₀) of each L. plantarum strain.

The μ_max was estimated by monitoring the OD₆₀₀ of four sequential 2-fold dilutions in five neighboring wells using the Bioscreen C (8, 37). The time to detection (TTD) was defined as the time at which a certain well reaches a specific OD₆₀₀ of 0.2 (or 0.15 for the condition close to the growth boundary). To ensure that the cells are in the exponential growth phase, the selected OD₆₀₀ value should be far below the asymptote of the sigmoid curves and above the detection limit of the media. Different OD₆₀₀ values were used to accommodate different conditions used during experiments because the maximum absorbance value of the growth curve was lower for unfavorable than for optimum conditions. The Bioscreen C was run for a certain period depending on the condition tested, which was up to 2 weeks for pH, a_w, and [HLa] and 30 days for the lower temperature experiments. The Bioscreen C was set at medium shaking for 15 s before each measurement. The μ_max was calculated as the negative reciprocal slope of the linear regression between the TTD and the natural logarithm of the initial bacterial concentration of the five wells. If the wells showed no changes in the OD values, the viability of the bacteria at the end of the experiment was verified by plating all of the content of the well. When the plate counting showed a reduction in number of bacteria in comparison to N₀ or total inactivation of bacteria, the μ_max was set to 0 h⁻¹. The maximal decrease in pH of the medium when the OD₆₀₀ reached 0.2 was 0.1 to 0.2 from the initial pH of 5.7 depending on the strain.

(iv) Quantification of variability factors and model fitting.

The experimental, reproduction, and strain variability factors were quantified using the previously described method (8) (see Fig. S1 in the supplemental material).

The secondary growth models used to fit the μ_max data as function of pH, temperature, a_w, and [HLa] were the selected best models from our previous study (8) (equations 2 to 5). The selected secondary growth model was used to fit all μ_max data per strain as a function of the variable to estimate the cardinal growth parameters for each strain. The μ_max data obtained from temperature experiments (pH 5.7, T = 30°C) and the [HLa] experiment (pH 4.5, T = 30°C, 0 mM [HLa]) were included in the fitting process of pH data. The obtained cardinal growth parameters were used to calculate the specific growth rate at the reference condition (μ_ref) (pH 5.7, a_w 0.993, temperature of 30°C, and 0 mM [HLa]) using the transformed growth models provided in section S1 in the supplemental material.

The pH model calculation was as follows:

$${\mu }_{\text{max}}={\mu }_{\text{opt}}\left({1-2}^{\frac{(\text{pH}\hspace{0.17em}-\hspace{0.17em}\text{p}{\text{H}}_{\text{min}})}{(\text{p}{\text{H}}_{\text{min}}-\hspace{0.17em}{\text{pH}}_{1/2})}}\right)$$ (2)

The temperature model calculation was as follows:

$$\sqrt{{\mu }_{\text{max}}}={\alpha }_T(T-T_{\text{min}})$$ (3)

The a_w model calculation was as follows:

$${\mu }_{\text{max}}={\mu }_{\text{opt}}\left(1-{\left(\frac{1-{\text{a}}_{\text{w}}}{1-{\text{a}}_{{\text{w}}_{\text{min}}}}\right)}^{{\alpha }_{{\text{a}}_{\text{w}}}}\right)$$ (4)

The [HLa] model calculation was as follows:

$${\mu }_{\text{max}}={\mu }_{\text{opt}}\left(1-{\left(\frac{[\text{HLa}]}{{[\text{HLa}]}_{\text{max}}}\right)}^{{\text{α}}_{[\text{HLa}]}}\right)$$ (5)

All fitting was done using Excel solver add-in (Microsoft) and confirmed using TableCurve 2D v5.01. Moreover, the lack-of-fit test (39) (equations 6a and 6b) was used to observe the goodness of fit of the selected secondary growth models for each strain:

$$\text{Lack-of-fit}=\frac{\text{MS}{\text{E}}_{\text{model}}}{\text{MS}{\text{E}}_{\text{data}}}$$ (6a)

$$\text{where}\hspace{0.17em}\text{MS}{\text{E}}_{\text{data}}=\frac{\text{RSS}}{\text{DF}}=\frac{{\text{Σ}}_{\text{A}=1}^{\text{i}}{\text{Σ}}_{\text{R}=1}^3{\text{Σ}}_{\text{E}=1}^2{({\text{X}}_{\text{ERA}}-{\text{X}}_{\text{A}})}^2}{\text{n}-\text{m}}$$ (6b)

where X_ERA is the observed μ_max (h⁻¹) obtained from each condition (e.g., A = pH 7, 6, 5, …, etc.) for specific strain, X_A is the average μ_max (h⁻¹) for each condition for a specific strain, n is the number of data points, and m is the number of conditions i.

Thermal inactivation experiments. (i) Culture preparation.

From the stock culture, a streak was made onto an MRS agar plate and incubated in microaerobic condition for 48 h at 30°C. A single colony was selected and inoculated in a 30-ml tube containing 10 ml of MRS broth and incubated for 24 h at 30°C. From the first culture, 0.5% (vol/vol) was inoculated in a 100 ml flask containing 50 ml of MRS broth and incubated for 24 h at 30°C.

(ii) Thermal inactivation.

The thermal inactivation experiments were performed in a water bath at 80 rpm (Julabo SW23; Julabo Labortechnik GmbH, Germany) set at 55°C (the duration was between 6 min for the most thermally sensitive strains and 120 min for the most thermally resistant strain), 58°C (between 1.7 min and 30 min), 60°C (between 0.75 min and 6 min), and 63°C (between 24 s and 2 min), according to a previously described method (9). Briefly, three sterile 250-ml flasks were prefilled with 40 ml of MRS broth and preheated in the water bath at the desired temperature. One flask was used to measure the temperature using a thermocouple (PeakTech 3150; Thermocouple K-Type), while the other two flasks were used to obtain duplicate inactivation experiments using the same culture. The stationary-phase culture was inoculated 1:100 (vol/vol; the final concentration was ∼10⁷ CFU/ml) in the preheated MRS to immediately start the inactivation, because in this way the observed temperature drop was negligible (±0.3°C). The same dilution (1:100) in nonheated MRS was also done for time point t = 0. At each time point, 1 ml of sample was diluted in 9 ml of PPS at room temperature, after which further decimal dilutions were made, and the appropriate dilution was plated in duplicate onto MRS agar plates using a spiral plater. For the time points with expected low concentrations of viable cells, 1 ml of sample was transferred into a sterile cup, rapidly cooled down on ice to room temperature, and spread plated onto three MRS agar plates. This method allowed us to have a detection limit of 1 CFU/ml. All plates were incubated for 5 days in microaerobic condition at 30°C, and the colonies were counted and are reported in log₁₀ CFU/ml. Each inactivation experiment was conducted in duplicate on the same day using the same culture to quantify experimental variability. Also, the inactivation experiments were reproduced at least two times on different days using freshly prepared cultures to quantify the biological or reproduction variability.

(iii) Growth history: effect of preculturing conditions and physiological state of the cells on thermal resistance.

Microorganisms might be challenged in food products because hurdle(s) are applied in foods in the form of lowered pH, low temperature, low a_w, etc., to control the growth of microorganisms to unacceptable levels, which can cause spoilage. The exposure of microorganisms to different hurdles during growth is known to influence their thermal resistance and therefore might have an impact on the efficacy of a heat treatment. To obtain knowledge of the effect and the magnitude of growth history on L. plantarum thermal resistance, three strains were selected based on their thermal resistance at 58°C, namely, the least thermally resistant strain (SF2A35B), the most thermally resistant strain (FBR05), and an intermediate thermally resistant strain (LMG18035). To determine the effect of preculturing condition, the cells were cultured until the stationary phase in MRS medium adjusted to certain suboptimal conditions, namely, pH 4, a_w 0.979, and 12°C, because those conditions can be found in food products such as low-acid food or when there is abuse in storage temperature. For pH experiments, the MRS broth was buffered using 100 mM sodium phosphate buffer, and the pH was adjusted to pH 4 using 1 M sulfuric acid and filter sterilized. For the a_w-adjusted medium, 2.5% NaCl was added to the medium, followed by sterilization for 15 min at 121°C, resulting in a medium with a a_w value of 0.979; for the temperature experiments, plain MRS broth was used. From the stock culture, a streak was made onto an MRS agar plate and incubated microaerobically for 48 h at 30°C. A single colony was selected and incubated in 10 ml of MRS broth for 24 h at 30°C. From this culture, 0.1% (vol/vol) was transferred into a 100-ml flask containing 50 ml of MRS broth and incubated at 30°C for 40 h (pH 4), 24 h (a_w 0.979), and 7 to 8 days (12°C) to obtain a stationary-phase culture. For the control condition, cells were grown in plain MRS medium at 30°C for 24 h until reaching the stationary phase. Moreover, microorganisms can also be found in their exponential phase in food products and therefore, to evaluate the effect of physiological state, cells were also subcultured in MRS broth at 30°C until an OD₆₀₀ of 0.5 was reached. All cultures were then inactivated at 58°C as described in “Thermal inactivation.”

(iv) Estimation of D and z values and quantification of variability factors and statistical analysis.

The log₁₀ surviving counts were plotted against the inactivation time to obtain the thermal inactivation curve of each data set. A modified Weibull model (equation 7) (40) was used to fit each thermal inactivation data set and to estimate the delta (Δ) 5 or 6 (time to reach a 5- or 6-decimal reduction). The model allows to fit linear, concave, and convex inactivation curves and is able to fit the different thermal inactivation curves of the strains. Points below the detection limit were not included in the fitting procedures:

$${\text{log}}_{10}{N}_t={\log }_{10}{N}_0-\Delta {\left(\frac{t}{\Delta D}\right)}^{\beta }$$ (7)

where log₁₀N_t is the log₁₀ number of surviving organisms (log₁₀ CFU/ml) at time t, log₁₀N₀ is the log₁₀ initial number (log₁₀ CFU/ml), t is the time (min or s), ΔD is the time to reach Δlog₁₀ reduction (5- or 6-log₁₀ reduction) (min or s), and β is the shape parameter. The fitting procedure was performed using Microsoft Solver Add-in and was confirmed using TableCurve 2Dv5.1. The average D value was then calculated as ΔD/Δ (delta 5 divided by 5 or delta 6 divided by 6). In this way, the effect of the β parameter was already taken into account in the average D value.

The log₁₀ average D values were used to quantify the experimental, reproduction, and strain variability according to a previously described method (see Fig. S1 in the supplemental material). The average D values among strains for each temperature were compared using analysis of variance, followed by a post hoc (Tukey HSD) test to classify strains based on their thermal resistance. The average D values were also used for calculating the z value per strain as being the negative reciprocal of the linear regression slope between the log₁₀ average D value (six values per temperature) and temperature. Finally, the effect of growth history condition was compared to the control condition using a t test and multiple linear regression (9). A comparison between the effect of growth history and strain variability on thermal resistance was made according to the scheme presented in Fig. S2 in the supplemental material and a previously described method (9).

(v) Benchmarking of the thermal resistance to literature data.

To compare the thermal resistance of L. plantarum obtained from this study and the available literature data, 121 D values of L. plantarum from various products were extracted from literature. In the case that thermal inactivation curves were available instead of D value, the average D values were estimated using the same method as used here. The literature data were further processed according to the method of Van Asselt and Zwietering (41) to obtain a global z value. The literature data were then used to benchmark the strain variability and variability introduced by growth history quantified in the present study to all variability in thermal resistance as found in literature.

Comparison of strain variability in growth and thermal inactivation.

The cardinal growth parameters, the average μ_ref and the average D values, which already took into account the effect of the β parameter, were used to predict the growth and inactivation of L. plantarum in a model process (growth in milk: pH 6.6 ± 0.1, a_w 0.997 ± 0.003, T = 7°C; thermal inactivation at 60°C for 2 min). The gamma modeling approach without interaction (42) (equations 8 and 9) was used to predict the μ_max, and the logistic growth model (equation 10) and the linear inactivation model (equation 11) were used to predict the final level of L. plantarum. Both linear and nonlinear inactivation models can be used. The linear model then uses the average D value, and the nonlinear model uses both β parameter and the average D value. However, similar conclusions were obtained from both models, and the linear model was therefore selected to present the results. Since the gamma approach is based on a reference condition, each secondary growth model used to calculate the gamma factor was transformed using the reference conditions of pH 5.7, a_w 0.993, temperature 30°C, and 0 mM [HLa] (the characteristics of plain MRS medium) (see section S1 in the supplemental material).

$$\gamma (total)=\gamma (pH)·\gamma (a_w)·\gamma (T)·\gamma (HLa)$$ (8)

$${\mu }_{max}={\mu }_{ref}·\gamma (total)$$ (9)

$$\text{lo}{\text{g}}_{10}{N}_t=\text{lo}{\text{g}}_{10}{N}_0-\text{lo}{\text{g}}_{10}\left(1+\left(\frac{N_{\text{max}}}{N_0}-1\right)\text{exp}(-{\mu }_{\text{max}}{t}_{\text{d}})\right)$$ (10)

$$\text{Lo}{\text{g}}_{10}{\text{N}}_t=\text{Lo}{\text{g}}_{10}{N}_0-\frac{t_{\text{m}}}{\text{average}\hspace{0.17em}\hspace{0.17em}D\hspace{0.17em}\hspace{0.5em}\text{value}}$$ (11)

where μ_max is the maximum specific growth rate (h⁻¹), μ_ref is the specific growth rate at the reference condition (pH 5.7, a_w 0.993, temperature of 30°C, and 0 mM [HLa]) calculated using the transformed secondary growth models (h⁻¹) (see section S1 in the supplemental material), N_t is the bacterial concentration at time t (CFU/ml), N₀ is the initial bacterial concentration (CFU/ml), N_max is the maximum bacterial concentration (CFU/ml), t_d is the storage time (days), the average D value is the time needed to kill 1 log₁₀ of bacterial concentration (min) and t_m is the thermal process time.

RESULTS

Growth kinetics of L. plantarum.

The growth kinetics of 20 L. plantarum strains as function of pH, temperature (T), water activity (a_w), and undissociated lactic acid ([HLa]) are presented in Fig. 1 to illustrate the variabilities observed in maximum specific growth rate (μ_max). As expected, the differences in μ_max between duplicate measurements using the same culture (Fig. 1A, D, G, and J) were lower than the differences in μ_max obtained from independent reproductions carried on different experimental days (Fig. 1B, E, H, and K) and the differences in μ_max among strains (Fig. 1C, F, I, and L). In general, experimental variability and reproduction variability varied among strains.

FIG 1.

Growth kinetics of 20 L. plantarum strains as a function of pH (A to C), a_w (D to F), undissociated lactic acid concentration ([HLa]) at pH 4.5 (G to I), and temperature (J to L). Panels A, D, G, and J show the duplicate growth kinetics curves of FBR05 using the same culture; panels B, E, H, and K show the growth kinetics curves of FBR05 from three independent reproductions.

For strain LMG18035, growth or no growth was already observed at pH 3.4, whereas at pH 3.3 most of strains grew at least in one of the three reproductions, but no μ_max could be obtained. The experiment at a lower pH value of pH 3.2 could not be tested since precipitation of the medium was observed at this pH. FBR26 showed growth or no-growth behavior at pH 5 and below, and therefore the result of FBR26 was excluded from the variability calculation as function of pH and the secondary model fitting for pH.

For the water activity (a_w) variable, most strains grew at least in one reproduction in the medium of a_w 0.948. Fewer strains grew when the a_w of the medium was lowered to 0.943, and only three strains (FBR01, FBR22, and LMG6907) showed growth in one of the three reproductions.

When the effect of undissociated lactic acid ([HLa]) on growth kinetics was tested, strain FBR26 already showed inconsistent growth at control condition of pH 4.5 and was therefore excluded also from the variability calculation as function of [HLa] and the secondary model fitting for [HLa]. When 30 mM [HLa] was added to MRS broth, most strains were able to grow in one, two, or in all reproductions.

For the temperature variable, the μ_max was square root transformed since the variance was not distributed evenly over the temperature range. In general, the transformed data looked linear (Fig. 1L), although this was not always the case for an individual set of μ_max data of all strains (Fig. 1J and K).

(i) Variability in growth kinetics.

The quantified experimental (E), reproduction (R), and strain (S) variabilities for each variable are presented in Fig. 2. The variability as function of pH (Fig. 2A), a_w (Fig. 2B), and temperature (Fig. 2D) followed the same trend, in which strain variability had a magnitude similar (P > 0.05) to that of reproduction variability, and both variabilities were significantly higher (P < 0.05) than the experimental variability. A different trend was observed for variable [HLa], for which the strain variability was significantly lower (P < 0.05) than the reproduction variability (Fig. 2C), but both variabilities were also significantly higher (P < 0.05) than experimental variability.

FIG 2.

Calculated variability factors (columns E, experimental; columns R, reproduction; and columns S, strain) presented as the root mean square error (RMSE) based on the μ_max as a function of pH (A), the μ_max as a function of a_w (B), the μ_max as a function of undissociated lactic acid concentration ([HLa]) (C), and the square-root μ_max as a function of temperature (D).

(ii) Variability in cardinal growth parameters.

The secondary growth models were used to fit all μ_max data per strain as function of pH, temperature, a_w, and [HLa], resulting in the cardinal growth parameter estimates per strain (Fig. 3). The minimum pH estimated for the 19 strains ranged from pH 3.2 to pH 3.5, and LMG6907, which was isolated from pickled cabbage, was estimated to have the lowest pH_min of 3.17 (95% confidence interval [CI] = 3.08 to 3.27). The estimated a_w,min for the 20 L. plantarum strains was between 0.936 and 0.953, and strain LMG6907 was also estimated to have the lowest a_w,min of all 20 strains. The [HLa_max] at pH 4.5 estimated for L. plantarum was between 29 and 38 mM. The CIs of most of the [HLa_max] estimates were high since at the highest concentration used in this study most of the strains were still able to grow, resulting in model extrapolation beyond the [HLa] concentration which was available. The T_min estimated using the square-root model was between 3.4 and 8.3°C, and strain FBR29 and WCFS1 were estimated to have the lowest T_min values of all 20 strains.

FIG 3.

Cardinal growth parameters pH_min, a_w,min, HLa_max, and T_min estimated using the secondary growth models of equations 2 to 5. The error bars indicate the 95% confidence intervals of the estimated parameters.

The specific growth rate at the reference condition (μ_ref) (see Fig. S3 in the supplemental material) was calculated from the cardinal parameters obtained in the present study using the transformed growth models. The μ_ref of the variables pH and [HLa] was lower than the μ_ref obtained for variables T and a_w, most probably due to the characteristic of the selected secondary pH model. The μ_opt of the secondary pH model was the μ_opt at pH infinite. If the μ_max value of the higher pH point decreased, such as in the case of FBR01 and FBR05 (see Fig. S4 in the supplemental material), these values would influence the μ_opt estimate, resulting in underestimation of μ_opt by the pH model. Since the μ_ref was calculated from the μ_opt, the lower value of μ_opt would result in the lower estimate of μ_ref. To predict the growth of L. plantarum strains, the average μ_ref obtained from four variables was used.

Thermal inactivation kinetics of L. plantarum. (i) Thermal inactivation kinetics of 20 strains L. plantarum and the effect of variability factors on thermal inactivation kinetics.

The thermal inactivation kinetics of 20 L. plantarum strains are presented in Fig. 4. Differences in log₁₀ counts between replicates (Fig. 4A, D, G, and J) were lower than the differences in log₁₀ counts observed from different independent reproductions (Fig. 4B, E, H, and K). The highest difference in log₁₀ counts was observed when the log₁₀ counts as a function of time among strains were compared (Fig. 4C, F, I, and L). Of all 20 strains, strain SF2A35B, which was isolated from sour cassava, had the lowest average D value at all temperatures. In contrast, FBR05, which was isolated from dressing, had the highest average D value at 55 and 58°C. However, its average D value was less than WCFS1 and FBR06 at 60 and 65°C.

FIG 4.

Thermal inactivation kinetics of 20 L. plantarum strains at 55°C (A to C), 58°C (D to F), 60°C (G to I), and 63°C (J to L). Panels A, D, G, and J show the thermal inactivation curves of FBR05 prepared using the same culture; panels B, E, H, and K show the thermal inactivation curves of FBR05 prepared from three independent reproductions.

The average D value and the shape parameter (β) of each thermal inactivation curve for each strain was estimated using the modified Weibull model. The average D value of 20 L. plantarum strains ranged from 0.8 to 19 min at 55°C, 0.22 to 3.9 min at 58°C, 3.1 to 45 s at 60°C, and 1.8 to 19 s at 63°C. These average D values were then used to estimate the z value of each strain. The z values obtained from the present study were between 3.9 and 6.0°C (Table 2). The value of the β parameter also varied per strain, but for most strains the β values was larger than 1 (see Section S2 in the supplemental material). In addition, there was no structural effect of temperature on the β values of all strains.

TABLE 2.

D and z values of 20 L. plantarum strains

Strain	D value (min)a				z value (°C)b
	55°C	58°C	60°C	63°C
FBR01	8.47 (1.21)K	1.94 (0.198)M	0.591 (0.0189)E,F,G	0.180 (0.0132)G,H	4.73 (4.53–4.93)
FBR02	4.20 (0.567)E,F	0.723 (0.0780)D,E	0.285 (0.0325)C	0.0980 (0.00500)D,E	4.91 (4.60–5.23)
FBR03	3.29 (0.0762)D	0.942 (0.0443)F,G	0.420 (0.0303)D	0.163 (0.00445)F,G	6.01 (5.75–6.26)
FBR04	4.64 (0.209)F,G	1.53 (0.208)J,K	0.611 (0.0570)F,G	0.187(0.0134)G,H,I	5.50 (5.29–5.70)
FBR05	18.6 (1.14)L	3.91 (0.223)N	0.609 (0.0414)F,G	0.190 (0.0112)G,H,I,J	3.88 (3.61–4.14)
FBR06	6.05 (0.515)H,I	1.56 (0.166)J,K,L	0.652 (0.0709)F,G	0.318(0.0228)L	6.19 (5.72–6.67)
FBR22	3.67 (0.372)D,E	0.416 (0.0766)B	0.149 (0.0269)B	0.0565 (0.00899)B	4.41 (3.98–4.85)
FBR23	7.55 (0.814)K	1.34 (0.0766)I,J	0.575 (0.0346)E,F	0.215 (0.00619)H,I,J,K	5.15 (4.78–5.52)
FBR24	4.20 (0.250)E,F	0.867 (0.0866)E,F	0.255 (0.0186)C	0.0987 (0.00358)E	4.83 (4.52–5.13)
FBR25	8.20 (0.523)K	1.78 (0.0545)K,L,M	0.550 (0.0138)E,F	0.232 (0.0281)I,J,K	5.07 (4.79–5.36)
FBR26	8.65 (0.228)K	1.58 (0.0743)J,K,L	0.559 (0.0169)E,F	0.237(0.0150)J,K	5.25 (4.89–5.61)
FBR27	1.99 (0.219)B	0.449 (0.0388)B	0.159(0.0398)B	0.0785 (0.00365)C,D	5.77 (5.22–6.33)
FBR28	6.60 (0.615)I,J	1.21 (0.150)H,I	0.513 (0.0413)D,E,F	0.224 (0.0177)H,I,J,K	5.59 (5.18–6.01)
FBR29	2.64 (0.192)C	0.570 (0.0482)C	0.144 (0.0263)B	0.0535 (0.00787)B	4.60 (4.28–4.92)
FBR30	1.89 (0.267)B	0.615 (0.0753)C,D	0.151 (0.00745)B	0.0533 (0.00474)B	5.00 (4.67–5.33)
WCFS1	7.23 (0.603)I,J,K	1.88 (0.0576)L,M	0.754 (0.0640)G	0.243 (0.0179)K	5.48 (5.33–5.64)
LMG18035	5.34 (1.01)G,H	1.07(0.0781)G,H	0.471 (0.0517)D,E	0.196 (0.00815)G,H,I,J,K	5.60 (5.17–6.03)
LMG23545	3.90 (0.446)D,E,F	0.588 (0.0622)C	0. 166 (0.00280)B	0.0801 (0.0222)C	4.63 (4.16–5.10)
LMG6907	7.60 (0.575)J,K	1.32 (0.0613)I,J	0.427 (0.0316)D	0.140 (0.0137)F	4.57 (4.33–4.82)
SF2A35B	0.796 (0.0393)A	0.219 (0.0126)A	0.0521 (0.0134)A	0.0297 (0.00468)A	5.34 (4.74–5.94)
Avgc	5.77 (3.79)	1.23 (0.809)	0.405 (0.212)	0.154 (0.0801)	5.13 (0.576)

^aThe values in parentheses are the standard deviations for six D values. Shared superscript letters within a particular column show comparable thermal resistances (post hoc Tukey HSD test [P = 0.05]).

^bThe 95% confidence intervals obtained from linear regression of log₁₀ D values against temperatures using Table Curve 2D v5.01 are indicated in parentheses.

^cThe values in parentheses for this row of data indicate the standard deviations from the D or z value of all 20 L. plantarum strains.

The experimental, reproduction, and strain variability of the log₁₀ average D values are expressed in root mean square error (RMSE) (Fig. 5). Strain variability was much higher (P < 0.05) than the reproduction and experimental variabilities at all temperatures. Strain variability was about 6 times higher than the reproduction variability and more than 10 times higher than the experimental variability.

FIG 5.

Variability factors (E, experimental; R, reproduction; and S, strain) presented as the RMSE calculated from the log₁₀ D values obtained at 55°C (A), 58°C (B), 60°C (C), and 63°C (D).

(ii) Effect of growth history and physiological state of the cells on thermal resistance.

The thermal inactivation kinetics as influenced by growth history and physiological state of the cells are presented in Fig. 6. The cells grown in MRS medium containing NaCl of a_w 0.979 had kinetics similar to those of the cells grown until stationary phase in plain MRS for strain SF2A35B, as the representative of the least heat-sensitive strains, and strain LMG18035, as the representative of the intermediate heat-resistant strains. Slight differences were observed for strain FBR05, in which the cells grown in the medium with lower a_w unexpectedly had a lower average D value than those grown in plain medium.

FIG 6.

Effect of growth history and physiological state of the cells of strains FBR05 (A and D), LMG18035 (B and E), and SF2A35B (C and F) on thermal inactivation kinetics at 58°C. *, significantly different from the stationary-phase cells grown in MRS at 30°C (P < 0.05).

The thermal resistance of cells grown in the media with lower pH (pH 4) was not different from the cells grown in plain MRS medium (pH 5.7) for strains FBR05 and SF2A35B (Fig. 6D to F). However, growing the cells in the MRS at pH 4 significantly decreased the average D value of strain LMG18035. Growing the cells until the stationary phase at 12°C or until the exponential phase greatly reduced the average D value compared to the stationary cells grown in plain media at 30°C for all three strains.

The effect of growth history on thermal resistance was also analyzed using multiple linear regression to determine the factors influencing the average D value. This analysis confirmed that both preculturing temperature and exponential-phase-grown cells significantly influenced the average D value (Fig. 6). When the effect of growth history on thermal resistance was compared to the effect of strain variability using the previously described scheme (9) (see Fig. S2 in the supplemental material), the strain variability was slightly higher than the variability caused by growth history (P = 0.03).

(iii) Benchmarking of the thermal resistance of L. plantarum to literature data.

To benchmark the strain variability and variability introduced by growth history, these variability factors were compared to the variability found in D values reported in literature. In all, 121 D values were collected from different studies. These studies used different methods, strains, and treatments and different types of heating media, including food products. Following an approach similar to that used in a study by Van Asselt and Zwietering (41), the 95% prediction intervals of the data were obtained (Fig. 7A) to quantify the overall variability found in literature.

FIG 7.

Meta-analysis of thermal inactivation data. (A) Thermal inactivation data from literature and its 95% prediction interval (PI, all data). (B) Thermal inactivation data as function of matrices. (C) Thermal inactivation data at truncated temperature of 50 to 63°C. (D) Benchmarking experimental data to literature data (22–24, 59–61, 65–72).

When all data from the literature were used (48.5 to 80°C) (Fig. 7A), the slope of the linear regression between the log₁₀ D value and the temperature was rather low, so the estimated z value of L. plantarum from literature data was rather high (12°C) compared to the z value of our experimental data, which was between 3.9 and 6.0°C. The higher z value of the literature data was due to the effect of different matrices included in the meta-analysis. When the literature data of L. plantarum was split into different categories, namely, laboratory media, milk, and juices, the estimated z values were 7.2, 12.8, and 13.3°C, respectively (Fig. 7B). When only D values at the temperature range of our study (50 and 63°C) (Fig. 7C) was used for the regression analysis, the estimated z value was 6.5°C. When our data were benchmarked to the intervals of all literature data, the strain variability explained most of the variability in D values found in literature (Fig. 7D). When our data were benchmarked to the intervals of literature data at a truncated temperature range or to the intervals of literature data obtained from laboratory media, strain variability explained all of the variability found in literature, but with bias at the higher temperatures of 60 and 63°C (Fig. 7D). When the data of growth history effect was added, our data explained all variability found in literature, although with a slight bias (Fig. 7D).

Comparison of strain variability in growth and thermal inactivation of L. plantarum.

Direct comparison on the effect of variability observed in growth and thermal inactivation kinetics could not be made due to differences in the data format/unit. Therefore, the cardinal parameters and average D values data of 19 strains were used to visualize the growth and inactivation kinetics in a model process, namely, growth in milk (pH 6.6, a_w 0.997 ± 0.003, and T = 7°C) using the gamma approach, followed by thermal inactivation at 60°C for 2 min. The illustration (Fig. 8) shows that the impact of strain variability in thermal inactivation was much higher than in growth kinetics, as indicated by ∼2-log₁₀ CFU/ml differences between the most- and least-robust strains in growth and >10-log₁₀ CFU/ml differences after thermal treatment.

FIG 8.

Illustration on the effect of strain variability on growth and thermal inactivation of 19 L. plantarum strains.

In addition, no correlation could be found between strain origin and the phenotypic characteristic of L. plantarum in growth and thermal resistance kinetics, except for variable pH. Strains isolated from low-pH foods such as dressing (pH 3.6 to 4.2), ketchup (pH 3.3 to 3.6), and fermented cabbage (pH 3.4 to 3.5) (43–47) had lower pH_min values than strains isolated from meat, milk, and plant-based products. However, inconsistency was also observed since strain SF2A35B, which was isolated from sour cassava (pH 3.4 to 3.9 [48]), had a higher pH_min than the other strains from low-pH foods.

DISCUSSION

The strain variability in growth kinetics and thermal inactivation kinetics of L. plantarum, except for growth as a function of [HLa], were between 1.3 and 2.6 times higher than that previously reported for the food-borne pathogen L. monocytogenes (8, 9). As in L. monocytogenes (8, 9), the strain variability was similar (P > 0.05) to the reproduction variability in growth for the variables pH, a_w, and temperature and was significantly higher (P < 0.05) than the reproduction variability for all temperatures tested in thermal inactivation kinetics. The impact of strain variability on growth as illustrated in Fig. 8 resulted in 2-log₁₀ CFU/ml differences between the most- and least-robust strains of L. plantarum using milk as the growth medium. This result was more or less similar to the growth illustration in laboratory media using L. monocytogenes, in which the difference between the most and the least robust strains was between 2 and 4 log₁₀ CFU/ml (8). Although strain differences in the log₁₀ number of bacteria were observed in growth, the magnitude was less than the differences observed among strains for thermal inactivation.

The strain variability observed in L. plantarum might be related to the high genetic diversity reported for this species (1, 35, 36), which corresponded to the observed phenotypic diversity, including the strain diversity in stress tolerance. A clear example for the observed strain variability in growth kinetics is given for strain FBR26. The result of FBR26 was excluded from the analysis of pH and [HLa] since growth or no growth was already observed at pH 5 and below. Using the μ_max as a function of the pH available for FBR26, the pH_min was estimated 3.86 (CI = 3.64 to 4.08). This value was higher than the estimated pH_min of the other 19 strains in our study (pH 3.2 to 3.5), and the latter range corresponded to the pH_min reported in the literature (49–51). Interestingly, the growth of FBR26 was observed in one of the experiments performed at pH 3.4, but no μ_max at this pH level could be obtained for FBR26. Additional investigation on the effect of aerobic, microaerobic, and static incubation with different volumes of headspace using 10 L. plantarum strains showed that the growth of strain FBR26 was temporarily disrupted during the exponential phase in aerobic growth. This disruption led to a much lower growth rate estimated for aerobic growth than for microaerobic and static growth (data not shown). This lower growth rate in aerobic growth was also reported in a previous study with L. plantarum ATCC 8014 and L. plantarum P5 (52, 53). In our study, the growth disruption during the exponential phase was only observed for strain FBR26, because no difference in growth kinetics was observed from the other nine L. plantarum strains, including strain WCFS1 in the three different incubation conditions. The phenomenon observed for FBR26 was not new since a previous study also reported a temporary growth stagnation in early exponential phase of strain WCFS1 grown aerobically in MRS medium (54), which was correlated to the limited CO₂ concentration in the medium. This reported stagnation for WCFS1 during aerobic growth, however, was not observed in our study and in the study of Watanabe et al. (55). Whether the growth disruption during aerobic growth correlated to the growth or no-growth behavior of strain FBR26 at pH below 5, when tested using Bioscreen C, is not yet clear. Moreover, less strain variability was observed when the strains were incubated under microaerobic conditions than under static and aerobic conditions. This can be an indication that the microaerobic condition might be more suitable to study the growth kinetics of L. plantarum strains (especially strain FBR26) than the method using Bioscreen C. However, FBR26 was able to grow to the same extent as the other 19 L. plantarum strains when the other experiments as function of a_w and temperature were performed using Bioscreen C. Further investigation on correlation between pH and aerobic growth might be needed to explain the behavior of strain FBR26 at low pH values. However, since this phenomenon provided a disadvantage rather than an advantage over growth kinetics, this might not be of interest compared to the effects of other conditions, which support growth or protect cells from being inactivated by certain processes.

The higher confidence intervals of [HLa_max] obtained in this study could be explained by the fact that most of the strains were still able to grow even at the highest [HLa] used. When data in the growth or no-growth boundary are available, then the confidence intervals of the growth limit might be smaller. In our study, higher concentrations than 30 mM [HLa] were not used since this might influence the water activity of the medium. At the concentration of 20 to 30 mM, the measured medium a_w was 0.991 ± 0.002, which is close to the a_w of the plain MRS medium. Comparing the estimated [HLa_max] obtained in our study with the one reported in literature was rather complicated, since [HLa_max] might be influenced by pH media and incubation temperature used in the studies. However, a previous study reported that the influence of pH on the MIC of sodium lactate depended on the type of microorganisms and that temperature did not have a specific influence on the MIC of sodium lactate (32). The pH had a minor influence on the MICs of sodium lactate for lactic acid bacteria M18, M52, M75, Lactococcus lactis subsp. cremoris, and Lactococcus lactis SK3 (32). The sodium lactate MICs for these strains were between 268 and 714 mM at pH 5.7 and at an incubation temperature of 20°C or corresponded to 3.82 to 10.17 mM [HLa_max], which was lower than what was estimated in our study. When we considered only the effect of initial pH medium, in which the growth at pH 4.5 would be slower than the growth at pH 5.7, one might expect that a lower [HLa] would be needed at pH 4.5 than at pH 5.7 to inhibit the growth of L. plantarum. However, as also described by Houtsma et al. (32), three factors played a role in determining the growth of microorganism when lactate was added to the medium: pH, [HLa], and a_w. At the higher pH value of pH 7 the inhibitory effect of sodium lactate was mostly due to lowering effect of a_w, whereas at the lower pH the effect of undissociated form of the organic acid became more important (32). The addition of 268 to 714 mM sodium lactate in peptone-yeast extract broth (a_w = 0.998) by Houtsma et al. (33) resulted in a medium a_w of between 0.992 and 0.977. The influence of a_w and the type of microorganism might then be the reason for the difference between the [HLa_max] values obtained in our studies and those reported in the literature.

Most of the L. plantarum strains in our study had an estimated T_min between 4.7 and 8.3°C, except for the two strains FBR29 and WCFS1. These two strains had T_min estimates between 3 and 4°C, which was similar to the reported T_min estimate for L. plantarum (34). Notably, the square-root μ_max data as function of temperature for some L. plantarum strains in this study seemed to slightly deviate from linearity, as indicated by the lack-of-fit of the square-root model for 10 of 20 strains. However, no structural deviation of the model was observed for those 10 strains since the deviation was not always found at the same location or temperature point. This phenomenon is different from that observed with L. monocytogenes and L. innocua, where in certain cases a deviation was found at the same temperature point (56, 57), and therefore a two-phase temperature model was used in these studies. Thus far, no deviations in linear relationship between square-root μ_max and temperature have been reported for L. plantarum.

Heating temperature seemed not to have an influence on strain variability of L. plantarum since the strain variability in the log₁₀ average D value was remarkably similar (P > 0.05) at all temperatures. Moreover, whereas the average D value for all strains was temperature dependent, there was no structural effect of temperature on the β parameter. A similar result was also observed in a previous study on the application of the Weibull model for thermal inactivation of vegetative cells (58), although linear dependency of the β parameter with temperature was also reported.

As for L. monocytogenes (8), the physiological state of the cells had the biggest effect on the thermal resistance, but the magnitude was similar (P > 0.05) to the effect of preculture at a low temperature before thermal treatment. Culturing the cells at a low pH seemed to have a limited impact on the thermal resistance of strains FBR05 and SF2A3B compared to cells cultured in plain medium, as indicated by the similarity (P > 0.05) between the average D values of cells incubated in low pH and plain media. This can be explained by the fact that when the cells were grown until stationary phase for 24 h in plain medium, the pH of the medium dropped to between 3.9 and 3.8. This reference culturing condition therefore also exposed cells to a lowered pH before the thermal process. Although the medium for low-pH growth (pH 4) was buffered, the pH decreased to 3.2 and 3.4 when the cells reached stationary phase. This limited difference in end pH of both culturing conditions might explain why both conditions showed no difference in the thermal resistance result. However, the effect of preculturing at low pH was observed for strain LMG18035, in which the average D value of cells grown in plain medium was 1.8 times higher than that of cells grown in low-pH medium. No study reported the effect of preculturing in low-pH medium on the thermal resistance of L. plantarum. However, a decrease in thermal resistance of the cells precultured in low-pH medium was also observed for L. monocytogenes (9).

The average D value of FBR05 cells precultured in lower a_w medium was 0.8 times the average D value of cells precultured in plain media, indicating a decrease in heat resistance. In contrast to our result, enhanced thermal resistance was reported for L. monocytogenes (9) and B. cereus (39) precultured in the presence of a medium with a higher NaCl concentration or a lower a_w. The decrease in thermal resistance of strain FBR05 could not be related to its sensitivity to NaCl or a low a_w since it was able to grow up to a_w 0.948 in the growth experiment. No report about the decreasing effect of NaCl/a_w on thermal resistance was found for lactic acid bacteria and for other mesophilic bacteria. Testing the effects of NaCl and a_w on thermal resistance for other L. plantarum strains could confirm whether the decreased effect is strain specific.

The higher z value, when all literature data were used, might be due to the effect of different matrices included in the meta-analysis. The effect of food matrix on thermal resistance was also reported for Salmonella spp. in chocolate (z value = 20.4°C) (41) and L. plantarum in milk (20°C) (59) and in apple juice (15°C) (60), highlighting the effect of heating menstruum on thermal inactivation. Moreover, higher D values between 63 and 80°C, which were mostly obtained from experiments using milk and were available only in fewer numbers than those at lower temperature, might also contribute to the lower slope of the regression. The estimated z value of 6.5°C, when the D values at the temperature range of our study (50 and 63°C) were used, corresponded more or less to the reported z values of vegetative cells, which are between 5 and 7°C (41, 61, 62).

It is not easy to clearly define and separate variability and uncertainty on the basis of the available data (63). In general, our experimental studies showed that the magnitude of experimental variability, which can be considered as an uncertainty factor, was at most one-third of the strain and reproduction variabilities for growth kinetics and less than one-tenth for thermal inactivation kinetics. Unlike strain and reproduction (biological) variability, which is inherited, the magnitude of experimental variability in this study could have been reduced by performing additional measurements (64). Although Nauta (63) pointed out that the separation between uncertainty and variability influenced the result of quantitative microbial risk assessment, the uncertainty factor in our case (experimental variability) was much less important than the reproduction and strain variabilities. This experimental variability might become important when no assurance on the implementation of good laboratory practice is made, and therefore the integration of this experimental variability factors in quantitative microbial risk assessment model can be considered.

Conclusions.

The phenotypic diversity in growth and thermal resistance of L. plantarum was quantified. In general, the impact of strain variability was much higher for thermal resistance than for growth, as indicated by ∼2-log₁₀ CFU/ml differences between the most- and least-robust strains in growth and >10-log₁₀ CFU/ml differences after thermal treatment. Strain variability in thermal resistance was also higher than the effect of growth history, but the combined effects of strain and growth history were able to explain all of the variability found in the literature, although with bias. The quantitative knowledge obtained on experimental, reproduction, and strain variabilities can be used to improve experimental designs and to adequately select strains for challenge growth and inactivation tests. Further validation of growth and thermal inactivation kinetics in food models should also be conducted to validate the results obtained using laboratory media and to quantify the food product factor. Moreover, integration of strain variability in prediction of microbial kinetics will result in more realistic predictions of L. plantarum growth and inactivation dynamics.

Funding Statement

The research is funded by TI Food and Nutrition, a public-private partnership on precompetitive research in food and nutrition. The funders had no role in study design, data collection and analysis, or preparation of the manuscript.