Modeling and Validation of the Ecological Behavior of Wild-TypeListeria monocytogenes and Stress-Resistant Variants

Karin I. Metselaar,a,b Tjakko Abee,a,b Marcel H. Zwietering,a,b Heidy M. W. den Bestenb

Top Institute Food and Nutrition, Wageningen, the Netherlandsa; Laboratory of Food Microbiology, Wageningen University, Wageningen, the Netherlandsb

ABSTRACT

Listeria monocytogenes exhibits a heterogeneous response upon stress exposure which can be partially attributed to the presenceof stable stress-resistant variants. This study aimed to evaluate the impact of the presence of stress-resistant variants of Listeriamonocytogenes and their corresponding trade-offs on population composition under different environmental conditions. A setof stress robustness and growth parameters of the wild type (WT) and an rpsU deletion variant was obtained and used to modeltheir growth behavior under combined mild stress conditions and to model their kinetics under single- and mixed-strain condi-tions in a simulated food chain. Growth predictions for the WT and the rpsU deletion variant matched the experimental datagenerally well, although some deviations from the predictions were observed. The data highlighted the influence of the environ-mental conditions on the ratio between the WT and variant. Prediction of performance in the simulated food chain proved to bechallenging. The trend of faster growth and lower stress robustness for the WT than for the rpsU variant in the different steps ofthe chain was confirmed, but especially for the inactivation steps and the time needed to resume growth after an inactivationstep, the experimental data deviated from the model predictions. This report provides insights into the conditions which canselect for stress-resistant variants in industrial settings and discusses their potential persistence in food processing environ-ments.

IMPORTANCE

Listeria monocytogenes exhibits a heterogeneous stress response which can partially be attributed to the presence of genetic vari-ants. These stress-resistant variants survive better under severe conditions but have, on the other hand, a reduced growth rate.To date, the ecological behavior and potential impact of the presence of stress-resistant variants is not fully understood. In thisstudy, we quantitatively assessed growth and inactivation behavior of wild-type L. monocytogenes and its stress-resistant vari-ants. Predictions were validated under different conditions, as well as along a model food chain. This work illustrates the effectsof environmental factors on population dynamics of L. monocytogenes and is a first step in evaluating the impact of populationdiversity on food safety.

Diversity exists within bacterial populations which can, for ex-ample, be observed by tailing of inactivation curves upon

stress exposure. This tail can be caused by either phenotypic orgenotypic heterogeneity. Phenotypic heterogeneity refers to tran-siently increased resistance with a physiological or epigeneticbackground. Reasons for phenotypic heterogeneity can includethe presence of persisters (1), bistability caused by noise in sto-chastic gene expression (2–4), or epigenetic phenotype switching(5). Genotypic heterogeneity refers to the presence of stable stress-resistant variants with an inheritable stress-resistant phenotypecaused by genomic alterations (6). These stable stress-resistantvariants have been repeatedly isolated from the foodborne patho-gen Listeria monocytogenes upon exposure to different types ofstress, e.g., heat, high hydrostatic pressure (HHP), and low pH(7–11).

L. monocytogenes stress-resistant variants have been shown tocomprise a wide range of phenotypic features that are differentfrom those of the main wild-type (WT) population. Apart fromresistance toward the selection stress, numerous variants showed amultiple-stress-resistant phenotype (12, 13). It was shown thatdifferent types of stress lead to selection for different types of vari-ants. Although many phenotypic features are overlapping, the ge-netic basis for the increased resistance was shown to be partiallyselection stress dependent (12).

A large fraction of the heat- and HHP-selected variants had a

mutation in the class III heat shock repressor gene ctsR (11, 13),while this mutation was not found in the acid stress-selected vari-ants. In a large fraction of the acid stress-selected variants, a mu-tation in rpsU, encoding ribosomal protein S21, appeared to beresponsible for the stress-resistant phenotype (12). An interestingobservation in all these variants is that increased stress resistanceseems to be at the cost of another feature. The growth rate formany of the variants was lower than for the WT, although in somecases it was impaired only under specific conditions. Generally,the most resistant variants showed a significant growth defect, anda clear correlation between acid resistance and growth rate wasestablished (9).

Received 12 February 2016 Accepted 21 June 2016

Accepted manuscript posted online 24 June 2016

Citation Metselaar KI, Abee T, Zwietering MH, den Besten HMW. 2016. Modelingand validation of the ecological behavior of wild-type Listeria monocytogenesand stress-resistant variants. Appl Environ Microbiol 82:5389 –5401.doi:10.1128/AEM.00442-16.

Editor: D. W. Schaffner, Rutgers, The State University of New Jersey

Address correspondence to Marcel H. Zwietering, marcel.zwietering@wur.nl.

Supplemental material for this article may be found at http://dx.doi.org/10.1128/AEM.00442-16.

Copyright © 2016, American Society for Microbiology. All Rights Reserved.

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The increased stress resistance of the variants can be consid-ered a trade-off; a variant may have an advantage under a certaincondition while having a disadvantage under another condition.The concept of stress resistance as a trade-off for growth has beenwell described in the literature (14–16). Specialization on survivaloften comes at the cost of slower multiplication. The underlyingmechanism can be found in resource allocation; energy expendi-ture has to be divided over vegetative growth and general stressresponse (14). This resource allocation is affected by the environ-mental conditions, but mutations have also been shown to cause ashift in the distribution of resources between reproduction andmaintenance (15). The ctsR and rpsU mutations in the stress-re-sistant L. monocytogenes variants seem to result in a shift awayfrom rapid reproduction and toward increased stress response.

During food processing and storage, bacterial cells encounterdifferent environments which can affect the behavior of the cells.Heat resistance has been shown to be affected by environmentalconditions like growth temperature, medium composition, andgrowth stage (17). Growth at mild pH stress can induce increasedresistance to lethal acid stress but also to other stresses, like ther-mal stress (18). It was also shown that the different variants havedifferent degrees of mild stress-adaptive behavior, affecting theirstress resistance (19). The differences in behavior and resourceallocation between the WT and variants might have consequencesfor their growth and survival under processing conditions.

Information on whether these stress-resistant variants are apotential threat for the food industry or if the disadvantages, com-bined with their low prevalence in the population, counterbalancethe increased resistance is currently lacking. It would be of rele-vance to evaluate the impact of the presence of stress-resistantvariants and their corresponding trade-offs on population com-position. Therefore, this study aimed to quantify the growth andinactivation kinetics of WT L. monocytogenes and acid-resistantvariants under different environmental conditions and to use thequantitative data obtained to predict the behavior along a simu-lated model food chain. It was hypothesized that the WT has anadvantage during growth but that the variants have an advantageduring inactivation steps. A modeling approach was used to pre-dict the behavior of the WT and variants under different combi-nations of mild and severe stress conditions, and the genetic back-ground of one rpsU variant was used to evaluate predictions inmixtures in which the WT and an rpsU deletion variant were dis-tinguished by specific primers. This study highlights the potentialimpact of the environmental conditions on population dynamicsof WT L. monocytogenes and its acid-resistant rpsU variant in se-quential niches.

MATERIALS AND METHODSBacterial strains and culture conditions. WT Listeria monocytogenesLO28 (Wageningen UR Food & Biobased Research, the Netherlands) and8 of 23 acid-resistant variants isolated from the tail of this WT strain afteracid exposure (9) were used in this study. The selected variants were 3, 7,9, 12, 13, 14, 15, and 23, based on their genotypic and phenotypic charac-teristics representing different clusters (12, 19). The stock cultures werekept in 15% (vol/vol) glycerol (Fluka) at �80°C, and before the experi-ments, cells from stock were grown for 2 days at 30°C on brain heartinfusion (BHI; BD) agar plates. A single colony was used to inoculate 20ml of BHI broth (Oxoid) in an Erlenmeyer flask. After overnight growth(18 to 22 h) at 30°C (Innova 4335; New Brunswick Scientific, Edison, NJ)with shaking at 160 rpm, a 0.5% (vol/vol) inoculum was added to freshBHI broth. Cells were grown in BHI at 30°C until the late exponential

growth phase (optical density at 600 nm [OD600] � 0.4 to 0.5 after 4 to 5h) or stationary phase (18 to 22 h of growth; OD600 � 2.0). Bacteria werespiral plated (Eddy Jet; IUL Instruments) or spread plated on BHI agar.For inactivation experiments, plates were incubated for 4 to 6 days at 30°Cto allow recovery of the cells. For all other experiments, plates were incu-bated for 2 days at 30°C.

Determination of the maximum specific growth rate. The maximumspecific growth rate (�max) was determined under various mild stressconditions, namely, at different pH conditions, water activities (aw), andtemperatures (T). BHI broth (Oxoid; aw, 0.997; pH 7.3) was used as a plainmedium for all growth experiments, with 30°C as the reference tempera-ture. The effect of mild pH was determined by adjusting the pH of sterileBHI with 10 M HCl to pHs 6.0, 5.0, and 4.7, followed by filter sterilization(0.22-�m filter). The water activity was lowered by adding 42, 65, 83, and91 g of NaCl (Merck) per liter of BHI broth, resulting in aw values of 0.971,0.957, 0.946, and 0.940, respectively (Labmaster aw; Novasina). Values for�max at 7°C and 37°C were available from our previous study (9) and wereextended in the current study at 20°C and 30°C to determine the effect oftemperature on �max. The �max for the WT and each variant was deter-mined by the 2-fold dilution (2FD) method as described by Biesta-Peterset al. (20). Briefly, overnight cultures were used for this experiment anddiluted in BHI broth to an initial concentration of �5 � 105 CFU/ml,which was confirmed by plating on BHI agar plates. From this culture, fivesequential 2-fold dilutions in BHI broth were made in duplicate in a100-well honeycomb plate, and the final volume in each well was 200 �l.The plate was incubated in a Bioscreen C (Oy Growth Curves AB Ltd.).The Bioscreen C was set at the appropriate temperature with mediumconstant shaking, and the OD600 was measured every 10 or 30 min de-pending on the conditions. This was done for up to 2 weeks, or until allwells reached an OD600 of at least 0.2 (time to detection [TTD]). The �max

was determined for the WT and each variant for each condition by takingthe negative reciprocal of the slope between TTD and ln(N0). For morestressful conditions in which an OD600 of 0.2 was barely reached, a TTD of0.12 was used since 0.12 was in the linear part of the OD600 growth curvefor all conditions and variants. Wells not showing an increase in OD600

during the time of the experiments were plated on BHI plates to confirmthe absence of growth. Experiments were repeated on different days usingfresh cultures to obtain biologically independent duplicates or triplicates.

Estimating cardinal growth parameters. Secondary growth modelsto estimate cardinal growth parameters were chosen based on the selec-tion described by Aryani et al. (21). Generally, errors for all variables werehomoscedastic; however, for the data as a function of temperature, errorsincreased at higher temperatures and a square root transformation wasneeded to stabilize the variance. This has been observed previously for L.monocytogenes (21) as well as for Lactobacillus plantarum (22). The squareroot model (23) was used to describe the �max as a function of tempera-ture (T):

��max � b�T � Tmin� (1)

in which b is the slope parameter and Tmin (degrees Celsius) is the theo-retical minimum temperature for growth, estimated from the regressionline through the data for a rate of 0, i.e., the intercept of the line with thetemperature axis. The �max as a function of pH was described by thereparameterized model of Aryani et al. (21):

�max � �opt�1 � 2�pH � pHmin �

�pHmin � pH1⁄2 �� (2)

in which �opt (per hour) is the �max at optimum pH, pHmin is the pH atwhich no growth is observed anymore, and pH1/2 is the pH at which the�max is half of the �opt. The �max as a function of aw was described by themodel of Luong (24):

�max � �opt�1 � � 1 � aw

1 � aw, min�d� (3)

in which �opt (per hour) is the �max at optimum aw, aw, min is the aw atwhich no growth is observed anymore, and d is the shape parameter. The

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models were fitted to all independent replicate �max data together usingTableCurve 2D v5.01. For the aw model, a lack-of-fit test (25) was per-formed, in the cases where 1 was in the confidence interval of d, in order toselect a more simple, linear model. The lack-of-fit test evaluates if theshape parameter can be removed by comparing the residual sum ofsquares (RSS) of the full model (with d) to the RSS of the reduced model(without d, equivalent to a d of 1).

Growth modeling. Cardinal growth parameters obtained were used asinput in the gamma model (26) to predict the growth of the WT andvariants under combined mild stress conditions. The gamma model with-out inclusion of an interaction factor was used, and therefore, only amultiplicative effect of the combined mild stress conditions was assumed(27). Predictions of �max were made by

�max � �ref � ��T� � ��pH� � ��aw� (4)

in which �ref (per hour) is the average of the estimated �max in BHI at30°C, pH 7.3, and an aw of 0.997 according to equations 1 to 3 and �(T),�(pH), and �(aw) are the gamma factors for each individual condition (x),which is determined by

��x� ��max�x�

�ref(5)

in which �max (x) is calculated by equations 6 to 8 (21):

�max�T� � �ref�T � Tmin�2

�Tref � Tmin�2 (6)

�max�pH� � �ref

�1 � 2�pH�pHmin �

�pHmin �pH1⁄2 ���1 � 2

�pHref�pHmin ��pHmin �pH1⁄2 ��

(7)

�max�aw� � �ref

�1 � � 1 � aw

1 � aw, min�d�

�1 � � 1 � aw, ref

1 � aw, min�d� (8)

The �max values for combined stress conditions resulting from equa-tion 4 were used as input into the widely used three-phase linear model(28) to predict the growth of the WT and variants under the definedconditions. The lag time (�) was assumed to be reciprocally proportionalto the �max (25, 29). It has been described before that the product of theequation �max � � generally ranges between 0 and 4 (25), and thereforethese values were considered to predict the growth intervals (25). AverageNmax (the maximum number of organisms reached) was set at 9.5 log10

CFU/ml, based on counts of fully grown overnight cultures (data notshown). For the growth intervals, a range from 9.25 to 9.75 log10 CFU/mlwas assumed, based on reproduction variability of the measured Nmax

values.Heat inactivation. Heat inactivation experiments were performed for

the WT and rpsU variant 14 as described in reference 12. This variant waschosen as a representative rpsU variant based on the genetic background,which allowed for validation as described below. Briefly, 400 �l of a late-exponential- or stationary-phase culture was transferred into 40 ml ofpreheated BHI broth in a 250-ml Erlenmeyer flask, in a shaking (160 rpm)water bath (SW23; Julabo) at 55, 60, or 62°C. At appropriate time inter-vals, a 1-ml sample was taken and either used to make a 10-fold dilutionseries in peptone physiological saline (PPS; 0.1% peptone and 0.8% NaCl)or transferred into a sterile cup that was placed on ice in case the undilutedsample was to be plated. A separate Erlenmeyer containing BHI broth atroom temperature was used for the time zero measurement. Fifty-micro-liter volumes of appropriate dilutions were spiral plated in duplicate onBHI agar, or, in the case of the undiluted samples, 1 ml was spread plated(divided over 3 plates), resulting in a detection limit of 1 CFU/ml. Theresulting inactivation curves were described with any of the followingmodels to determine the D value. In the case of nonlinear inactivation andthe presence of a shoulder and tail, the model of Geeraerd et al. (30) in itsreparameterized version (9) (equation 9) was fitted to the data:

log10�Nt� � log10�N0� � log10��1 � 10log10�f�� � exp ��ksens � t�

�exp�ksens � Sl�

1 � �exp�ksens � Sl� � 1� � exp��ksens � t�� 10log10�f�

� exp�� kres � t� � � exp�ksens � Sl�1 � �exp�ksens � Sl� � 1� � exp�ksens � t��

kres

ksens� (9)

in which Nt is the number of cells at time t (in minutes), N0 is the numberof cells at time zero, ksens and kres are the specific inactivation rates of thesensitive population and the resistant fraction, respectively (per minute),Sl is the shoulder length (in minutes), and f is the stress-resistant fraction.When the shoulder length was not significant, equation 10 was fitted tothe data:

log10�Nt� � log10�N0� � log10��1 � 10log10�f��� exp��ksens � t� � �10log10�f�� � exp��kres � t�� (10)

When the tail was also not significant, the model was further reduced to alinear inactivation model:

log10�Nt� � log10�N0� � log10�exp��k � t�� (11)

The D value of the sensitive and resistant fractions for equations 9 to 11was calculated by equation 12:

D �ln �10�

k(12)

In the case that no tailing was present, a linear model with shoulder andthe reparameterized Weibull model (equation 13) (9) was fitted to thedata. The Weibull model was preferred, as this model also considers theshoulder in D value determination, whereas the linear model with shoul-der does not.

log10�Nt� � log10�N0� � � � � t

t�D�

(13)

in which is the number of decimal reductions, tD is the time needed toreduce the initial number of microorganism with decimals (in min-utes), and is a fitting parameter that defines the shape of the curve. wasset at 5, since the measured data covered a range of at least 5 log10 reduc-tions, and the other parameters were estimated. This procedure results inan average D value over the whole 5-log reduction while fitting the datawith the nonlinear Weibull model, circumventing a large correlation be-tween delta and the shape parameter (9). All models were fitted to the datausing TableCurve 2D v5.01. An F-test was performed to test if the fittingperformance of the model was statistically accepted. The f value was cal-culated using the following equation (31):

f �MSEmodel

MSEdata(14)

in which MSEmodel is the mean square error of the model and MSEdata isthe mean square error of the data for replicate values. The resulting f valuewas tested against a critical F table value with a 95% confidence level. Forthe inactivation curves showing tailing and therefore described by equa-tion 9 or 10, the reparameterized Weibull model (equation 13) was alsofitted to the data without taking the tail into consideration in order to beable to compare the WT and variant 14 at different temperatures andgrowth phases. The D values were calculated by dividing the t5D by 5.From these D values, the z value was calculated by taking minus the in-verse of the slope between the log10 D value and temperature for the WTand variant 14 in the late exponential and stationary phases.

Acid inactivation. Acid inactivation experiments were performed asdescribed in reference 9 for late-exponential- and stationary-phase cul-tures. Briefly, 10-ml (stationary phase) or 50-ml (late exponential phase)cultures were centrifuged and resuspended in 1 ml of PPS, and this cellsuspension was added to 9 ml of BHI set to pH 2.5 with 10 M HCl,prewarmed at 37°C. The tube was placed in a shaking water bath (160rpm) at 37°C, and samples were taken at appropriate time intervals, di-rectly diluted in BHI broth, and spiral plated on BHI agar. Inactivation

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kinetics were described as was done for the heat inactivation data de-scribed above by equations 9 to 12.

DNA extraction and reverse transcription (RT)-PCR quantification.DNA of the WT and variant 14 or mixtures of them was extracted fromcell cultures by the Qiagen DNeasy blood and tissue kit, using the pre-treatment protocol for Gram-positive bacteria with some modifications.Lysozyme and proteinase K incubations were done for 60 min, and wash-ing steps were repeated twice. Elution was done in 50 �l of 10 mM Tris-HCl (pH 8.3), and the eluate was diluted 10 times in nuclease-free water.DNA was stored at 4°C for up to 5 days until PCR quantification. Primerswere designed in the rpsU region to specifically amplify only the WT oronly the variant DNA. The WT-specific primers (forward [FW], 5=-CGCGCTTTCTGGATTCTTGC-3=; reverse [RV], 5=-ACGAATCGCTTGAAGATGCTC-3=) were designed within the rpsU gene, since variant 14 lacksthis gene completely. For variant 14-specific primers (FW, 5=-CGATGCCCGATGATTAAAA-3=; RV, 5=-GCGTCAACTGCCATAACAAC-3=)were designed in such a way that the FW primer bridged the 1,300-bpdeletion of this variant and therefore this primer could bind only to vari-ant 14 (12). The primers were validated and confirmed to be specific.Quantification was done using a quantitative PCR (qPCR) machine(Bio-Rad CFX96), at an annealing temperature of 60°C using PowerSYBRgreen mastermix (Applied Biosystems). Threshold cycle (CT) valueswere determined with automatic baseline settings. Standard curves wereobtained from a series of decimally diluted DNA to determine PCR effi-ciency of the primers and from DNA extractions from a series of decimallydiluted overnight cultures. The highest concentration was plated and astandard curve, correlating log10 CFU/milliliter to CT values, was ob-tained in this way. This standard curve was used to quantify the viable cellsin mixtures of the WT and variant 14. The dynamic range of quantifica-tion was determined to be �4.5 to 9.5 log10 CFU/ml.

Growth validations. Growth predictions were validated for the WTand variant 14 in BHI for 3 conditions: 7°C, pH 6.6, and aw of 0.997,mimicking milk (BHI-M); 7°C, pH 6.0, and aw of 0.965, mimicking ham(BHI-H); and 37°C, pH 5.2, and aw of 0.997 (BHI-S). BHI-S was chosen,as it provides conditions under which, based on Fig. 1, growth is expectedto be similar for the WT and variant 14. Also, these are conditions whichcan be encountered in the body. Milk and ham conditions were takenfrom the work of Aryani et al. (21). BHI was prepared, and the aw was setby adding NaCl before autoclaving. The pH was set after autoclaving, andthe medium was filter sterilized using a 0.22-�m filter. Validations weredone in Erlenmeyer flasks in a shaking incubator (200 rpm) set at thecorrect temperature. Overnight cultures (cultured in BHI at 30°C) werediluted in the corresponding medium and inoculated in the Erlenmeyerflasks with a starting concentration of �4 log10 CFU/ml, as this was justbelow the detection limit of the PCR quantification method. This wasdone for the WT and variant 14 in single cultures and for the WT andvariant 14 mixed in equal amounts. For BHI-M and BHI-H, samples weretaken once per day, and for BHI-S, this was done every 2 h. Samples weredecimally diluted in PPS and appropriate dilutions were plated on BHIagar. For the mixed cultures, an additional 1-ml sample was taken at eachtime point and centrifuged for 10 min at 5,000 � g, and the pellet wasfrozen at �20°C until DNA extraction and PCR quantification of the WTand variant 14 as described above. Validations were done in independentduplicates. Model performance was evaluated by determining the accu-racy factors (Af) and bias factors (Bf) as introduced by Ross (32). Althoughoriginally developed to assess the performance of models predicting gen-eration times, in this study we used Af and Bf to evaluate predicted countsagainst observed counts as done previously (33–35):

Af � 10log10�log10�Nt�predicted ⁄ log10�Nt�observed� ⁄n (15)

Bf � 10log10�log10�Nt�predicted ⁄ log10�Nt�observed� ⁄n (16)

Bias factors of �1 are caused by predicted values higher than theobserved values, and bias factors of �1 are caused by predicted valueslower than the observed values (32). In the case of evaluating predictedlog10(Nt) against measured log10(Nt), bias factors of �1 give a fail-dan-

gerous prediction. Af and Bf were calculated on the average growth pre-diction (�max � � � 2 and log10Nmax � 9.5).

Chain analysis. The behavior of the WT and variant 14 was also eval-uated in a chain of growth and inactivation conditions. The principle wasto simulate a milk pasteurization chain, followed by cooled storage andlow pH exposure, simulating stomach passage, adjusted in such a way thatthe complete chain could be validated under laboratory conditions insingle and mixed cultures, taking into account the detection limitations.The chain therefore consisted of the following steps: growth at 7°C for 4days (step 1), a heat inactivation step of 10 s at 61°C (step 2), growth at 7°Cfor 3 days (step 3), growth at 10°C for 4 days (step 4), and an acid inacti-vation step of 4 min at pH 2.5 (step 5). Predictions for growth were madeusing the gamma model, based on the estimated cardinal growth param-eters of the WT and variant 14 in Table 1. Three scenarios were chosen,namely, no lag time, a theoretical maximum lag time (�max � � � 4), andan average lag time (�max � � � 2).

Predictions for inactivation were made using the D and z values andinactivation kinetics as described in Table 2. Only late-exponential-phaseheat resistance was considered, since the predictions indicated all cells tobe still in the moment of heat inactivation. For the acid inactivation step,both late exponential and stationary phases were included in the modelprediction (Table 3). Growth steps (1, 3, and 4) were all performed inErlenmeyer flasks containing 50 ml of BHI-M in a shaking incubator (200rpm), set at the correct temperature. Samples were taken once per day forplating and RT-PCR quantification as described above.

From step 3 on (after heat inactivation), the samples for DNA extrac-tion were treated with propidium monoazide (PMA) before freezing toprevent amplification of DNA of dead cells. PMA treatment was done asdescribed by Pan and Breidt (36). Briefly, 2.5 �l of 20 mM PMA solutionwas added to 1 ml of cell culture. This mixture was incubated in the darkat room temperature for 5 min. Subsequently, the tubes were exposed tolight in a PMA-Lite light-emitting diode (LED) photolysis device (Bi-

0.0

0.4

0.8

1.2

0.92 0.94 0.96 0.98 1.000.0

0.4

0.8

1.2

0.92 0.94 0.96 0.98 1.00

0.0

0.5

1.0

1.5

0 20 400.0

0.5

1.0

1.5

0 20 40

0.0

0.4

0.8

1.2

4 6 80.0

0.4

0.8

1.2

4 6 8

Temperature (°C) Temperature (°C)

pH pH

aw aw

μ max

(h-1

)√μ

max

(h-1

/2)

μ max

(h-1

)

BA

DC

FE

FIG 1 Maximum specific growth rate (per hour) of WT (A, C, and E) andacid-resistant variant 14 (B, D, and F) under different temperature (A and B),pH (C and D), and aw (E and F) conditions in BHI (reference conditions: 30°C,pH 7.3, aw of 0.997). Cardinal growth parameters were estimated with thesecondary growth models in equations 1 to 3. Dashed line, WT; solid line,variant 14.

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otium) for 15 min to cross-link the PMA to the DNA. The PMA treatmentwas repeated another time since it was shown that double PMA treatmentgave optimal inhibition of the PCR amplification (36). After the secondPMA treatment, the cells were centrifuged for 10 min at 5,000 � g and thepellet was stored at �20°C until DNA extraction. Heat inactivation wasdone as follows. The complete culture (50 ml) was centrifuged (5 min at2,880 � g), resuspended in 1 ml of BHI-M, and centrifuged again (5 minat 2,880 � g). The pellet was resuspended in 100 �l of BHI-M and trans-ferred into a 200-�l PCR tube. The heat inactivation was done in a PCRmachine set at 61°C for 10 s, after which the sample was cooled to 7°C.When the tubes reached 7°C, the content was transferred to 50 ml of BHIand precooled to 7°C, a sample was taken for plating, and the flask wasplaced in a 7°C shaking incubator (step 3).

Acid inactivation (step 5) was done as for the acid inactivation exper-iments described above. Samples were taken after 2 min and 4 min ofexposure to pH 2.5 and corrected for volume. Validations were done inindependent duplicates. The limitations for this method were that thecounts could be quantified only within the dynamic range of the qPCR(�4.5 to 9.5 log10 CFU/ml) and the PMA treatment only allowed a max-imum of 6 log10 CFU/ml of dead cells to be present within at least 4 log10

CFU/ml of viable cells (36). These limits were experimentally confirmed(data not shown). Model performance for each step and the overall chainwas evaluated by determining the accuracy factors (Af) and bias factors(Bf) as described above.

Variant fractions within WT population. The heat and acid inactiva-tion kinetics of the WT and variant 14 were used to calculate the theoret-ical fraction of rpsU variants within the WT population during stressexposure. This was done as described by Van Boeijen et al. (11). Thefraction of rpsU variants was then calculated at each time point (t) usingequation 17:

ft, rpsU �Nt, rpsU

Nt, total(17)

The fraction (ft, rpsU) is equal to the probability of isolation of an rpsUvariant at this time point. Due to their phenotypic clustering (12), it wasassumed that the 11 rpsU variants all show the same inactivation kinetics.The initial fraction of rpsU variants in the first step of the chain wasassumed to be 5 � 10�7 (37).

RESULTSGrowth under mild stress conditions. Cardinal growth parame-ters were estimated based on the �max values obtained at differenttemperatures, pH values, and water activity values. The data andmodel fittings are shown in Fig. 1 for the WT and variant 14 andfor the other variants in Fig. S1 in the supplemental material.From these figures and the parameter estimates in Table 1, it canbe seen that the different variants showed distinct behavior underdifferent environmental conditions. The rpsU variants (14, 15,and 23) showed a reduced growth rate, which was more pro-nounced closer to the lower temperature growth limits, whereasthe same variants have growth rates similar to that of the WT at thelower limits of growth for pH and aw at 30°C. This resulted insignificantly higher Tmin estimates for the rpsU variants than forthe WT (Table 1), indicating that these variants are less psychro-tolerant. Variants 9, 12, and 13, on the other hand, showed a lower�max over the complete temperature range tested, with the mostdramatic shift observed for variant 9. However, this variant, whilegrowing much slower under optimal pH conditions, had a pHmin

similar to that of the WT and an even lower minimal estimated aw,

min than the WT. For all variants, the shape parameter (d) in the aw

model was not significant and could be excluded according to thelack-of-fit test. Variant 9 was the only variant for which the shapeparameter could not be excluded, since this would have led to the

TA

BLE

1E

stimated

cardinalgrow

thparam

etersfor

WT

L.monocytogenes

and

eight

acid-resistant

variants

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perature,pH

,and

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ined

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ations

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Water

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)b

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pt (h

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�4.05

(�7.48,�

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(4.50,4.71)5.13

(4.94,5.32)0.95

(0.82,1.07)0.928

(0.921,0.935)0.97

(0.89,1.06)N

SV

ariant

3�

3.83(�

6.76,�0.89)

0.027(0.024,0.029)

4.61(4.55,4.67)

5.09(4.99,5.20)

0.92(0.85,0.99)

0.924(0.916,0.932)

0.96(0.87,1.05)

NS

Varian

t7

�2.77

(�4.28,�

1.25)0.026

(0.025,0.028)4.63

(4.57,4.69)4.97

(4.90,5.05)0.81

(0.75,0.87)0.920

(0.910,0.930)0.84

(0.75,0.93)N

SV

ariant

92.08

(0.26,3.91)0.025

(0.023,0.026)4.58

(4.39,4.77)4.86

(4.70,5.02)0.44

(0.35,0.52)0.921

(0.894,0.948)0.49

(0.41,0.57)2.14

(0.14,4.15)V

ariant

12�

3.29(�

4.96,�1.61)

0.024(0.023,0.025)

4.63(4.56,4.70)

4.91(4.83,4.99)

0.64(0.58,0.69)

0.922(0.907,0.936)

0.65(0.56,0.74)

NS

Varian

t13

�3.15

(�6.46,0.15)

0.023(0.021,0.026)

4.66(4.61,4.71)

4.94(4.86,5.02)

0.68(0.62,0.74)

0.937(0.931,0.943)

0.70(0.64,0.77)

NS

Varian

t14

1.59(�

0.30,3.49)0.028

(0.026,0.031)4.65

(4.58,4.72)4.91

(4.81,5.00)0.66

(0.59,0.73)0.930

(0.920,0.940)0.66

(0.57,0.75)N

SV

ariant

150.31

(�1.10,1.72)

0.027(0.025,0.028)

4.66(4.59,4.72)

4.95(4.85,5.04)

0.66(0.60,0.73)

0.933(0.927,0.939)

0.67(0.61,0.73)

NS

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t23

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(0.027,0.029)4.65

(4.59,4.72)4.95

(4.84,5.06)0.69

(0.61,0.77)0.932

(0.923,0.942)0.70

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ifican

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1,with

confi

rmation

bylack-of-fi

ttest

that

the

parameter

could

berem

oved.

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unrealistic aw, min estimate of �0.88. It was experimentally con-firmed that variant 9 was not able to grow at such a low aw, andtherefore, the d parameter was included, despite not being signif-icant. Variant 3 showed behavior similar to that of the WT underall growth conditions tested. Variant 7 had a slightly reducedgrowth rate under optimal conditions compared to that of theWT, but its growth rate became similar to that of the WT when thepH and aw conditions were more stressful.

Growth predictions and validations. The cardinal growth pa-rameters were used to predict the growth of the WT and eightvariants under combinations of mild stresses. From Fig. S2 in thesupplemental material, it can be seen that depending on the com-bination of environmental conditions, the variants performeddifferently. Under the milk conditions (see Fig. S2A), the rpsUvariants and variant 9 were the slowest growers, with the lowtemperature contributing mostly to the gamma factor. Under theham condition, the temperature is still the most growth limitingfactor; however, the low aw reduced the growth rate even further in

all cases. The gamma factor for pH (pH 6.0) had almost no influ-ence on the predicted growth rate of the variants. Figure S2Cshows that when grown at 37°C and pH 5.2, there is almost nodifference in �max between the variants and WT. This is due to thefact that the pH is the growth-limiting factor, and at pH 5.2 thereis no dramatic difference in predicted �max between the WT andvariants. The predictions of the three growth scenarios displayedin Fig. S2 were experimentally evaluated both in single and inmixed cultures of the WT and variant 14. As can be seen from Fig.2A, the counts in single and mixed cultures for the WT in BHI-Mwere well in accordance with the predictions in BHI-M, which wasconfirmed by a Bf of 1.02. Variant 14, however, showed a slightlyhigher �max than predicted, resulting in a relatively low Bf, 0.80,and a high Af, 1.25, indicating a systematic deviation from theprediction. Both the variant and WT did not seem to have anobvious lag time. In mixed cultures of the WT and variant, the WTPCR counts were similar to the total plate counts, indicating thatthe WT was the dominating population. Variant 14 followed thesame growth as in single culture up to �150 h, after which growthwas arrested. This growth inhibition coincides with the entry intostationary phase of the WT. In BHI-H, both the WT and variantcounts matched the prediction well in single cultures (Fig. 2B) andBfs were 1.04 and 0.94, respectively. Interestingly, the growth ofthe WT matched the prediction with the maximum lag time,whereas the variant did not seem to have a lag time at all. Anotherinteresting observation is that when mixed with the WT, variant14 seemed to perform better than when cultured alone, as indi-cated by higher counts in mixed cultures than in single cultures. InBHI-S cultures, the predictions suggested the variant and WT togrow at similar speeds (Fig. 2C1 and 2C2). This was confirmed bythe growth validations both in single and in mixed cultures, al-though both grew slower than predicted. Both the WT and variantseemed to have a lag phase, most likely caused by the transitionfrom pH 7.3 of the overnight culture to pH 5.2 of the BHI-S. Biasfactors of 1.11 for the WT and 1.18 for the variant also indicatedthat both predictions are slight overestimations.

Stress resistance. Heat resistance was evaluated in late expo-nential and stationary phases for the WT and variant 14 at 55, 60,and 62°C. As can be seen from Fig. 3, the inactivation curvatureswere different depending on the temperature and growth phasetested. This resulted in different inactivation models giving thebest fit, making comparison and especially the calculation of Dand z values difficult. Because the major part of the reduction

TABLE 2 Inactivation parameter estimates D and upon heat exposure by fitting the reparametrized 5D-Weibull model to the data without takingthe tail into considerationa

Strain Parameter

Value for:

Late exponential phase Stationary phase

55°C 60°C 62°C 55°C 60°C 62°C

WT D 1.92 (1.73, 2.15) 0.28 (0.24, 0.33) 0.11 (0.08, 0.17) 24.0 (21.4, 27.3) 1.17 (1.04, 1.33) 0.71 (0.63, 0.79) NA NA NA NA NA 1.59 (0.98, 2.21)

Variant 14 D 15.7 (14.6, 16.9) 0.65 (0.63, 0.68) 0.32 (0.28, 0.39) 29.9 (28.8, 30.9) 2.70 (2.42, 3.05) 1.97 (1.92, 2.02) 2.06 (1.49, 2.63) 1.73 (1.45, 2.00) NA 2.43 (1.96, 2.90) NA 1.46 (1.35, 1.58)

a For the Weibull model, the values for D (in minutes) were obtained by dividing t5D by 5. The linear model was used when the shape parameter was not significantly different from1, the F-test confirmed a statistically acceptable fit of the linear model, and the lack-of-fit test confirmed that the shape parameter could be removed. In all other cases, the Weibullmodel was used. NA, the linear model was fitted and therefore an estimate for was not applicable. The 95% confidence intervals of the parameter estimates are indicated inparentheses.

TABLE 3 Inactivation parameter estimates of WT LO28 and variant 14upon exposure to BHI set to pH 2.5 by 10 M HCl at 37°C in lateexponential or stationary phase by fitting the biphasic model withshoulder or linear model to the data

Strain Parameter

Value forc:

Late exponential phase Stationary phase

WTa log10 N0

(log10 CFU/ml)9.8 (9.4, 10.3) 9.5 (9.1, 10.0)

ksens (min�1) 4.98 (2.66, 7.30) 0.81 (0.64, 0.98)kres (min�1) 0.73 (0.25, 1.21) 0.13 (�0.03, 0.29)Shoulder (min) 1.7 (1.0, 2.4) 4.8 (2.2, 7.4)Resistant fraction 10�4.72

(10�5.92, 10�3.52)10�5.22

(10�7.22, 10�3.22)

Variant 14 log10 N0

(log10 CFU/ml)9.6 (9.1, 10.1) 10.2 (9.7, 10.6)

ksens (min�1)b 1.66 (0.35, 2.97) 0.27 (0.25, 0.31)kres (min�1) 0.43 (0.12, 0.74)Shoulder (min) 5.2 (3.0, 7.4)Resistant fraction 10�2.46

(10�4.10, 10�0.82)a Data for the WT in late exponential phase were taken from Metselaar et al. (9).b ksens for variant 14 in late exponential phase; for stationary-phase cells, variant 14 hasonly one k value.c The 95% confidence intervals of the parameter estimates are indicated in parentheses.

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range is most important for the validation experiments, it wasdecided to also fit an inactivation model to the data without con-sidering the tail. Either the 5D-Weibull model (equation 13) or thelinear inactivation model (equation 11) could be fitted to all theinactivation curves, allowing for D-value estimation based onthe major part of the reduction range (Table 2). Corresponding zvalues were 5.7 and 4.0 for the WT and variant, respectively, in lateexponential phase and 4.4 and 5.7 for the WT and variant, respec-tively, in stationary phase. Both fits, with and without tail, can beseen in Fig. 3. Whereas in late exponential phase the difference inheat resistance between the WT and variants became smaller withhigher temperatures, the difference between the WT and variantwas smaller at lower temperatures in stationary phase. This wasalso reflected by a higher z value in stationary phase for the variantthan for the WT and a higher z value for the WT in late exponential

phase. Also, for acid inactivation (Fig. 4) there was a clear differ-ence between the WT and variant 14, as well as a clear differencebetween the late exponential and stationary phases. In both thelate exponential and stationary phases, the increased resistance ofthe variant was characterized by a longer shoulder period and alower inactivation rate (Table 3).

Probability predictions. The inactivation kinetics were usedto estimate the fraction of the rpsU variant within the WTpopulation at any given time during stress exposure. The prob-ability of isolating an rpsU variant under different stress con-ditions was evaluated. To do so, the inactivation kinetics dis-played in Fig. 3 and 4 were used. The initial rpsU variantfraction in an exponentially growing culture was determined asdescribed by Van Boeijen et al. (11) and estimated to be �5 � 10�7

(37). Two different scenarios are shown in Fig. 5. Figure 5A shows the

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FIG 2 Growth predictions and validations for WT L. monocytogenes LO28 (black diamonds) and acid-resistant variant 14 (gray squares). Growth predictionsaccording to the three-phase linear model were based on cardinal growth parameters as shown in Table 1 and the gamma model. Three scenarios were considered:milk (BHI-M; pH 6.6, aw of 0.997, and 7°C) (A), ham (BHI-H; pH 6.0, aw of 0.965, and 7°C) (B), and BHI at pH 5.2 and 37°C (BHI-S) (C). For each scenario twosituations were considered, namely, no lag phase (upper line) and a maximum lag phase (� � � � 4) (lower line). Validations were done by plate counts in singlecultures (1) and mixed cultures (2). For the mixed cultures, total plate counts (circles) are displayed by the open symbols, and individual contributions of WTand variant 14 in the mixture were deducted from CT values and the standard curves correlating CT values to log CFU/ml counts (closed symbols). Modelperformance was evaluated by calculating Af and Bf for the WT and variant 14 based on an average lag time (� � �) of 2. This resulted in the following Af and Bf:for panel A1, 1.05 and 1.02 for the WT and 1.25 and 0.80 for the variant; for panel B1, 1.05 and 1.04 for the WT and 1.07 and 0.94 for the variant; and for panelC1, 1.11 and 1.11 for the WT and 1.18 and 1.18 for the variant.

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probability that a heat treatment of 55°C would have resulted inisolation of an rpsU variant. This probability increases over timeand reaches a maximum of �11% after 30 min. At this time point,however, the total population is already quite small, around 100CFU/ml. However, if higher initial cell numbers were present, a

significant number of cells would still be present after 30 min.Exposure to pH 2.5 (Fig. 5B) led to a different distribution, and itcan be seen that the predicted probability of isolating variants atpH 2.5 had a peak distribution. These data indicate that the prob-ability of isolating a specific variant highly depends on the inacti-vation kinetics of both the variant and WT, the specific processconditions, and the initial variant fraction within the WT popula-tion.

Chain analysis and validation. The growth and inactivationdata were combined to make predictions about the behavior of theWT and variant 14 along a simulated model food chain. Due totechnical limitations of the experimental setup, the different pro-cessing steps were adjusted according to the detection limitations.After each step in the chain, the predicted N0 was adjusted to themeasured N0 for visualization purposes. From Fig. 6 it can be seenthat generally higher growth rates and higher inactivation rateswere predicted for the WT than for variant 14. In the first growthstep, the WT data match very well with the prediction, resulting ina Bf of 1.00. The numbers for the variant, however, are higher thanpredicted, which leads to a Bf of 0.85 in the first step. This is mostlydue to the predicted lag time, which is not apparent. In Fig. S4 inthe supplemental material, the prediction without lag time is alsoconsidered, and it can be seen that in this case also the variantcounts are in accordance with the prediction. The first heat inac-tivation step gave a much higher inactivation than predicted forthe WT. Also, the subsequent predicted lag time (� � � � 4) didnot seem sufficiently long, as both the WT and variant 14 neededa longer recovery time to resume growth after the heat treatment.The acid inactivation step gave a larger reduction in viable num-bers than predicted, especially for the WT but also for the variant.Overall, the general trend of better growth for the WT and higherstress resistance for the variant was clearly confirmed along thismodel food chain, although the plate counts did not match thepredictions very well for every step along the chain model. Thebias factors indicated a better overall fit for variant 14 than forthe WT (Table 4). In the mixed culture (Fig. 6C), the trend was

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FIG 3 Heat inactivation kinetics of WT L. monocytogenes LO28 (black) and acid-resistant variant 14 (gray) in BHI in late exponential phase (A to C) andstationary phase (D to F) at 55°C (A and D), 60°C (B and E), and 62°C (C and F). Biphasic, linear, or Weibull models were fitted to the complete inactivation data(solid line) depending on the best-fitting model. For those curves where the biphasic model had the best-fitting performance, also the reparameterized Weibullmodel or the linear inactivation model was fitted to the sensitive fraction only (dashed line).

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FIG 4 Acid inactivation kinetics of WT L. monocytogenes LO28 (black) andacid-resistant variant 14 (gray) in BHI set at pH 2.5 by 10 M HCl in lateexponential phase (A) and stationary phase (B) at 37°C. A biphasic, linearmodel with a shoulder or linear model has been fitted to the inactivation data(solid line) depending on the best-fitting model.

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generally the same as in single cultures, but some differences wereobserved. Due to the technical limitations of the qPCR quantifi-cation and PMA method, the counts for WT and variant could beobtained only when plate counts were higher than 6 log10 CFU/mlafter heat treatment. Despite this limitation, faster growth for theWT than for variant 14 could be confirmed. When the cells startedgrowing again after the heat treatment, the WT in the mixed cul-ture reached higher numbers than the WT in single culture. Thisindicated that either the WT was still present in higher numbersafter the heat treatment in the mixed culture than in the singleculture or the WT cells grew faster in the mixed culture than in thesingle culture. At the end of the “single culture” chain, more cellswere present for variant 14 than for the WT. At the end of thechain in the mixed culture, there was a significant amount of cellsleft and the reduction was similar to the reduction observed forvariant 14. However, the amount of dead cells in the culture wastoo high (�6 log10 CFU/ml) to confirm that the surviving cellswere either the WT or variant 14, as the PMA method does notcorrectly distinguish dead cells from living cells when more than 6log10 CFU/ml of dead cells are present.

DISCUSSION

This study aimed to quantify the behavior of WT L. monocytogenesand acid-resistant variants under different environmental condi-tions in order to get more insight into the potential behavior ofthese variants in a food chain and during stomach passage. The

obtained set of fitness and robustness parameters (�opt, Tmin,pHmin, aw,min, heat inactivation, and acid inactivation) providedmore insight into the behavior of the different variants and high-lighted the diversity within the L. monocytogenes population. This

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FIG 5 Probability of isolating rpsU variants upon heat and acid inactivation oflate-exponential-phase cells at 55°C (A) and pH 2.5 (B). The initial fraction ofrpsU variants within a late-exponential-phase culture was estimated to be5.2 � 10�7 (37). This fraction, combined with the inactivation kinetics of theWT (black line) and rpsU variant 14 (gray line), was used to determine the rpsUvariant fraction (dashed line) at each time point during the inactivation curveaccording to the method of Van Boeijen et al. (11).

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7 °C7 °C4 days4 days

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pH 2.5pH 2.54 min4 min

A

B

C

FIG 6 Performance of the WT (black) and variant 14 (gray) along a model foodchain. The chain was simulated in BHI-M (pH 6.6). Growth and inactivationbehavior was predicted (solid lines) based on growth and inactivation kinetics asshown in Tables 1 to 3 and Fig. 1, 3, and 4. Predictions were validated in BHI set topH 6.6 by 10 M HCl, simulating milk characteristics. In the first growth step anaverage lag time (� � �) of 2 was chosen, and in the growth step after heat treat-ment a maximum lag time of 4 was chosen. Stress resistance predictions werebased on late-exponential-phase cells, as stationary phase was not reached before.After each step in the chain, the predicted N0 was adjusted to the measured N0 (forvisualization purposes). Validations were done in single cultures (WT [A] andvariant 14 [B]) and in mixed cultures (C). Open symbols represent the plate countsand closed symbols the individual contributions of the WT (black) and variant 14(gray) in the mixture as deducted from CT values and the standard curves corre-lating CT values to log CFU per milliliter.

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diversity was already established qualitatively by Metselaar et al.(12), but the current set of parameters provided quantitative dataon this behavior, which were subsequently used for prediction ofpopulation dynamics under different environmental conditions.Predictions based on cardinal growth parameters and the gammamodel confirmed the disadvantage variant 14 has under mostgrowth conditions but also indicated that there are combinationsof mild stress conditions where the growth rates of the variant andthe WT were rather similar. The gamma model allowed for pre-diction of growth under combined mild stress conditions, assum-ing no interaction between the different growth-limiting factors(38). The gamma theory is, however, not always pertinent, and itsapplicability seems to depend on the organism, as well as on thecombination of mild stress factors (27, 39, 40). Especially aroundthe growth boundaries, the gamma model has shown poor agree-ment with experimental observations when no synergy factor wasincluded (41). However, for L. monocytogenes, among other or-ganisms, it was shown that further away from the growth bound-aries, the gamma model without synergy generally performs wellto describe the combined effect of water activity, pH, and temper-ature on growth (42).

Also, from the growth validations in Fig. 2, the gamma theorywithout synergy seems to be valid since the prediction describedthose data generally well. In BHI-M, the variant even grew fasterthan predicted (Fig. 2B). A possible explanation for this deviationfrom the model could be that the variant has a slightly lower pHopt

than the WT, which can be observed in Fig. S1B in the supplemen-tal material. pH 7.3 was considered for the WT and all variants,and a lower pHopt can lead to underestimation of the growth ratearound the actual pHopt. A possibility is that only the mean cardi-nal parameter estimates were included in the prediction. Whenthe lower and upper 95% confidence intervals of the cardinal pa-rameter estimates were taken into account, the data points fellwithin the prediction (see Fig. S3 in the supplemental material).Including this experimental and biological variability, as well asbest- and worst-case scenarios for the lag time duration, resultedin a very wide prediction interval, but using the upper 95% limitwith no lag time, the prediction can be considered fail-safe. Thegrowth rate at 37°C at pH 5.2 was lower than predicted for boththe WT and variant, and even when taking the 95% confidenceinterval into account, the counts were on the lower limit of theprediction. This could be due to the fact that the pH of 5.2, which

is the most growth-limiting factor in this scenario, is in the steeppart of the curvature of the cardinal pH model (Fig. 1), and accu-rate prediction is therefore more prone to errors. In the mixedcultures, the WT is generally the dominating population. As ex-pected based on the Jameson effect (43, 44), the variant reachedstationary phase as soon as the WT reached stationary phase. Thisis possibly due to nutrient limitation, as pH was still above thegrowth boundary for L. monocytogenes and is therefore less likelyto be the growth-limiting factor. Another interesting observationis that variant 14 performed better in BHI-H when mixed with theWT than in a single culture. This would indicate an interactionbetween the WT and variant in mixed cultures, and this is a com-plicating factor in making accurate predictions of the populationdynamics during growth.

Prediction of microbial behavior in a sequential chain ofgrowth and inactivation conditions remains a challenge in predic-tive microbiology. The use of accuracy and bias factors on countsin log10 CFU per milliliter instead of generation times does notallow for using the criteria for acceptable or unacceptable modelperformance, which are commonly used for generation time val-idations (45). Nonetheless, these performance indices are usefulfor getting a quantitative measure of model performance and forcomparison of performance of different steps along a model foodchain. In this study, the use of predictive modeling, combinedwith a validation method based on the genetic background of therpsU variants, proved to provide valuable information on the pop-ulation dynamics of L. monocytogenes under changing environ-mental conditions, despite the sometimes poor agreement be-tween model predictions and experimental data. Growth phaseand growth history are well-known factors affecting stress resis-tance of bacterial cells. Many researchers have shown the effect ofculturing cells at low temperatures on thermal resistance and thegeneral agreement is that D values decrease with decreasing pre-culturing temperatures (17, 18, 46, 47), which is in accordance toour results. In addition to temperature, other environmental fac-tors, as well as age and growth phase of the culture, have beenshown to affect stress resistance (17, 48). Aryani et al. (49) showedthat the growth phase is the growth history factor affecting theheat resistance to the greatest extent, above different tempera-tures, pH, and salt levels during preculturing. Therefore, we choseto use late-exponential-phase cells as the most “sensitive” case formodel predictions instead of preculturing the cells at 7°C. How-ever, in the chain model experiment, cells were in exponentialphase and grown at a low temperature, which resulted in moreheat-sensitive cells than the prediction for late-exponential-phasecells grown at 30°C. This indicates a multiplicative effect on heatsensitivity of growth at low temperature and late exponentialgrowth phase. Also, the acid inactivation step resulted in a higherreduction than predicted. This is possibly also due to the growth at7°C, as Ivy et al. showed that L. monocytogenes is more sensitive tolow pH when grown at 7°C than at 30 or 37°C, in both exponentialand stationary phases (50). Also, the cells did not seem to be in lateexponential phase yet at the end of step 1 and step 4, which couldalso explain the higher sensitivity toward the inactivation treat-ments.

Another factor that was not taken into account in the model,but seems to be a major factor influencing the performance of themodel, is the recovery time that is needed after the heat inactiva-tion step. Even the maximum theoretical lag phase (i.e., � � � �4) was not sufficient to describe the recovery time after heat treat-

TABLE 4 Bias factors and accuracy factors for the WT and variant 14along a model food chaina

Step

WT Variant 14

Af Bf Af Bf

7°C, 4 days 1.02 1.00 1.18 0.8561°C, 10 s 1.55 1.55 1.07 1.077°C, 3 days 1.20 1.11 1.06 1.0510°C, 4 days 1.35 1.35 1.14 1.14pH 2.5, 2 min 2.94 2.94pH 2.5, 4 min 1.48 1.48

Total 1.28 1.24 1.17 1.04a The chain was simulated in BHI-M (Fig. 6). Validations for each step were done inBHI-M for the WT and variant 14. Bias factors (Bf) and accuracy factors (Af) werecalculated for each step separately and for the complete chain based on dailymeasurements.

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ment, especially for the WT. It has been well documented that heattreatment leads to sublethal damage of cells, and several studieshave shown that lag times can vary widely between individual cellsin a population and that the variability in the lag time of single cellsincreases with severity of treatment (51, 52). Therefore, with lowcell numbers and severe stress treatments, the lag phase can in-crease well above the maximum lag time of (� � � � 4) that wasused in the model chain (53). Also, the recovery conditions play animportant role in the number of viable cells that can be retrievedafter lethal stress treatment (54), and the 7°C BHI-M, which con-stituted the recovery conditions in the model food chain, is notoptimal for the cells. The extended time needed for recovery ismore pronounced for the WT than for the variant, since the lagtime was predicted to be shorter for the WT after heat treatmentthan for the variant, but the validations showed that the recoverytimes were similar for the two types of cells. Like for the growthpredictions, only the mean values of the parameter estimationswere considered in the chain model, as this was sufficient to getmore insight in the behavior along a series of growth and inacti-vation events. When the aim is to make more realistic and fail-safepredictions, the biological and experimental variability, reflectedin the 95% confidence intervals of the cardinal parameter esti-mates, should also be taken into account.

Many factors are known to affect thermal resistance of L.monocytogenes (reviewed in the works of Doyle et al. [17] andAryani et al. [49]) showed that growth history and strain variabil-ity are the most important factors affecting thermal resistance.Growth history also seems to be a cause of the lower heat resis-tance leading to overestimation of the numbers of culturable cellsin the chain model compared to the prediction. Many food prod-ucts, on the other hand, are known to increase heat resistance ofmicroorganisms (48, 55). Evaluating the current chain model inlaboratory medium and to take all the different variability factorsinto account were already challenging; translating such a model toactual food matrices will be even more demanding. Nonetheless,the current chain model gives a good indication of the possiblepopulation dynamics along a food chain.

For experimental reasons, the amount of variant and WT werechosen to be the same in the first step, but the actual rpsU variantfraction in a WT population is very small and was shown to be�5 � 10�7 (37). It should be noted that the fraction of resistantcells is higher (around 10�5) but that not all resistant cells arestably resistant, and not all stably resistant variants are rpsU vari-ants. The probability that an rpsU variant is present in a batch offood product therefore depends not only on the environmentalconditions encountered but also on the initial contamination leveland the batch size. Low contamination levels and small batch sizewill not likely result in selection for stress-resistant variants, sim-ply because the fraction is too low, but in larger batches or withhigher initial concentrations, the probability that resistant vari-ants are present and are selected for becomes pertinent. The vari-ant fraction can also change upon different processing conditions,as illustrated in Fig. 5. On the other hand, small changes in variantfraction and in inactivation kinetics, which are also affected by thegrowth history, can dramatically affect the chances that certainprocessing conditions lead to selection of stably resistant variants.Multiple stress cycles may also affect the fraction of variants in thepopulation. Van Boeijen et al. (11) reported that heat-resistantvariants were not found after a single heat treatment due to the lowprobability of finding them due to their low prevalence, but after a

few cycles, the fraction of heat-resistant variants increased signif-icantly. Also the presence of L. monocytogenes in biofilms wasshown to affect the stress resistance of the cells (19). It can bespeculated that under more stringent heat treatment, the variantcan become the dominating population and, with its slow growth,become a persister in industrial settings. Another important as-pect in assessing the risk of these variants is their virulence poten-tial. Although the virulence was not studied in vivo, the data ob-tained until now did not provide indications that virulence of theresistant strains is attenuated compared to that of the WT. Besideshigher acid resistance, which can enhance efficacy of stomach pas-sage, these variants have higher H2O2 resistance, which may pro-vide increased survival of human host defense (the so-called oxi-dative burst). Additionally, their growth rate at 37°C and in vitrophospholipase and hemolysin activities are similar to those of theWT (12). Previously, virulence of the WT and variants was as-sessed in a mouse infection assay, which showed reduced perfor-mance of some variants, including two ctsR mutants, but all vari-ants remained infective (56). Similar studies with selected rpsUmutants may provide further information on their virulence po-tential.

In the current study, only an rpsU mutant was quantitativelycharacterized in detail, since this was the only variant for which amutation was known that allowed for discrimination from theWT by qPCR. As can be seen from Table 1, the other types ofacid-resistant variants show different behavior and are also knownto display different degrees of resistance (12). All these differentfactors need to be taken into consideration when making realisticpredictions on the population composition of L. monocytogenesand the conditions that can select for stress-resistant variants. Itcan be concluded that the increased stress resistance as observed inthe variants can be considered a trade-off. It seems that resourceallocation was shifted toward stress resistance and away fromrapid multiplication. In the simulated model food chain, the WTclearly has a higher fitness (higher growth rate), while the rpsUvariant is more robust toward stress. On the other hand, there arecombinations of mild stress conditions allowing for equal growthof the WT and variant. The combination and sequence of envi-ronmental conditions encountered by the population determinethe composition of the mixed population and can result in a netoutcome of similar population level. Translation to actual foodmatrices and inclusion of more factors, like multiplicative effectsof history on stress resistance and the effect of recovery conditionson stress survival, would be the next challenging step in makingmore realistic predictions on the effect of stress resistant variantson population composition in food products and processing en-vironments. The current data illustrate the effect that environ-mental factors can have on population dynamics of L. monocyto-genes and are a first step in evaluating the potential impact ofpopulation diversity on food safety.

ACKNOWLEDGMENT

We thank Myriam Krieg for her contributions to method optimization.

FUNDING INFORMATIONThe research is funded by TI Food and Nutrition, a public-private part-nership on precompetitive research in food and nutrition. The fundershad no role in study design, data collection and analysis, decision to pub-lish, or preparation of the manuscript.

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