Influence of Stress on Individual Lag Time Distributions of Listeria monocytogenes

The effects of nine common food industry stresses on the timesto the turbidity (T_d) distribution of Listeria monocytogeneswere determined. It was established that the main source ofthe variability of T_d for stressed cells was the variabilityof individual lag times. The distributions of T_d revealed thatthere was a noticeable difference in response to the stressesencountered by the L. monocytogenes cells. The applied stressesled to significant changes of the shape, the mean, and the varianceof the distributions. The variance of T_d of wells inoculatedwith single cells issued from a culture in the exponential growthphase was multiplied by at least 6 and up to 355 for wells inoculatedwith stressed cells. These results suggest stress-induced variabilitymay be important in determining the reliability of predictivemicrobiological models.

INTRODUCTION

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Introduction

Listeria monocytogenes has been recognized as an important food-bornepathogen that causes listeriosis. Outbreaks of listeriosis havebeen associated with milk, cheese, vegetables and salads, andmeat products. The organism is particularly problematic forthe food industry because it is widespread in the environment(17) and because of its ability to grow within a wide rangeof temperatures (–1.5 to 45°C), pH values (4.39 to9.4), and osmotic pressures (NaCl concentrations up to 10%).

So, extensive research was carried out on predictive modelsdescribing the behavior of this pathogen in foods. Today, themodels describing the environment effect on growth rate of L.monocytogenes are sufficiently accurate to be used by manufacturers,regulators, and scientists to assess microbial risks associatedwith the consumption of foods or to evaluate the relevance ofrisk management options (1, 2). On the other hand, the modelsdescribing the lag time must be improved to make the predictionmore reliable (22, 29).

Some secondary models have been published to describe the influenceof the environment on the bacterial lag time (5, 14, 41). Manyreviews and discussions concerning their applicability havebeen published (28, 32, 35, 38). But the prediction of the lagtime in foods still seems difficult to obtain and it is necessaryto improve predictions (20, 37). As natural contaminations offoods occur with very few cells which are occasionally stressedby the food processing and the industry environment, it is essentialto improve models by taking into account injuries encounteredby the cells before they contaminate the foods and by usinga stochastic approach dealing with the variability of the individualbehavior of microbial cells. Models have been developed to takethe effect of injuries on the bacterial lag times into account(11, 12, 39). Similarly, the individual response was also tackledby some authors such as Baranyi (6), who showed the relationshipbetween the individual lag time distributions and the lag timeof the bacterial population. Recently, some individual lag timedistributions have been characterized (23, 33). The variabilityof individual lag times seems to be wider as microorganismsare injured (4, 33, 34, 39) or as growth conditions are unfavorable(23, 24, 27).

The aim of this study was to investigate and to compare theimpacts of nine stresses usually met in the food industry onthe distributions of individual lag times of L. monocytogenes.For this, the distributions of times to the turbidity (T_d) ofmicroplate wells inoculated with single L. monocytogenes cellspreviously subjected to stress were characterized in optimalgrowth conditions.

MATERIALS AND METHODS

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Materials and Methods

Strains and culture conditions.
L. monocytogenes 14 (serotype 4b, industrial environment origin)was maintained at –25°C in 50% glycerol. The strain14 is a reference strain of the French program in predictivemicrobiology Sym'Previus. Prior to each experiment, a culturewas incubated at 30°C for 24 h in tryptone soy broth (Oxoid,Unipath Ltd., Basingstoke, United Kingdom) supplemented with0.6% yeast extract (AES Laboratoire, Combourg, France) (TSBye).The first bacterial culture was diluted as needed to obtainan initial bacterial suspension of approximately 10³ cells ml^–1in TSBye. That initial bacterial concentration was further incubatedin TSBye for 20 h at 25°C to obtain 10⁸ cells ml^–1in the exponential growth phase.

Stress experiments.
Nine different stresses were applied on cultures in the exponentialgrowth phase. First, before each stress, once TSBye had beeneliminated by centrifugation (5,000 x g, 10 min, 4°C), L.monocytogenes cells were washed in 0.85% of NaCl (Prolabo, Paris,France) (diluent) at 25°C, pH 7, and centrifuged again (5,000x g, 10 min, 4°C). Centrifugation did not have any influenceon the individual lag time distribution of L. monocytogenescells in the exponential growth phase (data not shown); thisstage did not modify the physiological state of the cells. Secondly,the supernatant was eliminated and cells were recovered in thefollowing conditions: (i) for mineral acid stress, in diluentat 25°C adjusted to pH 3 with HCl (Prolabo) for 34 min;(ii) for organic acid stress, in diluent at 25°C adjustedto pH 4.6 with lactic acid (Prolabo) for 48 h; (iii) for alkalistress, in diluent at 25°C adjusted to pH 12 with NaOH (Prolabo)for 22 min; (iv) for the first disinfectant stress, in diluentat 25°C supplemented with 4 mg liter^–1 of benzalkoniumchloride (BAC) (Fluka, Buchs, Switzerland) for 13 min; (v) forthe second one, in diluent at 25°C supplemented with chlorineat 2.4 ppm for 1.5 min; (vi) for cold stress, in diluent dispatchedin 1-ml aliquots directly placed at –25°C for 48 h;(vii) for heat stress, in diluent then diluted (1:100) in physiologicwater at 55°C for 3 min; (viii) for osmotic stress, in pH7 salt solution at 25% (wt/vol) at 25°C for 25 h; and (ix)for starvation stress, a second washing was realized in diluentto ensure the complete elimination of nutrient and the cellswere recovered in diluent at 30°C for 24 h. The time ofexposure to each stress was the necessary time to obtain a 1.5log₁₀ CFU ml^–1 loss by enumeration on tryptone soy agar(Oxoid, Unipath Ltd., Basingstoke, United Kingdom) supplementedwith yeast extract at 0.6 g liter^–1 (AES Laboratoire)(TSAye). The loss of 1.5 log₁₀ CFU ml^–1 was chosen becauseof the shape of the inactivation curve observed for the starvationstress. For this stress, a more significant loss would havebeen more difficult to achieve. This loss of cultivability alsopresented the advantage of being significantly higher than theerror of the viable count enumeration method.

Bioscreen growth experiments.
Turbidity growth curves were generated with an automatic BioscreenC (Labsystem France SA, Les Ulis, France) reader. From L. monocytogenescells in the exponential growth phase and stressed cells, serialdilutions were made in tryptone salt (Oxoid) broth in orderto reach in the final dilution a maximum concentration of 1.4cells ml^–1 in TSBye preheated at 30°C. Wells of twoBioscreen plates were inoculated with 300 µl of this suspensionto obtain a target value of 0.42 cells well^–1, increasingthe probability of having one cell in wells showing growth.Assuming a Poisson distribution of the cells in the wells (18),the maximum concentration of 0.42 cells well^–1 correspondsto a maximum of 35% of wells showing growth and allowed us tosay that less than 20% of these wells contained more than onecell. Then the plates were placed in the Bioscreen C readerat the incubation temperature of 30°C. The increase in turbiditywas monitored at 600 nm (optical density [OD]). Measurementswere taken every 10 min, and the plates were shaken at the mediumintensity for 30 s/min. For each stress experiment, 150 wellswere kept for stressed cells, and the 50 left over were dedicatedto L. monocytogenes cells in the exponential growth phase. Eachexperiment was replicated at least three times.

Relation between turbidity growth curves and individual lag times.
The individual lag times of L. monocytogenes cells were estimatedthrough the time of detection (T_d), which is the time requiredfor the microbial population to generate a 0.05 increase ofthe initial baseline value of OD (OD₀). This optical densitycorresponds to a cell density estimated by a viable count ofapproximately 1.8 x 10⁷ L. monocytogenes cells well^–1.

Assuming an exponential bacterial growth at a constant specificgrowth rate (µ) until the detection time, T_d is relatedto the lag time of the culture (lag) by the following formulaproposed by Baranyi and Pin (7):

(1)
whereN_d is the bacterial number at T_d and N₀ the number of cellsinitiating growth in the considered well.

Components of the variance of detection times.
In order to estimate the part of the variability of T_d explainedby the variability of lag, we tried to estimate the componentsof the variance of T_d. From equation 1, we can write

(2)
where is the covariance term and ${varepsilon}$ is an error term corresponding to the reading inaccuracyof the Bioscreen C reader. The Bioscreen C reading inaccuracywas assumed negligible.

When the initial number of cell N₀ is high, we can assume thatlag and N₀ are independent (6), and then the term of covarianceis negligible as N_d, µ, and lag are independent. In thiscase, equation 2 can be written

(3)
Moreoverwe have

(4)
where K is a constant quantifyingthe "physiological state" of the initial population (42); andthen we have

(5)
From an experimentcarried out with a high inoculum of cells in the exponentialgrowth phase (3.3 x 10⁴ cells well^–1 instead of 0.42),we estimated from viable count and OD curves (3) a maximum specificgrowth rate, µ, of 0.90 h^–1 and a lag time, lag,of 0.32 h. K was found to be equal to 0.29. As K is greatlysmaller than 1,

(6)
Equation 3 becomes

(7)
The Taylor's series approximation allows us towrite for two independent variables A and B

(8)
Thereforewe have for a high initial number of cells

(9)
Itwas checked experimentally that Var(T_d) = 0.007. N_d was foundto correspond by viable count to a concentration of 1.77 x 10⁷CFU well^–1. Yet, it was not possible to identify preciselywhich part of the observed T_d is explained by the terms of equation9. Indeed we had estimations of N₀, N_d, and µ from viablecounts but no sufficiently reliable information on their variance.Nevertheless, we were able to estimate the maximum possiblevalue of Varand Var(ln(N_d)) from the experimentalresult. Varis maximum if Var(ln(N_d)) = Var(ln(N₀))= 0, so

${2940_f10}$ (10)
and Var(ln(N_d))is maximum when Var(ln(N₀)) = Var= 0, so

(11)
As the covariance term in equation 2 is negative,we have

(12)
For experiments withsingle cells, N₀ was assumed to follow a Poisson distributionwith an average of 0.42 cells well^–1. For the estimationof Var(ln(N₀)),we used the positive values of the random samplesgenerated by this distribution (10,000 iterations). It was foundthat Var(ln(N₀)) ${approx}$ 0.0934. Var(ln(N_d)) and Varwere assumed to be independent of the inoculum's size and the initialphysiological state. So, from the values previously obtainedit was possible to estimate the minimum part of Var(T_d) explainedby Var(lag) for experiments with single cells.

With equation 12 and our results we have

(13)

Standardization of the datasets.
As we aimed at characterizing the statistical distribution ofT_d values, the datasets of replicates needed to be cumulatedand their standardization was necessary. The standardizationwas carried out in two steps in order to correct the sourcesof variability between experiments (VarBE). VarBE has two sourcesof variability: the variability between experiments due to thedifferences in the conditions of growth VarBE₁ and the variabilitybetween experiments due to the reproducibility variability inthe preparation of the stressed cells VarBE₂. VarBE was estimatedthrough the variance of means of T_d in replicates.

Standardization to correct VarBE₁.
For wells inoculated with stressed cells, the mean and the varianceof T_d values were very dependent on extreme values in a dataset. So, the impact of growth conditions was corrected by usingT_d values of the wells inoculated with cells in the exponentialgrowth phase, included in the same plate. It consisted of atransformation of the T_d values by centering the mean of eachdata set for the cell in the exponential growth phase.

(14)
where t_ij is the standardized value of T_d,ij,the ith value of T_d for the jth experiment; T_{ex, · j}is the mean of T_d values of the wells inoculated with cellsin the exponential growth phase of the jth experiment; and T_{ex,· ·} is the mean of T_{ex, · j}.

Standardization to correct VarBE₂.
A second step was proposed for the standardization of T_d valuesfor wells inoculated with stressed cells. This step aimed atcorrecting the heterogeneity between experiments of the preparationof the stressed cells. This step was carried out by using the5th percentile of the distribution of t_ij values. Indeed, the5th percentile was preferred to the mean, which is too muchdependent on extreme values, particularly when datasets aresmall.

(15)
where t'_ij is the standardizedvalue of t_ij (equation 14), t_5j is the 5th percentile of t_ijvalues of the jth experiment, and t_{5 ·} is the mean oft_5j.

An example of the standardization process is shown in Fig. 1.

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FIG. 1. Standardization steps of detection time values for the three datasets (#1, #2, and #3) of L. monocytogenes cells stressed by chlorine. (a) Optical density growth curves at 600 nm (OD-OD₀) in TSBye at 30°C of the wells showing growth. Dashed line: limit of detection (OD₀ + 0.05). (b) Histogram of observed detection times (T_d) issued from OD growth curves. (c) Histogram of transformed detection times after the first step of standardization (t). (d) Histogram of transformed detection times after the second step of standardization (t'). (e) Histogram of the cumulated values of t' of the three datasets (T_ds).

Fitting data.
The standardized detection times (T_ds), t for cells in the exponentialgrowth phase and t' for stressed cells, were fitted to variousparametric distributions using Regress+ (version 2.5.1 by MichaelP. McLaughlin; http://www.causaScientia.org/software/Regress_plus.html)or the nlinfit subroutine of MATLAB software (version 6.5.1;The Math Works Inc., Natick, MA). The cumulative distributionfunctions were issued from Regress+. The log-likelihood criterionwas chosen to select the theoretical distribution functionsfitting the best observed T_ds distributions. Quantile-quantileplots were also edited to check visually the goodness of fitof T_ds distributions.

RESULTS

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Results

Detection time distribution for L. monocytogenes cells in the exponential growth phase.
Taking into account the components of the variance of T_d allowedus to say that only 11% of the observed variability is explainedby the lag time variability (Table 1). An extreme value typeI distribution (or extreme value distribution with an upperbound) was fitted to the 544 values of T_ds obtained from 37datasets (Fig. 2).

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TABLE 1. Means and variances of observed (T_d) and standardized (T_ds) detection times of single cells of L. monocytogenes in different physiological states

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FIG. 2. Observed and fitted density distributions of the standardized detection times T_ds (in hours) of wells inoculated with L. monocytogenes cells in the exponential growth phase. Continuous curve: fitted extreme value type I distribution (cumulative density function and parameters in Table 2). Histogram: observed frequencies of T_ds.

Influence of the stresses on detection time distributions.
Using the standardization method for T_d values of stressed cellsmakes it possible to take into account the variance betweenexperiments and to group datasets. Table 1 depicts the meansand variances of T_d before and after standardization. The resultsof the standardization support the conclusion that the observedvariability was mainly explained by individual lag time variability.No effect of the physiological state of the cells was noticedon the growth rate. The distributions of detection times revealedthe importance of the increase of lag time for stressed L. monocytogenescells. By using the mean of T_ds to compare the impacts of thenine stresses, the following classification was obtained (ascendingimpact): HCl, cold, lactic acid, chlorine, NaOH, NaCl, starvation,BAC, and heat. Undoubtedly BAC and heat stresses had the greatestimpact on the lag time duration in our experimental conditions.The mean of T_ds was multiplied by 1.65 for BAC stress and by1.87 for heat stress in comparison with the mean of T_ds valuesfor cells in the exponential growth phase. On the other hand,acid and cold stresses didn't seem to have the same influenceand the mean was multiplied by a factor of 1.1.

The distributions of detection times revealed the importanceof the increase of cellular variability for stressed L. monocytogenescells. Variance was also used to compare the impacts of thenine stresses applied. By using this parameter, the followingclassification was obtained (ascending impact): HCl, lacticacid, cold, NaOH, starvation, NaCl, chlorine, heat, and BAC.For example, the variance of T_ds for L. monocytogenes cellsin the exponential growth phase was multiplied by 355 comparedto wells inoculated with BAC-stressed cells. The mineral acidstress, which had the smaller impact on the mean of detectiontimes, generated a multiplication of the variance by 6.

Figure 3 shows that the cumulative distribution of T_ds valuesturns into heterogeneous shapes. Theoretical distributions havebeen fitted to T_ds values. Six different theoretical distributionswere found (Table 2) for the nine stresses. Figure 4 clearlyreveals that they fit well the T_ds distributions. Extreme valuetype II distribution was fitted for acids, alkali, and chlorinestresses, a gamma distribution for starvation stress, and aWeibull distribution for heat-stressed cells. For cold and BACstresses, bimodal distributions were found to be suitable tofit T_ds. There is no a priori reason to choose a bimodal distributionfor cold-stressed L. monocytogenes cells, but the presence ofa few (10%) cells with very long detection times (Fig. 3 andFig. 4) suggests that a mixture of two distributions might beacceptable.

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FIG. 3. Observed cumulative distributions of the standardized detection times of L. monocytogenes in TSBye at 30°C. Dashed line: cumulative distribution of T_ds (in hours) for wells inoculated with cells in the exponential growth phase. Continuous curves: cumulative distributions of observed T_ds for wells inoculated with cells previously stressed by (a) HCl, (b) cold, (c) lactic acid, (d) NaOH, (e) chlorine, (f) starvation, (g) NaCl, (h) BAC, and (i) heat.

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TABLE 2. Theoretical distributions fitted to standardized detection time values of L. monocytogenes^a

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FIG. 4. Quantile-quantile plots of the sample quantiles of the standardized detection times (T_ds) versus theoretical quantiles from the fitted distributions for L. monocytogenes cells stressed by (a) HCl, (b) cold, (c) lactic acid, (d) NaOH, (e) chlorine, (f) starvation, (g) NaCl, (h) BAC, and (i) heat.

DISCUSSION

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Discussion

The aim of this study was to compare the impacts of nine differentstresses on the individual lag times of L. monocytogenes. Asmall number of previous studies have sought to examine thisphenomenon of the historical impact of stress on individuallag times; furthermore, they have essentially concerned onestress (4, 33, 34). By using a similar physiological parameter,the loss of cultivability, for each stress, we succeeded inclassifying the impacts of nine different stresses on the individuallag time distributions.

After observation of the sources of variability of detectiontimes (Table 2), it can be advanced that the method of turbiditydetection times produced by single cells is suitable to characterizelag time distributions of stressed cells. With a maximum of35% of positive wells on the microplates, it can be assertedthat the probability of having more than one cell in the wellsdid not have a deep impact on the distributions (Table 2). Theobserved variability cannot be explained by the presence ofmore than two cells in the same well. Indeed by choosing a maximumof 35% of positive wells, this results in an 80% probabilityof having a single cell. Other authors used an inoculation levelresulting in a 70% probability of having a single cell, forRobinson et al. (27), and a 60% probability, for Métriset al. (23).

The presence of cells in the exponential growth phase on thesame microplates with stressed cells allowed us to correct thevariability between experiments due to the differences in theconditions of growth. For the same loss of cultivability onTSAye, the mean of T_ds was multiplied by a factor between 1.1and 1.87. Heat and BAC stresses induced the greatest increaseof the mean of T_ds (Fig. 5). After observation of the variancesof T_ds (Table 1), the nine stresses can be classified in fourgroups. The first includes HCl stress, which has the weakestimpact on the total variance of T_ds. The second group is composedof lactic acid, NaOH, and cold stresses; their variance of T_dsis approximately 30 times more important than the variance ofT_ds for cells in the exponential growth phase. Starvation, NaCl,and chlorine stresses form the third group. The factor of multiplicationof the variance of T_ds for cells in the exponential growth phaseis 140 for this group. The last group is composed of heat andBAC stresses. For this last group the variance of T_ds is multipliedby 180 and 355, respectively, in comparison to the varianceof T_ds for cells in the exponential growth phase.

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FIG. 5. Standard deviations versus mean values of the standardized detection time (T_ds) distributions of L. monocytogenes cells for all the studied stresses.

With about 100 standardized data issued from at least threereplicates, we obtained suitable distributions. Regarding thevariability of lag time presented here, it can be noticed that100 values are often enough to precisely characterize a distribution,but when the variability becomes high, more than 100 valuesshould be obtained. That was the case with BAC stress and itshigh variance of detection time values (Table 1).

With cells subjected to nine different stresses and cells inthe exponential growth phase, we obtained seven different shapesof distribution of detection times. The distributions fittedwere strongly adjusted to data (Fig. 4).

In our study, the distribution of detection times for inoculatedsingle cells in the exponential growth phase is skewed on theleft. That is not in agreement with the results of Wu et al.(40), who fitted a normal distribution to individual lag timesof cells in the exponential growth phase. However, their 40values are insufficient to properly characterize a distribution.Smelt et al. (33) also used cells in the exponential growthphase (Lactobacillus plantarum), and their detection time valuesfollowed, as our results, a left-skewed extreme value distribution.However, as we focused on the sources of variances of detectiontimes for cells in the exponential growth phase (Table 1), itis obvious that the variance of individual lag times is notthe main source of variability and their distribution cannotbe reached.

The gamma distribution that we obtained (Table 2) for starvedL. monocytogenes cells confirmed the findings of Métriset al. (23) who also fitted a gamma distribution to Listeriainnocua cells issued from a stationary-phase culture. Thesecells can be considered as undergoing a starvation stress andthus it should be considered that individual lag times for starvedcells of the main strains of Listeria may be gamma distributed.

For the three stresses involving a modification of pH (bothacid and alkali stresses), the same distribution was fittedon the standardized detection times: the extreme value typeII distribution. More generally, for the nine stresses presentedin our communication, right-skewed distributions were obtainedlike Smelt et al. and Stephens et al. (33, 34) obtained withheat-injured Salmonella and L. plantarum.

Contrary to the findings of Métris et al. (23) who founda good linear correlation relationship (r² = 0.94) between themeans and the standard deviations of the detection time valuesby studying the effect of environmental growth conditions, thelinear correlation between the means and the standard deviationswas weak (r² = 0.68) in our experiments (Fig. 5). The coefficientof variation of detection times for Métris et al. (23)rose from 5 to 10% as the growth conditions became less favorable.Treatments, which generated bacterial stress, appeared to havemore influence on the variability of individual lag times thanthe growth conditions. Indeed, the coefficient of variationof detection times in our study was between 5 and 28% for stressedcells.

The variability of lag times presented in this study confirmsthe findings of other fields of microbiology. Indeed, markedheterogeneity occurs between individual cells within a clonalpopulation. Such heterogeneity has already been revealed inalmost any phenotype which is determinable at the single celllevel, e.g., in the intracellular pH (13, 25, 31) or cell morphology(15, 16, 30, 36).

Because there are so many factors having an influence on theindividual lag behavior (35), accurate physiological explanationsof lag time heterogeneity are very difficult to obtain. An importantgeneral working hypothesis, formulated by Robinson et al. (26),states that lag is determined by two (hypothetical) quantities.The first quantity is the amount of work the cell has to performto recover a physiological state that allows the cell to multiply.For example, Hornbaek et al. (19) observed a trimodal intracellularpH cell distribution for Bacillus licheniformis. The capacityto multiply being correlated to intracellular pH, they revealedthat the subpopulation of cells exhibiting lower intracellularpH had significantly longer lag phases than populations of cellshaving higher intracellular pH. The second quantity is the rateat which the cell can perform that work. The rate may be identifiedin case of stress with metabolic processes of repair systems(21). These processes vary with the nature of the stress andinvolve the synthesis of ATP, RNA, and DNA (10). As these mechanismsof repair were present in low abundance, Booth (9) proposedthat their concentration in the cells would follow stochasticprocesses leading to their Poissonian distribution. Such animbalance in the cells could generate a different rate for cellshaving the same work to do to recover the capacity of growth.

This research sought to evaluate and classify the impacts ofstresses on individual lag time distribution of L. monocytogenes.The results of this study give information on the consequencesof food processing on L. monocytogenes lag time. As we haveshown, lag time distribution is dependent on the stress undergoneby the cell. It results in an increased variability of lag timesand in their particular distribution. Increased understandingof the individual behaviors after stress and the factors thataffect them will contribute to the development of improved predictivemodels. These results reinforce the need to move about a stochasticapproach of bacterial growth, especially when predictive microbiologyis used for assessing the exposure to microbiological hazards(8). In the future we will focus on the study of the individuallag time variability by applying successive stresses correspondingto food processing events in order to optimize the evaluationof processing methods with respect to bacteriological safetyand the quality of the food.

ACKNOWLEDGMENTS

This study was supported by a grant from the Ministèresde la Recherche et de l'Agriculture (convention R02/04 programmeAliment-Qualité-Sécurité) and belongs tothe French national program for predictive microbiology Sym'Previus.

L. Guillier is a recipient of a doctoral fellowship from Arilait-Recherchesand the Association Nationale de la Recherche Technique.

FOOTNOTES

* Corresponding author. Mailing address: Unité Mixte de Recherche ENVA-INRA RISQUAL, Ecole Nationale Vétérinaire d'Alfort, 7 avenue du Général de Gaulle, F-94704 Maisons-Alfort, France. Phone: 33 0 143 967043. Fax: 33 0 143 967121. E-mail: lguillier{at}vet-alfort.fr.

REFERENCES

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