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FOODMICROBIOLOGY

0740-0020/$ - se

doi:10.1016/j.fm

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Food Microbiology 25 (2008) 460–470

www.elsevier.com/locate/fm

Comparison of primary predictive models to study the growth ofListeria monocytogenes at low temperatures in liquid culturesand selection of fastest growing ribotypes in meat and turkey

product slurries

Amit Pal, Theodore P. Labuza, Francisco Diez-Gonzalez�

Department of Food Science and Nutrition, University of Minnesota, 1334 Eckles Avenue, St. Paul, MN 55108, USA

Received 31 October 2007; received in revised form 17 January 2008; accepted 22 January 2008

Available online 2 February 2008

Abstract

This study compared the performance of four primary mathematical models to study the growth kinetics of Listeria monocytogenes

ribotypes grown at low temperature so as to identify the best predictive model. The parameters of the best-fitting model were used to

select the fastest growing strains with the shortest lag time and greatest growth rate. Nineteen food, human and animal L. monocytogenes

isolates with distinct ribotype were grown at 4, 8, and 12 1C in tryptic soy broth and slurries prepared from cooked uncured sliced turkey

breasts (with or without potassium lactate and sodium diacetate, PL/SD) and cooked cured frankfurters (with or without PL/SD).

Separate regressions were performed on semi-logarithm growth curves to fit linear (based on Monod) and non-linear (Gompertz,

Baranyi–Roberts, and Logistic) equations and performance of each model was evaluated using an F-test. No significant differences were

found in the performance of linear and non-linear models, but the Baranyi model had the best fit for most growth curves. The maximum

growth rate (MGR) of Listeria strains increased with the temperature. Similarly MGR was found significantly greater when no

antimicrobials were present in the formulation of turkey or frankfurter products. The variability in lag times and MGRs in all media as

determined by the Baranyi model was not consistent among strains. No single strain consistently had the fastest growth (shortest lag

time, fastest MGR, or shortest time to increase 100-fold), but nine strains were identified as fastest growing strains under most growth

conditions. The lack of association between serotype and fastest strain was also observed in the slurry media study. The fastest growing

strains resulting from this study can be recommended for future use in L. monocytogenes challenge studies in delicatessen meat and

poultry food matrices, so as to develop conservative pathogen growth predictions.

r 2008 Elsevier Ltd. All rights reserved.

Keywords: Listeria monocytogenes; Sliced turkey breasts; Frankfurters; Primary growth models; Growth kinetics; Predictive modeling

1. Introduction

Listeria monocytogenes is a foodborne bacterial patho-gen responsible for foodborne outbreaks worldwide(Lianou et al., 2006) causing at least 2500 infectionsand 500 deaths every year in the US (Mead et al., 1999).This microorganism cannot survive proper cookingtemperature but is capable of growing at refrigerationtemperature. Ready-to-eat (RTE) foods that are typicallypreserved at refrigeration temperatures such as frankfur-

e front matter r 2008 Elsevier Ltd. All rights reserved.

.2008.01.009

ing author. Tel.: +1612 624 9756; fax: +1 612 625 5272.

ess: fdiez@umn.edu (F. Diez-Gonzalez).

ters (hot dogs), deli/luncheon meats, pate and salami havebeen linked to previous listeriosis outbreaks and are knownto sustain Listeria growth. The survival and growth ofL. monocytogenes in these food products is dependent onthe product formulation and storage conditions as well ason the specific strain characteristics.Previously published challenge studies have been typi-

cally conducted with a single strain or mixture of strains(cocktail) that were not selected on the basis of fastestgrowth capability (Shelef and Addala, 1994; Barmpaliaet al., 2004). A few studies have shown that strains ofL. monocytogenes differ in their growth behavior undersimilar medium formulation and temperature conditions

ARTICLE IN PRESSA. Pal et al. / Food Microbiology 25 (2008) 460–470 461

(Barbosa et al., 1994; Begot et al., 1997; De Jesus andWhiting, 2003). Growth variations among strains of otherbacterial pathogens like Salmonella (Juneja et al., 2003)and Escherichia coli O157:H7 (Whiting and Golden, 2002)have also been documented. The use of the fastest growingL. monocytogenes strains has been recommended forestablishing safety-based ‘‘use-by’’ date labels for RTEfoods (NACMCF, 2005). Scott et al. (2005) suggestedscreening of variety of strains for the fastest growingor heat-resistant strain and developing a parsimoniousgrowth model based on the fastest growing strain underconditions of interest. However, most challenge studies ofL. monocytogenes in food products are not based on thefastest growing strains that would have accounted for theworst-case modeling scenario.

Out of 13 known serotypes of L. monocytogenes, 3serotypes, 1/2a, 1/2b, and 4b, are most frequently reportedas the sources of listeriosis cases (Farber and Peterkin,1991; De Jesus and Whiting, 2003). Of these, half thelisteriosis outbreak cases in humans belong to the 4bserotype; whereas, 1/2a and 1/2b are known for sporadiccases (De Jesus and Whiting, 2003). Lianou et al. (2006)highlighted the importance of validating strain selection indesigning and executing challenge studies for determiningthe behavior of pathogens in food products. Knowledge ofgrowth behavior differences can also be useful in betterunderstanding the virulence, distribution, and epidemio-logy of the pathogen (Lianou et al., 2006). The variation ingrowth response has been reported for a range of serotypes,ribotypes, or lineages of L. monocytogenes at differenttemperatures; however, these have mostly been done innon-selective broth media (Barbosa et al., 1994; Begotet al., 1997; De Jesus and Whiting, 2003; Lianou et al.,2006). Therefore, our knowledge on the variations amongL. monocytogenes isolates based on growth on any of theRTE meat or poultry product formulations is largelylimited.

A typical microbial growth curve consists of threephases—first a lag phase, followed by an exponentialphase, and finally a stationary phase (Monod, 1949). Anystrain of a microbial species can be considered a fastgrowing strain if it can exhibit a short lag phase and arelatively high growth rate during the exponential phaseunder conditions that mimic food matrices. Determinationof growth kinetic parameters is achieved using predictivemicrobial growth models using the concepts of predictivemicrobiology. The simplest and the earliest model describ-ing the exponential increment of microbial cell numberswas proposed by Monod (1949). The USDA’s PathogenModeling Program uses multivariate models based onthe Gompertz equation (McDonald and Sun, 1999).Another widely used model in predictive food microbiol-ogy is the equation of Baranyi and Roberts (1994). Theseavailable models differ in ‘ease of use’ and number ofparameters in the equation. Their selection in foodmicrobiology research application is often subjective andbased on convenience.

There is significant disagreement on a best-fitting modelin the predictive food microbiology literature. Zwieteringet al. (1990) concluded that the Gompertz model was thebest-fitting model for Lactobacillus planatarum and othermicroorganisms. Buchanan et al. (1997) reported that thethree-phase linear model was more robust than theGompertz and Baranyi models. Another report showedthat the Baranyi model was better than the modifiedGompertz model for L. monocytogenes (Xiong et al., 1999).The study by Schepers et al. (2000) chose the Richardsmodel as the best descriptive model for L. helveticus

growth. The usual measures of goodness-of-fit for modelcomparison in previous studies were done by calculating asquared correlation coefficient (R2) or bias (Bf) andaccuracy (Af) indices as proposed by Ross (1996). As Ross(1996) recommended, models describing pathogen growthrate with Bf in the range of 0.9–1.05 could be consideredgood, in the range of 0.7–0.9 or 1.06–1.15 consideredacceptable, and o0.7 or 41.15 considered unacceptable.However, Bf and Af indices are only extensions to modelvalidation steps and may not present statistical comparisonbetween the performances of different models for the sameset of observed data. As compared to the traditionalstatistical methods, the Bf and Af indices are not basedon the deviation between observed and mean response(te Giffel and Zwietering, 1999).Another model comparison method is to assess all

parameters within a model by least square analysis and theconstruction of a confidence region for the parameter ofparticular interest, so that the pre-specified model mostsimilar to the fitting model is then selected as the bestmodel (Schreuder and Swank, 1971). Thus, this approachgives the best-fitting model within the comprehensivefamily of models considered. Nevertheless, only a fewstudies evaluated the statistical comparison between theperformances of models using a comprehensive method asan estimate of the measuring error. The Schnute model is acomprehensive model nesting linear, logistic, or Gompertzmodels (Zwietering et al., 1990). The use of the F-test wasdemonstrated by Zwietering et al. (1990) to compare thegrowth predictions between different primary models.Selection or developing of a best-fitting model is deemedimportant since the growth parameters estimated from themodel become the basis in growth prediction, especially forone based on safety.The objectives of the current research were to first

identify the best-fitting primary growth model using theF-test and then to select the fastest growing strain(s) ofL. monocytogenes based on growth kinetic parameters.

2. Materials and methods

2.1. Strains and preparation of inoculum

Nineteen L. monocytogenes strains were providedDr. Martin Weidmann from Cornell University, Ithaca,NY. Their origin and ribotype are shown in Table 1.

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Table 1

List of the Listeria monocytogenes strains with respective ribotypes, serotypes, lineages, and isolation sources used in this study

Strain no. Ribotype Serotypea (lineage) Isolation source

1 DUP-1038 4b (I) Mexican style cheese, epidemic, L.A. 1985

2 DUP-1042 4b (I) Human epidemic (MA, USA), 1983

3 DUP-1053A 1/2a (II) Food (hot dog), sporadic, USA

4 DUP-1044A 4b (I) Food (hot dog), epidemic (USA), 1998–99

5 DUP-1042B 4b (I) Mexican style cheese, epidemic (NC, USA), 2000

6 DUP-1051B 1/2b (I) Chocolate milk, epidemic (IL, USA), 1994

7 DUP-10142 4b (III) Animal, goat, 1997

8 DUP-1038B 4b (I) Human sporadic case, 1988

9 DUP-1051D 1/2b (I) Human sporadic case, 1997

10 DUP-1052A 3b (I) Human sporadic case, 1996

11 DUP-1042C 3c (I) Human sporadic case

12 DUP-1030A 1/2a (II) Human sporadic case

13 DUP-1039B n.a (II) Human sporadic case, 1997

14 116-1501-S4 1/2c (II) Human, sporadic, WHO strain collection

15 DUP-1039C 3a (II) Human, sporadic, 1998

16 DUP-1059A 4a (III) Human sporadic case

17 116-110-S2 4a (III) Human sporadic case, 1996

18 DUP-1039E 1/2a (II) Animal, bovine, 1996

19 DUP-1052 1/2b (I) Animal, cow, 1989

an.a: not available.

A. Pal et al. / Food Microbiology 25 (2008) 460–470462

Strains were stored in vials containing tryptic soy broth(TSB, Neogen Corp., Lansing, MI) and 10% glycerol(Sigma Chemical Co., St. Louis, MO) at �55 1C. Forinoculum preparation, frozen suspensions were streaked ontryptic soy agar (TSA; Neogen Corp., Lansing, MI) andthe TSA plates were incubated at 37 1C for 24 h. Singlecolonies from the TSA plate were transferred to 10ml TSBtubes and were allowed to grow at 37 1C for 24 h.L. monocytogenes cultures were enumerated by seriallydiluting in 0.1% peptone water (Neogen Corp., Lansing,MI) and spread plating on TSA. Working cultures weremaintained on TSA slants at 4 1C for at least 4 weeks.

2.2. Preparation of turkey breasts and frankfurters slurries

Two different types of cooked uncured sliced turkeybreasts (average weight: 28 g per slice) and 2 types ofcooked cured frankfurters (average weight: 52.4 g per hotdog) were provided by a local producer and shipped invacuum-sealed bulk packages to the laboratory in icecoolers. The 2 types of sliced turkey breasts and frank-furters used for slurry preparation were: (1) a standardformulation without antimicrobials and (2) the addition of2% potassium lactate (PL) and 0.2% sodium diacetate(SD) to the formulation. As reported by the manufacturer,sliced turkey breasts contained 60–70% moisture, 18–22%protein, 1–3% fat, 1.8–2.2% salt, and included sugar,sodium bicarbonate, and carrageenan. Both frankfurtertypes were processed with minced meat of beef and pork ina 1:10 ratio (beef:pork) and the final products contained55–58% moisture, 27–29% fat, 10.5–11.5% protein, and2–2.25% salt and included sodium nitrite in the formula-tion with an initial concentration of 156 ppm. All theproducts were stored at �20 1C until the day of slurry

preparation. Within 5 days after storage in the freezer,one part of sliced turkey breasts or frankfurters werecombined with three parts of sterile 0.1% peptone waterin sterile filter stomacher bags (Two-Chamber FilterBag, Fisher Scientific, Pittsburgh, PA). The slurries wereprepared by homogenizing the product and peptonewater for 5min using a stomacher (Tekmar Company,Cincinnati, OH). The filtered homogenates were re-filteredin new filter stomacher bags and 30ml volumes wereaseptically transferred into sterile screw-capped test tubes(24mm� 150mm).

2.3. Growth studies

All nineteen L. monocytogenes strains were grown at 37 1Cfor 24h in TSB and then were serially diluted in 0.1%peptone water. From this 0.1ml aliquots containing102–104CFU were separately inoculated into: (1) 30mlTSB; (2) a slurry of the turkey breasts; and (3) a frankfurterslurry. The strains in the 3 media were then incubated at 4, 8,or 12 1C for at least 20, 12, or 9 days, respectively. At eachsampling time, two serially diluted 0.1ml aliquots werespread on a single plate or 1ml on four plates of tryptic soyagar containing 1 g/l esculin and 0.5 g/l ferric ammoniumcitrate (Sigma-Aldrich, St. Louis, MO) (efTSA) orPALCAM agar (Neogen Corp., Lansing, MI), respectively.Black colonies with a dark-gray halo were counted afterincubation of the agar plates at 37 1C for 48h. The data ateach level were the result of two independent experiments.

2.4. Curve fitting and comparison of growth models

Using the average microbial counts at each test timefrom the two trials (n ¼ 2), growth curves were generated

ARTICLE IN PRESSA. Pal et al. / Food Microbiology 25 (2008) 460–470 463

as the natural logarithm of CFU/ml vs. time for eachtemperature and medium condition. A comparison ofmodels was done using the growth curves of TSB-growncultures following the procedure from Zwietering et al.(1990). The best-fitting regression model was used tocompute lag times and maximum growth rates (MGR) ofL. monocytogenes strains in the TSB medium and 2 types ofmeat slurries. To integrate the combination of lag andexponential phases, both the lag time and the MGR werecombined to estimate the time a strain would take tomultiply 100-fold (TTR100), i.e. a 2 log cycle increase fromthe initial inoculum level.

Regression analyses on the growth curves of each strain asobtained at all three temperatures in TSB were performedusing four primary growth curve models. These growth curvemodels were based either on linear (derived from the Monodmodel) or non-linear (Gompertz, Logistic, and Baranyi)equations (Table 2) and re-parameterized to reflect microbialgrowth parameters as derived by Zwietering et al. (1990).The growth rate from a linear model was calculated using theslope of linear regression line on the exponential part of thegrowth curve (lnCFU/ml vs. t). The lag duration time in alinear model was calculated from the point of intersection ofthe regression line and the line originating from the initialinoculum level (Fu and Labuza, 1992). Performance of eachmodel was compared with the Schnute model using an F-test.The Gompertz, Logistic, and Schnute models were fitted tothe growth curves from TSB using DataFit 8.1 (OakdaleEngineering, Oakdale, PA). The curve fitting of the Baranyi’sequation was done using Baranyi–Roberts model program(Baranyi and Roberts, 1994) as kindly provided by Dr. JozefBaranyi.

The residual sum of squares (RSS, difference betweenobserved and predicted values) was calculated foreach growth curve and compared with the RSS of theSchnute model considering the degrees of freedom (DF)

Table 2

Primary growth models used to predict growth of Listeria monocytogenes

Model Equationa

Linear y ¼ exp½mðt� lÞ� t4ly ¼ 1 t4l

Gompertz y ¼ A exp½� expfme=Aðl� tÞ þ 1g�

Logistic y ¼A

1þ exp½ð4m=AÞðl� tÞ þ 2�

Baranyiy ¼ y0 þ mAðtÞ � ln 1þ

exp½mAðtÞ� þ 1

expðymax � y0Þ

� �

AðtÞ ¼ tþ1

mlnðexpðmtÞ þ expð�mlÞ � expð�mðtþ lÞÞ

Schnutey ¼ m

1� b

a

� �1� b expðalþ 1� b� atÞ

1� b

� �1=b

ay: Final count (ymax, CFU)/initial count (y0, CFU); m: maximum

growth rate; l: lag time; A, a, b: model coefficients.

available from each equation. The test models (linear,Logistic, and Gompertz) were compared with the Schnutemodel by testing f-value against the critical F-table valueshowing the 95% confidence level (Eq. (1)). Since theBaranyi and Schnute models have the same number ofparameters, their RSS values were directly compared(Eq. (2)):

f ¼ðRSStest � RSSschnuteÞ=DFtest �DFschnute

RSSschnute=DF schnute

against FDFtest�DFschnute

DFschnute(1)

f ¼RSSBaranyi

RSSschnute

against FDFBaranyi

DFschnute: (2)

If f-values were smaller than F-values for any growthcurve, the model was considered equivalent to a compre-hensive model indicating that the nested model is sufficientto describe a growth curve.

2.5. Statistical analysis

A best-fitting model was considered as the one which hadthe greatest number of growth curves for all temperatureconditions and formulations showing replacement of acomprehensive model at all three temperatures (Po0.05).The numbers of good-fitting curves out of a total of 57growth curves (19 strains at 3 temperatures in TSB) werecalculated and performance of each model was comparedwith the other three models from the P-value estimated bya two-sided Fisher’s exact test using PROC FREQ of SAS(2004).Following model screening, the growth parameters were

estimated using the best-fitting model. The statisticaldifference between the growth parameters at P ¼ 0.05was estimated by comparing the 95% confidence intervalscalculated from the average7(1.96� standard error). Thefinal selection of the fastest strain was based on the shortestlag time, the greatest MGR, or the shortest TTR100 in allmedia and temperature conditions.

3. Results

A total of 57 growth curves were generated from 19L. monocytogenes strains at three different temperatures.The initial count of L. monocytogenes after inoculation onTSB ranged from �0.1 to 0.8 log10 (CFU/ml). Theperformance of the linear model and the non-linear modelswas evaluated by the F-test using microbial growth datagenerated in TSB medium (Figs. 1 and 2, respectively).When the f-values were plotted against the F-values foreach L. monocytogenes strain at 4, 8, and 12 1C, theBaranyi–Roberts model had the maximum number ofcurves (52 out of 57 curves) where f-values were smallerthan the critical F-table values (Table 3). The Baranyi–Roberts model was the best curve-fitting model formost curves but there was no significant difference

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f and

F v

alue

s

-1

1

3

5

7

9

1

4 °C

-1

1

3

5

7

9

°

8 °C

-1

1

3

5

7

9 12 °C

Strain number

4 7 10 13 16 19

1 4 7 10 13 16 19

1 4 7 10 13 16 19

Fig. 1. F-test on Listeria monocytogenes growth data as fitted by the linear

model at 4, 8, and 12 1C. (’) f-value; (n) F-value.

f and

F v

alue

s

-1

1

3

5

7

9

1-1

1

3

5

7

9

-1

1

3

5

7

9

-1

1

3

5

7

9

05

1015202530

05

1015202530

Strain

4 7 10 13 16 19 1 4 7

1 4 71 4 7 10 13 16 19

1 4 7 10 13 16 19 1 4 7

Gompertz Lo

Fig. 2. F-test on Listeria monocytogenes growth data as fitted by the non-linear

(n) F-value.

A. Pal et al. / Food Microbiology 25 (2008) 460–470464

(P40.05) among the models (Table 3). Therefore, theBaranyi–Roberts model was chosen to calculate lag timesand MGRs of all the strains as obtained in different liquidmedium at the three temperatures.At all three temperatures, the growth of L. monocyto-

genes was influenced by the strain and media type. Fig. 3shows a representative growth behavior in different culturemedia of two strains—DUP-1044A and DUP-1038. In TSBmedium, significant variability was observed among strainsfor MGR and no single strain was the fastest growingisolate at all three temperatures (Table 4). The range ofMGRs was 0.5170.06–1.0370.09, 1.8770.07–2.4570.11,and 3.4670.19–4.1070.30 day�1, respectively at 4, 8, and12 1C. The differences between the strains diminished whenthe growth temperature increased. The shortest lag timenoted by any strain was 3.2, 1.1, and 0.7 days at 4, 8, and12 1C, respectively, but no differences were noted for lagtimes between the strains based on the 95% confidenceintervals. Also, the strain with the shortest average lagtime did not necessarily have the greatest average MGR atthat temperature. Therefore, growth comparison involvingboth phases also was made for each strain by determiningthe time a culture of 1CFU/ml will take to reach theconcentration of 100CFU/ml (TTR100). The final selectionof the fastest strain in TSB medium was based on theshortest lag time, the greatest MGR, and the shortestTTR100 criterion. The four strains, DUP-1042B, DUP-1051D, DUP-1038B, and DUP-1044A, were considered

-1

1

3

5

7

9 4 °C

-1

1

3

5

7

9 8 °C

05

1015202530 12 °C

number

10 13 16 19 1 4 7 10 13 16 19

1 4 7 10 13 16 1910 13 16 19

10 13 16 19 1 4 7 10 13 16 19

gistic Baranyi

models (Gompertz, Logistic, and Baranyi) at 4, 8, and 12 1C. (’) f-value;

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Table 3

Number of growth curves with statistical good fit as compared with a

more comprehensive Schnute model at three temperature conditions in

tryptic soy broth

Model Number of significant good fitting curves (out of 57 growth

curves)

Temperature (1C)

4 8 12 Total (%)a

Linear 13 15 18 46 (80.7) A

Gompertz 17 19 9 45 (78.9) A

Logistic 18 16 8 42 (73.6) A

Baranyi 17 18 17 52 (91.2) A

aTotal curves with same letter as superscript are not significantly

different (P40.05).

List

eria

mon

ocyt

ogen

es c

ount

(log

10 C

FU/m

l)

0

2

4

6

8

10

0

TSB T-L T-C F-L F-C

0

2

4

6

8

10

0Time (days)

5 10 15 20 25

5 10 15 20 25

Fig. 3. Growth of Listeria monocytogenes strains (a) DUP-1044A and (b)

DUP-1038 in different liquid media at 4 1C illustrating growth difference

as influenced by the strain and the media. Each data point is an average of

two replicates. TSB: tryptic soy broth; T-L: slurry of sliced turkey breasts

processed with 2% potassium lactate and 0.2% sodium diacetate; T-C:

slurry of control turkey breasts; F-L: slurry of frankfurters processed with

2% potassium lactate and 0.2% sodium diacetate; F-C: slurry of control

frankfurters.

A. Pal et al. / Food Microbiology 25 (2008) 460–470 465

the fastest growing strains in TSB medium under thetested conditions, of which three of them were a 4b serovar(Table 5, first row).

The initial inoculum level in slurry media experiments atthe three temperatures ranged from 1.7 to 4.2 log10 (CFU/ml)with 90% of the growth curves having an average initialinoculum between 3.0 and 3.5 log10 (CFU/ml). All strains,except the ribotype 116-1501-S4 (strain number 14), wereable to be isolated on the PALCAM agar when plated fromslurries of turkey breasts or frankfurters. In our preliminarywork with slurry media, the counts of ribotype DUP-1044Aon the PALCAM or efTSA agars were similar, althoughefTSA agar plate also contained background flora andtherefore PALCAM agar remained the medium of choice forall the strains (data not shown).In the slurry of sliced turkey breasts, the average MGR

remained significantly (Po0.05) lower when antimicro-bials, PL and SD, were present in the initial formulation(Fig. 4). In general, the MGR in slurries prepared fromcontrol turkey breasts were two times the MGR in slurriesof antimicrobial-containing sliced products. In all cases,there was a consistent increase in the rates and decrease inthe lag time when growth temperature increased. Unlikethe lag times in the TSB medium, significant differences inlag times between strains were noted in slurry cultures.However, there was no significant variation between thestrains when grown in slurries of turkey breasts with andwithout antimicrobials (Fig. 5). The strains with theshortest average lag phase were not necessarily the fastestin the exponential phase (Table 5). Also, the fastestgrowing strains in slurries were not all similar when theantimicrobials were present in turkey breasts formulation(Table 5). Using a similar fastest strain selection strategyas for the TSB medium, the ribotypes DUP-1051B,DUP-1042B, and DUP-1044A were commonly fastest inboth turkey breasts slurry types (data not shown forTTR100 in slurry media).The differences in the MGRs and the lag times in slurries

of frankfurters with and without antimicrobials weresimilar to turkey breast slurry, with greater averageMGR and shorter average lag time in the absenceof antimicrobials (Figs. 6 and 7). However, with theaddition of sodium nitrite as a curing salt in frankfurters asopposed to uncured sliced turkey breasts, the MGRs inthe frankfurter slurries were smaller than the turkey breastslurries at any temperature. Although no single strain wasfound to be consistently fastest in all media and growthparameters, the strains DUP-1042B, DUP-1044A, DUP-1039C, DUP-1030A, DUP-10142, DUP-1038B, DUP-1051B, DUP-1042C, and DUP-1039E appeared fastestwith either shortest lag time, greatest MGR, or shortestTTR100 under most growth conditions (at least three timesin Table 5).

4. Discussion

In this study, the performances of linear and non-linearprimary growth models were tested in the TSB mediumfollowing the procedure from Zwietering et al. (1990).Assuming that the Schnute model is a more comprehensive

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Table 4

Average growth kinetic parameters (7standard error) of Listeria monocytogenes strains in tryptic soy broth at 4, 8, and 12 1C as determined by

Baranyi–Roberts model

Strain no.a Maximum growth rate (day�1) Lag time (days) Time to reach 100b (days)

Temperature (1C)

4 8 12 4 8 12 4 8 12

1 0.6270.07 2.0470.09 3.9570.29 3.972.2 1.470.3 1.070.3 11.473.0 3.770.4 2.270.4

2 0.8970.07 2.3870.20 3.0970.28 4.571.6 2.270.9 0.870.4 9.671.9 4.171.1 2.370.5

3 0.9470.01 1.8770.07 3.9070.30 5.572.1 1.570.3 1.170.3 10.472.6 3.970.4 2.270.4

4 0.7870.04 1.9470.08 4.1070.30 4.571.1 1.570.3 1.170.3 10.471.5 3.970.4 2.270.4

5 1.0370.09 2.2170.48 3.8770.37 5.071.8 1.570.4 1.170.4 9.572.2 3.670.5 2.370.5

6 0.8670.06 1.9270.10 3.4670.19 4.071.5 1.470.4 1.070.2 9.471.8 3.870.5 2.370.3

7 0.8270.13 2.3370.25 3.8070.30 5.072.9 1.370.6 1.170.3 10.673.7 3.370.8 2.370.4

8 0.8270.05 2.4570.11 3.5870.34 4.171.3 1.170.3 0.770.4 9.771.6 3.070.4 2.070.5

9 0.7570.10 2.0570.12 4.0470.17 3.272.3 1.670.4 1.270.2 9.373.1 3.870.6 2.370.2

10 0.8270.07 2.3970.11 3.9070.26 5.771.8 1.470.4 0.970.3 11.372.2 3.370.4 2.170.4

11 0.7770.09 2.1370.09 3.8870.28 7.272.4 1.670.3 1.070.3 13.173.0 3.770.4 2.270.4

12 0.9070.10 2.2570.09 4.0370.32 6.372.5 1.870.3 1.070.3 11.473.0 3.870.4 2.270.4

13 0.7470.08 2.0170.12 3.9070.22 5.872.2 1.570.5 1.070.2 12.072.8 3.870.6 2.270.3

14 0.5170.06 2.3470.10 3.7370.28 5.972.6 1.770.3 1.070.3 15.073.6 3.670.4 2.270.4

15 0.7570.12 2.1270.14 3.9570.24 3.272.9 1.270.5 0.970.3 9.473.8 3.470.6 2.170.3

16 0.8170.12 2.1470.08 4.0870.28 4.372.7 1.670.3 1.170.3 10.073.4 3.770.3 2.370.4

17 0.7370.18 1.9570.10 4.0170.33 7.775.0 1.370.4 1.070.3 14.076.2 3.770.5 2.270.4

18 0.9570.16 2.4470.10 3.9770.24 7.273.5 1.570.3 1.170.3 12.174.2 3.470.4 2.370.3

19 0.8470.10 2.2270.08 3.8470.29 4.772.2 1.470.3 1.070.3 10.272.8 3.570.4 2.270.4

Overall average 0.81 2.17 3.85 5.1 1.5 1.0 11.0 3.64 2.21

aRefer Table 1 for strain identification.bTotal time to reach 100 times any initial population calculated based on maximum growth rate and lag time.

Table 5

List of fastest growing Listeria monocytogenes strains (greatest maximum growth rate, shortest lag time, or shortest time to reach 100-fold) as grown in

different liquid media at 4, 8, and 12 1C

Mediuma,b Temperature (1C) 4b serotype

proportion (%)4 8 12

Maximum

growth rate

Lag time TTR100c Maximum

growth rate

Lag time TTR100 Maximum

growth rate

Lag time TTR100

TSB DUP-1042B DUP-

1051D

DUP-

1051D

DUP-1038B DUP-

1038B

DUP-

1038B

DUP-1044A DUP-

1038B

DUP-

1038B

3/4 (75)

T-L DUP-1051B DUP-

1042B

DUP-

1039C

DUP-1059A DUP-

1039E

DUP-

1039E

DUP-1044A DUP-

1051B

DUP-

1039E

2/6 (33)

T-C DUP-1042 DUP-

1042B

DUP-

1030A

DUP-1052A DUP-

10142

DUP-

10142

DUP-1044A DUP-

1051B

DUP-

1042C

4/8 (50)

F-L DUP-1059A DUP-

1030A

DUP-

1042B

DUP-1042C DUP-

1042C

DUP-

1042C

DUP-1039C DUP-

1030A

DUP-

1039C

1/5 (20)

F-C DUP-1044A DUP-

1030A

DUP-

1030A

DUP-10142 DUP-

1030A

DUP-

10142

DUP-1053A 116-110-

S2

116-110-

S2

2/5 (40)

aTSB: tryptic soy broth; T-L: slurry of sliced turkey breasts processed with 2% potassium lactate and 0.2% sodium diacetate; T-C: slurry of control

turkey breasts; F-L: slurry of frankfurters processed with 2% potassium lactate and 0.2% sodium diacetate; F-C: slurry of control frankfurters.bSlurry prepared by homogenizing one part sliced turkey breast or frankfurters and three parts of sterile 0.1% peptone water for 5min in a stomacher.cTotal time to reach 100 times any initial population calculated using maximum growth rate and lag time.

A. Pal et al. / Food Microbiology 25 (2008) 460–470466

model than the tested models and exactly predicts themicrobial counts, the RSS of the Schnute model wasconsidered as an estimate of the measuring error. Sincegrowth models may have a different number of parametersand curve fitting improves with the increase in number ofparameters in equations, RSS (or mean square error, MSE)

value alone is not the best measure of model comparison(Zwietering et al., 1990). Direct comparison of RSS orMSE values is meaningful only when used between modelswith the same number of parameters. For example,Giannuzzi et al. (1998) reported that when the logisticand the Gompertz models were fitted for microbial growth

ARTICLE IN PRESSM

axim

um g

row

th ra

te (d

ays-1

)

0

1

2

3

1

4 °°C

0

2

4

6 8 °C

0

6

4

2

8 12 °C

Strain number

2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

With antimicrobialsWithout antimicrobials

Fig. 4. Average maximum growth rates (7standard error, n ¼ 2) of

Listeria monocytogenes strains in turkey slurries at 4, 8, and 12 1C. See

Table 1 for strain identification. Sliced turkey breasts with antimicrobials

contained 2% potassium lactate and 0.2% sodium diacetate in the final

formulation. Slurries were prepared with one part of sliced turkey breast

homogenized with three parts of sterile 0.1% peptone water. Filtered

slurries were inoculated with approx. 3 log10CFU/ml.

Lag

time

(day

s)

0

2

4

6

8

10

12

1

Without antimicrobials With antimicrobials 4 °C

0

2

4

6 8 °C

0

2

4 12 °C

Strain number

2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

Fig. 5. Average lag time (7standard error, n ¼ 2) of Listeria mono-

cytogenes strains in turkey slurries at 4, 8, and 12 1C. See Table 1 for strain

identification. Sliced turkey breasts with antimicrobials contained 2%

potassium lactate and 0.2% sodium diacetate in the final formulation.

Slurries were prepared with one part of sliced turkey breast homogenized

with three parts of sterile 0.1% peptone water. Filtered slurries were

inoculated with approx. 3 log10CFU/ml.

A. Pal et al. / Food Microbiology 25 (2008) 460–470 467

prediction in refrigerated beef, RSS comparison betweenmodels was found to be adequate as they had same numberof parameters in their equations. Thus the F-test deter-mines the significance of using a more complicated modelhaving a greater number of parameters over a simplermodel. Based on the F-test, Zwietering et al. (1990) showedthat the modified Gompertz equation was statisticallysufficient to describe the growth data of L. planatarum andeasy to use. After the study by Zwietering et al., theequation from Baranyi–Roberts (1994) became a widelyused model in the field of predictive food microbiology.The current study showed that no significant differenceexisted between the predictions of linear, Gompertz,logistic, and Baranyi models although the Baranyi modelshowed the best goodness-of-fit for the most number ofcurves. Our results matched with that of Lopez et al. (2004)who showed that the Baranyi model best determined the

growth parameters although with no difference fromlinear, Richards and Weibull models. Therefore, in thisstudy the subsequent analysis of L. monocytogenes growthcurves generated using the slurries of meat and poultryproducts was conducted only using the Baranyi’s equation.Usage of liquid medium has an advantage over solid

food as numerous strains can be independently studiedin a lab scale setup. Comparative studies of growth ofL. monocytogenes strains have been reported in laboratoryculture medium but not in food slurries (Barbosa et al.,1994; Begot et al., 1997; De Jesus and Whiting, 2003).Food slurries can provide a better simulation of realfood-related environments than the culture broths.Slurries of turkey and frankfurters have been reportedfor studying the survival kinetics of L. monocytogenes

under thermal or antimicrobials presence (Schlyter et al.,

ARTICLE IN PRESSM

axim

um g

row

th ra

te (d

ays-1

)

0

1

2

3 4 °C

0

2

4

6 8 °C

0

2

4

6

8 12 °C

Strain number 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

With antimicrobialsWithout antimicrobials

Fig. 6. Average maximum growth rates (7standard error, n ¼ 2) of

Listeria monocytogenes strains in frankfurter slurries at 4, 8, and 12 1C. See

Table 1 for strain identification. Frankfurters with antimicrobials

contained 2% potassium lactate and 0.2% sodium diacetate in the final

formulation. Slurries were prepared with one part of frankfurter

homogenized with three parts of sterile 0.1% peptone water. Filtered

slurries were inoculated with approx. 3 log10CFU/ml.

Lag

time

(day

s)

0

4

8

12

16

1

4 °C

0

2

4

6 8 °C

0

2

4 12 °C

Strain number

2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19

With antimicrobialsWithout antimicrobials

Fig. 7. Average lag time (7standard error, n ¼ 2) of Listeria mono-

cytogenes strains in frankfurter slurries at 4, 8, and 12 1C. See Table 1 for

strain identification. Frankfurters with antimicrobials contained 2%

potassium lactate and 0.2% sodium diacetate in the final formulation.

Slurries were prepared with one part of frankfurter homogenized with

three parts of sterile 0.1% peptone water. Filtered slurries were inoculated

with approx. 3 log10CFU/ml.

A. Pal et al. / Food Microbiology 25 (2008) 460–470468

1993; Schultze et al., 2006). In the current study, theslurries were not pasteurized or sterilized, which allowedthe inoculated strains of L. monocytogenes to grow againstcompetition with background microflora inherent with thesliced turkey breasts or frankfurters.

In our study, strains from human or animal listeriosiswere selected to provide diversity in serotypes, ribotypes,lineages, or sources. Recently, Lianou et al. (2006) reportedthat the lag times of 25 L. monocytogenes strains in TSBsupplemented with 0.6% yeast extract were not signifi-cantly different and provided little information for straincomparison. This observation was similar to our study inthe TSB medium where no significant difference in lag timewas noted between the strains at either of the storagetemperatures. However, significant lag time differencesbetween strains were observed when studied in slurrymedia. De Jesus and Whiting (2003) compared strainsbelonging to different lineages of L. monocytogenes in brain

heart infusion broth supplemented with 0.1M lactate andreported that lineage II had a significantly shorter lag timecompared to lineages I and III at 7 1C. These findingssuggest that in typical laboratory broths the lag phaseof L. monocytogenes, irrespective of its strain type, isminimally affected even under refrigeration temperatures.However, in a suboptimal or complex medium (possiblybecause of the presence of antimicrobials, lack of sufficientglucose, etc.), microbial strains may exhibit physiologicaldifferences during their lag phases under similar growthconditions. The effect of stress conditions on lag time ofL. monocytogenes was first studied by Whiting and Bagi(2002). Guillier et al. (2004) evaluated the impacts ofdifferent stress conditions common in the food environ-ment on the distributions of individual lag times of

ARTICLE IN PRESSA. Pal et al. / Food Microbiology 25 (2008) 460–470 469

L. monocytogenes. Their results suggested the importanceof stress-induced variability in lag time in determining thereliability of any predictive microbiology models. There-fore, studying strain comparison in food slurry media orfood matrices becomes important since differences in bothlag and exponential phases between strains are moreevident under those conditions.

The effect of the combination of PL and SD in inhibitingor delaying L. monocytogenes growth has been widelystudied (Schlyter et al., 1993; Stekelenburg, 2003; Schultzeet al., 2006). Similarly in this study, the MGR of most ofthe strains grown in slurries prepared from sliced turkey orfrankfurter without any lactate/diacetate was significantlygreater than in the slurries that included antimicrobials. Inthose few cases when the MGR were not smaller in theslurries of antimicrobial-containing sliced turkey or frank-furter, the difference of MGR compared to its counterpartslurries were not significant. With respect to the differencesin lag times, usually strains in slurries of both sliced turkeyand frankfurter formulated with or without antimicrobialremained similar at all three temperatures. This discre-pancy in the effect of lactate and diacetate on growth rateand lag time has not been explained before. As analyzedfrom the data of Schlyter et al. (1993), at 25 1C there wasno effect on the lag time of L. monocytogenes in turkeyslurry containing no antimicrobial, 0.1% SD, or combina-tion of 0.1% SD and 2.5% sodium lactate, althoughthe MGRs were 3.78, 3.38, and 1.42 day�1, respectively.It can be hypothesized that diluted antimicrobials subse-quent to slurry preparation affected the metabolism ofL. monocytogenes involved in the exponential phase growthwith no or little effect on the metabolic activity involved inthe lag phase.

The observations that the growth variation amongstrains did not follow a regular pattern, and that the varia-bility in growth rate among strains decreased with increasein temperature are consistent with other L. monocytogenes

growth comparative studies (De Jesus and Whiting, 2003;Lianou et al., 2006). Additional information in the currentstudy, which was not addressed in the previous investiga-tions, was the effect of sodium nitrite on L. monocytogenes

growth. The variability in growth rates and lag timesincreased with the inclusion of sodium nitrite in thefrankfurter slurry as compared to the uncured sliced turkeyslurry. The tendency of L. monocytogenes strains to exhibitsimilar growth kinetics with decreased variation at or nearoptimum growth conditions could be attributed to lessdemand for cellular energy expenditure, needed to over-come stress conditions (Robinson et al., 1998).

We found that the variations in lag times or MGRs of allthe tested strains at the three temperatures increased frombroth with minimum to maximum inhibitory factors (TSB,slurries of control turkey breasts, slurries of controlfrankfurters, slurries of antimicrobials containing turkeybreasts, and slurries of antimicrobials containing frankfur-ters). The average lag time of all the tested strains at threetemperatures in different media also increased in the same

order, but this sequence appeared to be growth phase-specific. The average value of MGRs of all the testedstrains followed the descending order of-slurries of controlturkey breasts, slurries of control frankfurters, TSB,slurries of antimicrobials containing turkey breasts, andslurries of antimicrobials containing frankfurters. Thoseobservations further suggested that induction of stresslevels from the media to L. monocytogenes strains was notconsistent for lag and exponential phase.At any given condition (except at 8 1C in TSB and

slurries of frankfurter with antimicrobials), the strain withthe shortest lag time did not essentially exhibit the fastestgrowth rate, as similar to other published reports (De Jesusand Whiting, 2003; Uyttendaele et al., 2004). However,based on the shortest lag time, the greatest MGR, or theshortest TTR100, the strains DUP-1042B, DUP-1044A,DUP-1039C, DUP-1030A, DUP-10142, DUP-1038B,DUP-1051B, DUP-1042C, and DUP-1039E were deter-mined to be fastest ribotypes under most of the studiedgrowth conditions. The TTR100 values also were calculatedby adding the time from both the lag and the exponentialphases with the rationale that the fastest growing strain willhave the shortest TTR100. The total time for L. mono-

cytogenes strains to increase by 1-log (TTR10) and 3-log(TTR1000) also were calculated (data not shown). However,the difference in values of TTR1000 and greater betweenstrains were reflective predominantly of the difference inthe MGR with a little effect of the lag phase duration;therefore, TTR100 values which provide a balanced effectof lag and exponential phases were estimated. Also,100CFU/g is an action level for L. monocytogenes indelicatessen foods in certain countries (Todd, 2007).It should be noted that two of these strains belong to 4b

serotype, but the association between fastest strains andserotypes was not observed since another strain of 4bserotype and lineage I (DUP-1038) was found to have aslower growth rate under most conditions. The lack ofassociation between serotype and fastest strain was alsoobserved in the slurry media of the current study and thatof Lianou et al.’s (2006). In their study, Barbosa et al.(1994) compared the growth kinetics of different serotypesand found that at 4 1C, serotype 3a had the shortest lagtime and 3b had the greatest exponential growth rate andat 10 1C, serotype 1/2b consistently had the shortest lagtime and greatest rate constant. Our results were indisagreement to those of Barbosa et al. (1994), sincecomparison of strains in a more extensive media typesyielded no particular serotype with exclusive linkage withfastest growth characteristics. This also could be due tounequal number of strains belonging to a particularserotype or lineage used in our study.The results of this study showed that statistical

performance for goodness-of-fit was similar for linear,logistic, Gompertz, or Baranyi growth models and thegrowth variability existed amongst L. monocytogenes

strains. The variation between strains was dependent onthe growth conditions, i.e. temperature and medium

ARTICLE IN PRESSA. Pal et al. / Food Microbiology 25 (2008) 460–470470

complexity. Therefore, any predictive microbiology studyshould consider inclusion of the fastest growing strains toaccount for the worst-case scenario.

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