ORIGINAL PAPER Evaluation of temperature effect on

Chemical Papers 67 (7) 737–742 (2013) DOI: 10.2478/s11696-013-0365-1

ORIGINAL PAPER

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Evaluation of temperature effect on growth rate GG in milk using secondary models

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Ľubomír Valík*, Alžbeta Medveďová, Michal Čižniar, Denisa Liptáková Department of Nutrition and Food Quality Assessment, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Radlinského 9, 812 37 Bratislava, Slovakia Received 18 October 2012; Revised 17 January 2013; Accepted 21 January 2013

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The application of secondary temperature models on growth rates of Lactobacillus rhamnosus GG, the much studied probiotic bacterium, is investigated. Growth parameters resulting from a primary fitting were modelled against temperature using the following models: Hinshelwood model (H), Ratkowsky extended model (RTK2), Zwietering model (ZWT), and cardinal temperature model with inflection (CTMI). As experienced by other authors, the RTK2, ZWT, and CTMI models provided the best statistical indices related to fitting the experimental data. Moreover, with the biological background, the following cardinal temperatures of L. rhamnosus GG resulted from the study by the model application: tmin = 2.7 ◦C, topt = 44.4 ◦C, tmax = 52.0 ◦C. The growth rate of the strain under study at optimal temperature was 0.88 log10 (CFU mL−1 h−1 ). c 2013 Institute of Chemistry, Slovak Academy of Sciences

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Keywords: temperature, growth modelling, L. rhamnosus GG

Introduction

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Quantitative food microbiology and predictive modelling are usually closely focused on issues limiting food safety and quality. Within the risk assessment tools, quantification is generally concerned with the presence and growth of pathogens in foods and the proper determination of food shelf-life (Gibson & Roberts, 1989; McMeekin et al., 1993; McKellar & Lu 2004; Brul et al., 2007). Several primary and secondary models are used in quantitative or predictive microbiology to characterise the growth of microorganisms in relation to time and food environmental factors, respectively. On the other hand, they also serve as a basis for tertiary model systems used for the prediction of microbial behaviour in foods (Ross & McMeekin, 1994). However, the areas of food safety and food quality still provide relevant challenges for predictive microbiology, one of which is the growth description of lactic acid bacteria during food fermentations or probiotic microorganisms in food matrices. This would enable the use of modelling methodology *Corresponding author, e-mail: [email protected]

not only in dairy product quality but also in product functionality. These ideas were endorsed by the review by Roupas (2008). Lactobacillus rhamnosus is a Gram-positive, nonspore forming, facultative anaerobic or microaerophilic, non-motile, and catalase-negative microorganism. It is a mesophile but, depending on the strain, may grow at temperatures below 15 ◦C or above 40 ◦C. The optimal pH value for its growth is in the range from 6.4 to 6.9 (Liew et al., 2005) and the minimal pH can be found within the range from 4.4 to 3.4, depending on the buffering capacity of the medium (Helland et al., 2004). Its growth requirements include folic acid, riboflavin, niacin, pantothenic acid, and calcium (Curry & Crow, 2004). The metabolism of L. rhamnosus is facultative heterofermentative (lactobacilli Group 2). It converts hexoses into L(+) lactic acid, in accordance with the Embden–Meyerhof pathway; due to aldolase and phosphoketolase, pentoses are also fermented. Up to 1.5 % of lactic acid is usually produced in a glucose medium. In the absence of glucose, it produces lactic acid, acetic acid, formic

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Ľ. Valík et al./Chemical Papers 67 (7) 737–742 (2013)

Experimental L. rhamnosus GG was kindly provided by Dr. Salminen (University of Turku, Turku, Finland) through the mediation of Dr. Lauková (State Veterinary and Food Institute, Košice, Slovakia). The strain of L. rhamnosus GG was stored in de ManRogosa–Sharpe broth (MRS; Biomark, Pune, India) at (5 ± 1) ◦C. The standard suspension of the microorganism was prepared from an 18h culture grown in MRS broth at 37 ◦C. This culture was inoculated into ultra-pasteurised (UHT) milk (Rajo, Bratislava, Slovakia) at a concentration of approximately 103 CFU mL−1 . Three parallel static cultivations of 400 mL milk samples were carried out at appropriately ranked temperatures from 6 ◦C to 50 ◦C. At the due times, the samples were withdrawn to determine the number of L. rhamnosus GG on MRS agar in accordance with Slovak Technical Standard STN ISO 15214 (Slovak Office of Standards, Metrology and Testing, 2002). The growth curves of L. rhamnosus GG were modelled with a DMFit tool, specifically with the scale-free Dmodel for bacterial growth developed by Baranyi and Roberts (1994). Three parallel curves were used at each temperature. The growth parameters calculated from the primary model were modelled against temperature. The growth rates (Gr) calculated by the above curve fitting were modelled as a function of temperature with the following models as applied by Rosso et al. (1993), the Hinshelwood model (H), the extended square-root model described by Ratkowsky et al. (1982) (RTK), the Zwietering model (ZWT), and the Rosso cardinal temperature model with inflection (CTMI). The Hinshelwood model represents one of the mechanistic modifications of the Arrhenius type models (Ross & Dalgaard, 2004).

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acid, and ethanol (Jyoti et al., 2003; G¨ orner & Valík, 2004). Lactobacillus rhamnosus GG belongs to a group of probiotic strains with desirable properties and well-documented clinical effects fully described in the United States and European patents (US 4839281 and EP 0199535 A3) (Gorbach and Goldin (1989); see http://v3.espacenet.com/textdoc?DB= EPODOC&IDX=US4839281). Hickey (2005) regarded L. rhamnosus GG as the world’s most extensively clinically researched probiotic, proven to enhance natural resistance and a healthy digestive system in humans. This was endorsed in a review article by Dicks and Botes (2010). L. rhamnosus GG exhibited a high tolerance to the acidic conditions of the stomach (Tuomola et al., 2000; Lam et al., 2007) surviving the intestinal passage (Mattila-Sandholm et al., 1999) with the ability to adhere to intestinal mucus (Tuomola et al., 2000; Rinkinen et al., 2003; Collado et al., 2007) and transiently colonising the gastrointestinal tract after three days of treatment. The clinical effects of L. rhamnosus GG represent an increasing resistance to respiratory and gastrointestinal infections, reduced incidence of fever, and a healing effect on atopic eczema (Mattila-Sandholm et al., 1999). L. rhamnosus GG was also confirmed as able to inhibit the adhesion of Clostridium histolyticum, Cl. difficile, and Salmonella enterica. The combination of L. rhamnosus GG with L. rhamnosus LC705 inhibited the growth of Staphylococcus aureus, Escherichia coli, and Salmonella enterica. However, the most effective combination for inhibiting Clostridium difficile was L. rhamnosus GG, L. rhamnosus LC705, and Propionibacterium freudenreichii JS (Collado et al., 2007). In addition, the strains of L. rhamnosus GG and LC705 were found to bind aflatoxins efficiently (El-Nezami et al., 1996; Tuomola et al., 2000). Due to its probiotic and antimicrobial activities, L. rhamnosus GG may be used in food industry not only as a probiotic but also as a protective culture in fermented and non-fermented dairy products, beverages, ready-to-eat foods, dry sausages, and salads (Ty¨ opp¨ onen et al., 2003). The recent scientific opinion of the EFSA Panel on Dietetic Products, Nutrition and Allergies (EFSA Panel on Dietetic Products, Nutrition and Allergies, 2011) considered the maintenance of defence against pathogenic gastrointestinal microorganisms as a beneficial physiological effect, but not including the treatment of gastrointestinal infections. Despite the broad interest in and use of probiotics within the food industry, the growth data of specific strains, including the strain GG, are not generally available. This work sought to describe the growth dynamics of the probiotic strain L. rhamnosus GG in milk and to apply several models for the growth data found in relation to temperature in whole range.

Gr = A1 e−B1 /RT − A2 e−B2 /RT

(1)

where Gr/log(CFU mL−1 h−1 ) is the exponential growth rate estimated by the Baranyi model, A1 / log(CFU mL−1 h−1 ) and A2 /log(CFU mL−1 h−1 ) are the frequency factors, B1 /(J mol−1 ) and B2 /(J mol−1 ) comprise the activation energies, T/K is the temperature, and R (= 8.314 J mol−1 K−1 ) is the ideal gas constant. The extended square-root model (RTK2) was described by Ratkowsky et al. (1982) for the entire biokinetic range of growth temperatures. 2 Gr = b (T − Tmin) 1 − ec(T −Tmax )

(2)

where b/K−1 and c/K−1 are the model parameters and Tmin /K and Tmax /K are the theoretical minimum


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and maximum growth temperatures, i.e. the temperatures below and above which microorganism growth is no longer observed, respectively. The Zwietering model (ZWT) was proposed by Zwietering et al. (1991) as an alternative to the RTK model. 2 Gr = [b (T − Tmin )] 1 − ec(T −Tmax ) (3)

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The cardinal temperature model with inflection (CTMI) was developed empirically but it demonstrated the growth rate change as a function of cardinal temperature parameters, including their biological significance (Rosso et al., 1995). It was defined by Rosso et al. (1993) as follows: 2 Gr = Sup 0.0, Gropt (T − Tmax ) (T − Tmin ) (Topt − Tmin )[(Topt − Tmin )(T − Topt )− − (Topt − Tmax )(Topt + Tmin − 2T )] (4)

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where Topt /K is the optimal temperature for the microorganism growth. The above models were implemented using MATLAB (The MathWorks, 2006a). The function lsqcurvefit was used to fit the models detailed above to the data. It is an implementation of a general solver for solving the non-linear least squares problems provided by the Optimisation Toolbox (The MathWorks, 2006b) for MATLAB. Parameter starting values were chosen following the methodology described by Rosso et al. (1993). The starting values of the parameters for the CTMI model were chosen from a graphical examination of the data. For the other models, where the parameters have no biological interpretation and no direct graphical counterpart, their starting values were chosen by an empirical trial and error approach. The optimisation was performed with 20 different parameter starting values, located symmetrically on the corners of a hypercube centred on the first parameter estimate. The parameter values corresponding to the solution with the best fit to the data were then used for comparison of the models. The ordinary least-squares criterion was used to fit the models to the data. The sum of the squared residuals (RSS) was defined as follows: RSS =

n

k=1

(Grobserved − Grcalculated)2k

(5)

where n is the number of data points. The smaller the RSS, the better the fit.

Fig. 1. Graphical comparison of temperature models for fitting L. rhamnosus GG data. Symbols ( ) indicate growth rates estimated from fitted growth curves at incubation temperature. The lines were computed using the following models: Hinshelwood model (dashed curve), Ratkowsky extended model (dot–dashed curve), Zwietering model (dotted curve), and Cardinal temperature model with inflection (solid curve).

Results and discussion

Some of the growth curves covering the suboptimal temperature region of the probiotic L. rhamnosus GG strain were presented by Valík et al. (2008). In order to provide a growth description of the strain over the whole temperature range, additional growth experiments were carried out at optimal and beyond the optimal growth temperatures. Hence, more sophisticated models could be used in secondary modelling. According to Rosso et al. (1993), two different approaches can be used for the temperature models. The mechanistic approach is based on the Arrhenius equation and the hypothesis of the determining reaction responsible for changes in growth rate with temperature. The second approach is empirical: the models are constructed from a mathematical function and its suitability for fitting biological data. Four different models were used to describe the changes in growth rate as a function of temperature (t/ ◦C). The Hinshelwood model belongs to the mechanistic group of models. The other models, RTK2, ZWT, and CTMI, are empirical. In this study, these models were applied to the L. rhamnosus growth rates (in units log(CFU mL−1 h−1 )) and their estimated parameters are summarised in Table 1. The final graphical representations of all the models are shown in Fig. 1. A mutual visual comparison of the models by their predicted and observed rates can be seen in Fig. 2. From these figures, it appears that the best fit of experimental data was performed with the RTK and CTMI models. The following cardinal temperatures were estimated by the second model:

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Table 1. Estimated parameters provided by temperature models for fitting L. rhamnosus GG data Model Parameter

H

RTK2

ZWT

CTMI

Estimated value ± 95 % confidence interval ± ± ± ± – – – – – –

0.061 2485 0.42 17.9 0.0248 0.2116 1.66 54.58

– – – – ± ± ± ± – –

0.0018 0.1238 0.39 1.99

0.025 0.178 1.82 52.68

– – – – ± ± ± ± – –

0.005 0.055 0.35 0.41

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3.789 7266 58.53 469.5

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A1 /log(CFU mL−1 h−1 ) B1 /(J mol−1 ) A2 /log(CFU mL−1 h−1 ) B2 /(J mol−1 ) b c tmin / ◦C tmax / ◦C topt / ◦C Gropt /log(CFU mL−1 h−1 )

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Fig. 2. Representation of predicted against observed growth rates for temperature models applied for fitting L. rhamnosus GG data. The dashed line is an identity line. The symbols indicate the growth rates predicted by the Hinshelwood model (circles), Ratkowsky extended model (diamonds), Zwietering model (triangles), and Cardinal temperature model with inflection (squares).

tmin = 2.7 ◦C, topt = 44.4 ◦C, and tmax = 52.0 ◦C. Moreover, under optimal temperature conditions, the fourth and last parameter of this model provides the growth rate of 0.88 log(CFU L−1 h−1 ) which, after recalculation to specific growth rate (µ = 2.03 h−1 ) or time to double the number of CFU of 0.34 h (Baranyi & Roberts, 1994) can be useful for microbiologists and technologists in dairy practices. Recently, Alvarez et al. (2010) provided a biotechnologically-designed kinetic study on biomass growth, lactic acid production and lactose consumption by L. casei var. rhamnosus in deproteinised non-supplemented whey. However, they found the higher specific growth rate µ = 2.2 h−1 at 37 ◦C, the only temperature used in the experiments. To assess the statistical quality of the models, the

2.67 51.96 44.36 0.882

– – – – – – ± ± ± ±

0.30 0.37 0.27 0.010

F-test was used. The F-values calculated for each model were lower than the reference F-value (F95% = 1.79–1.80); therefore, the variance of all the models was equal to the reference variance so the model predictions were statistically acceptable (Table 2). The H-model appeared to fit the data almost as well. It showed higher residuals in the region of lower temperature, as demonstrated in the worst validation results. This is probably characteristic of this model, as was also observed by Zwietering et al. (1991). The Hinshelwood model was subject to criticism from both groups of modellers, Zwietering et al. (1991) and Rosso et al. (1993). Their main criticisms were: strong correlation of two parameters causing difficulties in their estimation; the very large confidence interval of the parameters; and unrealistic activation energies for an enzyme reaction and the high-temperature denaturation, resulting in doubts as to the biological meaning of the parameters. In the present study, the parameters B1 of the H-model were also associated with a large confidence interval. Further, a potential estimation of the activation energies from the parameters B2 and B1 would, respectively, result in a lower value for a denaturation reaction than for an enzyme-catalysed reaction. With reference to the character of these reactions and to the values of activation energies mentioned by Zwietering et al. (1991), we deemed this to be irrational. On the basis of the statistical criteria, the RTK2, ZWT, and CTMI models fit the data almost identically. In comparison with the ZWT and CTMI models, the RTK2 model provided not only the highest tmax value with a large confidence interval but also a large confidence interval of parameter c. As confirmation of our results, Rosso et al. (1993) also found strong positive correlations between parameters b and tmin, and negative correlations between c and b, c and tmin , as well as c and tmax . For these reasons, out of the models applied in this study, ZWT and Rosso’s CTMI model may be preferable. However, according to the authors

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Table 2. Parameters of statistical comparison of model performance L. rhamnosus GG MSE RMSE RSS F-test value = (SS2 /df2 )/(SS1 /df1 ) F-table value (95 % confidence) R2

H

RTK2

ZWT

CTMI

0.0011 0.0333 0.0411 0.8764 1.80 0.9910

0.0002 0.0126 0.0059 0.9998 1.80 0.9984

0.0002 0.0128 0.0061 0.9979 1.80 0.9983

0.0002 0.0136 0.0069 0.9880 1.79 0.9981

practical meaning of all four parameters of the model characterising the probiotic strain under study. Dairy practice and research can take into account the following cardinal temperatures of L. rhamnosus GG: (tmin = 2.7 ◦C, topt = 44.4 ◦C, and tmax = 52.0 ◦C) and optimal growth rate of 0.88 log(CFU mL−1 h−1 ) resulting from this study and CTMI model application. The growth of L. rhamnosus GG at temperatures of 5–7 ◦C was minimal and was not accompanied by a decrease in the pH of milk. This might allow food practice to consider its application in the production of fresh dairy products.

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of the CTMI model, this model provided all the parameters with the simple biological meaning required by microbiologists. The estimation of the cardinal values of such an important factor as temperature gives practical relevance to the parameters, which was also an aim of this study on growth of the probiotic strain L. rhamnosus GG. As there was a lack of comparable growth data available for this commercial strain in the literature, an internal validation was performed. The validation of the secondary models used was performed in accordance with Ross (1996) and Baranyi et al. (1999). Bias and accuracy factors test the hypothesis that the model under evaluation predicts the true meaning or better represents it than any other model. A bias factor > 1 indicates that the model is, in general, fail-safe (Baranyi et al., 1999) but for a bias factor of 0.90– 1.05, the model performance is still considered good (te Giffel & Zwietering, 1999). In addition, within the validation step, the growth rates of L. rhamnosus GG were compared with its rates in co-cultures with the strain S. aureus 2064 at 15 ◦C to 21 ◦C (Medveďová et al., 2009). At first glance, there were no indicators that S. aureus influenced the growth of L. rhamnosus GG in milk, which is why the four models applied in this study were validated on the basis of these independent and repeated trials. The practical assumption that S. aureus did not affect the growth of L. rhamnosus GG was confirmed, as the following bias factors of 0.883, 1.093, 1.092, and 1.094 resulted from validation of the H, RTK2, ZWT, and CTMI models, respectively. The corresponding calculated accuracy factors were 1.201, 1.103, 1.102, and 1.102, respectively, in the same order. For the growth rate of Leuconostoc mesenteroides as a broth culture, similar accuracy factors of 1.09–1.16 and a bias factor of 0.95–1.01 were found by ZureraCosano et al. (2006).

Conclusions In the current study, four existing models to describe the effect of temperature on the growth rate of L. rhamnosus GG were adopted. On the basis of the ordinary least square criterion (RSS), Ratkowsky’s extended model, followed by Zwietering’s and the cardinal temperature model with inflection, exhibited the best data fit. We are in accord with the authors of the CTMI model in appreciating the biological and

Acknowledgements. This work was financially supported by the Slovak Research and Development Agency under contracts nos. APVV-20-005605 and APVV-0590-10.

References

Alvarez, M. M., Aguirre-Ezkauriatza, E. J., Ramírez-Medrano, A., & Rodríquez-Sánchez, Á. (2010). Kinetic analysis and mathematical modeling of growth and lactic acid production of Lactobacillus casei var. rhamnosus in milk whey. Journal of Dairy Science, 93, 5552–5560. DOI: 10.3168/jds.20103116. Baranyi, J., Pin, C., & Ross, T. (1999). Validating and comparing predictive models. International Journal of Food Microbiology, 48, 159–166. DOI: 10.1016/s0168-1605(99)00035-5. Baranyi, J., & Roberts, T. A. (1994). A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology, 23, 277–294. DOI: 10.1016/01681605(94)90157-0. Brul, S., van Gerwen, S., & Zwietering, M. (2007). Modelling microorganisms in food. Cambridge, UK: Woodhead Publishing. Collado, M. C., Meriluoto, J., & Salminen, S. (2007). In vitro analysis of probiotic strain combinations to inhibit pathogen adhesion to human intestinal mucus. Food Research International, 40, 629-636. DOI: 10.1016/j.foodres.2006.11.007. Curry, B., & Crow, V. (2004). Lactobacillus casei group. In H. Roginski, J. W. Fuquay, & P. F. Fox (Eds.), Encyclopedia of dairy science (pp. 1479–1484). San Diego, CA, USA: Academic Press. Dicks, L. M. T., & Botes, M. (2010). Probiotic lactic acid bacteria in the gastro-intestinal tract: health benefits, safety and mode of action. Beneficial Microbes, 1, 11–29. DOI: 10.3920/bm2009.0012. EFSA Panel on Dietetic Products, Nutrition and Allergies (2011). Scientific opinion on the substantiation of a health claim related to Lactobacillus rhamnosus GG and maintenance of defence against pathogenic gastrointestinal microorganisms pursuant to Article 13(5) of Regulation (EC) No 1924/2006. EFSA Journal, 9, 2167. DOI: 10.2903/j.efsa.2011. 2167.

742


Ross, T. (1996). Indices for performance evaluation of predictive models in food microbiology. Journal of Applied Bacteriology, 81, 501–508. DOI: 10.1111/j.1365-2672.1996.tb03539.x. Ross, T., & McMeekin, T. A. (1994). Predictive microbiology. International Journal of Food Microbiology, 23, 241–264. DOI: 10.1016/0168-1605(94)90155-4. Ross, T., & Dalgaard, P. (2004). Secondary models. In R. C. McKellar, & X. W. Lu (Eds.), Modeling microbial responses in food (pp. 63–150). Boca Raton, FL, USA: CRC Press. Rosso, L., Lobry, J. R., & Flandrois, J. P. (1993). An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. Journal of Theoretical Biology, 162, 447–463. DOI: 10.1006/jtbi.1993.1099. Rosso, L., Lobry, J. R., Bajard, S., & Flandrois, J. P. (1995). Convenient model to describe the combined effects of temperature and pH on microbial growth. Applied and Environmental Microbiology, 61, 610–616. Roupas, P. (2008). Predictive modelling of dairy manufacturing processes. International Dairy Journal, 18, 741–753. DOI: 10.1016/j.idairyj.2008.03.009. Slovak Office of Standards, Metrology and Testing (2002). Slovak standard. Microbiology of food and animal feeding stuffs. Horizontal method for the enumeration of mesophilic lactic acid bacteria. Colony-count technique at 30 ◦C. STN ISO 15214. Bratislava, Slovakia. te Giffel, M. C., & Zwietering, M. H. (1999). Validation of predictive models describing the growth of Listeria monocytogenes. International Journal of Food Microbiology, 46, 135– 149. DOI: 10.1016/s0168-1605(98)00189-5. The MathWorks (2006a). Using MATLAB. Natick, MA, USA: The MathWorks, Inc. The MathWorks (2006b). Optimization toolbox for use with MATLAB: User’s guide. Natick, MA, USA: The MathWorks, Inc. Tuomola, E. M., Ouwehand, A. C., & Salminen, S. J. (2000). Chemical, physical and enzymatic pre-treatments of probiotic lactobacilli alter their adhesion to human intestinal mucus glycoproteins. International Journal of Food Microbiology, 60, 75–81. DOI: 10.1016/s0168-1605(00)00319-6. Ty¨ opp¨ onen, S., Petäjä, E., & Mattila-Sandholm, T. (2003). Bioprotectives and probiotics for dry sausages. International Journal of Food Microbiology, 83, 233–244. DOI: 10.1016/s0168-1605(02)00379-3 Valík, Ľ., Medveďová, A., & Liptáková, D. (2008). Characterization of the growth of Lactobacillus rhamnosus GG in milk at suboptimal temperatures. Journal of Food and Nutrition Research, 47, 60–67. Zurera-Cosano, G., García-Gimeno, R. M., Rodríguez-Pérez, R., & Hervás-Martínez, C. (2006). Performance of response surface model for prediction of Leuconostoc mesenteroides growth parameters under different experimental conditions. Food Control, 17, 429–438. DOI: 10.1016/j.foodcont.2005.02. 003. Zwietering, M. H., De Koos, J. T., Hasenack, B. E., de Witt, J. C., & van’t Riet, K. (1991). Modeling of bacterial growth as a function of temperature. Applied and Environmental Microbiology, 57, 1094–1101.

A

ut

ho

rc op y

El-Nezami, H., Salminen, S. J., & Ahokas, J. (1996). Biological control of food carcinogens with use of Lactobacillus GG. Nutrition Today, 31, 43S. Gibson, A. M., & Roberts, T. A. (1989). Predicting microbial growth: development of a mathematical model to predict bacterial growth responses. Food Australia, 41, 1075–1079. Gorbach, S. L., & Goldin, B. R. (1989). U.S. Patent No. US 4,839,281. Washington, DC, USA: U.S. Patent and Trademark Office. G¨ orner, F., & Valík, Ľ. (2004). Aplikovaná mikrobiológia požívatín (Applied Food Microbiology). Bratislava, Slovakia: Malé centrum. (in Slovak) Helland, M. H., Wicklund, T., & Narvhus, J. A. (2004). Growth and metabolism of selected strains of probiotic bacteria in milk- and water-based cereal puddings. International Dairy Journal, 14, 957–965. DOI: 10.1016/j.idairyj.2004.03.008. Hickey, M. (2005). Current legislation of probiotic products. In A. Tamime (Ed.), Probiotic dairy products (pp. 73–97). Oxford, UK: Blackwell Publishing. DOI: 10.1002/97804709957 85.ch4. Jyoti, B. D., Suresh, A. K., & Venkatesh, K. V. (2003). Diacetyl production and growth of Lactobacillus rhamnosus on multiple substrates. World Journal of Microbiology & Biotechnology, 19, 509–514. DOI: 10.1023/a:1025170630905. Lam, E. K. Y., Tai, E. K. K., Koo, M. W. L., Wong, H. P. S., Wu, W. K. K., Yu, L., So, W. H. L., Woo, P. C. Y., & Cho, C. H. (2007). Enhancement of gastric mucosal integrity by Lactobacillus rhamnosus GG. Life Sciences, 80, 2128–2136. DOI: 10.1016/j.lfs.2007.03.018. Liew, S. L., Arrif, A. B., Raha, A. R., & Ho, Y. W. (2005). Optimization of medium composition for the production of a probiotic microrganism, Lactobacillus rhamnosus, using response surface methodology. International Journal of Food Microbiology, 102, 137–142. DOI: 10.1016/j.ijfoodmicro. 2004.12.009. Mattila-Sandholm, T., Blum, S., Collins, J. K., Crittenden, R., de Vos, W., Dunne, C., Fondén, R., Grenov, G., Isolauri, E., Kiely, B., Marteau, P., Morelli, L., Ouwehand, A., Reniero, R., Saarela, M., Salminen, S., Saxelin, M., Schiffrin, E., Shanahan, F., Vaughan, E., & von Wright, A. (1999). Probiotics: towards demonstrating efficacy. Trends in Food Science & Technology, 10, 393–399. DOI: 10.1016/s09242244(00)00029-7. McKellar, R. C., & Lu, X. W. (Eds.) (2004). Modeling microbial responses in food. Boca Raton, FL, USA: CRC Press. McMeekin, T. A., Olley, J. N., Ross, T., & Ratkowsky, D. A. (1993). Basic concepts and methods. In T. A. McMeekin, J. N. Olley, T. Ross, & D. A. Ratkowsky (Eds.), Predictive microbiology: Theory and application (pp. 11–86). New York, NY, USA: Wiley. Medveďová, A., Valík, Ľ., & Studeničová, A. (2009). The effect of temperature and water activity on the growth of Staphylococcus aureus. Czech Journal of Food Science, 27(Special issue 2), S2-28–S2-35. Ratkowsky, D. A., Olley, J., McMeekin, T. A., & Ball, A. (1982). Relationship between temperature and growth rate of bacterial cultures. Journal of Bacteriology, 149, 1–5. Rinkinen, M., Jalava, K., Westermarck, E., Salminen, S., & Ouwehand, A. C. (2003). Interaction between probiotic lactic acid bacteria and canine enteric pathogens: a risk factor for intestinal Enterococcus faecium colonization? Veterinary Microbiology, 92, 111–119. DOI: 10.1016/s03781135(02)00356-5.