Growth/no growth interfaces of Bacillus cereus ... - Science Direct

Food Microbiology, 2001, 18, 659^668 Available online at http://www.idealibrary.com on

doi:10.1006/fmic.2001.0429

RESEARCH NOTE

Growth/no growth interfaces of Bacillus cereus, Staphylococcus aureus and Salmonella enteritidis in model systems based on water activity, pH, temperature and ethanol concentration Rosalba Lanciotti1,*, Milena Sinigaglia2, Fausto Gardini1, Lucia Vannini1 and Maria Elisabetta Guerzoni1 This study focuses its attention on the boundary between the growth and no growth of three strains of Salmonella enteritidis, Bacillus cereus and Staphylococcus aureus in the presence of growth controlling factors such as temperature, pH, water activity (Aw) and ethanol concentration. Preliminarly, the minimal values of pH, Aw and temperature, and the maximum ethanol concentrations allowing the growth of the considered micro-organisms were determined. The calculation of these values enabled the use of logistic model to evaluate the growth/no growth boundary for the bacteria in relation to the considered independent variables. The location of the growth/no-growth boundaries for S. enteritidis and Staph. aureus were strongly a¡ected, at the same ethanol concentration, by temperature, pH and Aw . Among the considered species, Staph. aureus was endowed with the highest sensitivity to low pH values while B. cereus’s growth/no growth interface, was quite una¡ected by the combination of the stresses, when the physico^chemical conditions were above the minimum for growth. The e¡ects of temperature, Aw and ethanol on the limitation of growth of the considered species were not merely additive. It was possible to identify the combinations of such factors preventing the growth of Salmo# 2001Academic Press nella enteritidis, Staph. aureus and B. cereus.

Received: 5 January 2001 1

Introduction Food manufacturing companies are in a continual state of £ux with respect to microbiological risk and hazards. This is due

*Corresponding author. Fax: +390512099782; Email: [email protected] 0740 -0020/01/060659 +10 $35.00/0

to the development of new products and processes, changes in the raw material sources as well as changes to their target customer group. Microbiologists are usually responsible for the assessment of the impact of such commercial changes on the risk. However, traditional microbiological methods for food safety assessment are time consuming. r 2001 Academic Press

Dipartimento di Protezione e Valorizzazione Agroalimentare, UniversitaØ degli Studi di Bologna,Via San Giacomo 7, 40126 Bologna, Italy 2 Instituto di Produzioni e Preparazioni Alimentari, UniversitaØ degli Studi di Foggia Via Napoli 25, 73100 Foggia, Italy

660 R. Lanciotti et al.

Predictive modelling provides a fast and relatively inexpensive way to get reliable ‘¢rst estimates’ on microbial growth and survival (McMeekin et al. 1993). This technique is increasingly gaining importance as a powerful tool in food microbiology. Predictive modelling can be used for describing behaviour of microorganisms at di¡erent physico^chemical conditions, as well as process design and optimization for production and distribution chains, based on microbial safety and shelf-life (Alavi et al. 1999). Essentially, predictive modelling involves the use of mathematical expressions to describe microbial behaviour. These include functions that relate microbial density to time, and growth rate to the environmental conditions such as temperature, pH, water activity (Aw) and presence of antimicrobial agents. However, while kinetic models make possible the calculation of the food shelf-life or the prediction of the time span in which signi¢cant microbial growth might occur, the probabilistic models focus their attention towards deciding whether a micro-organism might or might not grow. Consequently, probability modelling is particularly useful when pathogenic or toxinogenic species are involved. In this case, the growth rate of a micro-organism is of lesser importance than the fact that the organism is present, and potentially able to multiply up to infectious dose or toxic levels. Ratkowski and Ross (1995) proposed the application in food microbiology of the logistic regression model. This enables modelling of the boundary between growth and no growth for bacterial species when one or more growth controlling factors are used. This model was illustrated by the authors using data of Shigella £exneri inoculated in model systems. This approach was subsequently used by Presser et al. (1998) to de¢ne the growth limits of Escherichia coli as a function of temperature, pH, lactic acid concentration and water activity in cultural broth based systems. Using culture media, growth/no growth models were also developed for other microbial species such as E. coli, Listeria monocytogenes and Klebsiella oxytoca (Tiengunoon 1998, Ross 1999).The logistic model was further developed to determine growth/ no growth interface of L. monocytogenes in a

food-based system by Bolton and Frank (1999), who expanded the binary logistic model to include stasis as a third choice, resulting in an expansion of the number of safe formulations. The present study focuses its attention on the boundary or interface between growth and no growth of three strains of Salmonella enteritidis, Bacillus cereus and Staphylococcus aureus in the presence of growth controlling factors such as temperature, pH, water activity (or glycerol concentration) and ethanol concentration. These species were chosen because they are frequently involved in foodborne diseases and frequently isolated in human samples. According to USDA-FSIS data from 1993 to 1997 (Olsen et al. 2000), B. cereus, Staph. aureus and Salmonella spp. caused 14 outbreaks and 691 cases, 41 outbreaks and 1413 cases (one death) and 357 outbreaks and 32610 cases (13 deaths), respectively.The S. enteritidis and Staph. aureus strains used in this work were of human origin and were chosen in order to study their ability to grow under ranges of the controlling factors usually present in food systems. Moreover, they were chosen because they are characterized by di¡erent physiological features, transmission modalities and food carriers. In fact, Salmonella is a zoonotic micro-organism having mainly a vertical transmission from animal to foods, while foods are generally contaminated by Staph. aureus throughout manipulation. Bacillus cereus, a spore-forming species, is becoming a major concern in recent years because of its ability to survive and grow in mild thermally treated foods (Chaves Lopez et al. 1997).

Materials and Methods Micro-organisms The strains B. cereus FG1, S. enteritidis B5 and Staph. aureus S33, belonging to the culture collection of Istituto di Produzioni e Preparazioni Alimentari of Foggia University, were used. They were isolated from cooked spinach, human faeces and pharynges tampon, respectively. All cultures were maintained on Brain Heart Infusion (BHI, Oxoid, Basingstoke, UK) slants and transferred each month to maintain their viability.Working cultures were obtained

Growth/no growth interfaces 661

by inoculating a loopful of culture into 10 ml of BHI and incubating at 371C for 18^24 h.

Determination of the minimum values of Aw, temperature and pH, and the maximum ethanol concentration allowing the growth of the three micro-organisms To estimate the minimum Aw value (Awmin) for the growth of B. cereus FG1, S. enteritidis B5 and Staph. aureus S33, the Aw of BHI was modi¢ed before the inoculation by adding decreasing concentration of glycerol (Carlo Erba, Milan, Italy), before autoclaving, to reach Aw values of 0?93, 0?94, 0?95, 0?96, 0?97, 0?98 and 0?99. The Aw values were measured, after autoclaving, with an AquaLab model CX2 Water activity Meter (Decagon Devices Inc., Pullman, Washington, USA). Appropriately diluted working cultures were inoculated into 100 -ml £asks containing 50 ml of BHI.The inoculum levels of the three species were about 103 cfu mlÿ1. For B. cereus the inoculum was performed with vegetative cells. The absence of spores was microscopically veri¢ed. For the determination of the Awmin, the pH of the medium was 6?5 and no ethanol was added. During the incubation at 371C, the microbial growth was monitored by measuring the increase in optical density (OD) values at 600 nm with a Beckman DU 640 spectrophotometer (Beckman, Fullerton, California, USA). The OD values were measured from aliquots (2 ml) taken from £ask cultures. For the evaluation of the minimum pH for the growth (pHmin), the pH of the medium, having an Aw of 0?99 and not supplemented with ethanol, was adjusted with HCl 1N or NaOH 1N (Carlo Erba). The pH values considered were 8, 7, 6, 5 and 4 and they were measured after autoclaving with a Crison Micro 2001 pH-meter (Crison, Barcelona, Spain). The incubation temperature, after the inoculum, was 371C. For the determination of the maximum ethanol concentration (ETOHmax) which allows growth, the ethanol (Carlo Erba), previously sterilized by ¢ltration, was added

to the growth medium, just after the inoculation of the considered micro-organisms, to bring its ¢nal concentration values between 0 and 3% (v/v). Before the ethanol addition, the medium had pH 6?5 and Aw 0?99. The incubation temperature, after the inoculum, was 371C. Incubation temperatures ranging from 10 to 451C were used for the estimation of the minimum temperature for growth (Tmin) of B. cereus FG1, S. enteritidis B5 and Staph. aureus S33 inoculated in BHI not supplemented with ethanol and having a pH of 6?5 and an Aw of 0?99. The absorbance data were modelled according to the Gompertz equation as modi¢ed by Zwietering et al. (1990) in order to estimate the maximum growth rate (mmax,) expressed as DOD/h, in the di¡erent conditions. The values of Tmin, allowing the growth of the three micro-organisms were estimated by ¢tting the square root growth rate values to the models proposed by Ratkowski et al. (1983): pffiffiffiffi K ¼ bðT ÿ Tmin Þf1 ÿ exp½cðT ÿ Tmax Þg Eqn ð1Þ where K = growth rate; T = temperature in degree K; Tmin= a theoretical lower temperature limit for growth at and below which the predicted growth rate is zero; b = a parameter, the regression coe⁄cient of the square root of the rate versus sub-optimal temperature; Tmax = the upper temperature limit at and beyond which the predicted growth rate is zero; c = an additional parameter to enable the model to ¢t the data at temperature near and above the optimal temperature for the growth. The values of pHmin and Awmin were estimated according to McMeekin et al. (1992): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi K ¼ bðT ÿ Tmin Þ ðpH ÿ pHmin pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ÿ ðAw ÿ Awmin Þ; Eqn ð2Þ where Tmin, pHmin and Awmin are notional (that is not necessarily observable) lower-limiting values of temperature, pH and water activity, respectively, at which the growth rate is predicted to be zero. The extrapolation of the values of growth rate obtained in relation to ethanol concentrations allowed the estimation of the ETOHmax values for the three species.


Experimental design The e¡ects of pH, water activity (Aw), incubation temperature and ethanol concentration on the growth/no growth of B. cereus FG1, S. enteritidis B5 and Staph. aureus S33 were determined by modulating the chosen variables according to four-factor, ¢ve-level Central Composite Designs (CCD). For each micro-organism, two di¡erent CCDs were performed. They di¡ered for the ranges of some of the independent variables considered. The combinations obtained from the two CCDs are presented in Table 1. Three replicates for each run, obtained from three di¡erent initial cultures, were analysed. The basal medium was BHI (Oxoid). After the inoculations at levels

of 103 cfu mlÿ1, the di¡erent runs were incubated at the temperatures of the CCD.

Growth/no growth evaluation The occurrence of growth was tested after 48 h of incubation by recording a visible increase of the turbidity of the broth. When the results were doubtful, possible growth was recorded by cultural methods (direct plating on speci¢c growth media). The occurrence of the growth was veri¢ed after a week of incubation.

Modelling The growth/no growth data obtained from the di¡erent runs of the two CCD were ¢tted with

Table 1. Experimental designs used to evaluate the growth/no growth interfaces of Salmonella enteritidis, Staphylococcus aureus and Bacillus cereus. Temperature and ethanol concentration were kept at the same levels in the two designs, while Aw and pH were changed. Levels in the second design are reported within parentheses Run

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Experimental designs Aw

Temperature (1C)

pH

Ethanol (% v/v)

0?915 (0?960) 0?915 (0?960) 0?915 (0?960) 0?915 (0?960) 0?965 (0?980) 0?965 (0?980) 0?965 (0?980) 0?965 (0?980) 0?940 (0?970) 0?940 (0?970) 0?915 (0?960) 0?915 (0?960) 0?915 (0?960) 0?915 (0?960) 0?965 (0?980) 0?965 (0?980) 0?965 (0?980) 0?965 (0?980) 0?940 (0?970) 0?940 (0?970) 0?890 (0?950) 0?990 (0?990) 0?940 (0?970) 0?940 (0?970) 0?940 (0?970) 0?940 (0?970) 0?940 (0?970) 0?940 (0?970) 0?940 (0?970) 0?940 (0?970)

17?5 17?5 32?5 32?5 17?5 17?5 32?5 32?5 25?0 25?0 17?5 17?5 32?5 32?5 17?5 17?5 32?5 32?5 25?0 25?0 25?0 25?0 10?0 40?0 25?0 25?0 25?0 25?0 25?0 25?0

4?75 (5?5) 6?25 (6?5) 4?75 (5?5) 6?25 (6?5) 4?75 (5?5) 6?25 (6?5) 4?75 (5?5) 6?25 (6?5) 5?50 (6?0) 5?50 (6?0) 4?75 (5?5) 6?25 (6?5) 4?75 (5?5) 6?25 (6?5) 4?75 (5?5) 6?25 (6?5) 4?75 (5?5) 6?25 (6?5) 5?50 (6?0) 5?50 (6?0) 5?50 (6?0) 5?50 (6?0) 5?50 (6?0) 5?50 (6?0) 4?00 (5?0) 7?00 (7?0) 5?50 (6?0) 5?50 (6?0) 5?50 (6?0) 5?50 (6?0)

1?5 0?5 0?5 1?5 0?5 1?5 1?5 0?5 1?0 1?0 0?5 1?5 1?5 0?5 1?5 0?5 0?5 1?5 1?0 1?0 1?0 1?0 1?0 1?0 1?0 1?0 0?0 2?0 1?0 1?0


the equation using the logistic regression modelling procedure of Statistica for Windows (Statsoft, Tulsa, Oklahama, USA). The model was applied as a generalized linear regression using as ¢xed parameters the Awmin Tmin, pHmin and ETOH max estimated in the ¢rst phase of the work. In particular the model used was: logitðPÞ ¼ b0 þ b1 lnðT ÿ Tmin Þ þ b2 lnðpH ÿ pHmin Þ þ b3 lnðAw ÿ Awmin Þ þ b4 lnðETOHmax ÿ ETOHÞ Eqn ð3Þ where logit(P) = ln[P/(1 P)] and P is the probability that the growth occurs. Given a data set, the value 1 was assigned to P if the growth was observed at the particular combination of conditions at which the factors were measured, or the value 0 was assigned if growth was not observed. After ¢tting the logistic regression model, predictions of the position of the interfaces growth/no growth were made letting P = 0?1, corresponding to a 10 : 90 probability that the micro-organism may grow. The goodness of ¢t of the model was tested by using the likelihood-ratio w2 statistic.

Results and Discussion As a preliminary phase, the minimal values of pH, Aw and temperature, and the maximum ethanol concentrations allowing the growth of the considered micro-organisms were determined. In Table 2, the Tmin, pHmin and Awmin values as well as the ETOHmax concentration allowing the growth of S. enteritidis, Staph. aureus and B. cereus are presented. The minimal temperature for S. enteritidis growth (Fig. 1) was lower than the mean values reported in literature (ICMSF 1996). In fact,

the growth of most Salmonellae is prevented at temperatures lower than 71C. The capacity of Salmonellae to grow at temperatures lower than 51C has been reported (D’Aoust 1991), but in some cases it has not been con¢rmed except by observation of colonies on selective media. However, Tmin has to be regarded as a theoretical lower temperature limit for the growth below which the predicted growth rate is zero (Ratkowski et al. 1991). Moreover, it was surprising the relatively high value of Awmin for the growth of Staph. aureus. However, the Aw of the growth medium was decreased adding glycerol. It is well known that the minimum water activity for growth varies with species, strain, temperature and types of humectant. For example, Santos et al. (1994) reported minimum Aw values for Aeromonas hydrophila growth ranging from 0?940 and 0?973 in relation to strain, incubation temperature and solute type. Generally, solutes such as glycerol which, unlike sugars and salts, rapidly permeate into most bacteria, are less inhibitory. Nevertheless, Staph. aureus, a salt-tolerant species, is inhibited at higher Aw values by glycerol rather than sodium chloride (Gould 1989). The Aw lowering ability of ethanol has also a great signi¢cance, for non-osmotolerant microorganisms. The adverse e¡ects of increasing concentration of ethanol on micro-organisms could be attributed both to ethanol hydrophobic nature, which accounts for speci¢c e¡ects on cell membranes, and the reduction of the aw of the system (Guerzoni et al. 1994, Guerzoni et al. 1997). Salmonella enteritidis was more sensitive to ethanol addition than B. cereus and Staph. aureus. In fact, as reported by Kalathenos et al. (1995), Gram-negative bacteria are more sensitive to this molecule due to their lipopolysaccharide layer which is an ethanol target. The e¡ects of temperature, Aw, pH and ethanol concentration on the growth of the three

Table 2. Minimum values of pH (pHmin), temperature (Tmin), water activity (Awmin) and maximum concentration of ethanol (ETOHmax) allowing the growth of Salmonella enteritidis, Staphylococcus aureus, and Bacillus cereus Micro-organism S. enteritidis Staph. aureus B. cereus

pHmin

Tmin (1C)

Awmin

ETOHmax (% v/v)

3?67 4?15 4?75

4?69 10?87 15?48

0?948 0?948 0?951

2?75 4?88 4?06


micro-organisms are shown in Table 3. From the selected data reported, it is evident that S. enteritidis is a micro-organism endowed with the highest growth potential in relation to the stress factors applied, while Staph. aureus is the most sensitive.

The equations obtained by ¢tting the logistic regression model to the experimental data for the considered micro-organisms are reported in Table 4. After ¢tting the logistic regression model, predictions were made by letting P = 0?1, corresponding to 10% of probabilities

Table 3. E¡ect of temperature, Aw , pH and ethanol concentration on growth of Salmonella enteritidis, Staphylococcus aureus and Bacillus cereus Aw

Temperature (1C)

pH

Ethanol (% v/v)

S. enteritidis

Staph. aureus

B. cereus

17?5 32?5 32?5 17?5 17?5 32?5 32?5 25?0 17?5 17?5 32?5 32?5 17?5 17?5 32?5 32?5 32?5 25?0 25?0 25?0 10?0 40?0 25?0 25?0 25?0 25?0 25?0

6?50 5?50 6?50 5?50 6?50 5?50 6?50 6?00 5?50 6?50 5?50 6?50 5?50 6?50 5?50 6?50 4?75 5?50 6?00 6?00 6?00 6?00 5?00 7?00 6?00 6?00 5?50

0?5 0?5 1?5 0?5 1?5 1?5 0?5 1?0 0?5 1?5 1?5 0?5 1?5 0?5 0?5 1?5 1?5 1?0 1?0 1?0 1?0 1?0 1?0 1?0 0?0 2?0 1?0

0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1

0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1

0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1

0?960 0?960 0?960 0?980 0?980 0?980 0?980 0?970 0?960 0?960 0?960 0?960 0?980 0?980 0?980 0?980 0?965 0?940 0?950 0?990 0?970 0?970 0?970 0?970 0?970 0?970 0?990

The results presented here concern only selected combinations of the two CCDs-1-growth observed after 48 h; 0, no growth observed after 48.

Table 4. Equations obtained by ¢tting the logistic regression model to the growth/no growth data observed for of Salmonella enteritidis, Staphylococcus aureus, and Bacillus cereus. The predictors of goodness of ¢t (likelihood-ratio w2 and P-value) are also reported Micro-organism

Equations

S. enteritidis

logit(P)¼0?187+4?07ln(Tÿ4?69)+3?31ln(Awÿ0?948)+1?96ln(pHÿ3?97)+0?50ln(2?753ÿETOH) likelihood-ratio w2¼20?62, P-value ¼ 0?00038

Staph. aureus

logit(P)¼^4?75+6?73ln(Tÿ10?87)+6?33ln(Awÿ0?948)+11?90ln(pHÿ4?15)+1?74ln(4?88ÿETOH) likelihood-ratio w2¼26?025, P-value ¼ 0?00003

B. cereus

logit(P)¼5?09+0.81ln(Tÿ15?48)+1?69ln(Awÿ0?951)+0?97ln(pHÿ4?75)+0?58ln(4?05ÿETOH) likelihood-ratio w2¼7?995, P-value ¼ 0?09178


that the micro-organisms may grow. Some predicted pH and temperature values on the boundary for the growth/no growth interface for S. enteritidis, Staph. aureus and B. cereus

are reported in Tables 5 and 6, respectively. It is clear from these data that the e¡ects of temperature, water activity and ethanol on the limitation of the growth of the considered species

Table 5. Selected predicted values for the pH on the boundary of the growth/no growth interface (after 48 h) for Salmonella enteritidis, Staphylococcus aureus, Bacillus cereus, corresponding to P = 0?1 of growth Temperature (1C)

10?0 17?5 17?5 17?5 17?5 17?5 17?5 25?0 25?0 25?0 25?0 25?0 32?5 32?5 32?5 32?5 32?5 32?5 40?0

Aw

Ethanol (% v/v)

0?970 0?980 0?980 0?965 0?965 0?960 0?960 0?993 0?970 0?970 0?970 0?950 0?980 0?980 0?965 0?965 0?960 0?960 0?970

Predicted critical pH values S. enteritidis

Staph. aureus

B. cereus

9?04 4?37 4?44 5?15 5?34 6?44 6?09 4?07 4?28 4?25 4?36 *^ 4?06 4?05 4?24 4?20 4?39 4?46 4?07

* 6?05 6?12 6?58 6?68 7?00 6?89 5?26 5?62 5?57 5?68 6?78 5?16 5?12 5?44 5?39 5?55 5?61 5?12

* 4?82 4?83 4?99 5?05 5?38 5?27 4?76 4?79 4?78 4?80 *^ 4?76 4?76 4?80 4?79 4?83 4?86 4?77

1?0 0?5 1?5 0?5 1?5 1?5 0?5 1?0 1?0 0?0 2?0 1?0 1?5 0?5 1?5 0?5 0?5 1?5 1?0

*Predicted pH values had no signi¢cance (i.e. over 14).

Table 6. Selected predicted values for the temperature on the boundary of the growth/no growth interface (after 48 h) for Salmonella enteritidis, Staphylococcus aureus, Bacillus cereus, corresponding to P = 0?1 aw

0?990 0?990 0?980 0?980 0?980 0?980 0?970 0?970 0?970 0?970 0?970 0?965 0?965 0?965 0?965 0?960 0?960 0?960 0?960

PH

6?00 5?50 5?50 6?50 5?50 6?50 6?00 6?00 6?00 5?00 7?00 4?75 6?25 4?75 6?25 5?5 6?50 5?50 6?50

Ethanol (% v/v) 1?0 1?0 0?5 1?5 1?5 0?5 0?0 1?0 2?0 1?0 1?0 0?5 1?5 1?5 0?5 1?5 0?5 0?5 1?5

Predicted critical temperature values (1C) S. enteritidis

Staph. aureus

B. cereus

9?5 10?3 11?4 10?4 11?9 10?0 12?5 12?9 13?8 16?1 11?5 20?3 14?7 21?5 14?0 20?8 16?4 19?6 17?3

17?7 22?7 25?7 16?8 26?7 16?4 22?6 23?3 24?3 * 16?7 * 24?0 * 23?2 * 24?9 48?2 25?8

15?5 15?5 15?6 15?5 15?6 15?5 15?6 15?6 15?7 16?6 15?6 * 15?8 * 15?7 17?1 15?9 16?8 16?1

*Predicted temperature values had no biological signi¢cance (i.e, over 551C).


were not merely additive. On the other hand, it has been reported that both temperature and Aw have a signi¢cant e¡ect on the vapour pressure of ethanol and other volatile molecules and consequently on their toxicity (Lanciotti and Guerzoni 1993, Lanciotti et al. 1999). In fact, the interaction of certain volatile molecules, including ethanol, with microbial membranes depends on their physical state, which in turn is dependent on temperature and solute nature and concentration (Caccioni et al. 1997, Gardini et al. 1997, Lanciotti et al. 1999). Moreover, as reported by McMeekin et al. (2000) the microbial tolerance to low water activity and pH values is not optimal near the optimum temperature for growth. The combined e¡ects of the variables considered were particularly evident for S. enteritidis. In fact, in presence of 0?5% of ethanol and temperature higher than 17?51C, at water activities of 0?965 and 0?980, the minimum pH values at which S. enteritidis grew were 5?15 and 4?37, respectively (Table 5). Although a synergistic e¡ect can be also evidenced in B. cereus, the minimum pH for its growth seemed poorly a¡ected by temperature, water activity and ethanol changes, when these factors are at levels over the minimum for the growth. Aberrant pH predictions were obtained when one of the considered factors was near the minimum for the growth. These predictions, which have a mathematical meaning, have no biological signi¢cance. Although this fact can be a limit of the model applied, it stresses the importance of a biological interpretation of the mathematical models. In Table 6, selected predicted temperature values for the growth/no growth interface are presented. Also in this case an interactive effect of pH, water activity and ethanol concentration on the minimum values of temperature for the growth of all the considered micro-organisms could be observed. Among the species considered, Staph. aureus was the one characterized by the highest sensitivity to pH changes. In fact, its minimum temperatures for growth were, at Aw 0?980 and ethanol concentration of 1?5%, 16?8 and 26?71C at pH 6?5 and 5?5, respectively. The minimum temperatures for the growth of B. cereus, although affected by pH, ethanol concentration and Aw , ranged in a narrow interval of values (less than

Figure 1. mmax square root of Salmonella enteritidis (a) and Staphylococcus aureus (b) as a function of incubation temperatures.The experimental data are ¢tted with the kinetic Ratkowski model (Ratkowski et al. 1983).

271C). In other words, B. cereus seemed quite una¡ected by the combination of the considered stress conditions, when the physico^chemical conditions were above the minimum required for growth. The combination of more stress conditions a¡ects the growth rate of this species (Benedict et al. 1993, Quintavalla and Parolari 1993) but over the minimal values of the considered individual factors, their interactions play a weak role on the growth potential of this micro-organism. Similar considerations can be made for the critical Aw values for the growth of the three species: As shown by Fig. 2, relative to the Aw limits (P = 0?1) for detectable growth of Staph. aureus, the location of the growth/no growth boundary in the presence of 0?5% of ethanol was strongly a¡ected both by temperatures and pH values. Among the considered species, Staph. aureus was endowed with the highest sensitivity to low pH values. In fact, for


interface. In fact, as reported by McMeekin et al. (2000), many of the events occurring in this region will not be expected and may well be reversed as the interface is crossed.

Acknowledgements The authors wish to express their gratitude to Prof Carlo Lerici for his friendly and critical support.

References

Figure 2. Aw limits (P = 0?1) for detectable growth of Staphylococcus aureus within 48 h. Ethanol concentration was ¢xed at 0?5% (v/v).

B. cereus and S. enteritidis the growth/no growth interfaces were £at. Moreover, the critical Aw threshold increased only in relation to the most stringent temperature and pH conditions (data not shown).

Conclusions The results of this study underline the fact that, by modelling the growth/no growth interface, the synergistic interaction of temperature, water activity, pH and ethanol concentration can be quanti¢ed. Moreover, it is possible to identify the combinations of such factors preventing the growth of S. enteritidis, Staph. aureus and B. cereus. These results have a practical implication for the identi¢cation of the conditions which can be applied to food preservation in order to ensure that no growth of such dangerous micro-organisms will occur. In fact, as reported by McMeekin et al. (2000), the de¢nition of growth/no growth interface can provide a precise set of conditions upon which a new generation of mild food preservation techniques may be based. However, further investigations are needed to clarify the physiological mechanisms close to either side of the

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