Development and validation of predictive models for the effect of storage temperature and pH on the growth boundaries and kinetics of Alicyclobacillus acidoterrestris ATCC 49025 in fruit drinks

Food Microbiology 74 (2018) 40e49

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Development and validation of predictive models for the effect of storage temperature and pH on the growth boundaries and kinetics of Alicyclobacillus acidoterrestris ATCC 49025 in fruit drinks Myrsini Kakagianni a, Kelly Kalantzi b, Evangelos Beletsiotis b, Dimitrios Ghikas b, Alexandra Lianou c, Konstantinos P. Koutsoumanis a, * a

Laboratory of Food Microbiology and Hygiene, Department of Food Science and Technology, School of Agriculture, Faculty of Agriculture, Forestry and Natural Environment, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece Department of Molecular Microbiology, Quality Assurance Division, Delta Foods S.A., 23rd km National Road Athens-Lamia, 145 65 Agios Stefanos, Greece c Laboratory of Microbiology and Biotechnology of Foods, Department of Food Science and Human Nutrition, School of Food, Biotechnology and Development, Agricultural University of Athens, Iera Odos 75, Athens 11855, Greece b

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 28 February 2018

This study was undertaken to provide quantitative tools for predicting the behavior of the spoilage bacterium Alicyclobacillus acidoterrestris ATCC 49025 in fruit drinks. In the first part of the study, a growth/no growth interface model was developed, predicting the probability of growth as a function of temperature and pH. For this purpose, the growth ability of A. acidoterrestris was studied at different combinations of temperature (15e45
C) and pH (2.02e5.05). The minimum pH and temperature where growth was observed was 2.52 (at 35 and 45
C) and 25
C (at pH  3.32), respectively. Then a logistic polynomial regression model was fitted to the binary data (0: no growth, 1: growth) and, based on the concordance index (98.8%) and the Hosmer-Lemeshow statistic (6.226, P ¼ 0.622), a satisfactory goodness of fit was demonstrated. In the second part of the study, the effects of temperature (25e55
C) and pH (3.03e5.53) on A. acidoterrestris growth rate were investigated and quantitatively described using the cardinal temperature model with inflection and the cardinal pH model, respectively. The estimated values for the cardinal parameters Tmin, Tmax, Topt and pHmin, pHmax, pHopt were 18.11, 55.68, 48.60
C and 2.93, 5.90, 4.22, respectively. The developed models were validated against growth data of A. acidoterrestris obtained in eight commercial pasteurized fruit drinks. The validation results showed a good performance of both models. In all cases where the growth/no growth interface model predicted a probability lower than 0.5, A. acidoterrestris was, indeed, not able to grow in the tested fruit drinks; similarly, when the model predicted a probability above 0.9, growth was observed in all cases. A good agreement was also observed between growth predicted by the kinetic model and the observed kinetics of A. acidoterrestris in fruit drinks at both static and dynamic temperature conditions. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Alicyclobacillus acidoterrestris Fruit drinks Growth boundaries Growth model

1. Introduction For many years, heat processed fruit drinks were considered as microbiologically stable foods mainly due to their low pH (<4.0). During the 80's however, Alicyclobacillus acidoterrestris was identified as the causative agent of a large spoilage incident of apple juice in Germany (Cerny et al., 1984). Since then, this spore-forming bacterium has been recognized as a major quality problem by

* Corresponding author. E-mail address: [email protected] (K.P. Koutsoumanis). https://doi.org/10.1016/j.fm.2018.02.019 0740-0020/© 2018 Elsevier Ltd. All rights reserved.

manufacturers and processors in the fruit industry (Huang et al., 2015; Steyn et al., 2011; Vieira et al., 2002; Wang et al., 2014). The main characteristics of Alicyclobacillus spp. are the heat resistance of its spores and their ability to germinate and outgrow in acidic environments. After spore germination and outgrowth, the metabolically active cells can multiply up to critical cell concentrations and produce spoilage taint compounds leading to organoleptic rejection of the products with consequent large economic and credibility losses for the food industry (Gobbi et al., 2010). Undesirable effects on the sensory attributes of fruit juices and drinks are mainly attributed to the production of the metabolic

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

product guaiacol which causes “smoky, medicinal, phenolic, antiseptic disinfectant” off-flavors and/or off-odors (Bahçeci et al., 2005; Bevilacqua et al., 2009; Gocmen et al., 2005; Jensen, 2000), with normal or light sediment (Gocmen et al., 2005; Walker and Phillips, 2005). The lower limit of guaiacol detection in fruit juices by a trained sensory panel is 2 mg/l (2 ppb) while detectable offodors in fruit juices and drinks are generally reported when the levels of A. acidoterrestris reach about 104e105 CFU/ml (Bahçeci et al., 2005; Sinigaglia et al., 2003). Due to its high spoilage potential, A. acidoterrestris has been suggested as a possible target microbe in the design of pasteurization processes for acidic products such as fruit drinks (Vieira et al., 2002). However, standard pasteurization processes applied in the case of fruit drinks are not effective against Alicyclobacillus spores, while processing at higher temperatures is not feasible due to the negative effect on the quality of these products (Palop et al., 2000). As a result, control of Alicyclobacillus growth during distribution and storage is a key factor for the efficient risk management of fruit drinks’ spoilage. The fruit drink pH and the temperature during storage and distribution are the most important parameters affecting the growth of A. acidoterrestris. Research data have provided evidence that germination, outgrowth and subsequent vegetative growth of A. acidoterrestris spores would not be expected to occur when pasteurized fruit products of naturally low pH (<4.0) are stored below 20
C (Bahçeci and Acar, 2007; Bahçeci et al., 2005; Spinelli et al., 2009). However, the conditions prevailing in the supply chain of pasteurized fruit drinks are out of the manufacturers’ direct control and often deviate from specifications (Bahçeci et al., 2005; Heyndrickx, 2011), especially during the warmer months or in tropical and semitropical regions (Roig-Sagues et al., 2015). Thus, the estimation of the risk of spoilage constitutes a major target of quality managers, especially for products that are going to be distributed in hot climate countries. For assessing the risk of fruit drink spoilage caused by A. acidoterrestris, a growth model is required that is able to predict the microbial behavior during distribution and storage. However, within the domain of predictive microbiology literature, models for A. acidoterrestris growth kinetics are not available. The objective of the present study was the development of predictive mathematical models for the description of the effects of temperature and pH on the growth of A. acidoterrestris, and the evaluation of their performance in predicting growth in fruit drinks under isothermal and non-isothermal conditions simulating transportation, distribution and storage of the products before delivery to the consumer. Such validated models could be used for an effective risk management of fruit drinks' spoilage.

41

glucose; 1 g/l tween 80), adjusted to pH ¼ 4.0 with filtered 25% (w/ v) citric acid, and incubating at 45
C for 48 h. The 48-h culture of the strain was then heat shocked at 80
C for 10 min (IFU, 2007; Murray et al., 2007; Walls and Chuyate, 2000). The heat shock treatment was applied to A. acidoterrestris cultures in order to eliminate any vegetative cells and obtain uniform activation and germination of dormant endospores (Goto et al., 2008). Then, the heat shocked cultures were centrifuged (6000 rpm for 20 min) in a refrigerated centrifuge (4
C) (model PK120R, ThermoElectron Corporation, Waltham, MA). The pellet was resuspended in 5 ml of quarter-strength Ringer's solution (Lab M, Limited, Lancashire, UK) and used for inoculation. The initial concentration of the inoculum was determined by surface plating on K Agar. 2.2. Development of the growth/no growth interface model 2.2.1. Experimental design K broth was used as the basal medium for all experiments, while all experiments were performed using spores of A. acidoterrestris ATCC 49025 obtained as described in section 2.1. The growth ability of the spoilage microorganism was tested at different combinations of temperature (15, 18, 20, 25, 30, 35, 40 and 45
C) and pH (2.02, 2.31, 2.52, 2.72, 3.05, 3.32, 3.60, 3.87, 4.22, 4.62 and 5.05), with five replicates for each combination. These values were selected based on pH measurements of nine different industrial fruit drinks used during this study and the biokinetic range of the microorganism's growth. For all conditions, the pH of the medium was adjusted to the appropriate values with filtered 25% (w/v) citric acid, and was measured both before and after autoclaving (prior to inoculation) using a digital pH meter with an epoxy refillable pH probe. The abovementioned pH values were the ones measured after autoclaving and used for the purpose of model development. Portions of 180 ml of the modified K broth (K broth with modified pH) for each treatment were pipetted into wells of 100-well microtiter plates and 20 ml of the appropriate dilution of the inoculum were added to each well, with the initial inoculation spore level being approximately 104 CFU/well. In order to verify the exact inoculum density, immediately after inoculation 100 ml from each of the five wells were surface plated on K Agar (pH ¼ 4.0) and colonies were counted after incubation of the plates at 45
C for 48 h. The microtiter plates were then sealed with Parafilm (Parafilm ‘M’; American National Can, Greenwich, CT, USA) to avoid evaporation, and were stored in high-precision (±0.2
C) programmable incubators (model MIR 153, Sanyo Electric Co., Ora-Gun, Gunma, Japan) for 35 days. The temperature during storage of noninoculated microplates was recorded using electronic temperature-monitoring devices (Cox Tracer data logger; Cox Technologies, Belmont, NC, USA).

2. Materials and methods 2.1. Bacterial strain The type strain A. acidoterrestris ATCC 49025 was used for all experiments in the present study. The stock culture of the strain was stored frozen (70
C) onto Microbank™ porous beads (ProLab Diagnostics, Ontario, Canada). The working culture was stored refrigerated (5
C) on K Agar (2.5 g/l yeast extract; 5.0 g/l peptone; 1.0 g/l glucose; 1.0 g/l tween 80; 15 g/l agar) plates (IFU, 2007; Walls and Chuyate, 2000), and was renewed biweekly. After sterilization, the pH of the medium (K Agar) was adjusted to 4.0 with filtered 25% (w/v) citric acid (Merck, Darmstadt, Germany) using a digital pH meter with an epoxy refillable pH probe (Orion 3-Star pH Benchtop; Thermo Electron Corporation, Beverly, MA, USA). The microorganism was activated by transferring a loopful from the K Agar plates into 10 ml of Κ broth (2.5 g/l yeast extract; 5 g/l peptone; 1 g/l

2.2.2. Assessment of growth During the 35-day storage, the microtiter plate wells were measured for growth on a weekly basis by recording the optical density (OD) of the medium using the automated turbidimetric system Bioscreen C (Oy Growth Curves Ab Ltd., Raisio, Finland) set to read at the wideband filter (420e580 nm). Prior to each measurement, the microtiter plates were shaken for 15 s. Five wells containing 200 ml of sterile K broth (pH ¼ 6.73) served as negative controls. In order to define growth, the OD of a well was compared to the ODzero which is the average of OD values recorded in all 100 wells at time-zero. A given well (corresponding to a certain temperature-pH combination) was considered as positive for growth, if the difference between its OD and the ODzero was three times higher than the standard deviation of the ODzero (Daelman et al., 2013). Data were processed using Microsoft® Excel (Microsoft Corp., Redmond, WA, USA).

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M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

2.2.3. Data analysis For each replicate response of A. acidoterrestris, growth or no growth were scored as values of 1 or 0, respectively. Then, a logistic polynomial regression model was fitted to the obtained binary data using the commercial software SAS version 8 (SAS Institute, Cary, NC, USA), based on the approach described by Ratkowsky and Ross (1995). The combined effect of storage temperature and pH on the probability of growth of the organism was described using a polynomial model:

Logit ðPÞ ¼ a0 þ a1  T þ a2  pH þ a3  T  pH þ a4  T 2 (1) where P is the probability of growth (in the range of 0e1), Logit (P) is an abbreviation of ln[P/(1-P)], ai are coefficients to be estimated and T (
C) is temperature. The automatic variable selection option with a stepwise selection method was used to choose the most significant effects (P < 0.05). The concordance index (c-value) and the HosmerLemeshow (HL) statistic were used as measures of the goodness of fit of the developed model. In order to compare observed growth/no growth data with model predictions, estimated probabilities (P) at 0.1, 0.5 and 0.9 levels were calculated using Microsoft®

rðΤÞ ¼

8 > > > > <

48-h culture of the microorganism was decimally diluted in K broth, and an appropriate dilution was used to inoculate microtiter plates so that the range of initial bacterial attained was approximately 101e105 CFU/well. Optical density measurements were taken at 15-min intervals using the wideband filter (420e580 nm) of the instrument, for a total time period such that a considerable OD change was observed, if possible, for all five decimally diluted cultures. The microtiter plates were agitated for 15 s at medium amplitude prior to the OD measurements. The detection times (h) of five serial decimal dilutions of the bacterial culture were plotted against the natural logarithm of their initial concentrations, and mmax values were determined by linear regression (Dalgaard and Koutsoumanis, 2001). One experiment was conducted at each growth condition and five samples (i.e. quintuple wells) of five serially diluted cultures were analysed (n ¼ 5). 2.3.2. Data analysis The effect of temperature on mmax, derived from the experiments conducted in K broth (pH ¼ 4.5), was modelled using the cardinal temperature model with inflection of Rosso et al. (1993):

mmax ðTÞ ¼ mopt rðΤÞ

0

(2)

;

T  Tmin

;

Tmin < T < Tmax

;

T  Tmax

2

ðT  Tmax ÞðT  Tmin Þ        >  T  T T T T  Topt  Topt  Tmax Topt þ Tmin  2T opt opt > min min > > : 0

(3)

Excel Solver.

2.3. Development of the kinetic model 2.3.1. Experimental design The effect of temperature and pH on the growth kinetic behavior of A. acidoterrestris was assessed: (i) in K broth with pH ¼ 4.5 (optimum growth pH) adjusted with filtered 25% (w/v) citric acid, at incubation temperatures of 25, 27, 30, 35, 40, 45, 48, 50, 53, 55
C, and (ii) in K broth with pH 3.03, 3.32, 3.60, 3.78, 3.99, 4.32, 4.52, 4.80, 5.04, 5.29, 5.53, adjusted with filtered 25% (w/v) citric acid, at

rðpHÞ ¼

8 > > > > < > > > > :

where Tmin, Topt and Tmax are the theoretical minimum, optimum and maximum temperature (
C) for growth, respectively, and mopt is the optimum value for the maximum specific growth rate (i.e. when T ¼ Topt). The effect of pH on mmax, derived from the experiments conducted in K broth, was modelled using the cardinal type model of Rosso (Rosso et al., 1995):

mmax ðpHÞ ¼ mopt rðpHÞ

0 

ðpH  pHmax ÞðpH  pHmin Þ      pHopt  pHmin pH  pHopt  pHopt  pHmax ðpHmin  pHÞ 0

an incubation temperature of 48
C (optimum growth temperature). The above growth conditions were selected in an attempt to cover the growth region of the strain to the greatest possible extent. The maximum specific growth rate (mmax) values corresponding to each growth condition were estimated by means of absorbance detection times of serially decimally diluted cultures using the automated turbidimetric system Bioscreen C as described previously (Kakagianni et al., 2016; Lianou and Koutsoumanis, 2011). The

;

pH  pHmin

;

pHmin < pH < pHmax

;

pH  pHmax

(4)

(5)

where pHmin, pHopt and pHmax are the theoretical minimum, optimum and maximum pH, respectively, for growth and mopt is the optimum value for the maximum specific growth rate (i.e. when pH ¼ pHopt). The values of Tmin, Topt, Tmax, pHmin, pHopt and pHmax as well as the confidence and the predictions limits were determined by fitting the estimated mmax values to the above models using the Excel v4 format of the curve-fitting program TableCurve 2D (Systat

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

Software Inc., San Jose, CA, USA). The adequacy of the developed models to fit data was evaluated both graphically and numerically based on the values of the coefficient of determination (R2) and the Root Mean Square Error (RMSE) (Ratkowsky et al., 2004). Making the well established assumption that discrete environmental conditions exert independent effects on microbial growth (Buchanan et al., 1993), a multiplicative without interaction-type model, combining the above models for temperature and pH, was used to describe the combined effect of these two environmental parameters on mmax (Rosso et al., 1995):

mmax ¼ mopt ,rðpHÞ,rðΤÞ

(6)

where mopt is the maximum specific growth rate corresponding to optimum growth conditions. 2.4. Model validation in fruit drinks 2.4.1. Validation of the growth/no growth interface model The growth/no growth interface model was validated against the observed growth behavior of A. acidoterrestris in eight commercial pasteurized fruit drinks stored at constant temperatures ranging from 21 to 48
C for 35 days. The pH values of the tested drinks were measured prior to inoculation as described previously (sections 2.1 and 2.2). The water activity (aw) of the fruit drinks was measured with an AquaLab water activity meter (Model series 3; Decagon Devices, Inc., Pullman, WA, USA). The soluble solids content was measured with an Atago Digital Abbe Refractometer (Atago, Tokyo, Japan). Aliquots (200 ml) from each of the fruit drinks were dispensed in 500-ml Duran bottles and were inoculated with the appropriate dilution of the inoculum in order to obtain an initial concentration of approximately 103 CFU/ml. The artificially contaminated samples were stored under controlled isothermal conditions in high-precision programmable incubators (model MIR 153, Sanyo Electric Co.). The temperature of the incubator and fruit drink samples was recorded using electronic temperature-monitoring devices (Cox Tracer data logger; Cox Technologies). During incubation, the inoculated samples were examined at appropriate time intervals in order to allow for an efficient kinetic analysis of microbial growth. Appropriate serial decimal dilutions of samples in Ringer's solution were surface plated on K Agar plates (pH ¼ 4.0) for the enumeration of A. acidoterrestris populations. Colonies were counted after incubation of plates at 45
C for 48 h. Two independent experiments were conducted with two replicates (n ¼ 4). Growth was considered when a total increase of 1 log CFU/ml was observed during the storage period or between two sampling time intervals. The observed growth/no growth behavior in fruit drinks was compared to the probability of growth predicted by the model based on the pH of the drink and the storage temperature. Uninoculated samples tested as negative controls did not show any presence of indigenous A. acidoterrestris. 2.4.2. Validation of the kinetic model For validation of the kinetic model, the growth of A. acidoterrestris in fruit drinks was studied under static and dynamic temperature scenarios designed in the laboratory to simulate distribution and storage conditions likely to be encountered in the supply chain. For these experiments, fruit drink samples were stored in high-precision programmable incubators or at room temperature. The temperatures of the incubator/environment and fruit drinks were recorded at 10-min intervals using electronic temperature-monitoring devices as described previously. The inoculation and sampling procedure was the same with that described in section 2.4.1.

43

The observed growth of A. acidoterrestris in fruit drinks was compared graphically with the growth predicted by the model. For the purpose of growth prediction, the primary model of Baranyi and Roberts (1994) was used:

yðtÞ ¼ y0 þ mmax AðtÞ 

1 emmmax AðtÞ  1 ln 1 þ mðy y Þ m e max 0

! (7)

where mmax is the maximum specific growth rate of the cell population; ymax is the natural logarithm of the maximum population's concentration; y0 is the natural logarithm of the initial cell concentration; m is a curvature parameter characterizing the transition from the exponential to the stationary phase of growth and A(t) is a gradually delayed time variable described by the equation:

AðtÞ ¼ t þ

1

mmax

 ln emmax t þ eh0 þ emmax th0

(8)

where ho is a parameter characterizing the ‘adaptation work’ required by the cells, which in our case are spores, to adjust to the new environment (Baranyi and Roberts, 1994). Prediction of growth under dynamic temperature was based on the above equations which were numerically integrated with respect to time and the assumption that after a temperature shift, the growth rate is adopted instantaneously to the new temperature environment. The “momentary” mmax was calculated using the abovementioned multiplicative secondary model (Equation (6)). 3. Results and discussion 3.1. Model development 3.1.1. Growth/no growth interface model The growth ability of A. acidoterrestris was studied at different combinations of temperature (15, 18, 20, 25, 30, 35, 40 and 45
C) and pH (2.02, 2.31, 2.52, 2.72, 3.05, 3.32, 3.60, 3.87, 4.22, 4.62 and 5.05). In total, 440 samples were tested (88 combinations of temperature and pH with five replicates in each combination) and growth was observed in 218 samples. Among the 88 combination treatments, growth of A. acidoterrestris was observed in 40 conditions, no growth in 41 conditions, while in seven conditions growth occurred in some (but not all) of the five replicates (Fig. 1). The minimum pH and temperature where growth was observed was 2.52 (at 35 and 45
C) and 25
C (at pH  3.32), respectively. These

Fig. 1. Growth/no growth interface of Alicyclobacillus acidoterrestris in K broth with respect to temperature and pH predicted by the model (lines) compared to the data used to generate the model (points). Black symbols: growth in all replicates; white symbols: no growth in all replicates; grey symbols: growth in some replicates; lower line: predicted boundary P ¼ 0.1; middle line: predicted boundary P ¼ 0.5; upper line: predicted boundary P ¼ 0.9.

44

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

Table 1 Estimated values and fitting statistics for the parameters of the logistic polynomial regression model for the combined temperature and pH limits of Alicyclobacillus acidoterrestris growth in K broth. Coefficients

Estimate

Standard error

P value

a0 (Constant) a1(Temperature,(T)) a2 (pH) a3 (pHxT) a4 (T2)

25.9564 15.8016 1.63928 0.950885 0.0122219

9.99059 3.24411 0.549044 0.173144 0.0044819

0.009 0.000 0.003 0.000 0.006

Table 2 Probability of Alicyclobacillus acidoterrestris growth predicted by the growth/no growth boundaries model for different combinations of temperature and pH. Temperature (oC) 20

25

30

pH

Predicted probability of growth

2.5 3.0 3.5 4.0 4.5

0.025 0.112 0.387 0.759 0.940

0.061 0.777 0.995 1.000 1.000

0.082 0.981 1.000 1.000 1.000

35

40

45

0.063 0.998 1.000 1.000 1.000

0.027 0.999 1.000 1.000 1.000

0.006 1.000 1.000 1.000 1.000

results are in agreement with previous studies reporting that the temperature and pH for growth of Alicyclobacillus spp. ranges from <20 to 55e65
C and from 2.0 to 2.5 to 6.0e6.5, respectively (Jiang et al., 2008; Smit et al., 2011). Slightly higher pH limits (2.9e3.8) of A. acidoterrestris growth in apple and orange drink compared to the ~ a and present work have been reported by other researchers (Pen Rodríguez, 2006; Pena et al., 2011), which can be attributed to the different strain(s), media and acidifiers used. For the development of the growth/no growth interface model, the collected OD measurements, corresponding to different environmental conditions, were converted into binary data (0: no growth, 1: growth). A logistic polynomial regression model was then fitted to these binary data (Equation (1)), and the estimated model parameters of are summarized in Table 1. The parameters with no significant effect (P  0.05) were removed from the model. The c-value and the HL statistic were used as measures of the goodness of fit of the developed model. As demonstrated by the cvalue, the degree of agreement between the predicted probabilities and the observations was 98.8%. The HL goodness e of - fit statistic was 6.226 (c2, df 8; P ¼ 0.622). The goodness e of - fit was also

Table 3 Estimated values and fitting statistics for the parameters of the cardinal parameter models describing the effect of temperature and pH on the maximum specific growth rate (mmax) of Alicyclobacillus acidoterrestris in K broth. Parameter

Estimated valuea

Temperature mopt (1/h) Tmax Tmin Topt pH model mopt (1/h) pHmax pHmin pHopt

model 0.980 ± 0.013 55.68 ± 0.069 18.11 ± 0.40 48.60 ± 0.22

0.954 55.54 17.31 48.16

1.090 ± 0.014 5.90 ± 0.036 2.93 ± 0.011 4.22 ± 0.026

1.062 5.83 2.90 4.17

Lower

a b c

RMSEb

R2c

1.006 55.82 18.91 49.03

0.0010

0.986

1.118 5.97 2.95 4.27

0.0015

0.958

95% Confidence Limits

Values are means ± standard errors. RMSE: Root mean square error. R2: Coefficient of determination.

Upper

evaluated graphically by comparing the model predictions at probabilities of 0.1, 0.5 and 0.9 with the corresponding observed data (Fig. 1). The developed model can be used to predict both probabilities of growth and temperature-pH limits at a certain probability level. The predicted probabilities of A. acidoterrestris growth for representative combinations of temperature and pH are presented in Table 2. The application of the model to foods however, requires validation studies in order to evaluate the effect of factors such as food composition, strain variability, microbial interactions, physiological state of the cells etc. on its performance. 3.1.2. Kinetic model The effect of temperature and pH on A. acidoterrestris growth rate was investigated using the Bioscreen C method. Experiments were carried in (i) K broth, adjusted to pH ¼ 4.5 with citric acid, at isothermal storage temperature of 25, 27, 30, 35, 40, 45, 48, 50, 53, 55
C, and (ii) in K broth with pH 3.03, 3.32, 3.6, 3.78, 3.99, 4.32, 4.52, 4.8, 5.04, 5.29, 5.53, adjusted with citric acid, at an incubation temperature of 48
C. The average (±standard deviation) mmax (1/h) increased from 0.098 (±0.008) at 25
C to a maximum value of 1.031 (±0.008) at 48
C, while at temperatures > 48
C a gradual decrease of mmax was observed. Regarding the pH effect, the average (±standard deviation) mmax (1/h) increased from 0.179 (±0.030) at pH 3.03 to a maximum value of 1.036 (±0.014) at pH 3.99, while at higher pH values mmax gradually decreased. The above experimental data (mmax) were modelled as a function of temperature and pH using cardinal parameter models (Equations (2) and (4), respectively), for the estimation of Tmin, Topt, Tmax, pHmin, pHopt, pHmax. The R2 and RMSE values (Table 3), as well as the graphical evaluation of the fitting curves (Figs. 2 and 3), indicated a satisfactory performance of the model in describing the effect of temperature and pH on the mmax of A. acidoterrestris. The estimated values for the cardinal parameters Tmin, Tmax, Topt and the optimum maximum specific growth rate (mopt ) of A. acidoterrestris were found to be 18.11, 55.68, 48.60
C and 0.980 1/h, respectively (Table 3). For the effect of pH, the estimated values for pHmin, pHmax, pHopt and the mopt of A. acidoterrestris were found to be 2.93, 5.90, 4.22 and 1.090 1/h, respectively (Table 3). Despite the fact that the above cardinal parameters for the effect of temperature and pH are estimated based on different datasets the mopt values were very close. Although, to our knowledge, this is the first model on the effect of temperature and pH on Alicyclobacillus spp. growth rate, previous qualitative studies have shown a similar effect. Goto (2000) reported a temperature range for A. acidoterrestris growth between 20 and 55
C. Ikegami et al. (1996) studied the effect of pH on the growth of A. acidocaldarius and reported a similar trend, with a pH range of growth from 2.5 to 6.5 and an optimum pH between 4.5 and 5.5. 3.2. Validation of models in fruit drinks 3.2.1. Validation of growth/no growth interface model The growth/no growth interface model was further validated against observed growth data of A. acidoterrestris in fruit drinks. Validation experiments were performed with eight different commercial fruit drink products with a pH ranging from 2.59 to 3.83 at different storage temperatures from 21 to 48
C (Table 4). The aw of all tested drinks was very high (>0.990), while the soluble solids contents (oBrix) were similar ranging from 10.75 to 11.50. A comparison between the probability of growth predicted by the growth/no growth interface model and the observed behavior of A. acidoterrestris is presented in Table 4. The validation results showed a very good performance of the model. In all cases where the probability of growth predicted by the model was lower than 0.5, A. acidoterrestris was, indeed, not able to grow in the fruit

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

1.2

45

Observed Fitted

1.0

95th Confidence Interval 95th Prediction Interval

max

( 1/h)

0.8 0.6 0.4 0.2 0.0 15

20

25

30

35

40

45

50

55

60

Temperature (°C) Fig. 2. Effect of temperature on the maximum specific growth rate (mmax) of Alicyclobacillus acidoterrestris in K broth of pH 4.5. Points represent the observed mmax values, the solid line corresponds to the fitting of the cardinal temperature model with inflection to the data, and the dotted lines depict the 95% confidence and prediction intervals.

max

(1/h)

Observed 1.2

Fitted

1.0

95th Prediction Interval 95th Confidence Interval

0.8 0.6 0.4 0.2 0.0 2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

pH Fig. 3. Effect of pH on the maximum specific growth rate (mmax) of Alicyclobacillus acidoterrestris in K broth at 48
C. Points represent the observed mmax values, the solid line corresponds to the fitting of the cardinal pH model to the data, and the dotted lines depict the 95% confidence and prediction intervals.

drinks. Similarly, when the model predicted a probability above 0.9, growth was observed in all cases. The observed behavior of A. acidoterrestris in fruit drinks and the growth boundaries predicted by the model based on their pH and storage temperature are illustrated in Fig. 4. As shown in this figure, in six cases growth was not observed although the predicted probability by the model was higher than 0.5 (Fig. 4). This slight

over-prediction by the model of the growth ability of the organism could be attributed to the potential presence of natural antimicrobial compounds or indigenous competitive microflora in the fruit drinks, the effect of which has not been taken into account in model development (Yokota et al., 2008; McNamara et al., 2011). However, the overall effect of the above factors (or other factors not included in the model) on its performance was not found to be

46

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

Table 4 Comparison between observed behavior of Alicyclobacillus acidoterrestris and probability of growth predicted by the developed growth/no growth interface model in commercial pasteurized fruit drinks tested in validation studies. Products

Ingredients

pH

aw

o

Apple-orange-carrot

Natural juices of apple, orange and carrot from concentrated juices (50%), water, sugar, concentrated natural juice of lemon, flavorings, antioxidant: ascorbic acid

3.52

0.995

11.25

9 Fruits & 10 Vitamins

Natural juices of apple, grape, peach, pineapple, orange, apricot, grapefruit, passion fruit and e mango from concentrated juices and pure (99.9%), flavorings, vitamins: C, E, B1, B2, B6, B12, niacin, folic acid, pantothenic acid, biotin Natural orange juice from concentrated juice, orange cells (1.4%)

3.71

0.994

11.50

3.83

0.992

11.00

3.35

0.995

11.20

3.34

0.994

11.25

2.99

0.993

11.00

2.78

0.993

2.59

0.992

Orange

Apricot-apple-orange

Water, natural juices of apricot, apple and orange from concentrated juices and apricot e (40%), sugar, acidity regulator: citric acid, pure flavorings, antioxidant: ascorbic acid e from peach (30%), sugar, Water, natural pure acidity regulator: citric acid, flavorings, antioxidant: ascorbic acid

Peach

Mandarin and Blood Orange

Cranberry e Raspberry - Blueberry

Lemonade

Water, natural juice of mandarin and blood orange from concentrated juice (20%), sugar, acidity regulator: citric acid, colorant: concentrated natural elderberry juice, natural aroma of mandarin, antioxidant: ascorbic acid Water, natural juices of white and red grape from concentrated juices, sugar, cranberry and e (7.5%), natural raspberry and blueberry pure juice of acerola from concentrated juices, acidity regulator: citric acid, antioxidant: ascorbic acid, e content: flavorings. Total juice and fruit pure 20%. Water, natural lemon juice from concentrated juice (13.3%), sugar, lemon cells (0.5%), natural flavoring

Brix

Tested Storage TemperatureoC

Observed behavior

Predicted probability of growth

21 25 30 45 48 21 25 48

No growth Growth Growth Growth Growth No growth Growth Growth

0.692 0.995 1.000 1.000 1.000 0.832 0.999 1.000

21 25 48 21 25 48

No growth Growth Growth No growth Growth Growth

0.891 1.000 1.000 0.525 0.983 1.000

21 25 35 45 48 21 25 48

No growth Growth Growth Growth Growth No growth No growth Growth

0.515 0.981 1.000 1.000 1.000 0.198 0.763 1.000

10.75

21 25

No growth No growth

0.093 0.376

11.50

21 25 48

No growth No growth No growth

0.045 0.117 0.027

5.5

Predicted (p=0.1) Predicted (p=0.5)

5.0

Predicted (p=0.9) 4.5

Observed (No growth) Observed (Growth)

pH

4.0 3.5 3.0 2.5 2.0 1.5 15

20

25

30

35

40

45

50

55

Temperature (°C) Fig. 4. Comparison between predicted growth boundaries (lines) and observed behavior (points) of Alicyclobacillus acidoterrestris in fruit drinks. Black symbols: growth; white symbols: no growth; lower line: predicted boundary P ¼ 0.1; middle line: predicted boundary P ¼ 0.5; upper line: predicted boundary P ¼ 0.9.

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

7

40

6

35 4 30 3 25 2

20

15 3

1

15

1

0

10 100

0

40

60

80

25

4

2

20

30

5

20

0

35

(e)

10

5

0 0

50

100

Time (hours) 50

30

40

60

80

100

120

140

160

180

1

10 200

0

25

0

20

Time (hours) 50

7

(c) 7

45

6

40

5

35

4

30

3

25

2

20

1

15

1

10 200

0

0 40

60

80

100

120

140

160

180

40

Log10 (cfu/ml)

6 35

5

4 30 3

2

25

0

35

7

(d)

6

5

25

5

4

20

3

15

2

10

1

5

0

0 160

200

Time (hours)

Log10 (cfu/ml)

30

Temperature (°C)

6

120

20 100

30

60

90

120

20 150

Time (hours)

7

80

80

(g)

Time (hours)

40

60

Time (hours)

8

20

40

Temperature (°C)

20

15

Temperature (°C)

Log10 (cfu/ml)

0

35 3

2

20

1

40 4

Temperature (°C)

2

45

5

Temperature (°C)

30 3

Log10 (cfu/ml)

35 4

25

Log10 (cfu/ml)

300

50

6

40

5

Temperature (°C)

Log10 (cfu/ml)

6

Log10 (cfu/ml)

250

(f) 45

0

200

7

(b)

0

150

Time (hours)

7

0

Temperature (°C)

8

45

40

(h)

35

4 30 3

2

Temperature (°C)

Log10 (cfu/ml)

5

50

Log10 (cfu/ml)

(a)

6

Temperature (°C)

7

47

25

1

0 0

50

100

150

200

20 250

Time (hours)

Time (hours) Fig. 5. Comparison between observed (points) and predicted (solid line) growth of Alicyclobacillus acidoterrestris ATCC 49025 in: (a) K broth (pH ¼ 4.5) at 35
C, (b) apple - orange carrot drink (pH ¼ 3.52) at 30
C, (c) peach drink (pH ¼ 3.34) at 35
C, (d) 9 fruits & 10 vitamins drink (pH ¼ 3.71) stored at 5
C for 2 days followed by storage at 30
C, (e) apple orange - carrot drink (pH ¼ 3.52) stored at 5
C for 5 days followed by storage at 30
C, (f) apple - orange - carrot drink (pH ¼ 3.52) stored at dynamic temperature conditions (6 h at 25
C, 12 h at 35
C and 6 h at 45
C), (g) apple - orange - carrot drink (pH ¼ 3.52) stored at room temperature during the summer period in Greece, and (h) peach drink (pH ¼ 3.34) stored at stored at room temperature during summer period in Greece. Discontinuous lines indicate medium temperature during storage. For growth prediction, the parameters ymax (maximum population density) and h0 (physiological state parameter) of the primary model were fixed to 106.2 CFU/ml and 4.0, respectively.

significant. Indeed, Fig. 4 clearly shows that the 90% probability limits predicted by the model can be successfully used for describing the critical combination of temperature and pH which inhibits the growth of A. acidoterrestris in fruit drinks. 3.2.2. Validation of kinetic model The developed kinetic model was validated against observed growth data of A. acidoterrestris in fruit drinks at both static and dynamic temperature storage conditions. Prediction of growth was based on the combination of the secondary model (Equation (6))

with the differential equations of the Baranyi and Roberts primary model (Equations (7) and (8)), which were numerically integrated with respect to time. The parameter mopt used in the secondary model (Equation (6)) was the average of mopt values estimated from the models describing the distinct effects of temperature and pH on mmax (Equations (2) and (4)). For the purpose of growth prediction, the parameters ymax (maximum population density) and h0 (physiological state parameter) of the primary model (Equations (7) and (8)) were fixed to 106.2 CFU/ml and 4.0, respectively, based on the observed growth of A. acidoterrestris in K broth at static

48

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49

temperature conditions (Fig. 5a). In bacterial growth, ho represents the amount of “work” that a cell has to perform to adapt to its new environment. The parameter h0, also referred to as “work to be done” is estimated as the product of mmax and l (lag time) (Baranyi and Roberts, 1994). Several studies have reported a relation between mmax and l, with their product mmax*l being constant at different storage temperatures when the pre-inoculation history of the cells culture was the same (Gougouli et al., 2008; Koutsoumanis et al., 2006; Pin et al., 2002). In the experiments conducted in this study, the inoculum was constituted of spores which were produced under a well defined environment. Based on the above, we assumed that ho, which in this case refers to spore germination and outgrowth, is not affected by the storage temperature. The comparison between observed and predicted growth of A. acidoterrestris in apple-orange-carrot drink at 30
C and in peach drink at 35
C, is illustrated in Fig. 5b and c, respectively. In both cases, the model showed a good performance with a difference between predicted and observed growth being less than 1 log CFU/ ml. Pasteurized fruit drink products are commonly stored at the retail level at room temperature. Nonetheless, in the absence of disparate distribution systems for refrigerated and non-refrigerated products, the current practice of the fruit drink industry is to store and distribute these products under refrigeration before deliver to retail. In this context, the data presented in Fig. 5d and e simulate the latter scenario of distribution and storage. Specifically, Fig. 5d presents the validation of the model against observed growth of A. acidoterrestris in “9 fruits & 10 vitamins” drink (pH ¼ 3.71) stored at 5
C for 2 days followed by storage at 30
C. The model validation results against observed growth in apple-orange-carrot drink (pH ¼ 3.52) stored at a similar temperature profile with the refrigeration storage being extended to 5 days, are shown in Fig. 5e. A good agreement between predicted and observed growth of the spoilage organism was observed for both products and dynamic temperature conditions. In the later scenario, however, the observed lag time was longer than the predicted, indicating that the prolonged exposure to low temperature may result in a physiological stress and an additional lag time. Nevertheless, the prediction of the model at the exponential phase was very close to the observed growth (Fig. 5e). A periodic temperature profile involving 6 h at 25
C, 12 h at 35
C and 6 h at 45
C was tested for storage of apple-orange-carrot drink (Fig. 5f). At these temperature conditions, A. acidoterrestris exhibited a total growth of 4 log CFU/ml within 60 h which was satisfactorily predicted by the growth model. Fig. 5g and h presents the growth of the spoilage bacterium in apple-orange-carrot drink and peach drink, respectively, stored at room temperature during the summer period in Greece. The illustrated temperature fluctuations reflect the temperature differences between day and night time. Again, the growth predicted by the model, based on the pH of the products and the recorded temperature profile, described very well the observed microbial behavior. 4. Conclusions In conclusion, the results of the present study demonstrate that the effect of the environment on the growth/no growth interface and the growth kinetics of A. acidoterrestris can be quantitatively expressed using mathematical models. Extensive validation studies showed that the models developed in this study can be used to predict the behavior of this spoilage microorganism in fruit drinks. These models could bring benefits for the industry by identifying the conditions that should be applied during processing, distribution and storage in order to minimize the risk of A. acidoterrestris growth. Additional research data on the intra-species differences in the growth kinetics of A. acidoterrestris are certainly expected to

improve the model by incorporating strain variability in its predictions (Lianou and Koutsoumanis, 2013; Pouillot and Lubran, 2011). Furthermore, given that, in practice, fruit drinks are contaminated with low bacterial spore numbers, studies on the effect of processing and storage conditions on the variability of individual spores lag time will increase the precision and credibility of the developed model (Kakagianni et al., 2017; Stringer et al., 2011). Finally, further research on the quantification of the effect of environmental parameters on guiacol production in relation to A. acidoterrestris growth will enhance the model's value and applicability, allowing its utilization in spoilage predictions and shelf life assessment of fruit drinks. Acknowledgements This study was carried out with the financial support of “Understanding the impact of manufacturing processes in the ecology of microorganisms that spoil-contaminate milk products (ESL, evaporated milk) and fresh fruit juices. Development of molecular methodologies and mathematical models for the prediction of their shelf-life” within the framework of the action “Cooperation” (NSRF 2007-2013), that was co-financed by the European Social Fund (ESF) and National Resources. References Bahçeci, K.S., Acar, J., 2007. Determination of guaiacol produced by Alicyclobacillus acidoterrestris in apple juice by using HPLC and spectrophotometric methods, and mathematical modeling of guaiacol production. European Food Research and Technology 225, 873e878. € kmen, V., Acar, J., 2005. Formation of guaiacol from vanillin by Bahçeci, K.S., Go Alicyclobacillus acidoterrestris in apple juice: a model study. Eur. Food Res. Technol 220, 196e199. Baranyi, J., Roberts, T.A., 1994. A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23, 277e294. Bevilacqua, A., Sinigaglia, M., Corbo, M.R., 2009. Effects of pH, cinnamaldehyde and heat-treatment time on spore viability of Alicyclobacillus acidoterrestris. Int. J. Food Sci. Technol. 44, 380e385. Buchanan, R., Smith, J., McColgan, C., Marmer, B., Golden, M., Dell, B., 1993. Response surface models for the effects of temperature, pH, sodium chloride, and sodium nitrite on the aerobic and anaerobic growth of Staphylococcus aureus 196E. J. Food Saf. 13, 159e175. Cerny, G., Hennlich, W., Poralla, K., 1984. Fruchtsaftverderb durch Bacillen: isolierung und charakterisierung des verderbserregers. Z. Lebensm. Unters. Forsch 179, 224e227. Daelman, J., Vermeulen, A., Willemyns, T., Ongenaert, R., Jacxsens, L., Uyttendaele, M., Devlieghere, F., 2013. Growth/no growth models for heattreated psychrotrophic Bacillus cereus spores under cold storage. Int. J. Food Microbiol. 161, 7e15. Dalgaard, P., Koutsoumanis, K., 2001. Comparison of maximum specific growth rates and lag times estimated from absorbance and viable count data by different mathematical models. Journal Microbiol. Methods 43, 183e196. Gobbi, E., Falasconi, M., Concina, I., Mantero, G., Bianchi, F., Mattarozzi, M., Musci, M., Sberveglieri, G., 2010. Electronic nose and Alicyclobacillus spp. spoilage of fruit juices: an emerging diagnostic tool. Food Contr. 21, 1374e1382. Gocmen, D., Elston, A., Williams, T., Parish, M., Rouseff, R., 2005. Identification of medicinal off-flavours generated by Alicyclobacillus species in orange juice using GCeolfactometry and GCeMS. Lett. Appl. Microbiol. 40, 172e177. Goto, K., 2000. Thermoacidophilic spore-forming bacteria: Alicyclobacillus. J. Antibacterial Antifun Agents Japan 28, 13e38. Goto, K., Nishibori, A., Wasada, Y., Furuhata, K., Fukuyama, M., Hara, M., 2008. Identification of thermo-acidophilic bacteria isolated from the soil of several Japanese fruit orchards. Lett. Appl. Microbiol. 46, 289e294. Gougouli, M., Angelidis, A.S., Koutsoumanis, K., 2008. A study on the kinetic behavior of Listeria monocytogenes in ice cream stored under static and dynamic chilling and freezing conditions. J. Dairy Sci. 91, 523e530. Heyndrickx, M., 2011. The importance of endospore-forming bacteria originating from soil for contamination of industrial food processing. Appl. Environ. Soil Sci. 2011, 561975, 11. Huang, X.-C., Yuan, Y.-H., Guo, C.-F., Gekas, V., Yue, T.-L., 2015. Alicyclobacillus in the fruit juice industry: spoilage, detection, and prevention/control. Food Rev. Int. 31, 91e124. IFU (International Federation of Fruit Juice Producers), 2007. Method on the Detection of Taint Producing Alicyclobacillus in Fruit Juices. IFU Method No. 12. IFU, Paris, pp. 1e11. Ikegami, Y., Enda, M., Matsui, C., Nakagawa, K., 1996. Barenshia orenji jusu chu ni okeru kousansei kin no zoushoku. Toyo Shokuhin Kogyo College/Toyo Shokuhin

M. Kakagianni et al. / Food Microbiology 74 (2018) 40e49 Laboratories. Kenkyu Hokokusho 21, 117e122 (in Japanese). Jensen, N., 2000. Alicyclobacillus in Australia [Paper based on a presentation at the 10th World Congress of food science and technology (1999: Sydney)]. Food Aust. 52, 282. Jiang, C.-Y., Liu, Y., Liu, Y.-Y., You, X.-Y., Guo, X., Liu, S.-J., 2008. Alicyclobacillus ferrooxydans sp. nov., a ferrous-oxidizing bacterium from solfataric soil. Int. J. Syst. Evol. Microbiol. 58, 2898e2903. Kakagianni, M., Aguirre, J.S., Lianou, A., Koutsoumanis, K.P., 2017. Effect of storage temperature on the lag time of Geobacillus stearothermophilus individual spores. Food Microbiol. 67, 76e84. Kakagianni, M., Gougouli, M., Koutsoumanis, K.P., 2016. Development and application of Geobacillus stearothermophilus growth model for predicting spoilage of evaporated milk. Food Microbiol. 57, 28e35. Koutsoumanis, K., Stamatiou, A., Skandamis, P., Nychas, G.-J., 2006. Development of a microbial model for the combined effect of temperature and pH on spoilage of ground meat, and validation of the model under dynamic temperature conditions. Appl. Environ. Microbiol. 72, 124e134. Lianou, A., Koutsoumanis, K.P., 2011. Effect of the growth environment on the strain variability of Salmonella enterica kinetic behavior. Food Microbiol. 28, 828e837. Lianou, A., Koutsoumanis, K.P., 2013. Strain variability of the behavior of foodborne bacterial pathogens: a review. Int. J. Food Microbiol. 167, 310e321. McNamara, C.J., Wiebe, D., Gomez, M., 2011. Recovery of Alicyclobacillus from inhibitory fruit juice concentrates. J. Food Prot 74, 1370e1373. Murray, M.B., Gurtler, J.B., Ryu, J.-H., Harrison, M.A., Beuchat, L.R., 2007. Evaluation of direct plating methods to enumerate Alicyclobacillus in beverages. Int. J. Food Microbiol. 115, 59e69. Palop, A., Alvarez, I., Raso, J., Condon, S., 2000. Heat resistance of Alicyclobacillus acidocaldarius in water, various buffers, and orange juice. J. Food Prot 63, 1377e1380. Pena, W., De Massaguer, P., Zuniga, A., Saraiva, S., 2011. Modeling the growth limit of Alicyclobacillus acidoterrestris CRA7152 in apple juice: effect of pH, Brix, temperature and nisin concentration. J. Food Process. Preserv. 35, 509e517. ~ a, W., Rodríguez, P., 2006. Modeling the growth/no growth interface of AlicyPen clobacillus acidoterrestris CRA 7152 in orange juice as a function of pH, temperature, Brix and nisin concentration. J. Food Prot. 8, 1904e1912. n ~ ez, J.A., Baranyi, J., 2002. Analysing the lagPin, C., de Fernando, G.D.G., Ordo growth rate relationship of Yersinia enterocolitica. Int. J. Food Microbiol. 73, 197e201. Pouillot, R., Lubran, M.B., 2011. Predictive microbiology models vs. modeling microbial growth within Listeria monocytogenes risk assessment: what parameters matter and why. Food Microbiol. 28, 720e726. Ratkowsky, D.A., McKellar, R., Lu, X., 2004. Model fitting and uncertainty. In:

49

McKellar, R.C., Lu, X. (Eds.), Modeling Microbial Responses in Food. CRC Press, Boca Raton, Florida, pp. 151e196. Ratkowsky, D.A., Ross, T., 1995. Modelling the bacterial growth/no growth interface. Lett. Appl. Microbiol. 20, 29e33. ndez-Herrero, M., 2015. Improving the Roig-Sagues, A., Asto, E., Engers, I., Herna efficiency of ultra-high pressure homogenization treatments to inactivate spores of Alicyclobacillus spp. in orange juice controlling the inlet temperature. LWT-Food Sci. Technol 63, 866e871. Rosso, L., Lobry, J., Bajard, S., Flandrois, J., 1995. Convenient model to describe the combined effects of temperature and pH on microbial growth. Appl. Environ. Microbiol. 61, 610e616. Rosso, L., Lobry, J., Flandrois, J., 1993. An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. J. Theor. Biol. 162, 447e463. Sinigaglia, M., Corbo, M.R., Altieri, C., Campaniello, D., D'Amato, D., Bevilacqua, A., 2003. Combined effects of temperature, water activity, and pH on Alicyclobacillus acidoterrestris spores. J. Food Prot 66, 2216e2221. Smit, Y., Cameron, M., Venter, P., Witthuhn, R.C., 2011. Alicyclobacillus spoilage and isolationeA review. Food Microbiol. 28, 331e349. Spinelli, A.C.N., Sant'Ana, A.S., Rodrigues-Junior, S., Massaguer, P.R., 2009. Influence of different filling, cooling, and storage conditions on the growth of Alicyclobacillus acidoterrestris CRA7152 in orange juice. Appl. Environ. Microbiol. 75, 7409e7416. Steyn, C.E., Cameron, M., Witthuhn, R.C., 2011. Occurrence of Alicyclobacillus in the fruit processing environmentda review. Int. J. Food Microbiol. 147, 1e11. Stringer, S., Webb, M., Peck, M., 2011. Lag time variability in individual spores of Clostridium botulinum. Food Microbiol. 28, 228e235. Vieira, M.C., Teixeira, A.A., Silva, F.M., Gaspar, N., Silva, C.L., 2002. Alicyclobacillus acidoterrestris spores as a target for Cupuaçu (Theobroma grandiflorum) nectar thermal processing: kinetic parameters and experimental methods. Int. J. Food Microbiol. 77, 71e81. Walker, M., Phillips, C.A., 2005. The effect of intermittent shaking, headspace and temperature on the growth of Alicyclobacillus acidoterrestris in stored apple juice. Int. J. Food Sci. Technol. 40, 557e562. Walls, I., Chuyate, R., 2000. Isolation of Alicyclobacillus acidoterrestris from fruit juices. J. AOAC Int. 83, 1115e1120. Wang, Z., Cai, R., Yuan, Y., Niu, C., Hu, Z., Yue, T., 2014. An immunomagnetic separation-real-time PCR system for the detection of Alicyclobacillus acidoterrestris in fruit products. Int. J. Food Microbiol. 175, 30e35. Yokota, A., Fujii, T., Goto, K., 2008. Alicyclobacillus: Thermophilic Acidophilic Bacilli. Springer Science & Business Media.